Answer fast in steps

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

6

Step-by-step explanation:

2 ÷ 1/3

= 2 x 3

= 6

Therefore, 2 divided by 1/3 equals 6.

Hoped this helped.

Answer:

6

Step-by-step explanation:

2          1

-      /    -

1          3

then you can use keep switch flip to make it

2/1 x 3/1

3x2 = 6

1,005.44

Pir^2h

3.142*8*8*5

1,005.44

The equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).

The definitiοn οf an equatiοn οf the line is a linear equatiοn with degree 1. X and Y are twο variables in the equatiοn fοr the line. The slοpe οf the line, which reflects the elevatiοn οf the line, is the third parameter.

The general fοrm οf the equatiοn οf the line:-

y = mx + c

m = slοpe

c = y-intercept

Given that Line, v has an equatiοn οf y=–109x–3. Perpendicular tο line v is line w, which passes thrοugh the pοint (2,3).

The slοpe οf the required line will be inverse and the οppοsite οf the given line,

m = 1/109

The intercept will be calculated as,

y = mx + b

3 = (1/109)2 + b

3 = 2/109 + b

327/109 = 2/109 + b

325/109 = b

The equatiοn οf the line is written as,

y = (1/109)x + (325/109)

Therefοre, the equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).

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The percentage of students with a GPA of at least 1.76 is 100% - 2.5% = 97.5%.

In a bell-shaped distribution, the empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

To find the percentage of students with a GPA of at least 1.76, we need to calculate the number of standard deviations between the mean (2.52) and 1.76.

(2.52 - 1.76) / 0.38 ≈ 2 standard deviations below the mean

Since 95% of the data falls within two standard deviations of the mean, and we're considering two standard deviations below the mean, the remaining 5% is split between the tails. Therefore, 2.5% of the students have a GPA below 1.76.

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The initial value is 4 and the rate of change is negative 3 over 4. Option B is the correct answer.

A relationship in which one input value exactly equals one output value is known as a function. A function's starting value is a crucial component. A starting value or starting point is exactly what it sounds like: It is an initial value.

A function's starting value in mathematics denotes the function's y-intercept.

The initial value of a function is the value when x = 0.

From the graph we observe that the initial value, that is the value of the graph at x = 0 is y = 4.

Hence, the initial value is 4.

The rate of change of graph is nothing but the slope of the graph.

The two coordinates on the graph are:

(0, 4) and (4, 1)

The slope is given as:

m = (y2 - y1)/ (x2 - x1)

m = (1 - 4) / (4 - 0)

m = -3/4

Hence, the initial value is 4 and the rate of change is negative 3 over 4. Option B is the correct answer.

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Answer:

$16.98 per gallon

Step-by-step explanation:

We can set up a equation using ratios:

\(\frac{67.92}{4}=\frac{x}{1}\)

Solve by cross multiplication (multiply the numerator of the first fraction by the denominator of the second fraction and the denominator of the first fraction by the numerator of the second fraction):

67.92=4x

Divide both sides by 4 to isolate x

$16.98

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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The slope and intercept of the equation 3x + 4y = 12 are -3/4 and 3

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

3x + 4y = 12

making y the subject of the equation, we have

4y = 12 -3x

y = 12/4 - 3x/4

y = 3 - 3x/4

comparing the equation with equation of a straight line

y = mx + c

m which is slope = -3/4

c which is y-intercept = 3

In conclusion the slope of the line is -3/4 and the y-intercept is 3

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Answer:

X = 11

Step-by-step explanation:

The area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

To find the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ), we need to determine the limits of integration for θ.

First, let's find the values of θ where the circle and the vertical line intersect:

r = 4cos(θ)

sec(θ) = 4cos(θ)

To simplify the equation, let's convert sec(θ) to its reciprocal form:

1/cos(θ) = 4cos(θ)

Multiplying both sides by cos(θ), we get:

1 = 4\(cos^2\)(θ)

Rearranging the equation, we have:

4\(cos^2\)(θ) - 1 = 0

Using the identity \(cos^2\)(θ) - \(sin^2\)(θ) = 1, we can rewrite the equation as:

\(cos^2\)(θ) - \(sin^2\)(θ) = 1/4

Applying the double-angle formula for cosine, we get:

cos(2θ) = 1/4

Taking the inverse cosine of both sides, we have:

2θ = ± \(\cos^{-1}\left(\frac{1}{4}\right)\)

Solving for θ, we get two values:

θ = ± (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Since we are interested in the region to the right of the vertical line, we'll consider the positive value of θ:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Now, we can find the area by evaluating the integral:

A = ∫[θ, π/2] 1/2 (\(r^2\)) dθ

Substituting the equations for r, we have:

\(A = \int_{\theta}^{\frac{\pi}{2}} \frac{1}{2} (4\cos^2(\theta)) \, d\theta\)

Simplifying further:

\(A = \int_{\theta}^{\frac{\pi}{2}} 8\cos^2(\theta) \, d\theta\)

Using the double-angle formula for cosine, we have:

A = ∫[θ, π/2] 4(1 + cos(2θ)) dθ

Integrating term by term, we get:

