The Central Limit Theorem is important in Statistics because it allows us to use the normal distribution to make inferences concerning the population mean: O provided that the population from which the sample was drawn is normal and the sample size is reasonably large. O provided that the population size is reasonably large (whether the population distribution is known or not). O provided that the sample size is reasonably large (for any population). o provided that the population from which the sample was drawn is normal.

The conditions are: a large enough sample size, probability of success between 0.1 and 0.9, and number of successes and failures both ≥ 10.

The binomial probability must be satisfied to make the probabilities from a binomial probability distribution approximated well by using a normal distribution are:

The sample size, n, must be large enough. A general rule of thumb is that n should be greater than or equal to 20. This ensures that there are enough data points to create a normal distribution.

The probability of success, p, must be between 0.1 and 0.9. If p is too close to 0 or 1, the distribution becomes too skewed and the normal approximation is not accurate.

The number of successes, np, and the number of failures, nq, must both be greater than or equal to 10. This ensures that the normal approximation is accurate enough to be useful.

If these conditions are met, then the probabilities from a binomial probability distribution can be approximated well by using a normal distribution with a mean μ = np, and a standard deviation σ = √(npq). This approximation can be useful in calculating probabilities and making statistical inferences.

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The mean of the given data set is 98.70

To find the mean of the given data set, we need to sum up all the values and then divide the sum by the total number of values.

Sum of the values = 23.4 + 35.6 + 73.1 + 58.0 + 18 + 723.4 + 35.6 + 73.1 + 58.0 + 18.7 + 33.8 + 33.8 = 1184.5

Total number of values = 12

Mean = Sum of values / Total number of values = 1184.5 / 12 =98.708

To round the answer to the nearest hundredth, we look at the digit in the third decimal place, which is 3. Since this digit is less than 5, we round down the second decimal place, giving us the final answer of:

Rounding to the nearest hundredth, we get the mean as 98.708

Therefore, the mean of the given data set is 98.70

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Rita's estimate of $50 is a good estimate, but it's not precise. If she works 10 hours a week and makes $9 an hour, her total will be $90. Half of 90 is 45. This means her spending money each week is $45.

The angles A and C are complementary angles.

In this problem we find six possible angles, from which we must determine two angles that are complementary angles. Two angles are complementary when the total measure is equal to 90°. The algebraic formula representing the situation is shown below:

α + β = 90°

Where α, β are angles.

If we know that α = 61° and β = 29°, then the result is:

m = α + β

m = 61° + 29°

m = 90°

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Answer:

A and C

Step-by-step explanation:

a complementary angle is when 2 angles add up to 90 degrees

As for A and C, A’s degree is 29 when C’s 61

29+61 is 90

You are approximately 161.5566 feet away from the base of the tree.

To determine the distance from the base of the tree, we can use trigonometry and the concept of tangent.

Let's denote the distance from the base of the tree as "x."

We have a right triangle formed by the tree, the distance from the base, and the angle of elevation. The opposite side of the triangle is the height of the tree, which is 280 feet, and the adjacent side is the distance from the base, denoted as "x."

Using the tangent function, we have:

tan(60°) = opposite/adjacent

tan(60°) = 280/x

To solve for x, we can rearrange the equation:

x = 280 / tan(60°)

Using a calculator, we can evaluate the expression:

x ≈ 280 / 1.7321 ≈ 161.5566

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Answer: 8

Step-by-step explanation:

Substitute a-b for the equations given:

8x+4 - (8x-4) = 8x+4-8x+4 = 8

The time Joshua plays the video game is the independent variable. Option B

In scientific research, an independent variable is a variable that is manipulated or controlled by the experimenter. It is also known as the predictor variable because it is used to predict changes in the dependent variable.

In the given scenario, the level of the game passed by Joshua is dependent on the time he spends playing the game. The more time he spends playing the game, the more levels he is likely to pass.

Therefore, the time spent playing the game is the independent variable as it is being manipulated and is expected to cause a change in the dependent variable.

The other options such as the number of levels the game has or the points scored by Joshua are not being manipulated in the scenario and do not have a direct effect on the number of levels passed.

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Por lo tanto, si Julia compra la lavadora haciendo uso de los descuentos, pagaría 950.4 soles por todo.

Si la lavadora cuesta 1200 soles y se ofrece un descuento del 10% por campaña, entonces el precio de la lavadora después del primer descuento sería:

Precio después del primer descuento = 1200 - (10% * 1200) = 1200 - 120 = 1080 soles

Luego, si se ofrece un descuento adicional del 12% por el día de la madre, entonces el precio de la lavadora después de ambos descuentos sería:

Precio después de ambos descuentos = 1080 - (12% * 1080) = 1080 - 129.6 = 950.4 soles

Por lo tanto, si Julia compra la lavadora haciendo uso de los descuentos, pagaría 950.4 soles por todo.

