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3 years ago

Solve for the missing side to the nearest tenth. 19 X 51

Mathematics

1 answer:

telo118 [61]3 years ago

3 0

Answer:

x = 30.2 units

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

Selecting any of the acute angles, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides and the hypotenuse.

The given right triangle has an angle of measure 51° and its adjacent leg has a measure of 19 units. It's required to calculate the hypotenuse of the triangle.

We use the cosine ratio to calculate x:

$\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}$

$\displaystyle \cos 51^\circ=\frac{19}{x}$

Solving for x:

$\displaystyle x=\frac{19}{\cos 51^\circ}$

$\displaystyle x=\frac{19}{0.6293}$

x = 30.2 units

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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 330 grams and a standard deviati

just olya [345]

Answer:

Weights of at least 340.1 are in the highest 20%.

Step-by-step explanation:

Problems of normally distributed samples are 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:

$\mu = 330, \sigma = 12$

a. Highest 20 percent

At least X

100-20 = 80

So X is the 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.842.

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

$0.842 = \frac{X - 330}{12}$

$X - 330 = 12*0.842$

$X = 340.1$

Weights of at least 340.1 are in the highest 20%.

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3 years ago

Conver the equation y=2 to polar form. Then solve the resulting equation for r. Thanks :)

maksim [4K]

This is something to memorize

y = r*sin(theta)

so if y = 2, then

2 = r*sin(theta)

Divide both sides by sin(theta) to get

r = 2/sin(theta)
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3 years ago

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Step-by-step explanation:

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2 years ago

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Sergeeva-Olga [200]

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3 years ago

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A motorcycle can go 50 miles using one gallon of gas. About how many gallons of gas will be used to go 150 kilometers? (Hint: 1

gayaneshka [121]

Answer:

The answer to your question is 1.875 gallons

Step-by-step explanation:

Data

distance = 50 mi

volume of gas = 1 gal

volume for 150 km = ?

Process

1.- Convert 50 mi into kilometers

1 mile ------------------- 1.6 km

x ------------------ 150 km

x = (150 x 1)/1.6

x = 93.75 mi

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x = (93.75 x 1)/50

x = 93.75/50

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3 years ago