If you roll a regular die 5 times what is the probability of rolling a 6 at least twice?

If probability of winning a teddy bear at a carnival is 0.89 and 40 turns are taken, then he should have won about 35 teddy bears.

The probability of winning a teddy bear at a carnival is = 0.89, then

The probability of not winning a teddy bear is = 1 - 0.89 = 0.11,

We use binomial-distribution to calculate the probability of winning "k" teddy bears in "n" turns,

Where probability of winning (p) = 0.89,

The formula for the binomial distribution is,

⇒ P(k) = C(n,k) × p^k × (1-p)^(n-k),

The probability of winning "k" teddy bears in 40 turns is :

⇒ P(k) = C(40,k) × 0.89^k × 0.11^(40-k),

To find "expected-number" of teddy bears won, we multiply the probability of winning k teddy bears by k, and sum over all possible values of k,

⇒ E(number of teddy bears won) = \(\[ \sum_{k=0}^{40} \]\) k × P(k),

⇒ \(\[ \sum_{k=1}^{40} \]\) k × C(40,k) × 0.89^k × 0.11^(40-k),

On further solving ,

We get,

⇒ E(number of teddy bears won) ≈ 35.6,

Therefore, we expect to win about 35 teddy bears if we take 40 turns .

Learn more about Probability here

https://brainly.com/question/4293666

#SPJ4

Answer:

D

Step-by-step explanation:

Integers found in:

A: -5, 9/3 = 3

B: 4

C: -12

Hope this helped! ^^

Answer:

b=a √3

Step-by-step explanation:

Answer:

2 - 30ft²

3 - 57yd²

Step-by-step explanation:

Hey There!

The first step in solving this problem is finding the formula for area of a trapezoid

\(A = \frac{a+b}{2} h\)

a = base 1

b = base 2

h = height

For the first one the dimensions are

a = 6

b = 9

h = 4

now we just plug in the values

\(A=\frac{6+9}{2} 4\\6+9=15\\\frac{15}{2}=7.5\\7.5*4=30\)

so the area of the first trapezoid is 30 ft²

For the second one the given dimensions are

a = 8

b = 11

h = 6

now we just plug in the values

\(A=\frac{8+11}{2} 6\\8+11=19\\\frac{19}{2} =9.5\\9.5*6=57\)

so the area of the second trapezoid is 57 yd²

The back-to-back stem-and-leaf plot or parallel boxplots can be use to compare. GPAs for successful students are generally higher. A significant relationship exists between GPA and credit hours for successful students. An applicant with a 3.5 GPA is likely to be successful, as the predicted value is closer to successful students' values.

To compare the GPAs for the two groups, an appropriate graphical display could be a back-to-back stem-and-leaf plot or parallel boxplots. Based on the graph, we can observe that successful students generally have higher GPAs than unsuccessful students.

To determine if there is a significant relationship between GPA and mean number of credit hours per semester for successful students, we can use a t-test for the slope or linear regression t-test.

Given the provided computer output, with a t-value of -5.90 and a p-value of 0.000, we can reject the null hypothesis and conclude that there is a significant relationship between GPA and mean number of credit hours per semester for successful students.

Using the regression equation to predict the number of credit hours for an applicant with a GPA of 3.5,

For the successful group predicted hours = 23.514 – 2.7555(3.5) = 13.86975

For the unsuccessful group predicted hours = 24.200 – 3.485(3.5) = 12.0025

we get a predicted value of 13.86975 for successful students and 12.0025 for unsuccessful students.

Since the actual value of 14 is closer to the predicted value for successful students, we can infer that this applicant is likely to be successful in the Ph.D. program.

To know more about Null hypothesis:

https://brainly.com/question/28920252

#SPJ4

--The given question is incomplete, the complete question is given

" The statistics department at a large university is trying to determine if it is possible to predict whether an applicant will successfully complete the Ph.D. program or will leave before completing the program. The department is considering whether GPA (grade point average) in undergraduate statistics and mathematics courses (a measure of performance) and mean number of credit hours per semester (a measure of workload) would be helpful measures. To gather data, a random sample of 20 entering students from the past 5 years is taken. The data are given in photo.

a. Use an appropriate graphical display to compare the GPAs for the two groups.(provide names only) Write a few sentences commenting on your display.

b. For the students who successfully completed the Ph.D. program, is there a significant relationship between GPA and mean number of credit hours per semester?

Give a statistical justification to support your response.

c. If a new applicant has a GPA of 3.5 and a mean number of credit hours per semester of 14.0, do you think this applicant will successfully complete the Ph.D. program? Give a statistical justification to support your response. "--

The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.

