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3 years ago

(Fg)(-10)=? Snapped a pic of full question!

Mathematics

1 answer:

maria [59]3 years ago

4 0

There are two ways to do this
Method 1:

Find (fg)(x) first
(fg)(x) = f(x)*g(x)
(fg)(x) = (x^2-19)*(20-x)
(fg)(x) = 20x^2-x^3-380+19x
(fg)(x) = -x^3+20x^2+19x-380

Then plug in x = -10
(fg)(x) = -x^3+20x^2+19x-380
(fg)(-10) = -(-10)^3+20(-10)^2+19(-10)-380
(fg)(-10) = -(-1000)+20(100)+19(-10)-380
(fg)(-10) = 1000+2000-190-380
(fg)(-10) = 3000-570
(fg)(-10) = 2430

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

Method 2:

Find f(-10)
f(x) = x^2 - 19
f(-10) = (-10)^2 - 19
f(-10) = 100 - 19
f(-10) = 81

Find g(-10)
g(x) = 20-x
g(-10) = 20-(-10)
g(-10) = 20+10
g(-10) = 30

Multiply the two results
(fg)(-10) = f(-10)*g(-10)
(fg)(-10) = 81*30
(fg)(-10) = 2430

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

Whichever method you pick, the answer is: 2430

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The length of each side of a cube is x + 1 inches. What is the volume of the cube in cubic inches?

castortr0y [4]

Answer:

V = x³ + 3x² + 3x + 1 in³

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ( where s is the side ) , then

V = (x + 1)³

= (x + 1)(x + 1)(x + 1) ← expand second pair using FOIL

= (x + 1)(x² + 2x + 1) ← distribute

= x³ + 2x² + x + x² + 2x + 1 ← collect like terms

= x³ + 3x² + 3x + 1

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3 years ago

1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

Natalija [7]

Answer:

0.6826 = 68.26% probability that you have values in this interval.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

X~N(8, 1.5)

This means that $\mu = 8, \sigma = 1.5$

What is the probability that you have values between (6.5, 9.5)?

This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So

X = 9.5

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

$Z = \frac{9.5 - 8}{1.5}$

$Z = 1$

$Z = 1$ has a p-value of 0.8413.

X = 6.5

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

$Z = \frac{6.5 - 8}{1.5}$

$Z = -1$

$Z = -1$ has a p-value of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that you have values in this interval.

7 0

3 years ago

Help me please i don’t get it

Fofino [41]

Answer:

Step-by-step explanation:

Both triangles are the same shape, just to different scales. In order to find out the length of side AB in triangle ABC, you have to find out the length of side PQ in triangle PQR and how much bigger than side AB is.

You can tell that sides AC and PR are similar, and 30/5 is 6. You see also that sides BC and QR are similar, and 42/7 is also 6. We have now discovered that triangle PQR is 6 times bigger than triangle ABC.

So now, to find the length of the missing side, we have to shrink side PQ by 6. 24/6 is 4. Therefore, the length of side AB is 4.

7 0

2 years ago

A swimming pool measures 35 feet wide by long. What is the ratio of the length to the perimeter in simpiest form

guapka [62]

<h3><u>Question:</u></h3>

A swimming pool measures 35 feet wide by 50 feet long. What is the ratio of the length to the perimeter

<h3><u>Answer:</u></h3>

The ratio of length to perimeter of pool is 5 : 17

<h3><u>Solution:</u></h3>

Given that, swimming pool measures 35 feet wide by 50 feet long

Therefore,

Length = 50 feet

Width = 35 feet

Swimming pool is usually of rectangular shape

<em><u>The perimeter of rectangle is given as:</u></em>

Perimeter = 2(length + width)

Perimeter = 2(50 + 35)

Perimeter = 2(85) = 170

Thus perimeter of pool is 170 feet

<em><u>Ratio of length to perimeter:</u></em>

$\frac{Length}{Perimeter } = \frac{50}{170}\\\\\frac{Length}{Perimeter } = \frac{5}{17}$

Thus ratio of length to perimeter of pool is 5 : 17

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3 years ago

Joshua uses a rule to write the following sequence of numbers 1/6,1/2,5/6,----------,11/2 What rule did Joshua use? What is the

Pani-rosa [81]

Answer: The missing number in the sequence is $\frac{7}{6}$

Step-by-step explanation:

Since we have given that

$\frac{1}{6},\frac{1}{2},\frac{5}{6},----------,\frac{11}{2}$

First term = a= $\frac{1}{6}$

Common difference = d is given by

$d=a_2-a_1\\\\\frac{1}{2}-\frac{1}{6}\\\\=\frac{6-2}{12}\\\\=\frac{4}{12}=\frac{1}{3}\\\\Similarly,\\d=a_3-a_2\\\\=\frac{5}{6}-\frac{1}{2}\\\\=\frac{10-6}{12}\\\\=\frac{4}{12}\\\\=\frac{1}{3}$

Therefore, it forms an arithmetic sequence.

Since, $a_4$ is missing,

So,

$a_4=a+3d\\\\a_4=\frac{1}{6}+3\times \frac{1}{3}\\\\a_4=\frac{1}{6}+1\\\\a_4=\frac{1+6}{6}\\\\a_4=\frac{7}{6}$

Hence, the missing number in the sequence is $\frac{7}{6}$

4 0

3 years ago

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