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Lerok [7]
3 years ago
13

Simplify the expression. −3x + 8x + 2 - 3x + 8x + 2

Mathematics
1 answer:
beks73 [17]3 years ago
6 0

Answer:

10x + 4

Step-by-step explanation:

Combine like terms.

First combine the numbers that have the letter x:

  • <u>-3x</u> <u>+ 8x</u> + 2 <u>- 3x</u> <u>+ 8x</u> + 2
  • <u>-3x + 8x -3x +8x</u> + 2 + 2
  • <u>10x</u> + 2 + 2

Then combine the ones that don't have the letter x

  • 10x <u>+ 2</u> <u>+ 2</u>
  • 10x + 4

Answer is 10x+4

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A fair die is rolled 12 times. the number of times an even number occurs on the 12 rolls has
bonufazy [111]

Answer:

Step-by-step explanation:

For a fair die, there are six likely options; 1, 2, 3, 4, 5, and 6

the probability of a even number is 3/6 = 0.5

Since the results of the die roll is independent and each trial is mutually exclusive, the distribution to explain the probability of occurrence will follow a binomial distribution such that n is the number of trials

x = number of successful throws

therefore for a Binomial distribution where

P(X =x) = nCx . P^x . (1-P)^ (n-x)

since p = 0.5, and n = 12, the distribution follows

P(X = x) = 12Cx . 0.5^x . (1 - 0.5)^(12- x)

= 12Cx . 0.5^x . 0.5)^(12- x)

where x = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)

since we are interested in the probability of the number of times an even number occurs

it can occur either as P(X = 0), P(X =1), P(X =2), P(X =3), P(X =4), P(X =5), P(X =6), P(X =7), P(X =8), P(X =9), P(X =10), P(X =11), and P(X =12)

For no even number in 12 rolls,

P(X = 0) = 12C0 . 0.5^0 . 0.5^(12- 0) = 0.000244

For one even number in 12 rolls,

P(X = 1) = 12C1 . 0.5^1 . 0.5^(12- 1) = 0.002930

For two even number in 12 rolls,

P(X = 2) = 12C2 . 0.5^2 . 0.5^(12- 2) = 0.016113  

For three even number in 12 rolls,

P(X = 3) = 12C3 . 0.5^3 . 0.5^(12- 3) = 0.053711  

For four even number in 12 rolls,

P(X = 4) = 12C4 . 0.5^4 . 0.5^(12- 4) = 0.120850

For five even number in 12 rolls,

P(X = 5) = 12C5 . 0.5^5 . 0.5^(12- 5) = 0.193359

For six even number in 12 rolls,

P(X = 6) = 12C6 . 0.5^6 . 0.5^(12- 6) = 0.225586

For seven even number in 12 rolls,

P(X = 7) = 12C7 . 0.5^7 . 0.5^(12- 7) = 0.193359

For eight even number in 12 rolls,

P(X = 8) = 12C8 . 0.5^8 . 0.5^(12- 8) = 0.120850

For nine even number in 12 rolls,

P(X = 9) = 12C9 . 0.5^9 . 0.5^(12- 9) = 0.053711

For ten even number in 12 rolls,

P(X = 10) = 12C10 . 0.5^10 . 0.5^(12- 10) = 0.016113

For eleven even number in 12 rolls,

P(X = 11) = 12C11 . 0.5^11 . 0.5^(12- 11) = 0.002930

For twelve even number in 12 rolls,

P(X = 12) = 12C12 . 0.5^12 . 0.5^(12- 12) = 0.000244

Final test summation[P(X)] =  1

i.e.

P(X = 0) + P(X =1) + P(X =2) + P(X =3) + P(X =4) + P(X =5) + P(X =6) + P(X =7) + P(X =8) + P(X =9) + P(X =10) + P(X =11) + P(X =12) = 1

Hence since 0.000244 + 0.002930 + 0.016113 + 0.053711 + 0.120850 + 0.193359 + 0.225586 + 0.193359 + 0.120850 + 0.053711 + 0.016113 + 0.002930 + 0.000244 = 1.000000,

the probability value stands

7 0
3 years ago
The earth has a diameter of 7917.5 mi. What is the arc length of half the earth?
Serhud [2]

Answer:

Arc length is 12436.8m

Step-by-step explanation:

arc length  = \frac{M degree}{360degree} * πD

where M is the angle measure of the arc

and D is the diameter

considering the earth as a circle and half the earth as a semi circle the angle measure of the arc will be = 180 degrees

\frac{180}{360} * π * 7917.5 = 12436.8m

5 0
3 years ago
The Sahara Desert has an area of approximately 9,400,400 km2. While estimates of its average depth vary, they center around 150
horrorfan [7]

It would take 65433661 years to re-create the Sahara Desert

<h3>How many years would it take to re-create the Sahara Desert?</h3>

The given parameters are:

Surface area = 9,400,400 km^2

Depth = 150 m

This means that the volume is

Volume = Surface area * Depth

So, we have

Volume = 9,400,400 km^2 * 150 m

Express as meter square

Volume = 9,400,400 * 1000000 m^2 * 150 m

Evaluate the product

Volume = 9,400,400 * 150,000,000 m^3

A small dump holds 20.5 m^3 for 30 seconds.

So, the duration is:

Time = (9,400,400 * 150,000,000 m^3)/(20.5 m^3 per 30 seconds)

Evaluate the product and quotient

Time =  2.0635024e+15 seconds

1 second = 3.171e-8 year.

So, we have:

Time =  2.0635024e+15 * 3.171e-8 year

Evaluate the product

Time = 65433661.104 years

Approximate

Time = 65433661 years

Hence, it would take 65433661 years to re-create the Sahara Desert

Read more about rates at:

brainly.com/question/19493296

#SPJ1

4 0
1 year ago
B(x)=x+4, what is b(-10)
vovikov84 [41]

Answer:

B(-10)=-6

Step-by-step explanation:

we have

B(x)=x+4

we know that

B(-10) is the value of the function B(x) for the value of x=-10

so

substitute the value of x=-10 in the function

B(-10)=-10+4=-6

therefore

B(-10)=-6

8 0
3 years ago
ALL MY QUESTIONS GETTING IGNORED PLS HELP
Novosadov [1.4K]

Answer:

x=9

Step-by-step explanation:

a scale drawing means all the sides are multiplied by the same amount. to find this amount, you can divide the larger side by the bigger side by the smaller side.

15/5 = 3

12/4 = 3

therefore the scale factor is 3. to get the value of x, multiply the value of the third side by 3.

3*3=9

x=9

4 0
2 years ago
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