A = [4θ + 2sin(2θ)] evaluated from θ to π/2

Now, Substituting the limits of integration, we get:

A = [4(π/2) + 2sin(2(π/2))] - [4θ + 2sin(2θ)] evaluated from θ to π/2

Simplifying:

A = 2π + 2sin(π) - (4θ + 2sin(2θ))

Since sin(π) = 0, we can simplify further:

A = 2π - (4θ + 2sin(2θ))

Now, we need to substitute the value of θ, which we found earlier:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Substituting this value, we have:

A = 2π - (4(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(2(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)))

Simplifying:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(\(\cos^{-1}\left(\frac{1}{4}\right)\)))

Since cos(\(\cos^{-1}\left(x\right)\)) = x, we have:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(1 - (1/4)^2)))

Simplifying further:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(15/16)))

A = 2π - 2 \(\cos^{-1}\left(\frac{1}{4}\right)\) - √15

So, the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

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the total amount is 9000

We can use the following identity:

(Xm, Ym) = X1+X2/2, Y1+Y2/2, where Xm and Ym are the midpoints of X and Y.

So, let's use it.

For question 11, X1 is -3, Y1 is 9, X2 is 3, and Y2 is -7.

Plugging in the points, we get:

-3 + 3 = 0 / 2 = 0 for x, and 9 + (-7) = 2 / 2 = 1 for y. Thus the midpoint is (0,1).

For question 12, X1 is -9, Y1 is -4, X2 is 1, and Y2 is 6. Plugging in the values we get:

-9 + 1 = -8 / 2 = -4 for x, and -4 + 6 = 2 / 2 = 1 for y. So the midpoint is (-4,1)

Answer:

Step-by-step explanation:

#11 (first photo): M = (0, 1)

basically, if you just count the units out (like i went from (-3,9) to (0,9) so i went 3 units to the right) and then do the same for the other point (making sure the number of units is equal so you would want to move 3 left) and then draw a line, you can then connect the other 2 points to create 2 triangles and where they intersect is the midpoint.

so in the picture, the bold green line is the original line, the purple line is the line created when you move units for both points, and the blue lines are the lines created when you fill in the blanks to make the triangles

#12 (picture 2): M = (-4, 1)

and the process is the exact same just change it for the points used

Answer:

2.4 inches

Step-by-step explanation:

Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. Tukey's procedure is used to identify differences in the true average bond strengths among the five protocols in Example 10.3.

Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. In this case, we are applying Tukey's procedure to the data in Example 10.3, which consists of bond strengths measured under five different protocols.

To perform Tukey's procedure, we first calculate the mean bond strength for each protocol. Next, we compute the standard error of the mean for each protocol. Then, we calculate the Tukey's test statistic for pairwise comparisons between the protocols. The test statistic takes into account the means, standard errors, and sample sizes of the groups.

By comparing the Tukey's test statistic to the critical value from the studentized range distribution, we can determine if there are statistically significant differences in the true average bond strengths among the protocols. If the test statistic exceeds the critical value, it indicates that there is a significant difference between the means of the compared protocols.

Using Tukey's procedure on the data in Example 10.3 will allow us to identify which pairs of protocols have significantly different average bond strengths and provide insights into the relative performance of the protocols in terms of bond strength.

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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Step-by-step explanation:

hope it helps you..........

Answer:

\((\frac{2}{5} )^{3}\) = \(\frac{8}{125}\) \(cm^{3}\)

Step-by-step explanation:

The probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99

The greatest number that can be formed by the two wheels is 99

Let event A be multiple of 4

Multiples of 4 between 1 to 9 is 4,8

Probability that at least one wheel land at a multiple of 4 is

\(\frac{2}{9} + \frac{2}{9}\) = 4/9

Let event B be first value greater than 9

P(B) = 9/99 = 1/11

P(A∩B) = 0

Probability of at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8

P(A∪B) = P(A) + P(B) - P(A∩B)

= 4/9 + 1/11 - 0

= \(\frac{4(11)}{9 (11)} + \frac{1 (9)}{11(9)}\\\\ \frac{44 + 9}{99}\\\\ \frac{53}{99}\)

Therefore, the probability that at least one wheel lands on a multiple of 4 or the first value is strictly greater than 8 is 53/99

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Answer:

The coordinate of C' is (0,7).

Step-by-step explanation:

Relative coordinates of each point of the ABC-Triangle are obtained first:

\(A_{rel} = A - O_{dil}\)

\(B_{rel} = B - O_{dil}\)

\(C_{rel} = C - O_{dil}\)

Where:

\(A, B, C\) - Absolute coordinates of the vertices of the ABC-Triangle.

\(O_{dil}\) - Coordinates of the center of dilation.

\(A_{rel}, B_{rel}, C_{rel}\) - Relative coordinates of the vertices of the ABC-Triangle.

