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DaniilM [7]
3 years ago
9

Find the value of x rounded to the nearest tenth

Mathematics
2 answers:
just olya [345]3 years ago
7 0

Answer:  The correct option is (C) 12.5 units.

Step-by-step explanation:  We are given to find the value of x rounded to the nearest tenth.

From the figure, we see a right-angled triangle with one acute angle measuring 28°.

With respect to the angle with measure 28°, the length of the base is 11 units and the length of the hypotenuse is x units.

So, from trigonometric ratios, we have

\cos28^\circ=\dfrac{11}{x}\\\\\\\Rightarrow 0.8829=\dfrac{11}{x}\\\\\\\Rightarrow x=\dfrac{11}{0.8829}\\\\\Rightarrow x=12.4589.

Rounding to nearest tenth, we get

x = 12.5 units.

Thus, the required value of x is 12.5 units.

Option (C) is CORRECT.

elena-14-01-66 [18.8K]3 years ago
5 0
Cos28=11/x
x=11/cos28
it will be c
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Sharon paid 14.40 for 3 1/4 yards of fabric. how much did sharon pay per yard of fabric.
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Step-by-step explanation:

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3 years ago
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Vsevolod [243]

Answer:

a) The standard deviation of this sampling distribution is 2.07.

b) The missing number is 4.14.

c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

\mu = 272, n = 840, \sigma = 60

(a) If we take many samples, the sample mean x⎯⎯⎯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?

Using the Central Limit Theorem:

s = \frac{\sigma}{\sqrt{n}} = \frac{60}{\sqrt{840}} = 2.07

The standard deviation of this sampling distribution is 2.07.

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?

Within 2 standard deviations of the mean.

So, 2*2.07 = 4.14

The missing number is 4.14.

(c) What is the 95% confidence interval for the population mean score μ based on this one sample?

Within 4.14 of the mean

272 - 4.14 = 267.86

272 + 4.14 = 276.14

The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

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Given that the two cone are similar, then
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