39 inches is the right answer just did the test on edge

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

X + y = 10

Rewrite as y = 10-x

Y - x = 6

Replace y

10-x -x = 6

Simplify:

10-2x = 6

Subtract 10 from both sides:

-2x = -4

Divide both sides by -2:

X = 2

Now replace x in the first equation:

2 + y = 10

Subtract 2 from both sides:

Y = 8

The two numbers are 8 and 2

Answer:  46

Step-by-step explanation:

Let the 3 consecutive even numbers be x, (x-2) and (x+2) respectively.

According to the question,

x + (x - 2) + (x + 2) = 132

or, x + x - 2 + x + 2 = 132

or, 3x = 132

or, x = 132 ÷ 3

or, x = 44

So, first even number = 44

Required third number = 44 + 2

= 46

Answer:

A right angle

Step-by-step explanation:

Answer:

Right angle. Its angle is in the corner and measured 90 degrees.

Step-by-step explanation:

Probability (Ball goes into hole) = 0.22388 or 22.388%

Step-by-step explanation:

Given:

Ball goes into hole = 15 times

Ball miss the hole = 52 times

Find:

Probability (Ball goes into hole)

Computation:

Total number of tries = 15 + 52

Total number of tries = 67

Probability (Ball goes into hole) = 15 / 67

Probability (Ball goes into hole) = 0.22388 or 22.388%

Answer:

Step-by-step explanation:

I think its B, (30)

Answer:

2

Step-by-step explanation:

Given the quadratic equation

3x²+2x-1=0

Let tthe root be α and β

Sum of root α+β = -b/a

Product of root αβ = c/a

Given that;

a = 3, b = 2 and c = -1

α+β = -2/3

αβ = -1/3

To get 1/α + 1/β

Find the LCM

1/α + 1/β

= (α+β)/αβ

= (-2/3)/(-1/3)

= -2/3 * 3/-1

=  2

Hence the required answer  is 2

Answer:

In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation you’re familiar with where one quantity changes constantly in relation to another quantity. How are the two quantities in the situation related? If you represent the two quantities on a graph, what will it look like?

Step-by-step explanation:

Given:

The equation of parallel line is [tex]y=6[/tex].

The line contains the point (-1,1).

To find:

The equation of the line.

Solution:

The slope intercept form of a line is:

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

Where, m is the slope and b is the y-intercept.

The equation of parallel line is

[tex]y=6[/tex]

It can be written as

[tex]y=(0)x+6[/tex]

The slope of this line is 0.

The slopes of two parallel lines are always equal. So, the slope of the required line is also 0. It passes through the point (-1,1) so the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-1=0(x-(-1))[/tex]

[tex]y-1=0[/tex]

[tex]y=1[/tex]

Therefore, the equation of the required line is 1.

Answer:

you are right

Step-by-step explanation:

Use the law of law of cos

c^2=a^2+b^2﹣2abcos√angle

(2√13)^2=52=4+36-24cos(a)

cos(a) = -12/24 =  -1/2

a = 120 degrees

so yes, you are right

Answer:

a 15

b 42

c 12

trust me

Answer:

1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

factors:

1, 2, 3, 6, 9, 18, 27, 54.

Therefore, all the factor pairs for 54 is 1, 2, 3, 6, 9, 18, 27, 54..

Answer: (1,54) (2,27) (3,18) (6,9)

Step-by-step explanation: 54 x 1 = 54    27 x 2 = 54    3 x 18 = 54   6 x 9 = 54

Answer:

[tex]\huge\boxed{\sf 168\ in.\²}[/tex]

Step-by-step explanation:

Surface area of the base:

= Length * Length

= 6 * 6

= 36 in.²

Surface Area of 1 Lateral Face:

= [tex]\sf \frac{1}{2} (Base * Height)[/tex]

Base = 6 inches

Height = 11 inches

= 1/2 (6*11)

= 3 * 11

= 33 in.²

Surface Area of 4 lateral faces:

= 33 * 4

= 132 in.²

Surface Area of the whole pyramid:

= 132 + 36

= 168 in.²

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

SA = 168 in.²

Step-by-step explanation:

The surface area is the sum of the area of the base and the areas of the 4 congruent triangular sides.

s = side of the base

h = height of each side

SA = s² + 4(sh/2)

SA = (6 in.)² + 4(6 in.)(11 in.)/2

SA = 36 in.² + 132 in.²

SA = 168 in.²

Complete question :

Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.

Answer:

0.10935

0.3718

0.9778

0.606

Step-by-step explanation:

μ = 721 ; σ = 454 ; n = 50

P(x > 800)

Zscore = (x - μ) / σ/sqrt(n)

P(x > 800) = (800 - 721) ÷ 454/sqrt(50)

P(x > 800) = 79 / 64.205295

P(x > 800) = 1.23

P(Z > 1.23) = 0.10935

2.)

Less than 700

P(x < 700) = (700 - 721) ÷ 454/sqrt(50)

P(x < 700) = - 21/ 64.205295

P(x < 700) = - 0.327

P(Z < - 0.327) = 0.3718

Between 700 and 850

P(x < 850) = (850 - 721) ÷ 454/sqrt(50)

P(x < 850) = 129/ 64.205295

P(x < 700) = 2.01

P(Z < 2.01) = 0.9778

P(x < 850) - P(x < 700) =

P(Z < 2.01) - P(Z < - 0.327)

0.9778 - 0.3718

= 0.606

Answer:The answer is c

Step-by-step explanation:

The best estimate of the number of boxes Graphic DesignWorks is able to store is 1440000 boxes.

Volume is the three-dimensional space enclosed by a three-dimensional object.

We have to find the volume of the box and the volume of the storage space.

Volume = length × breadth × height

= 24 × 18× 16 in³

=6912 in³

Volume = length × breadth × height

= 400 × 240 × 60 ft³

= 5760000 ft³

Therefore, 5760000 ft³ = 5760000 × (12)³ in³

Number of boxes that can fit inside the storage space = (5760000 × (12)³ in³)/6912 in³

= 1440000 boxes.

Thus, the best estimate of the number of boxes Graphic DesignWorks is able to store is 1440000 boxes. The correct answer is option B.

Learn more about volume here-https://brainly.com/question/25736513

#SPJ2

Answer:

the third option

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer:

4(3) - 7 = 4(3 - 1) - 3

12 - 7 = 4(2) - 3

5 = 8 - 3

= 5

They are equivalent because when they are both simplified they have the same answer 5

Answer:

Well it would be a total of 2 Cup Cakes

Step-by-step explanation:

1/3 + 1/3 + 4/3 =2

2/3 +4/3 = 6/3

ye

Answer:

Step-by-step explanation:

it would be 2

Answer: it triples by 3 so 15,45, 135

Step-by-step explanation: this is by 3 because it goes on by 15,45,135

Answer:

[tex]y = -x -1[/tex]

Step-by-step explanation:

Given

Passed through (-5,4)

Parallel to: y=-x + 6

Required

Determine the line equation

If it is parallel to: y=-x + 6, then it means that they have the same slope.

A linear equation y = mx + b has the slope m.

So, by comparison of y = mx + b  to y = -x + 6

[tex]m = -1[/tex]

The line equation is then calculated as:

[tex]y=m(x - x_1) + y_1[/tex]

Where

[tex]m = -1[/tex]

[tex](x_1,y_1) = (-5,4)[/tex]

So:

[tex]y = -1(x - (-5)) + 4[/tex]

[tex]y = -1(x +5) + 4[/tex]

[tex]y = -x -5 + 4[/tex]

[tex]y = -x -1[/tex]

I think 710 is the answer

266+266+89+89= 710

(x*5)-10=45=equation

im extra so x would be 7

Answer:

5n+5-15=0

5n-10=0

5n=10

therefore n = 10/5 = 2

therefore n=2

Answer:

∆EDA~∆ECB (AAA)

3÷ (15+3) = AB ÷ (12+AB)

AB = 2.4

2y

Step-by-step explanation:

16y^5-3/4)

16y²/4)

4y²)1/2

2y