Peyton is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. The equation p=0. 025x+80p=0. 025x+80 represents peyton's total pay on a day on which she sells xx dollars worth of computers. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?.

Answer:

8

Step-by-step explanation:

Plug in the value of k into your expression and solve.

40-4k^3

40-4(2)^3

40-4(8)

40-32

8

Answer:

A. All sides with the equal length.

A rhombus and a rectangle both have opposite sides with equal lengths.

What is a rhombus?

A rhombus is a quadrilateral that has 4 equal sides. However, not a single angle is a right-angle.

What is a rectangle?

A rectangle is a parallelogram with one of is angle is a right-angle.

Here, option: B is correct. A rhombus and a rectangle both have opposite sides with equal lengths.

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The Maclaurin polynomials of orders n=0, 1, 2, 3, and 4 for the function 5/(1+x) are P0(x) = 5, P1(x) = 5 - 5x, P2(x) = 5 - 5x + 5x^2, P3(x) = 5 - 5x + 5x^2 - 5x^3, and P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, respectively.

The Maclaurin polynomials are a way to approximate a function using a polynomial expansion centered at x = 0. The Maclaurin polynomial of order n for a function f(x) is given by Pn(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ... + (f^n(0)/n!)x^n, where f'(0), f''(0), f'''(0), ..., f^n(0) are the derivatives of f(x) evaluated at x = 0.

In this case, the given function is f(x) = 5/(1+x). To find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4, we evaluate the function and its derivatives at x = 0 and substitute them into the general formula for the Maclaurin polynomials.

For n=0, P0(x) = 5, as f(0) = 5.

For n=1, P1(x) = 5 - 5x, as f(0) = 5 and f'(0) = -5.

For n=2, P2(x) = 5 - 5x + 5x^2, as f(0) = 5, f'(0) = -5, and f''(0) = 10.

For n=3, P3(x) = 5 - 5x + 5x^2 - 5x^3, as f(0) = 5, f'(0) = -5, f''(0) = 10, and f'''(0) = -30.

For n=4, P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, as f(0) = 5, f'(0) = -5, f''(0) = 10, f'''(0) = -30, and f^4(0) = 120.

These Maclaurin polynomials provide polynomial approximations of the given function 5/(1+x) for different orders. The higher the order (n), the more terms are included in the polynomial expansion, resulting in a more accurate approximation of the original function around x = 0.

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Answer:

Step-by-step explanation:

Apple Unit Rate = 1.77666666667 ($ for a pound of apples)
Banana Unit Rate = 0.61857142857 ($ for a pound of bananas)

(you can round these numbers)

Here they have provided us with the total price, price of apples, and the pounds of apples and bananas,

First I would find the unit rate of the apples by dividing the price by the amount.

5.33/3 = 1.77666666667 ($ for a pound of apples)

Then we can subtract the total from the total cost for apples to find the total cost of bananas.

9.66-5.33 = 4.33 ($ for 7 pounds of bananas)

Then we can use the same method to find the unit rate of a banana.

4.33/7 = 0.61857142857 ($ for a pound of bananas)

Answer:

Unit Rate Apples = 1.78

Unit Rate Bananas = 0.62

Step-by-step explanation:

Total cost $9.66

Apples cost $5.33

To find the cost for the bananas it is total - apples = bannanas

9.66 - 5.33 = b

b = 4.33

bananas cost $4.33

now to find the unit rate for the apples take apples cost and divide it by how many pounds you got

5.33/3 = 1.7766666667

round up since its a 6 and the unit rate for apples is 1.78

now to find the unit rate for the bananas take bananas cost and divide it by how many pounds you got

4.33/7 = 0.6185714285714

round up since its an 8 and the unit rate for bananas is 0.62

Answer:

amt of 25% solution to mix=6 gal

amt of 40% solution to mix=3 gal

Step-by-step explanation:

let x=amt of 25% solution to mix

9-x=amt of 40% solution to mix

25%x+40%(9-x)=30%*9

.25x+3.6-.40x=2.7

.15x=0.90

x=6

9-x=3

Answer:

x = 62.7°

Step-by-step explanation:

