What is the slope from (−7, 5) to (−3, 4)?

To construct a confidence interval, we need to determine the critical value based on the confidence level and sample size. For a 95% confidence level and a sample size of 7, the critical value is 2.571.

The critical value is used to calculate the margin of error for a confidence interval. It is based on the confidence level and sample size, and it is determined from a t-distribution table or a calculator.

For a 95% confidence level and a sample size of 7, we can find the critical value by looking at the t-distribution table with 6 degrees of freedom (df = n - 1). The 95% confidence level corresponds to a two-tailed test with an alpha level of 0.05, and the critical value for a t-distribution with 6 degrees of freedom and an alpha level of 0.025 (half of 0.05) is 2.571.

Therefore, to construct a 95% confidence interval for a sample size of 7, we can use the formula:

sample mean ± (critical value) x (standard error of the mean)

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

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The total number of personal training sessions they would have received after 5 renewals is given as follows:

20 training sessions.

The total number of personal training sessions they would have received after 5 renewals is obtained applying the proportions in the context of the problem.

The person gets four free sessions after each renewal, hence after five renewals, the number of training sessions is given as follows:

5 x 4 = 20 training sessions.

(the proportion is applied as we get the number of sections for each renewal, hence for n renewals, we simply multiply the number n by the constant).

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Answer:

[B] 3

Step-by-step explanation:

We can set up a proportion to solve for x:

[tex]\frac{15}{10} =15+\frac{x}{12}[/tex]

[tex]10(15 + x) = 15(12)[/tex]         >> Distribute

[tex]150 + 10x = 180[/tex]               >> Subtract 150 from both side

[tex]10x = 30[/tex]                          >> Divide both side by 10

[tex]x=3[/tex]                               >> Solution

~ Lenvy ♥~

Answer:

Step-by-step explanation:

To find the average rate of change for an exponential function over an interval, we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where “a” and “b” are the endpoints of the interval, and “f” is the exponential function.

In this case, the interval is from x = 1 to x = 3, so a = 1 and b = 3. We are given the values of the function for these inputs:

f(1) = 7

f(2) = 9

f(3) = 13

Substituting these values into the formula, we get:

average rate of change = (f(3) - f(1)) / (3 - 1)

average rate of change = (13 - 7) / 2

average rate of change = 3

Therefore, the average rate of change for this function over the interval from x = 1 to x = 3 is 3.

The probability of a penny falling out is,

⇒ 3 / 11

We have to given that;

A cup has some coins in it.

And, The cup tips over and 1 coin falls out.

Here, By given table;

Total number of coins are,

⇒ 3 + 5 + 2 + 1

And, Number of penny coins are,

⇒ 3

Hence, The probability of a penny falling out is,

⇒ P = number of penny / total number of coins

⇒ P = 3 / 11

So, The probability of a penny falling out is,

⇒ 3 / 11

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Answer:

Step-by-step explanation:

65 degrees since opposite side also has 65

The light should be placed in the middle of the triangle parkway in order to meet the aim of having it at the same distance from each of the three roadways.

Since we want the light to be equally far from all three streets in this scenario, that means we want it to be equally far from each side of the triangle parkway.

In light of this requirement, the lamppost ought to be put in the middle of the triangle parkway. This is due to the incenter's equidistant location from all three sides, which ensures that the distance between the lamppost and each side of the triangle is equal.

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The option that would have the same value as required is option A.

Equivalent exponents are any two or more exponents that, when added to a base number, produce the same value or result. In other words, equivalent exponents are various ways of expressing the same exponentiation-based mathematical action.

We now have that;

[tex](49^2/5) (7^- 3/4)\\(7^2)^2/5 (7^-3/4)\\(7^4/5) (7^-3/4)\\7^ (4/5 - 3/4)\\7^ 1/20[/tex]

Thus the correct expression is the one that is shown in option A above here.

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The profit function of the company is P(x) = 448x - 7200

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

Cost function. C(x) = 7200 + 52x

Revenue function. R(x) = 500x

the profit function of the company is calculated as

P(x) = R(x) - C(x)

substitute the known values in the above equation, so, we have the following representation

P(x) = 500x - 7200 - 52x

Evaluate

P(x) = 448x - 7200

Hence, the profit function of the company is P(x) = 448x - 7200

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We can list all possible outcomes in a table and count the number of outcomes that meet the criteria. There are 9 such outcomes, which gives a probability of 9/36, or 1/4.

