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3 years ago

-25 Points-

Mathematics

1 answer:

Nesterboy [21]3 years ago

7 0

Answer:

Step-by-step explanation:

If a figure A and a figure B are similar, then

$\dfrac{area_A}{area_B}=k^2$ (*)

<em>k</em><em> - similarity scale</em>

<em />

Calculate the similarity scale:

$k=\dfrac{6}{5}$

We have the surface area of the smaller prism 572 m².

Substitute to the formula (*):

$\dfrac{x}{572}=\left(\dfrac{6}{5}\right)^2\\\\\dfrac{x}{572}=\dfrac{36}{25}\qquad\text{cross multiply}\\\\25x=(36)(572)\\\\25x=20,592\qquad\text{divide both sides by 25}\\\\x=823.68\approx823.7\ m^2$

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IRINA_888 [86]

Hey there!

To solve this, divide the numbers 1/4 and 5 . . .

1/4 = 1/4

5 = 5/1

1 x 1 = 1

4 x 5 = 20

= 1/20

1/20 is already in it's simplest form, so it doesn't need to be simplified.

There are 1/20 liters of water in each glass.

Hope this helps you.
Have a great day!

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What is the area of a triangle with vertices (3,0) (9,0) (7,6)

Nezavi [6.7K]

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by the determinant of the following matrix:

$A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|$

In this question:

Vertices (3,0) (9,0) (7,6). So

$A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|$

$A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)$

$A = \pm 0.5*(63-21)$

$A = \pm 0.5*42 = 21$

The area of the triangle is of 21 units of area.

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3 years ago

The number of customers for a new online business can be modeled by y = 6x2 + 75x + 200, where x represents the number of months

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Plug in x=25 to get y=5825. So the answer is A.

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Answer the question in the picture

nekit [7.7K]

Recall the angle sum identities:

$\sin(x+y)=\sin x\cos y+\cos x\sin y$

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

Now,

$\tan(x+y)=\dfrac{\sin(x+y)}{\cos(x+y)}=\dfrac{\sin x\cos y+\cos x\sin y}{\cos x\cos y-\sin x\sin y}$

Divide through numerator and denominator by $\cos x\cos y$ to get

$\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}$

Next, we use the fact that $x,y$ lie in the first quadrant to determine that

$\sin x=\dfrac12\implies\cos x=\sqrt{1-\sin^2x}=\dfrac{\sqrt3}2$

$\cos y=\dfrac{\sqrt2}2\implies\sin x=\sqrt{1-\cos^2x}=\dfrac1{\sqrt2}$

So we then have

$\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}$

$\tan y=\dfrac{\sin y}{\cos y}=\dfrac{\frac1{\sqrt2}}{\frac{\sqrt2}2}=1$

Finally,

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3 years ago

The American Automobile Association reported that families planning to travel over the Labor Day weekend would spend an average

Anuta_ua [19.1K]

Answer:

0.7486 = 74.86% probability of family expenses for the weekend being more than $580.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions 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.

The American Automobile Association reported that families planning to travel over the Labor Day weekend would spend an average of $735.

This means that $\mu = 735$

Assume that the amount spent is normally distributed with a standard deviation of $230.

This means that $\sigma = 230$

What is the probability of family expenses for the weekend being: a. more than $580

This is 1 subtracted by the pvalue of Z when X = 580. So

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

$Z = \frac{580 - 735}{230}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514

1 - 0.2514 = 0.7486

0.7486 = 74.86% probability of family expenses for the weekend being more than $580.

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