Identify the sampling method that was used. a local restaurant collects business cards in a bowl by the register. a free dinner is given to the person whose business card is drawn.

When the radius is 9 cm, the area of the circular pool is increasing at a rate of 288π cm square/min.

To find how fast the area of the circular pool is increasing when the radius is 9 cm, we can use the formula for the area of a circle, which is A = πr^2, where A represents the area and r represents the radius.

Given that the radius is increasing at a rate of 4 cm/min, we can differentiate the formula for the area with respect to time (t) using the chain rule:

dA/dt = dA/dr * dr/dt

Here, dA/dt represents the rate of change of the area with respect to time, dr/dt represents the rate of change of the radius with respect to time, and dA/dr represents the derivative of the area with respect to the radius.

To find dA/dr, we can differentiate the formula for the area of a circle:

dA/dr = d/dt (πr^2)

= 2πr * dr/dt

Plugging in the given values, we have:

dr/dt = 4 cm/min

r = 9 cm

Substituting these values into the equation for dA/dr:

dA/dr = 2π(9) * 4

= 72π cm^2/min

Now, we can find dA/dt by multiplying dA/dr by dr/dt:

dA/dt = (72π cm^2/min) * (4 cm/min)

= 288π cm^2/min

To know more about chain rule refer here:

https://brainly.com/question/29498741#

#SPJ11

Answer:

Step-by-step explanation:

y = 1/2 x + 4 Final answer! We have the point ( -4 , 2 ) so x1 = -4 and y1 = 2.

Answer:

y = 2x + 12

Step-by-step explanation:

y = mx + b

m = 2

y = 2x + b

4 = 2(-4) + b

4 = -8 + b

b = 12

y = 2x + 12

Answer:

This is my best solution for your question

Answer:

$1.27

Step-by-step explanation:

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

Learn more about statistical process control here:

https://brainly.com/question/32323372

#SPJ11

Answer:

119 r 9

Step-by-step explanation:

Given constant acceleration a, the velocity of the car after 15 seconds would be given by:

\(v(15) = v(0) + 15a\)

The velocity of a car after t seconds is modeled by the following function:

\(v(t) = v(0) + at\)

In which:

In this problem, 15 seconds, hence \(t = 15\) and:

\(v(15) = v(0) + 15a\)

A similar problem is given at https://brainly.com/question/14516604

Answer:

Which two elements of drama divide the play and indicate shifts in location or scenery?

dialogue

act

character

monologue

scene

Step-by-step explanation:

The distance between two lines measured along a perpendicular line to the line is always the same is called as equidistant .

Given :

The distance between two lines measured along a perpendicular line to the line is always the same.

What is Equidistant ?

Distances between two points from a common points are equal then it is called as equidistant .

Formulas :

Midpoint = ( x1 + x2 / 2 , y1 + y2 / 2 )

Distance = \(\sqrt{(x2 - x1 )^2 - (y2 - y1)^2 }\)

These are two main formulas are used to find whether equidistant or not.

Learn more about the perpendicular here:

https://brainly.com/question/29268451

#SPJ4

Byron will need 6 cube-shaped containers to store his 384 centimeter cubes.

To determine the number of cube-shaped containers Byron needs to store his 384 centimeter cubes, we need to calculate the volume of each container and then divide the total volume of the cubes by the volume of each container.

The volume of a cube is calculated by cubing the length of one of its sides. In this case, the containers measure 4 cm on each side, so their volume is \(4^3\) = 64 cm³.

To find the number of containers needed, we divide the total volume of the cubes (384 cm³) by the volume of each container (64 cm³).

384 cm³ ÷ 64 cm³ = 6

Therefore, Byron will need 6 cube-shaped containers to store his 384 centimeter cubes.

For more such questions containers,click on

https://brainly.com/question/29398973

#SPJ8

- For the student-athlete research question, a chi-square test of independence should be conducted.
- For the shampoo company research question, a chi-square goodness of fit test should be conducted.
- For the pen manufacturer research question, a one-way ANOVA should be conducted.
- For the jam manufacturer research question, a chi-square goodness of fit test should be conducted.
Here are the appropriate hypothesis tests for each research question:

1. For the student-athlete's research question comparing jump rope abilities across different sports, you should use a **Chi-square test of independence**. This test is used to determine whether there is a significant association between two categorical variables (in this case, sport type and jump rope ability).

2. For the shampoo company's research question regarding hair types and product purchases, you should use a **Chi-square goodness of fit test**. This test is used to compare observed frequencies of categorical data (hair type) with expected frequencies (proportional representation in product purchases).