Here given adjacent is 3.9 and hypotenuse is 8.5.

cos(x) = adjacent/hypotenuse

cos(x) = 3.9/8.5

x = \(cos^{-1} \)(3.9/8.5)

x =  62.6887°

x = 62.7° ____if rounded to nearest tenth

Answer:

\(\frac83; \frac{512}{27}; 14\ 222.222 m^3\)

Step-by-step explanation:

In general, if in two similar solids the corrisponding linear measure (same side, same diagonal, etc) are in a ratio of K, surface measures will be in a ratio of \(K^2\) and volumes will be in a ratio of \(K^3\). We know the ratio of the surfaces, so we can say that

\(K^2 = \frac{320}{45} = \frac{64}9\)

1. the ratio of the scale factor can be easily found by the ratio of the surfaces, and it's \(K= \sqrt{K^2} = \sqrt{\frac{64}{9}} = \frac83\)

2. The ratio of the volumes is the cube of the ratio we just found:

\(K^3 = (\frac83)^3 =\frac{512}{27}\)

3. to find the volume of the larger solid you just multiply the ratio we found in the last point by the volume of the smaller solid.

\(V=750m^3\times \frac{512}{27} = \frac{128\ 000}{9} m^3 \approx 14\ 222.222 m^3\)

The number of ways to choose only republicans is 330.                               The number of ways to choose the committee consisting of 1 republican and 6 democrats is 5005.                                                                                       The number of ways to choose the committee consisting of 1 republican and 6 democrats is 55055.                                  

The formula for this is ⁿCm is n!/((n-m)!*m!).

The number of ways to choose only republicans  = ¹¹C₇ = 330

The number of ways to choose one republicans = ¹¹C₁ = 11!/((11–1)!*1!) = 11

The number of ways to choose six democrats is ¹⁵C₆ = 15!/((15–6)!*6!) = 5005.

The number of ways to choose the committee consisting of 1 republican and 6 democrats from 15 Democrats and 11 Republican is :

¹¹C₁ * ¹⁵C₆ = 11!/((11–1)!*1!) * 15!/((15–6)!*6!) = 11 * 5005 = 55055

There are 55055 possible committees consisting of 1 republican and 6 democrats.

The number of ways to choose four republicans = ¹¹C₄ = 11!/((11–4)!*4!) = 330

The number of ways to choose three democrats is ¹⁵C₃ = 15!/((15–3)!*3!) = 455

The number ow ways to choose the committee consisting of 4 republican and 3 democrats from 15 Democrats and 11 Republican is : ¹¹C₄ * ¹⁵C₃ = 330 * 455 = 150150

There are 150150 possible committees consisting of 4 republican and 3 democrats.

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(a) The utility function U(x, y) = x²y is homogeneous of degree 3 because if we multiply both x and y by a positive constant λ, the utility function becomes U(λx, λy) = (λx)²(λy) = λ³x²y. The function exhibits a degree of homogeneity equal to the exponent of λ, which in this case is 3.

(b) The budget constraint can be derived by equating the total expenditure to the agent's income. The price of good 1 is 4, so the expenditure on good 1 is 4x, and the price of good 2 is 2, so the expenditure on good 2 is 2y. Therefore, the budget constraint is given by 4x + 2y = 12. To graph this constraint, we plot x on the horizontal axis and y on the vertical axis. The resulting line has a slope of -2 and intersects the x-axis at x = 3 and the y-axis at y = 6.

(c) To compute the marginal utility of good 1, we take the derivative of the utility function with respect to x, which gives us MU₁(x, y) = 2xy. Similarly, the marginal utility of good 2 is given by MU₂(x, y) = x².

