where P is the principal amount, r is the interest rate, and n is the number of years. In this case, A is $1,000,000, r is 0.05, and n is 119. Thus, P = [tex]$1,000,000/(1+0.05)119 = $66,059.19.[/tex]
A. The investment of $1,000 in 1900 would be worth $97,792.96 today. This can be calculated by using the compound interest formula A=P(1+r)n, where P is the principal amount, r is the interest rate, and n is the number of years. In this case, P is $1,000, r is 0.05, and n is 119.
Thus, A = [tex]$1,000(1+0.05)119 = $97,792.96.[/tex]
B. If the investment has grown to $1 million in 2019, the principal amount invested in 1900 would be $66,059.19. This can be calculated by using the compound interest formula [tex]A=P(1+r)n[/tex]
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a number is five times a smaller number. find the larger number of their difference is 52
The larger number if the difference of the numbers is 52 is 65.
How to find the larger number?A number is five times a smaller number. Let's find the larger number when their difference is 52.
Therefore,
let
x = smaller number
larger number = 5x
There difference is 52. Hence,
5x - x = 52
4x = 52
divide both sides of the equation by 4
x = 52 / 4
x = 13
Therefore,
larger number = 5(13) = 65
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find the steady state response value yss and the steady state error value ess for the systems in figures 5.74 a,b, 5.75, 5.76 for unit step, unit ramp, and unit parabolic inputs.
Plug the corresponding R(s) for each input type and the transfer functions of the given systems into the equations above to find yss and ess for each case. Keep in mind that some systems might not have a finite steady-state response or error for specific input types, depending on the system's type (order and poles).
To determine the steady-state response (yss) and steady-state error (ess) values for the given systems, we need to use their transfer functions and input types (unit step, unit ramp, and unit parabolic). Unfortunately, without information about the specific transfer functions for figures 5.74 a, b, 5.75, and 5.76, it is not possible to provide a definitive answer.
In general, for a system with transfer function G(s), you can calculate the steady-state response and error using the Final Value Theorem:
yss = lim (s -> 0) s * Y(s), where Y(s) = G(s) * R(s) is the system's output.
ess = lim (s -> 0) s * E(s), where E(s) = R(s) - Y(s) is the system's error.
For different input types:
- Unit step input: R(s) = 1/s
- Unit ramp input: R(s) = 1/s^2
- Unit parabolic input: R(s) = 1/s^3
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carlos and juan take 5 hours to do a job. carlos alone takes 8 hours to do the same job. how long would it take juan to do the same job alone?
13.33 hrs long would it take juan to do the same job alone.
Here, we have,
given that,
carlos and juan take 5 hours to do a job.
carlos alone takes 8 hours to do the same job.
let, x hr long would it take juan to do the same job alone.
now, we have,
1 hr work of carlos = 1/8
1 hr work of juan = 1/x
1 hr work of both = 1/8 + 1/x = (x+8)/8x
we have,
So they together can do this job in = 5 hours
so, ATQ, we get,
(x+8)/8x = 1/5
or, (5x+40) = 8x
or, 3x = 40
or. x = 13.33
Hence, 13.33 hrs long would it take juan to do the same job alone.
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for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Company A will charge less than Company B for any mileage greater than 70 miles. For mileages less than 70 miles, Company B will be cheaper. The inequality solved is m > 70.
To determine for what mileages Company A will charge less than Company B, we can set up an inequality with m representing the number of miles driven.
Let's start by finding the total cost for each company based on the number of miles driven:
Company A: $138 (unlimited mileage)
Company B: $75 + $0.90m (where m is the number of miles driven)
To find the mileage for which Company A will charge less than Company B, we need to set up an inequality by equating the total cost for Company A to the total cost for Company B and then solving for m:
138 < 75 + 0.90m
Subtracting 75 from both sides, we get:
63 < 0.90m
Dividing both sides by 0.90, we get:
m > 70
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Complete question is:
Latoya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $138 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
1. A rain barrel collects water off the roof of a house during three hours of heavy rainfall. The height of the water in the barrel increases at the rate of r(t) = 47-15 feet per hour, where is the time in hours since the rain began. At time t = 1 hour, the height of the water is 0. 75 foot. What is the height of the water in the barrel at time = 2 hours? (A) 1. 361 ft (B) 1. 500 ft (C) 1. 672 (D) 2. 111
As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).
