The weights of Gala apples are normally distributed with a mean of 208 grams and a standard deviation of 30 grams.

A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.

Theoretical probability is based on what is expected to happen, or a theory, using reasoning. It is based on knowledge and mathematics. An experiment is not conducted to find theoretical probability.

The formula to calculate the theoretical probability of event A happening is:

P(A) = number of desired outcomes / total number of possible outcomes

For example, the theoretical probability that a dice lands on “2” after one roll can be calculated as:

P(land on 2) = (only one way the dice can land on 2) / (six possible sides the dice can land on) = 1/6

Thus, A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.

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Answer:

-16t^2 - 16t + 180 = 0

4t^2 + 4t - 45 = 0

t = (-4 + √(4^2 - 4(4)(-45))/(2×4)

= (-4 + √736)/8 = (-4 + 4√46)/8

= (-1 + √46)/2 = 2.89 seconds

The  "finite population correction factor" or the "finite population correction" (FPC) is used to adjust the standard error of a sample statistic when the sample size is relatively large compared to the population size.

The statement is referring to the "finite population correction factor" or the "finite population correction" (FPC) which is used to adjust the standard error of a sample statistic when the sample size is relatively large compared to the population size.

Therefore, the blank should be filled with:

Finite Population Correction Factor

The finite population correction factor states that if calculations are very cumbersome and if the sample size is no more than 5% of the size of the population, treat the selections as being independent by adjusting the standard error of the sample statistic using the formula (N-n)/(N-1), where N is the population size and n is the sample size. The FPC corrects for the fact that the sampling is done without replacement, and it can improve the accuracy of the statistical inference.

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There were 3,000 leopards in the wild in 1996. There are now only 70. There is decrease of 97.67 % in leopards.

We have been giving the leopards in 1996 as 3,000 and leopards today as 70.

Difference between the leopards = 3,000 - 70 = 2,930.

Percent decrease = difference in leopards / leopards in 1996 × 100

= 2930 / 3,000 × 100

= 97.67%.

The percentage drop formula is used to determine how much a variable's value has decreased. The variable can be population, cost, profit, or something else. Percent reduction denotes the percentage change in a value when it is decreased over time.

For example, a decrease in rainfall, a decrease in the number of Covid patients, and so on. The percent decrease formula can be used to determine percent decrease.

Simply divide the decreased number by the original value and multiply by 100 to get the percentage decrease calculation.

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The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

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

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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The competing hypotheses to determine whether the population mean is less than 150 are:

Null hypothesis (H0): The population mean is equal to 150.

Alternative hypothesis (Ha): The population mean is less than 150.

The null hypothesis assumes that there is no significant difference between the sample mean and the population mean. The alternative hypothesis assumes that there is a significant difference between the sample mean and the population mean, and that this difference is less than 150.

The purpose of these competing hypotheses is to allow for statistical testing to determine whether the sample data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The goal is to determine whether the sample mean is significantly lower than the population mean, and if so, whether this difference is large enough to be considered meaningful.

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The street dance group performed a total of 4.5 hours for 8 days during the summer.

From the given image, on the first two days which are Day-1 and Day-2 they performed for 1/4 hour which is  0.25 hours on each day. The next 3 days which are day-3, day-4, and day-5 they performed for 2/4 hour which is 0.5 hour on each day. For the next 2 days which is day-6 and day-7, they performed for 3/4 hours which is 0.75 hours for each day. On the final day which is day-8, they performed for 1 hour.

To find mathematically, the total hours they performed in 8 days is

Total hours = (2 x 0.25) + (3 x 0.5) + (2 x 0.75) + 1 (1)

                   = 0.5 + 1.5 + 1.5 + 1

                   = 4.5 hours

From the above analysis, we can conclude that the dance group performed for a total of 4.5 hours for 8 days.  

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Answer: 9.9

Step-by-step explanation: Diagonal is the side times the square root of 2.

The real-life story that models the system of equations is shown below

From the question, we have the following system of equations that can be used in our computation:

y = 1/2x + 4

y = -2x + 14

There are several real life stories we can use

One of them is as follows

Ridwan has $4 in his savings account and saves 50 cents every week. Lanre has $14 in his savings accounts and withdraws $2 every week.

Calculate the number of weeks where both would have the same amount in their accounts

The graph of the scenario is attached and the solution is (4, 6)

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The implementation of the `power` method that is called in a Java code snippet depends on the object being referred to when the method is called. In the given code snippet, the implementation of the `power` method called is provided by the `NaturalNumber2Override` class.

Based on the given code snippet, the implementation of the `power` method that will be called is the one provided by the `NaturalNumber2Override` class.

This is because the `j` variable is declared as type `NaturalNumber`, but it actually refers to an instance of the `NaturalNumber2Override` class. When a method is called on an object, Java looks for the implementation of that method in the class of the object being referred to, and if it's not found, in the parent classes or interfaces. In this case, the `NaturalNumber2Override` class overrides the `power` method of its parent class `NaturalNumber2`, so its implementation of the `power` method will be called.

