Out of people wederval for the true population proportion of people with kids Give your awer as decimals to the places

What is the correct terpretation for the confidence interval
a.The true proportion of people with kids is in the above interval, 954 of the time We know this
is true because the proportion of our sample is in the interval
b.With 95% confidence, the true proportion of people with kids wit be in the above interval
c.There is a 95% chance that the true proportion of people with kids will be in the above internal

The formula for the area of a circular petri dish can be represented as A = πr², where "A" represents the area and "r" represents the radius.

To find the approximate increase in the area when the radius increases from r₁ mm to r₂ mm, we can calculate the difference between the areas by subtracting the initial area (A₁ = πr₁²) from the final area (A₂ = πr₂²). This can be expressed as ΔA = A₂ - A₁ = πr₂² - πr₁².

In the second paragraph, let's explain the formula and how to calculate the approximate increase in the area of the bacterial colony on the petri dish. The area of a circular shape is given by the formula A = πr², where "A" represents the area and "r" represents the radius. By substituting the initial radius, r₁, into the formula, we can find the initial area, A₁ = πr₁².

Similarly, by substituting the final radius, r₂, into the formula, we can find the final area, A₂ = πr₂². To calculate the approximate increase in area, we subtract the initial area from the final area: ΔA = A₂ - A₁ = πr₂² - πr₁². This formula allows us to find the difference in the areas of the bacterial colony on the petri dish when the radius increases from r₁ to r₂.

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The total volume of ice cream in term of π is 42π³

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space.

The total volume of the ice cream = volume of cone + volume of half sphere

volume of a cone = 1/3 πr²h

= 1/3 × π × 3² × 8

= π×3 ×8

= 24π in³

volume of the half sphere = 4/6πr³

= 4/6 ×π × 3³

= 108π/6

= 18π in³

therefore the total volume of the ice cream

= 24π + 18π

= 42π in³

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The probability of selecting an even number card is: 50%

The number of the cards are given as:

4, 5, 6 and 7

Now, an even number are defined as any number that can be exactly divided by 2. Even numbers always end up with the last digit as 0, 2, 4, 6 or 8. Some examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16.

A number which is not divisible by “2” is called an odd number. An odd number always ends in 1, 3, 5, 7, or 9. Examples of odd numbers: 51 , − 543 , 8765 , − 97 , 9 , etc.

Thus, we have 4 cards and the even number are 2. Thus:

P(even) = 2/4 = 0.5

= 50%

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Answer:

Intercept Form.

You can directly solve for x by setting them to zero to which X= 3, X= -2

x-3 = 0  x+2 =0

x= 3  x= -2

(a) standard error (SE) = 2.0512

(b) probability that the sample mean is smaller than 128 = 0.1635

(c) probability that the sample mean is at least 131 = 0.3121

(a) To calculate the standard error (SE), we use the formula:

SE = (population standard deviation) / sqrt(sample size).

In this case, the population standard deviation is 20, and the sample size is 95.

Therefore,

SE = 20 / sqrt(95) ≈ 2.0512.

(b) To calculate the probability that the sample mean is smaller than 128, first find the z-value using the formula:

z = (sample mean - population mean) / SE.

In this case,

z = (128 - 130) / 2.0512 ≈ -0.98.

Then, use a z-table or calculator to find the probability associated with the z-value:

P(z < -0.98) ≈ 0.1635.

Thus, P(x < 128) = P(z < -0.98) = 0.1635.

(c) To calculate the probability that the sample mean is at least 131, first find the z-value:

z = (131 - 130) / 2.0512 ≈ 0.49.

Then, we need to find the probability P(z ≥ 0.49). Since z-tables provide the probability for z ≤ a given value, we can use the complement rule:

P(z ≥ 0.49) = 1 - P(z ≤ 0.49) ≈ 1 - 0.6879 = 0.3121.

Thus, P(x ≥ 131) = P(z ≥ 0.49) = 0.3121.

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The standardized residuals are -0.11, 0.75, -0.38, 2.08, and 2.16, respectively.

