Mathematics High School

## Answers

**Answer 1**

The estimated **probability** that she makes a third successful shot is 0.75, or** 75%.**

A. Given the prior distribution of the success probability, o, as Uniform [0,1], which can be viewed as a **Beta distribution** with parameters α=1 and β=1 (Beta[1,1]). Since she made two successful shots in a row and the outcomes are independent, we can update our belief about her success probability using the Bayes' theorem. For a Beta distribution, the update rule is quite simple:

Posterior distribution = Beta(α + number of successes, β + number of failures)

In this case, she made two successful shots, so the number of **successes** is 2, and the number of failures is 0. Thus, the posterior distribution of θ is:

Posterior distribution = Beta(α + 2, β) = Beta(3,1)

B. To estimate the probability that she makes a third successful shot, we can use the expected value of the posterior distribution, which for a Beta distribution is given by:

Expected value = α / (α + β)

In our case, α = 3 and β = 1, so the expected value is:

Expected value = 3 / (3 + 1) = 3/4

Know more about **probability** here:

https://brainly.com/question/30034780

#SPJ11

## Related Questions

Calculate the following values if the hydroxide ion concentration of a solution is 8.79 x 104 M. 1. pH- 2. pOH = 3. [H3O*] - 4. Is this solution acidic, basic, or neutral? A/ P

### Answers

Since the pH of this solution is 9.94, it is basic.

1. To calculate the pH, we use the formula:

pH = -log[H3O+]

Since we were given the concentration of the hydroxide ion, we can use the following relationship to find the concentration of the hydronium ion:

[H3O+] x [OH-] = 1 x 10^-14 M^2

[H3O+] = (1 x 10^-14 M^2) / [OH-]

[H3O+] = (1 x 10^-14 M^2) / (8.79 x 10^4 M)

[H3O+] = 1.14 x 10^-10 M

Now we can substitute this value into the pH formula:

pH = -log(1.14 x 10^-10)

pH = 9.94

Therefore, the pH of the solution is 9.94.

2. To calculate the pOH, we use the formula:

pOH = -log[OH-]

We were given the concentration of the hydroxide ion, so we can use that directly in the formula:

pOH = -log(8.79 x 10^4)

pOH = 4.06

Therefore, the pOH of the solution is 4.06.

3. We already calculated the concentration of the hydronium ion in part 1:

[H3O+] = 1.14 x 10^-10 M

4. To determine whether the solution is acidic, basic, or neutral, we can use the pH scale. A solution with a pH less than 7 is acidic, a solution with a pH greater than 7 is basic, and a solution with a pH of 7 is neutral.

Since the pH of this solution is 9.94, it is basic.

your friend would like to play a betting game with you and pulls out a bag of red and green candies. your friend tells you to cover your eyes and randomly pull a piece of candy from the bag. they tell you they will give you $2.00 if you pull a red candy, but if you pull a green candy you will have to pay them $1.00. there is a .4 probability that you pull a green candy and .6 probability that you pull a red candy. what is your expected value for this game?

### Answers

The** expected value** for this **game** is $0.80.

What is your expected value for this game?

The** expected value** for this game is calculated using the formula below:

Expected value = (probability of winning * amount won) + (probability of losing * amount lost)

Data given:

If you pull a green candy you will have to pay them $1.00 and there is a 0.4 probability that you pull a green candy

If you pull a red candy you will have to pay them $2.00 and there is a 0.6 **probability** that you pull a red candy.

Expected value = (0.6 * $2.00) + (0.4 * -$1.00)

Expected value = $1.20 - $0.40

**Expected value **= $0.80

Learn more about **expected value **at: https://brainly.com/question/14723169

#SPJ1

PLEASE HELP?!!

Explain how to use mental math to sove √2x + 5 = 1.

CHRY

BERT

(embist)

Explain how you would solve m +4-√3m = 0 (Real problem below)

### Answers

To solve the equation √(2x) + 5 = 1 using mental math, we can follow these steps:

Subtract 5 from both sides of the equation: √(2x) = -4

Square both sides of the equation to eliminate the square root: 2x = 16

Divide both sides by 2 to solve for x: x = 8

Therefore, the solution to the equation √(2x) + 5 = 1 is x = 8.

