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4 years ago

Which fraction is closest to zero? 3/8 4/12 2/6 1/4

Mathematics

2 answers:

GalinKa [24]4 years ago

5 0

Ok I hope this helps

3/8=38%
4/12=33%
2/6=33%
1/4=25%

So the answer is 1/4

Vesnalui [34]4 years ago

3 0

1/4 is the fraction closest to zero.

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If a:b=5:6and b:c=3:8 find a:b:c?

mr_godi [17]

Answer:

(a x b ) : (b x b ) : (b x c)

5x3 : 6x3 : 6 x 8

Step-by-step explanation:

15:18:48

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2 years ago

What is 3 times the sum of x plus 2 is less than 10 as an inequality?

erica [24]

3(x+2) < 10 //// that should be right!!

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3 years ago

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 Cell Phone company sells cellular phones and airtime in a State. At a recent meeting, the marketing manager states that the av

GarryVolchara [31]

Answer:

The null hypothesis is rejected.

There is enough evidence to support the claim that the average age of the customers differs from 40 years.

The sample does not support the manager claim (the average age seems to differ from 40 years).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The manager claims that the average age of customers is 40 years. As this is an equality, we will test if the average age differs from 40. If the null hypothesis failed to be rejected, the claim of the manager is right.

Then, the claim is that the average age of the customers differs from 40 years.

Then, the null and alternative hypothesis are:

$H_0: \mu=40\\\\H_a:\mu\neq 40$