(a) The estimated regression equation can be found by first calculating the sample means and sample standard deviations for both x and y, as well as the sample correlation coefficient, and then using these values to calculate the slope and intercept of the regression line:

x = (6 + 11 + 15 + 18 + 20)/5 = 14

y = (7 + 7 + 13 + 21 + 30)/5 = 15.6

sx = sqrt(((6-14)^2 + (11-14)^2 + (15-14)^2 + (18-14)^2 + (20-14)^2)/4) = 4.49

sy = sqrt(((7-15.6)^2 + (7-15.6)^2 + (13-15.6)^2 + (21-15.6)^2 + (30-15.6)^2)/4) = 8.25

r = ((6-14)(7-15.6) + (11-14)(7-15.6) + (15-14)(13-15.6) + (18-14)(21-15.6) + (20-14)(30-15.6))/4sxsy

= 0.962

b = r(sy/sx) = 1.71

a = y - b(x) = -9.23

Therefore, the estimated regression equation is y = -9.23 + 1.71x.

(b) The residuals can be found by subtracting the predicted values of y (based on the regression line) from the actual values of y:

xi

yi

y

Residuals

6

7

0.09

-0.09

11

7

6.38

0.62

15

13

13.31

-0.31

18

21

19.29

1.71

20

30

23.57

6.43

(c) The standardized residuals can be found by dividing each residual by its estimated standard deviation:

xi

yi

ŷ

Residuals

Standardized Residuals

6

7

0.09

-0.09

-0.11

11

7

6.38

0.62

0.75

15

13

13.31

-0.31

-0.38

18

21

19.29

1.71

2.08

20

30

23.57

6.43

2.16

The estimated standard deviation of the residuals can be found by calculating the root mean squared error (RMSE):

RMSE = sqrt(((-0.09)^2 + (0.62)^2 + (-0.31)^2 + (1.71)^2 + (6.43)^2)/4) = 3.04

Therefore, the standardized residuals are -0.11, 0.75, -0.38, 2.08, and 2.16, respectively.

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Excluding the boundary lines shown on the graph, (4 , 6) is the required ordered pair inside the region of the graph satisfies the given system of linear equation.

The budget of a website to advertise in local newspaper is $600 , and they plan to run no more than 10 advertisements. An ad in the weekend edition is $75, and an ad in the weekday paper is $50.

Let  x be equal to the number of weekend ads, and y be equal to the number of weekday ads.

We can compute the point inside the region of the graph that satisfies the system of linear equations that can be formed as,

75x + 50y = 600 ___(1)

x + y = 10 ___(2)

Solving the system of linear equations in (1) and (2) as,

From equation (2), x= 10- y

Substituting x in equation (1) with x= 10- y, we get,

75( 10- y )+ 50y = 600

⇒ 750 - 75y + 50y = 600

⇒ 25y = 150

⇒ y = 6

Thus, x = 10 - 6 = 4

Hence (x, y) = (4 , 6) inside the region of the graph satisfies the given system of equation.

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The probability that the randomly selected point falls in the green sector is 1/6.

Option B is the correct answer.

We have,

The area of the green sector can be found by using the formula for the area of a sector:

A = (θ/360)πr²,

Where θ is the central angle and r is the radius.

In this case,

θ = 60° and r = 6 inches,

So the area of the green sector is:

A = (60/360)π(6)²

A = π(6)²/6

A = 6π

So,

The total area of the spinner is π(6)² = 36π.

So the probability of the randomly selected point falling in the green sector is:

P = (Area of green sector)/(Total area of spinner)

P = (6π)/(36π)

P = 1/6

Therefore,

The probability that the randomly selected point falls in the green sector is 1/6.

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The tables are completed as follows:

For Table 1, we have an exponential function defined as follows:

f(x) = b^x.

We have that when x = 0.699, f(x) = 5, hence the base b is obtained as follows:

b^0.699 = 5

b = 5^(1/0.699)

b = 10.

Hence, when x = 1.477, the value of f(x) is given as follows:

f(x) = 10^1.477

f(x) = 30.

Table 2 is the inverse of table 1. For Table I, we have that when x = 1.301, f(x) = 20, hence for table 2, we have that f(x) = 1.301 when x = 20.

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The probability that a randomly selected point within the circle falls in the

red-shaded triangle is 0.14.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Area of the circle.

= πr²

= 3.14 x 15 x 15

= 706.5

Area of the shaded triangle.

= 1/2 x base x height
= 1/2 x 12 x 16

= 6 x 16

= 96

Now,

The probability that a randomly selected point within the circle falls in the

red-shaded triangle.

= Area of shaded triangle /Area of the circle

= 96/706.5

= 0.14

Thus,

The probability that a randomly selected point within the circle falls in the

red-shaded triangle is 0.14.

