10. Trevor rode his mountain bike 84 km in
3 h. Jillian rode 70 km in 2.5 h. Who is
the faster cyclist? How do you
know?

The focus (-8, -3) and the directrix y = -9, the standard form parabola The equation for is:

y = (1/24)\(x ^2\) + (2/3)x - 10/3

To find the parabola equation taking into account the focus and directrix, you can use the standard form of the parabola equation.

4p(y - k) = \((x - h)^2\)

Where (h,k) represents the vertices of the parabola and 'p' is the distance from the apex to the focal point and the distance from the apex to the directrix represents

From the information given, we know that the focus is at (-8, -3) and the guideline is the horizon y = -9.

Since the guideline is a horizontal line, the parabola opens up and down.

Let's start by finding the vertex of the parabola.

Since the vertex is halfway between the focal point and the guideline, the vertex's x-coordinate is -8, which is the same as the focal point's x-coordinate.

To find the y-coordinate of the vertex, average the y-coordinates of the focus (-3) and directrix (-9):

(-3 + (-9)) / 2 = -12 / 2 = -6

So the vertex of the parabola is (-8, -6).

Next we need to find the value of 'p' which is the distance between the vertex and the focal point or guideline.

In this case, we can find 'p' by measuring the perpendicular distance from the vertex to the directrix.

The guideline is a straight line y = -9, so the distance between the vertices (-8, -6) and the guideline is 6 units.

Now that we have vertices (-8, -6) and a "p" value of 6, we can plug these values ​​into the standard geometry equation.

4p(y - k) = \((x - h)^2\)

4(6)(y - (-6)) = \((x - (-8))^2\)

24(y + 6) = \((x + 8)^2\)

Expanding further, simplification:

24y + 144 = \(x^2\) + 16x + 64

24y = \(x^2\) + 16x - 80

Divide the whole equation by 24:

y = (1/24)x2 + (2 /3 )x - 10/3

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Answer:

\(y = \frac{2}{3}x+14\)

Step-by-step explanation:

i hope this helps :)

The value of the function f(1)-f(-7) = -11

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Given are a function,

For x = 1, take -x²-3x

f(1) = -1²-3 = -4

For x = -7, take |x+5|-9

f(-7) = |-7+5|-9 = -7

f(1)-f(-7) = -7-4 = -11

Hence, The value of the function f(1)-f(-7) = -11

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Proving\(f^-1(f(x)) = x and f(f-1(x)) = x\) for any bijective function f is easy. By ensuring the existence of a unique x in A, we can apply f-1 to both sides of the equation, resulting in f(f-1(x)) = x for all x in B.

Proving that \(f^-1(f(x)) = x, f(f^-1(x)) = x\) Given a function f: A -> B with its inverse f-1, we can prove that f-1(f(x)) = x and f(f-1(x)) = x in the following way: Proving f-1(f(x)) = x

If f is a bijective function, then we can guarantee that the inverse function f-1 exists and is also bijective. Hence, for any y in B, there is a unique x in A such that f(x) = y.

Therefore, if we apply the inverse function f-1 to both sides of this equation, we obtain:f-1(f(x)) = f-1(y)But since f(f-1(y)) = y, we can replace y by f(x) in the above equation to get:f-1(f(x)) = f-1(f(f-1(y))) = f-1(y) = x

we have shown that f-1(f(x)) = x for all x in A.Proving f(f-1(x)) = xIf f is a bijective function, then we know that there exists a unique x in A such that f(x) = y for any y in B. Therefore, if we apply f-1 to both sides of this equation, we obtain:f-1(f(x)) = f-1(y) = xHence, we have shown that f(f-1(x)) = x for all x in B. This is because f-1(x) is in A by definition of the inverse function f-1, so f(f-1(x)) is well-defined. Therefore, we can conclude that f-1(f(x)) = x and f(f-1(x)) = x for any bijective function f.

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To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

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Answer:

1. 9-2=7

2. -6-(-4)=-2

Step-by-step explanation:

a=9

b=2

c=-6

d=-4

Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The data points are within the Control limits, indicating that the candy production process is operating consistently and without any significant issues that would require intervention or adjustment.

The process is in control or out of control, we can utilize control charts and statistical methods. In this case, we will use a control chart called the X-Bar chart, which is used to monitor the process mean over time.

