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Answer:

15, 17, 19 and 21 it mst b them

The area of the smaller sector or minor sector is  125.66 yd².

The area of the larger sector or major sector is  326.73 yd².

The areas of the minor and major sectors is calculated by applying the following formulas follow;

Area of sector is given as;

A = (θ/360) x πr²

where;

The area of the smaller sector or minor sector is calculated as follows;

A = ( 100 / 360 ) x π ( 12 yd)²

A = 125.66 yd²

The area of the larger sector or major sector is calculated as follows;

θ = 360 - 100

θ = 260⁰

A =  ( 260 / 360 ) x π ( 12 yd)²

A = 326.73 yd²

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c) The inequalities are w + c ≤ 50, c  ≥  10, 35c +75w  ≥ 2350.

d) The coordinate of A is (15,35).

e) Jody invests 35 hours of work as a carpenter. He took less time to work as a carpenter than in web design. Because the earnings per hour in web design is more than a carpenter.

What is the solution to the system of equations?

A list of numbers x, y, z, etc. that simultaneously make all of the equations true is the solution of a system of equations. A system of equations' solution set is the whole of all possible answers. Finding all answers using formulas containing a certain number of parameters is known as solving the system.

Now solve the equations w + c ≤ 50 and 35c +75w  ≥ 2350.

Conver the inequality sign with an equal sign:

w + c = 50 ......(i)

35c +75w  = 2350  .....(ii)

Slove the equations by using the elimination method.

Multiply equation (i) by 35 and subtract it from equation (ii)

35c +75w  = 2350

35 w + 35c = 1750

______________

            40c = 600

c = 15

Putting c = 15 in the equation(i)

w + 15 = 50

w = 50 - 15

w = 35

The value of c is 15.

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Answer:

X = -9.1

Step-by-step explanation:

Add 9.1 and -2.4 together to get

x + 6.7 = -2.4

subtract 6.7 from both sides to get

x = -9.1

Answer:

I would say 32 but I'm so sorry if it's wrong

The probability that a high school junior will take less than 135 minutes to complete the SAT exam is 0.5745.

To determine the probability, the standard normal distribution table or calculator is utilized.

The standard normal distribution table, also known as the z-score table, is used to find the probability of a certain z-score or a range of z-scores.

The SAT exam's time is normally distributed, with a mean of 150 minutes and a standard deviation of 25 minutes.The formula for z-score is as follows:

z=(x-μ)/σ

Where x is the time to complete the SAT exam, μ is the mean of the time to complete the SAT exam, and σ is the standard deviation of the time to complete the SAT exam.

To calculate the z-score, the time of 135 minutes is substituted for x, the mean μ of 150 minutes is substituted for μ, and the standard deviation σ of 25 minutes is substituted for σ.The computation is as follows:

z=(135-150)/25= -0.60

Using the standard normal distribution table, the probability of getting a z-score of -0.60 is 0.2743.

To obtain the probability that a high school junior will complete the SAT exam in less than 135 minutes, the area under the standard normal curve to the left of z = -0.60 must be computed. Because the normal curve is symmetrical, the region to the right of z = -0.60 is equal to 1 - 0.2743 = 0.7257.

Finally, to obtain the region to the left of z = -0.60, 0.7257 must be subtracted from 1:1 - 0.7257 = 0.2743

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To determine a point estimate for the conditional mean of the response variable corresponding to a specified value of the predictor variable, we can use regression analysis.

Regression analysis helps us establish a relationship between the predictor variable and the response variable based on the given data. By fitting a regression model, we can estimate the conditional mean of the response variable at a specific value of the predictor variable.

Once the regression model is established, we can substitute the specified value of the predictor variable into the model equation to obtain the corresponding estimated value of the response variable. This estimated value serves as the point estimate for the conditional mean.

It's important to note that the accuracy of the point estimate depends on the quality and representativeness of the data, as well as the assumptions and limitations of the regression model used.

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Answer:

D. n= 0 or n= 4/5

Step-by-step explanation:

Factor and set each factor equal to zero.

n

=

0

,

4

5

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

n

=

0

,

4

5

Decimal Form:

n

=

0

,

0.8

Answer: c

Step-by-step explanation: distribute -7p by multiplying it by 8p first, which gives you -56p squared. Then multiply the -7p by -1 which gives you 7p as the two negatives will cancel out.

Answer:

-32

Step-by-step explanation:

((−4)(4))(2)

=−32

Answer:

-32

Step-by-step explanation:

hope this helps you out

Answer:

1. alternate exterior angles

2. co-interior angles

3. corresponding angles

4. alternate interior angles

5. corresponding angles

6. co-interior angles

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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Answer:

Df=9x-15

Step-by-step explanation:

The answer is on the question

We can say with 99% confidence that the true average number of sick days an employee who is 49 years old will take per year is between 0.85 and 3.30 sick days.