(d) The agent's marginal rate of substitution (MRS) represents the rate at which the agent is willing to trade one good for another while maintaining the same level of utility. It is given by MRS = MU₁/MU₂ = 2xy/(x²) = 2y/x. The slope of the budget constraint is equal to the negative ratio of the prices of the two goods, which is -4/2 = -2.

(e) To derive the agent's optimal consumption bundle, we need to find the combination of x and y that maximizes the agent's utility while satisfying the budget constraint. This occurs at the point where the indifference curve (representing constant utility) is tangent to the budget constraint. In this case, the indifference curve is U(x, y) = x²y, and the optimal consumption bundle can be found by solving the system of equations formed by the utility function and the budget constraint. The resulting bundle will depend on the specific values of x and y obtained. By plotting the bundle on the (x, y) plane along with the budget constraint and an indifference curve, we can visually represent the optimal consumption bundle. The slope of the budget constraint represents the rate at which the agent can trade one good for another while staying within the budget constraint.

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a. The server worked for about 2.5 hours to earn $35

b. the server earn $77 for 5 hours of work

c. the earnings will increase as the number of hours worked increases

This solved by tracing the information from the graph

Tracing the graph the information that coincides with earning $35 is about 2.5 hours

Tracing the graph the information that coincides with earning $77 is about 5 hours

The graph shows that increase in earning will lead to increase n hours of work

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The observation is located to the left of the mean by a distance of 1.2 standard deviations.

The z-score of an observation represents the number of standard deviations the observation is away from the mean.

If the z-score for a particular observation is z = -1.2, this means that the observation is 1.2 standard deviations below the mean.

If the mean is represented by μ and the standard deviation by σ, then we can express this observation as:

observation = μ + (z * σ)

observation = μ + (-1.2 * σ)

This means that the observation is located to the left of the mean by a distance of 1.2 standard deviations.

For example, The z-score represents the number of standard deviations an observation is above or below the mean of the distribution.

In this case, a z-score of -1.2 indicates that the observation is 1.2 standard deviations below the mean height of the group.

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Answer:  \(\textsf{4.86 per hour}\)

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Given: \(\textsf{Initial wage = 4.50, Increase = 8\%}\)

Find:  \(\textsf{New hourly wage}\)

Solution: The first step would be to create an expression to incapsulate the scenario and then we would solve for the new hourly wage and we would get our answer.

Create an expression

Simplify the expression

We were able to determine that the new hourly wage after an increase of 8% would be 4.86 per hour.

Answer:

y = a \(x^{2}\) + b x + c .

Step-by-step explanation:

Also (How to do it!):

We can find the vertex of a quadratic equation with these steps:

Get the equation in the form y = ax2 + bx + c.

Calculate -b / 2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.

Answer:

t = ±√(k - S)

Step-by-step explanation:

S = k – t²

t² + S = k

t² = k - S

t = ±√(k - S)

Answer: the correct answer is -8

Step-by-step explanation:

Substitute the given value of m into the expression:

-4|5 + (-3)|.

Then evaluate using the order of operations:

-4|5 + (-3)|

= -4|2|

= -4(2)

= -8

Substitute the given value of m into the expression:

-4|5 + (-3)|.

Then evaluate using the order of operations:

-4|5 + (-3)|

= -4|2|

= -4(2)

= -8

The first step in evaluating an expression is to substitute the given value of a variable into the expression. Then you can finish evaluating the expression using arithmetic.

A variable is a letter, for example, x, y, or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.

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There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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Using the conditional probability concept, it is found that the statement is true, as in a two-way probability table, we find the probability of each event B considering that each event A has happened.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem, considering the definition of conditional probability given above, the statement is true, as in a two-way probability table, we find the probability of each event B considering that each event A has happened.

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The forecasting technique described is a moving average forecast, which uses a weighted average of past time-series values to predict future values.

The forecasting technique described in the question is called a moving average forecast.

A moving average forecast is a time series forecasting method that calculates the average of a fixed number of past observations to predict the value of the time series in the next period. It uses a weighted average approach where each observation is assigned a weight, and the weights are typically equal.

