how many solutions do y=3x-4 y=-2x+7

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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A variable without a clear operational definition can greatly impact the accuracy and reliability of statistics performed on it. To ensure accurate and meaningful results, it is important to have clear, well-defined variables in any research study.

The lack of a clear definition can lead to inconsistencies in data collection, making it difficult to accurately interpret and analyze the results.

Step 1: When a variable has no clear operational definition, researchers may measure or interpret it in different ways, leading to inconsistencies in data collection.

Step 2: These inconsistencies can affect the reliability and validity of the collected data, which in turn impacts the accuracy of the statistical analysis performed.

Step 3: As a result, the findings from such analyses may not accurately represent the true relationships or patterns within the sample or the population, leading to incorrect conclusions.

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Answer:

Step-by-step explanation:

:(

The measurement of the two shorter sides in Monica's wrapping paper is 17 inches.

We can use proportions to solve this problem. Since Francisco's piece of paper is similar to Monica's piece of paper, the ratios of the corresponding sides will be equal. Specifically, we have:

17 / x = 34 / y

where x is the length of one of Francisco's shorter sides, and y is the length of one of Monica's shorter sides.

To solve for y, we can cross-multiply and simplify:

17y = 34x

y = 2x

So the length of one of Monica's shorter sides is half the length of one of her longer sides, or:

y = 1/2 * 34 = 17

Therefore, the measurement of the two shorter sides in Monica's wrapping paper is 17 inches. Answer: a. inches.

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Based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

Chebyshev's Theorem states that for any given number k greater than 1, at least (1 - 1/k²) of the data values in a dataset will fall within k standard deviations of the mean.

In this case, we have a sample size of 225 bags and a mean weight of 353 gm with a standard deviation of 6 gm.

To find a lower bound for the number of bags that weigh between 335 and 371 gm, we need to calculate the range within k standard deviations of the mean.

First, let's find the number of standard deviations for the given range:

Lower range: (335 - 353) / 6 = -3

Upper range: (371 - 353) / 6 = 3

Since we want to find the lower bound, we consider the lower range and use its absolute value: |-3| = 3.

Now, we can use Chebyshev's Theorem to find the lower bound:

(1 - 1/k²) ≤ (1 - 1/3²) = 1 - 1/9 = 8/9

This means that at least 8/9 of the bags will fall within 3 standard deviations of the mean.

To find the lower bound for the number of bags, we multiply this probability by the sample size:

Lower bound = (8/9) * 225 = 200

Therefore, based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

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Answer:

-1

Step-by-step explanation:

(-1) ^3

This is (-1) multiplied together 3 times

(-1) * (-1) * (-1)

-1

Answer:

leveled practice in 1-3, write an equivalent expression.

2.-2× + 7/3

-2a+7/3/3/3

1.8(y-7)

8(y-7)

3. 3× +2+3×

(x,y,z) = (x0,y0,z0) + tN(P)

where z0 is given by the above expression.

To find the normal and tangent vectors at a point on the surface defined by the equation (x^2 y^2)^2=9(x^2-y^2), we first need to find the gradient vector at that point. The gradient vector is perpendicular to the tangent plane and its direction gives the normal vector.

Finding the gradient vector at a point P(x0,y0):

∂f/∂x = 8x0^3y0^2 - 18x0

∂f/∂y = 8x0^2y0^3 + 18y0

The gradient vector at point P(x0,y0) is:

grad f(P) = (∂f/∂x, ∂f/∂y)|P = (8x0^3y0^2 - 18x0, 8x0^2y0^3 + 18y0)

Finding the tangent vector at point P:

To find the tangent vector, we need a direction vector that lies in the tangent plane. One possible choice is the partial derivatives evaluated at P:

T(P) = (∂f/∂x, ∂f/∂y)|P

Finding the normal vector at point P:

The normal vector at point P is given by the gradient vector:

N(P) = (∂f/∂x, ∂f/∂y)|P

Writing an equation for the tangent line at point P:

We can use the point-normal form of the equation of a plane to write the equation for the tangent plane at point P:

(x-x0, y-y0, z-f(x0,y0)) dot N(P) = 0

where (x0,y0) is the coordinates of point P and N(P) is the normal vector at point P. Since we don't have the value of z, we can rearrange this equation to obtain an equation for the tangent line in terms of x and y:

z = f(x0,y0) + ((x-x0, y-y0) dot N(P))/||N(P)||^2

Writing an equation for the normal line at point P:

