The value V of a classic car
appreciates exponentially and is
represented by V = 32,000(1.18)t
,
where t is the number of years
since 2020.
The rate of appreciation is
Answers
The rate of appreciation of the classic car is 18% per year.
Define exponentAn exponent is a mathematical operation that indicates how many times a number or expression is multiplied by itself. It is represented by a superscript number that is written to the right and above the base number or expression. The exponent tells us how many times the base is multiplied by itself.
The value V of the classic car appreciates exponentially, and it is represented by the formula:
V = 32,000[tex]1.18^{2}[/tex]
The term [tex]1.18^{t}[/tex] represents the factor by which the value of the car increases each year. If we calculate this factor for one year (t=1), we get:
(1.18)¹= 1.18
This means that the value of the car increases by 18% in the first year. Similarly, if we calculate the factor for two years (t=2), we get:
(1.18)² = 1.39
This means that the value of the car increases by 39% in the first two years (18% in the first year and an additional 21% in the second year).
Therefore, the rate of appreciation of the classic car is 18% per year.
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Related Questions
How can you use your knowledge of evaluating expressions involving square roots to
identify and correct an error in calculating the period of a pendulum?
the period of a pendulum is the time in seconds) it takes the pendulum to swing back
and forth. the period t is represented by t = 1.1vi, where l is the length of the
pendulum (in feet).
Answers
To use our knowledge of evaluating expressions involving square roots to identify and correct an error in calculating the period of a pendulum, we should first ensure that the formula mentioned (t = 1.1vi) is accurate.
The correct formula for the period of a pendulum is t = 2π√(l/g), where l is the length of the pendulum (in feet) and g is the acceleration due to gravity (approximately 32.2 ft/s²).
When evaluating the period t, make sure to use the correct formula and follow these steps:
1. Substitute the given length of the pendulum (l) into the formula.
2. Divide the length by the acceleration due to gravity (g).
3. Calculate the square root of the result.
4. Multiply the square root by 2π.
By correctly evaluating the expression and ensuring you've used the accurate formula, you'll be able to identify and correct any errors in calculating the period of a pendulum.
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Please help, I don't understand this geometry problem!!
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. What is the distance along the ground between the building and the sculpture? Round your answer to the nearest hundredth.
25.36 feet
27.98 feet
100.22 feet
128.67 feet
Answers
The distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
How to calculate the distance along the ground between the building and the sculptureFrom the problem statement, we know that angle BAC is 25 degrees and AC is 60 feet. We want to find AB, which is the horizontal distance between A and B.
We can use trigonometry to find AB. Let's use the tangent function:
tan(25) = AB / AC
Solving for AB, we get:
AB = AC * tan(25)
Substituting the values we know, we get:
AB = 60 * tan(25)
Using a calculator, we get:
AB ≈ 27.98 feet
Therefore, the distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
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Prove by cases that 25k^2 + 15k is an even integer whenever 5k- 3 is an integer.
Answers
We can prove that 25k² + 15k is an even integer whenever 5k - 3 is an integer by considering two cases: when k is even and when k is odd.
Let's assume that 5k - 3 is an integer. Then, we can write k as k = (5k - 3 + 3)/5 = (5k - 3)/5 + 3/5. Since (5k - 3)/5 is an integer, we can write it as (5k - 3)/5 = n, where n is an integer. Thus, we have k = n + 3/5.
Now, we can substitute this expression for k into 25k² + 15k as follows:
25k² + 15k = 25(n + 3/5)² + 15(n + 3/5)
Expanding the square, we get:
25(n² + 6n/5 + 9/25) + 15n + 9 = 25n² + 45n/5 + 34/5
Simplifying, we get:
25k² + 15k = 5(5n² + 9n) + 34/5
Since 5n² + 9n is an integer, we can write it as m, where m is an integer. Thus, we have:
25k² + 15k = 5m + 34/5
Now, we can consider two cases:
Case 1: k is even. In this case, k can be written as k = 2p, where p is an integer. Substituting this expression into 5k - 3, we get:
5k - 3 = 5(2p) - 3 = 10p - 3
Since 10p is even, we can conclude that 10p - 3 is odd. Therefore, m must be odd, since 5m + 34/5 is even. Thus, 25k² + 15k is even, since it can be written as 5m + 34/5, where 5m is even and 34/5 is even.
