The total number of cups of dried fruit Lucas need for his one dozen snacks are 3 cups of dried cherries and 6 cups of dried apricots
Cups used of dried cherries = 1/4
Cups used of dried apricots = 2/4
An element of a number or any number of equal pieces is represented by a fraction. A fraction with a numerator and denominator exists.
Lucas is making one dozen snacks, which means the total number of snacks made is = 12.
Calculating the total amount of dried cherries -
= 1/4 cup/serving x 12 servings
= 3 cups of dried cherries
Similarly,
Calculating the total amount of dried apricots -
1/2 cup/serving x 12 servings
= 6 cups of dried apricots
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math is too hard for me help
Answer:
Step-by-step explanation:
1/5(-25) + 16/8
-5 + 2 = -3
Option A
Please helpppppp! I really don't understand
Answer:
AB=8.1 and B=29.6
Step-by-step explanation:
1) To find the measure of AB, use the law of cosines
[tex]c^2=4^2+7^2-2(4)(7)cos(90)[/tex]
[tex]c^2 = 16+49 -56cos(90)\\c^2= 65\\c=8.1[/tex]
2) Use law of sines to find the measure of B
[tex]\frac{8.1}{sin(90)} =\frac{4}{sin(B)}[/tex]
B=29.6
Which equation can be used to find x, the measure of angle M in AAMP?
A = 180 +95 + 54
B x = 180 - 95 + 54
C x = 180- 149
D x = (95 +54) - 180
the correct equation to find x, the measure of angle M in AAMP is: [tex]x = 149[/tex]. Thus, option C is correct.
What is the equation for measure of angle?To find the value of x, we need to know the angles of triangle AMP.
Assuming that AAMP is a quadrilateral, we know that the sum of its angles is [tex]360[/tex] degrees.
Thus, we can write:
Angle AMP + Angle M + Angle A [tex]= 360[/tex]
We know that Angle AMP is [tex]180 - 95 - 54 = 31[/tex] degrees (since the sum of the angles in triangle AMB is 180 degrees, and we are given that Angle BAM = 95 degrees and Angle ABM = 54 degrees).
Substituting this value and the given value of Angle A (which is 180 degrees) into the equation above, we can solve for Angle M:
[tex]31 + Angle M + 180 = 360[/tex]
Angle [tex]M = 149[/tex] degrees
Therefore, the correct equation to find x, the measure of angle M in AAMP is: [tex]x = 149[/tex]
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if i have four boxes arranged in a $2 \times 2$ grid, in how many distinct ways can i place the digits $1$, $2$, and $3$ in the boxes, using each digit exactly once, such that each box contains at most one digit? (i only have one of each digit, so one box will remain blank.)
If i have four boxes arranged in a [tex]2 \times 2[/tex] grid, in 6 distinct ways can i place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit
If a student has four boxes arranged in a 2 × 2 grid, the distinct ways to place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit are six in number.
There are two possibilities for which box is left blank, so let's consider them separately:
Case 1: The top left box is left blank. In this case, the other three boxes must contain the digits 1, 2, and 3. There are three choices for what digit goes in the top right box, and then two choices for what digit goes in the bottom left box, and then one choice for what digit goes in the bottom right box.
This gives a total of 3·2·1 = 6 ways to place the digits in the boxes when the top left box is left blank.
Case 2: A different box is left blank. In this case, one of the digits must be left out. There are three choices for which digit is left out, and then three choices for which box is left blank. Once the digit and the blank box have been chosen, the remaining two digits can be placed in the other two boxes in any order, giving 2 ways.
This gives a total of 3·3·2 = 18 ways to place the digits in the boxes when a different box is left blank.
Therefore, the distinct ways to place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit are six in number.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru is able to estimate their wait time more consistently, and why?
Fast Chicken, because it has a smaller IQR
Fast Chicken, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Answer:
Fast Chicken, because it has a smaller IQR.
