Simplify 3x^2-10x-8/ x-4

A multiple-choice examination has 15 questions, each with five answers, only one of which is correct. Suppose that one of the st

Alex

Answer:

0.0111% probability that he answers at least 10 questions correctly

Step-by-step explanation:

For each question, there are only two outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent from other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

A multiple-choice examination has 15 questions, each with five answers, only one of which is correct.

This means that $n = 15, p = \frac{1}{5} = 0.2$

What is the probability that he answers at least 10 questions correctly?

$P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)$

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

$P(X = 10) = C_{15,10}.(0.2)^{10}.(0.8)^{5} = 0.0001$

$P(X = 11) = C_{15,11}.(0.2)^{11}.(0.8)^{4} = 0.000011$

$P(X = 12) = C_{15,12}.(0.2)^{12}.(0.8)^{3} \cong 0$

$P(X = 13) = C_{15,13}.(0.2)^{13}.(0.8)^{2} \cong 0$

$P(X = 14) = C_{15,14}.(0.2)^{14}.(0.8)^{1} \cong 0$

$P(X = 15) = C_{15,15}.(0.2)^{15}.(0.8)^{0} \cong 0$

$P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0001 + 0.000011 = 0.000111$

0.0111% probability that he answers at least 10 questions correctly

3 0

3 years ago

A triangle has an area of 10 square feet. The height is 5 feet. What is the length of the base (in feet)?

Nady [450]

Answer:

4 ft

Step-by-step explanation:

$A=\frac{1}{2} bh$

A=10 h=5

$10=\frac{1}{2} b(5)\\$

20=5b (multiply both sides by 2)

4=b (divide by 5)

7 0

3 years ago

5x-3=12x+11<br><br> Algebra problem, pls help

kupik [55]

Answer:

hope this helps \(owo)\

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

If 20 mangoes cost 850 naira , what is the cost of 15 Mangoes

Marianna [84]

In this math problem, we will be using rate of change.
850 naira’s / 20 mangoes
= 42.5 nairas for one mango.
Next, to find the cost of 15 mangoes, we will take the cost of our one mango and simply multiply it by 15.
= 42.5 nairas * 15
= 637.50 nairas
So, in conclusion, the cost of 15 mangoes is 637.50 naira.

3 0

3 years ago

avocados cost $3 per pound. write and graph an equation in two variables that represents the cost of buying avocados

EastWind [94]

Pounds will be represented by x and the cost will be represented by y. The equation is Y=3x. For the graph just use substition for x and then calculate the outcome and graph it.

4 0

3 years ago