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natali 33 [55]
3 years ago
9

Suppose that only 65% of all drivers in a certain state wear a seat belt. a random sample of 80 drivers is selected. what is the

probability that more than forty-two drivers wear a seat belt?
Mathematics
1 answer:
jonny [76]3 years ago
7 0

Answer:

Pr(X >42) = Pr( Z > -2.344)

                = Pr( Z< 2.344) = 0.9905

Step-by-step explanation:

The scenario presented can be modeled by a binomial model;

The probability of success is, p = 0.65

There are n = 80 independent trials

Let X denote the number of drivers that wear a seat belt, then we are to find the probability that X is greater than 42;

Pr(X > 42)

In this case we can use the normal approximation to the binomial model;

mu = n*p = 80(0.65) = 52

sigma^2 = n*p*(1-p) = 18.2

Pr(X >42) = Pr( Z > -2.344)

                = Pr( Z< 2.344) = 0.9905

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Answer:

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3 0
3 years ago
What is the measure of angle TMS? Pls explain your answer and I will mark brainliest!
Rudik [331]

Answer:

38 degrees

Step-by-step explanation:

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3 years ago
18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:
Ksenya-84 [330]

a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}

S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525

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3 years ago
Create a word problem using 30+2d as the answer
Tanzania [10]

Answer:

Sonya pays a flat fee of $30 for her phone bill and pays $2 per gigabyte she uses per month. Put Sonya's bill as an equation with <em>d</em> being how many gigabytes she uses per month.

Step-by-step explanation:

We get the flat fee of $30 from "30 + 2d" and the $2 per gigabyte from "30 + 2d" and since we want to find out Sonya's total bill, that's where the + in "30 + 2d" comes from. We want the variable to be <em>d</em> therefore <em>d</em> is how many gigabytes she uses per month.

4 0
3 years ago
Simplify the product (x-4)(x+3)
Kamila [148]

Answer:

Final answer is x^2-x-12.

Step-by-step explanation:

Given expression is \left(x-4\right)\left(x+3\right).

Now we need to find the product of the given expression \left(x-4\right)\left(x+3\right).

\left(x-4\right)\left(x+3\right)

=x\left(x-4\right)+3\left(x-4\right)

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combine like terms

=x^2-1x-12

=x^2-x-12

Hence final answer is x^2-x-12.

7 0
4 years ago
Read 2 more answers
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