Case 2: k is odd. In this case, k can be written as k = 2p + 1, where p is an integer. Substituting this expression into 5k - 3, we get:
5k - 3 = 5(2p + 1) - 3 = 10p + 2
Since 10p is even, we can conclude that 10p + 2 is even. Therefore, m must be even, since 5m + 34/5 is even. Thus, 25k² + 15k is even, since it can be written as 5m + 34/5, where 5m is even and 34/5 is even.
In both cases, we have shown that 25k² + 15k is an even integer whenever 5k - 3 is an integer. Therefore, the statement is proved.
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Peter owns a currency conversion shop.
Last Monday, Peter changed a total of £20,160 into a number of different currencies.
He changed
3/10
of the £20,160 into euros.
He changed the rest of the pounds into dollars, rupees and francs in the ratios 9:5:2
Peter changed more pounds into dollars than he changed into francs.
Work out how many more.
Answers
If Peter changed more pounds into dollars than he changed into francs then Peter changed £6,168 more into dollars than into francs.
First, we need to find out how much money Peter changed into euros:
(3/10) × £20,160 = £6,048
Next, we need to find out how much money Peter changed into dollars, rupees, and francs combined:
£20,160 − £6,048 = £14,112
We can use the ratios to find out how much of this total amount goes to each currency:
- Dollars: (9/16) × £14,112 = £7,932
- Rupees: (5/16) × £14,112 = £4,420
- Francs: (2/16) × £14,112 = £1,764
We can see that Peter changed more pounds into dollars than into francs. To find out how many more, we can subtract the amount changed into francs from the amount changed into dollars:
£7,932 − £1,764 = £6,168
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400 people attended a concert 10% of the people came from Scotland 25% of the people came form Wales How many more pepole came from Wales than Scotland
Answers
If 400 people attended a concert 10 percent of the people came from Scotland 25 percent of the people came form Wales, there were 60 more people from Wales than from Scotland.
To find out how many more people came from Wales than Scotland at a concert with 400 attendees, we'll first calculate the number of people from each region.
1. Determine the number of people from Scotland:
Since 10% of the people came from Scotland, we'll multiply the total attendees (400) by 10% (0.10).
400 * 0.10 = 40 people from Scotland.
2. Determine the number of people from Wales:
Since 25% of the people came from Wales, we'll multiply the total attendees (400) by 25% (0.25).
400 * 0.25 = 100 people from Wales.
3. Calculate the difference between the number of attendees from Wales and Scotland:
Subtract the number of people from Scotland (40) from the number of people from Wales (100).
100 - 40 = 60 more people from Wales than Scotland.
In conclusion, at the concert with 400 attendees, there were 60 more people from Wales than from Scotland.
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A production line operation is designed to fill cans with tomato sauce with a mean weight of 20 ounces. A sample of 25 cans is selected to test whether overfilling or under filling is occurring in the production line and they should stop and adjust it. Sample statistics (mean and standard deviation) are calculated. Assume the population of interest is normally distributed.
Let the p-value be 0. 067 for this sample. At 0. 05 level of significance, it can be concluded that the mean filling weight of the population is :_________
a. Significantly different than 20 ounces
b. Not significantly different than 20 ounces
c. Significantly less than 20 ounces
d. Not significantly less than 20 ounces
Answers
At a significance level of 0.05, the critical value is typically chosen as 1.96 for a two-tailed test. Comparing this critical value with the obtained p-value of 0.067, which is greater than 0.05, indicates that the result is not statistically significant.
At 0.05 level of significance, when we fail to reject the null hypothesis, it means that there is not enough evidence to support the alternative hypothesis. In this case, the null hypothesis states that the mean filling weight of the population is equal to 20 ounces. Since the data does not provide strong evidence to suggest otherwise, we conclude that the mean filling weight is not significantly different from 20 ounces.
Hence, the answer is (b) "Not significantly different than 20 ounces."
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Question 1(Multiple Choice Worth 2 points)
(Circle Graphs MC)
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Question 5(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answers
Answer:
Step-by-step explanation:
Car are the preferred transportation for 168 residents.Together, Walk and Streetcar are the preferred transportation for 55 residents.Bus is the preferred transportation for 45 residents.Bicycle is the preferred transportation for 50 residents.Question 2(Multiple Choice Worth 2 points)(Appropriate Measures MC)The box plot represents the number of tickets sold for a school dance.A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the numb
How you can solve real-life problems involving mean or expected value
Answers
Solving real-life problems involving mean or expected value can be quite useful in various situations, such as finance, statistics, and decision-making.