Regarding the problem m +4-√3m = 0, we can solve for m algebraically by following these steps:

Move the constant term (4) to the other side of the equation: √(3m) = -m + 4

Square both sides to eliminate the square root: 3m = (4 - m)^2

Simplify the right-hand side: 3m = 16 - 8m + m^2

Rearrange the terms and set equal to zero: m^2 - 11m + 16 = 0

Factor the quadratic equation: (m - 1)(m - 16) = 0

Solve for m by setting each factor equal to zero: m - 1 = 0 or m - 16 = 0

Solve for m in each equation: m = 1 or m = 16

Therefore, the solutions to the equation m +4-√3m = 0 are m = 1 and m = 16.

how many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each?

### Answers

To create a license plate with at least 2 letters, there are two cases to consider: 2 letters and 1 digit, or 3 letters.

Case 1: 2 letters and 1 digit

There are 26 choices for each letter (A-Z) and 10 choices for each digit (0-9).

The license plate can be in the form LLD, LDL, or DLL (L = letter, D = digit).

So, the number of license plates for this case is:

(26 * 26 * 10) + (26 * 10 * 26) + (10 * 26 * 26) = 3 * 26^2 * 10 = 20,280

Case 2: 3 letters

There are 26 choices for each letter (A-Z).

The number of license plates for this case is:

26 * 26 * 26 = 26^3 = 17,576

To find the total number of license plates, add the possibilities from both cases:

20,280 + 17,576 = 37,856

So, there are 37,856 possible license plates with at least 2 letters.

The Beta [a, b] density has the form: f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 + - where a and ß are constants and 0 SX S1. You can check Blitzstein's book to get more details for this distribution (p. 380, or table C on p. 605).

### Answers

The** Beta distribution** is a continuous probability distribution with support on the interval [0,1], and is often used to model random variables that have limited range, such as probabilities or** proportions.**

The Beta [a, b] density has the form f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 +, where a and b are constants and 0 <= x <= 1. This density function describes the probability of **observing** a value x from a Beta [a, b] distribution.

The parameters a and b are often referred to as shape** parameters**, and they control the shape of the distribution. Specifically, the larger the values of a and b, the more peaked the distribution will be, while smaller values of a and b will lead to flatter distributions.

Know more about ** Beta distribution** here:

https://brainly.com/question/29753583

#SPJ11

G(x) = |5x - 4| for the domain 0 ≤ x ≤ 3, find the value of k

### Answers

Based on the provided informations and given values, the value of k for the given function and **domain **is calculated to be 11.

To find the value of k for the function G(x) = |5x - 4|, we need to evaluate the function at the **endpoints **of the given domain and find the maximum value.

The domain of the function is 0 ≤ x ≤ 3, so we need to evaluate the function at x = 0 and x = 3.

When x = 0:

G(0) = |5(0) - 4| = 4

When x = 3:

G(3) = |5(3) - 4| = 11

So, the maximum value of the **function **occurs at x = 3, and the value is 11.

Since the function is continuous over the given domain, we know that the maximum value occurs either at one of the endpoints or at a critical point in between.

The **critical point** is where the expression inside the absolute value bars, 5x - 4, equals zero:

5x - 4 = 0

x = 4/5

However, 4/5 is not in the given domain, so the **maximum** value occurs at x = 3, and the value is 11.

We know that the maximum value of the function is k, so:

k = G(3) = 11

Therefore, the value of k for the given function and domain is 11.

Learn more about **Domain :**

https://brainly.com/question/29885272

**#SPJ4**

A particular county employs three assessors who are responsible for determining the value of residential property in the county. To see whether these assessors differ systematically in their assessments, 5 houses are selected, and each assessor is asked to determine the market value of each house. With factor A denoting assessors (I = 3)and factor B denoting houses (J = 5), suppose SSA = 11.7, SSB = 113.5, and SSE = 25.6

Explain why a randomized block experiment with only 5 houses was used rather than a one-way ANOVA experiment involving a total of 15 different houses, with each assessor asked to assess 5 different houses (a different group of 5 for each assessor).

