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finlep [7]
3 years ago
8

1/4(-8x - 12) + -4 = 3/4(-8x - 12)

Mathematics
1 answer:
nekit [7.7K]3 years ago
8 0

Here's our equation:

\frac{1}{4} (-8x-12)-4=\frac{3}{4} (-8x-12)

Factor out the left side

(-2x - 3) - 4 = 3/4 (-8x - 12)

Simplify

-2x - 7 = 3/4 (-8x - 12)

Factor out the right side

-2x - 7 = -6x - 9

Add 7

-2x = 6x - 2

Add 6x to isolate the variable

4x = -2

Divide by 4

x = - 1/2

Here is how I simplified both sides initially. I'll only be showing the right side because this is a LOT of typing.

Begin with 3/4 (-8x - 12)

Use rule a*\frac{b}{c} = \frac{a * b}{c} to multiply

3(-8x-12)/4

Factor 3(-8x-12)

(-8x - 12) = (-4 * 2x - 4 * 3)

Simplify (-4 * 2x - 4 * 3)

-3 * 4 (2x+3)

- 12 (2x + 3)

Now that we've factored  3/4 (-8x - 12), we're left with- 12 (2x + 3)/4.

12/4 =3, giving us -3(2x + 3)

Distribute and simplify, then you're done.

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Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both in case
olga nikolaevna [1]

Answer:

(a) The probability that both Dave and Mike will show up is 0.25.

(b) The probability that at least one of them will show up is 0.75.

(c) The probability that neither Dave nor Mike will show up is 0.25.

Step-by-step explanation:

Denote the events as follows:

<em>D</em> = Dave will show up.

<em>M</em> =  Mike will show up.

Given:

P(D^{c})=0.55\\P(M^{c})=0.45

It is provided that the events of Dave of Mike showing up are independent of each other.

(a)

Compute the probability that both Dave and Mike will show up as follows:

P(D\cap M)=P(D)\times P (M)\\=[1-P(D^{c})]\times [1-P(M^{c})]\\=[1-0.55]\times[1-0.45]\\=0.2475\\\approx0.25

Thus, the probability that both Dave and Mike will show up is 0.25.

(b)

Compute the probability that at least one of them will show up as follows:

P (At least one of them will show up) = 1 - P (Neither will show up)

                                                   =1-P(D^{c}\cup M^{c})\\=P(D\cup M)\\=P(D)+P(M)-P(D\cap M)\\=[1-P(D^{c})]+[1-P(M^{c})]-P(D\cap M)\\=[1-0.55]+[1-0.45]-0.25\\=0.75

Thus, the probability that at least one of them will show up is 0.75.

(c)

Compute the probability that neither Dave nor Mike will show up as follows:

P(D^{c}\cup M^{c})=1-P(D\cup M)\\=1-P(D)-P(M)+P(D\cap M)\\=1-[1-P(D^{c})]-[1-P(M^{c})]+P(D\cap M)\\=1-[1-0.55]-[1-0.45]+0.25\\=0.25

Thus, the probability that neither Dave nor Mike will show up is 0.25.

6 0
3 years ago
Read 2 more answers
50 points
NISA [10]
1. Using your straightedge, draw a reference line, if one is not provided.
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Please help!! | show work and do not guess. :)
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3 years ago
What is (6.89+14.52)+(-14.52)???
MrRa [10]
The answer is 6.89 because
6.89+14.52=21.41
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The density of ethanol is around 0.8g/mL. What is the mass of 20mL of ethanol?
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Answer: 0.7893g//mL

If 20 mL of ethanol (density =0.7893g//mL) is mixed with 40mL water (density = 0.9971g//mL)

Step-by-step explanation:

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