A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Find the mean and standard deviation for this binomial distribution.

Answer:

X ~ Norm ( 13 , 25 )

P ( X > 17 ) = 0.2119

16.37 days

Step-by-step explanation:

Solution:-

- We are given a distribution for the amount of time for a kidney stone to pass.

- The distribution is parameterize by the mean time taken ( u ) and the standard deviation ( s ) as follows:

                                 u = 13 days

                                 s = 5 days

- Here, we will define a random variable X: The time taken by a kidney stone to pass to be normally distributed with parameters ( u ) and ( s ). We express the distribution in the notation form as follows:

                              X ~ Norm ( u , s^2 )

                              X ~ Norm ( 13 , 25 )

- We are to determine that a randomly selected individual takes more than 17 days for the stone to pass through.

- We will first standardize the limiting value for the required probability by computing the Z-score as follows:

                            [tex]Z-score = \frac{X - u}{s} \\\\Z-score = \frac{17 - 13}{5} \\\\Z-score = 0.8[/tex]

- We will use the standard normal table to determine the probability of kidney stone passing in less than 17 days ( Z = 0.8 ); hence, we have:

                           P ( X < 17 ) = P ( Z < 0.8 )

                           P ( X < 17 ) = 0.7881

- To compute the probability of an individual taking more than 17 days would be " total probability - P ( X < 17 )  as follows" . Where the total probability of any distribution is always equal to 1.

                        P ( X > 17 ) = 1 - P ( X < 17 )

                        P ( X > 17 ) = 1 - 0.7781

                        P ( X > 17 ) = 0.2119

- Nest we are to determine the amount of days it would take for an individual to lie in the upper quarter of the spectrum. We can interpret this by looking at the limiting value corresponding to the P ( X > x ) = 0.25.

- The upper quartile of any distribution amounts to probabilities: " > x = 0.25 " or " < x = 0.75 ".

- We will use the standard normal table for ( Z-score ) and look-up the Z-score value corresponding to P ( Z < a ) = 0.75 as follows:

                       P ( Z < a ) = 0.75

                       a = 0.674

- Now we will use the standardizing formula used in previous part and compute the value of "x" associated with the limiting Z-score value:

                       [tex]Z-score = \frac{x-u}{s} = 0.674\\\\x = 0.674*s + u\\\\x = 0.674*5 + 13\\\\x = 16.37[/tex]

Answer: It would should take more than 16.37 days for an individual if he is to lie in the upper quartile of the defined distribution.

Answer:

Question 1: 3 - 5 hours.

Question 2: 0 - 1 hour

Step-by-step explanation:

Question 1: As you can see in the diagram, the guy is moving really slowly and is almost stuck, therefore, it is 3 - 5  hours.

Question 2:  In hours 0 - 1, you can see that the graph is the closest to vertical as it gets.

Answer:

(A)30

(D)15

Step-by-step explanation:

Factors of 30 are 1,2,3,5,6,10,15 and 30

A composite number is any number that is not prime.

From the given options, the factors of 30 are 30, 5 and 15.

However, 5 is not a composite number.

Therefore, the number that Lacey could be thinking of will either be 30 or 15.

Answer:

Let x be her initial distance from the building, then tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

Let y be her distance from the building after moving forward, then

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.

Answer: B. 17.6 ft.

Step-by-step explanation: I just did it on the edge 2023 assignment. Check attached image.

Step-by-step explanation:

1. 180 - (36 +36)= 108

2. angle ABC = 108 angle DBC = 108-72=36

3. angle DCB=angle DBC. This is because the base angles are equal

4 therefore triangle BDC is isoscles

Answer:

Because ΔABD is isosceles, ∠ABD ≅ ∠ADB = 72° because of Base Angles Theorem which states that the base angles of an isosceles triangle are congruent. Then, ∠BDC = 180° - ∠ADB = 108° because they are supplementary angles. Because ΔABC is isosceles, ∠BAC ≅ ∠BCA = 36° because of Base Angles Theorem, which means ∠CBD = 180° - 108° - 36° = 36° because of the sum of angles in a triangle. Therefore, ΔBCD is isosceles because of the Converse of Base Angles Theorem.

[tex]answer \\ = (6.5 \: 8.5) \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

Step-by-step explanation:

The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.

                                             1                                [tex](A + B) ^ 0[/tex] = 1

                                         1       1                            [tex](A +B ) ^ 1 = 1A + 1B[/tex]

                                   1          2        1          [tex](A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2[/tex]

By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is

1          9       36    84    126    126    84    36    9    1

Now, fill in AB in the gaps.

1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB

Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is

[tex]1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B[/tex]

Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B

[tex]1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9[/tex]

The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.

[tex]A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9[/tex]

Hope you can learn the method

Answer:

$17.72 left

Step-by-step explanation:

144 inches = 4 yards

4(0.15) + 3.5(0.48) = 0.6 + 1.68 = $2.28 SPENT

20 - 2.28 = $17.72 left in change

Answer:

Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 100, \sigma = 15[/tex]

If you scored 130, your score would be higher than approximately what percent of adults?