Step-by-step explanation:
Fast Chicken is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR) compared to Super Fast Food. The IQR is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The smaller the IQR, the more consistent the data is. In this case, the IQR for Fast Chicken is 4.5 (14.5-10) while the IQR for Super Fast Food is 7 (15.5-8.5). Therefore, Fast Chicken has a more consistent wait time estimate.
Range is a measure of the spread of the data, but it only considers the difference between the highest and lowest values in the data set. The range for Fast Chicken is 15 (20-5), and for Super Fast Food, it is 24 (27-3). Although Super Fast Food has a smaller range than Fast Chicken, it does not necessarily indicate that its wait time estimate is more consistent.
Therefore, the answer is Fast Chicken, because it has a smaller IQR.
Answer:
A
Step-by-step explanation:
because that’s what I got from doing my math because I was doing the math correctly and since I did it correctly I got the answer of .a so this is my absolutely amazing explanation.
write down a model that allows the variance of u to differ between men and women. the variance should not depend on other factors.
The model will be as follows: y = b0 + b1x1 + b2x2 + u
To write a model that allows the variance of u to differ between men and women, the best option is to use the heteroscedasticity model. This model will enable the variances to differ between the genders without depending on other factors.
The model will be as follows: y = b0 + b1x1 + b2x2 + u, Where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model. However, this model does not allow the variance of u to differ between men and women.
To achieve this, we need to modify the model to allow the variance of u to differ between men and women. This can be done by using the weighted regression model. The model will be as follows: y = b0 + b1x1 + b2x2 + u, where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model.
The weights can be represented as: wi = 1/σ^2i, where: wi = weight for observation, iσi = standard deviation of the ith observation. This model will allow the variance of u to differ between men and women without depending on other factors.
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which value of n makes the equation true
[tex]-\frac{1}{2}n=-8[/tex]
Answer:
Step-by-step explanation:
nothing makes it true
Ian owns a small business selling used books. He knows that in the last week 122 customers paid cash, 14 customers used a debit card, and 4 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
The probability that the next customer will pay with cash or a credit card is: 0.90
What is the probability?
The probability that the next customer will pay with cash or a credit card is the sum of the probabilities of these two events occurring.
The probability of the next customer paying with cash is the ratio of the number of customers who paid with cash to the total number of customers:
P(cash) = 122 / (122 + 14 + 4) = 0.870
Similarly, the probability of the next customer paying with a credit card is:
P(credit card) = 4 / (122 + 14 + 4) = 0.029
Therefore, the probability that the next customer will pay with cash or a credit card is:
P(cash or credit card) = P(cash) + P(credit card) = 0.870 + 0.029 = 0.899
Rounding this to the nearest hundredth, we get:
P(cash or credit card) ≈ 0.90 (rounded to the nearest hundredth)
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The height of a machine part should be 13.5 millimeters . The manufacturing tolerance is within 0.07 . Complete the statements. An absolute value equation that could be used to determine the maximum and minimum value of , the height of the machine part, is [DROP DOWN 1]. The minimum value the machine part could be is [DROP DOWN 2]. The maximum value the machine part could be is [DROP DOWN 3].
The machine part's maximum possible size is 13.5 + 0.07, or 13.57 millimeters.
what is equation ?Two mathematical expressions are shown to be equal in an equation, which is a declaration that is frequently denoted by the equals symbol (=). It implies that the amounts or values represented by both formulations are the same. Equations are a useful tool for representing the relationships between variables and for problem-solving because they allow you to identify the values of the unknown variables that the equation requires. They are frequently applied in the domains of math, physics, engineering, and other sciences as well as in daily activities like budgeting, time management, and cooking.
given
The following absolute value equation could be used to calculate the machine part's height's maximum and minimum values:
0.07 for |height - 13.5|
The machine part's minimum possible size is 13.5 minus 0.07, or 13.43 millimeters.
The machine part's maximum possible size is 13.5 + 0.07, or 13.57 millimeters.