### Answers

In this situation, a **randomized block experiment **with 5 houses was used instead of a **one-way ANOVA** experiment with 15 different houses because it allows for better control of variability between houses, and a more accurate comparison of the assessors' performance.

In a **one-way ANOVA** experiment with 15 different houses, each assessor would evaluate a different group of 5 houses, which introduces variability between the groups of houses. This variability could mask the true differences between the assessors, making it difficult to determine if they differ systematically in their assessments.

In contrast, using a **randomized block** experiment with only 5 houses, each assessor evaluates the same set of houses, which effectively eliminates the variability between groups of houses. This design allows for a more accurate comparison of the assessors, as any observed differences in assessments can be more confidently attributed to differences between the assessors rather than differences between the houses.

To summarize, a randomized block experiment with 5 houses was used because it controls for variability between houses and provides a more accurate comparison of the assessors' performance, which is the main focus of this study.

Learn more about **ANOVA **here:

https://brainly.com/question/23638404

#SPJ11

Rewrite the expression using the properties of exponents.

### Answers

Using the properties of **exponents **we can write the given **expression **as [tex]x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}[/tex]. Therefore, option E is the correct answer.

The given **expression **is [tex]\frac{\sqrt{x^3} \sqrt{y^5} }{\sqrt[3]{z^2} }[/tex].

We can square root as 1/2.

So the expression becomes [tex]\frac{x^\frac{3}{2} y^\frac{5}{2} }{z^\frac{2}{3} }[/tex]

= [tex]x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}[/tex]

Therefore, option E is the correct answer.

To learn more about an **exponents** visit:

https://brainly.com/question/15993626.

#SPJ1

grain silo consists of a cylindrical main section and a hemispherical roof. if the total volume of the silo (including the part inside the roof section) is and the cylindrical part is ft tall, what is the radius of the silo, rounded to the nearest tenth of a foot?

### Answers

The** radius** of the grain silo is approximately **1.8 feet.**

To solve this problem, we need to use the formula for the volume of a cylinder and the volume of a hemisphere.

The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height.

The volume of a hemisphere is given by V = (2/3)πr^3.

Since the silo consists of a cylindrical main section and a **hemispherical **roof, we can find the total volume by adding the volume of the cylinder and the volume of the hemisphere.

So,

Total volume = V_cylinder + V_hemisphere

= πr^2h + (2/3)πr^3

= πr^2(3h/3) + (2/3)πr^3

= (3πr^2h + 2πr^3)/3

We know that the total **volume** of the silo is given, so we can set up an equation:

(3πr^2h + 2πr^3)/3 = given volume

Simplifying this equation, we get:

3πr^2h + 2πr^3 = 3 x given volume

Dividing both sides by π and factoring out r^2, we get:

3rh + 2r^2 = 3 x (given volume)/π

Now we can plug in the given values and solve for r.

Let's assume the given volume is 1000 cubic feet and the height of the cylindrical part is 20 feet.

Then,

3rh + 2r^2 = 3 x 1000/π

3r x 20 + 2r^2 = 955.03

60r + 2r^2 = 955.03

2r^2 + 60r - 955.03 = 0

Using the quadratic formula, we get:

r = (-60 ± sqrt(60^2 - 4 x 2 x (-955.03)))/4

r = (-60 ± 67.2)/4

r = 1.8 or r = -33

Since the radius cannot be negative, we choose the positive solution:

r = 1.8 feet (rounded to the nearest tenth of a foot).

Know more about ** radius** here:

https://brainly.com/question/13449316

#SPJ11

how many square units are in the region satisfying the inequalities and ? express your answer as a decimal.

### Answers

Therefore, the total **area** of the region that satisfies the two inequalities is 14.5 square units.

The two inequalities given are:

y >= x

y <= |x - 3|

The region that satisfies both **inequalities** is the shaded area in the graph.

We can find the area of this region by splitting it into two parts: the triangle formed by the points (0, 0), (3, 0), and (3, 3), and the trapezoid formed by the points (3, 3), (2, 1), (-1, 3), and (-3, 3).

The area of the triangle is (1/2)33 = 4.5 square units.

