is 20% greater or less than 1/4 ​

Answer:

a) 0.1587 = 15.87% probability that a battery will last more than 20 hours.

b) 15.44 hours.

c) Approximately the 16th percentile.

d) 0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.

e) 0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this question, we have that:

[tex]\mu = 18, \sigma = 2[/tex]

(a) What is the probability that a battery will last more than 20 hours?

This is 1 subtracted by the pvalue of Z when X = 20. So

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

[tex]Z = \frac{20 - 18}{2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that a battery will last more than 20 hours.

(b) Find the 10th percentile of the lifetimes.

This is X when Z has a pvalue of 0.1. So X when Z = -1.28

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

[tex]-1.28 = \frac{X - 18}{2}[/tex]

[tex]X - 18 = -1.28*2[/tex]

[tex]X = 15.44[/tex]

So 15.44 hours.

(c) A particular battery lasts 16 hours. What percentile is its lifetime on?

We have to find the pvalue of Z when X = 16. So

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

[tex]Z = \frac{16 - 18}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

Approximately the 16th percentile.

(d) What is the probability that the lifetime of a battery is between 17.5 and 18.5?

This is the pvalue of Z when X = 18.5 subtracted by the pvalue of Z when X = 17.5. So

X = 18.5

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

[tex]Z = \frac{18.5 - 18}{2}[/tex]

[tex]Z = 0.25[/tex]

[tex]Z = 0.25[/tex] has a pvalue of 0.5987

X = 17.5

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

[tex]Z = \frac{17.5 - 18}{2}[/tex]

[tex]Z = -0.25[/tex]

[tex]Z = -0.25[/tex] has a pvalue of 0.4013

0.5987 - 0.4013 = 0.1974

0.1974 = 19.74% probability that the lifetime of a battery is between 17.5 and 18.5.

(e) Ten batteries are chosen at random, what is the probability that the mean lifetime is between 17.5 and 18.5?

Sample of 10 means that, by the Central Limit Theorem, [tex]n = 10, s = \frac{2}{\sqrt{10}} = 0.6325[/tex]

X = 18.5

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

[tex]Z = \frac{18.5 - 18}{0.6325}[/tex]

[tex]Z = 0.79[/tex]

[tex]Z = 0.79[/tex] has a pvalue of 0.7852

X = 17.5

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

[tex]Z = \frac{17.5 - 18}{0.6325}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a pvalue of 0.2148

0.7852 - 0.2148 = 0.5704

0.5704 = 57.04% probability that the mean lifetime is between 17.5 and 18.5

We are given r(x) and c(x).

p(x) = 8x - (3x + 12)

p(x) = 8x - 3x - 12

p(x) = 5x - 12

Done.

Answer:

$0.58

Step-by-step explanation:

There are 8 pencils per package. To find the value of each pencil, divide the cost by 8

4.64/8 = $0.58

Answer:

$0.58

Step-by-step explanation:

unit means one, or the rate or price of each pencil. so if the total was 4.64, youd divide 4.64 by 8, which comes out to $0.58 per pencil

Answer:

it's the3rd one

Step-by-step explanation:

it's is 182 feet

Answer: 18.25

Step-by-step explanation: Lets start off with this: 1/4 is the same as 25 (like if you use quarters, you know 4 quarters makes a dollar, and one quarter is 25)

So, since we have 18 and 25, converting it to a decimal is easy. Put the numbers together (18 and 25) Then just add decimal in the middle.

                                                         OR

18 x 4 (which is 72) then add 72 to the numerator (1) which will give you 73 (72 + 1) Finally, divide 73 by 4, (4 is denominator) which will then give you 18.25 :D

The mixed number  [tex]18\frac{1}{4}[/tex]  written as a decimal is 18.25.

To write [tex]18\frac{1}{4}[/tex] as a decimal, we can convert the mixed number into an improper fraction and then divide the numerator by the denominator.

The mixed number to an improper fraction.

[tex]18\frac{1}{4}[/tex] = (18 × 4 + 1)/4

= 73/4

Divide the numerator by the denominator.

73 ÷ 4

= 18.25

Therefore,  [tex]18\frac{1}{4}[/tex]  written as a decimal is 18.25.

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Answer:

m = 5/9

Step-by-step explanation:

rise = 5

run = 9

m = rise/run

m = 5/9

Answer:

m = 5/9

Step-by-step explanation:

Use the slope formula to find the slope m.

[tex]m = \frac{5}{9}[/tex]

Answer:

[tex]2^{-4}[/tex] = 1/16

[tex]6^{-5}[/tex] × [tex]6^{5}[/tex] = 1

Step-by-step explanation:

[tex]2^{-4}[/tex] = 0.0625

0.0625 = 1/16

[tex]6^{-5}[/tex] × [tex]6^{5}[/tex] = 1

The graph has the same y Intercept as the line shown is y = 5x - 5.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We take two points from the graph as (-5, 0) and (0, -5)

So, the slope of line

slope = (-5 - 0)/ (0- (-5))

slope= -5 / 5

slope= -1

Using slope intercept form

y= mx+ b

y= -x+ b

Now, put x= -5 and y= 0 then

0 = -(-5)+ b

b= -5

So, the equation of line is

y= -x - 5

Here, the y intercept is -5.

