The system
2.+ 3y = 8
4x - y = 2
is solved algebraically. Which of the following can be used to correctly solve this system by using the elimination method? Selec
А
-2(2x + 3y = 8)
-4. -6y = -16
B
2(2x + 3y = 8)
-43 - 6y = 8
4r
-40 - by = -16
43 - y = 2
by : 8
2
4.2
- 4x + 4.r - by - y = -16 + 2
44-6y y = 8 + 2
C
34 - y = 2)
12-3y = 6
D
22. + 3y = 8)
13 6y = 16
2x + 3y = 8
12 - 3y = 6
4a +6y16
2
2x + 12x + 3y - 3y = 8 + 6
431-6yy = 16 + 2x

When the value of the independent variable is increased by one unit from 5 to 6, the change in the dependent variable, y-hat, is an increase of 15 - the initial value of y-hat.

To find the change in the dependent variable, y-hat, when the independent variable is increased by one unit, you will need to substitute the values you found in steps 1 and 2 into the equation for the regression line. The equation for the regression line is in the form of y-hat = mx + b, where m is the slope and b is the y-intercept.

Let's say you found the slope, m, to be 2 and the y-intercept, b, to be 3.

Substituting these values into the equation, we have:

y-hat = 2x + 3

Now, if we increase the value of the independent variable, x, by one unit, we can substitute the new value into the equation and calculate the change in y-hat.

For example, if the initial value of x is 5, and we increase it by one unit to 6, we substitute x = 6 into the equation:

y-hat = 2(6) + 3
y-hat = 12 + 3
y-hat = 15

Therefore, when the value of the independent variable is increased by one unit from 5 to 6, the change in the dependent variable, y-hat, is an increase of 15 - the initial value of y-hat.

Remember to use the specific values you obtained in steps 1 and 2 to substitute into the equation for the regression line and calculate the change in y-hat accurately.

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Answer: I think that it is  62

Step-by-step explanation:

77 minus 15= 62

tell me if its right.

hope this helps

Answer:

I believe the answer is B, although im not quite sure.

The second ladder touches the wall approximately 11 feet higher than the shorter ladder, or equivalently, around 8 feet 8 inches higher.

Let's denote the height at which the second ladder touches the wall as h. We can set up a proportion based on the similar right triangles formed by the ladders and the building:

(6 6 feet) / (h) = (9 9 feet) / (5 5 feet 9 9 inches + h)

To solve for h, we can cross-multiply and solve the resulting equation:

(6 6 feet) * (5 5 feet 9 9 inches + h) = (9 9 feet) * (h)

Converting the measurements to inches:

(66 inches) * (66 inches + h) = (99 inches) * (h)

Expanding and rearranging the equation:

4356 + 66h = 99h

33h = 4356

Solving for h:

h = 4356 / 33 = 132 inches

Converting back to feet and inches:

h ≈ 11 feet

Therefore, the second ladder touches the wall approximately 11 feet higher than the shorter ladder, or equivalently, around 8 feet 8 inches higher.

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The future value of the annuity due with R = $400, i = 0.03, and n = 6 is approximately $2,476.47. The future value of the annuity due with R = $13,000, i = 0.07, and n = 6 is approximately $93,384.36.

To find the future value of an annuity due, we can use the formula:

S = R * [(1 + i) * ((1 + i)ⁿ - 1) / i]

where:

S is the future value of the annuity due

R is the periodic payment

i is the interest rate per period

n is the number of periods

(a) For the first annuity due with R = $400, i = 0.03, and n = 6, we can substitute the values into the formula:

S = $400 * [(1 + 0.03) * ((1 + 0.03)⁶ - 1) / 0.03]

 ≈ $2,476.47

Therefore, the future value of the annuity due is approximately $2,476.47.

(b) For the second annuity due with R = $13,000, i = 0.07, and n = 6, we can substitute the values into the formula:

S = $13,000 * [(1 + 0.07) * ((1 + 0.07)⁶ - 1) / 0.07]

 ≈ $93,384.36

Therefore, the future value of the annuity due is approximately $93,384.36.

In both cases, the future value represents the total amount accumulated at the end of the annuity due period, considering the periodic payments, interest compounding, and the specified interest rate.

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Answer:

a. Line BC and Line GH

b. Line AC and line AJ

c. No, because if they were perpendicular, they would intersect at a 90 degree angle.