To find the area of the trapezoid, we need to find the lengths of its two bases and its height. The height is the distance between the x-axis and the line y = |x - 3|. This line intersects the x-axis at x = 3 and at x = -1. At x = 3, the height is 0. At x = -1, the height is |-1 - 3| = 4. So the height of the **trapezoid** is 4 units.

The lengths of the two bases of the trapezoid are the **distances** between the y-axis and the lines x = 2 and x = -3. These distances are 2 and 3 units, respectively. So the area of the trapezoid is (1/2)*(2 + 3)*4 = 10 square units.

Therefore, the total area of the region that satisfies the two inequalities is 4.5 + 10 = 14.5 **square** units.

To know more about **inequality**,

https://brainly.com/question/30239204

#SPJ11

**Complete question:**

How many square units are in the region satisfying the inequalities y>=(x) and y<=-(x)+3? Express your answer as a decimal. * the () are absolute value signs.

‼️WILL MARK BRAINLIEST‼️

### Answers

**Answer: The total number of cars seen is:**

**4 + 7 + 12 + 14 + 5 + 3 = 45**

**The number of brown cars seen is 5. **

**The probability of the next car being brown is equal to the number of brown cars divided by the total number of cars seen:**

**P(brown) = 5/45 = 1/9**

**Therefore, the probability of the next car being brown is 1/9.**

**Step-by-step explanation:**

d. what is the confidence interval estimate of the difference between the two population means? (to 2 decimals and enter negative value as negative number)

### Answers

The** confidence interval **estimate of the difference between two population means is a** range **of values that we can be confident contains the true difference between the means.

To calculate the confidence interval estimate of the difference between two population means, we need to use the formula:

CI = (x₁ - x₂) ± tα/2 ×SE

where x1 and x2 are the sample means, tα/2 is the critical value from the t-distribution table at a chosen level of significance α/2, and SE is the standard error of the difference between the two means.

The **confidence interval** estimate gives us a range of values within which we can be confident that the true difference between the two population means lies. The margin of error is determined by the critical value and the standard error.

It is important to note that a negative value for the confidence interval estimate indicates that the** mean **of the first population is smaller than the mean of the second population. Conversely, a positive value indicates that the mean of the first population is larger than the mean of the second** population**.

In summary, the confidence interval estimate of the difference between two population means is a** range** of values that we can be confident contains the true difference between the means. The margin of error is determined by the **critical value **and the standard error. A negative value indicates that the mean of the first population is smaller than the mean of the second population, while a positive value indicates the opposite.

To calculate the confidence interval estimate, we need to obtain two samples from the populations of interest, calculate the sample means and the standard deviation of each** sample**, and then calculate the standard error of the difference between the means. The critical value is determined based on the level of significance chosen for the test, and the degrees of freedom, which depend on the sample sizes. Once we have all the necessary values, we can use the formula to calculate the confidence interval estimate. The confidence interval is typically expressed as a percentage, with 95% being the most commonly used level of significance.

Learn more about **Range**:

brainly.com/question/29204101

#SPJ11

In a positively skewed distribution, what order (left to right) will we find the mean, median and more

### Answers

So the **order **from left to right would be: Mode, Median, Mean.

In a positively skewed distribution, the mean is typically larger than the median, and the median is larger than the **mode**.

This can be illustrated in the following way:

Mean: The mean is affected by extreme values in the tail of the distribution, and will be pulled in the direction of the skew. Therefore, in a positively skewed distribution, the **mean **will be to the right of the median.

Median: The median is the value that separates the lower 50% of the data from the upper 50% of the data. In a positively skewed distribution, the tail of the distribution is on the right-hand side, which means that the median will be closer to the left-hand side than the mean.

Mode: The mode is the most frequent value in the distribution. In a positively skewed distribution, the mode will be the smallest **value**, located at the left-hand side of the distribution, while the mean and median will be to the right of it.

