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aalyn [17]
1 year ago
6

What us the measure of X in the triangle shiwn below

Mathematics
1 answer:
julia-pushkina [17]1 year ago
5 0

The figure appears to be a triangle with only two measures of its interior angles are given.

∠1 = x = uknown

∠2 = 43°

∠3 = 84°

For us to be able to determine the measure of x, let's recall that the sum of the interior angle of a triangle is 180°.

With this property of the triangle, we can find x. We get,

\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}

\angle1\text{ + }43^{\circ}\text{ + }84^{\circ}=180^{\circ}\angle1\text{ + }127^{\circ}=180^{\circ}\angle1\text{ }=180^{\circ}\text{ - }127^{\circ}\angle1\text{ }=x=53^{\circ}

Therefore, the measure of x is 53°

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Six more than the quotient of a number b and 45 is grater than 4
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A college counselor is interested in estimating how many credits a student typically enrolls in each semester. The counselor dec
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Answer:

(a) The usual load is not 13 credits.

(b) The probability that a a student at this college takes 16 or more credits is 0.1093.

Step-by-step explanation:

According to the Central limit theorem, if a large sample (<em>n</em> ≥ 30) is selected from an unknown population then the sampling distribution of sample mean follows a Normal distribution.

The information provided is:

Min.=8\\Q_{1}=13\\Median=14\\Mean=13.65\\SD=1.91\\Q_{3}=15\\Max.=18

The sample size is, <em>n</em> = 100.

The sample size is large enough for estimating the population mean from the sample mean and the population standard deviation from the sample standard deviation.

So,

\mu_{\bar x}=\bar x=13.65\\SE=\frac{s}{\sqrt{n}}=\frac{1.91}{\sqrt{100}}=0.191

(a)

The null hypothesis is:

<em>H</em>₀: The usual load is 13 credits, i.e. <em>μ</em> = 13.

Assume that the significance level of the test is, <em>α</em> = 0.05.

Construct a (1 - <em>α</em>) % confidence interval for population mean to check the claim.

The (1 - <em>α</em>) % confidence interval for population mean is given by:

CI=\bar x\pm z_{\alpha/2}\times SE

For 5% level of significance the two tailed critical value of <em>z</em> is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Construct the 95% confidence interval as follows:

CI=\bar x\pm z_{\alpha/2}\times SE\\=13.65\pm (1.96\times0.191)\\=13.65\pm0.3744\\=(13.2756, 14.0244)\\=(13.28, 14.02)

As the null value, <em>μ</em> = 13 is not included in the 95% confidence interval the null hypothesis will be rejected.

Thus, it can be concluded that the usual load is not 13 credits.

(b)

Compute the probability that a a student at this college takes 16 or more credits as follows:

P(X\geq 16)=P(\frac{X-\mu}{\sigma}\geq \frac{16-13.65}{1.91})\\=P(Z>1.23)\\=1-P(Z

Thus, the probability that a a student at this college takes 16 or more credits is 0.1093.

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The answer is c . I hope I helped
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