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the series meets the conditions to use the ratio test, and . what is the most specific conclusion that may be drawn?
The most specific conclusion that can be drawn from the given series is that it is convergent.
The Ratio Test is a common way of determining the convergence or divergence of an infinite series. It states that if the ratio of successive terms of a series converges to a limit less than one in absolute value, then the series is convergent.
In the case of the given series, it meets the conditions to use the ratio test, which means that the most specific conclusion that can be drawn is that the series is convergent. To explain this further, we need to examine what is meant by the condition that the series meets the ratio test.
First, we need to understand the definition of an infinite series. An infinite series is an expression of the form ∑an, where an is a sequence of numbers that has no upper bound. The limit of the sequence, as n tends to infinity, is referred to as the sum of the series. The ratio test states that the ratio of successive terms of a series converges to a limit less than one in absolute value.
In other words, if the ratio of successive terms of a series approaches zero as n tends to infinity, then the series is said to be convergent. This means that the most specific conclusion that can be drawn from the given series is that it is convergent. This is because the ratio of successive terms of the series converges to a limit less than one in absolute value, as required by the ratio test.
In conclusion, the most specific conclusion that can be drawn from the given series is that it is convergent. This is due to the fact that the ratio of successive terms of the series converges to a limit less than one in absolute value, which is the condition required by the ratio test for a series to be convergent.
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What is the LCM of x² - x and 3 - 3x?
The LCM of x² - x and 3 - 3x is given by the expression 6x² −3x³ −3x.
What are equatiοns?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.
LCM of unkone terms are given by their product:
(x² - x) × (3 - 3x)
= (3x² - 3x³) - (3x -3x²)
= 3x² - 3x³ - 3x + 3x²
= 6x² −3x³ −3x
Thus, the LCM of x² - x and 3 - 3x is given by the expression 6x² −3x³ −3x.
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PLEASE HELP - WORTH 60 POINTS! Ella's school choir is singing two songs for their school's Artist Showcase. The choir director put these song choices on the board.
Answer:9%
Step-by-step explanation:
Sorry for taking so long i didn't understand it at first
What is the solution of the equation (4x + 3)² = 18?
Answer:
third option
Step-by-step explanation:
(4x + 3)² = 18 ( take square root of both sides )
4x + 3 = ± [tex]\sqrt{18}[/tex] = ± [tex]\sqrt{9(2)}[/tex] = ± ([tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] ) = ± 3[tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
4x = - 3 ± 3[tex]\sqrt{2}[/tex] ( divide both sides by 4 )
x = [tex]\frac{-3+3\sqrt{2} }{4}[/tex] , x = [tex]\frac{-3-3\sqrt{2} }{4}[/tex]
Refer to the map of Florida. The distance on the map between Tampa and Orlando is 3.5 units. What is the actual distance between Tampa and Orlando?
in an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. what is the sum of the first $20$ terms of this sequence?
The sum of the first $20$ terms of the arithmetic sequence is $420$.
In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. The sum of the first $20$ terms of this sequence can be calculated using the following formula:
Sum of the first $20$ terms = $20$/2($a_1 + a_{20})$, where $a_1$ is the first term of the sequence and $a_{20}$ is the twentieth term of the sequence.
Therefore, we need to find the first term of the sequence and the twentieth term of the sequence. To find the first term, we use the following equation:
$5 = a_2 + a_8$, where $a_2$ is the second term and $a_8$ is the eighth term.
To find the twentieth term, we use the following equation:
$5 = a_4 \times a_5$, where $a_4$ is the fourth term and $a_5$ is the fifth term.
Solving both equations, we get $a_2 = 1$ and $a_{20} = 40$. Then, we can calculate the sum of the first $20$ terms of the sequence:
Sum of the first $20$ terms = $20$/2($1 + 40$) = $420$.
Therefore, the sum of the first $20$ terms of the arithmetic sequence is $420$.