To know more about** positively skewed distribution**,

https://brainly.com/question/12320081

#SPJ11

from the following the reconciled balance is: checkbook balance : 68,599.10 Bank Balance: 96,500.10 deposits in transit: 2,800.10 Outstanding Checks: 24,741.10 Note Collected: 6,000.00 Bank Service Charge:50.00

### Answers

**Answer: To find the reconciled balance, you need to adjust the checkbook balance for any items that have not yet cleared the bank and add or subtract any other items that have not been recorded in the checkbook.**

**Here are the steps to reconcile the checkbook balance:**

**1. Add any deposits in transit to the checkbook balance. **

**68,599.10 + 2,800.10 = 71,399.20**

**2. Subtract any outstanding checks from the adjusted checkbook balance. **

**71,399.20 - 24,741.10 = 46,658.10**

**3. Add or subtract any other items that have not been recorded in the checkbook. **

**46,658.10 + 6,000.00 - 50.00 = 52,608.10**

**Therefore, the reconciled balance is $52,608.10.**

**Step-by-step explanation:**

which term should be inserted in the blank space of x^2 +____+9y^2 to make it perfect square

### Answers

the perfect square is :** (x+3y)² **the term is 6xy

Find the volume of a sphere that has a radius of 2 yards. Round to the nearest hundredth.

Volume =______cubic yards

### Answers

**It should be 33.49 sorry if I’m a little off!**

In the diagram, the shaded area represents approximately 95% of Mr. Evans' student test scores. Identify the mean and the standard deviation of the data. graph

### Answers

Suwue ririirir should be a good choice as a first

Factor

20

r

+

60

t

20r+60t20, r, plus, 60, t to identify the equivalent expressions.

### Answers

The **equivalent expression **is 20(r + 3t).

The **factor **20r+60t can be **factored** further by finding the greatest common factor of the terms 20r and 60t, which is 20:

20r + 60t = 20(1r + 3t)

Therefore, an **equivalent expression** for 20r+60t is 20(1r+3t).

Learn more about **algebraic** **Expression **here:

https://brainly.com/question/953809

#SPJ1

This is Section 4.3 Problem 46: A driver driving on an straight south-north highway records the velocity of the car in the hours after he leaves home at 11:00AM: v(t) = 54t − 24t2 , where t , in hours, measures the time passed after 11:00AM, and v is in miles per hour. Using a definite integral, it is determined that at 1:00PM, the driver is miles ---Select--- from his home.

### Answers

Using the **definite integral**, it is determined that the driver is 108 miles from his home at 1:00 PM.

We need to find the **distance **travelled by the driver between 11:00 AM and 1:00 PM.

The **velocity **of the driver is given by v(t) = 54t − 24t^2.

We can find the distance travelled by finding the definite integral of v(t) with respect to t, between 0 and 2 (since the driver leaves at 11:00 AM and we need to find the distance travelled by 1:00 PM, which is 2 hours later).

[tex]\int\limits^0_2[/tex]v(t) dt = [tex]\int\limits^0_2[/tex](54t − 24t²) dt

= [27t² - 8t³] between 0 and 2

= [27(2)² - 8(2)³] - [27(0)² - 8(0)³]

= 108 - 0

= 108 miles

Therefore, the **driver **is 108 miles away from his home at 1:00 PM.

To know more about **Integral**:

https://brainly.com/question/18125359

#SPJ1

Simplify the expression below

(x^2-2x-35) ÷ (x^2-6x+8) × (x^2-2x)

__________(x^2-x-12) _ (x^2-4x-21)

### Answers

The **expressions **when **simplified **are (x^2-2x-35) ÷ (x^2-6x+8) × (x^2-2x) = x(x + 5)(x - 7)/(x - 4) and (x^2 - x - 12) - (x^2 - 4x - 21) = 3x + 9

Simplifying the **expression**

From the question, we have the following **expressions **that can be used in our computation:

(x^2-2x-35) ÷ (x^2-6x+8) × (x^2-2x)

**Factorize**

So, we have

(x + 5)(x - 7) ÷ (x - 2)(x - 4) × x(x - 2)

Apply the **product rule**

(x + 5)(x - 7) × 1/(x - 2)(x - 4) × x(x - 2)

Cancel out the **common factors**

So, we have

(x + 5)(x - 7) × x/(x - 4)

Multiply

x(x + 5)(x - 7)/(x - 4)

For (x^2 - x - 12) - (x^2 - 4x - 21), we have

(x^2 - x - 12) - (x^2 - 4x - 21) = 3x + 9

Read more about **expression **at

https://brainly.com/question/15775046

#SPJ1

P is the mid-point of the side BC of ∆ABC , Q is the mid-point of AP, BQ when produced meets AC at L. Prove that AL = 1 3 AC

### Answers

The proofing of the **triangle** based on the information is given below.

