An athlete runs around a circular track which has a diameter of 100 m how far does each lap around the track

Answer:

$7

Step-by-step explanation:

56/8 =7

I dont understand, sorry. I dont understand the diffrtence between the orders It makes no sense whatsoever

Answer:

C, B, A.

Step-by-step explanation:

The probability that the locker combination will consist if all even numbers is 14/323 or 0.043.

From combination formula, C(n, r) = n!/[r!(n - r)!]

Here range of locker combination numbers can be from 1 to 20.

That is the possible number of numbers = 20.

So, n = 20.

And the number of numbers in locker combination = 4.

Therefore, r = 4.

One number can not be repeated for twice.

So the number of locker combinations possible = C(20, 4)

Here from 1 to 20 the number of even numbers is 10.

So the number of lock combinations containing all even numbers = C(10, 4)

So the probability that the locker combination will consist if all even numbers = C(10, 4)/C(20, 4) = 14/323 or 0.043 [Rounding off to nearest thousandth]

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The simplification of the expression (4xy)(2x²y)(3xy)³ is 216x⁶y⁵.

The correct answer choice is option D

(4xy)(2x²y)(3xy)³

Raise the last monomial to the third power.

=(4xy)(2x²y)(3³x³y³)

=4xy(2x²y)(27x³y³).

Multiply the first two monomials; When we multiply powers with the same base, we add the exponents;

8x³y²(27x³y³)

We multiply these last two monomials, again adding the exponents;

216x⁶y⁵

In conclusion, (4xy)(2x²y)(3xy)³ is simplified as 216x⁶y⁵.

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Answer:

D

Step-by-step explanation:

took the test xx

Answer:

3/10

3/10 written as a decimal would be .30 which is greater then 0.25

we have f(20) - f(10) = 15,011 - y, the difference f(20) - f(10) represents the change in the number of stores between 20 and 10 years since 1987.

To find the change in the number of stores between 20 and 10 years since 1987, we need to calculate the difference in the values of the function f at these two time points.

Given that f(20) = 15,011, we don't have the exact value of f(10). However, we can still determine the change by subtracting f(10) from f(20).

Let's denote f(10) as y. Therefore, we have:

f(20) - f(10) = 15,011 - y

The difference f(20) - f(10) represents the change in the number of stores between 20 and 10 years since 1987. The value of this expression will give us the net increase or decrease in the number of stores during that time period.

Unfortunately, since we don't have the specific value of f(10) or any additional information about the function f,

we cannot determine the exact change in the number of stores between 20 and 10 years since 1987. We would need more information or a specific equation for the function f to calculate the precise change.

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Yes, they can use the walkie-talkies to talk to each other.

The distance between them is given as 28.2 meters.

The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.

This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.

Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.

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a. The standard equation of the ellipse with foci at (8, -1) and (-2, -1), and a length of the major axis of 12 units is: ((x - 5)² / 6²) + ((y + 1)² / b²) = 1.

b. The standard equation of the ellipse with vertices at (-5, 12) and (-5, 2), and a length of the minor axis of 8 units is: ((x + 5)² / a²) + ((y - 7)² / 4²) = 1.

c. The standard equation of the ellipse with a center at (-4, 1), a vertex at (-4, 10), and a focus at (-4, 9) is: ((x + 4)² / b²) + ((y - 1)² / 9²) = 1.

a. To determine the standard equation of the ellipse with foci at (8, -1) and (-2, -1), and a length of the major axis of 12 units, we can start by finding the distance between the foci, which is equal to the length of the major axis.

Distance between the foci = 12 units

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

√((x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, we can calculate the distance between the foci:

√((8 - (-2))² + (-1 - (-1))²) = √(10²) = 10 units

Since the distance between the foci is equal to the length of the major axis, we can conclude that the major axis of the ellipse lies along the x-axis.

The center of the ellipse is the midpoint between the foci, which is (5, -1).

The equation of an ellipse with a center at (h, k), a major axis of length 2a along the x-axis, and a minor axis of length 2b along the y-axis is:

((x - h)² / a²) + ((y - k)² / b²) = 1

In this case, the center is (5, -1) and the major axis is 12 units, so a = 12/2 = 6.

Therefore, the equation of the ellipse in standard form is:

((x - 5)² / 6²) + ((y + 1)² / b²) = 1

b. To determine the standard equation of the ellipse with vertices at (-5, 12) and (-5, 2), and a length of the minor axis of 8 units, we can start by finding the distance between the vertices, which is equal to the length of the minor axis.