1. Calculate the control limits:

  - First, we need to calculate the upper control limit (UCL) and lower control limit (LCL) for the X-Bar chart. The formula for the control limits is:

    UCL = mean + (3 * standard deviation)

    LCL = mean - (3 * standard deviation)

    Given:

    Mean = 16.8 grams

    Standard deviation = 0.7 grams

    UCL = 16.8 + (3 * 0.7) = 18.9 grams

    LCL = 16.8 - (3 * 0.7) = 14.7 grams

2. Plot the data points:

  - Plot the readings on the X-Bar chart using the given data points: 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 18.4.

3. Analyze the chart:

  - Examine the plotted data points to see if they fall within the control limits. If a data point falls outside the control limits, it suggests that the process may be out of control.

  In this case, we observe that all the data points fall within the control limits of 14.7 grams (LCL) and 18.9 grams (UCL). None of the points exceed these limits.

4. Conclusion:

  - Since all the data points fall within the control limits, we can conclude that the process is in control. There is no evidence of any special causes of variation present in the data.

the data points are within the control limits, indicating that the candy production process is operating consistently and without any significant issues that would require intervention or adjustment.

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The probability of rolling an even number first and an odd number second when six sided two cubes rolled is one fourth.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

As the probability of an event can not be more than the number 1.

Given information-

The total possible outcomes of the cubes is 36.

Total desired outcomes is 9.

When the six sided two cubes rolled, the number of pairs an even number first and an odd number second can appear are,

(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), and (6, 5).

Thus the total number of desired pair is 9.

As the total number of outcomes when  six sided two cubes rolled is 36 and the total number of desired outcomes is 9.

Thus the probability of getting these 9 results from total 36 outcomes is,

\(P=\dfrac{9}{36}\\P=\dfrac{1}{4}\)

Thus, the probability of rolling an even number first and an odd number second when six sided two cubes rolled is one fourth.

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Answer:

1/4

Step-by-step explanation:

Answer:

15

Step-by-step explanation: divide 10 by 6 the multiply the quotient by 9

Answer:

15

Step-by-step explanation:

6\2=3. 3x3=9 10/2=5 5x3=15

Answer:

Step-by-step explanation:

x = 174 + 180 - x

2x = 354

x = 177

180 - x  =  3

Answer:

The supplementary angle of an angle is the angle that, when added to the original angle, gives 180 degrees. So, if an angle measures 174 degrees more than the measure of its supplementary angle, then the two angles will add up to 354 degrees. This means that the measure of the original angle is 177 degrees, and the measure of the supplementary angle is 177 degrees.

Here is the solution in equation form:

Let x be the measure of the angle.

x = 180 - x + 174

2x = 354

x = 177

Therefore, the measure of the angle is 177 degrees, and the measure of the supplementary angle is 177 degrees.

Answer:

m = -2

Step-by-step explanation:

Look at the attached image. First, we divide both sides by 7 to get m + 5 = 3. Now, we subtract 5 from both sides to get m = -2. Now, we substitute m for -2. As we can see, it checks out.

The solution of expression is,

m = - 2

We have to give that,

An expression to solve,

7 (m + 5) = 21

Now, simplify the expression as,

7 (m + 5) = 21

Divide both sides by 7,

m + 5 = 21 / 7

m + 5 = 3

Subtract 5 both side,

m = 3 - 5

m = - 2

So, The solution is, m = - 2

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============================================================

Explanation:

The radius of the larger circle is CB = CA+AB = 8+3 = 11 inches.

The area of the larger circle with this radius is...

A = pi*r^2

A = pi*11^2

A = 121pi

The area of the smaller circle (radius CA = 8 inches) is

A = pi*r^2

A = pi*8^2

A = 64pi

The difference is 121pi-64pi = 57pi

This represents the exact area of the full ring. Refer to figure 1 below. Specifically the red region of that figure.

However, we don't want the full ring. We only want a small fraction of it (as figure 2 shows, which is the original diagram your teacher gave you). Specifically, we want (4*30)/360 = 120/360 = 1/3 of the full ring. The 4*30 refers to the idea we have four copies of the 30 degree angle.

So we'll take 1/3 of the 57pi to get (1/3)*57pi = (57/3)pi = 19pi

-----------------------------------

The value 19pi is the exact area of the entire shaded region.

From here, you can use a calculator to determine that

19pi = 19*3.1415926535898 = 59.6902604182061 which rounds to 59.7

If your teacher insists you use pi = 3.14, then 19*pi = 19*3.14 = 59.66 which also rounds to 59.7

Note that the depreciation for this vehicle using method 2 will be $340.

To calculate the depreciation using method 2, we need to multiply the cost of the car by the depreciation rate per mile, which is given in cents per mile.