3. For the pen manufacturer's research question about pen colors and writing performance, you should use a **Chi-square goodness of fit test**. This test is used to compare the observed frequencies of categorical data (pen colors) with expected frequencies (equal performance among colors).

4. For the jam manufacturer's research question on jam flavor sales and specific days, you should use a **Chi-square test of independence**. This test is used to determine if there is a significant association between two categorical variables (jam flavor and sales day).

Visit here to learn more about chi-square test brainly.com/question/14082240

#SPJ11

Answer:

Step-by-step explanation:

for the rectangle, it is (2l + 2w) - l = P (modified)

(2*4 + 2*2) - 4 = 8

for the triangle, the hypotenuse, is a^2 + b^2 = c^2

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

c = 4.5cm (rounded to the nearest tenth)

Now we add all the perimeters.

8 + 2*4.5 = 8 + 9 = 17cm

The value of the given sine function is √3/2, so the correct option is 2nd.

Given that an function Sin (-5π/3) we need to evaluate the expression,

To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.

Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.

To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).

Once adding 2:

(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3

Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.

Therefore, sin(-5π/3) = sin(π/3) = √3/2.

Hence the correct option is √3/2

Learn more about sine function click;

https://brainly.com/question/12015707

#SPJ1

The coefficients obtained by the student may be less efficient and have larger standard errors compared to the professor's regression.

If the student enters each observation twice, resulting in a sample size of 100 instead of the original 50, the assumption of independent observations is violated in Ordinary Least Squares (OLS) regression. The OLS assumption assumes that the observations are independent, meaning that the value of one observation does not depend on the value of another observation.

In this case, the student's dataset contains repeated observations, which introduces dependence between observations. This violation of the independence assumption can lead to biased and inconsistent parameter estimates in the regression analysis.

Regarding the slope coefficients, if the student runs a regression using the duplicated data, the estimated coefficients may be different from the professor's regression. The duplication of observations inflates the sample size, potentially affecting the precision and accuracy of the estimates.

However, the direction and overall relationship between the variables may still be captured by the student's regression, although the estimates may not be as reliable.

learn more about coefficients here

https://brainly.com/question/1594145

#SPJ11

Answer:

144

Step-by-step explanation:

Hope this helps! God bless you!

Since the line of best fit represents the best linear model given the data, we can see that if y = 44 (pounds), then we are looking at the expected length of a catfish that weighs 44 pounds.

The number of butterscotch bags is 2.75 and the number of chocolate bags is 5.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that you bought eight bags altogether chocolate chips cost three dollars and 50 Cent per bag and butterscotch chips cost $4.75 per bag and you spent $30.25 at the store how many bags of each time did you buy

The number of bags will be calculated as,

3.5C + 4.75B = 30.25

C + B = 8

Solve by elimination method,

3.5C + 4.75B = 30.25

3.5C + 3.5B = 28

________________

                 B = 2.75

The number of chocolate bags,

C + B = 8

C = 8 - 2.75

C = 5.25

Therefore, the number of butterscotch bags is 2.75 and the number of chocolate bags is 5.25.

To know more about an expression follow

https://brainly.com/question/13217021

#SPJ1

Elmo's lap time refers to the average time he spends swimming a single lap. At the beginning of the summer, Elmo's lap time was 25/10 = 2.5 minutes per lap. At the end of the summer, his lap time improved to 24/12 = 2 minutes per lap. Therefore, Elmo improved his lap time by 2.5 - 2 = 0.5 minutes per lap.

Improving one's lap time is important for competitive swimming, as it can greatly affect one's overall performance. By improving his lap time by 0.5 minutes per lap, Elmo can swim a 20-lap race 10 minutes faster than he could at the beginning of the summer. This could potentially lead to better race results and help Elmo achieve his goals as a swimmer.

To further improve his lap time, Elmo can work on his technique, endurance, and overall fitness. He can incorporate interval training, strength training, and drills to enhance his swimming skills and improve his lap time. By setting specific goals and consistently practicing, Elmo can continue to improve his lap time and achieve success as a swimmer.

Learn more about minutes  here:

https://brainly.com/question/15600126

#SPJ11

If B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

Given that B is midpoint of AC and C is the midpoint of BD.

We are required to prove that AB is equal to CD.

Midpoint is the point which divides the line segment into two equal parts.

If B is midpoint of AC then,

2AB=AC-----1

2BC=AC-----2

If C is midpoint of BD then,

2BC=BD-----3

2CD=BD-----4

From 1 & 2

2AB=2BC

AB=BC

Put the value of BC from 3.