To find the 99% confidence interval for the average number of sick days an employee will take per year, given the employee is 49, we first need to calculate the predicted value of sick days for an employee who is 49 years old using the estimated regression line:

Sick Days = 14.310162 - 0.2369(Age)

Sick Days = 14.310162 - 0.2369(49)

Sick Days = 2.073273

So, we predict that an employee who is 49 years old will take an average of 2.07 sick days per year.

Next, we need to calculate the 99% confidence interval using the formula:

CI = predicted value ± t-value (α/2, n-2) × standard error

where α = 0.01 (since we want a 99% confidence interval), n = 10 (from the sample size), and t-value (α/2, n-2) is the critical value from the t-distribution table with α/2 = 0.005 and n-2 = 8 degrees of freedom.

Looking up the t-value in the table, we find t(0.005,8) = 3.355.

Plugging in the values, we get:

CI = 2.073273 ± 3.355 × 1.682207/√10

CI = 2.073273 ± 2.228079

CI = (0.845194, 3.301352)

Therefore, we can say with 99% confidence that the true average number of sick days an employee who is 49 years old will take per year is between 0.85 and 3.30 sick days

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Full Question:  The personnel director of a large hospital is interested in determining the relationship (if any) between an employee's age and the number of sick days the employee takes per year. The director randomly selects ten employees and records their age and the number of sick days which they took in the previous year. Employee 1 2 5 3 4 5 6 7 8 9 10 Age 30 50 40 55 30 28 60 25 30 45 Sick Days 7. 4 3 2 9 10 0 8 5 2

The estimated regression line and the standard error are given.

Sick Days=14.310162−0.2369(Age).

se=1.682207

Find the 99% confidence interval for the average number of sick days an employee will take per year, given the employee is 49. Round your answer to two decimal places.

Answer:

30%

Step-by-step explanation:

The rate of change in miles per hour between 2pm and 10pm is 26.25 miles/hour

Given,

The distance travelled by a traveler at 2pm = 350 miles

The distance travelled by a traveler at 10pm = 560 miles.

We have to find the rate of change in miles per hour between 2pm and 10pm.

Rate of change in miles per hour = Total distance travelled / Time taken

Here,

Total distance travelled between 2pm and 10 pm = 560 - 350 = 210 miles

Time taken = 10 - 2 = 8 hours

Now,

Rate of change in miles per hour = 210 / 8

Rate of change in miles per hour = 26.25

That is, the rate of change in miles per hour, between 2pm and 10pm is 26.25 miles/hour.

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The \(\( R^{2} \)\) value for this regression is 0.625, indicating a moderate level of goodness of fit. There is a significant mean squared error present, a considerable deviation between the predicted and actual.

The \(\( R^{2} \)\) value is a statistical measure used to assess the proportion of the variance in the dependent variable that can be explained by the independent variables in a regression model. In this case, the \(\( R^{2} \)\) value is 0.625, which means that approximately 62.5% of the variance in the dependent variable can be accounted for by the independent variables included in the model. This indicates a moderate level of goodness of fit, suggesting that the model captures a substantial portion of the relationship between the variables.

On the other hand, the mean squared error (MSE) measures the average squared difference between the predicted and actual values. A significant MSE implies that there is a substantial deviation between the predicted and actual values, indicating that the model's predictions may not be accurate. Therefore, despite the moderate level of goodness of fit indicated by the \( R^{2} \) value, the presence of a high MSE suggests that there may be room for improvement in the model's predictive accuracy. It is important to further investigate the causes of this error and potentially refine the model to reduce the discrepancy between predicted and actual values.

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On solving the provided question, we can say that Considering that the test statistic inside the lower tail the rejection zone, the null hypothesis should be rejected.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

\(H0:p=0.25\) (null hypothesis)

\(H0:p \neq 0.25\) (alternative hypothesis)

Do not reject the null because the test statistic\((-1.2) is >\) \(the critical value (-1.7531)\)

Considering that the test statistic is inside the lower tail of the rejection zone, the null hypothesis should be rejected.

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a. population mean

The mean of all possible sample means is equal to the population mean.

This is known as the sampling distribution of the sample mean. When we take multiple random samples from a population and calculate the mean of each sample, the average of these sample means will converge to the population mean.

This is a fundamental result of statistics known as the Central Limit Theorem. As the sample size increases, the variability of the sample means decreases and they become centered around the population mean.

Therefore, the mean of all possible sample means provides an unbiased estimate of the population mean.

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The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The equations that give the volumes of each solid are given as follows:

Then the increases are given as follows:

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Answer:

2 17/20

Step-by-step explanation:

a) The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

b) A Chi-Square goodness of fit test.

a) A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported and that's why we know that the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

Chi-Square goodness of fit is used to find out how the observed value of a given phenomenon is significantly different from the expected value. In Chi-Square goodness of fit test, the sample data is divided into intervals.

In this case, we have one categorical variable which is the distribution of individuals within several social groups. We want to see if the actual distribution of the variable is significantly different from the distribution within several social groups as claimed(expected) by the newspaper.

Hence, we will use chi-square goodness of fit test for this case.

b) A Chi-Square goodness of fit test.