First, we need to calculate the total depreciation for the car in cents by multiplying the miles driven by the depreciation rate per mile:

Total depreciation = Miles driven x Depreciation rate per mile

Total depreciation = 10,000 x 3.4 cents per mile

Total depreciation = 34,000 cents

Next, we need to convert the total depreciation from cents to dollars by dividing it by 100:

Total depreciation = 34,000 cents ÷ 100 cents/dollar

Total depreciation = $340

Therefore, the depreciation for this vehicle using method 2 will be $340.

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According to the information, the mean is 9.33, the median is 9 and the standard deviation is is 3.99

To find the mean, we add up all the ages and divide by the total number of students; To find the median, we first need to order the ages from lowest to highest, and To find the standard deviation, we first need to find the variance, which is the average of the squared deviations from the mean as it's shown in the following:

Mean = (16 + 14 + 16 + 9 + 8 + 9 + 14 + 11 + 12 + 5 + 5 + 8 + 12 + 11 + 7 + 8 + 6 + 5 + 8 + 8 + 4) / 21 = 9.33

Median:

4, 5, 5, 5, 6, 7, 8, 8, 8, 8, 9, 9, 11, 11, 12, 12, 14, 14, 16, 16, 16

Median = (9 + 9) / 2 = 9

Standard deviation:

Variance = [(16-9.33)^2 + (14-9.33)^2 + ... + (4-9.33)^2] / 21 = 15.95

Standard deviation = sqrt(15.95) = 3.99

On the other hand, the distribution is relatively spread out, as indicated by the moderate standard deviation.

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Answer:

112 weeks

Step-by-step explanation:

784/7=112

Answer:

112 weeks............

The probability of event A given that event B has occurred is equal to the probability of event A, which is 0.7.

If A and B are independent events, then the occurrence of event B does not affect the probability of event A. Therefore, we can use the formula for conditional probability, P(A|B) = P(A ∩ B) / P(B), to calculate the probability of event A given that event B has occurred.

However, since A and B are independent, we know that P(A ∩ B) = P(A) x P(B), which gives us:

P(A | B) = P(A ∩ B) / P(B) = (P(A) x P(B)) / P(B) = P(A) = 0.7

This makes sense because the independence of A and B implies that knowing the outcome of event B does not provide any additional information about the probability of event A.

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Answer:

might be a diff answer

Step-by-step explanation:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Answer:

3/2

Step-by-step explanation:

y=kx

use a point

3=k2

k=3/2

Answer:

El sistema de ecuaciones para calcular la cantidad de niños y adultos que acudieron a la función es:

x+y=270

175x+200y=88,250

Step-by-step explanation:

La información proporcionada indica que a la función entran 470 asistentes entre adultos y niños y con esta información puedes decir que la suma de niños y adultos que entran a la función es igual a 470:

x+y=270, donde

x es el número de niños

y es el número de adultos

Además, se indica que se recaudaron $88,250 y tienes los precios de cada entrada por lo que puedes expresar que la suma de los resultados de multiplicar cada precio por la cantidad de personas que entraron por ese precio es igual a $88,250:

175x+200y=88,250

De acuerdo a esto, la respuesta es que el sistema de ecuaciones para calcular la cantidad de niños y adultos que acudieron a la función es:

x+y=270

175x+200y=88,250

Answer:

477 ft

Step-by-step explanation:

1 yard = 3 feet

159 x 3 = 477

A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

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The optimal first guess for the simplified Mastermind game with three positions and three colors of pegs is "ABC" (where A, B, and C represent the three different colors).

In the simplified Mastermind game, each position can be filled with any of the three available colors. Therefore, there are a total of 3^3 = 27 possible secret codes.

To find the optimal first guess, we need to choose a guess that maximizes the number of possible secret codes it eliminates. The guess "ABC" covers all the available colors and positions, ensuring that no matter the secret code, it will match at least one peg.

By selecting "ABC" as the first guess, we eliminate a maximum number of secret codes. For any possible score, there will always be at most 18 remaining possible secret codes (since we eliminate 9 possibilities). This is the highest elimination rate among all possible first guesses.

Hence, "ABC" is the optimal first guess in the simplified Mastermind game, as it maximizes the elimination of possible secret codes and provides the best starting point for subsequent guesses.

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The amount of shovels that can be produced in h hours is 960 shovels

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

In the given equation,

The number of shovels produced are

C(x)=26*20+400

=520+400

=920 shovels

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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Answer: Third option

Answer:

x#2 and x-2 is the same

Step-by-step explanation:

Answer:

Its 8

Step-by-step explanation:

This is the highest peak