The 1st graders at City Elementary were asked whether they like dogs or cats best. The results are shown in the table. Relative Frequency Table by Row What conclusion can you draw about the relative frequency of the results?
A) A girl in this group is most likely to prefer cats.
B) A boy in this group is most likely to prefer cats.
C) A boy in this group is most likely to prefer dogs.
D) There is no association between the variables.

Answer: A girl in this group is most likely to prefer dogs

To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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Step-by-step explanation:

(i)

that is really simple. for each point go vertically and horizontally to the x and y axis and see at what numbers you hit the axis.

A is -2 on x and +3 on y. so, it's coordinates are (-2, 3).

B is (4, 6).

(ii)

the gradient is also called the slope. it describes the "tilt" of the line.

the gradient or slope is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.

from (-2, 3) to (4, 6) :

x changes by +6 units (from -2 to 4).

y changes by +3 units (from 3 to 6).

so, the gradient/slope = 3/6 = 1/2

(iii)

the general line equation is

y = ax + b

a is the gradient/slope and is always the factor of x.

b is the y-intercept (the y value when x = 0, meaning the point the line crosses the y-axis).

we have already the gradient or slope.

we get b either by reading that point from the chart (it looks like (0, 4)) or by using the coordinates of one of the known points as x and y values in the equation and solve for b. I just picked (4, 6) :

6 = (1/2)×4 + b = 2 + b

b = 4

hey, we were right before !

so, the full line equation is

y = (1/2)x + 4 or simple x/2 + 4

System of equations used to represent the amount of money spend by Juan on buying roses and camations is given by :

3x + 1.50y = 18 , y = 3x.

Number of roses bought by 2.4 and camations is 7.2.

No ,it is not viable.

As given in the question,

Total amount of money spend by $18

Cost of each rose = $3

Cost of each camations = $1.50

Number of camations = 3 times the number of roses

Let 'x' represents the number of roses

And 'y' represents the number of camations

System of equation is given by :

3x + 1.50y = 18

y = 3x

Simplify the system of equation using substitution we get,

3x +(1.50)(3x) = 18

⇒ 3x + 4.5x = 18

⇒ 7.5x = 18

⇒ x= 18/7.5

⇒x = 2.4

⇒y = 7.2

Number of roses and camations are in decimal .

Solution is not viable.

Therefore, the system of equation for the given condition is given by

3x + 1.50y = 18 , y = 3x and solution is not viable.

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Each spinner has 5 numbers, the total combinations would be 5 x 5 = 25 combinations,

The answer is 25

The percent frequency for S&P 100 companies in the Consumer Staples sector is 8.2%

From the pie chart of the dataset (see attachment for the pie chart), we have:

Consumer Staples = 8.2%

This means that the percent frequency for S&P 100 companies in the Consumer Staples sector is 8.2%

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The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

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The margin of error at a 90% confidence level is approximately $1.645.

To find the margin of error at a 90% confidence level, we can use the formula:

Margin of Error = Z * (σ / √n)

Where:

Z is the z-score corresponding to the desired confidence level. For a 90% confidence level, the z-score is approximately 1.645.

σ is the population standard deviation, which is given as $4.

n is the sample size, which is 16.

Plugging in the values:

Margin of Error = 1.645 * ($4 / √16)

              = 1.645 * ($4 / 4)

              = 1.645 * $1

              = $1.645

Therefore, the margin of error at a 90% confidence level is approximately $1.645.

