44 pointsWhich rotation angles will map a regular nonagon (9 sides) onto itself? Check all that apply.

Given:

Number of cans he bought = 36

mean = 11.29

standard deviation = 0.21

The confidence interval (C.I) can be found using the formula:

The z-score at 95% confidence level is 1.960

Substituting the given values into the formula:

Answer:

Confidence interval : (11.7214, 11.8586)

Is pepsi filling the cans with less than 12 ounces of soda?

From the confidence interval, we can be 95% certian that the population mean lies in the range (11.7214, 11.8586).

Yes, Pepsi is filling cans with less than 12 ounces of soda

The vectors v1 and v2 are:v1 = -3/5 i - 3/10 jv2

= 18/5 i - 47/10 j which is approximately 3.6i - 4.7j.

The option that represents the vectors v1 and v2 is (C) v1 = 56/13 i + 52/13, v2 = 59/13 i - 527/65 j.

To find vectors v1 and v2 , the following steps should be followed:

Compute the projection of vector v onto vector w which gives the parallel component of vector v to vector w which is v1 = projw(v).

Compute the vector which is perpendicular to w by subtracting v1 from vector v which is v2 = v - v1.

Given vectors are v = 3i - 5j and

w = 3i + j.

We have to decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.

First, we need to calculate the projection of vector v onto vector w as follows:v1 = project (v)

= (v⋅w/||w||^2) w

where v⋅w is the dot product of vectors v and w and ||w|| is the magnitude of vector w.v⋅w = (3i - 5j)⋅(3i + j)

= 9 - 15 + 0

= -6||w||^2

= (3i + j)⋅(3i + j)

= 9 + 1

= 10v1

= (-6/10) (3i + j)

= -3/5 i - 3/10 j

The projection of vector v onto vector w is v1 = -3/5 i - 3/10 j.

Next, we can find the vector which is orthogonal to w by subtracting v1 from vector v:v2 = v - v1

= (3i - 5j) - (-3/5 i - 3/10 j)

= 18/5 i - 47/10 j

Therefore, the vectors v1 and v2 are:v1 = -3/5 i - 3/10 jv2

= 18/5 i - 47/10 j which is approximately 3.6i - 4.7j.

The option that represents the vectors v1 and v2 is (C) v1 = 56/13 i + 52/13, v2 = 59/13 i - 527/65 j.

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Given:

A graph of bell peper patch is given as below

Find:

we have to find the Maximum possible area of bell peper patch represented by the function p corresponding to the length of the tomato patch x.

Explanation:

From the given graph of function p(x), it is observed that the function has maximum value at x = 6.

Therefore, when x = 6, we get

as the function p represents the area of the bell peper patch,

Therefore, Maximum possible area of the bell peper patch is p = 18 square feet, when the length of the zomato patch is x = 6 feet.

Step-by-step explanation:

given that

p= "I do my chores"

q= "I get my allowance."

The statement that uses p as hypothesis is, if  "I do my chores",  which leads to the conclusion of  "I get my allowance."

hence the test/ hypothesis is  if  "I do my chores", i get my allowance

Using the box-whisker plot approach, it is computed that 50% of the data values are more than 45.

In a box-whisker plot, as seen in the illustration, The minimum, first quartile, median, third quartile, and maximum quartiles are shown by a rectangular box with two lines and a vertical mark. In descriptive statistics, it is employed.

Given the foregoing, the box-whisker plot depicts a specific collection of data. A vertical line next to the number 45 shows that it is the 50th percentile in this instance and that 45 is the median of the data.

It indicates that 50% of the values are higher than 45 and 50% of the values are higher than 45.

Using this technique, we can easily determine the proportion of data for which the value is higher or lower. Data analysis and result interpretation are aided by it. Therefore, 50% of values exceed 45.

Note: The correct question would be as

The box-and-whisker plot below represents some data sets. What percentage of the data values are greater than 45?

0

H

10

20

30 40

50 60

70 80 90 100

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Answer:

4(2x - 5)

Step-by-step explanation:

6(2x - 3) - 2(2x + 1)

(distribute)

12x - 18 - 4x - 2

(subtract)

12x - 20 - 4x

(combine terms)

8x - 20

(find common factor)

4(2x - 5)

there you go! hope that helps :)

Answer:

4. 175

5. 2

6. 72

7. 48

8. 45

9. 5

10. 18

11. 3

12. 10

13. 30

14. 12

15. 1

16. 2

17. 2

18. 8

The integers that are closest to the number in the middle will be 89 < 90 < 91.

