If you add​ Natalie's age and​ Fred's age, the result is 39 If you add​ Fred's age to 3 times​ Natalie's age, the result is 69 Write and solve a system of equations to find how old Fred and Natalie are

The alternative hypothesis for a dependent samples t-test would be μd≠0.

In a dependent samples t-test, also known as a paired samples t-test, the goal is to compare the means of two related variables or measurements taken from the same sample.

The null hypothesis assumes that the mean difference between the paired measurements is zero (μd = 0). The alternative hypothesis, on the other hand, proposes that there is a significant difference between the means of the two variables.

Among the given options, μ>30 and μd<=0 do not represent the alternative hypothesis for a dependent samples t-test. These options suggest a specific value or direction of the mean, rather than a difference between means.

The option μ1−μ2≠0 is also not the correct alternative hypothesis as it represents the null hypothesis (μd = 0). The option μd ≠ 0, however, accurately represents the alternative hypothesis for a dependent samples t-test. It states that there is a significant difference between the means of the two variables being compared.

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The equation for the plane through the point Po(-5, -4, 3) and perpendicular to the line x = -5 + t, y = -4 + 3t, z = -5t is 3x + 9y - 5z = -64.

To find the equation of a plane, we need a point on the plane and a normal vector perpendicular to the plane. The given point on the plane is Po(-5, -4, 3). To find the normal vector, we can use the direction vector of the given line, which is parallel to the plane. The direction vector is (1, 3, -5). Since the plane is perpendicular to this direction vector, the normal vector of the plane is (-1, -3, 5), which is the negative of the direction vector.

Now we can use the point-normal form of a plane equation. Let (x, y, z) be any point on the plane. The vector from Po to (x, y, z) is given by (x + 5, y + 4, z - 3). We can take the dot product of this vector with the normal vector (-1, -3, 5) and set it equal to zero to get the equation of the plane:

(-1, -3, 5) · (x + 5, y + 4, z - 3) = 0

-1(x + 5) - 3(y + 4) + 5(z - 3) = 0

Simplifying the equation gives us:

-1x - 3y + 5z + 64 = 0

Rearranging the terms, we obtain the equation for the plane: 3x + 9y - 5z = -64.

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False, the linearity assumption in ANOVA is not assessed using a QQ-plot of the residuals.

The linearity assumption in ANOVA refers to the assumption that the relationship between the independent variable(s) and the dependent variable is linear. This assumption is typically assessed by examining the residuals (the differences between the observed values and the predicted values) of the model. However, a QQ-plot is not specifically used to assess linearity.

A QQ-plot is commonly used to assess the assumption of normality in the residuals, which is another important assumption in ANOVA. It helps to visually compare the distribution of the residuals against a theoretical normal distribution. The linearity assumption is typically evaluated through other diagnostic plots, such as scatterplots of the residuals against the predicted values or the independent variable(s).

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Answer:

Step-by-step explanation:

12 oz is better

Answer:

they will skip 4

Step-by-step explanation:

Answer:

They will have to skip the ones that are less desirable to them

Answer: Your Answer would be A

Step-by-step explanation:

The PV factor formula is given below: The formula for PV factor is: PV Factor = [1 - (1 + r)⁻ⁿ] / r

where r = discount rate, and n = number of periods.

PV factor can be used to calculate the present value of an annuity. If the amount of each payment and the number of periods are known, the present value of the annuity can be calculated using the following formula:

Present value of annuity = Payment × PV factor.

For example, suppose that you have an annuity that pays $1,000 per year for 5 years.

The discount rate is 8%. We can calculate the PV factor using the formula:

PV factor = [1 - (1 + r)⁻ⁿ] / r= [1 - (1 + 0.08)⁻⁵] / 0.08= 3.9936

The present value of the annuity can be calculated by multiplying the payment by the PV factor:

Present value of annuity = Payment × PV factor= $1,000 × 3.9936= $3,993.6

Therefore, the present value of the annuity is $3,993.6.

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The balance outstanding on the loan immediately after the seventh quarterly payment, using an interest rate of 16% p.a. compounded quarterly and equal quarterly payments, is R$310.39.

