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3 years ago

Determine if the given lines are parallel, perpendicular, or neither.

Mathematics

1 answer:

Leni [432]3 years ago

4 0

Answer:

The lines are parallel.

Step-by-step explanation:

Given the lines

$-2x-3y=9$

$4x+6y=24$

Writing the equations in the slope-intercept form

$y=mx+b$

where m is the slope and b is the y-intercept

$-2x-3y=9$

$y=-\frac{2}{3}x-3$

Thus, the slope = m₁ = -2/3

also

$4x+6y=24$

$y=-\frac{2}{3}x+4$

Thus, the slope = m₂ = -2/3

We know that parallel lines have equal slopes

m₁ = m₂

Thus, the lines are parallel.

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You are still debating about the two different computers. If you are paid $10.00/hour and your deductions are FICA (7.65%), fede

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Answer:

89 hours

Step-by-step explanation:

First solve all the deductions.

For each multiply the $10, which you are paid, and the percentage.

For FICA: $10 x 0.0765 = $0.77 per hr

For Fed tax: $10 x 0.12 = $1.2 per hr

For State tax: $10 x 0.08 = $0.8 per hr

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3 years ago

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

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

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Answer:

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