Writing algebraic expressions for: A number decreased by 5 is 12

A state end-of-grade exam in American History is a multiple-choice test that has 50 questions with 4 answer choices for each que

Assoli18 [71]

Answer:

Q1) The student has a 0.01% probability of passing the test.

Q2) She has a 99.91% probability of passing in the test.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he gets it correct, or he gets it wrong. So we solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

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

And $\pi$ is the probability of X happening.

For this problem, we have that:

Question 1.

There are 50 questions, so $n = 50$ .

The student is going to guess each question, so he has a $\pi = \frac{1}{4} = 0.25$ probability of getting it right.

He needs to get at least 25 question right.

So we need to find $P(X \geq 25)$ .

Using a binomial probability calculator, with $n = 50$ and $\pi = 0.25$ we get that $P(X \geq 25) = 0.0001$ .

This means that the student has a 0.01% probability of passing the test.

Question 2.

Now, we need to find $P(X \geq 25)$ with $\pi = 0.70$ . So $P(X \geq 25) = 0.9991$

She has a 99.91% probability of passing in the test.

7 0

3 years ago

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If c (x) = StartFraction 5 Over x minus 2 EndFraction and d(x) = x + 3, what is the domain of (cd)(x)?

Volgvan

Answer:

The domain of the function (cd)(x) will be all real values of x except x = 2.

Step-by-step explanation:

The two functions are $c(x) = \frac{5}{x - 2}$ and d(x) = x + 3

So, (cd)(x) = $(\frac{5}{x - 2})(x + 3) = \frac{5(x + 3)}{x - 2}$

Then, for x = 2 the function (cd)(x) will be undefined as zero in the denominator will make the function (cd)(x) undefined.

Therefore, the domain of the function (cd)(x) will be all real values of x except x = 2. (Answer)

8 0

3 years ago

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The hypotenuse of a 45°-45°-90° triangle measures units.

Sholpan [36]

This an isosceles right triangle. The sides opposed to the angle 45° are congruent. Let x be this side==> x²+x² =(7√2)² (Pythagoras)

2x² = 49(2) ==> 2x²= 98 ==> x²=49 & x=7

5 0

2 years ago

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Factor completely, then place the answer in the proper location on the grid.<br><br> a^6 - 25b^2

Solnce55 [7]

This is the difference of 2 squares

square root of a^6 = a^3
and square root of 25 b^2 = 5b so we get

(a^3 + 5b)(a^3 - 5b)

Thats the answer

5 0

3 years ago

How to write this standard form?<br><br> 2y=-3x+5

Schach [20]

Answer:

3x + 2y - 5 = 0

Step-by-step explanation:

Standard form: ax + by + c = 0

2y = -3x + 5

+3x - 5 to both sides

2y + 3x - 5 = 0

Change order.

3x + 2y - 5 = 0

4 0

2 years ago

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