The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.
In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.
∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922
So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:
0.75 + 0.922 = 1.672 feet
Therefore, the correct option is (C).
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Help please, I will give brainiest
Type the correct answer in each box. Round your answers to the nearest hundredth.
City Cat Dog
Lhasa Apso Mastiff Chihuahua Collie
Austin 24. 50% 2. 76% 2. 86% 3. 44% 2. 65%
Baltimore 19. 90% 3. 37% 3. 22% 3. 31% 2. 85%
Charlotte 33. 70% 3. 25% 3. 17% 2. 89% 3. 33%
St. Louis 43. 80% 2. 65% 2. 46% 3. 67% 2. 91%
Salt Lake City 28. 90% 2. 85% 2. 78% 2. 96% 2. 46%
Orlando 37. 60% 3. 33% 3. 41% 3. 45% 2. 78%
Total 22. 90% 2. 91% 2. 68% 3. 09% 2. 58%
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is ______%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is ______%
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.
The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.
The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .
2.76% + 2.86% + 3.44% + 2.65% = 11.71%
11.71/3.44 = .2937
.2937 = 29.37%
Probability is just the way that logical something is to occur.
Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.
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Which value is equivalent to x+4/4+x?
O-4
O-1
O 1
O4
The correct option for the given radical equation is option C. The value after operation is equal to 1.
Given radical expression:
[tex]\frac{x+4}{4+x}[/tex]
Now, we know that the addition is commutative.
Using commutative property, 4+x = x+4,
So,
[tex]\frac{x+4}{x+4}[/tex]
Both numerator and denominator has same value, hence they could be cancelled.
[tex]\frac{x+4}{4+x}[/tex] = [tex]\frac{x+4}{x+4}[/tex]
[tex]\frac{x+4}{x+4}[/tex] = 1.
Therefore, the value which is equivalent to x+4/4+x is equal to 1.
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answer based on working with the 5.5 chapter practice file. what is the total cost for the trip reserved under santos albert's name? $450 $900 $1500 $1100
The total cost for the trip reserved under Santos albert's name is $1,500 (option c).
In Excel, we can use the SUM function to add up a range of numbers. To do this, we first need to select the range of cells containing the costs associated with Santos Albert's reservation. In this case, the costs are located in columns C through G for the row corresponding to Santos Albert.
Once we have selected the range of cells containing the costs, we can use the SUM function to add them up. The formula for this would be "=SUM(C5:G5)", where C5 is the first cell in the range and G5 is the last cell in the range. This formula will add up all of the costs in the range and give us the total cost for Santos Albert's reservation.
So, to answer the question, the total cost for the trip reserved under Santos Albert's name is $1500.
Hence the correct option is (c).
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An environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5, 28.7). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval? A For all water in the region, 99 percent of the water contains a level of the contaminant between 22.5 ppb and 28.7 ppb. B We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb. We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb. D There is a 0.99 probability that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb. E There is a 0.99 probability that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb.
The correct interpretation of the 99 percent confidence interval (22.5, 28.7) is B: We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.
This does not indicate that the mean level of the contaminant in all the water in the region is necessarily between 22.5 ppb and 28.7 ppb.
Confidence intervals provide an estimate of the population mean based on a sample. In other words, they indicate the range of values that are likely to include the true mean of the population. Therefore, the interval (22.5, 28.7) indicates that we are 99 percent confident that the mean of the sample (which is used to estimate the true population mean) lies between 22.5 ppb and 28.7 ppb. However, this does not guarantee that the true population mean (i.e., the mean of all the water in the region) lies between 22.5 ppb and 28.7 ppb.
