The geometric mean between 16 and 20 is

The point that partitions segment AB in a 1:4 ratio is (-1, -0.4).

In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 4.

In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:

Q(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

Q(x, y) = [(1(7) + 4(-3))/(1 + 4)],  [(1(-10) + 4(2))/(1 + 4)]

Q(x, y) = [(7 - 12)/(5)],  [(-10 + 8)/5]

Q(x, y) = [-5/5],  [(-2)/(5)]

Q(x, y) = [-1, -2/5]

Q(x, y) = [-1, -0.4]

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The new coordinates of point s after the dilation are (12x, 12y)

A dilation is a type of transformation that changes the size of an object. It can be thought of as a resizing or stretching of the object. In this case, we are dilating a point with a center at the origin (0,0) and a scale factor of 12.

The center of dilation is the point around which the dilation occurs. In this case, the center of dilation is the origin. This means that the point will be resized relative to the origin.

The scale factor is a number that determines the amount by which the object is resized. In this case, the scale factor is 12. This means that the point will be enlarged 12 times its original size.

To find the new coordinates of the point after the dilation, we multiply the original coordinates by the scale factor. Let the original coordinates of the point be (x, y). Then, the new coordinates of the point after the dilation are:

New x-coordinate = 12 × x

New y-coordinate = 12 × y

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Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

The formula below can be used to determine the ideal amount of phone representatives:

=>  MR = MC

Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.

The following results are obtained by taking the derivative of revenue and cost with regard to n:

=> MR=dR/dn = k

=>  dC/dn = 12 for MC.

When we set MR equal to MC, we obtain:

=> k = 12

Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.

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Each student should receive 1/2 kg of soil.

To find out how much soil each student will have, we need to first add up the total amount of soil collected and then divide it equally among the 10 students.

Let's start by converting all the amounts of soil to a common unit, such as kilograms:

3 students brought 1/4 kg each, so they brought a total of 3/4 kg.

4 students brought 1/2 kg each, so they brought a total of 2 kg.

3 students brought 3/4 kg each, so they brought a total of 2 1/4 kg.

Adding up these amounts, we get:

3/4 + 2 + 2 1/4 = 5 kg

So the total amount of soil collected is 5 kg.

To redistribute this soil equally among the 10 students, we need to divide it by 10:

5 kg ÷ 10 = 1/2 kg per student

Therefore, each student should receive 1/2 kg of soil.

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Answer:

We can check which dimensions are possible for the rectangle by finding the product of the width and length and seeing if it equals the given area of (24x + 30) square units.

Let's check each option:

width 6 units; length (4x + 5) units

Area = 6(4x + 5) = 24x + 30

This option is possible.

width 4 units; length (6x + 7) units

Area = 4(6x + 7) = 24x + 28

This option is not possible since the area is not equal to (24x + 30).

width 3 units; length (21x + 27) units

Area = 3(21x + 27) = 63x + 81

This option is not possible since the area is not equal to (24x + 30).

width 8 units; length (3x + 4) units

Area = 8(3x + 4) = 24x + 32

This option is not possible since the area is not equal to (24x + 30).

width 2 units; length (15 + 12x) units

Area = 2(15 + 12x) = 30 + 24x

This option is not possible since the area is not equal to (24x + 30).

Therefore, the only possible dimension for the rectangle is width 6 units and length (4x + 5) units.

The probability of being able to toast at least 7 pieces of bread before the toaster catches on fire and destroys itself is approximately 0.0128

We can approach this problem using the negative binomial distribution, which models the number of successful trials (toasting without the toaster catching on fire) before a specified number of failures (the toaster catching on fire and destroying itself) occur.

Let X be the number of successful toasting trials before the toaster catches on fire and destroys itself. We want to find P(X ≥ 7), the probability that at least 7 pieces of bread can be toasted before the toaster is destroyed.

The negative binomial distribution can be expressed as

P(X = k) = (k+r-1)C(r-1) × p^r × (1-p)^k

where r is the number of failures (the toaster catching on fire and destroying itself), p is the probability of success (toasting without the toaster catching on fire), and (k+r-1)C(r-1) is a combination factor that represents the number of ways to arrange k successes and r-1 failures in a sequence.

In this case, r = 1 (we want to know the probability of the first failure occurring after at least 7 successes), p = 0.75 (the probability of successfully toasting a piece of bread), and we want to find P(X ≥ 7).