Here the variable is the distribution of individuals purchasing season pass at an amusement park. The variable has 4 categories based on the age group of the individuals.

A tourist company wants to test the actual distribution of individuals within each age group and wants to check if it is significantly different from the expected distribution i.e the one claimed by the amusement park.

The tourist company randomly sampled 200 individuals entering the park.

The proportion of individuals within each group as claimed by the amusement park is given.

Hence, we will use chi-square goodness of fit test to test if the actual distribution within each group is significantly different or not from the claimed distribution.

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Answer:

You would need to know the area and the base so then

Step-by-step explanation:

answer:

there is a pattern with the ratios of corresponding sides. you can see that the measurement of each side of the first triangle divided by two is the measure of the corresponding side of the second triangle. use patterns like this to problem solve the length of missing sides of similar triangles.

good luck :-)

hopefully, this helps

have a great day !!

The area of the largest rectangle is 25 square units.

It is given that the radius of the semicircle is \(4\).

It is required to inscribe a rectangle of maximum area.

Consider a rectangle of sides \(x\), \(y\) as shown in the given figure.

From the attached figure,\(AB=x\), \(OB=r\) and \(OB=\frac{y}{2}\).

Now, in the triangle OAB, apply Pythagoras' theorem as,

\((OA)^{2}=(OB)^{2}+(AB)^2\)

\(r^2=(\frac{y}{2} )^2+x^2\\\\\)

\(16=\frac{y}{4}+x^2\)

\(y^2=4(16-x^2)\)

\(y=2\sqrt{16-x^2}\)

So, the area of the rectangle will be,

Area,

\(A = 2x \times y\)

= \(2x \times \sqrt{(16 - x^2)}\)

Differentiate the area with respect to ,

\(A' = 2 \times \sqrt{(16 - x^2)} - 2x^2/(16 - x^2)\)

Differentiate the area twice as,

When\(x = 0, y = 5\) and when \(x = 5, y = 0\), \(area = 0\).

It implies that area is maximum when the value of x lies between 0 and 5.

This will occur where \(A'= 0\).

⇒ \(2 \times \sqrt{(16 - x2) }- 2x^2/(16 - x^2) = 0\)

⇒\(2 \times \sqrt{(16 - x^2)} = 2x^2/(16 - x^2)\)

On simplification, we get,

⇒ \(2 \times (16 - x^2) = 2x^2\)

⇒ \(16 - x^2 = x^2\)

⇒ \(2x^2= 16\)

⇒ \(x^2 = 16/2\)

⇒ \(x = \sqrt{8}\)

Now, \(y = \sqrt{(16 - x^2)}\) becomes

⇒\(y = \sqrt{(16 - (\sqrt8)^2)}\)

⇒ \(y = \sqrt{(16 - 8)}\)

\(y =\sqrt{8}\)

Maximum area = 2xy

\(=2(\sqrt{8)}(\sqrt{8})\)

\(=16\)

Therefore, the area of the largest rectangle is 16 square units.

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The formula for the probability of the union of two events A and B is P(A U B) = P(A) + P(B) - P(A ∩ B). Using this formula, we can rearrange the terms to get P(A U B) - P(A ∩ B) = P(A) + P(B) - 2P(A ∩ B).

Substituting the given probabilities, we get:

P(A U B) - P(A ∩ B) = 0.7 + 0.9 - 2P(A ∩ B)
P(A U B) - P(A ∩ B) = 1.6 - 2P(A ∩ B)

To maximize the value of P(A U B) - P(A ∩ B), we need to minimize the value of P(A ∩ B). The largest possible value of P(A ∩ B) is the minimum possible overlap between A and B. In other words, if A and B are completely independent, then P(A ∩ B) = P(A) x P(B) = 0.7 x 0.9 = 0.63.

Substituting this value, we get:

P(A U B) - P(A ∩ B) = 1.6 - 2(0.63)
P(A U B) - P(A ∩ B) = 0.34

Therefore, the largest possible value of P(A U B) - P(A ∩ B) is 0.34. The answer is (b) 0.34.

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Answer:

\(6x + 14y + 13\)

Step-by-step explanation:

\(6x + 12y + 5 + 2y + 8 \\(6x ) + (12y + 2y) + (5 + 8) \\ 6x + 14y + 13\)

The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.

Hence, the marginal utility of the fifth apple equals :

Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)

= (250 - 220) = 30

Hence, marginal utility per dollar: Marginal utility/price per apple

Price per apple = $0.5

Marginal utility of 5th apple = 30

Marginal utility of 5th apple = 30 / 0.5

Marginal utility of 5th apple = 60

Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

Complete question :

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

a) 20

b) 30

c) 40

d) 60

Number of apples ____total utility

2__________________130

3__________________180

4__________________220

5__________________250

6__________________270

7__________________280

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The number that was left out is 70.

Average is the sum of a set of numbers divided by the total numbers in the data set.

Average = sum of numbers / total numbers

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Answer:

2385 watts of power each day

Step-by-step explanation:

265*9