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Once again, plot the points (-2, 5), (0, -4), and (5, 3) to find the distance and the midpoint.

The expression is :  [tex](2x-3y)^5 = 32x^5-240x^4y+720x^3y^2-1080x^2y^3+810xy^4-243y^5[/tex].

To expand the expression [tex](2x-3y)^5[/tex], we can use the binomial theorem or Pascal's triangle. However, using the binomial theorem can be time-consuming for large exponents. Instead, we can use Pascal's triangle to determine the coefficients of each term.

First, write out the coefficients of [tex](2x)^5[/tex] and [tex](-3y)^5[/tex] separately. Using Pascal's triangle, we get 1, 5, 10, 10, 5, and 1 for [tex](2x)^5[/tex] and 1, -3, 3, -1, 0, and 0 for [tex](-3y)^5[/tex].

Next, multiply each coefficient by its corresponding term and combine like terms. The resulting expanded form is [tex]32x^5-240x^4y+720x^3y^2-1080x^2y^3+810xy^4-243y^5[/tex].
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The simplified form of 13¹/3 + 2¹/3 - 10/2 is a fraction 64/6 that can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2 the final answer is 32/3.

Given

13¹/3+2¹/3-10/2​

Required simplified it =?

First, we have simplified both constants separately

13¹/3 = (3 * 13 + 1) / 3 = 40/3

2¹/3 = (3 * 2 + 1) / 3 = 7/3

now the expression become = 40/3 + 7/3 - 10/2

now taking LCM of 3 and 2 which is 6.

                                                = 80/6 + 14/6 - 30/6

 now we have to simplify this fraction by dividing by 2 = 64/6

Therefore, the simplified form of 13¹/3 + 2¹/3 - 10/2 is 32/3.

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The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.

According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.

Ratio of sauce to oregano:

6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano

Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:

8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano

Therefore, for 8 servings, we would need:

8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce

Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

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Answer:14

Step-by-step explanation: just trust me

The number of boxes that the librarian would need, given the capacity, would be 5 boxes.

In the given scenario, the librarian is tasked with the responsibility of packing 28 books into boxes. To determine the number of boxes required, we consider that each box has the capacity to hold 6 books.

Dividing the total number of books by the capacity of each box allows us to ascertain the number of complete boxes needed.

The number of boxes needed is therefore :

= 28 / 6

= 4. 66

= 5 boxes

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Number of car sold are 98.

Number of trucks sold are 66.

Given,

Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .

Let number of cars sold are x.

Let number of cars sold of y .

Now,

For dealership 1 equation will be,

x + y = 164  ......(1)

For dealership 2 equation will be,

As the cars are sold twice and trucks are sold half .

2x + y/2 = 229......(2)

Solving 1 and 2,

y = 66

x = 98

Thus number of car sold are 98.

Thus number of trucks sold are 66.

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The number of elements in the Q complement set, n(Q') is 7

From the question, we are to determine the number of elements that are in the given set.

To find n(Q'),

First, we will determine the elements in Q'

NOTE: Q' means Q complement, that is, the elements that are present in the universal set but not in Q

The universal set is

ξ = {numbers between 3 and 19}

That is,

ξ = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

From the given information,

Q = {3, 5, 6, 7, 9, 10, 12, 13, 17, 18}

Therefore,

Q' = {4, 8, 11, 14, 15, 16, 19}

The value of n(Q') is the number of elements in the q' set

That is,

n(Q') = 7

Hence, n(Q') = 7

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The producer surplus is $1365.77. Therefore, the correct answer is option B.

The producer surplus is the difference between the total revenue and the cost of producing the good. We can use the following formula to calculate the producer surplus:

Producer surplus = Total revenue - Cost of producing the good

Total revenue = Selling price x Quantity

Therefore, the producer surplus for the given supply curve is calculated as:

Producer surplus = (250 x z) - (180 + 0.3x³)

Substituting z = 250 in the equation, we get:

Producer surplus = (250 x 250) - (180 + 0.3 x 250³)

= 62500 - (180 + 1827.76)

= 62500 - 2007.76

= 60592.24

The producer surplus is $1365.77. Therefore, the correct answer is option B.

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Answer:

On the graph,

1 square Unit =25 Square Feet

1 Unit =5 feet.

Therefore:

Length of the diagonal of square C

Step-by-step explanation:

Using a graphing calculator to sketch the graph of the quadratic equation, -x² - 15x - 56, the x-intercepts are

d. ( 7, 0); ( 8, 0)

Quadratic equations are algebraic equations of the second degree, which means they involve variables raised to the power of two (squared terms).

A general quadratic equation can be written in the form:

ax² + bx + c = 0

The graph of quadratic equation traces same path as a parabola, the given equation -x² - 15x - 56 when graphed has x intercepts at ( 7, 0); ( 8, 0).

The graph is attached

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The amplitude of the function graphed will be 3.

Since, We know that,

The amplitude of a function is the amount by which the graph of the function travels above and below its midline, i.e. it is the height from the mean value of the function to its maximum or minimum.