Let patient admitted with heart disease represented by P(H)

P(H) = 12%

       = 0.12

And patient admitted for cancer disease represented by P(C)

P(H) = 16%

       = 0.16

Percent of patient received both coronary and oncology = 4%

P( H∩C ) = 0.04

Probability of randomly selected patient admitted for coronary, oncology or both is :

P( H∪C ) = P(H) + P(C) - P(H∩C )

⇒P( H∪C ) = 0.12 + 0.16 - 0.04

⇒ P( H∪C ) = 0.24

Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by  P( H∪C ) = 0.24.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer: Negative 6

Step-by-step explanation:

Remove parentheses

= -4 - 2

Subtract the number -4 - 2 = -6

Answer is negative 6.

Answer:

volume of the prism=(1/2×(6+12)×4)×10

=36×10

=360 cm³

Answer:

x = 26

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle is half the length of the third side, thus

x + 9 = \(\frac{1}{2}\)(3x - 8) ( multiply both sides by 2 to clear the fraction )

2(x + 9) = 3x - 8

2x + 18 = 3x - 8 ( subtract 2x from both sides )

18 = x - 8 ( add 8 to both sides )

26 = x

Answer:

Angles are rays with a shared endpoint.

Lines extend forever in either direction.

Rays AB and AC extend forever in either direction.

Step-by-step explanation:

Answer:

An angle is defined as two rays with a common endpoint, so CAB (or BAC) is an angle. A line is described as an infinite set of points that extend forever in either direction, which these rays also do.

Step-by-step explanation:

The rewritten expression in the form of xⁿ is \(x^{\frac{-3}{16}}\)

Expression:

In math, the expression refers the combination of variables, constants and exponents.

Given,

Here we have the expression \(\sqrt{x^{^{\scriptsize\dfrac34}}x^{-1}}\)

Now, we have to rewrite this expression into the form of xⁿ.

As per the law of exponents, we have rewrite the given expression as,

=> \((x^{^{\scriptsize\dfrac34}}x^{-1})^{\frac{1}{2})\)

Now, as per the law of exponent of multiplication, we can write it as,

=> \(x^{\frac{3}{8}}x^{\frac{-1}{2}}\)

Now, it can be further simplified as,

=> \(x^{\frac{-3}{16}}\)

To know more about Expression here.

https://brainly.com/question/14083225

#SPJ4

( 6 / 10 ) x = 51

( 1 / 10 ) x = 51 / 6

x = 510 / 6

x = $85

The logarithm of a number raised to a power is  the product of the power. The logarithm of a quotient of two numbers is the difference of the logarithms. The logarithm of a product of two numbers is the sum.

In the given statements, logarithms are used to express relationships between exponentiation, division, and multiplication.

For the first statement, log(4) = 6 implies that 4 raised to the power of 6 is equal to 4. This demonstrates the property that the logarithm of a number raised to a power is equivalent to the power multiplied by the logarithm of the number.

In the second statement, log(2) = log(4) - 8 indicates that the logarithm of 2 is equal to the difference between the logarithms of 4 and 8. This illustrates the property that the logarithm of a quotient of two numbers is equal to the difference of their logarithms.

Lastly, in the third statement, log(4.8) = log(4) + 3 shows that the logarithm of the product 4.8 is equal to the sum of the logarithms of 4 and 3. This property signifies that the logarithm of a product of two numbers is equal to the sum of their logarithms.

These properties of logarithms are fundamental in simplifying calculations involving exponentiation, division, and multiplication.

Learn more about logarithms here:

brainly.com/question/30226560

#SPJ11

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

Learn more about " binomial distribution" : https://brainly.com/question/15246027

#SPJ11

a)0.1587 (or 15.87%)

b)0.6827 (or 68.27%)

c)0.0228 (or 2.28%)

1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).

2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).

3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).

Learn more about Probability

brainly.com/question/29381779

#SPJ11

Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

Answer:

117

Step-by-step explanation:

x+63 = 180

Subtract 63 from each side

x +63-63 = 180-63

x=117

Answer:

A = 1600π cm²

Step-by-step explanation:

We are given that a circle's radius increases 4 cm every second.

We want to know how large the area of the circle is after 10 seconds.

We first need to find how large the radius will be.

We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.

We can write this as a proportion:

\(\frac{4 cm}{1 s} = \frac{x}{10s}\)

We can cross multiply to get:

4 cm * 10 s = x * 1 s

Divide both sides by 1 s

(4 cm * 10 s) / (1 s) = 40cm = x

So, after 10 seconds, the radius will be 40cm.