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how would i graph my question when the x and y intercept is (10,140) when the slope is -14
The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
What is point-slope form?When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).
The y value of the y-intercept point is denoted by the symbol b in the formula.
The general form of a linear equation is y-y1=m(x-x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
So, in the given situation:
The point-slope form is: y = mx + b
Then y is y and b is the x value and m is the slope.
Now, insert values as follows:
y = mx + b
140 = -14x + 10
Graph the equation as follows:
(Refer to the graph attached below)
Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
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describe what the terms interposition and nullification mean and how the terms differ from each other.
Interposition refers to the belief that a state has the right to intervene between the federal government and its citizens to protect them from unconstitutional laws, while nullification is the belief that a state has the power to declare federal laws null and void within its borders.
Interposition and nullification are two theories of state sovereignty that were debated during the early years of the United States. Interposition refers to the belief that a state has the right to interpose itself between the federal government and its citizens to protect them from unconstitutional laws.
On the other hand, nullification is the belief that a state has the power to declare federal laws null and void within its borders. The main difference between interposition and nullification is the extent of state power they propose.
Interposition allows a state to protect its citizens from unconstitutional federal laws, while nullification allows a state to effectively veto a federal law within its borders. While interposition has been recognized as a legitimate theory of state sovereignty.
Nullification has been largely discredited and is not recognized as a valid legal doctrine under the U.S. Constitution.
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Clark is 8 years older than John. In 5 years, Clark will be twice as old as John. How old are they now?
Step-by-step explanation:
Let the John age be x
Clark is 8 years older than John will be written as :
x+8 = x
In 5 years, Clark will be twice as old as John will be written as :
(x+8)+5 = 2(x+8)
Simplify it
x+13 = 2x+16
x-2x = 16-13
-x = 3
x = -3
Their current age :
Clarke:= x+8
= -3+8 ( x = -3)
= 5
John:=2(x+8)
=2(-3+8)
=-6+16
=10
Present age John and Clark are 3 and 11 years respectively .
Let the John present age be J and Clark present age be C
Clark is 8 years older than John will be written as :
C= J + 8
In 5 years, Clark will be twice as old as John will be written as :
C+ 5 = 2(J + 5)
Substitute,
C = J + 8
Simplify it
J + 8 + 5 = 2J + 10
J = 3
C = J + 8
C =11
Thus their present ages are :
Clark = 11 years
John = 3 years
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A box contains eight cards labeled P,Q ,R ,S ,T ,U ,V , and W. One card will be randomly chosen. What is the probability of choosing a letter from P to R?
Write your answer as a fraction in simplest form.
Answer:3/7
Step-by-step explanation:
(Trig word problems)
Aiden leans a 30-foot ladder against a wall so that it forms an angle of 78° with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
The horizontal distance between the base of the ladder and the wall is 29.34 feet.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of the properties and functions of angles, as well as the relationships between these angles and the lengths of the sides of triangles. Trigonometry has many practical applications in fields such as engineering, physics, astronomy, and surveying, among others. Some common concepts in trigonometry include the sine, cosine, and tangent functions, as well as the Pythagorean theorem and the unit circle.
We can use trigonometry to solve this problem. Let x be the horizontal distance between the base of the ladder and the wall.
We know that the ladder is 30 feet long and forms an angle of 78° with the ground. Let's call the angle between the ladder and the wall θ.
Using trigonometry, we can write,
cos θ = x/30
We want to find x, so we can rearrange this equation to solve for x,
x = 30 cos θ
Now we just need to substitute the value of θ into this equation. We know that the ladder forms an angle of 78° with the ground, so the angle between the ladder and the wall is θ = 90° - 78° = 12°
Substituting this value into the equation, we get,
x = 30 cos 12°
Using a calculator, we can evaluate cos 12° to be approximately 0.9781. Multiplying this by 30, we get:
x ≈ 29.34
So the horizontal distance between the base of the ladder and the wall is approximately 29.34 feet. Rounded to the nearest hundredth of a foot, the answer is x ≈ 29.34 feet.