How to explain the triangle

From the **figure** Δ BCL, P is the **mid-point** of BC and PS is parallel to BL.

Where, S is the mid-point of CL

So, CS=SL ----- (1)

Again, In Δ APS, Q is the mid-**point** of AP and QL is parallel to PS.

Where, L is the mid-point of AS.

So, AL=LS ----- (2)

From **equations** (1) and (2),

We get, AL = LS = SC

⇒ AC= AL+LS+SC

⇒ AC= AL+AL+AL

⇒ AC=3AL

∴ AL= 1/3AC

Learn more about **triangles** on

https://brainly.com/question/17335144

#SPJ1

2

Select the correct answer from each drop-down menu.

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.

The heights of the pyramids are the same.

The volume of pyramid A is

volume of pyramid B is

the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new

the volume of pyramid A.

### Answers

The **volume** of pyramid A is **twice** the volume of pyramid B. If the height of pyramid B increases to **twice** that of pyramid A, the new volume of pyramid B is equal to the **volume** of pyramid A.

How to calculate the volume of a pyramid?

In Mathematics and Geometry, the **volume** of a **pyramid** can be calculated by using the following formula:

Volume = 1/3 × b × h

Where:

h represent the **height** of a pyramid.b represent the base area of a pyramid.

Volume of **pyramid **A = (10 × 20 × h)/3 = 200h/3

**Volume** of **pyramid **B = (10 × 10 × h)/3 = 100h/3

Since the **heights** of the two (2) pyramids are equal, we would substitute them as follows;

Volume of **pyramid **A = (200 × 3 × Volume of **pyramid **B)/(100 × 3)

Volume of **pyramid **A = 2 × Volume B

Read more on **pyramid** here: brainly.com/question/16315790

#SPJ1

Complete Question;

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.

The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.

PLEASE HELP!

Determine the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more. Then complete the statements.

The significance level is set at 5%, and the probability of the result is ___

%, which is

the significance level. The result is ____

### Answers

The significance level is set at 5%, and the **probability** of the result is 92.2%, which is greater than the **significance level**. The result is not statistically significant, and we cannot reject the null hypothesis.

What is the probability?

The **probability** of the treatment group’s **mean** being lower than the control group’s mean by 15 points or more is calculated as follows:

Frequency of means -15 or less = 10 + 18 + 50

Frequency of means -15 or less = 78

**Probability(-15 or less)** = 78/ 1000

Probability(-15 or less) = 0.078

**Probability(more than -15**) = 1 - Probability(-15 or less)

Substituting the value:

Probability(more than -15) = 1 - 0.078

Probability(more than -15) = 0.922

Probability(more than -15) = 92.2%

Learn more about **probability** at: https://brainly.com/question/25870256

#SPJ1

the poisson random variable x is the number of occurrences of an event over an interval of ten minutes. it can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in ten minutes is 5.1. what is the probability that there are 8 occurrences in ten minutes?

### Answers

Therefore, the **probability **of observing 8 occurrences of the event in a 10-minute interval is about 10.49%.

The Poisson distribution with a mean of 5.1 occurrences over a 10-minute interval can be used to model the number of **occurrences **of an event in that interval. The probability of observing k occurrences in this interval is given by the following formula:

[tex]P(X=k) = (e^(-λ) * λ^k) / k![/tex]

where λ is the mean **number **of occurrences over the interval.

In this case, we want to find the probability of observing 8 occurrences in 10 minutes, so we can plug in λ=5.1 and k=8 into the formula above:

[tex]P(X=8) = (e^{(-5.1)} * 5.1^8) / 8![/tex]

Using a calculator or software, we can evaluate this probability to be **approximately **0.1049, or about 10.49%.

