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Harman
2 months ago
10

Mark sold 2 7/8 gallons of lemonade. Regan sold 2/3 as much as Mark. How much did Regan sold in gallons? can you solve it step b

y step please??
Mathematics
1 answer:
Svet_ta [12.7K]2 months ago
0 0

Answer:

Step-by-step explanation:

The expression "twice as much lemonade" indicates that if Mark sold 2 gallons and Regan sold double that amount, Regan would have 2 * 2, equating to 4 gallons, right? The same principle applies to "2/3 as much." Since 2/3 is less than 1, multiplying a quantity by 2/3 results in a value smaller than the original quantity.

If Mark sold 2 7/8 gallons while Regan sold 2/3 of that amount, then Regan's total is:

2\frac{7}{8}*\frac{2}{3}

To simplify calculations, I advise my algebra students to convert the mixed number into an improper fraction before multiplication:

\frac{23}{8}*\frac{2}{3}=\frac{46}{24}=\frac{23}{12}=1\frac{11}{12}

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A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFract
AnnZ [12381]

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

y=\frac{-7}{4}x+\frac{5}{2}

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

y=\frac{3}{4}x-3

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).

5 0
2 months ago
Read 2 more answers
RANDOMLY CHOOSING TWO POTENTIAL CLIENTS
Svet_ta [12734]
Let Jacob, Carol, Geraldo, Meg, Earvin, Dora, Adam, and Sally be denoted as J, C, G, M, E, D, A, and S respectively. In part IV, we need to identify the pairs of potential clients that could potentially be selected. The sample space consists of all possible outcomes, therefore we create a set of all valid pairs, listed as follows: {(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S), (C, G), (C, M), (C, E), (C, D), (C, A), (C, S), (G, M), (G, E), (G, D), (G, A), (G, S), (M, E), (M, D), (M, A), (M, S), (E, D), (E, A), (E, S), (D, A), (D, S), (A, S)}. We can verify the number of elements in the sample space, n(S) is 1+2+3+4+5+6+7=28. This gives us the answer to the first question: What is the count of pairs of potential clients that can be randomly selected from the pool of eight candidates? (Answer: 28.) II) What is the chance of a certain pair being chosen? The chance of picking a specific pair is 1/28, as there’s just one way to select a particular pair out of the 28 possible options. III) What is the probability that the selected pair consists of Jacob and Meg or Geraldo and Sally? The probability of selecting (J, M) or (G, S) is 2 out of 28, which equates to 1/14. Answers: I) 28 II) 1/28 ≈ 0.0357 III) 1/14 ≈ 0.0714 IV) {(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S), (C, G), (C, M), (C, E), (C, D), (C, A), (C, S), (G, M), (G, E), (G, D), (G, A), (G, S), (M, E), (M, D), (M, A), (M, S), (E, D), (E, A), (E, S), (D, A), (D, S), (A, S).}
6 0
1 month ago
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Employee Number
Zina [12379]
The average years of employment is 14

with 73% having worked for at least 10 years.

To find the mean, add up the years of service and divide by the number of employees. The total years worked is 417, so the formula yields:

average years worked = 417/30 = 13.9, rounded to approximately 14 years.

To determine the percentage of employees with ten or more years, count those with 10 or more years and divide by the total employee count, converting the result into a percentage:

(10 years or over)/(total number) = 22/30 = 0.73 repeating, which approximates to 73%.

Using a spreadsheet tool can make this calculation simpler, as it can quickly compute the average and help tally how many employees have worked for 10 years or more.

3 0
25 days ago
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Describe two ways to solve the equation 2(4x-11)=10
AnnZ [12381]
2(4x-11) = 10

Method 1:
Divide both sides by 2:
\frac{2(4x-11)}{2} = \frac{10}{2}

4x-11 = 5

Then add 11 to both sides:

4x-11+11 = 11+5

4x = 16

Finally divide both sides by 4

\frac{4x}{4} = \frac{16}{4}

x = 4

Method 2:

Use the distributive property:

2(4x-11) = 10

2*4x- 2*11 = 10

8x - 22 = 10

Add 22 to both sides:

8x - 22+22 = 10+22

8x = 32

Then divide both sides by 8

\frac{8x}{8} = \frac{32}{8}

x = 4
6 0
1 month ago
What is the cosine ratio for angle F?
babunello [11817]

Response:

option D

Step-by-step reasoning:

Provided in the prompt is a right-angled triangle FGH.

Base of triangle = 12

Height of triangle = 5

Hypotenuse of triangle = 13

To solve the question, we'll apply trigonometric identities.

cos(F) = adjacent / hypotenuse

cos(F) = height / hypotenuse

cos(F) = 5 / 13

Thus, the cosine ratio for angle F is 5 / 13

6 0
25 days ago
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