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Answer:

Simply -95.75

Step-by-step explanation:

3/4 or 3 ÷ 4= 0.75

-95 + -0.75 = -95.75

Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

The solution for the given equation when expressed in a factored form is \(-x^3 - 12x^2y^2 + 24x^2y - 13xy^2 + 10xy + 9y^3\)

Given this equation;

\((x+y)(2(12xy-11y)-(x+y)(12xy-11y-x))\)

First expand the second term in the given expression,

\((x+y)(2(12xy-11y)-(x+y)(12xy-11y-x))\\= (x+y)(2(12xy-11y)-(12xy-11y)x + (12xy-11y)y)\\= (x+y)(24xy - 22y - 12xy^2 + 11xy - 11y^2)\)

Then expand the first term in the expression, which gives;

\((x+y)(24xy - 22y - 12xy^2 + 11xy - 11y^2)\\= 24x^2y + 2xy^2 - 22xy - 2y^2 - 12x^2y^2 + 11xy^2 - 11y^3\)

Follow by expansion of the third term, we have

\((x - 11xy)(2x - y)\)

By multiplying the last two terms in the expression, we have;

\((x^2 - 11xy)(x - y)\)

By combining the expressions, we have;

\((x+y)(2(12xy-11y)-(x+y)(12xy-11y-x)) + (x - 11xy)(2x - y) - (x^2 - 11xy)(x - y)\\= 24x^2y + 2xy^2 - 22xy - 2y^2 - 12x^2y^2 + 11xy^2 - 11y^3 + 2x^2 - xy - 22xy + 11y^2 - x^3 + 12x^2y + 11xy^2\\= -x^3 - 12x^2y^2 + 24x^2y - 13xy^2 + 10xy + 9y^3\)

Therefore, the final expression in factored form is given as

\(-x^3 - 12x^2y^2 + 24x^2y - 13xy^2 + 10xy + 9y^3\)

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The given function is f(x)=2.3+5.8x−2.4x² (a) Determine the critical numbers.To determine the critical points, we have to first find the derivative of the function. That is, f'(x). f(x) = 2.3 + 5.8x - 2.4x² The derivative of the function is obtained as follows:

f'(x) = 5.8 - 4.8x From the derivative, we can see that there is only one critical point because the first derivative is linear.The critical point is obtained by setting the derivative equal to zero and solving for x.

5.8 - 4.8x = 0-4.8x = -5.8x = 5.8/4.8

.The critical number is x = 1.2083.(a) The critical number(s) is/are 1.2083

(b) List the interval(s) where the function is increasing.The intervals where the function is increasing are found by analyzing the sign of the first derivative.f'(x) > 0 implies f(x) is increasing.f'(x) < 0 implies f(x) is decreasing.f'(x) = 0 implies a critical point.To determine the intervals where f(x) is increasing, we will choose a number from each of the intervals created by the critical number and analyze the sign of the derivative in those intervals.Choosing a number less than 1.2083, say x = 0, we have:

f'(0) = 5.8 > 0.

This implies that the function is increasing to the left of the critical point.Choosing a number greater than 1.2083, say x = 2, we have:f'(2) = -7.6 < 0. This implies that the function is decreasing to the right of the critical point.

So, the function is increasing on (-∞, 1.2083).

(b) The function is increasing on (-∞, 1.2083).

(c) List the interval(s) where the function is decreasing.

To determine the intervals where f(x) is decreasing, we will choose a number from each of the intervals created by the critical number and analyze the sign of the derivative in those intervals.Choosing a number less than 1.2083, say x = 0, we have:

f'(0) = 5.8 > 0.

This implies that the function is increasing to the left of the critical point. Choosing a number greater than 1.2083, say x = 2, we have:

f'(2) = -7.6 < 0.

This implies that the function is decreasing to the right of the critical point.So, the function is decreasing on (1.2083, ∞).(c) The function is decreasing on (1.2083, ∞).

Answer: (a) The critical number(s) is/are 1.2083

(b) The function is increasing on (-∞, 1.2083).

(c) The function is decreasing on (1.2083, ∞).

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Answer:

Amy is right

Step-by-step explanation:

4.32-2.6 = 1.72

Answer:

Amy is correct

Step-by-step explanation:

4.32-2.6 = 1.72

Answer:

\(\pi\) is infinite. 3.14 only has three numbers.

Step-by-step explanation:

so \(\pi\) multiplied by any number (except 0) will have infinite numbers

Answer:

See below ↓

Step-by-step explanation:

When multiplying a number by 3.14, which is the simplified version of pi, it will give a constant term. But, when multiplying by π, the actual value is equal to 22/7, and it is a non-terminating decimal. Therefore, when you multiply any number with 3.14, it will be slightly lesser than when you multiply with π.

