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There are 380 ways to determine the first and second place in the race.

In a race, there are 20 runners. Trophies for the race are awarded to the runners finishing in first and second place. In how many ways can first and second place be determined?When the trophies for the race are awarded to the runners finishing in first and second place, then it means that there are only two trophies to be awarded. Now, the number of ways in which the two trophies can be awarded can be calculated by permutation, which is a way of counting the arrangements or selections of objects in which order is important.

To determine the number of ways first and second place can be determined in a race with 20 runners, we can use the concept of permutations.

The first-place finisher can be any one of the 20 runners. After the first-place finisher is determined, there are 19 remaining runners who can finish in second place. Therefore, the number of ways to determine the first and second place is given by:

Number of ways = 20 * 19 = 380

So, there are 380 ways to determine the first and second place in the race.

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The volume of the solid with a circular base of radius 3, where every plane cross-section perpendicular to the x-axis is an equilateral triangle, is option D) 36√3.


When each plane cross-section perpendicular to the x-axis is an equilateral triangle, we can see that the height of each equilateral triangle is equal to the diameter of the circular base, which is 6. Therefore, the height of the solid is 6.

To find the volume of the solid, we can use the formula for the volume of a cone, since the solid resembles a cone with equilateral triangular cross-sections. The volume of a cone is given by V = (1/3)πr^2h, where r is the radius of the circular base and h is the height.

Plugging in the values, we have V = (1/3)π(3^2)(6) = 18π. Simplifying, we get V = 54π.

Now, since the answer choices are in terms of √3, we can approximate π as 3.14. Therefore, V ≈ 54(3.14) = 169.56.

Rounding to the nearest whole number, the volume is approximately 170.

However, none of the answer choices provided are 170. The closest option is D) 36√3, which is approximately 187.45. Therefore, the correct answer is D) 36√3.


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Answer:

(63a+54b) and (2xy+11yz)

Step-by-step explanation:

9*7a is 63a

9*6b is 54b

2x*y is 2xy

11z*y is 11yz

The equation rearranged to isolate c is c = b / (a - b/d).

To isolate c in the equation a = b(1/c - 1/d), we can follow these steps:

Start with the equation a = b(1/c - 1/d).

Distribute b to the terms inside the parentheses: a = b/c - b/d.

Move the term b/c to the other side of the equation by subtracting it from both sides: a - b/c = -b/d.

Multiply both sides of the equation by c to eliminate the denominator in the left term: c(a - b/c) = -b/d * c.

Simplify the left side by distributing c: ac - b = -bc/d.

Move the term -bc/d to the other side of the equation by adding it to both sides: ac - b + bc/d = 0.

Factor out c on the right side of the equation: ac + c(-b/d) - b = 0.

Combine like terms: ac - (b/d)c - b = 0.

Factor out c: c(a - b/d) - b = 0.

Add b to both sides of the equation: c(a - b/d) = b.

Finally, isolate c by dividing both sides of the equation by (a - b/d): c = b / (a - b/d).

Therefore, the equation rearranged to isolate c is c = b / (a - b/d).

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Answer:

y=7, x=7

Step-by-step explanation:

They both equal y, so you can set the right part of the equations equal to each other

4x-21=2x-7

solve for x

2x-21=-7

2x=14

x=7

knowing x, we can now substitute back into one of the original equations to find y

y=4(7)-21=28-21=7

or

y=2(7)-7=14-7=7

Answer:

6t(2t - 1)

Step-by-step explanation:

12t² - 6t

Common factor: 6t

Factored:

6t(2t - 1)

The statement is incorrect since one stadium can hold only 80,000 people while the population of Dallas is approximately 1.3 million. 10 stadiums would, therefore, hold a total of 800,000 people.

The Cowboys Stadium in Dallas is a world-famous stadium, with a capacity of up to 80,000 people. The population of Dallas, Texas, USA, is approximately 1.3 million, according to data from 2020.

In other words, Gabriel's assertion that the whole of Dallas could be seated in ten Cowboys Stadiums is incorrect.

Although that's a significant figure, it's just over half of the city's entire population, and more than half of its people would have to be turned away if there were only ten Cowboys Stadiums present.

Therefore, it is essential to double-check such assertions before making them and presenting them as facts. It is better to research and verify information, rather than make claims that are incorrect and spread false information.

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Answer:

for the first part:

Oxygen and glucose are both reactants in the process of cellular respiration.

Step-by-step explanation:

The mass of hydrogen is conserved during cellular respiration as it follows the Law of Conservation of Matter...This shows that hydrogen has been conserved throughout the entire process as the product has the same amount of hydrogen as the reactants.

