Solve.

32.3 = 14.8 + 8.4x

Enter your answer as a mixed number in simplest form in the box

The mean salary for employees in the R&D department of company A is $1500 higher than for those in company B.

(a) To test the equality of population variances, we can use the F-test. The null hypothesis (H₀) states that the variances of the two populations are equal,

while the alternative hypothesis (H₁) states that they are not equal.

H₀: σ₁² = σ₂² (the variances are equal)

H₁: σ₁² ≠ σ₂² (the variances are not equal)

To perform the hypothesis test, we calculate the F-statistic using the formula:

F = (s₁² / s₂²)

where s₁² is the sample variance of company A and s₂² is the sample variance of company B

Calculating the F-statistic:

F = (s₁² / s₂²)

F = (5,000² / 6,500²)

F ≈ 0.5966

To determine the critical F-value, we need to consider the significance level and degrees of freedom. With a 0.1 level of significance, and degrees of freedom df₁ = n₁ - 1 and df₂ = n₂ - 1, we can consult an F-distribution table or use statistical software to find the critical value.

Assuming the degrees of freedom are df₁ = 15 and df₂ = 12, the critical F-value for a two-tailed test at α = 0.1 is approximately 2.67.

Since the calculated F-statistic (0.5966) is not greater than the critical F-value (2.67), we fail to reject the null hypothesis. There is not enough evidence to conclude that the population variances of the two companies are significantly different.

(b) Now, we will perform a hypothesis test to determine if the mean salary for employees in the R&D department of company A is $1500 higher than for those in company B. We will use a 0.05 level of significance.

The null hypothesis (H₀) states that there is no difference in the means:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ > 0 (since we want to test if the mean salary of company A is higher)

To perform the hypothesis test, we can calculate the test statistic using the formula are the sample means, s₁ and s₂ are the sample standard deviations, n₁ and n₂ are the sample sizes, and Δ is the hypothesized difference in means ($1500).

Given:

Company A s₁ = $5,000

Company B: = $6,500

Δ = $1500

Calculating the test statistic:

t = [(83,150 - 80,500) - 1500] / sqrt[(5000² / 16) + (6500² / 13)]

t ≈ 2.5884

To determine the critical t-value, we need to consider the significance

level and degrees of freedom. With a 0.05 level of significance and degrees of freedom df = n₁ + n₂ - 2, we can consult a t-distribution table or use statistical software to find the critical value.

Assuming the degrees of freedom are df = 16 + 13 - 2 = 27, the critical t-value for a one-tailed test at α = 0.05 is approximately 1.703.

Since the calculated t-statistic (2.5884) is greater than the critical t-value (1.703), we reject the null hypothesis. There is sufficient evidence to conclude that the mean salary for employees in the R&D department of company A is $1500 higher than for those in company B, at a 0.05 level of significance.

(ii) To calculate the p-value for this case, we can use statistical software or consult a t-distribution table with the degrees of freedom df = 27. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

Assuming the degrees of freedom are df = 27, the p-value for the calculated t-statistic (2.5884) can be determined to be approximately 0.0075.

Since the p-value (0.0075) is less than the significance level (α = 0.05), we reject the null hypothesis. There is strong evidence to support the conclusion that the mean salary for employees in the R&D department of company A is $1500 higher than for those in company B.

Learn more about statistics here: brainly.com/question/30967027

#SPJ11

A Bill of Material (BOM) is a list of all the materials that are required to build a particular product.

The Bill of Material can be used to determine the cost of each product as well as the total cost of all the products produced. BOMs are also used to ensure that all the required materials are available before production starts. Now, let us answer your question: What is the question that needs to be answered about the product and the Bill of Materials?

Thank you for providing the additional information. However, it seems that the content you mentioned as "loaded" is still missing. Could you please provide the specific details of the bill of materials, the master production schedule for D, and the inventory sheets for items B and C?

This will allow me to provide a more accurate response to your query.

To know more about the word product visits :

https://brainly.com/question/31815585

#SPJ11

Parallel slope = 2

This is because the original line has slope 2. Parallel lines have equal slopes.

--------------------------

Perpendicular slope = -1/2

The original slope 2 or 2/1 turns into -1/2 after flipping the fraction and the sign. Note the original slope and perpendicular slope multiply to -1. This is true for any pair of perpendicular lines where neither line is vertical.

Answer:

the slope of  the parallel line is 2x

the slope of line perpendicular is -1/2

Step-by-step explanation:

Answer:

x=2, y=3

Step-by-step explanation:

This is a system of equations.

To solve a system of equations, we use the substitution method.

We can plug in the first equation, \(x=2y-4\), into the value for x in the second equation. Now, the second equation looks like this:

\(2*(2y-4)+y=7\)

We simplify and solve for y:

→ \(4y-8+y=7\)

→ \(5y=15\)

→ \(y=3\)

Now, we plug in the value for y, which is 3, into either equation. I will just use the first equation:

→ \(x=2*3-4\)

→ \(x = 2\)

Let me know if my explanation is unclear.

We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

Learn more about interior angles at:

https://brainly.com/question/24966296

#SPJ1

Applying the Pythagoras Theorem, the length of RS = 8 units.

According to the figure,

Diameter = 16 +4 = 20 units

So, the Radius = Diameter/2 = 20/2 = 10 units

Now,

Let the center be M, then

MT = 10 - 4 = 6 units

RT = x units

The radius is perpendicular to the chord,

So, MTR will be a right-angled triangle,

We will apply the Pythagoras theorem,

So, we have :

\(RT^{2} +TM^{2} =RM^{2}\)

Here, RT = x units

TM = 6 units and RM = radius = 10 units

Putting these values in the Pythagoras theorem,

\(x^{2} +6^{2} =10^{2}\\x^{2} + 36 = 100 \\x^{2} = 100 - 36 = 64\\x^{2} = 64 \\x = 8\)

Thus, the length of RS = 8 units.

To read more about Pythagoras's theorem, visit https://brainly.com/question/343682

#SPJ9

If an individual exercises 20 minutes daily, the predicted percentage of body fat would be approximately 21.63%.

To determine the predicted percentage of body fat for an individual who exercises 20 minutes daily, we can use linear regression to estimate the relationship between exercise duration and percentage of body fat.

First, let's calculate the slope and intercept of the regression line:

Mean of Exercise (min):

(10 + 18 + 26 + 33 + 44) / 5 = 22.2

Mean of % Fat:

(30 + 25 + 18 + 17 + 14) / 5 = 20.8

Calculate the deviations from the means for Exercise (min) and % Fat:

Exercise (min) deviations: 10 - 22.2, 18 - 22.2, 26 - 22.2, 33 - 22.2, 44 - 22.2

% Fat deviations: 30 - 20.8, 25 - 20.8, 18 - 20.8, 17 - 20.8, 14 - 20.8

Sum of the product of the deviations:

Σ(Exercise deviation × % Fat deviation) = (10 - 22.2) × (30 - 20.8) + (18 - 22.2) × (25 - 20.8) + (26 - 22.2) × (18 - 20.8) + (33 - 22.2) × (17 - 20.8) + (44 - 22.2) × (14 - 20.8)

Sum of Exercise (min) deviations squared:

Σ(Exercise deviation²) = (10 - 22.2)² + (18 - 22.2)² + (26 - 22.2)² + (33 - 22.2)² + (44 - 22.2)²

Calculate the slope (b):

b = Σ(Exercise deviation × % Fat deviation) / Σ(Exercise deviation²)

Calculate the intercept (a):

a = mean of % Fat - (slope × mean of Exercise)

Now we can substitute the given exercise duration of 20 minutes into the equation to find the predicted percentage of body fat:

Predicted % Fat = a + (b × 20)

Let's calculate these values:

Exercise deviations: -12.2, -4.2, 3.8, 10.8, 21.8

% Fat deviations: 9.2, 4.2, -2.8, -3.8, -6.8

Σ(Exercise deviation × % Fat deviation) = (-12.2 × 9.2) + (-4.2 × 4.2) + (3.8 × -2.8) + (10.8 × -3.8) + (21.8 × -6.8) = -305.24

Σ(Exercise deviation²) = (-12.2)² + (-4.2)² + (3.8)² + (10.8)² + (21.8)² = 1154.68

b = (-305.24) / 1154.68 ≈ -0.2648

Mean of Exercise (min) = 22.2

Mean of % Fat = 20.8

a = 20.8 - (-0.2648 × 22.2) ≈ 26.9496

Predicted % Fat = 26.9496 + (-0.2648 ² 20) ≈ 21.63

Therefore, if an individual exercises 20 minutes daily, the predicted percentage of body fat would be approximately 21.63%.

Learn more about linear regression click;

https://brainly.com/question/32505018

#SPJ4

Complete question =

A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded.

Individual: 1, 2, 3, 4, 5

Excercise (min): 10, 18, 26, 33, 44

% Fat: 30, 25, 18, 17, 14

Based on the above data, if an individual exercises 20 minutes daily, his predicted % body fat would be ?

21.63

27.74

27.88

23.75

mama ate koya bonso tatay lola

Answer:

5338 \(m^{3}\)

Step-by-step explanation:

The volume for a cylinder is solved by using this equation;

\(V= \pi \times r^2\times h\)

Where we would use 3.14 in place of \(\pi\).

10 would be the radius because the radius is half of your diameter which is 20.