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lilly and paul played video games for a total of 21 hours over the weekend. the amount of time lilly played can be represented by x. the amount of time paul played is 2 times the amount lilly played. what is x, the amount of time played by lilly?
Answer: :)
Step-by-step explanation:
2x + x = 21
Lets x = the amount of time Lilly played
2x = 2 * x = the amount of time Paul played (2 times the amount Lilly played)
:)
Find the HEIGHT of a cylinder if the volume is 1607 and the radius is 4.
Answer:
Step-by-step explanation:
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
We are given that V = 1607 and r = 4. We can plug these values into the formula and solve for h:
1607 = π(4^2)h
1607 = 16πh
h = 1607/(16π)
h ≈ 25.5
Therefore, the height of the cylinder is approximately 25.5 units. Note that we rounded the answer to one decimal place since the radius was given to one decimal place.
PLEASE HELPP I NEED HELP WITH THIS MATHS PLEASE
1. It will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.
2. An annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.
3 A principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.
How to solve the questionsa. Using the TVM Solver function in Excel, we can input the following information:
Present value (PV): -$35,000 (since it's an outgoing cash flow)
Future value (FV): $70,000 (since we want the tithe to double in value)
Interest rate per period (Rate): 7.75%/12 (since the APR is compounded monthly)
Number of periods (Nper): unknown (what we're solving for)
Payment (Pmt): 0 (since there are no recurring payments)
Solving for Nper, we get 96.16 months, or approximately 8 years.
Therefore, it will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.
b. Present value (PV): -$22,500 (since it's an outgoing cash flow)
Future value (FV): $50,000
Interest rate per period (Rate): unknown (what we're solving for)
Number of periods (Nper): 14*2=28 (since the interest is compounded semi-annually, we need to double the number of years)
Payment (Pmt): 0
Solving for Rate, we get 4.84% APR.
Therefore, an annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.
c. Using the TVM Solver function in Excel, we can input the following information:
Present value (PV): unknown (what we're solving for)
Future value (FV): $40,000
Interest rate per period (Rate): 4%/4 (since the APR is compounded quarterly)
Number of periods (Nper): 9*4=36 (since the interest is compounded quarterly, we need to multiply the number of years by 4)
Payment (Pmt): 0
Solving for PV, we get $26,512.18.
Therefore, a principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.
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If f(x) = 3x + 2, find f(2).
a. 2
b. 5
c. 8
d. 9
e. 12
Answer:
C
Step-by-step explanation:
Since the number in the parenthesis is treated as "x", for f(2), replace "x" with 2. So the equation will be f(2) = 3(2) + 2. Then multiply. f(2) = 6 + 2. Lastly add them up. f(2) = 8. The answer is 8.
seventy homes that were for sale in gainesville, florida in spring of 2019 were randomly selected. a regression model to predict house price was run based on square footage and the indicator variable for within 3 miles of campus (1 if the near campus, 0 if not). how would an interaction term be created? group of answer choices the interaction term would be the sum of the indicator variable and square footage. the interaction term would be the product of the price and square footage. the interaction term would be the sum of the price and square footage. the interaction term would be the product of the indicator variable and square footage.
The answer is 'The indicator variable and square footage would be combined to get the interaction term'
Define the term Variable?In an equation or formula, a variable is a symbol or letter that stands in for an unknowable or varying quantity or value.
To create an interaction term in this regression model, we would multiply the indicator variable (1 if the house is within 3 miles of campus, 0 if not) by the square footage. This would allow us to examine whether the effect of square footage on house price is different for houses that are within 3 miles of campus compared to those that are not.
So, the answer is: The indicator variable and square footage would be combined to get the interaction term.
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if matt has 4 times as many nickels as dimes and they have a combined value of 180 cents, how many of each coin does he have?
Matt has 6 dimes coins and 24 nickel coins.
