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3 years ago

10

Manuel bought 9 pounds of apples. He has eaten 3/4 of a pound so far and has $15 worth of apples left. Write and solve an equati

on to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?

1 answer:

mash [69]3 years ago

8 0

We can form a ratio equation. the ratio would be the amount of original apples to the cost versus the new amount of apples and new cost. we know all amounts except original cost.

pounds/cost = new pounds/new cost

9/x = (3/4)9 / 15

9/x = (27/4) / 15

9/x = 27/60

9/x = 9/20

cross multiply

9x = 180
x = 20

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Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

A research team is testing whether a fuel aditive increases a car's gas mileage. The maker of the additive claims that the addit

Thepotemich [5.8K]

Answer:

Yes there is sufficient evidence to reject the company's evidence

Step-by-step explanation:

From the question we are told that

The sample size is n = 25

The mean is $\= x = 5.3 \ mpg$

The standard deviation is $\sigma = 1.8 \ mpg$

The z-score is z = -1.94

The null hypothesis is $H_o : \mu = 6 \ mpg$

The alternative hypothesis is $H_a : \mu \ne 6$

Generally the p-value is mathematically evaluated as

$p-value = 2 * P( Z$

From the z table the area under the normal curve to the left corresponding to -1.94 is

$P( Z$

=> $p-value = 2 * 0.02619$

=> $p-value = 0.052$

Let assume the level of significance is $\alpha = 0.05$

Hence the $p-value > \alpha$ this mean that

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to reject the company's evidence

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3 years ago

Sain has a student loan for $22,990. This loan has a simple interest rate of 5%. What is the amount of interest Sain will be cha

djyliett [7]

Answer:

3448.5

Step-by-step explanation:

I=PRT

I=22990×0.05×3

=$3448.5

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3 years ago

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Answer:

1 1/4 or 5/4

Step-by-step explanation:

Divide 5 by 4

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