Answer:G

Step-by-step explanation:This is because $3 per pound and pound respents n .Which means 3n.And since $20 is what you have to spend you can spend $20 or equal to $20 .So it would be the less then or equal to symbol. Which means G.

Hope it helps.

Answer:

A.

Step-by-step explanation:

Sorry I can't really explain

for the columns where is less than or equal zero, use the first line of the function to calculate the value of f(x)

\( { ( \frac{1}{3} ) }^{ - 2} - 1 = 9 - 1 = 8 \\ { ( \frac{1}{3} ) }^{ - 1} - 1 = 3 - 1 = 2 \\ { ( \frac{1}{3} ) }^{ 0} - 1 = 1 - 1 = 0\)

for every x greater than zero, use the second line to determine the value

\( {3}^{1} - 2 = 3 - 2 = 1 \\ {3}^{2} - 2 = 9 - 2 = 7\)

hope this helps and gives some insight what to do.

if there are open questions left, feel free to ask them in the comments

have a beautiful day

-Alex

Answer:

Median is 5.

Step-by-step explanation:

Step 1: Arrange the data;

2, 2, 5, 7, 14

Formula:

\(\frac{n+1}{2}\)

\(\frac{5+1}{2} \\\frac{6}{2} \\3rd value\)

Median=5

For the function f(x) = 2x^2 + 3x + 5: 1. First derivative: f'(x) = 4x + 3 2. Second derivative: f''(x) = 4 (constant) For the function y = 5x^3 - 7x^2 + 5: 1. First derivative: y' = 15x^2 - 14x 2. Second derivative: y'' = 30x - 14

Use the formula f'(x) = Tim 10 - 100 to find the derivative of the function, we need to substitute the function into the formula.

So, for f(x) = 2x^2 + 3x + 5, we have: f'(x) = Tim 10 - 100 = 20x + 3 This is the derivative of the function.

To find the second derivative of the function y = 5x^3 - 7x^2 + 5, we need to take the derivative of the derivative.

So, we first find the derivative: y' = 15x^2 - 14x And then we take the derivative of this function: y'' = 30x - 14 This is the second derivative of the function.

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The submarine must lower at least 2698 measures and the submarine must rise at least 516.45 measures. Trigonometric angles are the angles in a right- angled triangle using which different trigonometric functions can be represented.

Given that, the sonar system detects an icicle 4000 measures ahead, with an angle of depression of 34 ∘ to the bottom of the icicle.

What are trigonometric angles?

Trigonometric angles are the angles in a right- angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

a) We know that, tan θ = ( vertical/ Base)

Let the number of measures must the submarine lower to pass under the icicle bex.

tan θ = x/ 4000

⇒ tan 34 ° = x/ 4000

⇒0.6745 = x/ 4000

⇒ x = 0.6745 × 4000

⇒ x = 2698 measures

b) Let the number of measures must the submarine rise to pass over the sunken boat bey.

tan θ = y/ 1500

⇒ tan 19 ° = y/ 1500

⇒0.3443 = y/ 1500

⇒ y = 0.3443 × 1500

⇒ y = 516.45 measures

thus, the submarine must lower at least 2698 measures and the submarine must rise at least 516.45 measures.

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Answer:

x = 2

y = 5

Step-by-step explanation:

A system of equations is a set of two or more equations that contain multiple variables. To solve a system of equations, you can use different methods such as substitution, elimination or graphing.

The given system of equations is:

y = 2x + 1

y = x + 3

We are trying to find the x and y values that make both equations true at the same time.

One way to solve this system is to use the substitution method, by replacing one of the variables in one equation with the other equation.

Let's replace y from the second equation with the first equation:

x + 3 = 2x + 1

Subtract x from both sides:

3 = x + 1

Subtract 1 from both sides:

2 = x

Now that we have the value of x, we can substitute it back into either one of the original equations to find the value of y.