Step-by-step explanation:

a. Whenever two lines share identical little triangle marks - such as line BC and line GH in this case - it indicates that those lines are parallel.  

b. The little red square at the intersection of line AC and line AJ indicates a 90 degree angle. Whenever two lines intersect at a 90 degree angle, it means they are perpendicular. So, Line AC and line AJ would be perpendicular.

c. The upside down T symbol means "perpendicular," so the question is asking if line BC and line AJ are perpendicular. However, they cannot be since there is no indication on the diagram that they do - no symbols of 90 degree angles - that we can use to prove that they are perpendicular.

x = (11/14) = 10^(log(11/14))

To solve the equation 6x - 6 = 5 - 8x, we can start by simplifying the equation:

6x + 8x = 5 + 6

14x = 11

Next, divide both sides of the equation by 14 to isolate x:

x = 11/14

The exact answer for x is 11/14.

If you want to express this answer using logarithms, you can write it as:

x = (11/14) = exp(ln(11/14))

This representation uses the natural logarithm (base-e) to express the result.

Alternatively, if you prefer to use base-10 logarithm, you can write:

x = (11/14) = 10^(log(11/14))

Both expressions provide the exact answer for x in terms of logarithms, allowing you to evaluate it more precisely if needed.

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Answer:

4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

15-7=8

8+7=15

Answer:

16

Step-by-step explanation:

1) Subtract 7 from 15. 15-7=8

2) Multiply 8 by 2. 8x2=16

Therfore your answer is 16.

The domain and codomain of the function f(n) = n^2 + 1 are both the set of integers. The range of the function is all positive integers (including zero).

To find the domain, codomain, and range of the function f(n) = n^2 + 1:

1. Domain: The domain is the set of all possible input values for the function. In this case, since the function is defined for "the set of integers," the domain is the set of all integers.

2. Codomain: The codomain is the set of all possible output values for the function. In this case, the function is defined as f(n) = n^2 + 1, where n is an integer. Therefore, the codomain is also the set of integers.

3. Range: The range is the set of all actual output values that the function produces for the given inputs. To find the range, we can substitute various integer values for n and observe the corresponding outputs. Since the function is defined as f(n) = n^2 + 1, the smallest possible output value is 1 (when n = 0), and there is no upper limit for the output. Hence, the range is all positive integers (including zero).

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Answer: The area of the region enclosed by the curves y=x, y=2x, x=y^2, x=4y^2 in the first quadrant is 119/5 square units.

Step-by-step explanation:

Let's begin by sketching the region in the first quadrant enclosed by the given curves:

We can see that the region is bounded by the lines y=x and y=2x, and the parabolas x=y^2 and x=4y^2.

To get the area of this region, we can use the change of variables u=y and v=x/y. This transformation maps the region onto the rectangle R={(u,v): 1 ≤ u ≤ 2, 1 ≤ v ≤ 4} in the uv-plane. To see why, note that when we make the substitution y=u and x=uv, the curves y=x and y=2x become the lines u=v and u=2v, respectively.

The curves x=y^2 and x=4y^2 become the lines v=u^2 and v=4u^2, respectively.Let's determine the Jacobian of the transformation. We have:

J = ∂(x,y) / ∂(u,v) =

| ∂x/∂u ∂x/∂v |

| ∂y/∂u ∂y/∂v |

We can compute the partial derivatives as follows:∂x/∂u = v

∂x/∂v = u

∂y/∂u = 1

∂y/∂v = 0

Therefore, J = |v u|, and |J| = |v u| = vu.

Now we can write the integral for the area of the region in terms of u and v as follows

:A = ∬[D] dA = ∫[1,2]∫[1,u^2] vu dv du + ∫[2,4]∫[1,4u^2] vu dv du

= ∫[1,2] (u^3 - u) du + ∫[2,4] 2u(u^3 - u) du

= [u^4/4 - u^2/2] from 1 to 2 + [u^5/5 - u^3/3] from 2 to 4

= (8/3 - 3/4) + (1024/15 - 32/3)

= 119/5.

Therefore, the area of the region enclosed by the curves y=x, y=2x, x=y^2, x=4y^2 in the first quadrant is 119/5 square units.

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Answer:

a=3 , b=2

Step-by-step explanation:

The volume of the right prism with a base area of 10 square feet and a height of 6 feet is 60 cubic feet.

A prism is a polyhedron that has a base and a top face that are the same in size and shape, with sides connecting them that are rectangles in a right prism.

A right prism is a prism in which all of the side faces are perpendicular to the base.