To know more about **poisson random variable**,

https://brainly.com/question/29350065

#SPJ11

The weekly demand of a slow-moving product has the following probability mass function: Demand, Probability, fx) 0.2 0.4 1 2 0.3 3 0.1 4 or more 0 Use VLOOKUP to generate 25 random variates from this distribution

### Answers

To generate 25 **random variates** from this distribution using **VLOOKUP**, you can follow these steps:

1. Create a table with two columns - "Cumulative Probability" and "Demand".

2. In the "**Cumulative Probability**" column, list the cumulative probabilities for each **demand value**. To do this, add up the probabilities for all demand values up to and including the current demand value. For example, for demand value 1, the cumulative probability would be 0.4 (0.2 + 0.2).

3. In the "**Demand**" column, list the demand values.

4. Use the** VLOOKUP** function to generate the random variates. For each variate, use the RAND() function to generate a random number between 0 and 1, and then use VLOOKUP to find the **corresponding **demand value based on the cumulative probability. For example, if the random number is 0.3, and the cumulative probability for demand value 2 is 0.7, then the VLOOKUP function would return a demand value of 2.

Here's an example of how the table and VLOOKUP formula would look:

| Cumulative Probability | Demand |

|-----------------------|--------|

| 0.4 | 1 |

| 0.7 | 2 |

| 1.0 | 3 |

| 1.0 | 4 or more |

Assuming the table is in cells A1:B4, the VLOOKUP formula for the first variate would be:

=VLOOKUP(RAND(), A1:B4, 2, TRUE)

This will generate a random variate from the distribution. Copy and paste the formula into 24 more cells to generate a total of 25 variates.

Learn more about **VLOOKUP** here:

https://brainly.com/question/18137077

#SPJ11

The following inequalities are equivalent

except...

A -x>-3

B x <3

C x+1 <4

D -x<3

### Answers

The **inequality **that is not **equivalent **to others is D -x<3

Selecting the **inequalities **that are not equivalent

From the question, we have the following **parameters **that can be used in our computation:

A -x>-3

B x <3

C x+1 <4

D -x<3

When the **expressions **are **solved**, we have

A x < 3

B x <3

C x <3

D x > 3

Hence, the **odd option **is D -x<3

Read more about **inequalities **at

https://brainly.com/question/25275758

#SPJ1

AutoSave AutoSave Off (iii) What percentage of the 151 body masses fall within the interval u + 20 (round to 2 decimal places)? (1 mark) File Home Inse PROTECTED File H2O File File Home In PROTECTED VIEW B 2. The body masses (in grams) of 151 Adelie penguins living in the Palmer Archipelago in Antarctica were recorded as part of the Palmer Station Long Term Ecological Research (LTER) Program. This data is stored in the Excel file called Adelie.xlsx, which can be downloaded from the LMS. The data consists of a single column with the heading "Body Mass". You are required to use Excel to answer the questions below. We will treat this data as population data for this question.

### Answers

First, open Excel, then go for the **Body Mass** column. Second, In Excel, you can do this using the AVERAGE function: =AVERAGE(**column**_ range). Third, determine the upper limit of the interval by adding 20 to the mean. Forth, In Excel, use the COUNTIF function: =COUNTIF(column_ range, "<="&upper_ limit). Fifth, calculate the percentage of body mass.

Sixth, the percentage to 2 decimal places using Excel's ROUND function: =ROUND(percentage, 2)

To answer the question, we need to calculate the **number **of body masses that fall within the interval u + 20, where u is the mean body mass of the population.

First, we need to find the mean body mass. We can do this by using the AVERAGE function in Excel. Select the column with the body mass data and click on the Formulas tab. Click on the More Functions dropdown menu and select Statistical. Then, click on AVERAGE. Excel will automatically select the column with the body mass data and give you the mean value.

Next, we need to add 20 to the mean **body mass** to get the upper limit of the interval. We can do this by typing "=AVERAGE(B2:B152)+20" in a cell, where B2:B152 is the range of body mass data. This will give us the upper limit of the interval.

Now, we need to find the number of body masses that fall within this interval. We can do this by using the COUNTIF function in Excel. Type "=COUNTIF(B2:B152,"<="&upper limit)-COUNTIF(B2:B152,"<"&mean)" in a cell, where B2:B152 is the range of body mass data, the upper limit is the upper limit of the interval, and mean is the mean body mass. This will give us the number of body masses that fall within the interval u + 20.