It should be noted that an integer simply means a whole number that can be positive, negative, or zero.

It should be noted that on this case, we have to look for the numbers that are closest to 90 one has to be less than 90 and the other one should be greater than it.

Therefore, the numbers that fits the information will be 89 and 91.

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Answer:

Linear Function

Step-by-step explanation:

A linear function has constant slope

That means the ratio of y differences to x differences must be the same throughout the function. In other words the rate of change of the function y value is the same throughout the function

IF we look at the table we see that as x increases by 1, y decreases by 15

For example at x = 0, y = 20 and at x = 1, y = 5

So change in y/change in x = 0  = (5-20)/(1-0) = -15/1 = -15

If we look at another pair of points, say x = 1, y=5 and x = 2, y = -10

we get the rate of change = (-10 - 5)/(2-1) = -15/1 = -15

This is the same for any two x, y pair of values

So it is a linear function

Product of the given expression -2.8 (-1.7) is equal to 4.76.

As given in the question,

Given expression is equal to :

-2.8 (-1.7)

There are two numbers -2.8 and -1.7.

Both the numbers are negative.

Multiply negative to a negative number is positive number.

Result of -2.8 and -1.7 is positive number.

Required product of the given expression is equal to :

-2.8 (-1.7)

= (-1) × (2.8) × (-1) × (1.7)

Multiply (-1) to (-1) is equal to positive (1) :

= 2.8 × 1.7

= 4.76

Therefore, product of the given expression -2.8 (-1.7) is equal to 4.76.

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Answer:

8 students

Step-by-step explanation:

17 ÷ 2  1/8 = 8

Answer: 42 chairs

Step-by-step explanation: Provided in the attached image. First, set up a proportion where the numerator is the number of tables and the denominator is the number of chairs. Therefore, the fractions would be 2/7 and 12/y (I accidentally wrote x for y in the photo). Then, solve for the number of chairs by cross multiplying. 12x7 and 2 times y. Solve for y and you would get 42 chairs.

The ratio of tables to chairs in the restaurant is 2:7, so for every 2 tables there are 7 chairs. When this ratio is set equal to 12 tables over y chairs and solved, it provides the answer that the restaurant has 42 chairs.

This problem requires knowledge of ratios. Given that the ratio of tables to chairs is 2:7, for every 2 tables there are 7 chairs. What you need to do is create a proportion to solve this problem.

To do so, set the known ratio 2:7(equal to 2/7) on one side and create a ratio with the number of tables (12) and the unknown number of chairs (y) on the other side like: 2/7=12/y

By cross multiplying, you get: 2y = 7*12, which simplifies to 2y = 84. Finally, solve for y by dividing both sides by 2.

y = 84 / 2 = 42

Therefore, if there are 12 tables in the restaurant, there are 42 chairs.

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a) The expected return for stocks a and b is 13.56% and 20.02% respectively.

b) The standard deviation for stocks a and b are 8.32% and 32.60%.

a) Expected return = Probability of recession × Return during recession + Probability of normal × Return during normal + Probability of boom × Return during boom

Expected return for stock A = 0.21 × 0.04 + 0.61 × 0.12 + 0.18 × 0.30

The expected return for stock A = 0.1356

The expected return for stock A = 13.56%

Expected return for stock B = 0.21 × (-0.41) + 0.61 × 0.31 + 0.18 × 0.54

The expected return for stock B = 0.2002

The expected return for stock B = 20.02%

b) Standard deviation of stock = √{Probability(Recession) × (Rate during recession - expected rate )² + Probability(Normal)(Rate during normal - expected return)² + Probability(Boom) × (Rate in boom - Expected return)²}

Standard deviation of stock A = √[(0.21 × (0.04-0.1356)² + 0.61 × (0.12 - 0.1356)² + 0.18 × (0.30-0.1356)²)]

The standard deviation of stock A = 0.0832

The standard deviation of stock A = 8.32

Standard deviation of stock B = √(0.21 × (-0.41-0.2002)² + 0.61(0.31 - 0.2002)² + 0.18 × (0.54-0.2002)²)]

The standard deviation of stock B = 0.3260

The standard deviation of stock B = 32.60%

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Given:

Manuel wants to earn at least $44 trimming trees.

He charges $6 per hour and pays $4 in equipment fees.

To find:

The possible numbers of hours Manuel could trim trees.

Solution:

Let t be the numbers of hours Manuel could trim trees.