To begin, identify the problem that requires the calculation of mean or expected value.
The mean is the average of a set of numbers, while expected value is the anticipated result based on probability distribution.
Next, collect the necessary data for the problem.
In calculating the mean, gather all values in the data set.
For expected value, you'll need the probability of each outcome and its corresponding value.
To calculate the mean, add all the values together and divide by the total number of values. For expected value, multiply each outcome's value by its probability and then sum up the results.
Once you have the mean or expected value, apply it to the real-life problem to make informed decisions or predictions. This can help in areas such as budgeting, risk assessment, and determining the likelihood of future events.
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To solve 6÷1/4, james thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. what is the quotient of 6 and 1/4? enter your answer in the box.
Answers
The quotient of 6 and 1/4 is 24.
We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.
We can represent this condition in either of the two ways.
Denominator < Numerator
(Or)
Numerator > Denominator
We are given a numerical expression which is 6÷ 1/4 and we have to solve this.
To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.
The reciprocal of 1/4 is 4.
Therefore,
6÷ 1/4
= 6 × 4
= 24
Therefore, the quotient of 6 and 1/4 is 24.
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Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.
Sample Standard Deviation
red box 3.868
blue box 2.933
Then complete each statement.
The sample size of the session regarding the number of people would purchase the red box,
, is
.
The sample size of the session regarding the number of people would purchase the blue box ,
, is
.
The standard deviation of the sample mean differences is approximately
.
Answers
The standard deviation of the sample mean differences is; 0.6898
How to find the standard deviation of the mean differences?From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45
From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60
Formula for standard deviation of the sample mean differences is;
σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]
Thus;
σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]
σm₁ - σm₂ = 0.6898
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a manufacturing machine has a 80% defect rate. if 109 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
Answers
The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).
Percent of defective rate in manufacturing machine = 80%
Random number of items chosen = 109
The correct wording for the random variable in this situation is,
The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.
Number of defective items is successes.
A common symbol for the number of successes in a binomial distribution is X.
Use X to represent the random variable in this situation.
The notation for the binomial distribution is usually written as,
X ~ B(n, p)
where X is the random variable,
n is the sample size,
and p is the probability of success on each trial.
X ~ B(109, 0.8).
Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to X ~ B(109, 0.8).
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Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
Answers
The area of the triangle is 6 square units.
How to solveOnce you have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
Or you could use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
then find area
A=1/2bh
1/2(3*4)
6
Thus, the area of the triangle is 6 square units.
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An angle measure 94 less than the measure of its supplementary angle. What is the measure of each angle?
Answers
The angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
What is the supplementary angle?In geometry, the supplementary angle of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. In other words, two angles are supplementary if their sum is 180 degrees.
For example, if an angle measures 60 degrees, its supplementary angle would measure 120 degrees, since 60 degrees + 120 degrees = 180 degrees.
According to the given informationLet x be the measure of the angle in degrees.
By definition, the supplementary angle of x measures 180 - x degrees.
We are given that the angle measures 94 degrees less than its supplementary angle, so we can write:
x = (180 - x) - 94
Simplifying and solving for x, we get:
2x = 180 - 94
2x = 86
x = 43
Therefore, the angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
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Find g(x), where g(x) is the translation 1 unit left of f(x)=x2.
write your answer in the form a(x–h)2+k, where a, h, and k are integers.
Answers
To find g(x), the translation 1 unit left of f(x) = x², we need to replace x with (x+1) because moving left means we need to subtract 1 from x. Therefore, g(x) = f(x+1) = (x+1)².
To write g(x) in the form a(x-h)² + k, we need to expand (x+1)² first. Using the formula (a+b)² = a² + 2ab + b², we get:
g(x) = (x+1)² = x² + 2x + 1
Now we can write g(x) in the vertex form by completing the square. We add and subtract (2/2)² = 1 to the expression to get:
g(x) = x² + 2x + 1 - 1 + 1
= (x+1)² + 0
Therefore, g(x) = (x+1)² + 0 is the vertex form of g(x), where a=1, h=-1, and k=0. This means that the vertex of the parabola g(x) is (-1,0), and it opens upwards. The translation 1 unit left of f(x)=x² results in a horizontal shift of the parabola to the left by 1 unit without changing its shape or orientation.
