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3 years ago

One number is eight more than twice another. If their difference is 25, what is the larger number?

1 answer:

7 0

You can set up an system of equations
x=2y+8
x-y=25

Substitute x in to the second equation
2y+8-y=25
y+8=25
y=17

Substitute the y back in to the first equation.
x=2(17)+8=42

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Find the greatest common factor! Please help with these 2 questions

Aleksandr-060686 [28]

Hello!

The greatest common factor (GCF) is self explanatory. We find the factors of each number, and find the largest ones that are in common

12: 1,12,2,6,3,4

33:1,33,3,11,

As you can see, the greatest number these two have in common is 3.

Now for the next set.

45: 1,45,3,15,5,9

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As you can see, our GCF is 5.

Therefore, our answers are below.

9) 3

10) 5

I hope this helps!

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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:

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

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

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

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3 years ago