Find an equation for this line.

Answer:

0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 50, \sigma = 1.5, n = 10, s = \frac{1.5}{\sqrt{10}} = 0.4743[/tex]

What is the probability that the sample mean hardness for a random sample of 10 pins is at least 51

This is 1 subtracted by the pvalue of Z when X = 51. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{51 - 50}{0.4743}[/tex]

[tex]Z = 2.11[/tex]

[tex]Z = 2.11[/tex] has a pvalue of 0.9826

1 - 0.9826 = 0.0174

0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51

Answer:

2,000

Step-by-step explanation:

if you divide 600,000 by 300 you get 2,000.

Answer:

D

Step-by-step explanation:

0.2x+5=8

0.2x=3

x=15

Therefore, the correct answer is choice D. Hope this helps!

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Answer:

1 .angle S is 90 degree

2. 12

3. 155 degree

1. x = 3

hope it helps .....

Answer:

Minimum population of fish in lake = 2400 - 155 = 2245

Maximum population of fish in lake = 2400 + 155 = 2555

Step-by-step explanation:

population of fish in lake = 2400

Variation of fish = 155

it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.

For example

for increase

population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc

but it cannot be beyond 2400 + 155.

It cannot be 2400 + 156

similarly for decrease

population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc

but it cannot be less that 2400 - 155.

It cannot be 2400 - 156

Hence population can fish in lake can be between 2400 - 155 and 2400 + 155

minimum population of fish in lake = 2400 - 155 = 2245

maximum population of fish in lake = 2400 + 155 = 2555

Answer:

[tex]6cm^2[/tex]

Step-by-step explanation:

Let x and y be the sides of the rectangle.

Area of the Triangle, A(x,y)=xy

From the diagram, Triangle ABC is similar to Triangle AKL

AK=4-y

Therefore:

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

[tex]4x=6(4-y)\\x=\dfrac{6(4-y)}{4} \\x=1.5(4-y)\\x=6-1.5y[/tex]

We substitute x into A(x,y)

[tex]A=y(6-1.5y)=6y-1.5y^2[/tex]

We are required to find the maximum area. This is done by finding

the derivative of Aand solving for the critical points.

Derivative of A:

[tex]A'(y)=6-3y\\$Set $A'=0\\6-3y=0\\3y=6\\y=2$ cm[/tex]

Recall that: x=6-1.5y

x=6-1.5(2)

x=6-3

x=3cm

Therefore, the maximum rectangle area is:

Area =3 X 2 =[tex]6cm^2[/tex]

Answer:

x = 3, -7

Step-by-step explanation:

Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:

x - 3 = 0

x + 7 = 0

x = 3, -7

Answer:

3 or -7

Step-by-step explanation:

For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer:

Center, radius, chord, diameter... are Words related to circle

Answer:

Approximately 68% of the customer accounts have payment made between 23 and 37 days.

Step-by-step explanation:

We want to calculate what two values will approximately 68% of the numbers of days be.

For a bell shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.

Then, for a mean of 30 and standard deviation of 7, we can calculate the two values as:

[tex]X_1=\mu+z_1\cdot\sigma=30-1\cdot 7=30-7=23 \\\\X_2=\mu+z_2\cdot\sigma=30+1\cdot 7=30+7=37[/tex]

Answer:

   The answer is 16 and 44 days.

Step-by-step explanation:

This is the correct answer for this question.

Answer:

384cm2

Step-by-step explanation:

surface area

12×12=144

10×12/2=60

60×4=240

240+144=384cm2

Answer:

25%

I cannot really describe how I did it but I am pretty sure it is correct.

Answer:

Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds.

Step-by-step explanation:

Dilation is a transformation process in which the dimensions of a given figure are resized to produce an image with the same shape. This is done with respect to a scale factor and center of dilation.

In the given question, the center of dilation is at the middle of side DC of rectangle ABCD (i.e on side DC).

Given that the scale factor is  [tex]\frac{4}{3}[/tex],

EF = HG =  [tex]\frac{4}{3}[/tex]  × AB = [tex]\frac{4}{3}[/tex] × 6 = 8 units

FG = EH =  [tex]\frac{4}{3}[/tex]  × BC =  [tex]\frac{4}{3}[/tex]  × 3 = 4 units

Therefore, rectangle EFGH is the result of dilation of ABCD.

Answer:

A. Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds

Step-by-step explanation:

Answer:

X+5= -x-3

2x = 2

X=1

then y1 is 4

y2 is -1

Answer:

Answer is 4, 1. If you graph the lines, they intersect at 4, 1.

Step-by-step explanation:

Answer:

y-7=1/2(x-8)

y-4=1/2(x-2)

Step-by-step explanation:

Slope: 3/6, or 1/2

y-7=1/2(x-8)

y-4=1/2(x-2)

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Step-by-step explanation:

We can assume that the following model can be used:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Answer:

4/15 ÷ x + 0.4

When x = 1

4/15 ÷ 1 + 0.4

x = 2/3

When x = 4/9

4/15 ÷ 4/9 +0.4

x = 1

When x = 1 ⅓ = 4/3

4/15 ÷ 4/3 + 0.4

x = 3/5

Hope this helps.

Answer: 13 weeks

Step-by-step explanation:

y = -24x + 379

67 = -24x + 379

24x = 379 - 67

x = 312 / 24

x = 13

Answer:

the answer is 13 weeks

Step-by-step explanation:

y = amount left

y = 67

67 = -24x+379

-312 = -24x

x = -312 / -24

x = 13

Answer:

Your answer is 3.16227766

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

[tex]24*2-7=\\48-7=\\41[/tex]

Answer:

b. becomes narrower.

Step-by-step explanation:

Since the 95% confidence interval for a population mean could find out from 100 to 120

And based on this, the coefficient confidence level is declined to 0.90

Therefore the confidence interval for mean should become narrowed

As a 95% confidence interval represents narrower and 99% confidence interval represents wider

Therefore the option B is correct

Using confidence interval concepts, the correct option is:

b. becomes narrower

The margin of error of a confidence interval is given by:

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

In which:

The lower the confidence level, the lower the value of z, hence, the margin of error decreases and the interval becomes narrower, which means that option b is correct.

A similar problem is given at https://brainly.com/question/14377677

Answer:

[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]

Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%

Step-by-step explanation:

Let X the random variable of interest "number of bridges in the sample are structurally deficient", on this case we now that:

[tex]X \sim Binom(n=100, p=0.085)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=6)[/tex]

And if we use the probability mass function and we replace we got:

[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]

Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

  9.233 ft, 23.233 ft

Step-by-step explanation:

If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...

  x^2 + (x +14)^2 = 25^2

  2x^2 +28x +196 = 625

  x^2 +14x = 214.5

  x^2 +14x +49 = 263.5

  (x +7)^2 = 263.5

  x = -7 +√263.5 ≈ 9.23268

The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.

Answer: 9 ft, 23 ft

Step-by-step explanation:

We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.

(x-14)²+x²=25²

(x²-28x+196)+x²=625

2x²-28x+196=625

2x²-28x-429=0

When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].

Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.

Answer:

x-9

Step-by-step explanation:

Answer:

Raspberry: 30%

Strawberry: 15%

Apple: 20%

Lemon: 35%

Step-by-step explanation:

18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)

18 out of 60 = 30%

9 out of 60 = 15%

12 out of 60 = 20%

21 out of 60 = 35%

Please mark Brainliest

Hope this helps

Answer:

Raspberry Worms: 30%

Strawberry Worms: 15%

Apple Worms: 20%

Lemon Worms: 35%

Step-by-step explanation:

Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%

Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%

Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%

Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%