What is the cost of r grapefruits, if each grapefruit costs s?

(4x³- 4 + 7x) - (2x³ - x - 8) is equivalent to expression 2x³ + 8x + 4. Option B

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)  is equivalent to expression 3x⁴ - 3x² + 5x - 7. Option D

(x² - 2x) (2x + 3) is equivalent to expression 2x³ - x² - 6x. Option A

From the information given, we have that the expressions are;

(4x³- 4 + 7x) - (2x³ - x - 8)

expand the bracket, we have;

4x³ - 4 + 7x - 2x³ + x + 8

collect the like terms, we have;

2x³ + 8x + 4

(-3x² + x⁴ + x) + (2x⁴ - 7+ 4x)

expand the bracket, we have;

-3x² + x⁴ + x + 2x⁴ - 7+ 4x

collect the like terms

3x⁴ - 3x² + 5x - 7

(x² - 2x) (2x + 3)

expand

2x³ + 3x² - 4x² - 6x

2x³ - x² - 6x

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The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

The straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:

Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life

The annual depreciation expense for the equipment is:

Depreciation expense = (cost - residual value) / useful life

Depreciation expense = ($212,000 - $14,000) / 15

Depreciation expense = $12,533.33 per year

The total depreciation expense for the first five years is:

Total depreciation expense = Depreciation expense x number of years

Total depreciation expense = $12,533.33 x 5

Total depreciation expense = $62,666.65

To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:

Book value = Cost - Total depreciation expense

Book value = $212,000 - $62,666.65

Book value = $149,333.35

Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

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Considering the definition of probability, the probability that the next customer will pay with a debit card is \(\frac{12}{139}\).

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases.

\(P(A)=\frac{number of favorable events}{ total number of possible events}\)

The probability of event A can only be a number between 0 and 1; although it can also be written as a percentage.

In this case, you know:

Replacing in the definition of probability:

\(P(A)=\frac{12}{ 139}\)

Finally, the probability that the next customer will pay with a debit card is \(\frac{12}{139}\).

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The value of x is 2.

Triangles are one of the most basic shapes in geometry and have a wide range of applications in mathematics, science, and engineering.

The three sides of a triangle are called edges, and the three angles are called vertices. Triangles can be classified based on the lengths of their sides and the measures of their angles.

Since DE is parallel to AC, we can use the intercept theorem to relate the lengths of the corresponding sides of triangles ABD and CBE.

In triangle ABD and CBE, we have:

AD/CE = AB/BC

Substituting the given values, we get:

2/1 = (x+2)/4

Cross-multiplying, we get:

8 = 2(x+2)

Simplifying, we get:

x+2 = 4

x = 2

Therefore, the value of DB is 2.

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Answer:

8

Step-by-step explanation:

\( a = 1 - \sqrt{2} \)

\( (a - \dfrac{1}{a})^3 = \)

\( = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 \)

\( = (\dfrac{a^2 - 1}{a})^3 \)

\( = (\dfrac{(a + 1)(a - 1)}{a})^3 \)

\( = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 \)

\(= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3\)

\(= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3\)

\(= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3\)

\(= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3\)

\( = 2^3 \)

\( = 8 \)

Answer:

(2,3)

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

First, find the equation of the line:

put it in the form y = mx + b where m is the slope and b is the y-intercept

You already have m = 2, so y = 2x + b.

Then, since you know (1, 3) is a solution so you can plug x = 1 and y = 3 into the equation to find out what b is.

3 = 2 * 1 + b

3 = 2 + b

1 = b

This means the equation of the line is y = 2x + 1.

Then, since you're trying to find out what y is when x = 2, you can plug in x = 2 into the equation:

y = 2 * 2 + 1

y = 4 + 1

y = 5

5 is the answer

Answer:

no se ve bien no puedes subirla en foto?

Step-by-step explanation:

Answer: 2nd option "The degree of rotation is the angle measure that the object will be rotated."

Answer: it’s (4), I took the test too so I know it’s most likely right.

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer:

40%

Step-by-step explanation:

40÷ 100=0.4

0.4×20=8

8+20=28

another way

28-20=8

8÷20=0.4

0.4×100=40

40%

The parallelogram ABCD with vertices A(-8, 5), B(-7, 8), C(-1,6), and D(-2, 3) is a rectangle as two sides are equal, so option A is correct.

A unique kind of quadrilateral created by parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but for it to be a parallelogram, its opposite sides must be parallel.

Given data:

The parallelogram ABCD with vertices A(-8, 5), B(-7, 8), C(-1,6), and D(-2, 3),

Calculate the distance of sides as shown below

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

AB = \(\sqrt{[-7-(-8)]^2 + (8-5)^2}\)

AB =  √(1² + 3²)

AB = √10

Calculate

BC = \(\sqrt{[-1-(-7)]^2+(6 - 8)^2}\)

BC = √(36 + 4)

BC = √40 or 2√10

Similarly,

CD = √10

And AD = 2√10

Here AB = CD and BC = AD, opposite sides equal, so it is a rectangle. Therefore, the parallelogram ABCD with vertices A(-8, 5), B(-7, 8), C(-1,6), and D(-2, 3) is a rectangle as two sides are equal.

