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3 years ago

Let (fx) = –5x – 4 and g(x) = 6x – 7. Find (fx) + g(x).

1 answer:

5 0

f(x) + g(x) Substitute/plug in (-5x - 4) into "f(x)" since f(x) = -5x - 4, and plug in (6x - 7) into "g(x)" since g(x) = 6x - 7

(-5x - 4) + (6x - 7) Combine like terms(terms that have the same variable and power/exponent)

-5x + 6x - 4 - 7 (I rearranged the terms to be next to their like term)

x - 11 Your answer is D

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LCM of 20 and 50 and GCF of 20 and 50 (Show all work) ( explain the steps you took to find the LCM and GCF)

Ksju [112]

"In order to get the Least Common Multiple of 50 and 20 we need to factor each value and then we need to choose all of the factors which appear in any column and then multiply them."

50: 2 55

20: 225

LCM: 2255

The (LCM) is: 2 x 2 x 5 x 5 = 100

"To find the Greates Common Factor (GCF) of 20 and 50 we need to factor each value first and then choose all the copies of factors and then multiply them."

20: 255

50: 55

The GCF is: 2 and 5 so you need to multiply and then you will get The Greates Common Factor. The greates common factor is: 2 x 5 = 10

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3 years ago

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He prism below, the shortest distance between point B and point E is 20.4 inches, and the shortest distance from point D and poi

JulijaS [17]

The answer is probably C

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3 years ago

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Let X equal the number of flips of a fair coin that are required to observe

Nataliya [291]

Answer:

(a) I attached a photo with the diagram.

(b) $f(x) = \big( \frac{1}{2} \big)^{x-1}$

(d) 4

(e) $k^2/2$

Step-by-step explanation:

(a) I attached a photo with the diagram.

(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.

To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.

1 - Your first outcome is HEADS and all the others are different except the last one.

2 - Your first outcome is TAILS and all the others are different except the last one.

Therefore the probability of the event is

$f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}$

(c)

P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.

$E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}$

(d)

Remember that this is a geometric distribution therefore

$E[X] = p/(1-p)$ , in this case $p = 1/2$ so $E[X] = 1$ and

$E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4$

Also

(e)

This is a geometric distribution so its variance is

$Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2$

And using properties of variance

$Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2$

3 0

4 years ago

Find the length of . Round answer to nearest tenth. PLS HELP ASAP

umka21 [38]

$\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =75 \end{cases}\implies s=\cfrac{(75)\pi (7)}{180}\implies s=\cfrac{35\pi }{12}\implies s\approx 9.2$