Answer:

121 centimeters ²

Step-by-step explanation:

Area of a square = length ²

Each side of a square = 5x

find the area of the square when x = 2.2 centimeters

Area of a square = length ²

= (5x)²

= 5x * 5x

= 5(2.2) * 5(2.2)

= 11 * 11

= 121 centimeters ²

Area of a square = 121 centimeters ²

Answer:

-2, -1, 0, 4, 9

Step-by-step explanation:

Answer:

Step-by-step explanation: 1.4 x the amount of years = 7 then 23000 divided by 7 = 3,285.7

Area= 1/2 (a+b)h

1/2(1in. +3in.)1in.

1/2(4in.)1in.

2in.× 1in.

2in. Therefore the area is 2in.

The counterclockwise circulation of the vector field F around the closed curve C is 112/3 (or approximately 37.33).

To compute the counterclockwise circulation of the vector field F = (-2x + 10y)i + (6x - 8y)j around the closed curve C, we can apply Green's Theorem.

Green's Theorem states that the counterclockwise circulation of a vector field around a closed curve C is equal to the double integral of the curl of the vector field over the region R enclosed by the curve.

First, let's obtain the curl of the vector field F:

curl(F) = (∂F₂/∂x - ∂F₁/∂y)k

= (6 - (-2))k

= 8k

Now, let's obtain the region R enclosed by the curve C. The curve is described by two functions:

Upper curve: y = -3x^2 + 7

Lower curve: y = 4x^2

To get the limits of integration, we need to determine the x-values where the curves intersect. Setting the upper and lower curves equal to each other:

-3x^2 + 7 = 4x^2

7 = 7x^2

x^2 = 1

x = ±1

Since we are only considering the first quadrant, we take the positive value, x = 1.

The limits of integration for x will be from 0 to 1.

For y, the limits are determined by the upper and lower curves:

y = -3x^2 + 7

y = 4x^2

The limits of integration for y will be from 4x^2 to -3x^2 + 7.

Now, we can set up the double integral to calculate the counterclockwise circulation using Green's Theorem:

Circulation = ∬R curl(F) · dA

= ∬R 8k · dA

= 8 ∬R dA

Integrating with respect to x and y over the region R:

Circulation = 8 ∫[0,1] ∫[4x^2, -3x^2 + 7] dy dx

Evaluating the double integral will give us the counterclockwise circulation of F around the closed curve C.

Circulation = 8 ∫[0,1] ∫[4x^2, -3x^2 + 7] dy dx

First, we integrate with respect to y:

Circulation = 8 ∫[0,1] [y] |[4x^2, -3x^2 + 7] dx

= 8 ∫[0,1] ((-3x^2 + 7) - 4x^2) dx

= 8 ∫[0,1] (-7x^2 + 7) dx

= 8 [-7/3 * x^3 + 7x] |[0,1]

= 8 [(-7/3 * 1^3 + 7 * 1) - (-7/3 * 0^3 + 7 * 0)]

= 8 [-7/3 + 7]

= 8 [-7/3 + 21/3]

= 8 [14/3]

= 112/3

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a. The third-order Taylor polynomial,  P3(x) = f(xo) + f'(xo)(x - xo) + (f''(xo)(x - xo)^2)/2 + (f'''(xo)(x - xo)^3)/6.

b. The polynomial P3(x) obtained in part a can be used to approximate f(0.1).

c. The polynomial P3(x) obtained in part a can be used to approximate the integral of (1+x)/(1+x^2) from 0 to 0.1.

a. To calculate the third-order Taylor polynomial P3(x) about xo for f(x), we need to find the values of f(x), f'(x), f''(x), and f'''(x) at x = xo. Once we have these values, we can use the formula: P3(x) = f(xo) + f'(xo)(x - xo) + (f''(xo)(x - xo)^2)/2 + (f'''(xo)(x - xo)^3)/6. Plugging in the values of f(xo), f'(xo), f''(xo), and f'''(xo) will give us the third-order Taylor polynomial.

b. The polynomial P3(x) obtained in part a can be used to approximate the value of f(0.1). We can substitute x = 0.1 into P3(x) to obtain the approximation.

c. Similarly, the polynomial P3(x) obtained in part a can be used to approximate the integral of (1+x)/(1+x^2) from 0 to 0.1. We can evaluate the polynomial P3(x) at x = 0.1 and substitute the result into the integral expression.

In summary, the third-order Taylor polynomial P3(x), about xo, for f(x) is calculated using the formula involving the values of f(xo), f'(xo), f''(xo), and f'''(xo). This polynomial can then be used to approximate the value of f(0.1) and the integral of a given function.

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Given: A = 43.7°, a = 8.7, and b = 10.3We can find the number of possible triangles by using the Law of Sines, which states that a / sin A = b / sin B = c / sin C, where a, b, and c are the side lengths and A, B, and C are the opposite angles. Let's first use the Law of Sines to find the value of sin B: a / sin A = b / sin B => sin B = b sin A / a.