Distance between the vertices = 8 units

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

√((x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, we can calculate the distance between the vertices:

√((-5 - (-5))² + (12 - 2)²) = √(0² + 10²) = 10 units

Since the distance between the vertices is equal to the length of the minor axis, we can conclude that the minor axis of the ellipse lies along the y-axis.

The center of the ellipse is the midpoint between the vertices, which is (-5, 7).

The equation of an ellipse with a center at (h, k), a major axis of length 2a along the x-axis, and a minor axis of length 2b along the y-axis is:

((x - h)² / a²) + ((y - k)² / b²) = 1

In this case, the center is (-5, 7) and the minor axis is 8 units, so b = 8/2 = 4.

Therefore, the equation of the ellipse in standard form is:

((x + 5)² / a²) + ((y - 7)² / 4²) = 1

c. To determine the standard equation of the ellipse with a center at (-4, 1), a vertex at (-4, 10), and a focus at (-4, 9), we can observe that the major axis of the ellipse is vertical, along the y-axis.

The distance between the center and the vertex gives us the value of a, which is the distance from the center to either focus.

a = 10 - 1 = 9 units

The distance between the center and the focus gives us the value of c, which is the distance from the center to either focus.

c = 9 - 1 = 8 units

The equation of an ellipse with a center at (h, k), a major axis of length 2a along the y-axis, and a distance c from the center to either focus is:

((x - h)² / b²) + ((y - k)² / a²) = 1

In this case, the center is (-4, 1), so h = -4 and k = 1.

Therefore, the equation of the ellipse in standard form is:

((x + 4)² / b²) + ((y - 1)² / 9²) = 1

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For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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Twice a number decreased by four is less than 8 is x< 6.

2x - 4 < 8

2x < 8 + 4

2x < 12

x < 12 / 2

x < 6

Inequality refers to the unequal distribution of resources, opportunities, and outcomes among individuals or groups in a society. It can manifest in various forms, including economic inequality, social inequality, gender inequality, and racial inequality. Economic inequality refers to the unequal distribution of wealth and income, where some individuals or groups have access to more resources and opportunities than others.

Social inequality refers to the unequal distribution of social status and power, which can lead to marginalized groups being excluded from certain societal benefits. Gender and racial inequality refer to the unequal treatment and opportunities that certain genders or races face in society. Inequality can have negative consequences on individuals and society, including lower levels of social trust, reduced economic growth, and increased social tensions.

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Complete Question: -

Twice a number decreased by four is less than 8 is equation or inequality

The area of the whole quilt, considering that the quilt is formed by squares, is given as follows:

595.35 in².

The area of a square of side length s is given by the square of the side length, as follows:

A = s².

Each patch has a side length of 3.5 inches, hence the area of each patch is given as follows:

A = 3.5²

A = 12.15 inches².

The quilt had a 7 × 7 array of different color square patches, hence the total number of patches is given as follows:

7 x 7 = 49 patches.

Then the total area of the whole quilt is given as follows:

49 x 12.15 = 595.35 in².

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Answer:

The area of the whole quilt, considering that the quilt is formed by squares, is given as follows:

595.35 in².

Step-by-step explanation:

How to obtain the area of a square?

The area of a square of side length s is given by the square of the side length, as follows:

A = s².

Each patch has a side length of 3.5 inches, hence the area of each patch is given as follows:

A = 3.5²

A = 12.15 inches².

The quilt had a 7 × 7 array of different color square patches, hence the total number of patches is given as follows:

7 x 7 = 49 patches.

Then the total area of the whole quilt is given as follows:

49 x 12.15 = 595.35 in².

A criteria for construction of triangle include the following: B. SAS.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

Generally speaking, the side, angle, side (SAS) criterion is essential for the construction of any triangle such as the following:

Based on the side, angle, side (SAS) criterion, a statement which is necessary to prove that two (2) triangles are congruent is that one of its side must be equal to another side because their angles are equal in measure or magnitude.

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Answer

6 inches

Step-by-step explanation:

Answer:

X=2.87

Step-by-step explanation:

Sin x= Opposite/hypotenuse

Sin35=x/5

X=5sin35

X=AC=2.87

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

1. A

2. i think c not sure

Step-by-step explanation:

Answer:

12/8 and then you just make it an mixed number! Tell me if u need help with the mixed number part!

Answer:

0.09375 as decimal or 3/32

Step-by-step explanation:

multiply both numerator and denominator, make sure they both get multiplied.

The coefficients obtained by the student may be less efficient and have larger standard errors compared to the professor's regression.

If the student enters each observation twice, resulting in a sample size of 100 instead of the original 50, the assumption of independent observations is violated in Ordinary Least Squares (OLS) regression. The OLS assumption assumes that the observations are independent, meaning that the value of one observation does not depend on the value of another observation.