To find the proportion of scores that are lower than, we find the pvalue of Z when X = 130. So

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

[tex]Z = \frac{130 - 100}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

0.9772*100 = 97.72%.

Your score would be higher than 97.72% of adults, that is, higher than approximately 98% of adults.

Answer:

(a)The total sales of ice-cream last month is 702 gallons.

(b)The total sales of broccoli last month is 510 pounds.

Step-by-step explanation:

Part A

Total Sales of gallons of ice cream this month = 597

Since it represents a decrease of 15% of last month's sales

Let the total sales of ice-cream last month =x

Then:

(100-15)% of x =597

85% of x=597

0.85x=597

x=597/0.85

x=702 (to the nearest integer)

The total sales of ice-cream last month is 702 gallons.

Part B

Total Sales of broccoli this month = 617 pounds

Since it represents an increase of 21% of last month's sales

Let the total sales of ice-cream last month =y

Then:

(100+21)% of y =617

121% of y=617

1.21y=617

y=617/1.21

y=510 (to the nearest integer)

The total sales of broccoli last month is 510 pounds.

Answer:

Volume = 14.5 cm³

Step-by-step explanation:

Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]

Where r = 2 and h = 3.46

Volume = [tex](3.14)(2)^2\frac{3.46}{3}[/tex]

Volume = (3.14)(4)(1.15)

Volume = 14.5 cm³

Answer: 3.9

Step-by-step explanation: Khan Academy

The length of BD if The angle ∠ DAC is equal to the angle ∠ BAD is 3.92.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The angle ∠ DAC = angle ∠ BAD

As we can see that the triangle BAD and triangle DAC are similar By SAS similarity,

AC / AB = CD / BD  (By the proportional theorem of similarity)

5.6 / 5.1 = 4.3 / BD

1.09 = 4.3 / BD

BD = 4.3 / 1.09

BD = 3.92

Thus, the length of BD is 3.92.

To know more about Triangles:

https://brainly.com/question/16886469

#SPJ2

Answer:

(D)Equilateral Triangle

Step-by-step explanation:

Given a circle centre M; and

The measure of major arc JL = 300 degrees

The triangle formed by radii ML and MJ and chord JL is Triangle JLM.

Since ML=MJ (radii of a circle), the base angles are equal.

Therefore:

[tex]\angle MLJ= \angle MJL\\\angle LMJ =60^\circ\\$Therefore:\\\angle LMJ+2\angle MLJ=180^\circ\\60^\circ+2\angle MLJ=180^\circ\\2\angle MLJ=180^\circ-60^\circ\\2\angle MLJ=120^\circ\\\angle MLJ=60^\circ[/tex]

We can see that all the angles of triangle JLM are 60 degrees, therefore Triangle JLM is an Equilateral Triangle.

Answer:

[tex]z=-\frac{20}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3z}{10}-4=-6\\\\\frac{3z}{10}-4+4=-6+4\\\\\frac{3z}{10}=-2\\\\\frac{10\cdot \:3z}{10}=10\left(-2\right)\\\\3z=-20\\\\\frac{3z}{3}=\frac{-20}{3}\\\\z=-\frac{20}{3}[/tex]

Best Regards!

Answer:

radius r of the zorb is ≅ 1.40 m

Step-by-step explanation:

GIven that;

the  radius r of a sphere with surface area A is given by;

[tex]r = \sqrt{\dfrac {A}{4 \pi }}[/tex]  which is read as : (r equals StartRoot StartFraction Upper A Over 4 pi EndFraction EndRoot .)

We are to calculate the radius of a zorb whose outside surface area is  24.63 sq  ( the missing part of the question)

Given that the outside surface area is : 24.63 sq

Let replace the value of the outside surface area which 24.63 sq for A in the equation given from above.

SO:  A = 24.63 sq

[tex]r = \sqrt{\dfrac {A}{4 \pi }}[/tex]

[tex]r = \sqrt{\dfrac {24.63}{4 \pi }}[/tex]

[tex]r = \sqrt{1.9599}[/tex]

r = 1.399

radius r of the zorb is ≅ 1.40 m

Answer:

how many hours do you spend on your laptop

Answer:

the question is 17 hours - 2 hours

Answer:

Bb

Step-by-step explanation:

Answer:

81.64

Step-by-step explanation:

To find the circumference of this circle we take pi or 3.14 and multiply it by 2

3.14 * 2 = 6.28

Then we multiply 6.28 by 13

6.28 * 13 = 81.64

Answer:

10 and 8

Step-by-step explanation:

10 and 8 are the factors in this equation because factors are the numbers that are mutiplied together to get the product (The answer to a mutiplication problem) Therefore the factors in this equation are 10 and 8 because those are the numbers that are mutiplied together to get the product.