To calculate the probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice, we first need to determine the total number of possible outcomes when rolling the dice. Since each die has 6 possible outcomes, there are a total of 6 x 6 = 36 possible outcomes when rolling 2 fair dice.

| Die 1 | Die 2 | Sum |
|-------|-------|-----|
| 1     | 3     | 4   |
| 1     | 4     | 5   |
| 1     | 5     | 6   |
| 2     | 2     | 4   |
| 2     | 3     | 5   |
| 3     | 1     | 4   |
| 3     | 2     | 5   |
| 4     | 1     | 5   |
| 5     | 1     | 6   |

There are a total of 9 outcomes where the sum is greater than 3 but not exceeding 6. Therefore, the probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice is 9/36, which simplifies to 1/4.
The probability of rolling a sum greater than 3 but not exceeding 6 with 2 fair dice can be calculated by dividing the number of outcomes where the sum is greater than 3 but not exceeding 6 by the total number of possible outcomes.

There are a total of 36 possible outcomes when rolling 2 fair dice, as each die has 6 possible outcomes. To determine the number of outcomes where the sum is greater than 3 but not exceeding 6, we can list all possible outcomes in a table and count the number of outcomes that meet the criteria. There are 9 such outcomes, which gives a probability of 9/36, or 1/4.

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The probability of the sum of two dice being greater than 3 but not exceeding 6 is 1/3 as there are 12 successful outcomes out of a total 36.

This question is about the probability in rolling two dice.

Therefore, the probability of this event is 12/36 or 1/3.

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For every product sold, the employee's earnings increase by $225.

Option C is the correct answer.

We have,

The expression for the amount of money an employee earns monthly after selling n products is given as:

$1,500 + $225n.

Here,

$1,500 is the fixed monthly earning, and $225n represents the earning from selling n products.

Thus,

For every product sold, the earning increases by $225.

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When testing the goodness of fit for the logistic regression model, if the obtained chi-square is less than the critical value, one would " Accept the null hypothesis". The correct option is c.

In the goodness of fit test for the logistic regression model, the null hypothesis states that there is no significant difference between the observed and expected values. If the obtained chi-square value is less than the critical value, it means that the difference between the observed and expected values is not significant, and hence, we fail to reject the null hypothesis. Therefore, we accept the null hypothesis and conclude that the model fits the data well. On the other hand, if the obtained chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the model does not fit the data well.

The correct option is c.

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The exponential regression of the data is  y = 3.143 * 6.064ˣ

Exponential regression is a statistical technique used to model and analyze data that follows an exponential trend. It involves finding the equation of an exponential function that best fits a set of data points. The exponential regression equation has the general form:

y = abˣ

where y is the dependent variable, x is the independent variable, and a and b are the regression coefficients to be determined.

From the given data;

The regression equation is y = 3.143 * 6.064ˣ

The correlation of the data (r) = 0.9941

The r-squared of the data (r²) = 0.9883

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A sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.

Margin of error = Z-score * (σ / √n)
where Z-score is the critical value for the level of confidence (in this case, 95%), σ is the population standard deviation (which is equal to the square root of the variance, so σ = 12), and n is the sample size.

We want the margin of error to be less than or equal to 5, so we can set up the following inequality:
5 ≥ Z-score * (σ / √n)

To find the value of the Z-score for 95% confidence, we can use a standard normal distribution table or calculator. The Z-score for 95% confidence is approximately 1.96.

Substituting the values we have into the inequality, we get:
5 ≥ 1.96 * (12 / √n)

Solving for n, we get:
n ≥ ((1.96 * 12) / 5)²
n ≥ 138.2976

Since we cannot have a fractional sample size, we need to round up to the nearest whole number:
n = 139

Therefore, a sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.

In summary, the long answer to your question is that we used the formula for the margin of error, substituted the given values, solved for n, and rounded up to get a sample size of 139.

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Answer:

1.5.1 : constant difference is 8

1.5.2: When there are 10 chairs stacked, it's 127 cm tall.

Step-by-step explanation:

There is a linear relationship between the height of the stack and the number of chairs.

1 chair = 55 cm + 0 extra cm = 55cm

2 chairs = 55cm + 8cm = 63 cm

3 chairs = 55cm + 8(2)cm = 71 cm

4 chairs = 55cm + 8(3)cm = 79 cm

1.5.1 the constant difference between all the underlined numbers above is 8.