Earnings of Manuel in one hour = $6

Earnings of Manuel in t hour = $6t

He pays $4 in equipment fees. So, we will subtract this from the income.

\(\text{Total earnings}=6t-4\)

Manuel wants to earn at least $44 trimming trees. It means, total earnings must be greater than or equal to 44.

\(6t-4\geq 44\)

\(6t\geq 44+4\)

\(6t\geq 48\)

Divide both sides by 6.

\(t\geq \dfrac{48}{6}\)

\(t\geq 8\)

Therefore, the required number of hours must be greater than or equal to 8 hours.

0.25

That' s the answer

Answer:

3/12=0.25

Step-by-step explanation:

3÷3

12÷3=1/4

1÷4

=0.25

The component that is missing from the biologist's process is:

c) The biologist did not randomly assign each of the bats to the treatment groups.

When carrying out a research study where you have groups created that you want to study, differences between and within groups can be satisfactory ensuring that they are not systematic when subjects are randomly assigned to groups.

Given, A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area.

a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2).

Thus, it gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently ascribed to experimental treatments.

Therefore, the component that is missing from the biologist's process is: c. The biologist did not randomly assign each of the bats to the treatment groups.

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The arithmetic average return is found by adding up the returns and dividing by the number of years:

Arithmetic average = (22% + 9% - 7% + 13%) / 4 = 9.25%

To find the geometric average return, we need to use the formula:

Geometric average = (1 + R1) x (1 + R2) x ... x (1 + Rn) ^ (1/n) - 1

where R1, R2, ..., Rn are the annual returns.

So for this stock, the geometric average return is:

Geometric average = [(1 + 0.22) x (1 + 0.09) x (1 - 0.07) x (1 + 0.13)] ^ (1/4) - 1

                  = 0.0868 or 8.68%

Therefore, the arithmetic average return is 9.25% and the geometric average return is 8.68%.

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The probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.

Standard deviation = sqrt(variance) = sqrt(40,000) = 200

z = (x - μ) / σ

where z is the standardized value, x is the value of interest, μ is the mean, and σ is the standard deviation.

For x = 1000:

z1 = (1000 - 1100) / 200 = -0.5

For x = 1520:

z2 = (1520 - 1100) / 200 = 2.1

Using a calculator, we can use the normal cdf function with the z-scores to find the area between z1 and z2:

P(z1 < z < z2) = normal cdf(-0.5, 2.1) ≈ 0.9192

Rounding to four decimal places, we get:

P(1000 < x < 1520) ≈ 0.9192

Therefore, the probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.

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Answer:

It is not a function

Step-by-step explanation:

This is not a function because it does NOT pass the vertical line test. The vertical line test is just as it sounds: if you were to draw a vertical line from 3 to -3, it would pass through two outputs for every one input. Therefore, it's not a function.

An example of a function which is differentiable function on the real line r with exactly two roots but its derivative having 5 roots is\(f(x) = (x+2)(x-3)^2\)

The given information implies that the function f(x) has two x-intercepts and the derivative of f(x), denoted as f'(x), has five x-intercepts. Therefore, the graph of f(x) must have two local extrema (one minimum and one maximum) and the graph of f'(x) must have three local extrema (two minima and one maximum).

To construct an example of such a function, consider the following:

\(f(x) = (x+2)(x-3)^2\)

The function f(x) has two roots at x = -2 and x = 3, and its derivative is:

\(f'(x) = 3(x-3)^2 + 2(x-3)(x+2)\)

Simplifying f'(x), we get:

\(f'(x) = 5(x-3)^2 - 4(x-3)(x+2)\)

The derivative f'(x) has roots at x = -2, x = 1, x = 3, x = 5, and x = 9, implying that f(x) has local extrema at x = 1 and x = 5.

Thus, this example function satisfies the given conditions.

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Answer:

6+1.25t

Step-by-step explanation:

W(in the 1st month)=6+1.25

W(in the 2nd month)=6+1.25+1.25

W(in the 3rd month)=6+1.25+1.25+1.25

W(in the t months)=6+t(1.25)

♡Answer:♡

Its false, why? bc the domain of every rational function is need not be the set of real numbers

♡Step-by-step explanation:♡

♡ ∩_∩

（„• ֊ •„)♡

┏━∪∪━━━━┓

♡ good luck 。 ♡

┗━━━━━━━┛

The domain values of a rational function are not only restricted to the only set of all real numbers making the given statement false

The domain of a function is the input values of the function for which it exists.