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The ratio of English books to Math books is 5:9.If there 28 more Math books than English books. How many Math and English books are there?
Answers
Answer: 35 English Books and 63 Maths Books
Step-by-step explanation:
5:9
x:(x+28)
Cross multiplication...
9x=5x+140
9x-5x=140
4x=140
14/4 = 35 = x
English Books = x= 35
Maths Books = x+28 = 63
Gebhardt Electronics produces a wide variety of transformers that it sells directly to manufacturers of electronics equipment. For one component used in several models of its transformers, Gebhardt uses a 3-foot length of. 20 mm diameter solid wire made of pure Oxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity and increases the likelihood it will break, and this critical component is difficult to reach and repair after a transformer has been constructed. Therefore, Gebhardt wants to use primarily flawless lengths of wire in making this component. The company is willing to accept n more than a l in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardt also occasionally uses smaller pieces of the same wire in the manufacture of other compo- nents, so the 3-foot segments to be used for this component are essentially taken randomly from a long spool of. 20 mm diameter solid OFE copper wire Gebhardt is now considering a new supplier for copper wire. This supplier claims that its spools of. 20 mm diameter solid OFE copper wire average 50 inches between flaws. Gebhardt now must determine whether the new supply will be satisfactory if the supplier's claim is valid. Managerial Report In making this assessment for Gebhardt Electronics, consider the following three questions:
1. If the new supplier does provide spools of. 20 mm solid OFE copper wire that aver age 50 inches between flaws, how is the length of wire between two consecutive flaws distributed?
2. Using the probability distribution you identified in (I), what is the probability that Gebhardt's criteria will be met (i. E. , a l in 20 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless)
3. In inches, what is the minimum mean length between consecutive flaws that would result in satisfaction of Gebhardt's criteria
4. In inches, what is the minimum mean length between consecutive flaws that would result in a l in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless?
Answers
we need to determine the minimum mean length between consecutive flaws that would result in a 1 in 100 chance that a randomly selected 3-foot segment of wire provided by the new supplier will be flawless.
First, we need to convert the length of the wire provided by the new supplier (50 inches) into feet, which is 4.17 feet (50 inches divided by 12).
Next, we can use the Poisson distribution formula to calculate the probability of getting at least one flaw in a 3-foot segment of wire:
P(X >= 1) = 1 - e^(-λ)
Where X is the number of flaws in a 3-foot segment, and λ is the mean number of flaws per 3-foot segment.
Since the supplier claims that the average length between flaws is 4.17 feet, we can calculate λ as:
λ = 1/4.17 = 0.239
Now, we can plug in the values and solve for the probability:
P(X >= 1) = 1 - e^(-0.239) = 0.208
This means that there is a 20.8% chance of getting at least one flaw in a 3-foot segment of wire provided by the new supplier.
To find the minimum mean length between consecutive flaws that would result in a 1 in 100 (or 0.01) chance of getting a flawless 3-foot segment, we can rearrange the Poisson formula:
P(X = 0) = e^(-λ)
0.01 = e^(-λ)
ln(0.01) = -λ
λ = 4.605
This means that the mean length between consecutive flaws would need to be at least 4.605 feet (55.26 inches) in order to have a 1 in 100 chance of getting a flawless 3-foot segment from the new supplier.
In conclusion, if the new supplier's claim is valid and the mean length between consecutive flaws is at least 55.26 inches, then Gebhardt Electronics can expect to get a flawless 3-foot segment of wire with a 1 in 100 probability.
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Choose the system for the graph.
Answers
The system of equations which represents the given graph is:
(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3
What are systems of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
A group of equations comprising one or more variables is known as a system of equations.
The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
So, the lines have slopes of 7/3 and 2/5, based on the solutions. (We could verify this by close examination of the graph.)
The shade is above (greater than) the line with a slope value of 2/5, and below (less than) the line with a slope value of 7/3.
So, using the symbols, we need to find two inequalities:
y ≥ 2/5x ...
y ≤ 7/3x ...
Choice C contains this combo.
Therefore, the system of equations which represents the given graph is:
(C) y ≥ 2/5x + 1 and y ≤ 7/3x + 3
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f (x) = ¹4 - 6. Find the inverse of f(x) and its domain.
