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Usimov [2.4K]
3 years ago
7

In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation. Aft

er an 8-week exercise program Grace lost 45 pounds. She now weighs 122 pounds. How much did Grace weigh before she started her exercise program?
Mathematics
1 answer:
notka56 [123]3 years ago
7 0

Answer:

Grace weighed 167 pounds before she started her exercise program.

Step-by-step explanation:

Given,

Weight lost by Grace = 45 pounds

Weight of Grace after exercise weeks = 122 pounds

Let,

x represents the weight of Grace before she started the exercise program.

Loss means subtraction, therefore,

We will subtract the lost weight from original weight.

Original weight - Weight lost = Weight after exercise weeks

x - 45 = 122

Adding 45 on both sides

x - 45+ 45= 122+45

x=167   pounds

Grace weighed 167 pounds before she started her exercise program.

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Answer:

The homework  grade, to the nearest integer, for a student with a test grade of 68 is 69.

Step-by-step explanation:

The general form of the linear regression equation is:

y=a+bx

Here,

<em>y</em> = dependent variable = test grade

<em>x</em> = independent variable = homework grade

<em>a</em> = intercept

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a=\frac{\sum Y\cdot \sum X^{2}-\sum X\cdot\sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}\\\\=\frac{(592\times 44909)-(591\times45227)}{(8\times44909)-(591)^{2}}\\\\=-14.316                b=\frac{n\cdot \sum XY-\sum X\cdot\sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}\\\\=\frac{(8\times 45227)-(591\592)}{(8\times44909)-(591)^{2}}\\\\=1.195

The linear regression equation that represents the set of data is:

y=-14.316+1.195x

Compute the value of <em>x</em> for <em>y</em> = 68 as follows:

y=-14.316+1.195x

68=-14.316+1.195x\\1.195x=68+14.316\\1.195x=82.316\\x=68.884\\x\approx 69

Thus, the homework  grade, to the nearest integer, for a student with a test grade of 68 is 69.

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Kyla alternates between walking and jogging on an 11-mile trail. Her walking speed is 4 mi/h, and her jogging speed is 6 mi/h. K
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Answer:

Kyla walked 2 miles and jogged 9 miles

Step-by-step explanation:

Let the distance Kyla walked be x

and the distance Kyla jogged be y

Since the trail is 11-mile long, then

x + y = 11

Now, from the question,

Her walking speed is 4 mi/h and her jogging speed is 6 mi/h

Let the time spent to walk be t₁ and the time spent to jog be t₂

From

Distance = Speed × Time

Then, the distance walked x is

x = 4 mi/h × t₁

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y = 6 mi/h × t₂

From the question, Kyla takes 2 hours to go from the beginning to the end of the trail, that is

t₁ + t₂ = 2 hours

∴t₁ = 2 - t₂

Since

x + y = 11, then we can write that

(4 mi/h × t₁) + (6 mi/h × t₂) = 11

But t₁ = 2 - t₂

Then,

(4 mi/h × t₁) + (6 mi/h × t₂) = 11; becomes

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2t₂ = 11 - 8

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t₂ = 3/2

t₂ = 1.5 hours

This is the time spent to jog

Then, from t₁ = 2 - t₂

t₁ = 2 - 1.5

t₁ = 0.5 hour

This is the time spent to walk

Now, For the distance Kyla walked, x

x = 4 mi/h × t₁

x = 4 mi/h × 0.5

x = 2 miles

Hence, she walked 2 miles

and for the distance Kyla jogged, y

y = 6 mi/h × t₂

y = 6 mi/h × 1.5

y = 9 miles

Hence, she jogged 9 miles

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