We can use the point-normal form of the equation of a line to write the equation for the normal line at point P:

(x,y,z) = (x0,y0,z0) + tN(P)

where (x0,y0,z0) is the coordinates of point P, N(P) is the normal vector at point P, and t is a parameter. To find z0, we can substitute the coordinates of point P into the equation of the surface:

(x0^2 y0^2)^2 = 9(x0^2 - y0^2)

Solving for z0:

z0 = f(x0,y0) = (x0^2 y0^2)^2/9(x0^2 - y0^2)

Substituting this value into the equation of the normal line, we get:

(x,y,z) = (x0,y0,z0) + tN(P)

where z0 is given by the above expression.

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Answer:

66244.7

Step-by-step explanation:

70• 943.353 (1 liter into milliliters)=66244.7

The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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Answer: y^7 - 8

Step-by-step explanation:

It is an algebra equation. It can't be factor or solve further!

Answer:

(4,-2)

Step-by-step explanation:

Going to Desmos and you will see the the graph and you can push on the vertex and see the answer

Answer:

The percent of increase from 20 to 26 is 30 %

Step-by-step explanation:

Answer:

x = -14

Step-by-step explanation:

y = 3x

x = 2y +70

(replace)

x = 2(3x) + 70

(simplify)

x = 6x + 70

-5x = 70

x = -14

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Step-by-step explanation:

Let :d=dimes and q=quarters

d=2-5(q)

Answer:

15 rooms

Step-by-step explanation:

18/6 = 3 so multiply 3 times 5 and that equals 15!

Answer:

15 rooms.

Step-by-step explanation:

since they can clean 5 rooms in 6 hours, and it's asking how many rooms they can clean in 18 hours:

5/6=x/18

solve for x:

6x=90

x=15

Or you could've just multiplied 5 by 3 since 6(3)=18.

The domain of the inverse function will be y ≥ 6, and the range of the inverse function will be x > 4.

When the domain is restricted to the portion of the graph with a positive slope, it means that only the values of x that result in a positive slope will be considered.

In the given function, f(x) = |x – 4| + 6, the portion of the graph with a positive slope occurs when x > 4. Therefore, the domain of the function is x > 4.

The range of the function can be determined by analyzing the behavior of the absolute value function. Since the expression inside the absolute value is x - 4, the minimum value the absolute value can be is 0 when x = 4.

As x increases, the value of the absolute value function increases as well. Thus, the range of the function is y ≥ 6, because the lowest value the function can take is 6 when x = 4.

Now, let's consider the inverse function. The inverse of the function swaps the roles of x and y. Therefore, the domain and range of the inverse function will be the range and domain of the original function, respectively.

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Answer:

1 4/5

Step-by-step explanation:

On the number line, for every whole integer, the line is divided into fifths. The dot is one fifth away from the number two. Therefore, it is 4/5 in from 1 and the answer is 1 \(\frac{4}{5}\).

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

divident

Step-by-step explanation:

Company A has a higher risk percentage (55%) compared to Company B (3%).

To compute the Coefficient of Variation (CV) for each company, we need to use the formula:

CV = (Standard Deviation / Mean) * 100

Let's calculate the CV for each company:

For Company A:

Risk Percentage = 55%

Return = 14%

For Company B:

Risk Percentage = 3%

Return = 14%

Since we don't have the standard deviation values for each company, we cannot calculate the exact CV. However, we can still compare the riskiness of the two companies based on the provided information.

The Coefficient of Variation measures the risk relative to the return. A higher CV indicates higher risk relative to the return, while a lower CV indicates lower risk relative to the return.

In this case, Company A has a higher risk percentage (55%) compared to Company B (3%), which suggests that Company A is riskier. However, without the standard deviation values, we cannot make a definitive conclusion about the riskiness based solely on the provided information. The CV would provide a more accurate measure for comparison if we had the standard deviation values for both companies.

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Answer:

t = 16

Step-by-step explanation:

if you do 448 divided by 28 you get 16.

if you do 28 x 16 you get 448

A 2 ×× 2 ×× 2 factorial design indicates that the experiment includes two independent variables, option C.