1.5.2 You could just keep calculating above until you get 127 cm. (Your teacher might not like that, but it's an option!)

You can find the equation & either solve for the number of chairs OR graph it.

So if we let C = the number of stacked chairs, our equation for H (height) would be:

H = 55 + 8(C-1)

If we substitute H = 127, solve for C.

127 = 55+ 8(c-1)

127 = 55+ 8c-8

127 = 47 + 8c

127 -47 = 8c

80 = 8c

10=c

When there are 10 chairs stacked, it's 127 cm tall.

Check that the answer works:

55 cm (1st chair) + 8*9 (8cm for each additional chair) = 55+ 72 = 127 cm

Answer:

Step-by-step explanation:

(a) Event "X and Y": F

(b) Event "X or Y": A, B, C, D, F

(c) The complement of the event X: E, F, G

(a) Event "X and Y": F

The letter "F" satisfies both conditions: it comes before "E" (Event X) and it is found in the word "FACE" (Event Y).

(b) Event "X or Y": A, B, C, D, F

The letters A, B, C, D, and F satisfy either condition: they come before "E" (Event X) or they are found in the word "FACE" (Event Y).

(c) The complement of the event X: E, F, G

The complement of Event X includes all the letters that do not come before "E". In this case, the letters E, F, and G do not satisfy the condition of coming before "E".

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The term that best describes the disorder that Ahmed has is given as follows:

c. major depression.

What differs depression from the other disorders cited in this problem is the length of the duration of the symptoms.

Ahmed has been feeling the symptoms for the past three weeks, which is a large time, as the other disorders such as anxiety and panic attacks have an alternance of time where the person feel the symptoms with times where the people is feeling good, without the symptoms.

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The probability of getting someone who tested positive, given that he or she had the disease is 0.17.

Given that, the individual actually had the disease

                 Yes       No

Positive      145      25

Negative      8        122

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

The probability of getting someone who tested positive, given that he or they did not have the disease, is computed as

P(Positive|No) = P(Positive ∩ No)/P(No)

P(Positive ∩ No)= 25/(145+25+8+122)

= 25/300

P(No)= (25+122)/(145+25+8+122)

= 147/300

P(Positive|No) = 25/300 ÷ 147/300

= 25/147

= 0.17

Therefore, the probability of getting someone who tested positive, given that he or she had the disease is 0.17.

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The expression that represents the perimeter of the triangle is 5x - 2.

Writing an expression

From the question, we are to write an expression that represents the perimeter of the triangle

From the given information,

"The length of the base of the triangle is represented by x"

and

"The legs are 1 unit less than twice the length of the base"

∴ One leg of the triangle = 2x - 1

The perimeter of a rectangle is the sum of all the sides

Thus,

Perimeter of the isosceles triangle = 2x - 1 + 2x - 1 + x

Perimeter of the isosceles triangle = 2x +2x + x - 1 - 1

Perimeter of the isosceles triangle = 5x - 2

Hence, the expression that represents the perimeter of the triangle is

5x - 2

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complete question:

In an isosceles triangle (a triangle where two of the three sides called legs are equal), the legs

are 1 unit less than twice the length of the base. If the length of the base of the triangle is

represented by x, create an expression that represents the perimeter of the triangle.

The solution set of the inequality is the one in option B;

x> 1 or x < -1

Remember that the absolute value inequality can be descomposed into two inequalities.

Here we have the simple inequality:

|x| > 1

Then we can decompose this into a compound inequality:

x > 1

x < -1

Then the solution is:

x > 1 or x < -1

The correct option is B.

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The amount of grain can the container hold is 953.78 inch³ as it in the form of cylinder

Diameter of cylinder = 9 in

Radius of cylinder = 9 / 2 in

Radius of cylinder = 4.5 in

Height of cylinder = 15 inch

Volume of cylinder = Amount of grain can this container hold

Volume = πr²h

Substitute the values of radius and height

Volume = (3.14)(4.5)²(15)

Amount of grain can this container hold = 953.78 inch³

Hence, the amount of grain can the container hold is 953.78 inch³

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Answer:

The answer to your question is B) d≥ 5 because the best inequality that represents the number of days Amaya practices the guitar is "greater than or equal to 5". This is because Amaya practices the guitar at least 5 days a week, so the inequality that represents this would be d≥ 5.

