3y - 21 = 12x
Help please

Answer:

12w + 8d = 100

Step-by-step explanation:

Given:

Price of wall calendars = $12

Price of desk calendars = $8

Total amount pay = $100

Computation:

w = wall calendars

d = desk calendars

So,

Price of wall calendars(w) + Price of desk calendars(d) = Total amount

12w + 8d = 100

Answer:

It will decrease

Step-by-step explanation:

A lower number will lower the average of all the numbers.

Answer: 5

Step-by-step explanation:

Answer:

The distance is 16.28 units

Step-by-step explanation:

Given

See attachment for grid

Required

Distance AC

From the attachment:

\(A = (-7,6)\)

\(C = (5,-5)\)

Distance (d) is calculated using:

\(d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2\)

This gives:

\(d = \sqrt{(-5 - 6)^2 + (5 - (-7))^2\)

\(d = \sqrt{121 + 144\)

\(d = 16.28\)

Answer:

Step-by-step explanation:

f(x) = x^3 - 3x^2 - 28x + 60

x(x^2-3x-28)+60

Factor the inside of the parenthesis

Multiples of 28: (1X28),(2X14),(4X7). 7-4=3, 7 & 4 is the correct multiple.

x(x-7)(x+3)+60

Roots: 0,7,-3,6

Also you can plug your function into Desmos and see where it crosses the x-axis.

Answer:

22.25

Step-by-step explanation:

178/8=22.25

Answer:

22.25

Step-by-step explanation:

178 divided by 8

Answer:

-5

Step-by-step explanation:

the next coordinate that follows the line lands on 2,-5

Answer:

-5.

Step-by-step explanation:

Just follow the X axis to 2 and then go down to where the line intersects the Y axis at -5

The probability that Tessa takes out blue marbles in both draws will be 6.25%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

The number of marbles of different colors stored in a hat is listed below:

8 red marbles

10 green marbles

6 blue

Without looking in the hat, Tessa takes out the marble randomly.

She replaces the marble and then takes out another marble from the hat.

Then the probability that Tessa takes out blue marbles in both draws will be

Total marbles = 6 + 10 + 8 = 24

Then we have

\(\rm P = \dfrac{6}{24} \times \dfrac{6}{24}\\\\P = \dfrac{1}{16}\\\\P = 0.0625\\\\P = 6.25\%\)

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Answer:

4)a. A = π(3²) = 9π

b. h = 10

c. V = 9π(10) = 90π

Answer:

68.9 in^2

Step-by-step explanation:

first lets find the height of the blue triangle

hypotenuse = 15 in

one side is 12 in whereas other has to be find.

take 50 degree as reference angle

using sin rule

sin 50 = opposite/hypotenuse

0.76 = opposite/15

0.766*15 = opposite

11.49 = opposite

area of triangle = base*height/2

=12*11.49/2

=136.88/2

=68.94

=68.9 in^2

Answer:

A = 68.9 in²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) ab sinC ( a, b are 2 sides and C the angle between them )

Here a = 12, b = 15 and C = 50° , then

A = \(\frac{1}{2}\) × 12 × 15 × sin50°

   = 6 × 15 × sin50°

   = 90 × sin50° ≈ 68.9 in² ( to the nearest tenth )

Answer:

The quotient of the given expression is;

Explanation:

Given the expression;

To solve, let us convert the mixed fraction to improper fraction.

Then we can now divide the fractions to get the quotient;

Therefore, the quotient of the given expression is;

Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Henry scored 85, 76, 84, and 69, and let's suppose he scored 'x' marks in the fifth exam.

Average = sum of all marks/total number of exams

  80 =(85 + 76 + 84 + 69 + x)/5

 80 = 314 + x/5

 80 * 5 = 314 + x

 400 = 314 + x

  x = 400 - 314

  x = 86

Hence, Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

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For the utility function U(x, y) = \((x^4)/(y^4)\), we can derive the indifference curve equations by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  \((x^4)/(y^4) = 1\)

 \(x^4 = y^4\)

  Taking the fourth root of both sides, we get:

  x = y

2. When U = 2:

  \((x^4)/(y^4) = 2\)

  \(x^4 = 2y^4\)

  \(x = (2^(1/4)) * y\)

3. When U = 3:

  \((x^4)/(y^4) = 3\)

  \(x^4 = 3y^4\)

  \(x = (3^(1/4)) * y\)

The indifference curves for this utility function are shaped like a rectangular hyperbola, where the ratio of x to y remains constant along each curve.