In this case, the student's dataset contains repeated observations, which introduces dependence between observations. This violation of the independence assumption can lead to biased and inconsistent parameter estimates in the regression analysis.

Regarding the slope coefficients, if the student runs a regression using the duplicated data, the estimated coefficients may be different from the professor's regression. The duplication of observations inflates the sample size, potentially affecting the precision and accuracy of the estimates.

However, the direction and overall relationship between the variables may still be captured by the student's regression, although the estimates may not be as reliable.

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Answer:

x=-2,x=1-\(\sqrt{3}\)i,x=1+\(\sqrt{3}\)i

Step-by-step explanation:

Let d represent Bill's riding distance.

Bill's effective rate when riding against the wind is 9 mph, so this is how long it will take him to travel d:

time against wind = d/9

Bill travels the same distance d in the following amount of time when riding against the wind since his effective pace is 15 mph:

wind time = d/15

The sum of these two times represents the entire amount of time Bill needs to complete his bicycle ride:

total = time with wind + time against wind

Total time = 9 + 15 days.

This phrase can be made simpler by locating a common denominator:

Total time equals (5 + 3 days) / 45.

time in total = (8d) / 45

Therefore, an equation representing the number of hours (h) it takes Bill to complete his bicycle ride is h = 8d/45.

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Answer:

A={5,1,-7}

Step-by-step explanation:

domain = x

choose domain {-2,0,4} to 2x+y=1

range = y

range is

2(-2)+y =1 ,y =5

2(0)+y=1, y= 1

2(4)+ y=1, y=-7

range = {5,1,-7}

a. Using intersection of events probability of FUA is 0.0165

b. Using complement rule, the probability of F'UA is 0.9835

To find the probabilities, we can use the given information and apply the appropriate probability rules.

(a) FUA represents the event that the driver is female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the formula: P(FUA) = P(F ∩ A), where ∩ denotes the intersection of events.

P(FUA) = P(F) * P(A|F)

Given information:

P(F) = 0.2868 (probability that the driver is female)

P(A) = 0.1828 (probability that the driver is 24 years old or less)

P(A|F) = 0.0576 (probability that the driver is 24 years old or less given that the driver is female)

P(FUA) = 0.2868 * 0.0576 ≈ 0.0165

Therefore, the probability of FUA is approximately 0.0165.

(b) F'UA represents the event that the driver is not female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the complement rule: P(F'UA) = 1 - P(FUA).

P(F'UA) = 1 - P(FUA) ≈ 1 - 0.0165 ≈ 0.9835

Therefore, the probability of F'UA is approximately 0.9835.

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Step-by-step explanation:

Area of circle = 2πr²

diameter = 14 cm

so,

after inserting values in the formula we got,

2 × 22/7 × 14

→ 2 × 22 × 2 = 44 × 2 = 88 cm²

hence, area of the circle is 88cm²

hope this answer helps you dear

Answer:

The answer is True, mitosis divides nuclei that produces another identical nuclei.

Answer:

the sum of all exterior angles equal 360

Step-by-step explanation:

Summed, the exterior angles equal 360 degrees. A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.

Answer:

16

Step-by-step explanation:

(2 means squared) (c is the hypotenuse)

a2+b2=c2

a2+ (12×12) = (20×20)

a2+144=400

a2=256

a=16

Upper Control Limit for R Chart: UCL = D4 * R-Bar , UCL = 2.114 * 1.000, UCL ≈ 2.115 cm. Therefore, the correct answer is 2.115 cm(d).

To calculate the upper control limit for the R Chart, we need to use the following formula:

Upper Control Limit (UCL) = D4 * R-Bar

Where:

- D4 is a constant value based on the sample size (n=5 in this case).

- R-Bar is the average range of the samples, which is given as 1.000 cm.

The value of D4 for a sample size of 5 is 2.114. (You can find this value in statistical reference tables.)

Now, we can calculate the UCL:

UCL = D4 * R-Bar

   = 2.114 * 1.000

   = 2.114 cm

Rounding to 3 decimal places, the upper control limit for the R Chart is 2.114 cm.

Therefore, the correct option is: d. 2.115 cm

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The complete question is :

Repeated sampling of a certain process shows the average of all sample ranges to be 1.000 cm. There are 12 random samples and the sample size has been 5. What is the upper control limit for R Chart? Must compute in 3 dec pl. Select one: O a. 2.745 cm O b. 3.005 cm O c. 1.725 cm d. 2.115 cm e. 2.000 cm