Answer:

B

Step-by-step explanation:

Based on the given number line, we can see that the number of days Amaya practices the guitar falls on and to the right of the number 5. Since the number line is inclusive of 5, it means that Amaya practices for 5 days or more in a week.

Therefore, the inequality that BEST represents the number of days, d, she practices is:

B) d ≥ 5

This inequality indicates that the number of days Amaya practices (d) is greater than or equal to 5.

The Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.

To find the Lagrange form of the polynomial that fits the given data, we can use the following formula:

Lagrange form:

L(x) = ∑ [y * l_i(x)], i=0 to n

where

l_i(x) = ∏ [(x - x_j)/(x_i - x_j)], j=0 to n, j ≠ i

In this formula, x and y are the given data points, n is the number of data points (n+1 is the degree of the polynomial), and L(x) is the polynomial that fits the data.

Using the given data x = {1, 2, 3, 5} and y = {0, 5, 26, 164}, we can compute the Lagrange form as follows:

l_0(x) = (x - 2)(x - 3)(x - 5)/(1 - 2)(1 - 3)(1 - 5) = -(x^3 - 10x^2 + 31x - 30)/4
l_1(x) = (x - 1)(x - 3)(x - 5)/(2 - 1)(2 - 3)(2 - 5) = (x^3 - 9x^2 + 23x - 15)/2
l_2(x) = (x - 1)(x - 2)(x - 5)/(3 - 1)(3 - 2)(3 - 5) = -(x^3 - 8x^2 + 13x - 6)/2
l_3(x) = (x - 1)(x - 2)(x - 3)/(5 - 1)(5 - 2)(5 - 3) = (x^3 - 6x^2 + 11x - 6)/4

L(x) = 0l_0(x) + 5l_1(x) + 26l_2(x) + 164l_3(x)
= (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3

Therefore, the Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.

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Consider the sample mean in random samples of size n from a given population to be a random variable because the outcome of the sample mean is unpredictable.

Outcome of the sample mean can vary from one random sample to another.

The sample mean is computed as the sum of the values in the sample divided by the sample size.

And since the sample is a random sample, the values in the sample are random variables themselves.

This implies, the sample mean is a function of those random variables and, as a result, it is also a random variable.

In other words, the sample mean is not a fixed quantity.

But rather a value that varies depending on the particular random sample that is chosen from the population.

This randomness in the value of the sample mean makes it a random variable.

Therefore, sample mean from a random sample can be random variable because the outcome is unpredictable.

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The term that best describes the type of data collected specifically for a particular research project is derived from primary data.

This type of data is collected directly from the source, such as through surveys or experiments, and is tailored to answer specific research questions that have not been satisfactorily addressed by existing secondary data sources. Derived primary data is typically more expensive and time-consuming to collect than secondary data, but it can provide valuable insights that are not available elsewhere.
It is important to note that derived primary data should be collected using sound research methods to ensure its validity and reliability. This includes careful consideration of sampling methods, data collection techniques, and data analysis procedures. Researchers should also be transparent about the limitations of their data and any potential sources of bias or error that could affect their findings.
In contrast, referential data refers to data that are collected from existing sources, such as databases or published reports, and syndicated data refers to data that are collected by third-party research firms and sold to multiple clients. Cohort data refers to data that are collected from a specific group of individuals over time to track changes and trends. While each of these types of data can be useful for research, derived primary data is often the most valuable for answering specific research questions and generating new insights.

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We often take information from a sample from the population in the process of a statistical investigation because it is often impractical or impossible to collect data from the entire population.

In statistical investigation, a sample is a subset of a population that is selected for study. Collecting data from an entire population can be impractical or impossible due to cost, time, or other constraints. By studying a representative sample, statistical inferences can be made about the entire population with a certain degree of confidence.

The size and selection of the sample are important factors that affect the accuracy of the statistical inference. Generally, larger samples are more representative of the population and lead to more accurate estimates of population parameters.

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The value of the complementary angle of 54° is determined as  B = 36°.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

So if the measure of one angle is 54°, the value of its complementary angle is calculated as follows;

Mathematically, the formula for calculating the complementary angle of 54° is given as;

B + 54° = 90

B = 90 - 54°

B = 36°

Thus, the value of the complementary angle of 54° is determined as 36° since both angles will add up to 90 degrees.

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The complete question is below:

Use your knowledge of complementary and vertical angles to hit

this shot.

If angle A is 54° and angle B is its complementary angle. Angle B = ?