To calculate the balance outstanding after the seventh quarterly payment, we need to use the formula for the present value of an ordinary annuity:

P = PMT * (1 - (1 + r)^(-n)) / r

Where:

P = Principal amount of the loan (R$1,000)

PMT = Equal quarterly payment

r = Interest rate per period (16% p.a. compounded quarterly = 4% per quarter)

n = Number of periods (10 payments)

First, we calculate the equal quarterly payment (PMT) using the present value of an ordinary annuity formula rearranged to solve for PMT:

PMT = P * (r / (1 - (1 + r)^(-n)))

PMT = 1000 * (0.04 / (1 - (1 + 0.04)^(-10))) = R$129.09

Next, we calculate the balance outstanding after the seventh quarterly payment. We can consider it as the present value of the remaining three payments:

Balance = PMT * (1 - (1 + r)^(-n_remaining)) / r

Where: n_remaining = Number of remaining payments (10 - 7 = 3)

Balance = 129.09 * (1 - (1 + 0.04)^(-3)) / 0.04 = R$310.39

Therefore, the balance outstanding on the loan immediately after the seventh quarterly payment is R$310.39.

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Answer:

C

Step-by-step explanation:

CHOOSE C

Answer:

[tex] f(x) = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]

Step-by-step explanation:

Given:

Score of 37 with 107 minutes on social media.

Score of 41 with 73 minutes on social media.

The two pieces of information above can be thought of as two points on a line. Since the quiz score is a function of the number of minutes on social medial, let the number of minutes on social media be x and the score be y. The given information gives us two ordered pairs: (107, 37) and (73, 41).

Now we need to write the equation of a line that passes through these two points.

The two-point form of the equation of a line is:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

We have [tex] x_1 = 107 [/tex], [tex] y_1 = 37 [/tex], [tex] x_2 = 73 [/tex], and [tex]y_2 = 41[/tex].

[tex] y - 37 = \dfrac{41 - 37}{73 - 107}(x - 107) [/tex]

[tex] y - 37 = \dfrac{4}{-34}(x - 107) [/tex]

[tex] y - 37 = -\dfrac{2}{17}(x - 107) [/tex]

[tex] 17y - 629 = -2x + 214 [/tex]

[tex] 17y = -2x + 843 [/tex]

[tex] y = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]

[tex] f(x) = -\dfrac{2}{17}x + \dfrac{843}{17} [/tex]

Answer:

The answer is 5x - 13

Step-by-step explanation:

All we do is add the x's and the other numbers.

2 + 3 = 5 and 10 + 3 = 13

So, the equation is 5x - 13

Hope this helps! :)

Answer:

#1=8

#2=3

Step-by-step explanation:

Im assuming a hexagon pyramid/cone???

Bc when you look at a square triangle its only called that becoause of its base??

Answer:

it's hexagon cone

someone said that so yeah

Answer:

3x^2 - 17x + 24

Step-by-step explanation:

(x – 3)(3x – 8)

3x^2 + (-8x) + (-9x) + 24

3x^2 - 17x + 24

Answer:

A= 12 Ft^2

Step-by-step explanation:

Reminder the Area formula is A=B(Base) times H(Height).

Take The base (6) and the Height (6) then multiply.

Hence, the reason is 12 Ft squared.

Answer:

the answer is c or 35x^2 + 210x +315

Step-by-step explanation:

The area of the square is "d" and since it asks for the combined area of the triangle and square it has to be more than that, hope that helps.

Answer:

No

Step-by-step explanation:

She needs at least another 2 coordinate pairs to test if her evaluation is correct. For instance, the next pair could be (7,22). Then, the pattern wouldn't be increasing by 4. It would not have a constant of proportionality.

Answer:

1

70 75

60 65

80 85 90

o

60 65

70 75 80 85 90

60 65 70 75 80 85 90

o

60 65

70 75 80 85

90 95 105 120 125 130 135 140 145

The box and whisker plot which correctly displays the given data set is option 3.

Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.

Given is a data set.

88  85  86  82  66  75

A box and whisker plot is used to summarize the data using boxes which shows the quartiles in the plot.

Arranging the data set in increasing order,

66  75  82  85  86  88

Highest value in the data set = 88

Lowest value = 66

The plot which correctly displays these two points are options 2 and 3.

Now, find the median of the data set.

Median is the average of 3rd and 4th element since this consist of even number of data sets.

Median = (82 + 85) / 2 = 83.5

This is correctly marked in option 3.

