Bounce Testing and Creating a Model Page 3 of 3 6) What are the coordinates for the vertex,(h, k), of the parabola? Round the x-value to two decimal places. (2.le, 12.8) 7) Substitute the coordinates for the vertex into the vertex form of a parabola: s(t) = alt-h2+k s(t)= alt-2.66) 2 + 12.8 8) Now we can solve for a if we know just one point on the parabola. Any point will do, but it is always nice when you can use a zero. The zeros for this function occur at the times at which the ball bounces on the floor. Select a value for t in which the ball will bounce on the floor (s = 0). t= 3.2 a= 9) Substitute the coordinates for the zero into the function and then solve for a. Round your answer to two decimal places. (3.2)= a (3.2-2.66) - + 12 - 12,8 = al.)2 36a 10) What function models one bounce of Type A Bouncy Ball? -12.2 36 = 35,5-6 s(t) = -35.56 (t- 2.6+ /2.8 Test your function by graphing it on a calculator. 11) Create a model for one bounce of Type B Bouncy Ball. Vertex (2.4,7, 2) 20 s(t) = a (t-2.42 + 7.2. 157 10 1 2 3.2 15.1 5 Tan 11.7

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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The given problem is related to hypothesis testing. we can conclude that there is enough evidence to reject the claim at a = 0.01.

The given null hypothesis and the alternate hypothesis are given below: Hypothesis TestingH0: p = 0.40 (Null Hypothesis)

H1: p ≠ 0.40 (Alternate Hypothesis)

Where, p represents the proportion of customers who have call waiting service.

For this problem, the significance level is given as a = 0.01. Level of significance (α) = 0.01

To test the given hypothesis, we use the Z-test since the sample size is greater than 30, which is given by: Z = (p - P) / √(PQ/n)

Where, P represents the population proportion, Q represents the population proportion minus the sample proportion, p represents the sample proportion, n represents the sample size.

Substituting the given values, we get:

Z = (0.37 - 0.40) / √((0.40 * 0.60) / 100)Z = -0.57 / 0.077Z = -7.4

Since the test is a two-tailed test, we split the significance level equally on both sides. α/2 = 0.01/2 = 0.005

The area from the normal distribution table corresponding to 0.005 is 2.58.

Now, we compare the calculated value of Z with the tabulated value of Z.

Since the calculated value of Z is less than the tabulated value of Z, we can reject the null hypothesis and accept the alternate hypothesis. Therefore, we can conclude that there is enough evidence to reject the claim at a = 0.01.

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Answer:

47 degrees

Step-by-step explanation:

180-133=47

Answer:

∠Q = 44°

Step-by-step explanation:

∠R = 180° - 133°  = 47°

∠Q = 180° - 89° - 47° = 44°

Answer:

34 degrees C

Step-by-step explanation:

30+30+30+35+35+35+34=229

229/7=32.714

and when you round up you get 33

The multiplier can be calculated by determining the marginal propensity to consume (MPC) and using the formula: multiplier = 1 / (1 - MPC).

To calculate the multiplier, we need to find the marginal propensity to consume (MPC) from the consumption function. In this case, the MPC is the coefficient of income (Y) in the consumption function, which is 0.5.

Using the formula: multiplier = 1 / (1 - MPC), we can substitute the value of MPC into the equation:

multiplier = 1 / (1 - 0.5) = 1 / 0.5 = 2.

Therefore, the multiplier is 2.

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Determined by various factors such as sample size, statistical significance, and the chosen level of confidence. the probability that the test will fail to decide that the true value is 72.5 when it is indeed 72.5.  

In order to calculate the probability of a Type II error, one would need to know the specific details of the test being used, such as the sample size, the statistical power of the test, and the chosen level of significance.

In general, the probability of a Type II error increases as the sample size decreases and the level of significance decreases. This means that if the test being used is not sufficiently powered or if the level of confidence is too low, there is a higher probability of failing to detect a true effect.

If the test is not able to accurately determine if the statement is true or not when the actual value is 72.5, then there is a possibility that a Type II error has occurred. The probability of this error depends on the specific details of the test being used and cannot be determined without further information.

The probability of a test failing to decide a certain hypothesis is true, when it is actually true, can be determined using the concept of Type II error or false negative rate. In statistical hypothesis testing, Type II error (β) refers to the probability of failing to reject a false null hypothesis. These factors influence the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. The power of the test (1 - β) is complementary to the probability of making a Type II error.

