Solve the following equation for x: 5x + 3y = 15.

Mathematics

1 answer:

zepelin [54]3 years ago

8 0

Answer:

B) x = (-3/5)y + 3

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

first, subtract 3y from btoh sides:

5x + 3y (-3y) = 15 (-3y)

5x = -3y + 15

Next, divide 5 from both sides:

(5x)/5 = (-3y +15)/5

x = (-3/5)y + 3

B) x = (-3/5)y + 3 is your answer.

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A multiple-choice examination has 20 questions, each with five possible answers, only one of which is correct. Suppose that one

kari74 [83]

Answer:

The probability that the student answers at least seventeen questions correctly is $8.03\times 10^{-10}$ .

Step-by-step explanation:

Let the random variable X represent the number of correctly answered questions.

It is provided all the questions have five options with only one correct option.

Then the probability of selecting the correct option is,

$P(X)=p=\frac{1}{5}=0.20$

There are n = 20 question in the exam.

It is also provided that a student taking the examination answers each of the questions with an independent random guess.

Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.

The probability mass function of X is:

$P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...$

Compute the probability that the student answers at least seventeen questions correctly as follows:

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

$=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}$