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3 years ago

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The parabola graphed below represents a side view of a parabolic microphone dish. The directrix is drawn in as well. The end of

the microphone is placed on a feedhorn that will need to be placed at the focus of the parabola to pick up the sound. The scale of the graph is in inches.
Based on the graph, the engineers should make the feedhorn _____ inches long.

1 answer:

marysya [2.9K]3 years ago

6 0

I do not know the answer

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The Slow Ball Challenge or The Fast Ball Challenge.

cupoosta [38]

Answer:

Fast ball challenge

Step-by-step explanation:

Given

Slow Ball Challenge

$Pitches = 7$

$P(Hit) = 80\%$

$Win = \$60$

$Lost = \$10$

Fast Ball Challenge

$Pitches = 3$

$P(Hit) = 70\%$

$Win = \$60$

$Lost = \$10$

Required

Which should he choose?

To do this, we simply calculate the expected earnings of both.

Considering the slow ball challenge

First, we calculate the binomial probability that he hits all 7 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 7$ --- pitches

$x = 7$ --- all hits

$p = 80\% = 0.80$ --- probability of hit

So, we have:

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

$P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}$

$P(7) =1 * 0.80^7 * (1 - 0.80)^0$

$P(7) =1 * 0.80^7 * 0.20^0$

Using a calculator:

$P(7) =0.2097152$ --- This is the probability that he wins

i.e.

$P(Win) =0.2097152$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 -0.2097152$

$P(Lose) = 0.7902848$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.2097152 * \$60 + 0.7902848 * \$10$

Using a calculator, we have:

$Expected = \$20.48576$

Considering the fast ball challenge

First, we calculate the binomial probability that he hits all 3 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 3$ --- pitches

$x = 3$ --- all hits

$p = 70\% = 0.70$ --- probability of hit

So, we have:

$P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}$

$P(3) =1 * 0.70^3 * (1 - 0.70)^0$

$P(3) =1 * 0.70^3 * 0.30^0$

Using a calculator:

$P(3) =0.343$ --- This is the probability that he wins

i.e.

$P(Win) =0.343$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 - 0.343$

$P(Lose) = 0.657$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.343 * \$60 + 0.657 * \$10$

Using a calculator, we have:

$Expected = \$27.15$

So, we have:

$Expected = \$20.48576$ -- Slow ball

$Expected = \$27.15$ --- Fast ball

<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>

5 0

2 years ago

What is the unit rate of $120 15 books

Svetlanka [38]

I think its 8? someone correct me if im wrong.

3 0

3 years ago

Read 2 more answers

How many times larger is 4x10^7 than 5x10^5

irina1246 [14]

Answer:

8 times larger

Step-by-step explanation:

4 · $10^{7}$ = 4 · 10 · 10 · <u>10</u> · <u>10</u> · <em>10</em> · <em>10</em> · 10

4 · 100 · <u>100</u> · <em>100</em> · 10

400 · 10000 · 10

= 40000000

5 · $10^{5}$ = 5 · 10 · 10 · <u>10</u> · <u>10</u> · 10

50 · 100 · <u>100</u> · 10

5000 · 1000

= 5000000

40000000 ÷ 5000000 = 8

5 0

3 years ago

Cannnn someone help me

Eva8 [605]

Answer:

55 ft... The ladder must extend 55ft

Step-by-step explanation:

$c = \sqrt{a ^{2} + b ^{2} } \\ = \sqrt{33 ^{2} + 44 ^{2} } \\ = \sqrt{1089 + 1936 } \\ = \sqrt{3025} \\ c = 55$

4 0

2 years ago

Sophia is dilating a figure. One of her pre-image points with coordinates (-3, 5) has an image with coordinates (-9, 15). If one

Galina-37 [17]

The dilation factor Sophia is using appears to be
(image coordinate)/(original coordinate) = -9/-3 = 15/5 = 3

Then the problem tells us
(pre-image point)×3 = (3, 1)
so we conclude
(pre-image point) = (3, 1)/3 = (1, 1/3)

8 0

2 years ago

Read 2 more answers