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NikAS [45]
3 years ago
11

The life span of a battery is the amount of time the battery will last. The distribution of life span for a certain type of batt

ery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour. Suppose one battery will be selected at random. Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?
a. 0.055
b. 0.110
c. 0.445
d. 0.890
e. 0.945
Mathematics
1 answer:
Andrew [12]3 years ago
5 0

Answer:

a. 0.055

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 2.5, \sigma = 0.25

Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?

This is the pvalue of Z when X = 2.1.

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.1 - 2.5}{0.25}

Z = -1.6

Z = -1.6 has a pvalue of 0.055.

So the correct answer is:

a. 0.055

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15x^2 + 41x + 28 <br><br>STEP BY STEP ANSWER PLSSS​
maria [59]

Answer:

(3x+4)(5x+7)

Step-by-step explanation:

15x^2 +41x+28

Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2 +ax+bx+28. To find a and b, set up a system to be solved.

a+b=41

ab=15×28=420

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.

1,420

2,210

3,140

4,105

5,84

6,70

7,60

10,42

12,35

14,30

15,28

20,21

Calculate the sum for each pair.

1+420=421

2+210=212

3+140=143

4+105=109

5+84=89

6+70=76

7+60=67

10+42=52

12+35=47

14+30=44

15+28=43

20+21=41

The solution is the pair that gives sum 41.

a=20

b=21

Rewrite 15x^2 +41x+28 as (15x^2 +20x)+(21x+28).

(15x^2 +20x)+(21x+28)

Factor out 5x in the first and 7 in the second group.

5x(3x+4)+7(3x+4)

Factor out common term 3x+4 by using distributive property.

(3x+4)(5x+7)

7 0
3 years ago
Read 2 more answers
PLZ HELP FOR POINTS thank you
Liono4ka [1.6K]

Given : y = -25 and x = -5

We can notice that if we Multiply 'x' with 5 we get 'y'

That is (-5) × 5 = -25

⇒ x multiplied by 5 = y

(a) The Equation that relates x and y is 5x = y

(b) We found that the Equation of this Direct variation is : 5x = y

The Question is to find the value of y when x = 3

The Value of y at x = 3 can be found by simply substituting x = 3 in the equation we found.

⇒ y = 5x

⇒ y = 5 × 3

⇒ y = 15

So, the Value of y when x = 3 is 15

8 0
3 years ago
I have been stuck on this question please help
Hatshy [7]

Answer:

  • 3⁷

Step-by-step explanation:

  • (3⁴)⁻² * (3⁵)³ =
  • 3⁴⁽⁻²⁾*3⁵⁽³⁾ =
  • 3⁻⁸*3¹⁵ =
  • 3⁻⁸⁺¹⁵ =
  • 3⁷

Correct option is B. 3⁷

3 0
2 years ago
A marathon is 46,145 yards (about 26 miles) long. If Terrence has run 23,561 yards, estimate by rounding to thousands the number
barxatty [35]

Given:

The length of the marathon is L= 46,145 yards.

The length covered by terrence is d = 23,561 yrads.

The objective is to find the remaining distance need to cover by terrence.

To calculate the remaining distance, we will use the relation,

x=L-d

On plugging the values in the above relation, we get,

\begin{gathered} x=46145-23561 \\ =22584\text{ yards} \\ \approx23000\text{ yards} \end{gathered}

Hence, Terrence needs to run about 23000 yards.

5 0
1 year ago
PLEASE HELP !!! WILL BE MARKED AS BRAINLIST !! PLEASE !!!!
GrogVix [38]

x is 280........................

8 0
3 years ago
Read 2 more answers
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