P(X ≥ 7) = 1 - P(X < 7)

= 1 - Σ[k=0 to 6] (k+1) × p × (1-p)^k

≈ 0.0128

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The given question is incomplete, the complete question is:

I bought a cheap toaster. Every time I use it there is a chance that it will catch on fire with

probability p = 0.25, burn my toast, and destroy itself. But with probability (1 − p) it makes

perfect toast!

What is the probability I put at least 7 pieces of bread into my cheap toaster before it

destroys itself?

Answer:

there

Step-by-step explanation:

Answer:

Let's assume that the subset contains as many numbers as possible. We start by including all the numbers from 1 to 100 that are not divisible by 5. These are the numbers 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98, 99.

This gives us a subset of 81 numbers. However, we need to remove any numbers that are multiples of other numbers in the subset. For example, if we include the number 6, we must remove 12, 18, 24, etc. Similarly, if we include the number 9, we must remove 18, 27, 36, etc. We can see that the only numbers that have multiples in the subset are 2, 3, 7, 8, 13, 17, 18, 19, 27, 28, 37, 38, 39, 52, 53, 54, 57, 58, 59, 68, 69, 73, 74, 78, 79, 83, 84, 87, 88, 89, 92, 93, 94, and 98.

Therefore, we need to remove these 34 numbers from the subset. This leaves us with a subset of 81 - 34 = 47 numbers.

However, we can still include the number 5, since it is not a multiple of any other number in the subset. This adds one more number to the subset, giving us a total of 48 numbers.

Therefore, the largest number of members that such a subset can have is 48, which corresponds to answer choice (e).

a. The revenue function, r(x), is given by the product of the price x and the demand function d(x):

[tex] \sf r(x) = x \times d(x) = x \times (400 - 4x) = 400x - 4x^2[/tex]

The domain of this function is the set of possible prices that can be charged for the jeans, which is typically a positive real number, or in interval notation: (0, infinity).

b. If the price is $40, we can find the revenue by plugging in x = 40 into the revenue function:

[tex] \sf r(40) = 400(40) - 4(40)^2 = 16,000 - 6,400 = 9,600[/tex]

Therefore, the company will earn $9,600 in revenue if they sell their jeans at a price of 40

The doubling time of the culture is approximately 42.91 minutes.

The growth rate constant is a mathematical concept that is used to model the growth of a population. It represents the rate at which the population is increasing at any given moment. The doubling time is a measure of how long it takes for a population to double in size, and it can be calculated using the formula mentioned above.

The doubling time of a culture can be calculated using the formula: Doubling time = ln(2) / growth rate constant

Using the given growth rate constant of 0.01615468 min^-1, we can calculate the doubling time as:

Doubling time = ln(2) / 0.01615468 [tex]min^{-1}[/tex]

Doubling time ≈ 42.91 minutes

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Answer:

d ≈ 5.4

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (4, 7 )

d = [tex]\sqrt{(4-2)^2+(7-2)^2}[/tex]

   = [tex]\sqrt{2^2+5^2}[/tex]

  = [tex]\sqrt{4+25}[/tex]

  = [tex]\sqrt{29}[/tex]

 ≈ 5.4 ( to the nearest tenth )

Answer: b. 12

Step-by-step explanation:

16 + 4 − (5 x 2) + 2

= 16 + 4 - 10 + 2

= 20 - 12

= 12

Answer:

Step-by-step explanation:

8

In summary, understanding the probability of a basketball team's performance in a season can be done by examining conditional probabilities such as P(H) and P(W|H). This analysis can provide insights into the team's performance and help identify areas for improvement.

Based on the given information, it seems you are referring to the probability of a basketball team's performance in a season with specific characteristics, namely the probability of a home game (P(H)) and the probability of a win given a home game (P(W|H)).

In order to analyze these probabilities, we can use the concept of conditional probability. Conditional probability helps us understand the likelihood of an event occurring given that another event has occurred.

In this case, P(H) represents the probability of the team playing a home game, and P(W|H) represents the probability of the team winning given that they are playing a home game. Knowing these probabilities can help us understand the team's overall performance and the advantage of playing at home.

To calculate the overall probability of a win, we can use the following formula:

[tex]P(W) = P(W|H) * P(H) + P(W|A) * P(A)[/tex]

Here, P(W|A) represents the probability of a win given an away game and P(A) represents the probability of an away game. By calculating P(W), we can determine the team's overall chances of winning a game, taking into account both home and away games.