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The number of marginal means would be 24.

In a design that has 3 levels of factor A, 4 levels of factor B, and 2 levels of factor C, the total number of marginal means is 24.

Marginal means are the means for each factor level averaged across the other factors in the design. To calculate the number of marginal means, you simply multiply the number of levels for each factor together.

For example, in this design, there are 3 levels of factor A, 4 levels of factor B, and 2 levels of factor C, so there are 3 x 4 x 2 = 24 marginal means.

Each marginal mean represents the mean score for a particular combination of factor levels, averaged across the other factors in the design.

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The total distance the mouse scurries is 10 meters

To determine the value, we need to note that the Pythagorean theorem states that the square of the longest side of a triangle called the hypotenuse is equal to the sum of the squares of the other two sides.

This is represented as;

x² = y² + z²

Such that the parameters are;

From the information given, we have that;

x² = 2.2² + 3.6²

find the squares

x² = 4. 84 + 12. 96

add the values

x² = 17. 8

x= 4. 22 meters

The total distance = 2.2 + 3.6 + 4.2

Add the values

= 10 meters

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Each jar contains 8 ounces of tomato sauce. The total amount of tomato sauce used by Chef for the pasta dish is 32 ounces.

The total amount of tomato sauce used by Chef for the pasta dish is 32 ounces. Chef then divides the remaining 48 ounces of tomato sauce into six jars, resulting in 8 ounces of sauce in each jar.

To calculate the amount of tomato sauce used by Chef for the pasta dish, we first need to find 2/5 of 80 ounces, which is (2/5) x 80 = 32 ounces. Therefore, Chef uses 32 ounces of tomato sauce for the pasta dish.

After using 32 ounces of tomato sauce for the pasta dish, Chef is left with 80 - 32 = 48 ounces of tomato sauce. To divide this into six jars, we simply divide 48 by 6, which gives us 8 ounces of tomato sauce in each jar.

Therefore, each jar contains 8 ounces of tomato sauce.

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The value of c when  b = 11 and m = 196 is 954.8.

We have,

c varies jointly as b and the square root of m.

So, c = kbm

Now, put c= 168, b=10 and m= 36

168 = k (10)(36)

168 = k (360)

k = 168/360

k = 21 /45

k = 7/15

Now, we get the equation

c = 7/15 mb

Again, put b = 11 and m =196

c = 7/15 x 11 x 186

c = 14332/15

c= 954.8

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If the area of a rectangle is[tex]16\frac{1}{3}[/tex], the width is [tex]4\frac{2}{3}[/tex] in then length of rectangle is 49/14 inches.

Area of rectangle is length time width

Area = Length ×width

[tex]16\frac{1}{3}[/tex]=Length × [tex]4\frac{2}{3}[/tex]

Convert mixed fractions to improper

49/3 = Length × 14/3

Divide both sides by 14/3

length=49/3×3/14

Length=49/14

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Answer: 5/8

Step-by-step explanation:

The zeros of function f(x) are 8 and 6.

We have,

To find the zeros of the polynomial function f(x),

We need to solve for x in the equation f(x) = 0.

So,

f(x) = x² - 16x + 48

Setting f(x) = 0, we have:

x² - 16x + 48 = 0

We can factor this quadratic equation as:

(x - 8)(x - 6) = 0

Using the zero product property, we have:

x - 8 = 0 or x - 6 = 0

Solving for x.

x = 8 or x = 6

Therefore,

The zeros of function f(x) are 8 and 6.

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The hypotheses that the office manager should test to establish that the new electronic reporting system decreases the time employees spend filling out travel forms are:

Null hypothesis: The average time employees spend filling out travel forms with the new electronic reporting system is equal to or greater than 20 minutes (no significant difference).

Alternative hypothesis: The average time employees spend filling out travel forms with the new electronic reporting system is less than 20 minutes (a significant decrease).

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65% of female humpback whales are shorter than 14.1565 meters.

Given that, a normal distribution with a mean of 13.7 meters and a standard deviation of 0.5 meters.

We know that, Z=(x-μ)/σ

Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample

The z-score for the 65th percentile is 0.8416

Here, where x = the 65th percentile, μ = the mean value, and σ = the standard deviation.

So, we can rearrange the formula as follows:

x = z × σ + μ

Substituting the values:

x = 0.8413 × 0.5 + 13.7

x = 14.1565 meters

Therefore, 65% of female humpback whales are shorter than 14.1565 meters.