AB=BD/2

Now put the value of BD from 4.

AB=2CD/2

AB=CD

Hence proved

Hence if B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

Learn more about midpoint at https://brainly.com/question/5566419

#SPJ1

Answer:

507 x 8 in standard algorithim is equivelant to the answer.=

Step-by-step explanation:

     5 0 7

×         8

+   4 0 5 6

=  4 0 5 6

________________________

Therefore:

507 × 8 = 4056

Answer is attached

hope it helps you ⬆️

The product of the mathematical expression √10 · √10 is 10 option first 10 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have given a mathematical expression:

= √10 · √10

As we know,

√a² = a

or

√a×√a = a

By applying the above rule:

= √10×√10

= √10²

= 10

Thus, the product of the mathematical expression √10 · √10 is 10 option first 10 is correct.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ1

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

To learn more about Stock split, visit:

https://brainly.com/question/29754813

#SPJ11

Answer:

85, 68, 51

Step-by-step explanation:

Average: The sum of all the numbers divided by the number of numbers

If the ratio of the scores is 5 : 4 : 3, let's just set it as 5x : 4x : 3x

Then using the definition of an average, we can write this equation.

(5x + 4x + 3x) / 3 = 68

Multiply both sides by 3.

5x + 4x + 3x = 68 * 3

Simplify.

12x = 204

x = 17

Now, substitute x = 17 into the original scores (5x, 4x, and 3x)

5x = 5 * 17 = 85

4x = 4 * 17 = 68

3x = 3 * 17 = 51

Just in case, let's check this answer. Find the average of the 3 test scores.

(85 + 68 + 51) / 3 =

204 / 3 = 68

Thus, the answers are correct

Answer:

Student Ticket: $8

Adult $28

Step-by-step explanation:

To find out the price of each ticket create 2 equations, then solve for x & y

x = student tickets

y = adult tickets

25x + 28y = 984

25x + 25y = 900

To do this first put x on one side of the equation

25x = 900 - 25y

x = 36 - y

Now substitute this equation in x for the first equation

25(36 - y) + 28y = 984

Now distribute 25 in 36 - y, 900 - 25y + 28y = 984

After this combine like term, then subtract 900 from each side, 3y = 84

Then divide 3 on each side, y = 28

Lastly substitute 28 for y in any equation to solve for x, x = 8

x & y are the price of each ticket

The  size of the sample should be obtained at 2401 in order to be 95% confident

Given that:

Margi of error, \(ME=0.02\)

Population proportion, \(p=0.50\)

To Find: The size of the sample that should be obtained in order to be 95% confident

Let the size of the sample be n

Using formula,

\(n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401\)

Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident

Learn more about Population proportion here https://brainly.com/question/15703406

#SPJ4

The sum to infinity of the function is -3/2

from the question, we have the following parameters that can be used in our computation:

\(\sum\limits^{\infty}_{1} {3^n} \,\)

From the above sequence, we have

First term, a = 3

Common ratio, r = 3

The sum to infinity of the function is calculated as

Sum = a/(1 - r)

So, we have

Sum = 3/(1 - 3)

Evaluate

Sum = -3/2

Hence, the sum is -3/2

Read more about sequence at

https://brainly.com/question/30499691

#SPJ4

Question

Calculate the sum to infinity of the function for

\(\sum\limits^{\infty}_{1} {3^n} \,\)

The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Given data:

7, 11, 12, 18, 20, 22, 43.

To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.

That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.

The formula to find standard deviation is:

S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}

Where, N = sample size,

             x = each value of the data set,

    \bar{x} = mean of the data set

To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:

Mean = $\frac{7+11+12+18+20+22+43}{7}$

          = $\frac{133}{7}$

          = 19

Now, calculate the standard deviation:

$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D

                                                                                                                               = $\sqrt{\frac{1442}{7-1}}$

                                                                                                                                ≈ 10.31

To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.

Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$

                                                                                                                      = $\frac{43-19}{10.31}$

                                                                                                                      = 2.32

Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.

Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Learn more about Standard Deviation from the given link :

https://brainly.com/question/475676

#SPJ11

A pair of Political affiliation and residential status can be used as pair of varibles for which the researcher conduct the chi-square test of independence.

We have a researcher survey random sample of 750 college students about their political views.

This survey contains the following variables,

A Chi-square test of independence is conducted by researcher and the pair of variables can the researcher use here is political affiliation and residential status. Because the Chi-square independence test is used to determine if there is a significant relationship between two nomial categorical variable.

To learn more about Chi-Square independence test, refer:

https://brainly.com/question/29976112

#SPJ4