The other answers are incorrect because they do not reflect the fact that the interval provides an estimate of the population mean based on a sample.
Answer A is incorrect because it states that all of the water in the region must contain a level of the contaminant between 22.5 ppb and 28.7 ppb, which is not necessarily true.
Answer D is incorrect because it states that there is a 0.99 probability that the mean of the sample is between 22.5 ppb and 28.7 ppb, when in reality the interval indicates that we are 99 percent confident that the mean of the sample is between 22.5 ppb and 28.7 ppb. Finally,
Answer E is incorrect because it states that there is a 0.99 probability that the true population mean (i.e., the mean of all the water in the region) is between 22.5 ppb and 28.7 ppb, which is not necessarily true.
In summary, the correct interpretation of the 99 percent confidence interval (22.5, 28.7) is that we are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.
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the intersection of two events a and b is the event that: a) both a and b occur. b) the union of ac and bc occurs. c) the union of a and b does not occur. d) either a or b or both occur. e) either a or b, but not both. f) none of the above.
The intersection of two evens a and b is the event that both a and b occur that is option A is correct.
The intersection of two events A and B is defined as the event that occurs when both A and B occur simultaneously. It is denoted by A ∩ B, where the symbol ∩ represents intersection.
For example, if event A is "getting a head when flipping a coin" and event B is "rolling a 6 on a fair die", then the intersection of A and B would be the event "getting a head when flipping a coin and rolling a 6 on a fair die".
For example, suppose A represents the event "rolling an even number on a dice" and B represents the event "rolling a number greater than 3 on a dice". The intersection of A and B is the event that "rolling a number that is both even and greater than 3 on a dice", which consists of the outcomes {4, 6}.
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Complete Question:
the intersection of two events a and b is the event that:
a) both a and b occur.
b) the union of ac and bc occurs.
c) the union of a and b does not occur.
d) either a or b or both occur.
e) either a or b, but not both.
f) none of the above.
Suppose you select a number at random from the sample space {-3, -2, -1, 0, 1, 2, 3, 4). Find the probability. P(the number is less than 2 | the number is less than 4)
Evaluate 4!
Evaluate 6!
Evaluate 5!/3!
Answer:
Step-by-step explanation:
There are four numbers in the sample space that are less than 4: -3, -2, -1, and 0. Of these, three are less than 2: -3, -2, and -1. Therefore, the probability P(the number is less than 2 | the number is less than 4) is 3/4.
To evaluate 4!, we perform the multiplication 4 x 3 x 2 x 1, which equals 24.
To evaluate 6!, we perform the multiplication 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
To evaluate 5!/3!, we first calculate 5! (which is equal to 5 x 4 x 3 x 2 x 1, or 120) and then divide by 3! (which is equal to 3 x 2 x 1, or 6). Therefore, 5!/3! = 120/6 = 20.
what is $510,451 rounded to the nearest 1,000 dolllars?
Answer:
$510,000
Step-by-step explanation:
Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.
Remember, 4 or less, round down. 5 or more, round up.
Since the hundreds digit is 4, we do not need to round.
We only need to change the rest of the digits to 0.
So, our answer would be $510,000.
The following data points represent the number of points the Hawaii Eagles football team scored each game.
17, 33,28,23,10,42,3
Using the data, create and histogram
The class intervals are given as:
0 - 15 15-30 30-45
2 3 2
What is a Histogram?A histogram is a graphical representation of the distribution of numerical data. It is a way of summarizing the shape and spread of a set of continuous data values into a series of bins or intervals.
The histogram is a bar graph-like representation of the data, where the data is grouped into intervals or bins on the horizontal axis and the frequency or count of observations falling into each bin is represented by the height of the bar on the vertical axis.
Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.
