7 x B is less than 14, but greater than 7

Nora could run 7.5 minutes per mile to qualify for the state cross-country championships. The correct answer is option c.

To qualify for the state cross-country championships, Nora needs to run 4 miles in 30 minutes or less. So, her average rate should be:

average rate = total time / total distance

If she runs at the slowest rate possible to still qualify, then her average rate would be:

average rate = 30 / 4 = 7.5 minutes per mile

Therefore, the correct option is c) 7.5.

If she runs slower than this average rate, then her total time would exceed 30 minutes and she would not qualify.

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Answer:

1

Step-by-step explanation:

To find the distance between two points u going to use the equation √x2-x1)²+(y2-y1)² so √(2-1)²+(-4(-4))² =1

The factor that would have to be corrected is: The second arc should be centered at C.

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A correlation coefficient is a statistical measure that shows the degree of association between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation (as one variable increases, the other decreases), 0 indicates no correlation, and 1 indicates a perfect positive correlation (as one variable increases, the other also increases).

When plotted on a scatter plot, the correlation coefficient can help you determine the strength and direction of the relationship between the variables. If the coefficient is close to -1 or 1, the points on the scatter plot will be more tightly clustered around the line of best fit, indicating a stronger relationship between the variables. On the other hand, if the coefficient is closer to 0, the points will be more spread out, indicating a weaker relationship.

The line of best fit, also known as the regression line, is the line that best approximates the relationship between the variables based on the data points on the scatter plot. It is calculated using a mathematical formula that takes into account the values of both variables. The correlation coefficient can be used to help determine the slope and intercept of the line of best fit, which can be useful for making predictions about future data points. Overall, the correlation coefficient provides valuable information about the strength and direction of the relationship between two variables, which can help inform further analysis and decision making.

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In 11 hour 484 Keychains can be assembled.

We have,

A Machine assembles 44 keychains per hour.

So, In 11 hour number of Keychains can be assembled.

= 44 x 11

= 484 Keychains

Thus, In 11 hour 484 Keychains can be assembled.

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Answer:

hyp = 83.9 ~ 84

Step-by-step explanation:

our given is a triangle and those are side so their squere is equal to the squere of hypothenus .

(82in) ^2 + (18in)^2 = (hyp)^2

6724 + 324 = (hyp)^2

7048 = (hyp)^2

hyp = √7048

hyp = 83.9 ~ 84 so the hypothenus is 83.9 approximate to 84

Suppose in a population of adults there are 10% that are avid fly fishermen/women. If we were to choose a random sample of 10 adults from this population the Law of Large Numbers (LLN) says that as the sample size increases, the sample mean will approach the true population mean.

In this case, if we choose a random sample of 10 adults from the population of adults where 10% are avid fly fishermen/women, the LLN implies that the proportion of the sample who are avid fly fishermen/women will tend to approach 10%.

However, it's important to note that the LLN is a probabilistic statement about the behavior of sample means, so it does not guarantee that the sample proportion will be exactly 10%.

There is still a possibility that the sample proportion will differ from 10%, but the larger the sample size, the smaller this difference is likely to be.

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The area of the jogging path is 4L + 4W + 16 square meters.

To find the area of the jogging path in the park, we need to know the dimensions of the rectangle. Let's assume that the length of the rectangle is L and the width is W. Then, the new dimensions of the rectangle, including the jogging path, would be (L+4) and (W+4), since the jogging path is 2 meters wide on both sides of the rectangle.

Therefore, the area of the jogging path would be the difference between the area of the larger rectangle and the area of the original rectangle. The area of the larger rectangle is:

(L+4) × (W+4)

And the area of the original rectangle is:

L × W

So the area of the jogging path would be:

(L+4) × (W+4) - L × W

We can simplify this expression to get:

LW + 4L + 4W + 16 - LW = 4L + 4W + 16

Therefore, the area of the jogging path is 4L + 4W + 16 square meters.