Therefore, the height of the right prism is perpendicular to the base as well.

A right prism has a volume equal to the product of the base area and the height.

This formula can be represented as:

V = Bh

Here, B represents the area of the base, and h represents the height.

The volume of the right prism can be found by multiplying the area of the base by the height of the prism, according to the formula:

V = Bh.

In this problem, the area of the base of the prism is given to be 10 square feet.

The height of the prism is 6 feet.

We can simply substitute these values into the formula to obtain the volume of the right prism as follows:

V = BhV

   = 10 × 6V

   = 60

Therefore, the volume of the right prism is 60 cubic feet.

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Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Answer:

a

Step-by-step explanation:

the graph would continue on both sides; no asymptote

Range is set of y values

And it tends to -infinity with increase in x .

So

RAnge

Option D

The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.

Now,

Given:

Let 'x' be the value that gives the value of grades.

The absolute value equation to find the grades will be given by: | x - 82 | = 12

=> x - 82 = ± 12

For maximum value of the grades, x - 82 = 12

=> x = 82 + 12

=> x = 94.

For minimum value of the grades, x - 82 = -12

=> x = 82 - 12

=> x = 70.

Hence, The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.

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The volume of the solid generated by revolving the region R bounded by

y = \(e^{-2x}\), y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units

Given the region R bounded by y = \(e^{-2x}\), y = 0, x = 0, x = ln 9.

We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.

The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.

Then, volume, V = \(\int\limits^0_{ln9} {y^2} \, dx\)

                            = \(\int\limits^0_{ln9} {(e^{-2x})^2} \, dx\)

                            = \(\int\limits^0_{ln9} {e^{-4x}} \, dx\)

                            = \(\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}\)

                            = \(\frac{e^{-4 ln9}}{-4} +\frac{1}{4}\)

                            = \(\frac{9^{-4}+1}{4}\) ≈ 0.25 cubic units

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Answer:

s = 3*r

Step-by-step explanation:

sold = 3(people) * r(raffle tickets)

Answer:

B. f(x) is shifted left by 6 units

Step-by-step explanation:

when we talk about translations, we know they happen along the X axis, y axis or sometimes both, in this case we see that were subtracting x by six units, so we are moving left along the x axis

ways to remember this is:

 -you count up x the RIGHT way going right

 -you count UP y

and of cource by process of ellimination we know that decreasing X goes left and decreasing y goes down

ALSO NOTE: x always goes horizontally and y always goes vertically

The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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The metric unit most commonly used to measure the mass of objects, including the mass of a large dog, is the kilogram (kg). The kilogram is the base unit of mass in the International System of Units (SI) and is widely accepted and used worldwide.

Measuring the mass of a large dog in kilograms provides a standardized and universally understood unit of measurement. It allows for easy comparison of the dog's mass with other objects or animals, as well as for consistent record-keeping and communication among veterinarians, researchers, and pet owners.

Using kilograms to measure the mass of a large dog also provides a practical advantage. Kilogram-based scales are readily available and commonly used in veterinary clinics, animal hospitals, and homes. These scales allow for accurate and precise measurement of the dog's mass, ensuring proper monitoring of its health, diet, and medication dosages.

By utilizing the kilogram as the metric unit for measuring the mass of a large dog, it promotes consistency, clarity, and compatibility in scientific research, healthcare, and everyday life.The metric unit most commonly used to measure the mass of objects, including the mass of a large dog, is the kilogram (kg). The kilogram is the base unit of mass in the International System of Units (SI) and is widely accepted and used worldwide.

Measuring the mass of a large dog in kilograms provides a standardized and universally understood unit of measurement. It allows for easy comparison of the dog's mass with other objects or animals, as well as for consistent record-keeping and communication among veterinarians, researchers, and pet owners.

Using kilograms to measure the mass of a large dog also provides a practical advantage. Kilogram-based scales are readily available and commonly used in veterinary clinics, animal hospitals, and homes. These scales allow for accurate and precise measurement of the dog's mass, ensuring proper monitoring of its health, diet, and medication dosages.

By utilizing the kilogram as the metric unit for measuring the mass of a large dog, it promotes consistency, clarity, and compatibility in scientific research, healthcare, and everyday life.

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Answer:

Think your answer is 3 1/4

Answer:

B

Step-by-step explanation:

A parent function is the simplest function that still satisfies the definition of a certain type of function. One of those functions is exponential, which is b.

   Option (B) will be the correct option.

