Equivalent expression of 9(r + r + r+ r)

How do you Simplify this expression in algebra?<br><br> 9x + 2x (5 + 4) - 2(5x + 4x)

Minchanka [31]

One can solve this by first using order of operations, and then combining like terms.

First is parenthesis

9x + 2x(9) - 2(9x)

Now we do the multiplication

9x + 18x - 18x

Now we combine like terms

9x

3 0

2 years ago

A test has 20 true/false questions. What is the probability that a student passes the test if they guess the answers? Passing me

Minchanka [31]

Using the binomial distribution, it is found that:

The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.

For each question, there are only two possible outcomes, either the guess is correct, or it is not. The guess on a question is independent of any other question, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

There are 20 questions, hence $n = 20$ .

Each question has 2 options, one of which is correct, hence $p = \frac{1}{2} = 0.5$

The probability is:

$P(X \geq 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 15) = C_{20,15}.(0.5)^{15}.(0.5)^{5} = 0.0148$

$P(X = 16) = C_{20,16}.(0.5)^{16}.(0.5)^{4} = 0.0046$

$P(X = 17) = C_{20,17}.(0.5)^{17}.(0.5)^{3} = 0.0011$

$P(X = 18) = C_{20,18}.(0.5)^{18}.(0.5)^{2} = 0.0002$

$P(X = 16) = C_{20,19}.(0.5)^{19}.(0.5)^{1} = 0$

$P(X = 17) = C_{20,20}.(0.5)^{20}.(0.5)^{0} = 0$

Then:

$P(X \geq 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0148 + 0.0046 + 0.0011 + 0.0002 + 0 + 0 = 0.0207$

The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.

You can learn more about the binomial distribution at brainly.com/question/24863377

6 0

2 years ago

The ratio of art class to music class is 4:3. If there is 8 more students in art class, how many students are in music class

pishuonlain [190]

Answer:

9 students in music class.

Step-by-step explanation:

In art there are 4 and since there are 8 more 8 + 4 = 12. so there are 12 in Art.

4 x _ = 12. —> 4 x 3 = 12.
so we need to do the same for music class.

For music there are 3.
so we multiply by 3 like we did with the 4.

3 x 3 = _ —> 3 x 3 =9.
so there are 9 students in music class.

6 0

2 years ago

The perimeter of a isclose triangle is 24in and the length of the side is 4 in find the 2 other sides

Scrat [10]

Answer:

10 inches

Step-by-step explanation:

Given

Shape: Isosceles Triangle

$Perimeter=24\ in$

$Side = 4\ in$

Required

Find the length of the other two sides

Represent the other sides with x.

Since it is an isosceles triangle, 2 sides are equal.

So, we have:

$x + x + 4 = 24$

$2x + 4 = 24$

Collect Like Terms

$2x = 24-4$

$2x = 20$

Divide both sides by 2

$\frac{2x}{2} = \frac{20}{2}$

$x = \frac{20}{2}$

$x = 10$

<em>The other sides are 10in each</em>

4 0

2 years ago

When deciding how much money to spend on a new car, a good rule of thumb to follow is to budget about one-fifth of your monthly

Lapatulllka [165]

3750(0.20)=$750
1/5 as a percent is 20% and as a fraction it is 0.20

8 0

3 years ago