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The experimental probability that a randomly selected student plans to take band is 3/8, or 0.375 as a decimal.

We are aware that 12 of the 32 students surveyed intended to enroll in band. As a result, the following is the experimental probability that a student selected at random will choose to study band:

P(band) = total number of students polled / number of students who intend to take band

P(band) = 12/32

Simplifying the fraction, we get:

P(band) = 3/8

Therefore, the experimental probability that a randomly selected student plans to take band is 3/8, or 0.375 as a decimal.

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Answer:

3/8

Step-by-step explanation:

The ratio is given as 9 / 26

Total number of miles in the race: 26 miles

Number of miles you've run so far: 17 miles

Miles left to run = Total miles in the race - Miles you've run so far

Miles left to run = 26 miles - 17 miles

Miles left to run = 9 miles

Now, to find the ratio of the number of miles you have left to the total number of miles in the race:

Ratio = Miles left to run : Total miles in the race

Ratio = 9 miles : 26 miles

So the ratio is 9:26.

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Answer:

[tex]x(7-4x)[/tex]

Step-by-step explanation:

You can factor the expression [tex]7x - 4x^2[/tex] by factoring out an x value.

You will get:

[tex]x(7-4x)[/tex].

There is nothing else you can factor out of the equation.

The correct answers are:
a. The MPS equals 0.20 (not 1.20).
b. The multiplier equals 5.

If the Marginal Propensity to Consume (MPC) equals 0.80, then we can determine the Marginal Propensity to Save (MPS) and the multiplier using the following steps:
Calculate the MPS:

MPS = 1 - MPC
Calculate the multiplier: Multiplier = 1 / (1 - MPC)
Now, let's apply these steps using the given MPC of 0.80:
Calculate the MPS: MPS = 1 - 0.80 = 0.20
Calculate the multiplier: Multiplier = 1 / (1 - 0.80) = 1 / 0.20 = 5.

If the MPC (Marginal Propensity to Consume) equals 0.80, then the correct answer is (b) the multiplier equals 5.

The multiplier (k) is a measure of the change in equilibrium income resulting from a change in autonomous expenditure. It is calculated as the reciprocal of the MPS (Marginal Propensity to Save) or the inverse of one minus the MPC.

The formula for the multiplier is:

k = 1 / (1 - MPC) = 1 / MPS

Given that the MPC equals 0.80, the MPS is:

MPS = 1 - MPC = 1 - 0.80 = 0.20

Therefore, the multiplier is:

k = 1 / MPS = 1 / 0.20 = 5

This means that a change in autonomous expenditure (such as government spending, investment, or exports) will result in a five times greater change in equilibrium income.

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A chance that the sample mean income level falls between $49,000 and $51,000 is 39.38%.

Based on the given information, we know that the population mean (average income) in New York City is $50,000 and the population standard deviation is $10,000.

If we randomly sample 625 people and ask them what their income level is, we can use the central limit theorem to approximate the distribution of sample means.

The central limit theorem states that for a large enough sample size (in this case, n = 625), the distribution of sample means will be approximately normal, regardless of the distribution of the population.

To calculate the mean and standard deviation of the sample means, we can use the following formulas:

Mean of sample means = population mean = $50,000
Standard deviation of sample means = population standard deviation / square root of sample size
= $10,000 / sqrt(625)
= $10,000 / 25
= $400

Therefore, the mean income level of the 625 people in the sample is expected to be $50,000, and the standard deviation of the sample means is $400.

Using this information, we can also calculate the probability of certain income levels in the sample. For example, we can calculate the probability that the sample mean income level is between $49,000 and $51,000:

Z-score for lower limit = (49,000 - 50,000) / 400 = -0.25
Z-score for upper limit = (51,000 - 50,000) / 400 = 0.25

Using a standard normal distribution table or calculator, we can find the probability of a Z-score between -0.25 and 0.25 to be approximately 0.3938.