Rational functions are function that can be written as a ratio of two functions. For example given the function f(x) = 2/x-3

The domain values are the input values x. The values of x can be any values either real numbers, integers, or even natural numbers.

This means that the domain values of a rational function are not only restricted to the only set of all real numbers making the given statement false

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The given velocity components are:

u = 2xt - 3xyz + 4xyw = 3x - 5yzt + yz

To satisfy the continuity equation, the third velocity component must be of the form

v = -ux - wy

Thus,v = -2xt + 3xyz - 4xy (from u)v = -3x + 5yz t - yz (from w)

The third velocity component

v = -2xt + 3xyz - 4xy - 3x + 5yz t - yz

= -2xt + 3xyz - 4xy - 3x + 5yz (t - 1)

The velocity of the fluid particle is given by,

v = (u, v, w) = (2t, -2t + 3z, 3 - 5zt + y)at (1, 0, 1) and t = 1 (last digit),v = (2, -2, -2)

The acceleration of the fluid particle is given by,

a = (at, av, aw)

= (∂u/∂t, ∂v/∂t, ∂w/∂t)at (1, 0, 1) and t = 1 (last digit),a = (2, 3, -5)

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An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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Answer: B : 216

Step-by-step explanation:

a cube has 6 sides, so 36*6=216

Using the central limit theorem, for different sample sizes, we find the probabilities Pr(Y < 68) ≈ 0.9439, Pr(68 < Y < 69) ≈ 0.0590, and Pr(Y > 66) ≈ 0.0228.

a) In a random sample of size n = 69, we can approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 69 ≈ 0.7101. To find Pr(Y < 68), we calculate the z-score using the formula z = (x - μ) / σ, where x is the value we want to find the probability for.

z = (68 - 65) / √(0.7101) ≈ 1.5953

Using a standard normal distribution table or a calculator, we find the probability associated with z = 1.5953 to be approximately 0.9439. Therefore, Pr(Y < 68) ≈ 0.9439.

b) In a random sample of size n = 124, we can again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 124 ≈ 0.3952. To find Pr(68 < Y < 69), we calculate the z-scores for the lower and upper limits.

Lower z-score: z1 = (68 - 65) / √(0.3952) ≈ 1.5225

Upper z-score: z2 = (69 - 65) / √(0.3952) ≈ 2.5346

Using the standard normal distribution table or a calculator, we find the probability associated with z1 = 1.5225 to be approximately 0.9357 and the probability associated with z2 = 2.5346 to be approximately 0.9947. Therefore, Pr(68 < Y < 69) ≈ 0.9947 - 0.9357 ≈ 0.0590.

c) In a random sample of size n = 196, we can once again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 196 ≈ 0.2500. To find Pr(Y > 66), we calculate the z-score.

z = (66 - 65) / √(0.2500) = 2

Using the standard normal distribution table or a calculator, we find the probability associated with z = 2 to be approximately 0.9772. Therefore, Pr(Y > 66) ≈ 1 - 0.9772 ≈ 0.0228.

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Answer:

30 minutes

Step-by-step explanation:

6=45

4=x

6x2/3=4

45x2/3=30

x=30

Answer:

66 minutes

Step-by-step explanation:

The domain and the range of the graphare

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

The graph

The above graph is a quadratic function

The rule of an quadratic function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -2

So, the range is y > -2

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Question:

The velocity function, in feet per second, is given for a particle moving along a straight line. \(v(t) = t^2 - t - 42\)    \(1 \le t \le 12\)

Find the displacement

Answer:

The displacement is 42.17ft

Step-by-step explanation:

Given

\(v(t) = t^2 - t - 42\)    \(1 \le t \le 12\)

The displacement x, is calculated using:

\(x = \int\limits^a_b {v(t)} \, dt\)

\(x = \int\limits^{12}_{1} {t^2 - t - 42} \, dt\)

Integrate

\(x = \frac{1}{3}t^3 - \frac{1}{2}t^2 - 42t|\limits^{12}_{1}\)

Substitute 12 and 1 for t respectively

\(x = (\frac{1}{3}*12^3 - \frac{1}{2}*12^2 - 42*12) - (\frac{1}{3}*1^3 - \frac{1}{2}*1^2 - 42*1)\)

\(x = (576 - 72 - 504) - (\frac{1}{3} - \frac{1}{2} - 42)\)

\(x = (0) - (-42.17)\)

\(x = 42.17\)