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Kay [80]
3 years ago
10

1.Hannah walked the same number of miles each day for 5 days. Let m represent the total number of miles Hannah walked. Write a l

inear expression for the total number of miles she walked.
2.Jimmy brought 2 books per day to the book drive. Peter brought 4 books per day to the book drive. Let d represent the number of days of the book drive. Write a linear expression to represent the total number of books they brought.
3.Patricia buys clothes that are on sale with a 30% discount. Let c represent the cost of the clothes. Write a linear expression for the cost of the clothes.
4.A family of four had dinner together at a restaurant. Write two expressions for calculating their total bill if they leave a 15% tip. Let c represent the cost of their meal before tipping.
5.Tommy has $40 in his pocket. He sees a pair of pants that cost $37 and wants to buy them. If there's 10% sales tax where Tommy lives, can he afford to buy the pants? Write a linear expression and use it to solve the problem.
6.Add the expressions x + 18 and 3x − 12.
7.Subtract 3x − 4 from 5x + 7.
8.Subtract −4x + 1 from x − 2.
Mathematics
1 answer:
mamaluj [8]3 years ago
8 0

1) Given m represent the total number of miles Hannah walked.

Let us assume Hannah walked x miles each day.

So total number of miles Hannah walked in 5 days is m=5x.

2)Given Jimmy brought 2 books per day and Peter brought 4 books per day.

If d is the number of days the book drive, total number of books they brought

        =total number books brought by Jimmy+ total number of books brought by Peter                                                                          

        = 2d+4d = 6d

3) Given that c represent cost of the clothes.

Then 30% discount = 0.3c

Hence cost of the clothes = c-0.3c = 0.7c

4) Given c represent the cost of their meal before tipping.

And tip is 15% of the cost.

Hence tip = 0.15c

Hence total bill = c+0.15c=1.15c

5) Given that Tommy had 40$ in his pocket.

And pair of pants cost 37$ with 10% sales tax.

Hence cost of pants including sales tax = 37+37*0.1 = 40.1$ >40$

Hence Tommy cannot afford the pants with 40$ in his pocket.

For following problems, we should group the like terms together and then simplify.

6) (x+8)+(3x-12) = (x+3x)+8-12 = 4x-4

7) 5x+7-(3x-4) = 5x+7-3x+4 = (5x-3x)+7+4 = 2x+11

8) (x-2)-(-4x+1)=x-2+4x-1 = (x+4x)-2-1 = 5x-3

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Compute the standard deviation of the following set of data to the nearest whole number:
Klio2033 [76]

Answer:

Step-by-step explanation:

The standard deviation is the square root of the variance, and the variance is found by using the mean. So we will do that first. I will use the population variance as opposed to the sample variance since our set of numbers is small.

The mean: 8 + 12 + 15 + 17 + 18 = 70 and divide that by 5 to get

\bar{x}=14 and use this to find the variance in the formula:

s^2=\frac{\sum(x_i-\bar{x})^2}{n} it is a bit difficult to enter that formula in correctly, but here's how it works mathematically:

s^2=\frac{(8-14)^2+(12-14)^2+(15-14)^2+(17-14)^2+(18-14)^2}{5}

Squaring this ensures us that we don't end up with zero, which would be useless.

s^2=\frac{36+4+1+9+16}{5} so

s^2=13.2 which means that the standard deviation is

s = 3.633

(If you do it with n-1 = 4 in the denominator of the variance, you get a standard deviation of 4.062)

3 0
2 years ago
I have 8 slices of pizza in a box, all 8 are triangle shaped, my perimeter is 43.98 Octagon with each edge 5.49 inches. So, I ne
kondor19780726 [428]

Answer:

1) The area of the circle pizza is approximately 161.64 in.²

2) The area of the octagon shaped pizza is approximately 145.52 square inches

Step-by-step explanation:

The 8 slices of pizza combine to form the composite octagon

The parameters of the pizza are;

The perimeter of the octagon = 43.98 inches

The length of each (outer) edge of the octagon = 5.49 inches

The outer edge of the octagon = The base of the triangle shaped pizza

Let θ represent the vertex angle of the triangle shaped pizza

Therefore, we have;

θ = (The angle at the center point of the pizza)/8 = 360°/8 = 45°

The vertex angle of the triangle shaped pizza, θ = 45°

We note that a triangle shaped pizza is isosceles shaped, therefore, the base angles are given as follows;

The base angles of a piece of pizza = (180° - (angle at vertex))/2

∴ The base angles of a piece of pizza = (180° - 45°)/2 = 67.5°

The length, 'l', of the other sides of the triangle shaped pizza is given by sine rule as follows;

l/(sin 67.5°) = 5.49/(sin(45°)

∴ l = (sin 67.5°) × 5.49/(sin(45°)

l = (sin 67.5°) × 5.49/(sin(45°) ≈ 7.173

The length of the other sides of the triangle shaped pizza, l ≈ 7.173 inches

1) The length of the other sides of the triangle shaped pizza, l = The radius of the circle, r

The area of the circle = π·l²

∴ The area of the circle ≈ π × (7.173 in.)² ≈ 161.64 in.²

2) The area of each triangle piece of pizza is given as follows;

The area of a triangle, A = 1/2×l·b·sin(C)

∴ A = 1/2× 5.49 × 7.173 × sin(67.5°) ≈ 18.19

The area of each triangle piece of pizza, A ≈ 18.19 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 8 × A

∴ TA ≈ 8 × 18.19 inches² ≈ 145.52 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 145.52 inches²

4 0
2 years ago
What is the GCF of 14 and 21
n200080 [17]
Hey there the answer is, 

<span>The Greates Common Factor (GCF) is:   7
</span>

Hope I helped!!!<3

8 0
3 years ago
No rush. I need help on this question. I need an explanation pleaseeeeee. Thank you in advance!
Alina [70]

Answer:

1) 275

2)60

Step-by-step explanation:

1) 55 x 5 =275

2) 12 x 5 = 60

<em><u>Hope it helps!</u></em>

6 0
3 years ago
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