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3 years ago

5

4n+ 6 -2n = 2(n + 3) Please help me solve

2 answers:

neonofarm [45]3 years ago

6 0

Answer:

Equation is true no matter what number you plug in for n.

Step-by-step explanation:

4n + 6 -2n = 2(n + 3)

First we can divide the equation by 2 on both sides.

2n + 3 - n = n + 3

n + 3 = n + 3

n = n

Since n = n, this equation is always true no matter what number you plug in for n.

Paraphin [41]3 years ago

5 0

Answer is provided in the image attached.

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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

3 years ago

6. A publisher requires 2⁄3 of a page of advertisements for every 5 pages in a magazine. If a magazine has 98 pages, to the near

earnstyle [38]

We have (2/3)÷5 = 2/15 advertisments for 1 page;

Then, we have 98 · (2/15) = 12.2(6) advertisments for 98 pages;

The nearest whole page is 12.

7 0

3 years ago

A TV has an original price of $499. What is the new price after a 15% increase?

liubo4ka [24]

Given:

Original price of a TV = $499

Price increased by 15%.

To find:

The new price of the TV.

Solution:

According to the question,

New price of the TV = Original price + 15% of its original price.

$\text{New price of the TV}=499+\dfrac{15}{100}(499)$

$\text{New price of the TV}=499+74.85$

$\text{New price of the TV}=573.85$

Therefore, the new price of the TV is $573.85.

3 0

3 years ago

If the sales tax is 6% and the purchase price is $271, what is the amount of tax?

Rom4ik [11]

$100\%-price\ without\ tax\\100\%+6\%=106\%-price\ with\ tax\\\\271=106\%x\\271=1.06x\ \ \ \ \ |:1.06\\x=255.66\\\\271-255.66=15.34\\\\\\Tax\ is\ equal\ \$15.34$

8 0

3 years ago

Read 2 more answers

Write 21e-10 in standard form.

____ [38]

Answer:

you cant put this equation in standard form

Step-by-step explanation:

8 0

3 years ago