We have,

A graph,

Here, The highest value = 5

Lowest value = -1

So,

From the definition mentioned above,

Amplitude = (5 + |- 1|) / 2

                = 6 / 2

                = 3

We get,

Amplitude = 3

Hence, we can say that the amplitude of the function graphed will be 3.

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The amount of the isotope left after 36 hours is 22.5 mg

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.

Half life is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay .

The half life of the isotope is 9hrs this means that it will take 9hrs for half of the atom nuclei of the isotope to disintegrate.

Therefore;

1/2 = 9hrs

1/4 = 18hrs

1/8 = 27 hrs

1/16 = 36 hours

This means that 1/16 of the original atom will be left after 36 hours

= 1/16 × 360

= 360/16

= 22.5 mg

therefore 22.5 mg will be left after 36 hours

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The Probability that none of the compressors in a sample of 7 are defective is (9/16)^7.

1. To find the probability that all compressors in a sample of 7 are defective, we need to calculate the probability of selecting a defective compressor for each pick and multiply them together.

In this case, there are 7 defective compressors in a shipment of 16. So, for the first pick, the probability of selecting a defective compressor is 7/16. Since there are no replacements (each pick is independent), for the second pick, the probability remains the same: 7/16. We continue this process for all 7 picks.

P(all defective) = (7/16) * (7/16) * (7/16) * (7/16) * (7/16) * (7/16) * (7/16) = (7/16)^7

Therefore, the probability that all compressors in a sample of 7 are defective is (7/16)^7.

2. To find the probability that none of the compressors in a sample of 7 are defective, we need to calculate the probability of selecting a non-defective compressor for each pick and multiply them together.

In this case, there are 9 non-defective compressors in a shipment of 16. So, for the first pick, the probability of selecting a non-defective compressor is 9/16. Since there are no replacements, for the second pick, the probability remains the same: 9/16. We continue this process for all 7 picks.

P(none defective) = (9/16) * (9/16) * (9/16) * (9/16) * (9/16) * (9/16) * (9/16) = (9/16)^7

Therefore, the probability that none of the compressors in a sample of 7 are defective is (9/16)^7.

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Answer: 6765kg

Step-by-step explanation:

55*123=6765

Answer:6,765

Step-by-step explanation:

just multiply 123 by 55 to get 6,765

An initial investment of $5,951.71 is needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly.

To determine the amount of money needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly, we need to use the formula for compound interest.

The formula is A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

Using the given information, we can plug in the values and solve for P. A = $7,000, r = 0.025, n = 4, and t = 4.

A = P(1+r/n)^(nt)

A = P(1+0.025)^4
$7,000 = P(1+0.025/4)^(4*4)
$7,000 = P(1.00625)^16
P = $5,951.71
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Answer:

Step-by-step explanation:

The answer is “8”.

hope it helps!

Given that a country in Africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. To do so, local wildlife authorities put tags on 20 giraffes and release them. Later, they corral 570 giraffes; among these giraffes, 15 are tagged. So, the best estimate for the giraffe population is 760.

Now, we need to find the best estimate for the giraffe population.To find the estimated number of giraffes, we can use the concept of proportion.

Here, we can create the proportion of the number of tagged giraffes to the total number of giraffes as follows:20/x = 15/570where x is the estimated number of giraffes in the area.

Cross multiply the above equation to obtain: x × 15 = 20 × 570x = (20 × 570) / 15= 760Approximately 760 giraffes are estimated to be in the area.Answer: The best estimate for the giraffe population is 760.

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Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Where the above graph is given,  the correct answer is g(x) = (x + 9)².

Based on the information given,the function g(x)   is the translation of f(x) to the left by 2 units.

Since the vertex of f(x ) is at (-7, 0),the   vertex of g (x) will be at (- 7 - 2, 0), which simplifies to (- 9, 0).

 Therefore,the correct   answer is g(x) = (x + 9)². See the attached graph.

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To solve the inequality 2.5x - 10 > 45

What is Inequality?

To determine which scenarios could be represented by the inequality 2.5x - 10 > 45, we need to solve the inequality for x and analyze its meaning.

Let's solve the inequality step by step:

2.5x - 10 > 45

Add 10 to both sides:

2.5x - 10 + 10 > 45 + 10

2.5x > 55

Now, divide both sides by 2.5:

(2.5x)/2.5 > 55/2.5

x > 22

The solution to the inequality is x > 22. This means that any value of x greater than 22 would satisfy the inequality.

In terms of scenarios, here are a few examples:

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1. The length of side AC is 21.5 units.

2. The magnitude of ∠R is 36.9°

3. The length of side ML is 7.5 units.

3. The length of side JK is 8.5 units.

In order to determine the length of side AC, we would apply sine trigonometric ratio because the given side lengths represent the opposite side and hypotenuse of a right-angled triangle;

sin(θ) = Opp/Hyp

Where:

By substituting the given side lengths, we have:

sin(34) = 12/x

x = 12/sin(34)

x = 21.5 units.

Question 2.

For the magnitude of ∠R, we have:

TanR = opposite side/adjacent side

TanR = 6/8

∠R = tan⁻¹(0.75)

∠R = 36.9°.

