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3 years ago

5 over 4 multiplied by 12

Mathematics

2 answers:

leonid [27]3 years ago

8 0

Answer:

the answer is 15

Step-by-step explanation:

5/4 x 12 = 15

antiseptic1488 [7]3 years ago

6 0

Step by step Explanation

$\frac{5}{4} \times 12$

$\frac{60}{4}$

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A cereal box filling machine is designed to release an amount of 16 ounces of cereal into each box, and the machine’s manufactur

Paraphin [41]

Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:

$H_0: \mu = 16$

At the alternative hypothesis, it is tested if the mean is different, hence:

$H_1: \mu \neq 16$

<h3>What is the test statistic?</h3>

The test statistic is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the population.

n is the sample size.

The parameters for this problem are:

$\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150$ .

Hence:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}$

z = -2.1

<h3>What is the p-value and the conclusion?</h3>

Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.

Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

More can be learned about the z-distribution at brainly.com/question/16313918

#SPJ1

3 0

1 year ago

A customer enters a store and purchases a pair of slippers for 5 dollars. He pays with a 20 dollar bill. The merchant asks the g

Finger [1]

Answer:

he loses 5 dollars

Step-by-step explanation:

5+20=25

25-$20=5

5 0

3 years ago

"find the reduction formula for the integral" sin^n(18x)

dexar [7]

Let

$I(n,a)=\displaystyle\int\sin^nax\,\mathrm dx$
For demonstration on how to tackle this sort of problem, I'll only work through the case where $n$ is odd. We can write

$\displaystyle\int\sin^nax\,\mathrm dx=\int\sin^{n-2}ax\sin^2ax\,\mathrm dx=\int\sin^{n-2}ax(1-\cos^2ax)\,\mathrm dx$
$\implies I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$

For the remaining integral, we can integrate by parts, taking

$u=\sin^{n-3}ax\implies\mathrm du=a(n-3)\sin^{n-4}ax\cos ax\,\mathrm dx$ $\mathrm dv=\sin ax\cos^2ax\,\mathrm dx\implies v=-\dfrac1{3a}\cos^3ax$

$\implies\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx=-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{a(n-3)}{3a}\int\sin^{n-4}ax\cos^4ax\,\mathrm dx$

For this next integral, we rewrite the integrand

$\sin^{n-4}ax\cos^4ax=\sin^{n-4}ax(1-\sin^2ax)^2=\sin^{n-4}ax-2\sin^{n-2}ax+\sin^nax$
$\implies\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx=I(n-4,a)-2I(n-2,a)+I(n,a)$

So putting everything together, we found

$I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$
$I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)$
$I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$
$\dfrac n3I(n,a)=\dfrac{2n-3}3I(n-2,a)-\dfrac{n-3}3I(n-4,a)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$

$\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax$

7 0

3 years ago

A particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls invol

Phoenix [80]

Answer:

0.1091 or 10.91%

Step-by-step explanation:

We have been given that a particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls involve fax messages and consider a sample of 20 calls. We are asked to find the probability that exactly 6 of the calls involve a fax message.

We will use Bernoulli's trials to solve our given problem.

$P(X=x)=^nC_x\cdot P^x(1-P)^{n-x}$

$P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}$

$P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}$

$P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)$

$P(X=6)=38760\cdot (0.000064)(0.04398046511104)$

$P(X=6)=0.1090997009730$

$P(X=6)\approx 0.1091\\$

Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.

4 0

3 years ago

The lengths of the sides of a triangle are consecutive odd integers. If the perimeter is 1 less than 4 times the shortest side,

Lubov Fominskaja [6]

Let the shortest side be x. Then the other two sides will be x+1 and x+2.

Perimeter = P = sum of the lengths of all three sides = x + (x+1) + (x+2)

This perimeter = 4x -1 (1 less than 4 times the shortest side).

Then x + x + 1 + x + 2 = 4x - 1
or: 3x + 3 = 4x -1 Subtr. 3x from both sides:
3 = x - 1

x=4, x+1=5, and x+2=6

The 3 sides have lengths 4, 5 and 6.

4 0

3 years ago