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Hi so you have to do grid for the equation

Answer:

3

Step-by-step explanation:

Number of people in the choir = 80

Number of women = half of 80 = 40

Number of men in the choir is ¼ of the women = 40/4 = 10

Number of men plus women = 10 +40 = 50

Number of children = 80 - 50 = 30

Ratio of children to men = n:1 = 30:10

Divide both sides by 10

30:10 = 3:1

n = 3

The variance is 7.2.

We can use the binomial distribution formula to calculate the variance. The formula for the variance of a binomial distribution is

Variance = n × p × (1 - p)

where n is the number of trials, p is the probability of success on each trial, and (1 - p) is the probability of failure on each trial.

In this case, n = 30 (the number of homes on the route), p = 0.48 (the probability of a home having a dog), and (1 - p) = 0.52 (the probability of a home not having a dog).

The postal employee encountered 12 dogs, which means there were 18 homes without dogs. So, the actual probability of success in this case is

P(dogs) = 12/30 = 0.4

Using the formula above, we can calculate the variance

Variance = n × p × (1 - p)

= 30 × 0.4 × 0.6

= 7.2

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Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.

Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.

the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:

m∠MGS = 90°

Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.

m∠SGM = 1/2 (mSE - mGE)

where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.

Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.

mSE = 2mGS

mSE = 2(84°) = 168°

m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°

Therefοre, m∠SGM = 84°.

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The two numbers are 6 and 2.

Let's assume the first number is x and the second number is y.

From the first statement, we can write the equation x = y + 4.

From the second statement, we can write the equation 2x = 4y + 2.

Now, we can substitute x in terms of y from the first equation into the second equation:

2(y + 4) = 4y + 2

Simplifying this equation, we get:

2y + 8 = 4y + 2

2y = 6

y = 3

Substituting y = 3 in the first equation, we get:

x = y + 4 = 3 + 4 = 7

Therefore, 6 and 2 are the two numbers,


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Here are some examples:

Distance to endpoint: |2 - (-2)| = 4

Equation: |x - 2| = 4



When answering questions on Brainly, you should always be factually accurate, professional, and friendly. You should be concise and not provide extraneous amounts of detail. You should also use the following terms in your answer, if they are relevant to the question being asked.

In order to write an absolute value equation in the form |x-c|=d to satisfy a given solution set on a number line, you need to do the following:First, identify the number c, which is the midpoint of the solution set. This is because the absolute value of x-c is equal to the distance between x and c on the number line.

Next, identify the number d, which is equal to the distance between the midpoint c and one of the endpoints of the solution set. This is because the absolute value of x-c can never be greater than the distance between x and c, so the maximum value of x that satisfies the equation is c+d and the minimum value is c-d.Finally, write the equation in the form |x-c|=d using the values of c and d that you identified.

Set of solutions (-3, 1) In the middle: (-3 + 1)/2 = -1

Endpoint distance: |-1 - (-3)| = 2

Formula: |x + 1| = 2

Set of solutions (-4, 4)

Center: (-4 + 4)/2 = 0.

Endpoint distance: |0 - (-4)| = 4

Equation: 4 for |x| Set of solutions (-2, 6)

Center: (-2 + 6)/2 = 2

Endpoint distance: |2 - (-2)| = 4

Equation: 4 for |x - 2|

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The probability of selecting a brown bead from the bowl is 2/7 or approximately 0.29.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of selecting a brown bead can be calculated by dividing the number of brown beads by the total number of beads in the bowl:

Probability of selecting a brown bead = Number of brown beads / Total number of beads

In this case, there are 4 brown beads out of a total of 14 beads:

Probability of selecting a brown bead = 4 / 14

Simplifying this fraction, we get:

Probability of selecting a brown bead = 2 / 7

Therefore, the probability of selecting a brown bead from the bowl is 2/7 or approximately 0.29 (rounded to two decimal places).

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the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.

There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.

The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:

Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)

Expected gain = 38/13 - 10/13 - 18/13

Expected gain = 10/13 ≈ 0.77

Therefore, the expected gain is $0.77, rounded to the nearest cent.

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Answer:

Step-by-step explanation:

It is possible if your friend has a bigger glass than you.