O A. f¹(x) =
6 + 4, where x #-6
O B. f¹(x) =
6 +4, where x #4
O c. f¹(x) =
¹6-4, where x 4
OD. f¹(x) = 2¹6-4, where x#-6
Answers
The correct option is the first one, and the domain is the set of real numbers except for x = -6.
How to find the inverse?The inverse will be a function such that when we take the composition we get the identity, then we can write:
[tex]f(g(x)) = \frac{1}{g(x) - 4} - 6 = x[/tex]
We need to solve that for g(x), we will get:
[tex]\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4[/tex]
That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.
Then the correct option is the first one.
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the battery life of the iphone has an approximately normal distribution with a mean of 10 hours and a standard deviation of 2 hours. if you randomly select an iphone, what is the probability that the battery will last more than 10 hours?
Answers
If you randomly select an iphone, The probability that the battery will last more than 10 hours is 0.5000.
Population mean, µ = 10
Population standard deviation, σ = 2
The likelihood that the battery will survive more than 10 hours is equal to
[tex]= P( X > 10)\\= P( (X-\mu)/\sigma > (10 - 10)/2)\\= P( z > 0)\\= 1- P( z < 0)\\[/tex]
Using excel function:
= 1- NORM.S.DIST(0, TRUE)
= 0.5000
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes a large class of phenomena observed in nature, social sciences, and engineering. It is often called the bell curve because of its characteristic shape, which is symmetric and bell-shaped.
The mean and the standard deviation are the two factors that define the normal distribution. The mean is the center of the distribution, and the standard deviation measures how much the data varies from the mean. The normal distribution has several important properties, including that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
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18. Mr. Kamau wishes to buy some items for his son and daughter. The son's item costs sh. 324 while
the daughter item costs sh. 220 each. Mr. Kamau would like to give each of them equal amount of
money.
a) How many items will each person buys.
Answers
Answer:
if Mr. Kamau wants to give each of his children an equal amount of money, he can either:
Buy 1 item for his son (costing sh. 324) and 0 items for his daughter, giving each child sh. 162.
Buy 1 item for his son (costing sh. 324) and 1 item for his daughter (costing sh. 220), giving each child sh. 272.
Step-by-step explanation:
Let x be the number of daughter items that Mr. Kamau will buy for his daughter. Since the son's item costs sh. 324, we know that each child should receive sh. (324 + 220x)/2.
We want to find how many items each child will buy, so we need to solve for x in the equation:
(324 + 220x)/2 = 220
Multiplying both sides by 2, we get:
324 + 220x = 440
Subtracting 324 from both sides, we get:
220x = 116
Dividing both sides by 220, we get:
x = 0.527
Since we can't buy a fraction of an item, Mr. Kamau should buy either 0 or 1 daughter item for his daughter. If he buys 0 daughter items, he can give his son sh. (324 + 2200)/2 = sh. 162. If he buys 1 daughter item, he can give each child sh. (324 + 2201)/2 = sh. 272. Therefore, the possible scenarios are:
Mr. Kamau buys 0 daughter items. His son buys 1 item and his daughter buys 0 items.
Mr. Kamau buys 1 daughter item. His son buys 1 item and his daughter buys 1 item.
QUESTION IN PHOTO I MARK BRAINLIEST
Answers
The value of x in the given circle is 13.9.
Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,
Using the inscribed angle theorem,
It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.
So,
m ∠CFE = arc CE / 2
57 = 10x-25 / 2
10x-25 = 114
10x = 139
x = 13.9
Hence the value of x in the given circle is 13.9.
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A hotel offers two activity packages. One costs $192 and includes 3h of horseback riding and 2h of parasailing. The second costs $213 and includes 2h of horseback riding and 3h of parasailing. What is the cost for 1h of each activity?
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
let's assumed that
x = 1h of horseback
y = 1h of parasailing
3h of horseback = 3x
2h of parasailing = 2y
and
2h of horseback = 2x
3h of parasailing = 3y
if
3x + 2y = 192
2x + 3y = 213
to find y we have to remove the x
(3x + 2y = 192) × 2
(2x + 3y = 213) × 3
6x + 4y = 384
6x + 9y = 639
___________ -
-5y = -255
y = 51
substitute y to any equation to find x
3x + 2y = 192
3x + 2(51) = 192
3x + 102 = 192
3x = 192 - 102
3x = 90
x = 30
so the answers are 1h of horseback = $30 and 1h of parasailing = $51
#CMIIWIn right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (s)
Answers
In right triangle RST, the value of tan (s) is 12/5.
