A company has 3 employees, and each employee earns $15.50 an hour. The employees worked for 8 hours at regular pay and then for 2 hours at a higher overtime rate. The overtime rate is an extra $7.00 per hour. How much in total did the company pay the employees?​

The correct answer based on chi-square test is (c) No, because 0.12 > 0.05.

In a chi-square test, the p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. In this case, the null hypothesis is that there is no association between the two variables in the 2 x 2 table.

If the p-value is less than or equal to the significance level (0.05 in this case), then we reject the null hypothesis and conclude that there is a statistically significant association between the variables. However, if the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a significant association.

In this scenario, the p-value is 0.12, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that the chi-square test based on the 2 x 2 table is not statistically significant.

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The equation that represents the linear form of vector v is given as follows:

v = -9i - 6j.

The general format for the linear form of a vector is given as follows:

v = ai + bj.

In which:

The points of the vector are given as follows:

Hence the horizontal component of the vector is given as follows:

a = 1 - 10

a = -9.

The vertical component of the vector is given as follows:

b = 2 - 8

b = -6.

Hence the linear form of the vector is:

v = -9i - 6j.

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James had a longer commute to work than Samuel did.

We need to figure out how far each person went from their starting point to their destination in order to evaluate whose journey was longer. The formula for calculating the distance between two locations is as follows:

[tex]d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

For James:

Distance from his house to the gas station:

[tex]d_1 = \sqrt{((4 - 3)^2 + (1 - 4)^2)}\\ = \sqrt{(10)[/tex]

Distance from the gas station to his job:

[tex]d_2 = \sqrt{((9 - 4)^2 + (8 - 1)^2)}\\ = \sqrt{(90)}[/tex]

Total distance traveled:

[tex]d_1 + d_2 = \sqrt{(10)} + \sqrt{(90) }\\= 12.016[/tex]

For Samuel:

Distance from his house to his mother's house:

[tex]d_1 = \sqrt{((5 - 10)^2 + (8 - 2)^2)} \\= \sqrt{(74)[/tex]

Distance from his mother's house to his job:

[tex]d_2 = \sqrt{((4 - 5)^2 + (5 - 8)^2})\\ = \sqrt{(10)[/tex]

Total distance traveled:

[tex]d_1 + d_2 = \sqrt{(74)} + \sqrt{(10)} \\ =10.872[/tex]

Therefore, Samuel's journey to his job was shorter than James'

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The value of x in the cyclic quadrilateral is 37 degrees

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

Quadrilateral CDEF is inscribed in circle A.

Opposite angles of cyclic quadrilateral add up to 180

So, we have

3x - 10 + 2x + 5 = 180

Evaluate

5x = 185

Divide

x = 37

Hence, the value of x is 37

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Answer:

37

Step-by-step explanation:

The alternative Hypothesis is that at least one of the mean total cholesterol levels is different from the others in the four groups of subjects.

A researcher can use an analysis of variance (ANOVA) parametric statistical method to determine if the mean total cholesterol level of the population is the same for four groups of subjects (Group 1 = Diet Restriction; Group 2 = Exercise; Group 3 = Both Diet and Exercise; Group 4 = None).

a. Statistical Test is ANOVA.
b. Null Hypothesis is that the mean total cholesterol level of the population is the same for all four groups.
c. Alternative Hypothesis is that the mean total cholesterol level of the population is different for at least one group.

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Answer:63

Step-by-step explanation:

The average of the three points A, B and C is M(x, y) = (- 7 / 9, 17 / 9).

In this problem we need to find the average of three points (A, B, C), each point has different weights. The average can be found by means of following expression:

[tex]M(x, y) = \frac{\sum\limits_{i = 1}^{n} w_{i}\cdot P_{i}(x, y)}{\sum \limits_{i = 1}^{n}w_{i}}[/tex]

Where:

Then, the average of points A, B and C are described below:

M(x, y) = [1 · (8, - 6) + 4 · (9, - 5) + 4 · (- 6, 7)] / (1 + 4 + 4)

M(x, y) = [(8, - 6) + (9, - 5) + (- 24, 28)] / 9

M(x, y) = (- 7, 17) / 9

M(x, y) = (- 7 / 9, 17 / 9)

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The missing part of the table is completed as shown below

x      y

-1   1 / 6

0    1

3     216

Exponential function is a function of the form f(x) = a(b)^x

Considering the given problem,

the starting = a

the base = b

the exponents = x

Using the formula, y = 6^x the table is completed by substitution

for x = -1

y = 6^(-1) = 1/ 6

for x = 0

y = 6^(0) = 1

for x = 3

y = 6^(3) = 216

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Answer: The diver's elevation below sea level after both dives is 22 feet.

The diver starts 16 feet below sea level, and then dives another 6 feet. This means the diver is now 16 + 6 = 22 feet below sea level.

Step-by-step explanation:

The volume of the NaOH solution is 3.42 L.