We will check each option given for the definition of a parent function.

Option (A)

\(f(x)=-2^{x+1}\)

Parent function will be,

\(f(x)=2^x\)

Option (B),

\(f(x)=4^x\)

It's a simplest form of an exponential function.

Therefore, it's a parent function.

Option (C),

\(f(x)=e^{3x}-2\)

Parent function → \(f(x)=e^{3x}\)

Option (D),

\(f(x)=4x^2\)

Parent function → \(f(x)=x^2\)

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Answer: y = 1

Step-by-step explanation: Lets solve for y, step by step!

6 = 2(y + 2)

6 = ( 2 x y + 2 x 2)

6 = 2y + 4

2y + 4 = 6

2y + 4 - 4 = 6 - 4

2y = 2

y = 1

Answer:

To calculate the final cost of the meal, we need to first calculate the discount and then add the sales tax. Discount = 10% of $5.75 = $0.575 Price after discount = $5.75 - $0.575 = $5.175 Sales tax = 4% of $5.175 = $0.207 Final cost = Price after discount + Sales tax = $5.175 + $0.207 = $5.382 Therefore, you should charge the customer $5.382.

well, let's hmmm apply the 10% discount first

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5.75}}{\left( \cfrac{10}{100} \right)5.75} ~~ \approx ~~ 0.58~\hfill \stackrel{ 5.75~~ - ~~0.58 }{\approx\text{\LARGE 5.17}}\)

now let's apply the 4% tax to it

\(\stackrel{\textit{4\% of 5.17}}{\left( \cfrac{4}{100} \right)5.17} ~~ \approx ~~ 0.21\hspace{5em}\stackrel{ 5.17~~ + ~~0.21 }{\text{\LARGE 5.38}}\qquad \textit{final charge}\)

the capture rate will be lower than what is indicated in the confidence level.

A C% confidence interval gives an interval of plausible values for a parameter. The interval is calculated from the data and has the form, point estimate ± margin of error.

When the random and large counts conditions are met, a C% confidence interval for the population proportion p is

Point estimate ±margin of error

Ƹ± √Ƹ(1 − Ƹ)/

Where z is the critical value for the standard normal curve with C% of its area between –z and +z.

Your interval will look like: ______ < p <________

Confidence Intervals in a 4 Step Process:

Statistics Problems Demand Consistency

1. State: What parameter do you want to

estimate, and at what confidence level?

2. Plan: Identify the appropriate inference

method: check conditions.

3. Do: If the conditions are met, perform

calculations.

4. Conclude: Interpret your interval in the

context of the problem.

When constructing a confidence interval for a population proportion, it is checked that sample size is less than 10% of population size.

This condition is important due to the the fact that when sample size is less than of population size, observations are closer to independent.

If this requirement is not met, it is not possible to calculate standard deviation of distribution.

If this requirement is not met, it is not possible to calculate standard deviation of distribution correctly.

If standard deviation is not correct, confidence level will be inaccurate. There are less chances to obtain population parameter in confidence interval.

Therefore, the capture rate will be lower than what is indicated in the confidence level.

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The capture rate will be lower than what is indicated in the confidence level.

An interval of conceivable values for a parameter is provided by a C% confidence interval. The interval is formed as a point estimate with a margin of error and is calculated from the data.

A C% confidence interval for the population proportion p when the random and large counts requirements are satisfied is 

Point estimate margin of error

Ƹ± √Ƹ(1 − Ƹ)

Where z is the critical value for the standard normal curve with C% of its area between –z and +z.

Your interval will look like: ______ < p <________

Confidence Intervals in a 4-Step Process:

1. Clarify what parameter you wish to estimate and at what level of confidence.

2. Make a plan and decide which inference technique is best. Check the circumstances.

3. If the criteria are satisfied, run the calculations.

4. Summarize: Consider your interval in light of the issue.

It is ensured that the sample size is less than 10% of the population size when creating a confidence interval for a population proportion. This requirement is crucial because observations are more likely to be independent when the sample size is smaller than the population size. Calculating the distribution's standard deviation is impossible if this condition is not satisfied. The standard deviation of the distribution cannot be appropriately calculated if this condition is not satisfied. The confidence level will be incorrect if the standard deviation is incorrect. Population parameters are less likely to be found in a confidence interval. As a result, the capture rate will be lower than what the confidence level predicts.

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Answer:

A

Step-by-step explanation:

hope this helps

-SadAlpha-