(b) For the utility function U(x, y) = y - 2x, the indifference curves can be derived by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  y - 2x = 1

  y = 2x + 1

2. When U = 2:

  y - 2x = 2

  y = 2x + 2

3. When U = 3:

  y - 2x = 3

  y = 2x + 3

The indifference curves for this utility function are straight lines with a slope of 2. They have a positive slope, indicating a positive marginal rate of substitution between x and y.

(c) Both utility functions satisfy completeness, transitivity, and monotonicity.

1. Completeness: The preferences are complete if, for any two bundles of goods, the consumer can compare and rank them. Both utility functions provide a ranking of bundles based on their utility values, indicating completeness.

2. Transitivity: Transitivity implies that if bundle A is preferred to bundle B, and bundle B is preferred to bundle C, then bundle A must be preferred to bundle C. Both utility functions satisfy this assumption.

3. Monotonicity: Monotonicity assumes that more is better. If a bundle has higher quantities of both goods compared to another bundle, it should be preferred. Both utility functions satisfy this assumption as well.

The violations of these assumptions would affect the shape and properties of the indifference curves. For example, if completeness is violated, there may be some bundles that cannot be compared or ranked, resulting in incomplete indifference curves.

If transitivity is violated, there may be cycles of preferences, leading to inconsistent indifference curves. If monotonicity is violated, the indifference curves may not have a consistent upward slope. However, in the case of the given utility functions, all assumptions are satisfied, allowing for well-defined indifference curves.

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By Cavalieri's Principle, the volume of that slanted cylinder will be the same volume of a non-slanted cylinder with the same altitude.

so we have a cylinder with a radius of 3 and a height of 7 and a cone hitching a ride on it, with a radius of 3 and a height of 3, so let's simply get the volume of each.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=7\\ r=3 \end{cases}\implies V=\pi (3)^2(7) \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=3\\ r=3 \end{cases}\implies V=\cfrac{\pi (3)^2(3)}{3} \\\\[-0.35em] ~\dotfill\\\\ \pi (3)^2(7)~~ + ~~\cfrac{\pi (3)^2(3)}{3}\implies 63\pi +9\pi \implies 72\pi ~~ \approx ~~ \text{\LARGE 226.19}~in^3\)

The correct answer is 113. To forecast the sales of the ice rink on day 4 using the trend method, we need to determine the trend equation based on the given data points.

The trend equation represents the overall pattern or trend in the sales data and allows us to make predictions for future values.

First, we need to calculate the average increase in sales per day. The average increase is obtained by dividing the total increase in sales over the three days (102 - 80 = 22) by the number of days (3 - 1 = 2). Therefore, the average increase in sales per day is 22 / 2 = 11.

Next, we can use the average increase to forecast the sales for day 4. Starting from the last known sales value (102), we add the average increase to project the sales for the next day. Thus, the forecasted sales for day 4 would be 102 + 11 = 113.

Therefore, the correct answer is 113.

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In the formulas for constructing interval estimates based on sample proportions, the expression Pu (l - Pu) has a maximum value of 1/4.Let's discuss interval estimates based on sample proportions first. A proportion is the number of items in one category divided by the total number of items in all categories.

A sample is a smaller version of a population that we use to gather data and infer characteristics about the population. A confidence interval is a range of values that contains the true population parameter with a certain level of confidence. When we want to estimate the proportion of a population that has a certain characteristic, we use a sample proportion to estimate it.

A formula is used to construct a confidence interval around the sample proportion. The formula for constructing interval estimates based on sample proportions is given by: Lower Bound: P - zα/2 * sqrt(PQ/n)Upper Bound: P + zα/2 * sqrt(PQ/n)Where P is the sample proportion, Q is (1 - P), n is the sample size, and zα/2 is the z-score corresponding to the desired level of confidence. The expression Pu (l - Pu) has a maximum value of 1/4.

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To assess the significance of the observed difference, Andrey performed re-randomization simulations. This technique involves shuffling the observed data randomly between the two groups multiple times and recalculating the difference in success rates

Part 1:

Andrey conducted an observational study. In this study, he observed the outcomes of his calls without interfering or manipulating any variables. He randomly chose a greeting for each call by flipping a coin. By comparing the success rates of the conversations using each greeting, he sought to understand the potential impact of the greeting on selling insurance. Since he did not actively control or manipulate any variables, it falls under the category of an observational study.

Part 2:

Andrey used a randomized comparative experiment to compare the success rates of conversations starting with different greetings. By randomly assigning the greetings to the calls, he ensured that potential confounding variables were evenly distributed between the two groups. By comparing the success rates, he observed a 20 percent difference favoring the "Howdy!" greeting.