Therefore, the answer is (c) NaturalNumber2Override.

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If  n(E1 and E2) = 3 and n(E1) = 12, then  P(E2|E1) = 1/4. To find the probability P(E2|E1), given that n(E1 and E2) = 3 and n(E1) = 12, we'll use the conditional probability formula. The formula is P(E2|E1) = P(E1 and E2) / P(E1).

Step 1: Find the probabilities of the events.
P(E1) = n(E1) / total outcomes = 12 / total outcomes
P(E1 and E2) = n(E1 and E2) / total outcomes = 3 / total outcomes
Step 2: Plug the probabilities into the conditional probability formula.
P(E2|E1) = P(E1 and E2) / P(E1)

Step 3: Substitute the values from Step 1 into the formula.
P(E2|E1) = (3 / total outcomes) / (12 / total outcomes)
Step 4: Simplify the expression.
P(E2|E1) = 3/12
Step 5: Reduce the fraction to the simplest form.
P(E2|E1) = 1/4
So, the probability of event E2 occurring given that event E1 has occurred is 1/4 or 0.25.

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Answer:

It is not possible to conclude whether the population mean differs from the sample mean without additional information such as a confidence interval or hypothesis test. While the sample mean and standard deviation provide information about the central tendency and variability of the sample, it cannot be assumed to accurately reflect the population parameters. Since the population is not approximately normal, it is important to use appropriate methods for inference such as non-parametric tests or the Central Limit Theorem for large sample sizes.

Answer:(7x + 2)(x + 4)

Step-by-step explanation:

The correct option will be B 3x²+4x-6.

The given polynomial is 3x³-11x²-26x+30.

We need to divide it from x-5,

So,

Factoring the polynomial,

3x³-11x²-26x+30 = 3x²(x-5)+4x(x-5)+6(x-5)

= 3x²+4x-6(x-5)

Now dividing,

3x²+4x-6(x-5)  / (x-5) = 3x²+4x-6

Hence, the correct option will be B 3x²+4x-6.

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The z-value of -2.88 would support the alternative hypothesis that the population mean is less than 0 (μ < 0).

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Answer: the total number of possible outcomes.

Step-by-step explanation:

Jen's gross pay can be found to be $ 560

Jen's net weekly pay would be $ 492. 30

Jen's net monthly pay would be $ 1, 969. 20.

The gross pay for the week for Jen would be :

= Number of hours of work x Number of days per week x Payment per hour

= 7 x 5 x 16

= $ 560

The net weekly pay is:

= 560 - Income tax - EI - CPP - Payroll savings

= 560 - 23.50 - 5. 87 - 8. 33 - 30

= $ 492. 30

The monthly net pay would then be :

= 492. 30 x 4

= $ 1, 969. 20

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The radius of a circle is 13.33 centimeters and the area of a circle is 557.94 square centimeters.

Given that, the circumference of the hub cap of a tire is 83.71 centimeters.

We know that, the circumference of a circle is 2πr.

Here, 2πr=83.71

2×3.14×r=83.71

r=83.71/6.28

r=13.33

As we know, the area of a circle = πr²

Here, area = 3.14×13.33²

= 557.94 square centimeters

Therefore, the radius of a circle is 13.33 centimeters and the area of a circle is 557.94 square centimeters.

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The patient needs to swallow 0.35 teaspoons of the drug to receive the correct dose.

To determine the number of teaspoons of the drug the patient needs to swallow, we can set up a proportion based on the drug's strength.

Let x represent the number of teaspoons the patient needs to swallow.

We can set up the proportion as follows:

100 mg / 1 teaspoon = 35 mg / x teaspoons

To solve for x, we can cross-multiply and then divide:

100 mg * x teaspoons = 35 mg * 1 teaspoon

100x = 35

x = 35 / 100

x = 0.35

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Answer:

Postive, The coefficient of determination is a measure of how well the regression line fits the data points. It represents the proportion of variation in the dependent variable that can be explained by the independent variable. The coefficient of determination ranges from 0 to 1, with higher values indicating a stronger relationship between the variables. Importantly, it cannot be negative.

The coefficient of determination is equal to the square of the coefficient of correlation, which measures the strength and direction of the linear relationship between two variables. However, unlike the coefficient of determination, the coefficient of correlation can be negative or positive. A negative value indicates an inverse relationship between the variables, while a positive value indicates a direct relationship.

The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data. It represents the proportion of variation in the dependent variable that can be explained by the independent variable(s). R-squared ranges from 0 to 1, with higher values indicating a better fit. It cannot be negative, as it is a squared value. The square root of the coefficient of correlation is equal to the coefficient of determination. The coefficient of correlation can be negative or positive, indicating the direction of the relationship between the variables.

The length of line segment KJ is equal to 24 units.