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Answer:

-3 times n+7>-17

Step-by-step explanation:

The probability for each k value is from 15 to 25 and sum them up to get the final probability.

The situation you described is not a geometric distribution. Instead, it follows a binomial distribution. A binomial distribution is appropriate here because we have a fixed number of trials (25 coin flips), each trial has two outcomes (heads or tails), and the probability of success (getting heads) remains constant throughout the trials.

To calculate the probability of getting 15 or more heads in 25 coin flips, you can use the binomial formula:

[tex]P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)}[/tex]

where n is the number of trials (25), k is the number of successful outcomes (15 or more), p is the probability of success (0.5 for a fair coin), and C(n, k) represents the number of combinations of n items taken k at a time.

You'll need to calculate the probability for each k value from 15 to 25 and sum them up to get the final probability.

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The equation of the line in slope intercept form is: y = 3x - 5

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph given, we see that the y-intercept which is the point where the line crosses the y-axis is at: y = -5

To get the slope, we will use two points namely:

(0, -5) and (1, -2)

Thus:

Slope = (-2 + 5)/(1 - 0)

Slope = 3

Thus, the equation is:

y = 3x - 5

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{u, v, w} is linearly independent, and the statement is proved.

What is linear function?

A linear function is a mathematical function of the form f(x) = mx + b, where m and b are constants.

To prove this statement, we will use a proof by contradiction.

Assume that A is linearly dependent and that {u, v, w} is also linearly dependent. This means that there exist scalars α, β, and γ, not all zero, such that αu + βv + γw = 0.

Now, we will express w in terms of u and v:

w = u + 2v - tw1

Substituting w in the above equation, we get:

αu + βv + γ(u + 2v - tw) = 0

Simplifying this equation, we get:

(α + γ)u + (β + 2γ)v - γtw = 0

Since u, v, and w are distinct and none of them is the zerovector, α + γ ≠ 0 or β + 2γ ≠ 0 or -γt ≠ 0.

If -γt = 0, then γ = 0, which contradicts the assumption that not all scalars α, β, and γ are zero.

If -γt ≠ 0, then we can express t as t = γ' / (-γ) for some non-zero scalar γ'. Substituting t in the above equation, we get:

(α + γ)u + (β + 2γ)v + γ'w = 0

We can now express w in terms of u and v using the equation w = u + 2v - tw1, which gives:

(α + γ)u + (β + 2γ)v + γ'(u + 2v - tw) = 0

Simplifying this equation, we get:

(α + γ + γ')u + (β + 2γ + 2γ')v - γ'tw1 = 0

Since u, v, and w are distinct and none of them is the zerovector, it follows that the coefficients of u, v, and w1 are not all zero. Therefore, {u1, v1, w1} is linearly independent.

This contradicts the assumption that {u, v, w} is linearly dependent. Therefore, our initial assumption that {u, v, w} is linearly dependent must be false. Hence, {u, v, w} is linearly independent, and the statement is proved.

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The sentence written in the indicative mood is: "The team plays much better after a pep talk from their coach."

The grammatical mood known as the indicative is employed to state or inquire about facts.

The verb forms in the indicative mood show that the action or state described is actually occurring or has already occurred. For instance, the statement "I am walking to the store" is suggestive since it is a factual statement describing an action that is now occurring.

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Watershed should offer the promotion to the top 70 customers to maximize their profit from the intervention campaign.

To determine the optimal number of customers to offer the promotion to, Watershed should start by offering it to customers with the highest estimated unsubscribe probability and work their way down until the promotion budget is exhausted. This approach will maximize the chances of persuading customers who are most likely to unsubscribe.

Let's assume that Watershed has a budget of $1000 to spend on promotions. This means they can offer the promotion to a maximum of 100 customers (1000/10).

To calculate the expected profit, we need to consider the probability of a customer unsubscribing, the probability of the promotion persuading them to remain a customer, and the value of retaining a customer and offering a promotion.

If a customer unsubscribes and is not persuaded to remain, the cost to Watershed is $10. If they unsubscribe but are persuaded to stay, the value to Watershed is $50 ($60-$10). If they don't unsubscribe, the cost is $0.