To assess the significance of the observed difference, Andrey performed re-randomization simulations. This technique involves shuffling the observed data randomly between the two groups multiple times and recalculating the difference in success rates. By comparing the observed difference with the differences obtained through re-randomization, Andrey determined that the result was statistically significant and not likely due to random chance alone.

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Answer:

Total Surface Area is 20

Step-by-step explanation:

The formula for surface are with slant heigh is

SA = a^2 + 2×a×l

a = Base Edge (this case 2)

I = Slant Height (this case 4

2^2 + 2(2)(4) = 4+16=20

986.58 cubic meters  of water needs to be pumped into the chamber for one lift

To find the amount of water that needs to be pumped into the chamber for one lift, we need to find the volume of the chamber. the volume of the chamber can be calculated using the formula for volume which is

Volume = length × width × height

where

length = 42 m

width = 8.1 m and

height = 2.9 m.

Volume = 42 m × 8.1 m × 2.9 m

Volume = 986.58 cubic meters

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Answer:

\(2 = - ( - 1) + b\)

\(b = 1\)

\(y = - x + 1\)

Answer:

d = 0

Step-by-step explanation:

7.5d = 2.5d

Divided both sides by factors and we get

d = 0

The answer reads "40," is the correct response to the earlier question.

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.

There are data of 9 students and we need to arrange them in ascending order to find our answer.

So, the arrangement looks like the following:

⇒ 25, 35, 45, 50, 60, 80, 90, 95, 100

We are aware that

In all cases, the middle value is the median.

Therefore, it is safe to say that the Median of the aforementioned arrangement is 60.

Hence, Median of the numbers on the left of the median is 60=35+45/2 = 40

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Answer:

It is a function

Step-by-step explanation:

The vertical line test proves that it’s is a function because there is no place on the graph where a vertical line would pass through two points.

Answer: To prove that triangles △ABC and △DEF are similar, we would use the AA Similarity Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In other words, if the corresponding angles of two triangles are congruent, then the triangles are similar.

Step-by-step explanation:

Answer:

380 Stocks per client

Step-by-step explanation:

To solve:

95,000/250 (95,00 shares between 250 of her clients)

= 380 Stocks per client

Hope this helps!

The number of ways to select 9 players for the starting lineup from a team of 15 players  is 4862 ways.

The number of ways to select 9 players for the starting lineup from a team of 15 players can be calculated using the formula for combinations, which is given by:

C(n,k) = n! / (k! (n-k)!)

Where n is the total number of items, k is the number of items being selected, ! means factorial, and C(n,k) represents the number of combinations of k items from n.

Using this formula, the number of ways to select 9 players from a team of 15 players is:

C(15,9) = 15! / (9! (15-9)!) = 15! / (9! 6!) = 4,862

So, there are 4,862 ways to select 9 players for the starting lineup from a team of 15 players.

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Card B is a better deal than Card A when the total annual purchases exceed $4,750. This is because the additional 0.5% cash back on Card B compensates for the $95 annual fee.

To determine when Card B becomes a better deal than Card A, we need to compare the cashback earnings of both cards and take into account the annual fee of Card B.Card A offers a flat 1.5% cash back on every purchase, while Card B offers a higher 2% cash back but also has a $95 annual fee.

To find the break-even point, we need to calculate the difference in cash-back earnings between the two cards and equate it to the annual fee:

2% - 1.5% = 0.5% cash back difference

To cover the $95 annual fee, the total annual purchases must generate an additional 0.5% cash back compared to Card A:

0.5% of x = $95

Solving for x, we find that the total annual purchases must exceed $4,750 for Card B to be a better deal than Card A. At this threshold, the additional 0.5% cash back on Card B compensates for the annual fee, making it a more advantageous option for the cardholder.

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The profit of a perfectly competitive firm is calculated using the production function. The firm should adjust capital employment based on marginal returns and costs to maximize profits.

To calculate the profit, substitute the given values of labor, capital, and input prices into the production function and subtract the total cost from total revenue.

The profit-maximizing quantity of capital can be determined by taking the derivative of the profit function with respect to capital and setting it equal to zero.

This will provide the optimal capital level that maximizes profits. Comparing the profit at the current capital level to the profit at other potential capital levels can indicate whether increasing or decreasing capital employment will result in higher profits.

This decision should be based on evaluating the marginal returns of capital, considering factors such as diminishing returns and the cost of additional capital units.

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