To find tan(s), we first need to determine which side is opposite angle S and which side is adjacent to angle S.
In this case, RT is the side opposite angle S, and ST is the side adjacent to angle S. Since tangent (x) or tan(x) is defined as the ratio of the length of the opposite side to the length of the adjacent side, we can write the formula for tan(s) as follows:
tan(s) = (opposite side) / (adjacent side)
Now we can plug in the given side lengths to calculate the value of tan(s):
tan(s) = RT / ST
tan(s) = 12 / 5
Thus, tan(s) = 12 / 5.
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1. A triangle, △DEF, is given. Describe the construction of a circle with center C circumscribed about the triangle. (3-5 sentences)
2. ⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformations on ⊙O, prove that ⊙O and ⊙P are similar
Answers
Answer: Finally, translate the circles back to their original positions. This will not change their similarity. Therefore, ⊙O and ⊙P are similar.
Step-by-step explanation:
To construct a circle circumscribed about triangle △DEF, follow these steps:
Draw the perpendicular bisectors of the sides of the triangle. Each bisector should intersect the opposite side of the triangle at a point.
Find the point of intersection of any two perpendicular bisectors. This point is the center of the circle.
Measure the distance from the center to any of the vertices of the triangle. This distance is the radius of the circle.
Draw the circle with the center and radius found in the previous steps. The circle should pass through all three vertices of the triangle.
To prove that ⊙O and ⊙P are similar using similarity transformations, follow these steps:
Translate both circles so that their centers coincide with the origin. This will not change their relative positions.
Scale one of the circles by a factor equal to the ratio of the radii of the two circles. This will make the two circles have the same size.
Since both circles are centered at the origin and have the same size, they must be similar. This is because any two circles with the same size are either congruent or similar.
Finally, translate the circles back to their original positions. This will not change their similarity. Therefore, ⊙O and ⊙P are similar.
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1ST ONE TO ANSWER MY QUESTION WILL BE MARKED BRAINLIESTT! ANSWER 1 QUESTION!
Answers
2x²t + 7xy
Step-by-step explanation:To simplify, we will combine like terms.
Given:
5xy - x²t + 2xy + 3x²t
Reorder like terms:
5xy + 2xy + 3x²t - x²t
Combine like terms:
➜ 5 + 2 = 7
➜ 3 - 1 = 2
7xy + 2x²t
Reorder by degree:
2x²t + 7xy
A plane rose from take-off and flew at an angle of 11° with the ground. When it reached an
altitude of 500 feet, what was the horizontal distance the plane had flown?
Answers
A plane rose from take-off and flew at an angle of 11° with the ground, the horizontal distance the plane had flown when it reached an altitude of 500 feet is approximately 2755.3 feet.
To solve this problem, we can use trigonometry. We know that the angle between the ground and the plane's path is 11°, and the altitude of the plane is 500 feet. Let x be the horizontal distance the plane has flown.
We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle, to find x. In this case, the opposite side is the altitude (500 feet) and the adjacent side is x. So we have:
tan(11°) = 500/x
To solve for x, we can multiply both sides by x and then divide by tan(11°):
x = 500 / tan(11°)
Using a calculator, we get:
x ≈ 2755.3 feet
Therefore, the horizontal distance the plane had flown when it reached an altitude of 500 feet is approximately 2755.3 feet.
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The volume of this prism is 2990cm3. the area of the cross-section is 65cm2. work out x
Answers
After considering the given values provided in the question the value of x is 46cm, under the condition that the volume of this prism is 2990cm³. the area of the cross-section is 65cm².
The evaluated volume of a prism refers to the area of the cross-section multiplied by its length. Then, considering the volume of this prism is 2990cm³ and the area of the cross-section is 65cm², we can finally formulate a formula to evaluate the length of the prism by dividing the volume by the area of the cross-section.
So,
Length = Volume / Area of cross-section
= 2990 / 65
= 46
Then the value of x = 46cm.
