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2 years ago

50 points. Please explain each step

Mathematics

2 answers:

SashulF [63]2 years ago

8 0

Answer:

sin theta = 3 sqrt(21)/17

Step-by-step explanation:

cos theta = adj / hyp

We can find the opp by using the Pythagorean theorem

adj^2 + opp ^2 = hyp^2

10^2 +opp^2 = 17^2

100 + opp^2 = 289

opp^2 = 289-100

opp^2 = 189

Taking the square root

opp = sqrt(189)

opp = 3 sqrt(21)

Since we are in the first quad, opp is positive

sin theta = opp /hyp

sin theta = 3 sqrt(21)/17

3241004551 [841]2 years ago

7 0

<h3>Sin $\theta_{1}=\frac{3\sqrt{21}}{17}$ </h3>

Solution given:

Cos $\theta_{1}=\frac{10}{17}$

$\frac{adjacent}{hypotenuse}=\frac{10}{17}$

equating corresponding value

we get

adjacent=10

hypotenuse=17

perpendicular=x

now

by using Pythagoras law

Hypotenuse ²=perpendicular²+adjacent ²

substituting value

17²=x²+10²

17²-10²=x²

x²=17²-10²

x²=189

doing square root

$\sqrt{x²}=\sqrt{189}$

x= $3\sqrt{21}$

now

In I Quadrant sin angle is positive

Sin $\theta_{1}=\frac{perpendicular}{hypotenuse}$

<h3>Sin $\theta_{1}=\frac{3\sqrt{21}}{17}$ </h3>

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3 years ago

Read 2 more answers

The number of major earthquakes in a year is approximately normally distributed with a mean of 20.8 and a standard deviation of

SCORPION-xisa [38]

Answer:

a) 51.60% probability that in a given year there will be less than 21 earthquakes.

b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

Step-by-step explanation:

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:

$\mu = 20.8, \sigma = 4.5$

a) Find the probability that in a given year there will be less than 21 earthquakes.

This is the pvalue of Z when X = 21. So

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

$Z = \frac{21 - 20.8}{4.5}$

$Z = 0.04$

$Z = 0.04$ has a pvalue of 0.5160.

So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.

b) Find the probability that in a given year there will be between 18 and 23 earthquakes.

This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:

X = 23

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

$Z = \frac{23 - 20.8}{4.5}$

$Z = 0.71$

$Z = 0.71$ has a pvalue of 0.7611

X = 18

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

$Z = \frac{18 - 20.8}{4.5}$

$Z = -0.62$

$Z = -0.62$ has a pvalue of 0.2676

So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

5 0

3 years ago

Question 7: Which of the following statements is true?

yawa3891 [41]

Problem 7)

The answer is choice B. Only graph 2 contains an Euler circuit.

-----------------

To have a Euler circuit, each vertex must have an even number of paths connecting to it. This does not happen with graph 1 since vertex A and vertex D have an odd number of vertices (3 each). The odd vertex count makes it impossible to travel back to the starting point, while making sure to only use each edge one time only.

With graph 2, each vertex has exactly two edges attached to it. So an Euler circuit is possible here.

================================================

Problem 8)

The answer is choice B) 5

-----------------

Work Shown:

abc base 2 = (a*2^2 + b*2^1 + c*2^0) base 10

101 base 2 = (1*2^2 + 0*2^1 + 1*2^0) base 10

101 base 2 = (1*4 + 0*2 + 1*1) base 10

101 base 2 = (4 + 0 + 1) base 10

101 base 2 = 5 base 10

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2 years ago

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Answer: This is already in slope-intercept form. 0.2

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3 years ago

50 points. Please explain each step​

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