The angle marked a = 48°. Work out the angle marked x.

Mathematics

1 answer:

Mrac [35]2 years ago

7 0

Answer:

x =48° because it alternates with angle a

Alternate angles are equal.

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Solve the system of equations. 8x – 3y = 1 –2x + 3y = 11 A. (–1, –3) B. (–1, 3) C. (2, 5) D. (5, 2)

Makovka662 [10]

Answer:

C. (2, 5)

Step-by-step explanation:

Looking at the answer choices, you can see that solving for y will tell you which choice is correct. We can eliminate x from the equations by adding 4 times the second equation to the first:

(8x -3y) +4(-2x +3y) = (1) +4(11) . . . . . adding the equations to eliminate x

9y = 45 . . . simplified; next we divide by 9

y = 5 . . . . . matches choice C

_____

Check

8(2) -3(5) = 16 -15 = 1

-2(2) +3(5) = -4 +15 = 11 . . . . the answer checks OK in both equations

4 0

2 years ago

Construct the 95% confidence interval for the population mean using the appropriate distributions. a. A random sample of 50 peop

SSSSS [86.1K]

Answer: 95% confidence interval would be (26.01,29.39).

Step-by-step explanation:

Since we have given that

n = 50

Mean = 27.7

Standard deviation = 6.12

We need to construct 95% confidence interval for the population.

so, z = 1.96

So, it becomes,

$\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=27.7\pm 1.96\times \dfrac{6.12}{\sqrt{50}}\\\\=27.7 \pm 1.69\\\\=(27.7-1.69,27.7+1.69)\\\\=(26.01,29.39)$