So, Volume will be,

\(V=(3.14)\times (10)^{2} \times(17)\\V=3.14\times 100\times 17=5338 \quad {m^3}\)  

So volume will be 5338 \(m^{3}\).

Answer:

.

Step-by-step explanation:

there has to be more to this question you csnt just guess the minutes

Answer:

What is the rate

Step-by-step explanation:

The answer is:

Work/explanation:

A negative times a negative gives a positive:

\(\bullet\phantom{333}\bf{(-4)\times(-5)=20}\)

\(\bullet\phantom{333}\bf{(-8)\times(-10)=80}\)

\(\bullet\phantom{333}\bf{20\times80}\)

\(\bullet\phantom{333}\bf{1,600}\)

Answer:

$591.10

Step-by-step explanation:

First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.

oml! ill try give me a min tho

Answer:

8.) x×6=y

Step-by-step explanation:

1×6=6

2×6=12

4×6=24

5×6=30

25×6=150

For each of the others, multiply the value of x times the CoP for the y value and divide the value of y by the CoP to get the x value. I've attached the work for number 9.

Answer:

not sure what type you mean but here are options

Step-by-step explanation:

30+4=34

thirty-four

Answer:

A

Step-by-step explanation:

count how many 3's there are (1)

3^1

3^1 simplifies to just 3

3

count how many x's there are (4)

3x^4

count how many y's there are (4)

3x^4y^4

Answer:

The answer is Letter A

Explanation:

It's because based on the given formula there is only one 3 four x and four y , so the 3 remains itself and x raise fo four as well as y so Letter A

Answer:

24

Step-by-step explanation:

If 4/6 of the items are jackets and the rest are gloves, this means 1 - 4/6 = 2/6 = 1/3 of the items are gloves in Saginaw Elementary School's lost and found.

We do 72 total items × 1/3 items are gloves = 24 items in the lost and found are gloves

Answer:

Step-by-step explanation:

-i= -i

-i^2= 1

-i^3= -i * 1 = -i

-i^4= 1 * (-1)  = -1

-i^5= -i

-i^6= 1

Answer: -1

Step-by-step explanation:

Answer:

1: No, this is not direct variation

2: Yes, this is direct variation with k= 2.34

Step-by-step explanation:

I’m Just Built Different

There are 20,000 different phone numbers possible that is 7-digits long and start with either 824 or 825.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Based on the given information, all phone numbers are 7-digits long and starts with either 824 or 825. Hence, the four last digits will be the combination of numbers from 0 to 9.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is 20,000.

= (number of phone numbers starting with 824) + (number of phone numbers starting with 825)

= (10 x 10 x 10 x 10) + (10 x 10 x 10 x 10)

= 20,000

Learn more about counting principle here: brainly.com/question/16050707

#SPJ4

Answer:

A. x = -2,500.

Step-by-step explanation:

sqrt(-4x) = 100

(sqrt(-4x)^2 = (100)^2

-4x = 10,000

4x = -10,000

x = -2,500

Check your work...

sqrt(-4(-2,500))

= sqrt(4 * 2,500)

= sqrt(10,000)

= plus or minus 100

A. x = -2,500 is your answer.

Hope this helps!

Answer:

The answer would be A, x=-2500

Explanation:

To remove the radical on the left side of the equation, square both sides of the equation.

√ − 4 x^ 2 = 100^ 2

Simplify each side of the equation.

− 4 x = 10000

Divide each term by  

−4

and simplify.

x = -2500

Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so,  when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.\(\sum(x - \bar x) = 0\)

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.

Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

Learn more about the obtuse here:

https://brainly.com/question/1581660

#SPJ4

Answer:

I think that the middle one has the answer of 12, 24, 36, and 48.

Answer: i think the middle one is 24 ?

Step-by-step explanation:

No, f(x, y) = 3x - 3y^2 is not a harmonic function.

A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
                                                                            ∂²f/∂x² + ∂²f/∂y² = 0.

Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0

Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.

As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.

Read more about harmonic functions at:

https://brainly.com/question/30385079
#SPJ11

The distance of a point (x,y) from y-axis is the absolute value of the x-coordinate of the point. The distance of the point 5/12 from y-axis is 5/12.

To calculate the distance of the point 5/12 from y-axis, we can use the distance formula:

Distance = √(x2 – x1)2 + (y2 – y1)2

In the given problem, we assume the origin (0,0) as the point on the y-axis and the point (5/12, 0) as the given point. We need to calculate the distance between the two points.

Distance = √(x2 – x1)2 + (y2 – y1)2

Distance = √(5/12 – 0)2 + (0 – 0)2

Distance = √(5/12)2

Distance = 5/12

Therefore, the distance of the point 5/12 from y-axis is 5/12.

Learn more about distance here:

https://brainly.com/question/15256256

#SPJ4