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Answer:

(x-2)( x+2 )

Step-by-step explanation:

Answer:

(x+2)(x-2)

Step-by-step explanation:

x²-4
we going to rewrite 4 as in power so x²-2²
then we going to apply the difference of two squares formula since we have the same format which is x²-y²=(x+y)(x-y) , so x²-2² = (x+2)(x-2)
and that's the answer.

The time Jenna spent driving the rest of her road trip was 2/3 hours.

Let the time Jenna spent driving at 50 mph be t1 and the time spent driving at 40 mph be t2. Also, let the distance covered while it was not raining be d.

We know that t1 + t2 = total time, and d + 2t2 + 2t1 = 140 miles.

Since we know that Jenna drove 50 mph while it was not raining, we can find the distance she covered during that time as d = 50t1.

Similarly, we know that Jenna drove 40 mph while it was raining, so the distance covered during that time can be found as 80t2, since Jenna's speed relative to the road was only 10 mph (50 mph - 40 mph).

Substituting the above values in the second equation, we get:

50t1 + 80t2 = 60

Dividing by 10, we get:

5t1 + 8t2 = 6

Multiplying the above equation by 2, we get:

10t1 + 16t2 = 12

Now, substituting t1 + t2 = total time = 140/50 + t2, we get:

10t1 + 16t2 = 14

Subtracting the above equation from the previous one, we get:

6t2 = 2

Therefore, t2 = 1/3 hours.

Thus, the time Jenna spent driving at 50 mph was t1 = 1.4 - 2t2 = 1.4 - 2/3 = 2/3 hours.

So, the time Jenna spent driving the rest of her road trip was 2/3 hours.

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If a and b are positive integers and a | b, then a is less than or equal to b.

The notation a | b means that a is a divisor of b, or in other words, b is a multiple of a. Since a is a positive integer and a is a factor of b, it follows that a must be less than or equal to b. This is because b is composed of a and some multiple of a, and so it must be greater than or equal to a.

For example, if a = 3 and b = 15, we know that 3 | 15 since 15 is a multiple of 3. In this case, a is equal to 3 and b is equal to 15, and we can see that a is less than b.

This property is important in number theory and is often used in proofs involving divisibility and prime numbers.

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In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable(b).

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable. ANOVA is used to determine if there is a significant difference between the means of two or more groups, and the factor is the variable being studied that is believed to have an effect on the outcome. Variance is a measure of the variability or spread of the data, and ANOVA compares the variance between groups to the variance within groups to determine if there is a significant difference. The different levels of a treatment are also referred to as levels of the factor.

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The x coordinate for the patch (and any other patch) on the left face of an object is the smallest x value within the object's domain, as it corresponds to the position of the left face in relation to the coordinate system. All patches on the left face share this same x coordinate value, regardless of their location on the face.

To answer this question about the x coordinate for the patch on the left face, let's break it down:
1. Identify the left face: First, we need to recognize which face of the object is the left face. This is typically the side that faces left when looking at the object in its standard orientation.

2. Find the x coordinate: Since the left face of an object is perpendicular to the x-axis, the x coordinate for any point (or patch) on that face will be the same. This means that all patches on the left face share the same x coordinate value.
3. Determine the specific x coordinate value: To find the actual value of the x coordinate, examine the object's dimensions and/or coordinate system. The x coordinate for the left face will be the smallest x value within the object's domain.

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The transitivity of divisibility theorem says that for all integers a, b, and c, if a divides b and b divides c, then a divides c. In other words, if a is a factor of b and b is a factor of c, then a is also a factor of c.

This theorem can be written as follows: If a | b and b | c, then a | c. For example, if a = 2, b = 6, and c = 12, we know that 2 | 6 and 6 | 12, so by the transitivity of divisibility theorem, we can conclude that 2 | 12.

The transitivity of divisibility is an important property of integers and is often used in number theory and other mathematical areas. It allows us to make inferences about the factors of numbers and the properties of divisibility, and is a useful tool in proofs involving divisibility and prime numbers.

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Answer:

The quotient of a rational number by an irrational number is generally irrational.

The statement "for all x, if x is an apple then x is red or green" can be summarized as "apples are red or green." This means that every apple is either red or green in color.

This can be interpreted as asking for a statement that includes the terms "for all x", "x is red or green", and "apples are red or green". The statement can be phrased as follows:
For all x, if x is an apple, then x is red or green. This can be summarized as "apples are red or green."
Here's a step-by-step explanation:
1. "For all x" means that the statement applies to every element x in a given set or context.
2. "If x is an apple" is the condition that needs to be satisfied for the next part of the statement to be applicable.
3. "Then x is red or green" describes the property that x has if the condition in step 2 is met.
4. Summarizing the entire statement, we can say that "apples are red or green," which implies that if something is an apple, it must be either red or green.