Using the formula given, we can calculate the profit for different values of n (the number of customers offered the promotion):

n = 10:
Profit = 10 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $460

n = 20:
Profit = 20 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $780

n = 30:
Profit = 30 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $990

n = 40:
Profit = 40 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1090

n = 50:
Profit = 50 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1150

n = 60:
Profit = 60 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1180

n = 70:
Profit = 70 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1190

n = 80:
Profit = 80 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1180

n = 90:
Profit = 90 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1150

n = 100:
Profit = 100 * (0.6 * 50 + 0.4 * (-10)) + 0 * (-10) = $1100

From the calculations above, we can see that the maximum profit of $1190 occurs when the promotion is offered to 70 customers. Beyond this point, the cost of offering the promotion to less likely churners outweighs the benefit of retaining those customers.

Therefore, Watershed should offer the promotion to the top 70 customers to maximize their profit from the intervention campaign.

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The distance between the robin and the base of the pole is 6.77 meters

To determine the distance, we need to know the different trigonometric identities in mathematics.

These identities are given as;

From the information given, we have that;

The angle of depression, θ = 38 degrees

The distance is unknown

The hypotenuse side is 11 meters

Now, using the sine identity, we have;

sin 38 = d/11

Cross multiply the values

d = 0. 6156(11)

multiply the values

d = 6. 77 meters

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P(X = k) = (1 - p)^4   for k = 0
P(X = k) = 4p(1 - p)^3   for k = 1
P(X = k) = 6p^2(1 - p)^2   for k = 2
P(X = k) = 4p^3(1 - p)   for k = 3
P(X = k) = p^4   for k = 4

Note that these probabilities add up to 1, as they should for any probability distribution.

(a) The distribution of X can be modeled as a binomial distribution with parameters n = 4 and p, where p is the probability that the friend correctly identifies a milk-first cup as milk-first. Each cup that the friend tastes can either be identified correctly (success) or incorrectly (failure), and there are 4 cups that were poured milk-first in the experiment.

(b) To find the probability mass function (PMF) of X, we need to find the probability of each possible value of X. Since X is a binomial random variable, the PMF of X is given by:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, given by:

(n choose k) = n! / (k! * (n - k)!)

where n! denotes the factorial of n.

In this case, n = 4 and there are 4 cups that were poured milk-first, so we have:

P(X = 0) = (4 choose 0) * p^0 * (1 - p)^4 = (1 - p)^4

P(X = 1) = (4 choose 1) * p^1 * (1 - p)^3 = 4p(1 - p)^3

P(X = 2) = (4 choose 2) * p^2 * (1 - p)^2 = 6p^2(1 - p)^2

P(X = 3) = (4 choose 3) * p^3 * (1 - p)^1 = 4p^3(1 - p)

P(X = 4) = (4 choose 4) * p^4 * (1 - p)^0 = p^4

Since X can only take on values between 0 and 4, the PMF of X is given by:

P(X = k) = (1 - p)^4   for k = 0
P(X = k) = 4p(1 - p)^3   for k = 1
P(X = k) = 6p^2(1 - p)^2   for k = 2
P(X = k) = 4p^3(1 - p)   for k = 3
P(X = k) = p^4   for k = 4

Note that these probabilities add up to 1, as they should for any probability distribution.

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In the given triangle, the measure of side c is approximately 39 m

From the question, we are to calculate the measure of side c in the given triangle.

To determine the measure of side c, we will use SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given diagram,

Angle = 29°

Opposite = 19 m

Hypotenuse = c

Thus

sin (29°) = 19 / c

0.4848 = 19 / c

c = 19 / 0.4848

c = 39.1914

c ≈ 39 m

Hence,

The measure of c is 39 m

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Step-by-step explanation:

The y-axis intercept occurs when x = 0

put in 0 for 'x' and compute the intercept as

(0+2)(0-2)(0-A)   = 12

      -4 ( -A) = 12

       4A =12

         A = 3

The probability of rolling a sum of 3 these dice is 1/18.

Given that, a pair of standard dice are rolled.

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.

Number of favorable outcomes = 2

Total number of outcomes = 36

Here, probability = 2/36

= 1/18

Therefore, the probability of rolling a sum of 3 these dice is 1/18.

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The calculated value of the probability P(head) is 0.5 i.e. one half

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

Sections = 2

Sections = head and tail

Using the above as a guide, we have the following:

Head = 1

When the head section is flipped, we have

P(head) = head/section

The required probability is

P(head) = 1/2

Evaluate

P(head) = 0.5

Hence, the value is 0.5

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The surface area of the pyramid is 186 cm².