8. Spread = SD = sqrt(2*df)

9. The difference between the observed and expected frequencies of the outcomes of a set of events or variables.

10. Degrees of 1 freedom does the chi-square distribution.

11.  The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.

8. Describe the center and spread of the chi-square distributions.

Shape - skewed right because can't be zero

µ = df = tipping point

mode = df - 2 = peak

spread = SD = sqrt(2*df)

9. Chi-square test is a non-parametric test (a non-parametric statistical test is a test whose model does not specify conditions about the parameter of the population from which the sample is drawn.). It is used for identifying the relationship between a categorical variable and denoted by χ2.

10. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.

11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.

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The probability of finding 10 defective cores in a sample of 10 power cores is approximately 0.0000161, or about 0.0016%.

Assuming that each fuel rod is independent of each other and that the probability of finding a defective fuel rod is constant at 0.1%, we can model the number of defective fuel rods in a power core with a binomial distribution. Let X be the number of defective fuel rods in one power core, then X follows a binomial distribution with parameters n = 50000 and p = 0.1/100 = 0.001.

To find the probability of finding 10 defective cores, we can use the binomial distribution again, but with a different set of parameters. Let Y be the number of defective cores in a sample of 10 power cores, then Y follows a binomial distribution with parameters n = 10 and p = P(X ≥ 1), where P(X ≥ 1) is the probability of finding at least one defective fuel rod in one power core. We can find P(X ≥ 1) using the complement rule:

P(X ≥ 1) = 1 - P(X = 0)

= 1 - (1 - 0.001)^50000

≈ 0.3935

So, the probability of finding 10 defective cores in a sample of 10 power cores is:

P(Y = 10) = (10 choose 10) * (0.3935)^10 * (1 - 0.3935)^(10 - 10)

≈ 0.0000161

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Complete Question:

a power core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores.

The standard deviation for the number of people with the genetic mutation in a group of 1000 individuals is approximately 4.89.

To find the standard deviation for the number of people with a particular genetic mutation in a group of 1000 individuals, we first need to understand the concept of binomial distribution.

Binomial distribution is a statistical probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

In this case, the probability of success (having the genetic mutation) is 0.04, and the probability of failure (not having the mutation) is 0.96. Thus, we can model the number of people with the mutation in a group of 1000 individuals using a binomial distribution with n = 1000 and p = 0.04.

The formula for the standard deviation of a binomial distribution is:

σ = √(np(1-p))

Where σ is the standard deviation, n is the number of trials, and p is the probability of success. Plugging in the values, we get:

σ = √(1000 x 0.04 x 0.96) = 4.89

In other words, we can expect that the number of people with the genetic mutation in a group of 1000 individuals will vary around the mean of 40 (1000 x 0.04) by about 4.89, with about 68% of the observations falling within one standard deviation of the mean.

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The characteristics of each function has been explored based on the table below.

The graph of each function is shown in the image attached below.

In order to use the given functions to complete the table, we would have to substitute each of the values of x (x-values) into the function and then evaluate as follows;

A. f(x) = 2x

x                      process             f(x)

-2                  f(-2) = 2(-2)            -4

-1                   f(-1) = 2(-1)              -2

0                   f(0) = 2(0)               0

1                    f(1) = 2(1)                 2

2                   f(2) = 2(2)                4

B. G(x) = x²

x                      process             f(x)

-2                  f(-2) = (-2)²            4

-1                   f(-1) = (-1)²              1

0                   f(0) = (0)²               0

1                    f(1) = (1)²                 1

2                   f(2) = (2)²               4

B. H(x) = 2ˣ

x                      process             f(x)

-2                  f(-2) = (2)⁻²            1/4

-1                   f(-1) = (2)⁻¹              1/2

0                   f(0) = (2)⁰                1

1                    f(1) = (2)¹                 2

2                   f(2) = (2)²               4

In this scenario and exercise, we would use an online graphing calculator to plot each of the given functions as shown in the graph attached below.

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Answer:

The horizontal distance between the two x-intercepts is 7 units.

Step-by-step explanation:

The x-intercepts are the points at which the graph of a function or equation crosses the x-axis.  At these points, the value of y is zero.

Therefore, to find the x-intercepts of the given expression, set the expression equal to zero and solve for x:

(x - 3)(x + 4) = 0

This equation is true if and only if either x - 3 = 0 or x + 4 = 0, which means the x-intercepts are at x = 3 and x = -4.

The horizontal distance between these two points is the absolute value of the difference between the x-coordinates of the x-intercepts:

|3 - (-4)| = |3 + 4| = 7

Therefore, the horizontal distance between the two x-intercepts is 7 units.

Answer:33

Step-by-step explanation:45-12=33