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Answer:

a) the probability that the next ream out- lasts the present one by more than 2 days is 0.0787

b) the number of reams that must be purchased is 19

Step-by-step explanation:

Given the data in the question;

Lets X₁ and X₂ be the two random variables that represents the first and second ream lasts

given that both random variables follow normal distribution with mean 4 and standard deviation 1.

a)

Find the probability that the next ream out- lasts the present one by more than 2 days.

P( X₂  - X₁ > 2 ) = P( [(X₂  - X₁ - E(X₂  - X₁)) / √(V(X₂  - X₁)] > [ (2-E(X₂  - X₁))/√(V(X₂  - X₁) ]

= 1 - P( Z ≤ [2-(μ₂  - μ₁)] / [√( V(X₂) + V(X₁) ) ] )

= 1 - P( Z ≤ [2-(4  - 4)] / [√( 1 + 1 )] )

= 1 - P = ( Z ≤ 2 / √2 )

= 1 - p( Z ≤ 1.4142 )

from excel; p( Z ≤ 1.41 ) = 0.9213

P( X₂  - X₁ > 2 ) = 1 - 0.9213

P( X₂  - X₁ > 2 ) = 0.0787

Therefore, the probability that the next ream out- lasts the present one by more than 2 days is 0.0787

b)

How many reams must be purchased if they are to last at least 60 days with probability at least 80%

total value is 4n

standard deviation is nσ

so

P(nX ≥ 60 ) = 0.80

P( nX-nμ /nσ  ≥  60-nμ/nσ) = 0.80

P( Z ≥  60-4n/n) = 0.80

1 - P( Z ≥  60-4n/n) = 0.80

P( Z < z ) = 0.20

now since z = 60-4n/n

from standard normal table

critical value of z corresponding to cumulative area of 0.20 is -0.841

so

z = - 0.841

60-4n/n =  -0.841

60 - 4n =  -0.841n

60 = -0.841n + 4n

60 = 3.159n

n = 60 / 3.159

n = 18.99 ≈ 19

Therefore, the number of reams that must be purchased is 19

Answer:

10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 x 6 = 600,000,000.

Answer:

600000000

Step-by-step explanation:

10^8=100000000

6×100000000=600000000

hope this helps

Answer: The answer is 7mn+3m/2+5n/4

7mn + 3m/2 + 5n/4 is the algebraic expression which is a polynomial

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

A polynomial is an expression with variables and coefficients separated by addition and subtraction.

The following are used when determining if an expression is a polynomial:

i) Variables of a polynomial must not have negative exponent.

ii) Variables of a polynomial must not have fractional exponent.

iii) Dividing by an exponent is not allowed

iv) Exponent radicals are not allowed.

7mn + 3m/2 + 5n/4 is a polynomial because it has variables and seperated by operators addition and subtraction.

Hence, 7mn + 3m/2 + 5n/4 is the algebraic expression which is a polynomial

To learn more on Polynomials click:

https://brainly.com/question/11536910

#SPJ5

Answer:

.25 is the answer

Step-by-step explanation:

.5/2=.25

Answer:

128

Step-by-step explanation:

32 ÷ 4• 4 ÷ 2 • 2

8 .4.2.2

128

Answer: the answer is D “The center of circle A is translated left 2 and up 8, and the radius is enlarged by a scale factor of 4/3.”

Step-by-step explanation:

Answer:

Q1 = 40

Step-by-step explanation:

Set up numbers from least to greatest

21, 40, 52, 58, 72, 75, 96

First, find the median,

Median is: 58

Now Q1 is all numbers before the median (without counting the median)

21, 40, 52

The median here is 40

Answer:

D/40

Step-by-step explanation:

The answer is D because if you were to put them in the correct order it would be

21, 40, 52, 58, 72, 75, 96

      Q1        Q2       Q3

Q1 is quartile 1 so the answer is 40

Hope this helps!

Step-by-step explanation:

I want to say B) 130 but not 100% sure. Sorry if my answer is wrong.

Answer:

Since they have the same slope, they are parallel.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope. If two lines are parallel, they have the same slope.

4x−3y=6

Placing into the above format:

[tex]3y = 4x - 6[/tex]

[tex]y = \frac{4x - 6}{3}[/tex]

[tex]y = \frac{4x}{3} - 2[/tex]

The slope [tex]m = \frac{4}{3}[/tex]

y=4/3x−1

The slope is [tex]m = \frac{4}{3}[/tex]

Since they have the same slope, they are parallel.

Answer:

The diameter is in the 77th percentile.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

25.14 mm and standard deviation 0.08 mm.

This means that [tex]\mu = 25.14, \sigma = 0.08[/tex]

A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on?

This is the pvalue of Z when X = 25.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25.2 - 25.14}{0.08}[/tex]

[tex]Z = 0.75[/tex]

[tex]Z = 0.75[/tex] has a pvalue of 0.77.

The diameter is in the 77th percentile.

Answer:

SA of the sphere is 1333.17 and SA of the circle is 333.29

Step-by-step explanation:

Answer:

it's D 200 for sure my answer I correct

Answer:   y = 2x - 3/4

Step-by-step explanation:

y = mx + b where m is the slope, and b is the y-intercept.

y = 2x - 3/4

Answer:

m<P=130°

m<Q=130°

m<R=50°

Step-by-step explanation:

m<P=130

m<Q=130

m<R=50

Answer:

3/8

Step-by-step explanation:

this is because there are 8 students in all and only three of them are boys

Answer:

any how there are three consecutive positive numbers

Answer:

[tex] {3}^{n + 2} + \: ({3}^{n + 3} - \: {3}^{n + 1} ) \\{ 3 }^{n + 2} + {3}^{n + 1} ({3}^{2} + 1) \\ {3}^{n + 2} + {3}^{n + 1} (9 + 1) \\ {3}^{n + 1} (3 + 10) \\ {3}^{n + 1} 30 \\ {3}^{n} \times 3 \times 30 = 90 \times {3}^{n}[/tex]

second one 13/313

Answer:

The mass of the larger hummingbird is 7 1/2 or 15/2.

Step-by-step explanation:

Bee hummingbird = 1 1/4g

Larger hummingbird = 6x that

So,

1 1/4 x 6 = 7.5

7.5 as fraction = 7 1/2 or 15/2

Answer:

x = 31 degrees

Step-by-step explanation:

This is a triangle because there are 3 angles so they all add up to 180 degrees.

116 + 33 + x + 180   Add 116 and 33

149 + x = 180    subtract both sides by 149

x = 31

Answer:

3:12

4:36

Step-by-step explanation:

( pls dont report me let me kno if it wrong and i will fix it

Answer:

Step-by-step explanation:

Answer:

5.25/5 i think

Step-by-step explanation:

3/5 = 8/10 and 1/4 = 2.5/10

So if I do 8/10 + 2.5 / 10.

My reply is 10.5/10

And if I reduce as max, my reply is: 5.25 / 5