Given that the net diagram of a square pyramid, we need to find the surface area of the same,

SA = a² + 2al

a = side length, l = height

SA = 6² + 2×6×12.5

= 186 cm²

Hence, the surface area of the pyramid is 186 cm².

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The table of values of the equation h(x) = -4x + 5 is

x y

-2  13

-1   9

0   5

1   1

Given that

h(x) = -4x + 5

To find the values that complete the table for the given equation h(x) = -4x + 5, we substitute each value of x and evaluate y.

So the completed table is:

x    y

-2  13

-1   9

0   5

1   1

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The length of the lake of 4.042 miles in yards is 7113.92 yards

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

Lake has a length of 4.042 mi.

This means that

Length = 4.042 miles

From the table of values:

To convert inches to feet, we multiply the length value by 1760

So, we have

Length = 4.042 * 1760 yards

Evaluate

Length = 7113.92 yards

Hence, the length is 7113.92 yards

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The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025 or 2.5%

To find the probability that a randomly selected adult has an IQ greater than 134.4, we need to calculate the z-score and then find the corresponding area under the standard normal distribution curve.

The z-score is calculated as: [tex]z= \frac{x-μ}{σ}[/tex]

where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

Substituting the given values, we get:

[tex]z = \frac{(134.4 - 101.1)}{17}[/tex]

z = 1.96

Using a standard normal distribution table, we find that the area to the right of z = 1.96 is approximately 0.025. Therefore, the probability that a randomly selected adult has an IQ greater than 134.4 is 0.025 or 2.5%.

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a) Required probability is independent probability.

b) Required game is 0.000025.

c)Each at-bat is independent of the others.

d) Required probability is 0.0036.

e) Required probability is 0.9964.

a. The given incident is an example of independent probability.

b. The probability of getting seven hits in tonight's game is [tex]0.364^7 = 0.000025[/tex] (rounded to 3 decimal places).

c. Yes, we can assume that each at-bat is independent of the others.

d. The probability of not getting any hits in the game is [tex](1 - 0.364)^7 = 0.0036[/tex](rounded to 3 decimal places).

e. The probability of getting at least one hit is equal to the complement of the probability getting any hits, which is [tex]1 - 0.0036 = 0.9964[/tex] (rounded to 3 decimal places).

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The correct interpretation of the given confidence interval is C. We are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

The confidence interval is given as (-0.13, 0.09), which represents the range within which the true difference in proportions (p1 - p2) is likely to fall with a confidence level of 98%.

The negative value of -0.13 indicates that the proportion of obese clients losing weight under strategy 1 may be 13% less than the proportion under strategy 2.

The positive value of 0.09 indicates that the proportion of obese clients losing weight under strategy 1 may be 9% more than the proportion under strategy 2.

Since the confidence interval includes both positive and negative values, it suggests that the true difference in proportions could be either positive or negative.

The confidence level of 98% means that if we were to repeat the study and construct 100 different confidence intervals, about 98 of those intervals would capture the true difference in proportions (p1 - p2).

Therefore, we can conclude that we are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

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The experimental probability that the next time Audra rolls the number cube, she will roll a 2 is 3/22.

Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted. In this case, we want to find the experimental probability of rolling a 2.

Looking at the data provided, we can see that Audra rolled a 2 three times out of the total 22 rolls. So, the experimental probability of rolling a 2 can be calculated as:

Experimental probability = number of times the event occurred / total number of trials

Experimental probability of rolling a 2 = 3 / 22

Therefore, the correct option is (B) 3/22. This means that based on Audra's experiment, the probability of rolling a 2 is approximately 0.136 or 13.6%. It is important to note that this is the experimental probability based on a small sample size, and the actual probability of rolling a 2 in a large number of rolls may differ.

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The distance between two divers is 4 meters.

The distance (in meters)  of two divers from a shipwreck located at point X is shown by a number line.

Given,

A = -2.5

X = 0

B = 1.5

To find the distance between two divers, we have to find an expression using subtraction.

Distance between the two divers.

= | B - A |  or | A - B|

Substituting the values, we get

| 1.5 - (-2.5) |

 or

| -2.5 - 1.5|

or  1.5 - (-2.5)

1.5 - (-2.5)

If adding a number to the actual number gives the result 0, then that number is the additive inverse of the actual number.

Therefore, the additive inverse of -2.5 will be 2.5

1.5 + 2.5

= 4

Therefore, the distance between the two divers. = 4m

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