The class intervals are given as:
0 - 15 15-30 30-45
2 3 2
The histogram is provided below:
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need help x-y=11 2x+y=19
Answer:
(10, - 1 )
Step-by-step explanation:
x - y = 11 → (1)
2x + y = 19 → (2)
adding (1) and (2) term by term will eliminate y
(x + 2x) + (- y + y) = 11 + 19
3x + 0 = 30
3x = 30 ( divide both sides by 3 )
x = 10
substitute x = 10 into either of the 2 equations and solve for y
substituting into (2)
2(10) + y = 19
20 + y = 19 ( subtract 20 from both sides )
y = - 1
solution is (10, - 1 )
What is the percent of increase from 50 to 95?
A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use? A. A one-sample t-interval for a sample mean B. A one-sample t-interval for a population mean C. A one-sample z-interval for a population proportion D. A two-sample t-interval for a difference between means E. A two-sample z-interval for a difference between proportions
The correct inference procedure for the ecologists to use is A. A one-sample t-interval for a sample mean.
This is because they are trying to estimate the average number of eggs per nest for all robins in the region, so they will need to use a one-sample t-interval for a sample mean to draw inferences about the population.
Ecologists will choose a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. The correct inference procedure for the ecologists to use is A. A one-sample t-interval for a sample mean.
What is a t-interval for a sample mean?A t-interval for a sample mean is a type of confidence interval that estimates the unknown population parameter, μ, based on the data in a random sample. The t-distribution is used to estimate the population parameter because the population standard deviation is not known.
The following is an illustration of the method of calculating a confidence interval for the mean using a t-distribution:If a sample of n observations is drawn from a normal population, the mean x of the sample is normally distributed with the following properties:Mean: μx = μ.Standard deviation: σx = σ/√n.
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Factor completely x3 + 6x2 − 9x − 54.
A (x + 3)(x − 3)(x + 6)
B (x + 3)(x − 3)(x − 6)
C (x2 + 9)(x + 6)
D(x2 − 9)(x + 6
Answer:
A (x + 3)(x - 3)(x + 6)
Step-by-step explanation:
f(x) = x3 + 6x2 − 9x − 54
f(3) = 3^3 + 6(3)^2 - 9(3) - 54
= 27 + 54 - - 27 - 54 = 0
So (x - 3) is a factor.
f(-3) = 3^-3 + 6(-3)^2 - 9(-3) - 54
= -27 + 54 - 27 - 54 = 0
so (x + 3) is a factor
x + 3 * (x - 3) = x^2 - 9 and if we divide f(x) by
(x^2 - 9) we get x + 6.
Answer:
a
Step-by-step explanation:
took the test :)
Find the volume of a cylinder that has a diameter of 14mm
14 mm and a height of 8
m
m
8 mm.
Use
π=3.14
π=3.14 and round your answer to the nearest hundredth.
Step-by-step explanation:
as with any regular 3D object : the volume is
base area × height
in the case of a cylinder, the base area is a circle, abd the area of circle is
pi × r²
with r being the radius (= half of the diameter).
so, in our case we have the volume to be
pi × (14/2)² × 8 = 3.14 × 7² × 8 = 3.14 × 49 × 8 =
= 1,230.88 mm³
Camacho is buying a monster truck. The price of the truck is a dollars, and he also has to pay a 13% monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck? Choose 2 answers: D (1 + 0.13)x 13 100 13x X 1.13x Smy 13x + x
The expression which represents the given relatiοn is x(1 + 0.13). Thus, option A is cοrrect.
What are equations?Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign. It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.
In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side). Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.
If there is nο "equal tο" symbοl, a statement is nοt an equatiοn. When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.
Let the x represent the price οf mοnster truck
Then He has tο pay extra 13% οf the tοy = 0.13
Tοtal price = x + x × 0.13
simplifying
x + x × 0.13
x + 0.13x
x(1 + 0.13) ⇒ οptiοn A
x(1.13)
1.13x ⇒ οptiοn D
Thus, The expressiοn which represents the given relatiοn is x(1 + 0.13). Thus, οptiοn A and D is cοrrect.
