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2 years ago

If f(x) = 3x - 1 and g(x) = x + 2, find (f - g)(x).

Mathematics

1 answer:

Marat540 [252]2 years ago

6 0

Answer:

(f - g)(x) = 2x - 3

Step-by-step explanation:

(f - g)(x) is defined as subtracting the whole g(x) function from the f(x) function.

Hence, we can define it as:

(3x - 1) - (x + 2)

= 3x - x - 1 - 2

= 2x - 3

Therefore, (f - g)(x) = 2x - 3.

Hope this helped!

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Learn with an example

Daniel [21]

Answer: 10,000

11 * 2 = 22

5,000 * 2 = 10,000

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3 years ago

An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What

galina1969 [7]

Answer:

Part A:

The probability that all of the balls selected are white:

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

$P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

$P(D_i)=\frac{1}{6}$ for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

$P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}$

$P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}$

$P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}$

$P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}$

$P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}$

$P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0$

Part A:

The probability that all of the balls selected are white:

$P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)$

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find $P(D_3|A)$

The data required is calculated above:

$P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

7 0

3 years ago

What is the correct answer to the math problem<br> 20+30×0+1

Bumek [7]

21
is what I got on my calculator

6 0

3 years ago

Read 2 more answers

Two column proofs Beginner's

Darina [25.2K]

LETS prove the 2nd part of the Question

Here concept of right angles is used

We can see BA is perp to BD

and BC is perp to BE

We have to prove angle 1 = angle 3

i will denote angle by a

therefore we need to prove a1 = a3

as BA is perp to BD hence angle between them will be 90 degree

a1 + a2 = 90 degree

Similarly BC is perp to BE

a2 + a3 = 90 degree

as both equations add up gives 90 degree so will equate them

a1 + a2 = a2 + a3

which means a1 = a3

Hence Proved

To learn more about Right Angles:

brainly.com/question/7116550

#SPJ1

3 0

10 months ago

A 3-pound bag of bananas costs $2.88. What is the price per ounce?

Alborosie

Answer: 6 cents

Step-by-step explanation:

1 pound = 16 ounces

3 pounds = 48 ounces

2.88 ÷ 48 = 0.06

0.06 = 6 cents.

One ounce of bananas cost 6 cents.

Hope this helps!

4 0

3 years ago