In this case, the null hypothesis (H0) could be that the value is not equal to 72.5,

while the alternative hypothesis (H1) states that the value is equal to 72.5.

The probability you are looking for is the Type II error rate when the true value is 72.5.

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(a) Yes, a confidence interval for the true average lifetime can be calculated without assuming anything about the nature of the lifetime distribution.

(b) Using the given data, we can calculate a confidence interval with a 99% confidence level for the true average lifetime, with a mean of 1191.6 and a standard deviation of 506.6.

(a) It is possible to calculate a confidence interval for the true average lifetime without assuming any specific distribution. This can be done using methods such as the t-distribution or bootstrap resampling. These techniques do not require assumptions about the underlying distribution and provide a reliable estimate of the confidence interval.

(b) To calculate a confidence interval with a 99% confidence level for the true average lifetime, we can use the sample mean (1191.6) and the sample standard deviation (506.6). The formula for calculating the confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

The critical value depends on the desired confidence level and the sample size. For a 99% confidence level, the critical value can be obtained from the t-distribution table or statistical software.

The standard error is calculated as the sample standard deviation divided by the square root of the sample size.

Once we have the critical value and the standard error, we can calculate the confidence interval by adding and subtracting the product of the critical value and the standard error from the sample mean.

Interpreting the confidence interval means that we are 99% confident that the true average lifetime falls within the calculated range. In this case, the confidence interval provides a range of values within which we can expect the true average lifetime of individuals suffering from blood cancer to lie with 99% confidence.

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The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.

However, it is important to note that not all studies need to use random sampling in order to draw meaningful conclusions. In some cases, non-random samples may still provide valuable insights into the topic of interest.

In any case, if the study did use volunteers who self-selected to participate, it is important for the researchers to acknowledge this limitation in their conclusions and to avoid overgeneralizing the findings beyond the sample they studied.

The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.

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Answer:

D

Step-by-step explanation:

Your answer is Toys and treats

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Answer: y = 12/11 x + -12/11

Step-by-step explanation:

m = y2 -y1/x2 -x1

x1 = -4

x2 = 7

                  into m = y2 - y1/x2 -y1

y1 = -7

y2 = 5

m = 12/11

x = -4            into y = mx + b

y = -7

b = - 12/11

y = 12/11x + -12/11 into

y = mx + b :

y + 12/11x + -29/11

c <= 19/7 = 2.71

7c = 19

by algebra,

c × 7÷7 = 19 ÷ 7

c = 19 / 7

Hence c is equal to 2.71 or 19/7

Answer:

hope this helps you

Answer:

(3, 2)  

Step-by-step explanation:

it's A on edg

Answer:

8

Step-by-step explanation:

Answer:

8x⁴

Step-by-step explanation:

8x8 = 64

⁴x⁴ = ¹⁶

The value of b is 3.

The value of c is 1/8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

Two equations given are:

b = 24c ____(1)

(1/4)b + 4c = 5/4 _____(2)

Putting (1) in (2) we get,

(1/4)24c + 4c = 5/4

6c + 4c = 5/4

10c = 5/4

c = 5/40

c = 1/8

Putting c = 1/8 in (1) we get,

b = 24/8

b = 3

Thus,

b = 3.

c = 1/8.

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Answer:

8.  A = 22,   P = 26

9.  A = 44,   P = 30

Step-by-step explanation:

see attached

The distance between two points, x and y, on the number line is given by the absolute value of the difference between the coordinates of the two points.

The distance between two points on the number line can be determined by calculating the absolute value of the difference between the coordinates of the two points. Let's assume that point x has a coordinate of a, and point y has a coordinate of b. The distance between x and y can be expressed as |b - a|, where | | denotes the absolute value.

To understand why the absolute value is used, consider that the distance between two points can be positive or negative depending on their relative positions on the number line. The absolute value ensures that the result is always positive, representing the magnitude of the distance between the points regardless of their order. For example, if point x is located at -3 and point y is at 2, the absolute value of the difference, |2 - (-3)|, gives the distance of 5 units. Similarly, if point x is at 5 and point y is at -2, the absolute value of the difference, |(-2) - 5|, also yields a distance of 7 units. Thus, the expression |b - a| captures the concept of distance between two points on the number line.

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Answer:

x equals 14

Step-by-step explanation:

If u plug in 14 as X. The equation would equal 180.

Answer:

The graphs and the table is missing in the question.