Hence the correct option is third one.

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The complete question is given in the image below. :

Answer:

x = 1953125

Step-by-step explanation:

log x - log 5^3 = 2 log 5^3

log x - 3 log 5 = 6 log 5

log x = 9 log 5 = log 5^9

x = 5^9

 x = 1953125

50. 150 divided by 3

Answer:

x = 13y + 0.625

Step-by-step explanation:

4(2x - 3y) = y + 5

8x - 12y = y + 5

8x = y + 5 + 12y

8x = 5 + 13y

8x ÷ 8 = 5 + 13y ÷ 8

x = 5 + 13y ÷ 8

x= 13y + 5 ÷8

x = 13y + 0.625

The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is (0.41, 0.53). This means we can be 99% confident that the true difference in proportions falls within this interval.

Sample size of Democrats, n1 = 750

Number of Democrats who consider the environment as a top priority, x1 = 615

Sample size of Republicans, n2 = 850

Number of Republicans who consider the environment as a top priority, x2 = 306

Calculate the sample proportions:

Sample proportion of Democrats, p1 = x1 / n1 = 615 / 750 = 0.82

Sample proportion of Republicans, p2 = x2 / n2 = 306 / 850 = 0.36

Calculate the standard error of the difference in two sample proportions:

σd = sqrt{ [P1(1-P1) / n1] + [P2(1-P2) / n2] }

σd = sqrt{ [0.82(0.18) / 750] + [0.36(0.64) / 850] }

σd = sqrt{ 0.000180 + 0.000240 }

σd = sqrt{ 0.000420 }

σd ≈ 0.0205

Determine the level of confidence:

Given level of confidence, C = 99%

Find the critical value (z-score):

The z-score corresponding to the given level of confidence can be obtained from the standard normal table. For a 99% confidence level, the critical value is approximately z = 2.576.

Calculate the margin of error:

The margin of error is given by E = z * σd

E = 2.576 * 0.0205

E ≈ 0.0528

Construct the confidence interval:

The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is given by (D – d, D + d), where D is the difference in sample proportions and d is the margin of error.

(0.82 – 0.36 – 0.0528, 0.82 – 0.36 + 0.0528)

(0.41, 0.53)

Interpretation:

We can be 99% confident that the true difference in the percentages of Democrats and Republicans who prioritize protecting the environment falls within the interval (0.41, 0.53).

This means that there is a significant difference between the two groups in terms of the proportion that prioritize protecting the environment. The Democrats have a higher proportion compared to the Republicans.

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Answer:

The initial value, b = $3.50 is the skate rental fee

The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink

Step-by-step explanation:

From the question we have;

The charges of the roller skating rink = A skate rental fee + An hourly rate

The total cost to skate for 2 hours = $9.50

The total cost to skate for 5 hours = $18.50

The relationship between the total cost of skating and the duration in hours = Linear relationship

Let 'x' represent the number of hours skating and let 'y' represent the total cost, we have;

The form of the equation is y = m·x + b

Where;

m = The rate of change of the linear relationship

b = The initial value (y-intercept)

When x = 2, y = 9.50

Therefore, we can write;

9.50 = 2·m + b...(1)

When x = 5, y = 18.50

Therefore, we can write;

18.50 = 5·m + b...(2)

Subtracting equation (1) from equation (2) gives;

18.50 - 9.50 = 5·m - 2·m + b - b = 3·m

9.0 = 3 × m

∴ m = 9.0/3 = 3.0

The rate of change, m = 3.0

Similarly, we have;

From equation (1), we get;

9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b

9.50 = 6.0 + b

∴ b = 9.50 - 6.0 = 3.50

The initial value = 3.50

Therefore, the initial value, b = $3.50 is the skate rental fee while rate of change m = $3.0 is the hourly rate the rate.

Answer:

The answer of the function is y=x-5

Step-by-step explanation:

Area of Rectangle = Length x Width

Area of Top Rectangle =

[tex]22 \times (31 - 18) \\ = 22 \times 13 \\ = 286 {ft}^{2} [/tex]

Area of bottom Rectangle =

[tex]18 \times 9 \\ = 162 {ft}^{2} [/tex]

Area of Composite figure = Area of top Rectangle + Area of bottom rectangle

[tex] = 286 + 162 \\ = 448 {ft}^{2} [/tex]