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Complete question:
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a %13 monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?
Choose 2 answers:
(Choice A) (1+0.13)x
(Choice B) 13/100 x
(Choice C) 14x
(Choice D) 1.13x
(Choice E) 13x+x
Person 1 has X amount of shoes. Person 2 has two or more than three times Person 1's amount. Write an expression for total amount for both people.Person 1 has X amount of shoes. Person 2 has two or more than three times Person 1's amount. Write an expression for total amount for both people.
The expression for the total amount of shoes for both people is 4X + 2.
What is another word for total cost?As a result, total cost is the sum of fixed and variable costs, or TC = FC + VC = Kr+Lw.
Say Person 1 owns X pairs of shoes. So, Person 2 has two to three times as much as Person 1. This can be said as follows:
Person 2 possesses at least two more than three times Person 1's amount, so Person 2's amount is equal to 3X + 2.
By simply adding Person 1's and Person 2's shoe counts, we can determine the total number of shoes for both individuals, which results in:
Total equals the sum of the amounts given by Persons 1 and 2.
When we replace the value of Person 2's contribution, we obtain:
Amount total = X + (3X + 2)
If we simplify, we get:
Total = 4X plus 2
Hence, 4X + 2 is the total number of shoes for both individuals.
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An angle measures 62° more than the measure of its complementary angle. What is the measure of each angle?
Find exact values for x and y
The value of x and y for the given set of values in triangle are 8√3 units and 12 units.
What is triangle?A triangle is a polygon with three sides and three angles. It is the simplest polygon that can exist in Euclidean geometry. The sum of the three interior angles of a triangle is always 180 degrees. Triangles can be classified according to the length of their sides and the measure of their angles. The most common classifications are:
Scalene triangle: A triangle with all three sides of different lengths.
Isosceles triangle: A triangle with two sides of equal length.
Equilateral triangle: A triangle with all three sides of equal length.
Acute triangle: A triangle in which all angles are less than 90 degrees.
Obtuse triangle: A triangle in which one angle is greater than 90 degrees.
Right triangle: A triangle in which one angle is exactly 90 degrees.
Here,
Using the given information:
side1 = 8√3
angle1 = 60°
We can use trigonometric ratios to find the values of x and y:
sin(60°) = y / side1
Simplifying:
y = side1 * sin(60°)
y = 8√3 * sin(60°)
y = 8√3 * (√3 / 2)
y = 12
Therefore, x = 8√3 and y = 12.
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Proportional or not proportional?
Step-by-step explanation:
A is not proportional
Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6
And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end
Using the graph Value of y
(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)
Using the graph, find the value of x when y is 1 - 10)
1.2, 2.5, 5,.....
The slope of the graph also shows that it is not proportional
B is proportional
X is 0 and y is 0
When x is 5, y is 10
Ratio x: y = 5:10 = 1:2
When x is 10, y is 20
Ratio x:y is 10: 20 = 1:2 same as above
C is not proportional
When Moyra is 32, daughter is 8
When her daughter is 22, Moyra will also be 4years older, which is 36
32: 8 = 4:1
36: 12 =3:1
you have taken up gardening for relaxation and have decided to fence in your newrectangular shaped masterpiece. the length of the garden is 4 meters and 52 meters offencing is required to completely enclose it. what is the width of the garden?
If the length of the garden is 4 meters and 52 meters of fencing is required to completely enclose it, the width of the garden is 22 meters.
To find the width of the garden, we need to use the formula for the perimeter of a rectangle, which is:
P = 2l + 2w
Where:
P = perimeter of the rectangle
l = length of the rectangle
w = width of the rectangle
We know that the length of the garden is 4 meters and the perimeter is 52 meters, so we can plug in the values and solve for the width:
52 = 2(4) + 2w
52 = 8 + 2w
44 = 2w
w = 22
To verify our answer, we can check if the perimeter using this width is indeed 52 meters:
P = 2l + 2w = 2(4) + 2(22) = 8 + 44 = 52
As expected, the perimeter is 52 meters. This means that if we fence in the garden with a width of 22 meters and a length of 4 meters, we will require 52 meters of fencing to completely enclose it.