Step-by-step explanation:

The guidelines for interpreting correlation  co-efficient r are :

1. Strong correlation    0.7<|r|≤1

2. Moderate correlation   0.4<|r|<0.7

3. Weak correlation   0.2<|r|<0.4

4. No correlation  0≤|r|<0.2

Logarithmic regression

(i). Mean : \($ {\overset{-}{ln}x} = \frac{\sum ln x_i}{n}, \ \ \ {\overset{-}y} = \frac{\sum y_i}{n} $\)

(ii) Trend line : \($ y = A +B \ln x, \ \ B = \frac{S_{xy}}{S_{xx}}, \ \ A={\overset{-}y-B{\overset{-}{\ln x}}}$\)

(iii). Correlation coefficient : \($ r = \frac {S_{xy}}{\sqrt{S_{xx}} \sqrt{S_{yy}}} $\)

\($ S_{xx} = \sum (\ln x_i - {\overset{-}{\ln x}})^2 = \sum (\ln x_i)^2-n. ({\overset{-}{\ln x}})^2$\)

\($ S_{yy} = \sum(y_i - {\overset{-}y})^2 = \sumy_i^2 - n. {\overset{-}y^2}$\)

\($ S_{xy} = \sum(\ln x_i - {\overset{-}{\ln x}})(y_i-{\overset{-}y}) = \sum \ln x_i y_i - n. {\overset{-}{\ln x}}{\overset{-}y} $\)

Now using the technology we can calculate

The equation of the regression curve is y = A + B(lnx)

we get A = 30.72 , B = 17.19

The equation of regression curve is \($ \hat y$\) = 30.72 + 17.19(lnx)

The length of side a is determined as 13.92 by applying sine rule of triangle.

The length of side a is calculated by applying the following formulas shown below;

Apply sine rule as follows;

a / sin (83) = 13 / sin (68)

Simplify the expression as follows;

multiply both sides of the equation by " sin (83)".

a = ( sin (83) / sin (68) ) x 13

a = 13.92

Thus, the value of side length a is determined as 13.92 by applying sine rule as shown above.

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Answer:

D, (13, 4.5)

Step-by-step explanation:

(question asked for midpoint so my bad if this isnt what you wanted)

to calculate the median of a vector, you would have to do a simple calculation to get the answer

for the x coordinate, (9 + 17) / 2 would be 13

for the y coordinate, 5 + 4 / 2 would be 4.5

combining those would give you the answer (13, 4.5)

Answer:

Step-by-step explanation:

Expression on the board :

\(12.2x + 50.6 y + 3(1.4x - 2.6y)\\\\= 12.2x + 50.6y + 4.2x - 7.8y\\\\= 16.4x + 42.8y\)

Expression by the student :

Expression 1 :

\(4 ( 4.1x + 10.7 y ) \\\\= ( 4 \times 4.1x ) + ( 4 \times 10.7 y)\\\\= 16.4x + 42.8y\\\\\)

The expression 1 is equivalent to the expression on the board. Because the coefficients of x and y are same on both.

Expression 2 :

\(2 ( 6.1x + 25.3 y + 2.1x -3.9y)\\\\= 2 ( 8.2x + 21.4y)\\\\=( 2 \times 8.2x ) + (2 \times 21.4y)\\\\= 16.4x + 42.8y\)

The expression 2 is also equivalent to the expression on the board. Because the coefficients of x and y are the same.

Answer:

39 km

Step-by-step explanation:

13 x 3 = 39km

Hope that helps!

Answer:

3

Step-by-step explanation:

Not sure, but let's take 32 to be the answer

4(5+x)=32

4×5= 20

4×x= 4x

20-4x=32

4x=32-20

4x=12

12÷4

x=3

Answer:

4n - 5

Step-by-step explanation:

let the number be n then the product of 4 and this number is 4n

Subtract 5 from 4n gives

4n - 5

Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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Answer: B. 4.11

Step-by-step explanation:

Using Binomial distribution  ( as the arrival times of workers are independent).

Formula for standard deviation: \(\sqrt{{p(1-p)}{n}}\), where p= population proportion, n= sample size.

As per given ,

p= 0.06, n=300

Required standard deviation= \(\sqrt{0.06\left(1-0.06\right)300}\)

\(=\sqrt{(0.06)(0.94)(300)}\\\\=\sqrt{16.92}\approx4.11\)

Hence, the correct option is B.

Answer:

y = 1/4x -2

Step-by-step explanation:

If the slope is 1/4, then you must multiply x by 1/4. If we plug 0 into 1/4x, we get 0, but we need -2, so we must subtract 2 in the equation.