If \(O_{dil} = (-4, -9)\), \(A = (-4, -6)\), \(B = (3, -6)\) and \(C = (-2, -1)\), the relative coordinates are now computed:

\(A_{rel} = (-4,-6) - (-4,-9)\)

\(A_{rel} = (-4 + 4, -6 + 9)\)

\(A_{rel} = (0, 3)\)

\(B_{rel} = (3, -6) - (-4,-9)\)

\(B_{rel} = (3+4, -6 +9)\)

\(B_{rel} = (7,3)\)

\(C_{rel} = (-2, -1) - (-4,-9)\)

\(C_{rel} = (-2+4, -1 +9)\)

\(C_{rel} = (2, 8)\)

Each outcome is consequently dilated:

\(A'_{rel} = 2\cdot (0,3)\)

\(A'_{rel} = (0,6)\)

\(B'_{rel} = 2 \cdot (7,3)\)

\(B'_{rel} = (14, 6)\)

\(C'_{rel} = 2 \cdot (2,8)\)

\(C'_{rel} = (4,16)\)

The absolute coordinates of A', B' and C' are, respectively:

\(A' = O_{dil} + A'_{rel}\)

\(A' = (-4,-9) + (0,6)\)

\(A' = (-4+0, -9 + 6)\)

\(A' = (-4, 3)\)

\(B' = O_{dil} + B'_{rel}\)

\(B' = (-4,-9) + (14,6)\)

\(B' = (-4+14, -9+6)\)

\(B' = (10, -3)\)

\(C' = O_{dil} + C'_{rel}\)

\(C' = (-4,-9) + (4,16)\)

\(C' = (-4 + 4, -9 + 16)\)

\(C' = (0, 7)\)

The coordinate of C' is (0,7).

The to find the volume of the parallelepiped is V = |A · B × C| where A, B, and C are vectors representing three adjacent sides of the parallelepiped and | | denotes the magnitude of the cross product of two vectors.

The cross product of two vectors is a vector that is perpendicular to both the vectors, and its magnitude is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between the two vectors he three adjacent sides of the parallelepiped can be represented by the vectors v1, v2, and v3, and these vectors can be found by subtracting the coordinates of the vertices

:v1 = (-2, 5, -8) - (-2, -2, -5)

= (0, 7, -3)v2 = (-2, -8, -7) - (-2, -2, -5)

= (0, -6, -2)v3 = (-7, -9, -1) - (-2, -2, -5)

= (-5, -7, 4)

Using the formula V = |A · B × C|, we can find the volume of the parallelepiped as follows:

V = |v1 · (v2 × v3)|

where v2 × v3 is the cross product of vectors v2 and v3, and v1 · (v2 × v3) is the dot product of vector v1 and the cross product v2 × v3.Using the determinant formula for the cross-product, we can find that:

v2 × v3

= (-6)(4)i + (-2)(5)j + (-6)(-7)k

= -48i - 10j + 42k

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If she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188

For given question,

a basketball player makes approximately 69% of free throws.

So, the probability of success (p) = 0.69

the probability of failure (q) = 0.31

She plays in a game in which she shoots 7 free throws.

So, n = 7

We need to find the probability that she will make all 7.

Using Binomial probability Distribution,

For x = 7,

\(P(x = 7) =~ ^7C_7\times (0.67)^7\times (0.31)^{7-7}\\\\P(x=7)= 1\times 0.0606\times 0.31\\\\P(x=7)=0.0188\)

Therefore,  if she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188

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The equation for inequality is w ≤ 75.

"Inequality" refers to a relationship between expressions or values that are not equal to one another. Therefore, inequality results from imbalance.

When two quantities are equal, we use the symbol "=," and when they are not equal, we use the symbol "≠". In the event that two things are not equivalent, the principal worth can be either more prominent than (>) or lesser than (<) or more prominent than equivalent to (≥) or not exactly equivalent to (≤) the subsequent worth.

Given the condition a light bulb can be no more than 75 watts,

here "no more than" means "less than or equal to".

the sign for "less than or equal to" is ≤

and let the watt of bulb is given by w

equation is w ≤ 75.

Hence, equation is w ≤ 75.

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Answer:

11

Step-by-step explanation:

just do 62-51=11 which gets you the difference between points

Break horizontally in middle

Area of rectangle

Area of triangle

Total area

The coefficient of XY in 7xy is 7

Any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value is known as a coefficient in mathematics. In some phrases, a letter might be substituted for the usual number. For example, x is the variable and a and b are the coefficients in the formula: ax2 + bx + c.

What is a coefficient?

A coefficient is a quantity or number that is coupled with a variable. Frequently, an integer is multiplied by the variable and written next to it. The variables that don't have a corresponding number are presumed to have a coefficient of 1.

Seven is the coefficient of XY in 7xy.

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Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

Step-by-step explanation:

Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero

Step-by-step explanation:

Answer:

the answer is

7x+9y_19=0

the sceond one is

3x_2y_14=0

The distance, in feet, between the ground and the top of the ladder is 8 feet.

The diagram formed will be a right triangle having the hypotenuse, adjacent and opposite sides

To get the  distance, in feet, between the ground and the top of the ladder, we will use the Pythagoras theorem as shown:

Given the following sides

Substitute the given parameters into the formula to have:

10² = opp² + 6²

opp²=100 - 36

opp² = 64

opp = 8feet

Hence the distance, in feet, between the ground and the top of the ladder is 8 feet.

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