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3 years ago

What is the solution to this system of equations? Y= 2x - 3.5 x - 2y = -14

Mathematics

2 answers:

Rudiy273 years ago

8 0

Answer:

x = 7, y = 10.5.

Step-by-step explanation:

y = 2x - 3.5

-2y = -x - 14

Multiply the first equation by 2:

2y = 4x - 7

Now add this equation to the second one:

0 = 3x - 21

3x = 21

x = 7.

Now substitute x = 7 in the first equation to fund the value of y:

y = 2(7) - 3.5

y = 10.5.

goldfiish [28.3K]3 years ago

6 0

Answer:

x=7

y=10.5

Step-by-step explanation:

1. You can apply the method of substitution, as you can see below:

- Substitute $y=2x-3.5$ into the other equation and solve fo x:

$x-2(2x-3.5)=-14\\x-4x+7=-14\\x=7$

- Substitute the value of x obtain into the first equation, then the value of y is:

$y=2(7)-3.5\\y=10.5$

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Between which pair of decimals does the square root of 13 fall between

creativ13 [48]

Since 3 squared is 9 and 4 squared is 16, the square root of 13 will fall somewhere between 3 and 4

8 0

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.

5 0

3 years ago

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irga5000 [103]

9c + 4 = -23
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c = -3

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3 years ago

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Oxana [17]

So, the first thing you should do is break it down. First how much space can she have, and how many hotdogs and hamburgers would she have know the amount of space. Then you would find the amount of money she would make if she sold the food, and how much she would spend for inventory. Hope this helps!

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3 years ago

If m = 3 4/5 what is the value of 3m? 10 9 12 11

Irina-Kira [14]

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3 years ago