Therefore, there is a 39.38% chance that the sample mean income level falls between $49,000 and $51,000.

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The area of the 1/4 inch diameter circle, expressed to the nearest thousandth square inch, is 0.049 square inches.

The formula to find the area of a circle is A = π[tex]r^2[/tex].

Where,

r is the radius of the circle.

Since the diameter of the circle is given as 1/4 inch, the radius is 1/8 inch (radius = diameter/2).
Substituting the value of r in the formula, we get A = π(1/8) = π/64 square inches.
Now, to express the answer to the nearest thousandth square inch, we need to calculate the value of π/64 and round it to the nearest thousandth. Using a calculator, we get π/64 = 0.04908738521...
The area of a circle with a 1/4 inch diameter, we'll use the formula A = π[tex]r^2[/tex], where A is the area, and r is the radius.

First, we need to find the radius.

Since the diameter is 1/4 inch, the radius (r) is half of that: 1/8 inch.

Now, we'll calculate the area: A = π[tex]\frac {1}{8} ^{2}[/tex] = π(1/64) ≈ 0.0123 square inches. So, the area of the circle is approximately 0.0123 square inches to the nearest thousandth.
Rounding this value to the nearest thousandth gives us 0.049 square inches.

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The Surface area of the hemisphere is 628 cm².

A hemisphere is half of a sphere.

To calculate the surface area of the hemisphere, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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T-tests, F test for homogeneity of variance, and ANOVAs are all examples of parametric, inferential statistics.

So, the correct answer is C.

Parametric statistics assumes that the data being analyzed follows a normal distribution and that the samples being compared have equal variances.

T-tests are used to compare means between two groups, while ANOVAs are used to compare means across three or more groups.

The F test for homogeneity of variance is used to test if the variances between two or more groups are equal.

These tests are inferential statistics because they allow researchers to make inferences about a larger population based on a sample of data.

Hence, the answer of the question is C.

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The standard equation of parabola that has focus (5, 0) and directrix x = -5 is y² = 20x.

We have,

focus of the parabola is (5, 0).

Directrix x = -5

The standard equation of parabola,

(y - k)² = 4 p (x  - h)

where Vertex = (h, k)

So, (h, k)

= ((x coordinate of focus + directrix)/2 , 0)

= ((5 - 5)/2, 0)

= (0, 0)

and, p = distance from focus to the vertex = 5 - 0 = 5

Thus, The required equation of parabola,

(y - 0)² = 4 × 5(x - 0)

y² = 20x

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The speed difference between two satellites are 3400 mph.

From graph,

the speed from the slope of the graph

speed = (70000- 36000)/ (10-5)

speed = (34000)/ 5

speed = 6, 800.

and, From table the speed is

speed = (40800 - 23800)/ (12-7)

speed = 17000/5

speed= 3400

So, Speed difference = 6800 - 3400 = 3400 miles per hour

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The measurement of the indicated length is 36.

The measurement of the indicated length is calculated by applying proportion or fraction method on the entire length of the tape.

The length of the entire tape = 60

There are total  of 5 divisions on the entire length.

The length of each division is calculated as follows;

= total length / number of divisions

= 60 / 5

= 12

The indicated dimension = 3 x 12 = 36

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Answer:

Kylie drove at a speed of 60 miles per hour going to the soccer game.

Step-by-step explanation:

Let us assume that Kylie drove at speed x miles per hour going to the soccer game. On the way back, she had to drive at a speed of (x-10) miles per hour. We are given that the trip took 1 hour longer on the way back, which means that the time taken on the way back was greater than the time taken going to the soccer game. We can form an equation using the distance formula:

300/x = 300/(x-10) + 1

Simplifying this equation by cross multiplication, we get:

300(x-10) = 300x + x(x-10)

Simplifying further, we get:

300x - 3000 = 300x - 10x

Solving for x, we get:

x = 60

Therefore, Kylie drove at a speed of 60 miles per hour going to the soccer game.

