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Shtirlitz [24]
2 years ago
10

What is the value of x? enter your answer in the box x= ​

Mathematics
1 answer:
xz_007 [3.2K]2 years ago
4 0

Answer:

x = 20

Step-by-step explanation:

Given

The attached triangle

Required

Find x

The value of x will be found using the following equivalent ratios:

11 : 121 = 10 : 5x + 10

Convert to fraction

\frac{11}{121} = \frac{10}{5x + 10}

Factorize:

\frac{11}{121} = \frac{5*2}{5(x + 2)}

Simplify

\frac{1}{11} = \frac{2}{x + 2}

Cross Multiply

1 * (x + 2) = 2 * 11

x + 2 = 22

Collect Like Terms

x = 22-2

x = 20

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Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205
Crank

Answer:

P(205-0.3=204.7

z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778

z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778

So we can find this probability:

P(-1.778

And then since the interest is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches using the complement rule we got:

P = 1-0.9243 = 0.0757

Step-by-step explanation:

Let X the random variable that represent the diamters of interest for this case, and for this case we know the following info

Where \mu=205 and \sigma=1.5

We can begin finding this probability this probability

P(205-0.3=204.7

For this case they select a sample of n=79>30, so then we have enough evidence to use the central limit theorem and the distirbution for the sample mean can be approximated with:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

And we can find the z scores for each limit and we got:

z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778

z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778

So we can find this probability:

P(-1.778

And then since the interest is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches using the complement rule we got:

P = 1-0.9243 = 0.0757

6 0
3 years ago
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