Substituting the given values, we get: sin B = 10.3 sin 43.7° / 8.7≈ 0.641Now we know the value of sin B. We can use the inverse sine function (sin⁻¹) to find the possible values of angle B: B = sin⁻¹ (0.641)≈ 40.4° or B ≈ 139.6°Note that there are two possible angles for B because sine is a periodic function that repeats every 360°.Now that we know the possible values of angle B, we can use the fact that the sum of the angles of a triangle is 180° to find the possible values of angle C: C = 180° - A - B. For B = 40.4°, we get: C = 180° - 43.7° - 40.4° = 95.9°For B = 139.6°, we get: C = 180° - 43.7° - 139.6° = -2.3°Note that we get a negative value for angle C in the second case, which is not possible because all angles of a triangle must be positive. Therefore, the second case is not valid and we only have one possible triangle. Answer: There is only one possible triangle.

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Answer:

-5.75736     or    [tex]\frac{1}{-10+3√2}[/tex]

Step-by-step explanation

Realizing that the mental barriers of being scared to be wrong or too slow were getting in the way and stopping his kids from even attempting to solve problems, Gallin decided to change his approach.

Answer:

87°

Step-by-step explanation:

Answer:

4(x+5)

Step-by-step explanation:

according to your question

On average, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00.

The F-ratio is a statistic used in analysis of variance (ANOVA) tests to compare the variances between groups. In the context of hypothesis testing, the F-ratio measures the ratio of the variability between groups to the variability within groups. When the null hypothesis is false, it means that there is a significant difference between the groups being compared.

If the null hypothesis is false, it implies that there are systematic differences between the groups, resulting in larger variation between groups compared to within groups. This leads to a higher F-ratio value. The F-ratio is calculated as the ratio of the mean square between groups to the mean square within groups. As the differences between groups become more pronounced, the F-ratio increases, indicating a greater likelihood of rejecting the null hypothesis.

Therefore, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00, indicating significant variability between groups.

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Answer:

x >8

Step-by-step explanation:

Answer:

x > 8

Step-by-step explanation:

Solving an algebraic inequality is the same as solving an algebraic equation. One uses the technnique of inverse operations to undo every step in the expression to get the answer. The only difference is that with an inequality, one must remember to flip the inequality sign when dividing or multiplying by a negative. This rule does not apply to the given inequality.

5(x + 2) > 50

/5            /5

x + 2 > 10

  -2      -2

x > 8

Answer:

(-4, -2)

Step-by-step explanation:

A is initially (-4, 2); when we reflect over the y-axis, we will change from (x, y) to (x, -y). This gives us (-4, -2).

The coordinates of A' are (-5,-3).

If AABC is reflected across the y-axis, the coordinates of A' are (-5,-3).

The reflected graph is given below.

Therefore, the coordinates of A' are (-5,-3).

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F(x<=0) = 1/2.The correct option is (b) 1+e-2.

The probability distribution function of the random variable X is given by;

`f(x) = {(x+1), for x between -1 and 1, 0 elsewhere}.

The random variable Y is defined as Y = g(X), and y = g(x).

Find the probability that F(X) is less than or equal to 0. That is; F(x <= 0).

To find this, we need to evaluate the integral of the function over the interval (-infinity, 0).

Thus, F(x<=0) = ∫[from -∞ to 0] f(x) dx.

We know that the function is zero for all values of x, except when -1 < x < 1.

Therefore, we can break up the integral into two parts. We get:

F(x<=0) = ∫[from -∞ to -1] 0 dx + ∫[from -1 to 0] f(x) dx

Thus;

F(x<=0) = ∫[from -∞ to -1] 0 dx + ∫[from -1 to 0] (x + 1) dx

F(x<=0) = 0 + [(x^2/2) + x] [from -1 to 0]F(x<=0) = (0 - [(1/2) - 1]) = (1/2)

Therefore, F(x<=0) = 1/2.The correct option is (b) 1+e-2.

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Answer:

Graph B. is the one

Step-by-step explanation:

Can i have brainliest

Answer:

b is the right answer

Step-by-step explanation:

(x,y)

Answer:

she needs 1/3 chocolate bars

Step-by-step explanation:

8 × 2/3

=5 1/3

Answer:

D

Step-by-step explanation:

x = 2 and y = -7

Plug those values into the equation:

2(2) - (-7) = 11

Answer:

-5/4

Step-by-step explanation:

Pick two points on the line

(-4,0) and (0,-5)

We can use the slope formula

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

   = ( -5 -0)/(0 - -4)

    = (-5-0)/(0+4)

    = -5/4

Answer: -5/4

Step-by-step explanation:

Pick two points on the line

(-4,0) and (0,-5)

We can use the slope formula

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

  = ( -5 -0)/(0 - -4)

   = (-5-0)/(0+4)

   = -5/4

- Chilio