An important theorem in probability that states as the number of trials increase, the empirical probability approaches the theoretical probability is called the Law of Large Numbers.

This theorem is a fundamental concept in probability theory and has significant applications in many areas, including statistics, finance, and science.

The Law of Large Numbers provides a formal proof that the average of a large number of independent and identically distributed random variables tends to converge to the expected value of the random variables.

As the sample size increases, the sample mean approaches the population mean, and the sample variance approaches the population variance. This theorem is crucial in many statistical analyses and is used to draw reliable conclusions from large datasets.

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The given statement "The median and the average of any list are always close together" is False because the median and the average of a list are not always close together. In fact, the difference between the two can vary greatly depending on the shape of the distribution.

For example, in a skewed distribution with a long tail to one side, the mean can be pulled in the direction of the tail and can be quite far away from the median. On the other hand, in a symmetrical distribution such as a normal distribution, the mean and the median are equal and are located at the center of the distribution.

Therefore, it is important to consider both the mean and the median when analyzing a dataset, as they can provide different insights into the characteristics of the distribution.

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To generate the most original solution to the problem of adding a new building on an already crowded college campus, Lonnie can employ various techniques and strategies that are often used in the field of architecture and design.

Lonnie could take:

Research and Analysis:

Before developing a design solution, Lonnie can research and analyze the existing campus architecture and the surrounding environment.

By understanding the context, Lonnie can identify potential constraints, opportunities, and design challenges, which can inform his design decisions.

Creative Brainstorming:

Lonnie can brainstorm and generate a wide range of design ideas, without censoring or judging them.

This can be done individually or in a group, using various brainstorming techniques such as mind mapping, word association, or random stimulus.

Sketching and Modeling:

Lonnie can explore and refine his design ideas by sketching and modeling them in two- or three-dimensions.

This can help him visualize the design in different scales and perspectives, and experiment with different materials, textures, and colors.

Prototyping and Testing:

Lonnie can create physical or digital prototypes of the design to test its feasibility, functionality, and aesthetic qualities.

This can involve building mock-ups, conducting simulations, or using virtual reality tools.

Cross-Disciplinary Collaboration:

Lonnie can collaborate with experts from different fields, such as engineering, sustainability, psychology, or sociology, to incorporate their knowledge and perspectives into the design process.

This can help Lonnie generate innovative and holistic solutions that address multiple needs and values.

Lonnie can generate original and effective design solutions that meet the needs and aspirations of the campus community.

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The probability that the proportion of flops in a sample of 681 released films would be greater than 8% is ≈ 0.0043 (rounded to four decimal places) or 0.43%.

We shall calculate the probability using the normal approximation to the binomial distribution, since we have a large sample size (n = 681) and the probability of a flop (p = 0.06) is not too close to 0 or 1.

The mean of the binomial distribution = μ = np = 681 x 0.06 = 40.86,

The standard deviation = σ = [tex]\sqrt(np(1-p))[/tex] = [tex]\sqrt(681 * 0.06 * 0.94)[/tex] = 5.08.

We want to find the probability that the proportion of flops in a sample of 681 released films would be greater than 8%, which is equivalent to finding the probability that the sample proportion of flops (p-hat) is greater than 0.08.

To standardize the sample proportion, we can use the formula:

z = (p-hat - p) / [tex]\sqrt(p(1-p)/n)[/tex]

where:

p-hat = sample proportion,

p = the population proportion,

n = the sample size.

Plugging in the values, we get:

z = (0.08 - 0.06) / [tex]\sqrt(0.06 * 0.94 / 681)[/tex] = 2.62

Using a standard normal table or calculator, we can find that the probability of getting a z-score of 2.62 or greater is 0.0043.

Therefore, the probability that the proportion of flops in a sample of 681 released films would be greater than 8% is ≈ 0.0043 or 0.43% (rounded to four decimal places).

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We can express 5.8057 as a ratio of integers, we have shown that it is a rational number.

To show that 5.8057 is a rational number, we need to express it as a ratio of integers in the form of p/q, where p and q are integers and q is not equal to zero.

We can start by writing 5.8057 in fraction form:

5.8057 = 58057/10000

Notice that both the numerator and the denominator are integers. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 58057 and 10000 is 1, so we cannot simplify the fraction any further. Therefore, we have:

5.8057 = 58057/10000

Since we can express 5.8057 as a ratio of integers, we have shown that it is a rational number.

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The size of B is 5×m.

If A is a 4×5 matrix and AB is a 4×3 matrix, then the number of columns of A must equal the number of rows of B.

Let's represent the size of B as m×n. Then we have:

A: 4×5

B: m×n

AB: 4×3

To multiply A and B, we need the number of columns of A to be equal to the number of rows of B. Therefore, we must have n = 5. This is because the number of columns of B must be equal to the number of rows of the product AB, which is 3.

So the size of B is 5×m.

To summarize:

A: 4×5

B: 5×m

AB: 4×3

Therefore, the size of B is 5×m.

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The required probability for the parts which are examined for defects are ;

1. Probability of both the parts are good is equal to 0.375.

2. Probability represents exactly one part has major defect is 0.2333.

Here, we have,

Total number of parts to be examined for defects = 16

Number of good parts = 10

Number of parts with minor defects = 4

Number of parts with major defects = 2

Number of parts to be chosen at random without replacement = 2

Total number of outcomes = ¹⁶C₂

                                            = (16!) / ( 16 - 2 )!2!

                                            = 120

1. Probability of both the parts to be good

Number of favourable outcomes = ¹⁰C₂

                                                       = 10! / (8!)(2!)

                                                       = 45

Required Probability = 45 / 120

                                  = 0.375

2. Probability of exactly one major defect

Number of favourable outcomes= ²C₁ × ¹⁴C₁

                                                     = 2 × 14

                                                     = 28

Required Probability = 28/ 120

                                  = 0.2333

Therefore, the probability of both are good is 0.375 and probability of exactly one major defect is 0.2333.

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The above question is incomplete, the complete question is:

'16 parts are examined for defects. It is found that 10 are good, 4 have minor defects, and 2 have major defects. Two parts are chosen at random from the 16 without replacement; that is; the first part chosen is not returned to the mix before the second part is chosen:

1. What is the probability that both parts are good?

2. What is the probability that exactly one part has major defect?'

The surface area of the rectangular prism is 213 square meters.

To calculate the surface area of a rectangular prism, we need to find the areas of all its faces and then sum them up.

A rectangular prism has six faces: top, bottom, front, back, left, and right.

The top and bottom faces are identical and have the same dimensions as the base of the prism. So, the area of each of these faces is 6 m * 3.5 m = 21 m².

The front and back faces have dimensions of 6 m (width) and 9 m (height). So, the area of each of these faces is 6 m * 9 m = 54 m².

The left and right faces have dimensions of 3.5 m (width) and 9 m (height). So, the area of each of these faces is 3.5 m * 9 m = 31.5 m².

To find the total surface area, we sum up the areas of all the faces:

Total Surface Area = 2 * (Area of top face) + 2 * (Area of front face) + 2 * (Area of left face)

Total Surface Area = 2 * 21 m² + 2 * 54 m² + 2 * 31.5 m²

Total Surface Area = 42 m² + 108 m² + 63 m²

Total Surface Area = 213 m²

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Note that where the  figure has rotational​ symmetry, tell the angle of rotation any angle can be the angle of ration. (Option B)

In geometry, rotational symmetry, also known as radial symmetry, is the quality that a form exhibits when it looks the same after a partial turn rotation.

The degree of rotational symmetry of an item is the number of possible orientations in which it appears precisely the same for each revolution.

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