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Nitella [24]
3 years ago
11

The Benton Youth Soccer Team has 20 players on the team, including reserves. Of these, three are goalies. Today, the team is hav

ing a contest to see which goalie can block the most number of penalty kicks. For each penalty kick, a goalie stands in the net while the rest of the team (including other goalies) takes a shot on goal, one at a time, attempting to place the ball in the net. How many penalty kicks must be taken to ensure that everyone has gone up against each of the goalies?
Mathematics
1 answer:
inna [77]3 years ago
3 0

Answer:

57

Step-by-step explanation:

Subtract one player from the total number, because one has to block.

19

Multiply this by the number of goalies there are.

19*3=57

There will be 57 kicks.

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Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.
kari74 [83]

Answer:

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

Step-by-step explanation:

(2x + 3)⁵

₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵

Use Pascal's triangle to find nCr.

\left\begin{array}{c}1\\1\ 1\\1\ 2\ 1\\1\ 3\ 3\ 1\\1\ 4\ 6\ 4\ 1\\1\ 5\ 10\ 10\ 5\ 1\end{array}\right

1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵

(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

7 0
3 years ago
Find the axis of symmetry and the vertex and graph the following: f(x)=(x+2)(x-4)
algol [13]

something noteworthy is that the independent and squared variable in this case will be the "x", namely the graph of that quadratic is a vertical parabola.

\bf f(x) = (x+2)(x-4)\implies 0=(x+2)(x-4)\implies x = \begin{cases} -2\\ 4 \end{cases} \\\\\\ \boxed{-2}\rule[0.35em]{7em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}\stackrel{\downarrow }{1}\rule[0.35em]{10em}{0.25pt}\boxed{4}

so the parabola has solutions at x = -2 and x = 4, and its vertex will be half-way between those two guys, namely at x = 1.

since this is a vertical parabola, its axis of symmetry, the line that splits its into twin sides, will be a vertical line, and it'll be the x-coordinate of the vertex, since the vertex hasa a coordinate of x = 1, then the axis of symmetry is the vertical line of x = 1.

8 0
3 years ago
A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previousl
Goshia [24]

Considering the situation described, we have that:

  • The appropriate null hypotheses is H_0: \mu = 5.2.
  • The appropriate alternative hypotheses is H_1: \mu < 5.2.

<h3>What are the hypotheses tested?</h3>

At the null hypotheses, it is tested if the mean has not been reduced, that is, it still is of 5.2 hours, hence:

H_0: \mu = 5.2.

At the alternative hypothesis, it is tested if the mean has been reduced, that is, it is now of less than 5.2 hours, hence:

H_1: \mu < 5.2

More can be learned about hypotheses tests at brainly.com/question/26454209

4 0
1 year ago
Write the coordinates of the vertices after a reflection across the x-axis.
Stells [14]

Answer:

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Step-by-step explanation:

To reflect the rectangle over the x-axis, think of it as flipping it over the x-axis. On the graph, count the units from V to S, it's 6 units. So, from the x-axis, count 6 units up from V. S would lie on -6, 6. Do the same for W to T. T would lie on (2, 6). The remaining coordinates U and V don't change because it is <em>already </em>on the x-axis. <em> </em>

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3 years ago
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sasho [114]
1/4 because if you divide 4 and 16 by 4, you will get 1/4.
6 0
3 years ago
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