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Anit [1.1K]
3 years ago
12

What is the solution to the system of equations?

Mathematics
1 answer:
Leto [7]3 years ago
5 0

Answer:

  1. (x, y) = (8, -1)
  2. (x, y) = (7, 10.5)

Step-by-step explanation:

1. You can use the expression for y to substitute into the first equation:

  2x +4(1/4x -3) = 12

  2x +x -12 = 12 . . . . . . eliminate parentheses

  3x = 24 . . . . . . . . . . . add 12; next divide by 3

  x = 8 . . . . . matches choice C

__

2. You can use the expression for y to substitute into the second equation:

  x -2(2x -3.5) = -14

  -3x +7 = -14 . . . . . . eliminate parentheses

  21 = 3x . . . . . . . . . . add 3x+14; next divide by 3

  7 = x . . . . . matches the third choice

_____

When the answer choices are sufficiently different, you only need to find one value to determine which is the correct choice. (If you want to check your work further, you can substitute the other answer value into the two equations to see if it works.)

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9966 [12]

Answer:

a) P-value = 0.0968

b) P-value = 0.2207

c) P-value = 0.0239

d) P-value = 0.0040

e) P-value = 0.5636

Step-by-step explanation:

As the hypothesis are defined with a ">" sign, instead of an "≠", the test is right-tailed.

For this type of test, the P-value is defined as:

P-value=P(z>z^*)

being z* the value for each test statistic.

The probability P is calculated from the standard normal distribution.

Then, we can calculate for each case:

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P-value=P(z>1.30) = 0.0968

(b) 0.77

P-value=P(z>0.77) = 0.2207

(c) 1.98

P-value=P(z>1.98) = 0.0239

(d) 2.65

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(e) −0.16

P-value=P(z>-0.16) = 0.5636

7 0
3 years ago
405.5 divided by 12.5. Step by step
lyudmila [28]

Answer:

= 32.440

Step-by-step explanation:

Change the divisor 12.5 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

4055 ÷ 125 = 32.440

and therefore:

405.5 ÷ 12.5 = 32.440

Both calculated to 3 decimal places.

   

3 0
3 years ago
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