Answer:

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Step-by-step explanation:

Step(i):-

Given sample size 'n' =41

Mean of the sample(x⁻)  = 3.55

The estimated standard error

                                             [tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]

Given  estimated standard error ( S.E) = 3.478

Level of significance ∝=0.05

Step(ii):-

95% for the true average increase in total cholesterol under these circumstances

[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]

Degrees of freedom

ν= n-1 = 41-1 =40

t₀.₀₅ = 1.6839

95% for the true average increase in total cholesterol under these circumstances

[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]

( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )

(3.55 - 5.856 , 3.55 + 5.856)

(-2.306 , 9.406)

Conclusion:-

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Answer:

The 95% confidence interval for the average hourly wage of all information system managers is (39.14,42.36)

Step-by-step explanation:

In order to calculate the 95% confidence interval for the average hourly wage we would have to calculate first the margin of error as follows:

ME=t0.05/2,n-1s/√n

for n=75, t0.025,74=1.993

Therefore, ME=1.993*7/√75

ME=1.61

Therefore, the 95% confidence interval for the average hourly income of all syatem manager would be as follows:

(X-ME,X+ME)=(40.75-1.61,40.75+1.61)

=(39.14,42.36)

Answer:

x = ±2√2, ±i

Step-by-step explanation:

Step 1: Factor

(x² - 8)(x² + 1)

Step 2: Find roots

x² - 8 = 0

x² = 8

x = ±2√2

x² + 1 = 0

x² = -1

x = ±i

Answer:

The answer is B

Step-by-step explanation:

Step-by-step explanation:

positive angle =300+180=480.

negative angle = 300 -180=120

Answer:

83.29% probability that at least 2 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives late, or it does not arrive late. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

80 % of its flights arriving on time.

So 100 - 80 = 20% arrive late, which means that [tex]p = 0.2[/tex]

15 Southwest flights

This means that [tex]n = 15[/tex]

Find the probability that at least 2 flights arrive late.

Either less than two arrive late, or at least 2 do. The sum of the probabilities of these outcomes is 1. So

[tex]P(X < 2) + P(X \geq 2) = 1[/tex]

We want [tex]P(X \geq 2)[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

So

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

[tex]P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352[/tex]

[tex]P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329[/tex]

83.29% probability that at least 2 flights arrive late.

Answer:

The speed driven while returning is 88 mph.

Step-by-step explanation:

We are given that while traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return.

Also, the total distance of the roundtrip was 420 miles.

Let the speed driven while returning be 'x mph' which means that the speed driven while going was '(x - 40) mph' because it has been given that while returning we have increased the speed by 40 mph.

As we know that the Speed-Distance-Time formula is given by;

                         [tex]\text {Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]   or  [tex]\text {Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]

So, according to the question;

[tex]\frac{420}{x-40} -\frac{420}{x} = 4 \text{ hours}[/tex]       where Distance = 420 miles

[tex]\frac{420x-420(x-40)}{x(x-40)} = 4[/tex]

[tex]\frac{420x-420x+16800}{x^{2} -40x} = 4[/tex]

[tex]\frac{16800}{x^{2} -40x} = 4[/tex]

[tex]4x^{2} -160x= 16800[/tex]

[tex]4x^{2} -160x- 16800=0[/tex]

[tex]x^{2} -40x- 4200=0[/tex]

Now finding the roots of the above equation;

Here a = 1, b = -40 and c = -4200

[tex]D = b^{2} -4ac[/tex]

   =  [tex](-40)^{2} -4(1)(-4200)[/tex] = 18400

Now, the roots of a quadratic equation is given by;

[tex]x = \frac{-b\pm \sqrt{D} }{2a}[/tex]

[tex]x = \frac{-(-40)\pm \sqrt{18400} }{2\times 1}[/tex]

So, the two roots of x are : [tex]x = \frac{40-\sqrt{18400} }{2}[/tex]  and  [tex]x = \frac{40+\sqrt{18400} }{2}[/tex]

Solving these two we get; [tex]x = -47.8[/tex]  and  [tex]x = 87.8[/tex]

Here we ignore the negative value of x, so the speed driven while returning is 87.8 ≈ 88 mph.

Answer:

2h x (l+b)

2x10 X (12+10)

20 X 22

44 cm cube is your answer...

Answer:

(A)4 + 4 + 4 = 12

Step-by-step explanation:

Each cake needs [tex]\dfrac{17}{4}[/tex] cups of flour.

Now,

[tex]\dfrac{17}{4} =4.25 \approx 4[/tex]

Therefore, the best estimate of the number of cups of flour that Nika used to make the three loaves is:

4 + 4 + 4 = 12

Answer:

12 (A)

Step-by-step explanation:

u hate edge, i hate it more :3

Answer:

Just replace the variables with the number

d5

c4 (uh oh)

a2

b-3

f-7

d-c = 5 - 4 = 1

1/3 - 4(ab+f)

2 x -3 = -6

-6 + -7 = -13

-13 x 4 = -52

1/3 - -52 = 1/3 + 52 =

52 1/3

Hope this helps

Step-by-step explanation:

Answer:

c. [1.771;4.245] feet

Step-by-step explanation:

Hello!

The variable of interest is

X: height of a student at UH

X~N(μ;σ²)

You have to estimate the population standard deviation using a 95% confidence interval.

The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:

[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]

n=12

S= 2.5

[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]

[3.136; 18.016] feet²

Then you calculate the square root of both limits to get the CI for the population standard deviation:

[√3.136; √18.016]

[1.771;4.245] feet

I hope this helps!