To find the volume of the NaOH solution, we can use the formula:

concentration (M) = moles of solute / volume (L)

Rearranging this formula to solve for volume, we get:

volume (L) = moles of solute / concentration (M)

Plugging in the given values, we get:

volume = 1.90 mol / 0.555 M

Simplifying this expression, we get:

volume = 3.42 L

Therefore, the volume of the NaOH solution is 3.42 L.

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Answer:

Step-by-step explanation:

1. The determination of the predetermined overhead rate using the estimated direct labor costs is $5.30.

2. The actual overhead costs incurred are $2,426,200 while the amount of overhead cost applied to movies using the predetermined overhead rate is $2,438,000.

2b. Overhead is overapplied by $11,800.

3. The journal entry to close the overapplied overhead to the Cost of Goods Sold is as follows:

Debit Manufacturing Overhead $11,800

Credit Cost of Goods Sold $11,800

(To close the overapplied overhead to the cost of goods sold.)

Overhead is overapplied when the applied overhead is more than the actual overhead incurred.

The applied overhead is based on a predetermined overhead rate, which relies on estimates.

Overhead costs = $2,438,000

Direct labor costs = $460,000

Predetermined overhead rate = $5.30 ($2,438,000 ÷ $460,000)

Overhead costs incurred = $2,426,200

Direct labor costs = $460,000

Overhead Applied = $2,438,000 ($5.30 x $460,000)

Overhead overapplied = $11,800 ($2,438,000 - $2,426,200)

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Answer:

Step-by-step explanation:

Answer:72

Answer:

72 feet square

Step-by-step explanation:

18 x 8 ÷ 2 = 72

The points that would form a square are (2, 2), (2, -2), (-2, 2), (-2, -2)

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

Forming a square

As a general rule

A square has equal sides and the angles at the vertices are 90 degrees

Since it must make a point with origin at its center, then the center must be (0, 0)

So, we have the following points (2, 2), (2, -2), (-2, 2), (-2, -2)

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If these conditions/assumptions are met, then the two-sample test for means with independent samples can be used to determine if there is a statistically significant difference between the means of two independent groups.

In order for the two-sample test for means with independent samples to be appropriate, the following conditions/assumptions must be met:

Independent samples: The samples for each group should be selected independently of each other.

Normality: The population distributions should be approximately normal, or the sample sizes should be large enough (n > 30) for the central limit theorem to apply.

Equal variances: The variances of the two populations should be approximately equal. This assumption is important for calculating the pooled variance estimate, which is used in the t-test formula.

Random sampling: The samples should be randomly selected from the populations of interest.

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Answer:

a

Step-by-step explanation:

a

The equivalent expressions of 3(7+2) is 3(2+7) (optionD)

Equivalent expressions are expressions that work the same even though they look different.

If two algebraic expressions are equivalent, then the two expressions have the same value.

For example, 5(2x+10) is equivalent to 10x+50. And this two expression will have thesame value for any value of x.

Similarly, 3(7+2) is equivalent to 3( 2+7) , because this two will give us the same value.

3(7+2) = 21+6

= 27

also, 3(2+7)

= 6+ 21

= 7

therefore we can say that 3(7+2) is equivalent to 3( 2+7)

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To determine the relationship between drag force and speed, you can conduct an experiment using 5 coffee filters and a motion detector. First, set up the motion detector to track the speed of the coffee filters as they fall through the air. Then, drop each coffee filter one at a time and record the drag force measured by the motion detector.

Plot the drag force on the y-axis and the speed on the x-axis, and you should be able to observe a relationship between the two variables. As the speed of the coffee filter increases, the drag force will also increase. This relationship is due to air resistance, which causes the coffee filter to experience a drag force as it falls through the air.

By analyzing the data and creating a graph, you can determine the specific relationship between drag force and speed for these coffee filters. This information can be useful in understanding how air resistance affects the motion of objects and in designing experiments or models that take air resistance into account.

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The average rate of change in the stock's price between 2014 and 2020 would be $ 1. 89

The formula to find the average rate of change between the two periods is :

Average rate of change = (Stock price in 2020 - Stock price in 2014) / Number of years

The question gives the following details :

Stock price in 2020 = $ 37 .22

Stock price in 2014 = $ 25 .86

The average rate of change is;

= (  37. 22 - 25. 86 ) / 6

= 11. 36 / 6

= $ 1. 89

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The correct expression for f(x) is f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .

The given Maclaurin series suggests that the function f(x) is an even function since all the odd powers of x have coefficients of zero. To find an expression for f(x), we can examine the pattern in the series.

Let's break down the terms in the series:

Term 1: 1

Term 2: x² / (2!)

Term 3: x⁴ / (4!)

Term 4: x⁶ / (6!)

From this pattern, we observe that the coefficient of each term is given by [tex]\dfrac{x^{(2n)}} { (2n)!}[/tex], where n represents the index of the term.

Therefore, an expression for f(x) can be written as:

f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .....

This expression represents the summation of terms where each term is the power of x (2n) divided by the factorial of 2n, as indicated in the Maclaurin series.

So, the correct expression for f(x) is:

f(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + .....

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The value of x based on the stated expression using mathematical operations is -1.