The process involves selecting a window size, which determines the number of past observations to include in the average. For example, if the window size is set to three, the forecast for the next period will be the average of the three most recent observations. As new observations become available, the oldest observation is dropped, and the newest observation is added to the calculation. This allows the forecast to be continuously updated as new data is obtained.

The moving average forecast is a relatively simple technique that can be useful for identifying trends or patterns in a time series. However, it may not capture more complex relationships or seasonality present in the data. It is often used as a baseline or starting point for more sophisticated forecasting methods.

Other forecasting techniques mentioned in the answer choices include regression analysis, single exponential smoothing, and grassroots forecasting. Regression analysis involves using statistical techniques to model the relationship between a dependent variable and one or more independent variables. Single exponential smoothing is a method that assigns exponentially decreasing weights to past observations. Grassroots forecasting involves obtaining predictions from individuals or groups with domain expertise or local knowledge. These techniques have different underlying principles and may be more appropriate in certain situations depending on the nature of the data and the forecasting problem at hand.

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A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

n² - 12n - 10 = 0

By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;

n² - 12n - 10 + 10 = 0 + 10

n² - 12n = 10

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

n² - 12n + (12/2)² = 10 + (12/2)²

n² - 12n + 36 = 10 + 36

n² - 12n + 36 = 46

(n - 6)² = 46

By taking the square root of each side, we have:

n - 6 = ±46

n = 6 ±46

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Complete Question:

Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?

Add 10 to each side

Add 36 to each side

Factor n² - 12n - 10 = 0

Take the square root of each side

Answer:5 I think

Step-by-step explanation:

75-35=40 40 divided by 8 is 5

Answer:

The answer is 5=x (he is able to buy 5 videogames)

Step-by-step explanation:

First, you need to put this into an equation format with a variable (x) for the videogames. Here is what the equation should look like: 75 = 35 + 8x

75 being the total amount of money he has to spend, 35 being what he had to spend or knows he will spend on the controller, and the 8 is for each videogame. We put an 'x' behind the 8 to signal that we don't know how many games he can buy. So, then we need to solve the equation.

75=35+8x

-35 on both sides

So, 40=8x, then you divide by 8 to get x by itself

5=x

The 'x' in this equation is how many videogames he is able to buy. The way you could check your work is if you plugged 5 back into x. What I mean is this: 35+8(5) needs to equal 75, and it does, so you're good!

2

Step-by-step explanation:

rise/run = 4/2 = 2

Answer: The slope is 2.

Step-by-step explanation:

Hope this helps!!!!

Answer:

hi the answer is A

Step-by-step explanation:

Answer:

the frist one hope I helped

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

Answer:

-1.540

Step-by-step explanation:

H0 : μ = 18

H0 : μ ≠ 18

The sample size, n = 48

Sample mean, xbar = 17

Sample standard deviation, s = 4.5

α = 0.05

The test statistic :

(xbar - μ) ÷ (s/√(n))

(17 - 18) ÷ (4.5 / √48))

-1 ÷ 0.6495190

= -1.5396

= -1.540 (3 decimal places ).

Answer:

B = 82 c = 82

Step-by-step explanation:

These add up to 360 and since 98 + 98 + 82 + 82 = 360 b and c = 82 Hope this helps!

Answer:

9

Step-by-step explanation:

The interquartile range of the given list is 11 oz.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

To find the interquartile range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3) of the data.

To do this, we first need to order the data set from smallest to largest:

8 oz, 8 oz, 12 oz, 16 oz, 16 oz, 18 oz, 20 oz, 20 oz

Next, we find the median of the data set. Since there are 8 data points, the median is the average of the two middle values:

Median = (16 oz + 16 oz)/2 = 16 oz

Now we can find Q1 and Q3. Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.