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The complete question is
The volume of this prism is 2990cm³. The area of the cross-section is 65cm². Work out x
Diagram is not drawn to scale
rewrite the expression 4^-2 x 8^0 x 5^6
Answers
Now, we can rewrite the expression as:
4^-2 x 8^0 x 5^6 = (1/4^2) x 1 x 5^6
Simplifying further, we get:
(1/16) x 5^6
or
5^6/16
1)Change point A in the scatterplot to point (1,12). Calculate the correlation coefficient and note how much it differs from .96. (2)Change point A back to (1,2) and change point B to (4,15). Calculate the correlation coefficient and note how much it differs from .96. Did the correlation coefficient change more when the point you raised 10 units was in the middle of the scatterplot or at the edge of the scatterplot? Why do you think this is so? (3)Move only one point and make the correlation coefficient become negative. Write about what you did and why it made the correlation go negative.(4) Suppose you had a scatterplot with only two points. Assuming your two points don't define either a horizontal line (both y-values the same) or a vertical line (both x-values the same), what is the correlation coefficient? Why do you think this is true? What happens as you try different points (again, without defining a horizontal or vertical line)?(5)Enter the points (1,2) and (3,2) — this defines a horizontal line. Try to calculate the correlation coefficient. What did your graphing calculator tell you? What happened?(6) Enter the points (1,2) and (1,3) — this defines a vertical line. Try to calculate the correlation coefficient. What did your graphing calculator tell you? What happened? The following scatterplot was constructed by reversing the x- and y-values in the original scatterplot. Without calculating the new correlation coefficient, what do you think r is? Why? (7)Graph depicts 16 scatter plots on a coordinate plane without coordinate points. 7 scatter plots in quadrant 3, 1 scatter plot in quadrant 4, and 8 scatter plots in quadrant 1. The following scatterplot was constructed by taking the negative of each x-value in the original scatterplot. Without calculating the new correlation coefficient, what do you think r is? Why? What would the correlation coefficient be if we took the negative of all the x-values and all the y-values? Graph depicts 15 scatter plots on a coordinate plane without coordinate points. 7 scatter plots in quadra
Answers
The new regression coefficient is about 0.663, viz. lesser than the previous regression coefficient by 0.297. Thus, a single outlier creates a significant drop in the correlation
How to solveChanging A to (1,12) gives below scatterplot and regression parameters
(check image)
2. In this case, r is about 0.766, a drop of 0.194 which is substantial, but lower than the previous drop. The regression coefficient changed much more when the outlier was in the middle of the scatterplot. This happens because the data series itself is increasing.
So the effect of 10 points in a middle point is much more of an outlier compared to when this 10-point increase happens for the highest value of x. Hence, the r value drops more in the former case.
3. r can become negative if drop the point B to a highly negative y-value. Consider taking it to (4, -50). Then we get the following regression parameters
We obtain r = -0.275. Since the expected y-value was highest for point B, so changing it drastically to a large negative value leads to a negative correlation between the two variables.
4. With only two points that are parallel to neither of the axes, the correlation coefficient is always exactly either 1 or -1. The correlation is 1 if the slope of the line joining the two points is positive, and -1 if the slope is negative.
That is, there is always either a perfect positive correlation or a perfect negative correlation. This is so because there is always a unique line joining two points, which leads to a perfect correlation between them. Even by differing the pairs, this relation shall always hold true.
5. If the points are parallel to the X axis, we should obtain r=0, because it indicates no relation between the variables. So points (1, 2) and (3, 2) lead to r=0. This can be verified using any calculator.
A vertical line also leads to r=0. Since the y value does not change, so no correlation can be established. Actually, it is just like flipping the x and y variables, and we know flipping does not change the correlation coefficient. So we should obtain r=0 even for a vertical line.
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Taylor is making a large banner that
measures 6 yards in length. He split the
banner into 18 sections for him and
some of his friends to work on. How
many inches long is each section?
Answers
Answer:
12 is the answer
Step-by-step explanation:
6 y = 6 × 36 in. ( y = yards, in = inches )
do the math:
6(36) ÷ 18 = 12 ( for 18 sections of course )
12 × 18 = 6 × 36
becuase;
12 × 18 = 216 \
——- They are the same
6 × 36 = 216 /
= 216
Divide
216 ÷ 18 = 12
12 being the answer
Answer:
12 inches long
Step-by-step explanation:
One yard is equal to 36 inches, so 6 yards is equal to:
[tex]\sf:\implies 6 \times 36 = 216\: inches[/tex]
To find the length of each section, we need to divide the total length of the banner (216 inches) by the number of sections (18):
[tex]\sf:\implies 216 \div 18 = \boxed{\bold{\:\:12\:\:}}\:\:\:\green{\checkmark} [/tex]
Therefore, each section is 12 inches long.