We aren't done yet though, remember that the question wants us to find the area of the circle.

The area can be calculated using the equation A = πr², where r is the radius.

We can substitute 40 as r in the equation to get:

A = πr² = π * (40)² = 1600π cm²

If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

Learn more about triangle here:

https://brainly.com/question/28470545

#SPJ1

Because Old Navy has a higher standard deviation, we know that there is more variability in the wait times at Old Navy.

Overall, wait times at Old Navy are more spread out from the average; wait times at the Gap are closer to the average.
Based on the given information, we know that both Gap and Old Navy have an average wait time of 5 minutes. However, Gap has a standard deviation of 2 minutes, while Old Navy has a standard deviation of 5 minutes.

Because Old Navy has a higher standard deviation, we know that there is more variability in the wait times at Old Navy. Overall, wait times at Old Navy are more spread out from the average; wait times at the Gap are closer to the average.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is a widely used measure of the variability or spread of a data set. The standard deviation is the square root of the variance, which is the average of the squared differences from the mean.

A higher standard deviation indicates that the data points are more spread out from the mean, while a lower standard deviation indicates that the data points are closer to the mean. The standard deviation is typically used in combination with the mean as a measure of central tendency to provide a more complete description of the data.

Visit here to learn more about standard deviation brainly.com/question/23907081
#SPJ11

Answer:

x is 90 z is 60 and y is 30

Step-by-step explanation:

Step-by-step explanation:

8x-2=46

collect like terms

8x=46+2

8x=48

Divide both sides by 8

8x÷8=48÷8

x=6

Answer:

0.217

Step-by-step explanation:

hope this helps. . .<3

good luck!    uωu

200.017

Thousandths is the third digit after the decimal.

Answer:

At the faster rate (12 gallons per minute)

Time = 60t minutes

At the slower rate (8 gallons per minute)

Time = 120 - 60t minute

Step-by-step explanation:

From the question,

From the statement above, it means 12 gallons per minute is the faster rate and

8 gallons per minute is the slower rate

Also,

He adds water to the pool for a total of 2 hours. That is, the total time he spends adding water to the pool at both rates is 2 hours.

From the question, let t be the time in hours that he adds water to the pool at the faster rate. That is,

At the rate of 12 gallons/minute

Time = t hours (Convert to minute)

(NOTE: 1hour = 60 minute)

Time = t × 60 minute

Time = 60t minute

Since the total time spent was 2 hours, then

The time spent when adding water at the rate of 8 gallons / minute will be

Time = 2 - t hours (convert to minute)

Time = (2 - t) × 60 minutes

Time = 120 - 60t minutes

Hence, the algebraic expression for the time he spends adding water to the pool at the faster rate is

Time = 60t minutes

and for the slower rate

Time = 120 - 60t minute

Answer:

B.

Step-by-step explanation:

1) the given equation is provided in slope-interception form, then

2) the interseption is '-3', it means the point (0;-3) - the correct answer is either B or C;

3) the slope of the given line is more that 1 (3/2>1), it means the angle is [45°;90°], then the line of the answer B is satisfies this condition.*

4) finally, the correct answer is B.

* - if to substitute the point (2;0) then it will be true equality 0=0.

Answer: 8.94

Step-by-step explanation:

d = sqrt ((x2 - x1)^2+ (y2 - y1)^2)

d = sqrt (80)

d = 8.944272

3/8 as a decimal is 0.375. To change a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number).

To change 3/8 into a decimal without a calculator, you can use long division or mental math. Here's how to do it using long division:

1. Write 3 as the dividend and 8 as the divisor.

2. Divide 8 into 3. The quotient is 0, so write 0 above the division line.

3. Add a decimal point to the dividend and add a zero to the end. The new dividend is 30.

4. Divide 8 into 30. The quotient is 3, so write 3 above the division line.

5. Subtract 24 from 30 to get 6.

6. Add another zero to the end of 6 to get 60.

7. Divide 8 into 60. The quotient is 7 with a remainder of 4.

8. Add another zero to the end of 4 to get 40.

9. Divide 8 into 40. The quotient is 5 with no remainder.

It's also useful to remember that 3/8 is approximately equal to 0.375, which can be helpful for estimation and mental math.

To learn more about decimal click on,

https://brainly.com/question/20819492

#SPJ4

Answer:

I like it, I think it's cute

Step-by-step explanation: