Each lap around the track is 400 meters. How many meters does someone run if they run 5 laps?

Answer:

150.72

Step-by-step explanation:

C = 2*pi * r

C = 2* 3.14 * 6

C = 37.68

1 revolution = 37.68

4 revolutions = 4 * 37.68

4 revolutions = 150.72

Answer:

3/2 I'm not sure I think it's that

Answer:

more info?

Step-by-step explanation:

Answer:

$2050

Step-by-step explanation:

750+950+350

Answer:

81 Pesos

Step-by-step explanation:

Use a proportion.

$3 is to 2 Pesos as $121.10 is to x Pesos.

3/2 = 121.1/x

3x = 2 * 121.1

3x = 242.20

x = 80.7333...

Answer: 81 Pesos

Answer:  261,608in²

Step-by-step explanation:

A = bh

A = (1,234)(212)

A= 261,608in²

Answer:

8 shirts

Step-by-step explanation:

Answer:

2 14/15

Step-by-step explanation:

44/15= 2.9333333333333

2.9333333333333= 2 14/15

We need to prove that the sequence of functions fn(x) = (1/2)cos^2(√nx) converges uniformly to 0 on the real numbers.

To prove uniform convergence, we need to show that for any ε > 0, there exists a positive integer N such that |fn(x) - 0| < ε for all n > N and for all x in the real numbers.

Given fn(x) = (1/2)cos^2(√nx), we observe that as n increases, the argument √nx inside the cosine function becomes larger, causing the cosine to oscillate more rapidly between 0 and 1. Since we are multiplying the cosine by (1/2) and taking its square, fn(x) gradually approaches 0 as n increases.

To formally prove uniform convergence, we can start by fixing ε > 0 and then choose N such that √Nx > 1/ε. By selecting this N, we can show that for all n > N, |fn(x) - 0| < ε for any x in the real numbers. This demonstrates that the sequence of functions fn(x) converges uniformly to 0 on the real numbers.

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Answer: 360

Step-by-step explanation: Sum of exterior angles of any convex polygon is always 360, think about it.

To analyze the motor fuel octane ratings data, we can start by constructing a frequency distribution and then use it to create a histogram.

The frequency distribution will provide information about the distribution of the data across different octane rating ranges, while the histogram visually represents the distribution graphically.

a. To construct a frequency distribution, we divide the data into bins and count the frequency of values falling within each bin. In this case, we will use 8 bins. We determine the lower and upper limits for each bin and calculate the midpoint by averaging the limits. Then, we count the number of values within each bin and calculate the relative frequency by dividing the frequency by the total number of values.

b. Once the frequency distribution is constructed, we can use it to create a histogram. The histogram represents the frequency or relative frequency of values within each bin as vertical bars. The bins are plotted along the x-axis, and the height of the bars represents the frequency or relative frequency on the y-axis. The histogram allows us to visualize the distribution pattern of the motor fuel octane ratings data, showing if it is skewed, symmetric, or has other characteristics.

By constructing a frequency distribution and creating a histogram, we can gain insights into the distribution of the motor fuel octane ratings data. The frequency distribution table provides a summarized view of how the data is spread across different octane rating ranges, while the histogram visually represents the same information in a graphical form. Both the frequency distribution and the histogram aid in understanding the distribution pattern, identifying potential outliers or gaps, and informing further analysis or decision-making related to the data.

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Answer:

29 minutes

Step-by-step explanation:

Let

x = number of minutes

y = the height of the airplane above sea level in feet

y = 32,000 - 1000x

y = 3,000

Therefore,

y = 32,000 - 1000x

3,000 = 32,000 - 1000x

3,000 - 32,000 = -1000x

-29,000 = -1,000x

x = -29,000 / -1,000

x = 29 minutes

it will take 29 minutes for the airplane to land at an airport 3000 feet above sea level

Answer:

c = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

c² = 7² + 3² = 49 + 9 = 58 ( take the square root of both sides )

c = [tex]\sqrt{58}[/tex]

Answer:

Step-by-step explanation:

According to Pythagoras Theorem:

[tex] {7}^{2} + {3}^{2} = {c}^{2} [/tex]

Hence,

[tex] = > {c}^{2} = {7}^{2} + {3}^{2} [/tex]

[tex] = > {c}^{2} = 49 + 9[/tex]

[tex] = > {c}^{2} = 58[/tex]

[tex] = > c = \sqrt{58} [/tex]

So,

[tex]c = \sqrt{58} [/tex]

Is the answer.

Answer:

36

Step-by-step explanation:

3*12=36

Answer:

Ellipse. It is irregular at some points.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The first term of the arithmetic sequence is 16 and the 22nd term is 148.

To solve for the first term, we can use the following formula:

a_n = a_1 + d(n-1)

where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence

d is the common difference of the sequence

We know that the 4th term is 16 and the 37th term is 115. We can use these values to solve for d.

d = a_{37} - a_4 = 115 - 16 = 99

Now that we know d, we can solve for a_1 using the value of the 4th term.

a_1 = a_4 - d = 16 - 99 = -83

Finally, we can solve for the 22nd term using the value of a_1 and d.

a_{22} = a_1 + d(22-1) = -83 + 99(21) = 148

Therefore, the first term of the arithmetic sequence is 16 and the 22nd term is 148.

Here is a more detailed explanation of the solution:

The first step is to identify the common difference of the sequence. This can be done by subtracting any two consecutive terms in the sequence. In this case, the 4th term is 16 and the 37th term is 115. Subtracting these two terms, we get 115 - 16 = 99. This is the common difference of the sequence.

Once we know the common difference, we can solve for the first term by using any of the terms in the sequence. In this case, we will use the 4th term. The formula for the nth term of an arithmetic sequence is a_n = a_1 + d(n-1), where a_n is the nth term, a_1 is the first term, and d is the common difference. Substituting the 4th term, the common difference, and n = 4, we get a_4 = a_1 + d(4-1). Simplifying this equation, we get 16 = a_1 + 99. Solving for a_1, we get a_1 = -83.

Finally, we can solve for the 22nd term by using the first term and the common difference. The formula for the nth term of an arithmetic sequence is a_n = a_1 + d(n-1). Substituting the first term, the common difference, and n = 22, we get a_{22} = -83 + 99(22-1). Simplifying this equation, we get a_{22} = 148.

Therefore, the first term of the arithmetic sequence is 16 and the 22nd term is 148.

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It should be noted that Yes, there is evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers.

The sample data shows that 54.6% of urban dwellers (325/598) agree with the statement, while only 40.1% of rural dwellers (54/137) agree. This difference is statistically significant at the p < 0.05 level (two-tailed).

The test statistic is 2.83. The p-value for this test statistic is 0.0047. Since this p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers.

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The sample mean of the given data series is 33.7 and the population mean is 35.86. The difference between the two quantities, rounded to two decimal places, is -2.16.

Sample mean and population mean are important terms in statistics. The sample mean is the average of a set of data taken from a larger population, while the population mean is the average of an entire population.

To find the sample mean of the given data series, we add up all the values and divide by the total number of values. Therefore,

Sample mean = (15+26+25+23+26+28+20+20+31+45+32+41+54+23+45+24+90+19+16+75+29) / 21
Sample mean = 33.7

To find the population mean, we use the same formula but with all the values of the population included. Therefore,

Population mean = (15+26+25+23+26+28+20+20+31+45+32+41+54+23+45+24+90+19+100+75+29) / 21
Population mean = 35.86

Finally, to find the difference between the two quantities, we subtract the sample mean from the population mean. Therefore,

Difference = Population mean - Sample mean
Difference = 35.86 - 33.7
Difference = -2.16 (rounded to two decimal places)

Therefore, the difference between the sample mean and population mean is -2.16.

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Answer:

A box has 6 pencils. Each pencil weighs x grams. The 6 pencils weigh a combined total of 54 grams.

Step-by-step explanation:

Answer:

20,19,18

Step-by-step explanation:

because you have to go backwards

Answer:

26

Step-by-step explanation:

The integral that represents the length of the curve from the point (-3,6) to the point (2,36) is L = ∫[-3 to 2] √101 dx.

To find the length of the curve defined by the equation y = 47° + 10x from the point (-3,6) to the point (2,36), we can use the arc length formula for a curve:

L = ∫[a to b] √(1 + (dy/dx)^2) dx

First, let's find dy/dx by taking the derivative of the given equation:

dy/dx = d/dx(47° + 10x) = 10

Now we can substitute this value into the arc length formula:

L = ∫[-3 to 2] √(1 + (10)^2) dx

Simplifying:

L = ∫[-3 to 2] √(1 + 100) dx

L = ∫[-3 to 2] √101 dx

Thus, the integral that represents the length of the curve from the point (-3,6) to the point (2,36) is:

L = ∫[-3 to 2] √101 dx

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The resultant of the recurrence relation bn = 4bn-1-4bn-2 with initial values bo = 1 and b₁ = 2 is bn = (1 + (n/2)) 2ⁿ.

The given recurrence relation is

bn = 4bn-1 - 4bn-2 with initial values bo = 1 and b₁ = 2. Now, we have to find the solution to the recurrence relation. It can be observed that the given recurrence relation is a second-order recurrence relation. The characteristic equation of the recurrence relation is given by:

r² = 4r - 4, which can be simplified as r² - 4r + 4 = 0. We need to solve this equation. It can be solved as r = 2

The characteristic equation of the given recurrence relation has two equal roots r1 = r2 = 2. Therefore, the general result of the recurrence relation is given by:

bn = (A + Bn) 2ⁿ

For the given initial values b₀ = 1, and b₁ = 2 we can write:

b₀ = (A + B(0)) 2⁰ =&gt; A = 1b₁ = (A + B(1)) 2¹ =&gt; A + 2B = 2

On solving these equations, we get A = 1 and B = 1/2

The resultant to the recurrence relation is:

bn = (1 + (n/2)) 2ⁿ

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The continuity property of H is that it is:

c. right-continuous

Continuity property: A function is continuous if it has no jumps, i.e., the graph can be drawn without lifting the pencil from the paper. For any random variable X, the function H is right-continuous.

This is due to the fact that the limit of H(x) as x approaches any value from the right side is equivalent to H(x) as x approaches that value from the right side, so H is continuous from the right side.

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