In this problem we find the representation of a geometric system consisting in three circles and a right triangle. A circumference is described by the following equation:

s = 2π · r

Where:

The sum of the three circumferences is introduced below:

56π = 2π · (7 · x)

56π = 14π · x

x = 4

And the length of line segment KJ is now computed:

KJ = 6 · x

KJ = 6 · 4

KJ = 24

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Answer:

width = 16 in.; length = 20 in.

Step-by-step explanation:

The formula for perimeter, P, of a rectangle is

P = 2l + 2w, where l is the length and w is the width.

Since we're told that the length is 4 in. longer than the width, we know that

l = w + 4

We can substitute w +4 for l in the perimeter equation and plug in 72 for P.  This will allow us to first find the width:

72 = 2(w + 4) + 2w

72 = 2w + 8 + 2w

72 = 4w + 8

64 = 4w

16 in. = w

The width is 16 and since 4 more than 16 is 20, the length is 20 inches.

Now, we can check if when we plug in 72 for P, 16 for w, and 20 for l, we get 72:

72 = 2(16) + 2(20)

72 = 32 + 40

72 = 72

Therefore, our answers are correct

Answer: a/b

Step-by-step explanation:

There isn't really an explanation for this but

a ration number has to be able to be written as a fraction

for example, the number 6 is rational

we can prove this because 6 can be written as 6/1.

The pitcher contains 20 cups of water, not 10 cups as Josy mistakenly claimed.

A quart contains 4 cups of water. Therefore, a pitcher containing 5 quarts of water will have 5 x 4 = 20 cups of water.

Josy's statement that the pitcher contains 10 cups of water is incorrect. The pitcher contains 20 cups of water, as we just determined.

To verify this, we can use the conversion factor between quarts and cups. 1 quart equals 4 cups. Thus, to find the number of cups in 5 quarts of water, we multiply 5 by 4, which gives us 20 cups. Therefore, the correct number of cups the pitcher contains is 20 cups, not 10 cups as Josy had stated.

It is important to understand the relationship between different units of measurement when working with quantities such as volume or weight. In this case, knowing that 1 quart is equivalent to 4 cups allowed us to make the conversion easily and determine the correct number of cups in the pitcher.

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Answer: If Miss Reed combines one fluid ounce of oil with three fluid ounces of vinegar, she gets a total of four fluid ounces of salad dressing. Therefore, the ratio of oil to total dressing is 1:4, and the ratio of vinegar to total dressing is 3:4.

If Miss Reed wants to make a larger amount of salad dressing using the same ratio of oil to vinegar, she can simply scale up the quantities while maintaining the same ratio. For example, if she wants to make 12 fluid ounces of salad dressing, she would need:

She can combine these quantities to get a total of 12 fluid ounces of salad dressing, with the same oil-to-vinegar ratio as before.

The length of the rectangular prism is 7800 times the edge length of a cube, which is 7800 × (1/5) cm = 1560 cm.

To find the length of the rectangular prism, we need to consider the relationship between the number of cubes, the volume of the prism, and the dimensions of the prism.

The volume of a rectangular prism is given by the formula V = l × w × h, where l represents the length, w represents the width, and h represents the height.

In this case, we are given that the prism consists of 312 cubes, and each cube has an edge length of 1/5 cm. Since each cube has the same edge length, we can say that the width, height, and length of the prism are all multiples of 1/5 cm.

Let's assume the length of the rectangular prism is x times the edge length of a cube (1/5 cm). Therefore, the length of the prism is (1/5) × x cm.

The number of cubes (312) is equal to the volume of the prism. The volume of the prism can be calculated by multiplying the dimensions:

312 = (1/5) × x × (1/5) × (1/5)

Simplifying the expression:

312 = (1/25) × x

To solve for x, we multiply both sides of the equation by 25:

312 × 25 = x

x = 7800

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The statement that is not true of the transformation shown is A. The image is in Quadrant II.

The two figures are congruent because they can be shown to have the same shape and angles as well as orientation. The pre - image of FGH was also translated to be able to create the image of  F'G'H'.

We can also see that the orientation of the vertices did not change as the triangle still looks the same. However, one thing we can notice is that the image of F'G'H' is not located in Quadrant II but rather in Quadrant IV.

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The central limit theorem states that if we draw a simple random sample (SRS) from any population, regardless of the shape of the population distribution.

The sampling distribution of the sample mean will be approximately normal if the sample size is large enough. This means that the mean of the sampling distribution will be the same as the mean of the population, and the standard deviation of the sampling distribution will be the standard error of the mean, which is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, the central limit theorem allows us to make inferences about the population mean based on the sample mean, as long as we have a large enough sample size.
According to the Central Limit Theorem, if we draw a Simple Random Sample (SRS) from any population, the sampling distribution of the sample mean will APPROXIMATELY be normal, not exactly normal. This approximation improves as the sample size increases, especially when the sample size is large (usually n ≥ 30). The Central Limit Theorem allows us to make inferences about the population based on the sampling distribution.

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