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Answer:

y - 1 = (1/2)(x - 2)^2

Step-by-step explanation:

The appropriate equation for such a parabola has the form

y - k = a(x - h)^2, where (h, k) is the vertex:

y - 1 = a(x - 2)^2.  Since the y-intercept is (0, 3), we substitute 3 for y and 0 for x, obtaining:

3 - 1 = a(0 - 2)^2, or

2 = a(4).  Therefore, a = 1/2, and the equation of this parabola is:

y - 1 = (1/2)(x - 2)^2

B' would now have the following updated coordinates: (-6, 6)

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

If ABCD is dilated by a factor of 3

Then To enlarge this by a factor of three...

-2 * 3 = -6

2 * 3 = 6

B' would now have the following updated coordinates:

(-6, 6)

There are a few things to be aware of:

- A "scale factor" is three.

Hence B' would now have the following updated coordinates: (-6, 6)

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Answer:

25

Step-by-step explanation:

x = √7²+24² = √625 = 25

Answer:

37.5% probability of exactly 1 boy out of three​ children

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

b for boy, g for girl

b - b - b

b - b - g

b - g - b

b - g - g

g - b - b

g - b - g

g - g - b

g - g - g

There are 8 possible outcomes.

Exactly one boy:

b - g - g

g - b - g

g - g - b

3 outcomes

What is the probability of exactly 1 boy out of three​ children?

3/8 = 0.375

37.5% probability of exactly 1 boy out of three​ children

There is 37.5% probability of exactly 1 boy out of three​ children.

Given that,

To the right are the outcomes that are possible when a couple has three children.

Assume that boys and girls are equally​ likely, so that the eight simple events are equally likely.

We have to find,

The probability that when a couple has three​ children, there is exactly 1 boy.

According to the question,

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

The b denote the boy,

And g denote the girl

Therefore,

b - b - b

b - b - g

b - g - b

b - g - g

g - b - b

g - b - g

g - g - b

g - g - g

There are 8 possible outcomes.

The probability that when a couple has three​ children, there is exactly 1 boy.

b - g - g

g - b - g

g - g - b

There are 3 outcomes for exactly 1 boy.

Therefore,

The probability of exactly 1 boy out of three​ children is given by,

\(= \dfrac{ 3 \ outcomes\ for \exacatly\ 1 \ boy}{total \ possible \ outcomes }\\\\= \dfrac{3}{8}\\\\= 0.375\\\\= 37.5\ percent\)

 Hence, There is 37.5% probability of exactly 1 boy out of three​ children.

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Answer:

2 1/6

Step-by-step explanation:

2 1/2 - 1/3 = 2 1/6

Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.

Let's define the variables:

x = cost of the washer.

y = cost of the dryer.

We know that the cost combined is $1000, then:

x  + y = 1000

And the washer cost 3 times the cost of the dryer, then we will get:

x = 3y

So we have a system of equations, we can replace the second equation into the first one, so we will get:

3y + y = 1000

4y = 1000

y = 1000/4

y = 250

The cost of the washer is:

x = 3*250 = 750

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Answer:

decagon (10-sided polygon)

Step-by-step explanation:

A regular polygon has a minimum rotation of 360/n degrees about its center, where n is the number of sides in the polygon.

Therefore, the regular polygon with a minimum rotation of 36 degrees about its center is a polygon with 360/36 = 10 sides, or a decagon.

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Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Answer:

27a^3b^3 + 8b^3

Step-by-step explanation:

because

The first question:

"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"

Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.

To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:

P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.

Therefore, the probability of landing on both region three and region six is 1/64.

The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.

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The second question:

"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"

To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.

The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.

The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.

To find the probability of either event occurring, we add the probabilities together:

P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.

Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.

The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.

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The third question:

"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"

To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.

The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.

The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.

To find the probability of either event occurring, we add the probabilities together:

P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.

Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.

The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.

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The fourth question:

"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"

The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.

The probability of rolling an even number on the die is 3

/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:

P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.

Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.

The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: \(7\frac{2}{3} units^{3}\)

Step-by-step explanation:

Volume=lwh

Volume=23/4(4/3)

Volume=92/12

Volume=7 8/12

Volume=7 2/3

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.

V7 * V2 = V(7 * 2) = V14

Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.

This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.

In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

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The Distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.

The distance between two points in a coordinate plane. The distance formula is based on the Pythagorean theorem and calculates the straight-line distance between two points.

The coordinates of the first point as (x1, y1) = (4, -2) and the coordinates of the second point as (x2, y2) = (7, -9).

The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values:

d = sqrt((7 - 4)^2 + (-9 - (-2))^2)

d = sqrt((3)^2 + (-7)^2)

d = sqrt(9 + 49)

d = sqrt(58)

Hence, the distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.

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The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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