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2 years ago

What's the hinge theorem and it's converse?

1 answer:

7 0

The converse of the hinge theorem is also true: If the two sides of one triangle are congruent<span> to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second .</span>

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Find the 88th term of the arithmetic sequence 26, 28, 30,...

ICE Princess25 [194]

Answer:

200

Step-by-step explanation:

Given Arithmetic sequence is: 26, 28, 30,...

First term a = 26

Common Difference d = 2

n = 88

$\because t_n=a +(n-1) d \\ \therefore \: t_{88}=26 +(88-1) \times 2 \\ \therefore \: t_{88}=26 +87 \times 2 \\ \therefore \: t_{88}=26 +174 \\ \huge \red{ \boxed{ \therefore \: t_{88}=200}} \\$

4 0

2 years ago

Which statements describe a residual plot for a line of best fit that is a good model for a scatterplot? Check all that apply. T

lidiya [134]

Answer:

The points are randomly scattered with no clear pattern

The number of points is equal to those in the scatterplot.

Step-by-step explanation:

The points in the residual plot of the line of best fit that is a good model for a scatterplot are randomly scattered with no clear pattern (like a line or a curve).

The number of points in the residual plot is always equal to those in the scatterplot.

It doesn't matter if there are about the same number of points above the x-axis as below it, in the residual plot.

The y-coordinates of the points are not the same as the points in the scatterplot.

8 0

1 year ago

Read 2 more answers

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equ

kompoz [17]

Answer:

0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

Normal probability distribution.

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:

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

The Z-score measures how many standard deviations the measure 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.

In this problem, we have that:

$\mu = 800, \sigma = 40, n = 16, s = \frac{40}{\sqrt{16}} = 10$

Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

This probability is the pvalue of Z when $X = 775$ . So

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

$Z = \frac{775 - 800}{10}$

$Z = -2.5$

$Z = -2.5$ has a pvalue of 0.0062. So there is a 0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

5 0

2 years ago

The sides of a square are five to the power of two fifths inches long. What is the area of the square?

Feliz [49]

I believe the correct answer from the choices listed above is the first option. If the sides of a square are five to the power of two fifths inches long, then the are of the square would be <span>five to the power of four fifths square inches. Hope this answers the question.</span>

3 0

2 years ago

An observer from the top of a lighthouse 370 feet above sea level sees two sailboats in the water. The angles of depression to t

noname [10]

Answer:the sailboats are 358 feet apart.

Step-by-step explanation:

The diagram of the triangle representing the situation is shown in the attached photo.

B represents the position of the lighthouse.

D represents the position of the first sailboat.

C represents the position of the second sailboat.

x represents the distance between the two sailboats

We would apply trigonometric ratio

Tan # = opposite/adjacent

For triangle ABD,

Tan 12 = 370/AD

AD = 370/Tan 12 = 370/0.2126 = 1740.357 feet

For triangle ABC,

Tan 10 = 370/AC

AD = 370/Tan 10 = 370/0.1763 = 2098.695 feet

x = AC - AD = 2098.695 - 1740.357 = 358 feet

5 0

2 years ago