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3 years ago

One angle in an obtuse isosceles triangle measures 40°. What are the measures of the other two angles?

Mathematics

2 answers:

Ronch [10]3 years ago

7 0

Answer:

C.40° and 100°

Step-by-step explanation:

Damm [24]3 years ago

5 0

An obtuse triangle has one obtuse angle, or an angle that measures more than 90° but less than 180°. Options 1 and 2 are not correct, because these are acute angles.
So, one of the angles must be 40°, and the other may be 100° or 120°.
The measures of the angles in a triangle add up to 180°.
$40^\circ + 40^\circ +x = 180^\circ \\
80^\circ + x=180^\circ \\
x=180^\circ - 80^\circ \\
x=100^\circ$
The other two angles are 40° and 100°.

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nexus9112 [7]

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a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

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Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

This Zscore is how many standard deviations the value of the measure X is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

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

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

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

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

$Z = \frac{X - \mu}{\sigma}$

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$