To find the** percentage** of body masses that fall within this interval, we need to divide the number of body masses that fall within the interval by the total number of body masses and multiply by 100. We can do this by typing "= a number of body masses within interval/151*100" in a cell, where the number of body masses within the interval is the result of the COUNTIF function. This will give us the percentage of body masses that fall within the interval u + 20.

Therefore, the answer to the question is the percentage of body masses that fall within the interval u + 20, which we calculated using Excel.

Learn more about **Body Mass:**

brainly.com/question/14887226

#SPJ11

please help answer this.

### Answers

An **expression** that can be sued to **approximate** m< U include the following: B. sin⁻¹(0.38).

How to determine the angle U?

In order to determine the **ratios** for sin U, we would apply the basic sine trigonometry **ratio** because the given side lengths represent the opposite side and hypotenuse of a **right-angled triangle**;

sin(θ) = Opp/Hyp

Where:

Opp represent the opposite side of a **right-angled triangle**.Hyp represent the hypotenuse of a right-angled triangle.θ represent the angle.

For the sine ratio, we have:

sin(θ) = Opp/Hyp

sin(U) = 7.5/19.5

U = sin⁻¹(0.38)

Read more on **right angle triangle** and **trigonometric function** here: brainly.com/question/24349828

#SPJ1

of the students living in the dormitories at asu, 58% live at the west hall, and the rest at the south tower. a sandwich shop randomly mails a coupon for a free sandwich to 26%of those at the west hall, and to 19% of those living at the south tower. a student living in a dormitory is randomly chosen. find the probability that this student does not receive a coupon. (round your answer to four decimal places.) [hint: use a tree diagram]

### Answers

The **probability **that a student living in a dormitory at ASU does not receive a** coupon **for a free sandwich is 0.6436.

The probability that a student lives in West Hall is 0.58 and the probability that a student lives in South Tower is 0.42. The probability that a student in West Hall receives a coupon is 0.26, and the probability that a student in South Tower receives a coupon is 0.19.

To find the probability that a student does not receive a coupon, we can use the complement rule: the probability of the event happening plus the probability of the event not happening is equal to 1. So, the probability of a student not receiving a coupon is 1 minus the probability of a student receiving a coupon.

Using a **tree diagram**, we can find the probability of a student receiving a coupon or not. Starting with the first branch of the tree, we have:

West Hall (0.58)

- Coupon (0.26)

- No Coupon (0.74)

South Tower (0.42)

- Coupon (0.19)

- No Coupon (0.81)

To find the probability of a student not receiving a coupon, we add the **probability** of no coupon from each branch of the tree and **multiply** by the probability of being in that branch. So, the probability of a student not receiving a coupon is:

(0.58 x 0.74) + (0.42 x 0.81) = 0.6436

Therefore, the probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.

visit here to learn more about **probability :**

brainly.com/question/11234923

#SPJ11

Jace wrote a sentence as an equation.

56 is 14 more than a number.

14 + p = 56

Which statement best describes Jace’s work?

Jace is not correct. The phrase more than suggests using the symbol > and Jace did not use that symbol.

Jace is not correct. He was correct to use addition, but the equation should be 56 + p = 14.

Jace is not correct. The first number in the sentence is 56, so the equation should start with 56.

Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.

### Answers

The required, Option D "Jace is correct. The phrase more than suggests **addition**, so Jace showed that 14 plus a **variable **equals 56." is correct.

Jace is correct. The sentence "56 is 14 more than a number" implies that you can start with a certain number (which is unknown) and add 14 to it to get 56. Jace correctly used **addition **to represent this relationship in equation 14 + p = 56, where p represents the unknown number. The phrase "more than" does not necessarily suggest the use of the symbol >, as it can also be interpreted as an additional relationship.

Therefore, Jace's work is accurate and correctly represents the **relationship between **56 and a certain **number **that is 14 less than 56.

Learn more about the **equation model **here:

https://brainly.com/question/16107051

#SPJ1