The solution to this math problem is as follows:
Let the number of dimes be x Matt has 4 times as many nickels as dimes therefore the number of nickels is 4x. The combined value of the coins is 180 cents. We know that a nickel is worth 5 cents and a dime is worth 10 cents. Therefore we can write an equation:10x + 5(4x) = 180
Simplifying,10x + 20x = 180
30x = 180
x = 6
Therefore there are 6 dimes and 4 * 6 = 24 nickels.
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A survey conducted on a reasonably random sample of 203 undergraduates asked, among many other questions, about the number of exclusive relationships these students have been in. The histogram below shows the distribution of the data from this sample. The sample average is 3.2 with a standard deviation of 1.97. Estimate the average number of exclusive relationships Duke students have been in using a 90% confidence interval and interpret this interval in context. Check any conditions required for in- ference, and note any assumptions you must make as you proceed with your calculations and conclusions.
The average number of exclusive relationships Duke students have been in is between 2.972 and 3.428.
How to find the average number?Since the sample is reasonably random and the sample size is large enough (n > 30),So, we can estimate with 90% confidence that the average number of exclusive relationships Duke students have been in is between 2.972 and 3.428.
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Which equation of f(x) reveals the minimum or maximum value of f(x) without changing the form of the equation?
In option C, we can see that the equation is in vertex form.
What is parabola ?
A parabola is a symmetrical U-shaped curve formed by the graph of a quadratic function. It is a type of conic section that results from the intersection of a cone and a plane that is parallel to one of the sides of the cone. A parabola can also be defined as the set of points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. Parabolas have many applications in physics, engineering, and mathematics, including projectile motion, antenna design, and optimization problems.
According to the question:
The equation that reveals the minimum or maximum value of f(x) without changing the form of the equation is C f(x)=(x-2)²-16.
This equation is in vertex form, which is f(x) = a(x-h)² + k. In this form, the vertex of the parabola is at the point (h, k), and the value of "a" determines whether the parabola opens upwards or downwards.
In option C, we can see that the equation is in vertex form, where the vertex is (2, -16). Therefore, the minimum value of f(x) is -16, which occurs at x=2.
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a rectangle has an area that is decreasing at a rate of 541 square inches per hour with the width being held constant. determine the rate of change of the length if the width is 3 square inches.
The length is therefore shrinking at a rate of -541/3, or around -180.33 square inches per hour.
what is rectangle ?A rectangle is a flat, four-sided shape with parallel, equal-length opposite sides on each side. There are four right angles (90-degree angles). The distance between the two longer sides, also known as the longer sides or the longer edges, is the rectangle's length. The distance between the two shorter sides, also known as the shorter sides or the shorter edges, determines the rectangle's width. The perimeter of a rectangle is equal to the total of the lengths of all of its sides, and the area of a rectangle is equal to the product of its length and width.
given
Let A represent the rectangle's area, l its length, and w its width. So, we are aware of:
A = lw
By applying the derivative to time t, we obtain:
(d/dt) = dA/dt (lw)
l(dw/dt) + w(dl/dt) = dA/dt
dw/dt = 0 since the width is kept constant, which results in:
w(dl/dt) = dA/dt
We are informed that w = 3 in and that dA/dt = –541 in2/hour. By replacing these values, we obtain:
-541 = 3(dl/dt)
By calculating dl/dt, we obtain:
dl/dt = -541/3
The length is therefore shrinking at a rate of -541/3, or around -180.33 square inches per hour.
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2) A man spent 58% of his income and the amount of money left was GH210.00. Find his income.
Answer: Let x be the man's income.
He spent 58% of his income, which is 0.58x.
The amount of money left is the remaining 42% of his income, which is 0.42x.
According to the problem, 0.42x = GH210.00.
Solving for x, we get:
x = GH210.00 / 0.42
x = GH500.00
Therefore, the man's income is GH500.00.
Step-by-step explanation: