S is directly proportional to the fifth power of t

Answer:

2.4 or 2 2/5

Step-by-step explanation:

When you multiply 12/15 and 3 you get 2.4 or 2 2/5

Answer:

Exact form: 12/5

Decimal form: 2.4

Mixed number form: 2 2/5

Step-by-step explanation:

You multiply 12 by 3, and 15 by 1, then simplify your answer.

The value of the car at the end of the fifth year is approximately $5695.62, determined by the initial value of $24000 and a 25% annual depreciation rate. The nth term formula reflects the cumulative effect of depreciation on the car's value over n years.

Finding the value of the car at the end of the fifth year and how the nth term of the sequence is related to the value of the car at the end of each year.

Finding the value at the end of the fifth year (a₅):

We are given the formula for the value of the car at the end of each year: a_n = 24000 (3/4)^n, where n is the year.

We want to find the value at the end of the fifth year, so we need to substitute n = 5 into the formula: a_5 = 24000 (3/4)^5.

Calculating this expression, we get: a_5 = 24000 * 0.2373 ≈ $5695.62.

Therefore, the value of the car at the end of the fifth year is approximately $5695.62.

Understanding the nth term of the sequence:

The nth term of the sequence, a_n, represents the value of the car at the end of the nth year.

The formula for the nth term shows that the value of the car is determined by two factors:

Initial value: The initial value of the car is represented by 24000 in the formula. This is the value of the car when it is brand new.

Depreciation rate: The depreciation rate is represented by the fraction 3/4. This fraction indicates that the value of the car decreases by 25% each year. The exponent n in the formula tells us how many times this depreciation rate is applied.

Therefore, the nth term of the sequence tells us how much the car's value has depreciated after n years, starting from its initial value of $24000. The higher the value of n, the more the car has depreciated, and hence the lower its value will be.

Answer:

There are 3 equivalent fractions 28 /30, 42/45,56/6

Answer:

3/5 then 11/5

Step-by-step explanation:

These symbols "I  I" represent absolute values.

11/5 equals to 2 1/5

3/5 is less than 2 1/5

Answer:

1.97

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 250[/tex]

The alternate hypotesis is:

[tex]H_{1} \neq 250[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the hypothesis tested(null hypothesis), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

In this problem, we have that:

[tex]X = 251.6, \mu = 250, \sigma = 5.4, n = 44[/tex]

So

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{251.6 - 250}{\frac{5.4}{\sqrt{44}}}[/tex]

[tex]t = 1.97[/tex]

Given:

Given that the length of VX is 15.

The length of WX is 7.

We need to determine the altitude UX of the given triangle.

Altitude UX:

The value of the altitude UX can be determined using the altitude rule theorem.

Applying the theorem, we have;

[tex]\frac{left}{altitude}=\frac{altitude}{right}[/tex]

Substituting left = UX, altitude = VX and right = VW in the above formula, we get;

[tex]\frac{UX}{VX}=\frac{VX}{XW}[/tex]

Substituting the values, we get;

[tex]\frac{UX}{15}=\frac{15}{7}[/tex]

Multiplying both sides of the equation by 15, we have;

[tex]UX=\frac{15 \times 15}{7}[/tex]

[tex]UX=\frac{225}{7}[/tex]

[tex]UX=32.14[/tex]

Thus, the length of UX is 32.14 units.

Answer: Its 32.14

Step-by-step explanation:

Answer:

the answer is A(4.5)

Step-by-step explanation:

y/6 = 6/8

y=9/2 = 4.5

Answer:

The area can be found using the formula A = b h

The area is 21.96 m2.

Step-by-step explanation:

We conclude that the area of the parallelogram is 21.96m²,  so the correct option is the last one.

For a parallelogram of base b and height h, the area is:

A = b*h

In this case, we have that the base is 3.6m and the height is 6.1m, replacing that in the area equation we get:

A = 3.6m*6.1m = 21.96m²

Then we conclude that the area of the parallelogram is 21.96m²,  so the correct option is the last one.

If you want to learn more about area:

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Answer:

  $558.68

Step-by-step explanation:

The amount of each monthly payment is given by the amortization formula:

  A = P(r/n)/(1 -(1 +r/n)^(-nt)

where P is the principal borrowed, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

We want to find nA where we have n=12, r=0.21, t=1, P=500. Filling in these values, we get ...

  nA = Pr/(1 -(1 +r/n)^-n) = $500(0.21)/(1 -1.0175^-12) = $558.68

The total amount needed to repay the loan in 1 year is $558.68.

Answer:

$615.72

Step-by-step explanation:

Use the compound interest formula and substitute the given value: A=$500(1+0.21/12)^12(1)

Simplify using order of operations: A=$500(1.0175)^12=$500(1.231439315)

=$615.72

The area of a rectangle combined with a semi-circle can be found by adding the rectangular area calculated via Length x Width to the semi-circular area calculated by 0.5 x π x r². The total area in this case would be approximately 5981.75 m².

The area of a field that is shaped like a rectangle with a semi-circle at one end can be found by summing the area of the rectangle and the area of the semi-circle. The area of a rectangle is given by the formula Length x Width. So in this instance, the rectangle's area would be 100m x 50m = 5000 m². The area of a semi-circle is given by the formula 0.5 x π x r², where r is the radius of the semi-circle. Given one side of the rectangle is along the diameter of the semi-circle, the radius of the semi-circle would be half the width of the rectangle, i.e., 25m. So the area of the semi-circle would be 0.5 x π x 25m² = 0.5 x 3.1416 x 625 = 981.75 m² approximately.  Therefore, the total area of the field would be 5000 m² + 981.75 m² which is 5981.75 m² approximately.

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Answer:

We need a sample of at least 82 female white-tailed deer

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 99% confidence level, to within 6 pounds of the actual weight?

We need a sample of size at least n.

n is found when [tex]M = 6, \sigma = 21[/tex]. So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]6 = 2.575*\frac{21}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 21*2.575[/tex]

[tex]\sqrt{n} = \frac{21*2.575}{6}[/tex]

[tex](\sqrt{n})^{2} = (\frac{21*2.575}{6})^{2}[/tex]

[tex]n = 81.23[/tex]

Rounding up

We need a sample of at least 82 female white-tailed deer

Answer:

[tex]n=(\frac{2.58(21)}{6})^2 =81.54 \approx 82[/tex]

So the answer for this case would be n=82 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=21[/tex] represent the estimation for the population standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =6 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.005;0;1)", and we got [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(21)}{6})^2 =81.54 \approx 82[/tex]

So the answer for this case would be n=82 rounded up to the nearest integer

Answer:

They Bisect

Step-by-step explanation:

They don't have the same slope.

They aren't instersecting at a right angle (they aren't perpendicular)

They aren't parallel because they touch.

Answer:

16y + 32

Step-by-step explanation:

Expand each term.

(y+6)² - (y-2)²

= (y+6)(y+6) - (y-2)(y-2)

= y² + 12y + 36 - (y² - 4y + 4)

Subtract the second group by changing each term's signs

= y² + 12y + 36 - y² + 4y - 4

Collect like terms

= 16y + 32

Answer:

m<56. that is all I can help with

To determine the sample size needed for a 99% confidence interval with a maximum width of .18 for a coin flip experiment, we must rely upon statistical principles such as the law of large numbers and the relationship between sample size and confidence interval width. Although we cannot give a specific number without more details, it is generally true that a larger sample size (i.e., more coin flips) results in a narrower confidence interval.

Your question pertains to finding the necessary sample size for a particular width of a confidence interval in a coin-flip experiment. A confidence interval represents the range where we are certain that the parameter, in this case, the probability of getting a head, lies to a certain degree, say 99%. Narrowing down this interval or making it smaller would require a larger number of coin flips or trials. The probable outcome of our experiment does indeed align with the theoretical probability when a large number of trials is conducted, which is also known as the law of large numbers.

The calculation of the size of a confidence interval involves standard deviation, confidence level (z-score) and sample size. By adjusting these parameters, we can alter the size of a confidence interval. For example, a 90% confidence interval would be smaller compared to a 95% interval due to the decreased degree of certainty. However, without exact numbers we cannot directly calculate how many flips are required for a 99% confidence interval of a certain width.

As a general rule of thumb, when conducting confidence interval tests, it would be safe to suggest that a larger sample size (which for a coin flip experiment would mean more coin flips) will result in a narrower confidence interval. Therefore, to achieve a 99% confidence interval of width at most .18, one would need net a large number of trials, or flips.

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Answer:

Step-by-step explanation:

GIVEN: Suppose you want to make a cylindrical pen for your cat to play in (with open top) and you want the volume to be [tex]100[/tex] cubic feet. Suppose the material for the side costs [tex]\$3[/tex] per square foot, and the material for the bottom costs [tex]\$7[/tex] per square foot.

TO FIND: What are the dimensions of the pen that minimize the cost of building it.

SOLUTION:

Let height and radius of pen be [tex]r\text{ and }h[/tex]

Volume [tex]=\pi r^2h=100\implies h=\frac{100}{\pi r^2}[/tex]

total cost of building cylindrical pen [tex]C=3\times \text{lateral area}+7\times\text{bottom area}[/tex]

                                                                [tex]=3\times2\pi r h+7\times\pi r^2=\pi r(6h+7r)[/tex]

                                                                [tex]=\frac{600}{r}+7\pi r^2[/tex]

for minimizing cost , putting [tex]\frac{d\ C}{d\ r}=0[/tex]

[tex]\implies -\frac{600}{r^2}+44r=0 \Rightarrow r^3=\frac{600}{44}\Rightarrow r=2.39\text{ feet}[/tex]

[tex]\implies h=5.57\text{ feet}[/tex]

Hence the radius and height of cylindrical pen are [tex]2.39\text{ feet}[/tex] and [tex]5.57\text{ feet}[/tex] respectively.

Answer:

They should go on to launch the online edition

Step-by-step explanation:

Total surveyed = 400

A = accept if 15% above subscribes

B = reject if subscribers are less than 15%

on the survey it is clearly stated that 67 expressed interest.

 lets get 16% of total survey

      = 15% x 400

      = 60.

Since number of subscribers that showed interest is greater than number 15%

Hence the company can go ahead to launch the online edition

Accept A

Answer:

5 inches.

Step-by-step explanation:

We know that the circumference of a circle is equivalent to πr² or πd.

We need to know the radius given the circumference.

C = πr²

75 = 3.14(r^2)    (Divide both sides by 3.14)

23.88535031847134 = r^2    (Take the square root of both sides)

r ≈ 4.88726409338

r ≈ 5 inches.

Answer:

$24

Step-by-step explanation:

Since 25% is off the price of the shirt, she bought the shirt at 75% of it's cost price. This difference between the full cost and the 75% is what she saved (i.e. 25% was the savings)

So, if the shirt costs x dollars:

$6 = 25% of x

= ( 25/100)*X = 0.25X

X = $6/0.25 = $6x4

X = $24

8x² - 24 can be written in factorized form as  8 (x² - 3).

Step-by-step explanation:

Given expression is

8x² - 24

It can be factorized by taking the common factors as,

Since 8 is the common factor for both the terms and the expression can be written as,

8x² - 24

It can be expanded as,

= 8x² - 8×3

Now both the terms has 8, so it can be taken out and the expression can be written as,

= 8 (x² - 3)

So it can be written in factorized form as  8 (x² - 3).

Answer:

carmen winsted

Step-by-step explanation:

Answer:

y = 6x-4

Step-by-step explanation:

The slope intercept form of a line is

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

We know the slope is 6 and the y intercept is -4

y = 6x + -4

y = 6x-4

Slope-intercept form: y = mx + b (m = slope and b = y-intercept)

Slope (m) = 6

y-intercept (b) = -4

Put into its final form.

y = 6x - 4

Best of Luck!

Answer:

[tex] -1.64 = \frac{39.18 -\mu}{\sigma}[/tex]   (1)

[tex] 1.28 = \frac{73.23 -\mu}{\sigma}[/tex]   (2)

From equation (1) and (2) we can solve for [tex]\mu[/tex] and we got:

[tex] \mu = 39.18 + 1.64 \sigma[/tex]   (3)

[tex] \mu = 73.23 - 1.28 \sigma[/tex]   (4)

And we can set equal equations (3) and (4) and we got:

[tex] 39.18 +1.64 \sigma = 73.23 -1.28 \sigma[/tex]

And solving for the deviation we got:

[tex] 2.92\sigma = 34.05[/tex]

[tex]\sigma = 11.66[/tex]

And the mean would be:

[tex] \mu = 39.18 +1.64 *11.66 = 58.304[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the vehicle speed of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(\mu,\sigma)[/tex]  

For this case we know the following conditions:

[tex] P(X<39.18) = 0.05 [/tex]

[tex]P(X>73.23) = 0.1[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

We look for a one z value that accumulate 0.05 of the area in the left tail and we got: [tex] z_ 1= -1.64[/tex] and we need another z score that accumulates 0.1 of the area on the right tail and we got [tex] z_2 = 1.28[/tex]

And we have the following equations:

[tex] -1.64 = \frac{39.18 -\mu}{\sigma}[/tex]   (1)

[tex] 1.28 = \frac{73.23 -\mu}{\sigma}[/tex]   (2)

From equation (1) and (2) we can solve for [tex]\mu[/tex] and we got:

[tex] \mu = 39.18 + 1.64 \sigma[/tex]   (3)

[tex] \mu = 73.23 - 1.28 \sigma[/tex]   (4)

And we can set equal equations (3) and (4) and we got:

[tex] 39.18 +1.64 \sigma = 73.23 -1.28 \sigma[/tex]

And solving for the deviation we got:

[tex] 2.92\sigma = 34.05[/tex]

[tex]\sigma = 11.66[/tex]

And the mean would be:

[tex] \mu = 39.18 +1.64 *11.66 = 58.304[/tex]

Using the normal distribution, it is found that:

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

In this problem, 39.18 m/h is the 5th percentile, hence, when X = 39.18, Z has a p-value of 0.05, so Z = -1.645.

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

[tex]-1.645 = \frac{39.18 - \mu}{\sigma}[/tex]

[tex]39.18 - \mu = -1.645\sigma[/tex]

[tex]\mu = 39.18 + 1.645\sigma[/tex]

Additionally, 73.23 m/h is the 100 - 10 = 90th percentile, hence, when X = 73.23, Z has a p-value of 0.9, so Z = 1.28.

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

[tex]1.28 = \frac{73.23 - \mu}{\sigma}[/tex]

[tex]73.23 - \mu = 1.28\sigma[/tex]

[tex]\mu = 73.23 - 1.28\sigma[/tex]

Equaling both equations, we find the standard deviation, hence:

[tex]39.18 + 1.645\sigma = 73.23 - 1.28\sigma[/tex]

[tex]2.925\sigma = 34.05[/tex]

[tex]\sigma = \frac{34.05}{2.925}[/tex]

[tex]\sigma = 11.64[/tex]

Then, we can find the mean:

[tex]\mu = 73.23 - 1.28\sigma = 73.23 - 1.28(11.64) = 58.33[/tex]

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The optimal point where the cable splits into two branches for Springfield and Shelbyville is at point (4,0) on the x-axis. This is computed through calculus principles for optimization and the distance formula. The minimum total cable length connecting all three towns is about 11.66 units.

The subject of this problem is optimization in mathematics, specifically in coordinate geometry and calculus. The problem can be solved using the distance formula in the xy-plane as well as the principles of differential calculus.

Let's denote the point (x,0) where cable splits as P, Centerville as C, Springfield as S and Shelbyville as Sh. By using the distance formula, we can determine the lengths of the branch cables, CS and CSh.

The total length of the cable is the sum of these two distances. That gives us: Cable Length = sqrt[(8-x)²+7²] + sqrt[(8-x)²+(-7)²].

To find the minimum cable length, we differentiate the above function and equate it to zero to find the critical points. Using differential calculus, we can see that minimum cable length reduces to x = 4. Therefore, the point where cable splits is (4, 0).

Substitute x = 4 into the cable length equation to get the minimum total cable length, which is roughly 11.66 units.

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The location that minimizes the amount of cable is [tex](\frac{7}{\sqrt 3},0)[/tex], total length being 20.12 units.

To minimize the amount of cable needed in the Y-shaped configuration, we need to find the optimal point (x, 0) on the x-axis where the cable splits. This point should minimize the total length of cable from Centerville to Springfield and Shelbyville.

Step-by-Step Solution:

1. Identify the distances involved:

  - The distance from Centerville (8,0) to (x,0) on the x-axis.

  - The distance from (x,0) to Springfield (0,7).

  - The distance from (x,0) to Shelbyville (0,-7).

2. Define the distances mathematically:

  - The distance from Centerville to (x,0) is:

  [tex]\[ L_1 = |8 - x| \] - The distance from \((x,0)\) to Springfield \((0,7)\) is: \[ L_2 = \sqrt{x^2 + 7^2} = \sqrt{x^2 + 49} \] - The distance from \((x,0)\) to Shelbyville \((0,-7)\) is: \[ L_3 = \sqrt{x^2 + (-7)^2} = \sqrt{x^2 + 49} \][/tex]

3. Total length of the cable L:

[tex]\[ L = L_1 + L_2 + L_3 = |8 - x| + \sqrt{x^2 + 49} + \sqrt{x^2 + 49} \] \[ L = |8 - x| + 2\sqrt{x^2 + 49} \][/tex]

4. Optimize the total length L:

  To find the minimum, we need to consider the derivative of L with respect to x. Since L involves absolute value, we'll consider two cases: x ≤ 8) and x > 8.

  Case 1: x ≤ 8

[tex]\[ L = (8 - x) + 2\sqrt{x^2 + 49} \] \[ \frac{dL}{dx} = -1 + 2 \cdot \frac{x}{\sqrt{x^2 + 49}} \][/tex]

  Set the derivative equal to zero to find critical points:

[tex]\[ -1 + 2 \cdot \frac{x}{\sqrt{x^2 + 49}} = 0 \] \[ 2 \cdot \frac{x}{\sqrt{x^2 + 49}} = 1 \] \[ \frac{x}{\sqrt{x^2 + 49}} = \frac{1}{2} \] \[ x = \frac{\sqrt{x^2 + 49}}{2} \][/tex]

  Square both sides to solve for x:

[tex]\[ x^2 = \frac{x^2 + 49}{4} \] \[ 4x^2 = x^2 + 49 \] \[ 3x^2 = 49 \] \[ x^2 = \frac{49}{3} \] \[ x = \frac{7}{\sqrt{3}} = \frac{7\sqrt{3}}{3} \][/tex]

Case 2: (x > 8)

  This case would lead to a contradiction because the optimal point must lie on the interval [tex]\(0 \leq x \leq 8\)[/tex] for the Y-configuration to be practical.

Conclusion:

The point (x, 0) that minimizes the total length is:

[tex]\[x = \frac{7\sqrt{3}}{3}\][/tex]

[tex]1. \(d_1 = |x - 8| = \left| \frac{7}{\sqrt{3}} - 8 \right|\)\\2. \(d_2 = \sqrt{x^2 + 49} = \sqrt{\left(\frac{7}{\sqrt{3}}\right)^2 + 49}\)\\3. \(d_3 = \sqrt{x^2 + 49} = \sqrt{\left(\frac{7}{\sqrt{3}}\right)^2 + 49}\)[/tex]

[tex]\[ \text{Total length} = \left| \frac{7}{\sqrt{3}} - 8 \right| + 2\sqrt{\left(\frac{7}{\sqrt{3}}\right)^2 + 49} \]\[ \text{Total length} = \left| \frac{7}{\sqrt{3}} - 8 \right| + 2\sqrt{\frac{49}{3} + 49} \]\[ \text{Total length} = \left| \frac{7}{\sqrt{3}} - 8 \right| + 2\times \sqrt{16.33+49}\]\[ \text{Total length} = \left| 4.04 - 8 \right| + 2\times 8.08\][/tex]

[tex]\text{Total length}=3.96+16.16=20.12[/tex]

The probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.

To solve this problem, we need to find the probability that the sample proportion of defective cell phones will differ from the population proportion (19%) by more than 5%.

Given information:

- Population proportion of defective cell phones = 0.19 (or 19%)

- Sample size = 399

Calculate the standard error of the proportion.

[tex]\[\text{Standard error of the proportion} = \sqrt{\frac{p \times (1 - p)}{n}}\]Substituting the given values:\[\text{Standard error of the proportion} = \sqrt{\frac{0.19 \times (1 - 0.19)}{399}}\]\[\text{Standard error of the proportion} = \sqrt{\frac{0.19 \times 0.81}{399}}\]\[\text{Standard error of the proportion} = \sqrt{\frac{0.1539}{399}}\]\[\text{Standard error of the proportion} = 0.0196 \text{ or } 1.96\%\][/tex]

Calculate the maximum allowable difference from the population proportion.

Maximum allowable difference = 0.05 (or 5%)

Calculate the z-score for the maximum allowable difference.

z-score = (Maximum allowable difference - Population proportion) / Standard error of the proportion

z-score = (0.05 - 0.19) / 0.0196

z-score = -2.55

Find the probability using the standard normal distribution table or calculator.

The z-score of -2.55 corresponds to a probability of 0.0054 (or 0.54%) in the standard normal distribution table.

Since the question asks for the probability that the sample proportion will differ from the population proportion by more than 5%, we need to find the probability of both tails.

Probability of both tails = 2 × 0.0054 = 0.0108 or 1.08%

Therefore, the probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.

The probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.

To solve this problem, we need to find the probability that the sample proportion of defective cell phones will differ from the population proportion (19%) by more than 5%.

Given information:

- Population proportion of defective cell phones = 0.19 (or 19%)

- Sample size = 399

Calculate the standard error of the proportion.

[tex]\[\text{Standard error of the proportion}[/tex]=[tex]\sqrt{p \times (1 - p))/(n)[/tex]

Substituting the given values:[tex]\[\text{Standard error of the proportion} = \sqrt{(0.19 \times (1 - 0.19))/(399)[/tex]

[tex]\[\text{Standard error of the proportion} = \sqrt{(0.19 \times 0.81)/(399)}\\\text{Standard error of the proportion} = \sqrt{(0.1539)/(399)}\\\text{Standard error of the proportion} = 0.0196 \text{ or } 1.96\%\][/tex]

Calculate the maximum allowable difference from the population proportion.

Maximum allowable difference = 0.05 (or 5%)

Calculate the z-score for the maximum allowable difference.

z-score = (Maximum allowable difference - Population proportion) / Standard error of the proportion

z-score = (0.05 - 0.19) / 0.0196

z-score = -2.55

Find the probability using the standard normal distribution table or calculator.

The z-score of -2.55 corresponds to a probability of 0.0054 (or 0.54%) in the standard normal distribution table.

Since the question asks for the probability that the sample proportion will differ from the population proportion by more than 5%, we need to find the probability of both tails.

Probability of both tails = 2 × 0.0054 = 0.0108 or 1.08%

Therefore, the probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.

Answer:

QS + QR > RS

QR + RS > QS

RS + QS > QR

Step-by-step explanation:

JUST TOOK THE TEST

The complete Triangle Inequality is

The triangle inequality theorem defines the relationship between a triangle's three sides. The total of the lengths of the two sides of any triangle is always greater than the length of the third side, according to this theorem. In other words, the shortest distance between two unique points is always a straight line, according to this theorem.

According to Triangle Inequality " the sum of two side of the triangle is greater than the third side of Triangle."

Then, applying Triangle Inequality

QS + QR > RS

QR + RS > QS

RS + QS > QR

Learn more about Triangle Inequality here:

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Answer:

59/10

Step-by-step explanation:

5+9/10

50/10 + 9/10

=59/10

Answer:

it 59/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can use the simple one.

20*0.15*n year= answer

answer+20

or Compound

20*0.15 to de power of the year(s)

Answer:

0.13% probability that this selected sample has an average thickness greater than 53

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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 problem, we have that:

[tex]\mu = 50, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

What is the probability that this selected sample has an average thickness greater than 53?

This is 1 subtracted by the pvalue of Z when X = 53. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{53 - 50}{1}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a pvalue of 0.9987

1 - 0.9987 = 0.0013

0.13% probability that this selected sample has an average thickness greater than 53

Answer:

Its the neither option

Step-by-step explanation:

In a normal distribution, the mean and median are equal.

Option C is the correct answer.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

In a normal distribution,

The mean and median are both measures of central tendency.

The mean is calculated by adding up all the values in the distribution and dividing by the total number of values.

The median is the value that falls in the middle when the data is arranged in order.

Now,

In a perfectly symmetrical normal distribution, the mean and median are equal and they both fall at the exact center of the distribution.

However, if the distribution is skewed to one side or the other, the mean and median may be different.

Thus,

In a normal distribution, the mean and median are equal.

Learn more about mean here:

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Los tres puntos son (-3,0), (3,0), (0,4).

Por lo tanto, la respuesta es A, espero que esto ayude, que tenga un buen día.