Question 3.

For side length ML, we have the following:

Tan28 = 4/ML

ML = 4/tan28

ML = 7.5 units.

Question 4.

For side length JK, we have the following:

cos(θ) = Adjacent side/Hypotenuse

cos(58) = JK/16

JK = 16cos(58)

JK = 8.5 units.

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Answer:

C is 60 degrees

Step-by-step explanation:

The angles of a triangle always add to 180 degrees.

Sot add A and B. Which is 120 degrees.

Then subtract that from 180 to get C.

180 - 120 = 60

Angle C is 60 degrees

The label given to the original cost of buying and installing the existing floor coverings in the analysis used in deciding whether to do the remodel is called sunk cost. Sunk cost refers to a cost that has already been incurred and cannot be recovered, regardless of the decision made.

In this case, the cost of buying and installing the existing floor coverings is a sunk cost because it has already been paid for and cannot be recovered even if the remodel is not done.

When considering whether to do the remodel, Lovelace should not take the sunk cost into account as it is irrelevant to the decision-making process.

Instead, Lovelace should focus on the potential benefits and costs of the remodel, including the increased daily rental fees that may result from the remodel and the cost of removing and replacing all the existing floor coverings.

By analyzing the incremental costs and benefits of the remodel, Lovelace can make an informed decision that maximizes its profits and enhances the overall value of its luxury resort rental property.

In conclusion, when analyzing the potential benefits and costs of a remodel, it is essential to consider the sunk cost associated with the existing floor coverings. By understanding the concept of sunk cost, Lovelace can make a rational decision that considers only the relevant costs and benefits of the remodel.

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The shape of the distribution is negatively skewed, due to the larger difference of the median and Q1 then of Q3 and the median.

A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:

The left side of the box in this problem is greater than the right side of the box, hence we have a negatively skewed distribution.

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Answer:

1unit scale on map is equal to 100.16 km in real life

Step-by-step explanation:

since in map 12.cm =1262km in real life

1cm=(1262/12.6) km

therefore it gives us 100.158km which is approximately 100.16 km .

Joe should arrive earlier to the game, engage in a dynamic warm-up routine, and include regular hamstring strengthening and flexibility exercises in his workout regimen to reduce the risk of straining his hamstring tendon during softball games.

A practical recommendation for Joe, the weekend warrior, who keeps straining his hamstring tendon during softball games, would be to incorporate a more comprehensive warm-up routine before the game.

As an ACSM-EP (American College of Sports Medicine - Exercise Physiologist), I would suggest that Joe arrive at least 20-30 minutes prior to the game and follow a dynamic warm-up routine.

This routine should include exercises that engage the whole body, especially focusing on the hamstrings and surrounding muscles. Some examples are leg swings, high knees, butt kicks, and dynamic stretches such as walking lunges.

These movements not only increase blood flow and muscle temperature, but also improve flexibility and joint mobility, reducing the risk of injury during the game.

Additionally, Joe should consider incorporating regular hamstring strengthening and flexibility exercises into his overall fitness routine, as this can help prevent future strains.

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Therefore, the constant of variation for this seesaw is 70/x, where x is the weight of the other child in pounds.

To find the constant of variation for the seesaw, we need to use the formula for direct variation which is y = kx, where y is the weight on one side of the seesaw, x is the weight on the other side of the seesaw, and k is the constant of variation.

We can use the weight of the daughter, which is 70 pounds, and the weight of the other child, which we do not know, as our x and y values.

Let the weight of the other child be x pounds. Then we can set up the equation as follows:

70 = kx

To solve for k, we need to isolate it on one side of the equation.

We can do this by dividing both sides by

x:70/x = k

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According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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Answer:

the way in which factors are grouped in a multiplication problem does not change the product.

Step-by-step explanation:

The probability that it is raining if the flight has been delayed is approximately 0.111 or 11.1% when rounded to the nearest thousandth.

To solve this problem, we can use Bayes states:

P(A|B) = (P(B|A) × P(A)) / P(B)

Let's define the events:

A = It is raining

B = The flight has been delayed

Given information:

P(A) = 0.07 (probability that it will rain)

P(B) = 0.18 (probability that the flight will be delayed)

P(~A ∩ ~B) = 0.8 (probability that it will not rain and the flight will leave on time)

We want to find P(A|B), the probability that it is raining if the flight has been delayed.

To calculate P(B|A), the probability that the flight is delayed given that it is raining, we can use the formula for conditional probability:

P(B|A) = P(A ∩ B) / P(A)

From the given information, we can see that P(A ∩ B) is not directly given. However, we can use the complement rule to rewrite P(A ∩ B) as:

P(A ∩ B) = 1 - P(~A ∩ ~B)

Substituting the values, we get:

P(A ∩ B) = 1 - 0.8

= 0.2

Now, we can calculate P(B|A):

P(B|A) = (P(A ∩ B)) / P(A)

= 0.2 / 0.07

≈ 2.857

Finally, we can use Bayes to calculate P(A|B):

P(A|B) = (P(B|A) × P(A)) / P(B)

= (2.857 × 0.07) / 0.18

≈ 1.112

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