So, the equation with same y intercept is

y = 5x - 5

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Answer: Add each side to get perimeter so your total is 38ft

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

Answer:

The answer is 3.4

Step-by-step explanation:

5 or more, round up

4 or less, round down

rounding 6

round up

so...

3.4

(-2, -7) and (-4, -9)

Answer:

3.4Oz

Step-by-step explanation:

Step-by-step explanation:

Heueueirjrjkwugoystsitso5wpysoydlusktzlhskgdlysyldj

Answer:

Step-by-step explanation:

24/300 = 0.08 = 8%

Answer:

I Need Numbers Somthing....... Its Imposable to answer this

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

1/3 of 3/4 means

(1/3) x 3/4

3/12

0.25

Answer:

Step-by-step explanation:

i am not sure do they give you a number of tiles

Answer:

A: 6/50

Step-by-step explanation:

i think

Answer:

7x - 8

Step-by-step explanation:

eight less than product of seven and X

seven and x = 7x

eight less than = - 8

put it all together = 7x - 8

Answer:

7x - 8

Step-by-step explanation:

product of seven and X

7 X x = 7x

8 less than it

7X - 8

This is because we're looking for something that is smaller than 7X by 8

Answer:

A, D

Step-by-step explanation:

It's basic math, height times length = Area.

Answer:

A and D are the only ones that i can see that would be correct

Step-by-step explanation:

Answer:

21 x 33 = 693

16 x 7 divided by 2 = 216

17.6 x 17.6 divided by 2 = 154.9

19 x 7.8 = 148.2

7 + 2 x 5.5 divided by 2 = 24.8

10 x 12 = 120

Please wait for more responses if needed!

Answer:

81 samples

Step-by-step explanation:

According to the empirical rule :

Possible values of the sample mean is within 3 standard deviations of the population mean :

μ ± 3 sd(x) ; sd(x) = standard deviation of sampling distribution.

3 * sd(x) = 1

sd(x) = 1/3

Recall:

Standard deviation of sampling distribution, sd(x)

sd(x) = σ / sqrt(n)

1/3 = 3 / sqrt(n)

Square both sides

1/9 = 9/n

Cross multiply :

n * 1 = 9 * 9

n = 81

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

When you reflect a point of the x-axis you can apply:

(x,y) -> (x,-y)

Using this:

(2,-5) -> (2,5)

Since both the x and y places are positive, it is in quadrant 1.

Hope this helps!

Step-by-step explanation:

Step-by-step explanation:

[tex] \tt{} \frac{24}{10} [/tex]

[tex] \tt{} \frac{24 \div 2}{10 \div 2} [/tex]

[tex]\tt{} \frac{12}{5} [/tex]

[tex]\tt{}2 \frac{2}{5} \: \: \: \: \: = 2.4[/tex]

Answer:

2x + 2y + 2

Step-by-step explanation:

A is right

Answer:

(-4,8)

(12,0)

(4,4)

Step-by-step explanation:

graph it

Answer:

The volume of the cube is 77 inches.

9514 1404 393

Answer:

  a ≈ 4.68

Step-by-step explanation:

The law of cosines tells you ...

  a² = b² +c² -2bc·cos(A)

  a = √(b² +c² -2bc·cos(A))

  a = √(5² +8² -2·5·8·cos(33°)) = √(25 +64 -80·0.83867) ≈ √21.906

  a ≈ 4.68

Answer:

a≈4.68

Step-by-step explanation:

have a good one!!!

Answer: 10

Step-by-step explanation:

List out the numbers:

20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40

There are 10 odd numbers

Otherwise a faster method:

Odd numbers occur every other number

There are 40 - 20 = 20 numbers between 20 and 40

20/2 = 10

10 odd numbers

Answer:

22.7°

Step-by-step explanation:

22.714° to nearest 10th is 22.7

Step-by-step explanation:

20a + 158+6c=you will expand the brackets

= so it is 120+60+48

20a+158+6c=120+60+48

20a+ 6c=120+60+48-158

20a+6c=70

20a divide by 20+6c divide by 6 on both side

a + c = 0.58

Answer:

x^3y^5 + 5x^2y^3 - 4xy^2

Step-by-step explanation:

xy^2 (x^2y^3+5xy-4)

xy^2x^2y^3 + xy^2 x 5xy - 4xy^2

xy^2x^2y^3 = yx^2y^5

xy^2 x 5xy = 5x^2y^3

x^3y^5 + 5x^2y^3 - 4xy^2

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