Lower half: 8 oz, 8 oz, 12 oz, 16 oz

Upper half: 16 oz, 18 oz, 20 oz, 20 oz

Q1 = (8 oz + 8 oz)/2 = 8 oz

Q3 = (18 oz + 20 oz)/2 = 19 oz

Finally, we can calculate the IQR as the difference between Q3 and Q1:

IQR = Q3 - Q1 = 19 oz - 8 oz = 11 oz

Therefore,

The interquartile range of the given list is 11 oz.

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The cost of running the ad for three weeks by Enrique will be $207.

To estimate the overall cost for three weeks, we need the amount for one week. Further, we need the cost for six lines advertisement. So, performing calculation for the cost of advertisement of six lines in one week.

Total cost in one week = charge for first two lines + number of additional lines × cost of each additional line

Keep the values in formula. Out of six lines, the additional will be 4 as (6-2=4).

Total cost in one week = 42 + 4×6.75

Performing multiplication

Total cost in one week = 42 + 27

Performing addition

Total cost in one week = $69

Cost for three weeks = 69×3

Performing multiplication

Cost for three weeks = $207

Thus, Enrique will pay $207 for three weeks.

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Answer:

\( {x ^{2} = \frac{25}{64} } \\ x = \sqrt{ \frac{25}{64} } \\ x = \frac{5}{8} \: \: x = - \frac{5}{8} \)

a) The monthly payment for this fully amortising mortgage is approximately $10,331.25.
b) The monthly payment for this interest-only mortgage is approximately $14,360.33.

c) The new monthly payment after the interest rate increase is approximately $9,090.70.

d) The remaining loan balance is approximately $625,014.72.

A) To calculate the monthly payment of a fully amortising mortgage, we can use the formula:

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

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Total number of payments

For the given question, the loan amount is 81% of $1,175,378, which is $952,622.38. The annual interest rate is 11.6%, so the monthly interest rate would be 11.6% / 12 = 0.9667%. The mortgage term is 21 years, which means a total of 21 * 12 = 252 payments.

Plugging these values into the formula, we can calculate the monthly payment:

M = 952,622.38 * (0.009667 * (1+0.009667)^252) / ((1+0.009667)^252 - 1)

The monthly payment for this fully amortising mortgage is approximately $10,331.25.

B) To calculate the monthly payment of an interest-only mortgage, we can use the formula:

M = P * r

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate

For the given question, the loan amount is 80% of $1,495,863, which is $1,196,690.40. The annual interest rate is 14.4%, so the monthly interest rate would be 14.4% / 12 = 1.2%.

Plugging these values into the formula, we can calculate the monthly payment:

M = 1,196,690.40 * 0.012

The monthly payment for this interest-only mortgage is approximately $14,360.33.

C) To calculate the new monthly payment after an interest rate increase, we can use the same formula as in part A:

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

For the given question, the remaining loan balance is $700,134. The current interest rate is 14.5% per annum, and the loan term is 12 years.

To calculate the new interest rate, we need to add 1% to the current interest rate, which gives us 15.5% per annum, or 15.5% / 12 = 1.2917% as the monthly interest rate.

Plugging these values into the formula, we can calculate the new monthly payment:

M = 700,134 * (0.012917 * (1+0.012917)^144) / ((1+0.012917)^144 - 1)

The new monthly payment after the interest rate increase is approximately $9,090.70.

D) To calculate the remaining loan balance, we can use the formula:

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

Where:
B = Remaining loan balance
P = Loan amount
r = Monthly interest rate
n = Total number of payments
p = Number of payments made

For the given question, the monthly payment is $8,364. The annual interest rate is 12.4%, so the monthly interest rate would be 12.4% / 12 = 1.0333%. The remaining loan term is 10 years, which means a total of 10 * 12 = 120 payments have been made.

Plugging these values into the formula, we can calculate the remaining loan balance:

B = P * ((1+0.010333)^120 - (1+0.010333)^360) / ((1+0.010333)^360 - 1)

The remaining loan balance is approximately $625,014.72.

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