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Answer:

864

Step-by-step explanation:

12x12=144

144x6 because of all the sides

The probability that a student scored is 0.8.

To find the probability that a student scored less than 600 or took less than 4 years of math.

We need to add the probabilities of each of these events occurring separately, and then subtract the probability of both events occurring together.

Let P(L) be the probability that a student scored less than 600 and P(M) be the probability that a student took less than 4 years of math.

We are not given the joint probability of both events, so we need to calculate it using the formula:

P(L and M) = P(L) + P(M) - P(L or M)

where P(L or M) is the probability that a student scored less than 600 or took less than 4 years of math.

Assuming that the events of scoring less than 600 and taking less than 4 years of math are independent, we can calculate their probabilities separately:

P(L) = 0.35 (given)

P(M) = 0.25 (given)

To calculate P(L or M), we add the probability of scoring less than 600 to the probability of taking less than 4 years of math, and then subtract the probability of both events occurring together:

P(L or M) = P(L) + P(M) - P(L and M)

We don't have the value of P(L and M), so we cannot directly calculate P(L or M). However, we know that the sum of probabilities of all possible events is equal to 1.

Therefore, we can use the formula:

P(not L and not M) = 1 - P(L or M)

where P(not L and not M) is the probability that a student scored 600 or more and took 4 or more years of math.

Since we know that the events of not scoring less than 600 and taking 4 or more years of math are complementary to scoring less than 600 or taking less than 4 years of math.

We can use the complement rule to calculate P(not L and not M):

P(not L and not M) = 1 - P(L or M)

= 1 - (P(L) + P(M) - P(L and M))

= 1 - (0.35 + 0.25 - P(L and M))

= 0.4 - P(L and M)

Now we need to find P(L and M) to calculate P(not L and not M). We are not given this probability directly, so we cannot use the product rule.

However, we know that the number of students who scored less than 600 and took less than 4 years of math is 80, and the total number of students is 400. Therefore, we can use the formula:

P(L and M) = number of students who scored less than 600 and took less than 4 years of math / total number of students

= 80 / 400

= 0.2

Substituting this value in the formula for P(not L and not M), we get:

P(not L and not M) = 0.4 - P(L and M)

= 0.4 - 0.2

= 0.2

Therefore, the probability that a student scored less than 600 or took less than 4 years of math is:

P(L or M) = 1 - P(not L and not M)

= 1 - 0.2

= 0.8

So the probability that a student scored less than 600 or took less than 4 years of math is 0.8.

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If a sample of parts is measured and the mean of the measurements is outside the control limits, the process is considered to be out of control.

This means that there may be an issue with the process that is causing the measurements to vary significantly from the expected range, and corrective action may be necessary to bring the process back into control.

It is important to investigate the cause of the out-of-control condition and make any necessary adjustments to ensure that the process is producing parts that meet the desired specifications.

If a sample of parts is measured and the mean of the measurements is outside the control limits, it indicates that the process is out of control.

The control limits are the boundaries that are established based on the process's historical data to determine whether the process is in control or out of control.

When a process is in control, its output is predictable and stable within the control limits. However, when the process is out of control, its output is unpredictable and varies beyond the control limits, indicating that there is a problem with the process.

In such a situation, the next step is to identify the source of the problem and take corrective action to bring the process back into control.

This could involve identifying and correcting any issues with the equipment, materials, or methods used in the process.

Additionally, it may involve retraining or revising the procedures followed by the personnel involved in the process.

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Amount stolen in England (in US dollars) = 4 million * $1.26 = $5,040,000

We need to add the total stolen in Claire's cases to find the thief's total haul. However, the information about Claire's cases and the total stolen in those cases is not provided. Therefore, we cannot determine the thief's total haul.

To calculate the total amount of goods stolen in France and England in US dollars, we need to convert the amounts in Euro (€) and Pounds Sterling (£) to US dollars using the given exchange rates.

Given:

France: 2.5 million Euro (€), 1 € = $1.13

England: 4 million Pounds Sterling (£), 1 £ = $1.26

To find the total amount stolen in US dollars, we'll perform the following calculations:

Amount stolen in France (in US dollars) = 2.5 million € * $1.13/€

Amount stolen in England (in US dollars) = 4 million £ * $1.26/£

Let's calculate each value:

Amount stolen in France (in US dollars) = 2.5 million * $1.13 = $2,825,000

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