Let's substitute it back into the first equation:

y = 2(2) + 1

y = 5

So the solution to this system of equations is x = 2 and y = 5. It means that both equations are true when x = 2 and y = 5

You can also check your solution by substituting x and y back into the equations and see if both of them are true.

The picture has the dimension of a rectangle and will have the area of 66.166 in square feet.

We have to convert the length and width to be in same unit, before calculating for the area by multiplying the length by the width, and then convert the result to be in square feet.

1 cm = 0.394 inches

126 cm = 126 × 0.394 inches

126 cm = 49.644 inches

So the picture has length 16 inches and width 49.644 inches

area of picture = 16 inches × 49.644 inches

area of picture = 794.304 square inches

1 inch = 0.0833 feet

794.304 square inches = 794.304 × 0.0833 square feet

794.304 square inches = 66.166 square feet.

In conclusion, the picture has an area of 66.166 square feet.

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To find the height of the building, we need to use trigonometry. Let's call the height of the building "h" and the distance from point a to the building "x". From point a, the angle of elevation to the top of the building is given. Let's call this angle "θ".

Using trigonometry, we can write:

tan(θ) = h/x

We can rearrange this equation to solve for h:

h = x * tan(θ)

Now let's move to point b. We know that it is ft closer to the building than point a, so the distance from point b to the building is (x - ft). We also know the angle of elevation from point b, which we'll call "α".

Using the same equation as before, but with the new values, we get:

h = (x - ft) * tan(α)

Now we can set these two expressions for h equal to each other:

x * tan(θ) = (x - ft) * tan(α)

We can solve this equation for h:

h = x(tan(θ) - tan(α)) / (1 - tan(θ)tan(α))

This gives us the height of the building. We just need to plug in the values we were given for x, ft, θ, and α.

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Answer: 56

Step-by-step explanation:

Yes, the number of spaces you move random.

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A normal probability plot (also known as a normal plot or a probability plot) is a graphical tool that can be used to assess whether a set of data follows a normal distribution.

When the data being plotted follows a normal distribution, the points on the plot will appear roughly linear, with deviations from linearity being relatively minor. In other words, the plot will form a straight line.

If the plot deviates significantly from a straight line, it suggests that the data may not be normally distributed. The shape of the plot can indicate whether the data is skewed or has heavy tails compared to a normal distribution.

Therefore, a normal probability plot appearing linear indicates that the data follows a normal distribution. It is important to note that this is only one way to check for normality, and it is always recommended to use multiple methods to verify the normality assumption before applying statistical tests that assume normality.

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Answer:

I believe the ans is

A ⋂ B = { 6, 12 }

Explanation :

The set operation intersection contains only the elements that are in both set

A ⋂ B

The present value of the second option is $3,531.95.

(a) The future value of payments of $300 at the end of each month for 12 months can be calculated using the formula;FV = PMT [((1+r)n - 1)/r](1+r)Where PMT is the payment, r is the monthly interest rate and n is the number of months. Here,PMT = $300r = 2.5%/12 = 0.002083333n = 12FV = $3,668.19

Therefore, the future value of payments of $300 at the end of each month for 12 months is $3,668.19.

(b) In order to determine which option Jane should choose, we need to compare the present values of the two options. The present value of the $3500 bonus now is simply $3500.

To find the present value of the second option, we can use the formula;

PV = FV/(1+r)n

Where FV is the future value of the payments, r is the monthly interest rate and n is the number of months.

Here,FV = $3,668.19r = 2.5%/12 = 0.002083333n = 12PV = $3,531.95

Therefore, the present value of the second option is $3,531.95.

Since $3,531.95 is less than $3500, Jane should choose the $3500 bonus now.

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Answer:

x = -56

Step-by-step explanation:

x/7 = -8

Multiply each side by 7

x/7 *7 = -8*7

x = -56

Answer:

Step-by-step explanation:

1. No

2. Yes

3. Scale factor: 5:7