The calculation of x will be performed using mathematical operations in following format. Here are the steps -

Solve the parenthesis

18x + 72 = 54

Switch the position of number 72 from Left Hand Side to Right Hand Side

18x = 54 - 72

Performing subtraction on Right Hand Side of the equation

18x = -18

Rewrite the equation according to x

x = -18/18

Performing division on Right Hand Side of the equation

x = -1

Hence, the value of x is -1.

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Based on the information given, we can conclude that there is a significant difference between the two populations.

The calculated z-score of 1.51 is greater than the critical value of 1.96 (at the 5% level of significance), which indicates that the sample mean differences are unlikely to have occurred by chance. Therefore, we reject the null hypothesis and conclude that household debt is different in the two cities.
At this level of significance, we cannot conclude that there is a significant difference between the two populations.

Explanation:
To determine if there is a significant difference between the mean household debt of Regina and Saskatoon households at the 5% level of significance, we need to compare the calculated z-score of 1.51 to the critical z-score for a two-tailed test. For a 5% level of significance, the critical z-scores are -1.96 and 1.96. Since 1.51 is between -1.96 and 1.96, we cannot reject the null hypothesis, which means we cannot conclude that there is a significant difference between the two populations at the 5% level of significance.

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Without the degrees of freedom, we cannot provide a specific p-value. If the chi-square statistic is 2.71 or more, the p-value will be equal to or less than the value corresponding to 2.71 in the chi-square distribution table for the given degrees of freedom.

1. The chi-square statistic is a measure of the difference between observed and expected frequencies in a contingency table. When the observed frequencies are similar to the expected frequencies, the chi-square statistic is low. When they are different, the chi-square statistic is high.

2. The p-value is a probability that indicates how likely it is to observe a chi-square statistic as extreme as the one obtained, assuming the null hypothesis (i.e., no association between the variables) is true. A lower p-value means there is stronger evidence against the null hypothesis, suggesting an association between the variables.

3. To determine the p-value corresponding to a chi-square statistic of 2.71, you would look up the value in a chi-square distribution table or use statistical software. The p-value depends on the degrees of freedom, which is determined by the size of the contingency table.

Without the degrees of freedom, we cannot provide a specific p-value. However, if the chi-square statistic is 2.71 or more, the p-value will be equal to or less than the value corresponding to 2.71 in the chi-square distribution table for the given degrees of freedom.

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The probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.

The probability that a student lives in West Hall is 0.58 and the probability that a student lives in South Tower is 0.42. The probability that a student in West Hall receives a coupon is 0.26, and the probability that a student in South Tower receives a coupon is 0.19.

To find the probability that a student does not receive a coupon, we can use the complement rule: the probability of the event happening plus the probability of the event not happening is equal to 1. So, the probability of a student not receiving a coupon is 1 minus the probability of a student receiving a coupon.

Using a tree diagram, we can find the probability of a student receiving a coupon or not. Starting with the first branch of the tree, we have:

West Hall (0.58)
- Coupon (0.26)
- No Coupon (0.74)

South Tower (0.42)
- Coupon (0.19)
- No Coupon (0.81)

To find the probability of a student not receiving a coupon, we add the probability of no coupon from each branch of the tree and multiply by the probability of being in that branch. So, the probability of a student not receiving a coupon is:

(0.58 x 0.74) + (0.42 x 0.81) = 0.6436

Therefore, the probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.
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Answer:

1/3πr²h

Step-by-step explanation:

The formulas for calculating the volume of a cylinder and a cone are:

Volume of cylinder = πr²h

Volume of cone = 1/3πr²h

where r is the radius and h is the height of the shape.

Given that both shapes have a radius of 2 units and a height of 4 units, we can substitute these values into the formulas to calculate the volumes.

For the cylinder:

Volume of cylinder = πr²h

= π(2²)(4)

= 16π cubic units

Therefore, the volume of the cylinder is 16π cubic units.

For the cone:

Volume of cone = 1/3πr²h

= 1/3π(2²)(4)

= 8/3π cubic units

Therefore, the volume of the cone is 8/3π cubic units, which is approximately 8.38 cubic units (rounded to two decimal places).

Answer:

100

Step-by-step explanation:

To solve for y in the equation Y/1/5=20, we can multiply both sides of the equation by 1/5 to isolate y on one side of the equation. This gives us:

Y/1/5 * 1/5 = 20 * 1/5

Simplifying this expression gives us:

Y = 100

Therefore, the value of y is one hundred.

Answer:

Y = 4

Step-by-step explanation:

Now we have to,

→ Find the required value of Y.

The equation is,

→ Y/(1/5) = 20

Then the value of Y will be,

→ Y/(1/5) = 20

Simplifying the left hand side:

→ Y × (5/1) = 20

→ 5Y/1 = 20

→ 5Y = 20

Dividing 20 by the number 5:

→ Y = 20/5

→ [ Y = 4 ]

Hence, the value of Y is 4.

Answer:

x - 6 < 2x + 2

-8 < x, so x > -8

x = -1 and x = -5 are solutions to this inequality.