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This pre-image was reflected over the y-axis.
Use the segment tool to draw the image.
Segment
-10-9-8-7-6-5
H
10
9
8
←Undo
7
6
5
4
3
2
1
-3 -2 -10
y
N
-3
-
Redo
5
Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis. The pre-point image's (-3, 5) is mirrored to the image's point (3, 5).
What does the y-axis represent?The x-axis is the horizontal axis and the y-axis is the vertical axis in two-dimensional space. As seen in the image below, they are represented by two number lines that perpendicularly connect at (0, 0).
This is a reflection of the pre-image that was provided over the y-axis:
Segment
10 9 8 7 6 5 -5 -6 -7 -8 -9 -10
Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis, they are reflected to one another.
Similar to this, the pre-point image's (-3, 5) is reflected to the image's point (3, 5).
The x-coordinates of all other locations in the pre-image are negated in the image because they have corresponding points there that are equally spaced from the y-axis.
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Write a word sentence for the question
x - 14 = 52
Answer:
x-14=52|+14
x=52+14
x=66 candies
Step-by-step explanation: If Anna gives 14 candies to her sister, she remains with 52. How many candies does Anna have ?
suppose a recessive genetic disorder occurs in 9 percent of the population whst id the percentage of the populaation that is hetero
The percentage is 42% of the population is heterozygous for the recessive genetic disorder.
To determine the percentage of the population that is heterozygous for a recessive genetic disorder occurring in 9 percent of the population,
follow these steps:
1. Identify the frequency of the recessive allele (q) by taking the square root of the 9 percent occurrence (0.09). The square root of 0.09 is 0.3.
2. Calculate the frequency of the dominant allele (p) using the equation p = 1 - q. In this case, p = 1 - 0.3 = 0.7.
3. Determine the percentage of the population that is heterozygous using the equation 2pq. In this case, 2(0.7)(0.3) = 0.42 or 42%.
So, 42% of the population is heterozygous for the recessive genetic disorder.
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2. Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Kathy runs 8 mph slower than Dennis rides his bike. Find their speeds
Kathy's speed is 2 mph and Dennis's speed is 2+8 = 10 mph.
Let's assume that Kathy's speed is "x" mph. Since Dennis rides 8 mph faster than Kathy, his speed is "x+8" mph.
We know that Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Therefore, we can use the formula:
time = distance/speed
For Kathy: time = 2 miles / x mph
For Dennis: time = 10 miles / (x+8) mph
Since they both take the same amount of time, we can set these two equations equal to each other:
2 / x = 10 / (x+8)
We can then solve for "x" as follows:
2(x+8) = 10x
2x + 16 = 10x
16 = 8x
x = 2 mph
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A quadratic equation is usually written in the form ax² + bx+c = 0. What are a, b, and c for the following quadratic equations? Separate your answers with a comma. (a) 13x²14x + 5 = 0 a, b, c (b) 5x² 13x - 10 = 0 (c) x² - 4 = 0 (d)-9x² = 0
Answer:
a) a is 13
b is 14
c is 5
b) a is 5
b is 13
c is-10
c) a is 1
b is 0
c is -4
d) a is -9
b is 0
c is 0
Step-by-step explanation:
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For the following indefinite integral, find the full power series centered at
x=0 and then give the first 5 nonzero terms of the power series. [infinity]
Σ∫(e^9x - 1) / 6x dx
n=0
From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.
To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:
∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du
We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):
(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du
= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]
= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))
We can now simplify and group terms to obtain the power series centered at x=0:
(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))
To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:
n=0: (3/2) × 1 = 1.5
n=1: (3/2) × 9x = 13.5x
n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²
n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³
n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴
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