In a factorial design, the numbers before the "×" symbol represent the levels or categories of each independent variable, while the total number of factors indicates the number of independent variables.

In this case, there are three factors, each with two levels, resulting in a 2 × 2 × 2 factorial design. Therefore, there are two independent variables included in the experiment.

The numbers in a factorial design indicate the number of levels of each independent variable. In this case, there are two independent variables, each with two levels, resulting in a total of eight experimental conditions (2x2x2). So, the correct answer is C) two independent variables.

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Answer:

=========================

The law of sines is:

Find the value of ∠C using the angle sum theorem:

Find side a:

Note, the sides of a triangle are marked as:

Use two pairs with one unknown:

Substitute values and solve for a:

Find side b, similar to finding side a:

Answer:

a = 16.5 cm (nearest tenth)

b = 23.8 cm (nearest tenth)

Step-by-step explanation:

Definition

A, B and C are the angles and a, b and c are the sides opposite the angles.

From inspection of the triangle:

Interior angles of a triangle sum to 180°:

⇒ A + B + C = 180°

⇒ 42° + 75° + C = 180°

⇒ C = 180° -  117°

⇒ C = 63°

To find the missing side lengths a and b, use the Sine Rule:

\(\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

Substitute the given values into the Sine Rule formula:

\(\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}\)

Finding side a:

\(\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{22}{\sin 63^{\circ}}\)

\(\implies \sf a=\dfrac{22\sin 42^{\circ}}{\sin 63^{\circ}}\)

\(\implies \sf a=16.52162239...\)

Therefore, side a is 16.5 cm (nearest tenth).

Finding side b:

\(\implies \sf \dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}\)

\(\implies \sf b=\dfrac{22\sin 75^{\circ}}{\sin 63^{\circ}}\)

\(\implies \sf b=23.84984577...\)

Therefore, side b is 23.8 cm (nearest tenth).

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Answer:

\(g(f(6))= 17\)

Step-by-step explanation:

\(g(f(6))= 3(2(6) - 5) - 4\)

\(3(12 - 5) - 4\)

\(3(7) - 4\)

\(21-4\)

\(g(f(6))= 17\)

Answer:

g(f(6)) = 17

Step-by-step explanation:

f(x) = 2x - 5

g(x) = 3x - 4,

g(f(6))

First find f(6) = 2*6 -5 = 12-5 = 7

Then find g(7) = 3*7 -4 = 21-4 = 17

g(f(6)) = 17

Answer:

The answer is 2.5

Step-by-step explanation:

Your welcome! I sometimes get stuck on problems like you too for hours until I get it.

Answer:

Scale factor: 2.5

Step-by-step explanation:

Scale factor is the ratio between corresponding measurements. And a pre image is basically an (original image) while an image is the translated version of the original.

I'm not sure what the best way to explain my answer is, but you can either multiply or divide to find the answer.

4 x 2.5 = 10

8 x 2.5 = 20

10 x 2.5 = 25

5 x 2.5 = 12.5

10/4 = 2.5

20/8 = 2.5

25/10 = 2.5

12.5/5 = 2.5

Answer:

178 text messages

Step-by-step explanation:

You have do 7.05 times 3 and you get 21.15. Then you do 26.70 minus 21.15 and you get 5.55. Then you do 7.05 divided by 47 then you get 0.15.  SO each messages is 0.15 cents so you do 0.15 times 37 and you get 5.55 and then you add 21.15 and 5.55 and you get 26.70. Then you take 141 and add it to 37 and you get 178 as your answer          

The equation in slope-intercept form of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0 is :

y = (7/3)x - (19/3).

To write the equation in slope-intercept form, we need to find the slope of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0.

First, we need to rearrange the equation 3x + 7y = 0 into slope-intercept form:

7y = -3x
y = (-3/7)x

The slope of this line is -3/7.

Since the line we are trying to find is perpendicular to this line, its slope will be the negative reciprocal of -3/7:

m = 7/3

Now we can use the point-slope formula to write the equation of the line that passes through (1,8) with slope 7/3:

y - 8 = (7/3)(x - 1)

Finally, we can rearrange this equation into slope-intercept form:

y = (7/3)x - (19/3)

So, the equation in slope-intercept form of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0 is y = (7/3)x - (19/3).

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