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3 years ago

For each of the order pair, determine whether it is a solution to the system of the equation.

Mathematics

1 answer:

Doss [256]3 years ago

4 0

2x-3y=-8 /* 2 -------> 4x -6y = -16
9x+2y=-5 /*3 --------> 27x +6y = -15

4x -6y = -16
27x +6y = -15

31x = -31
x = -1

2x-3y=-8
2*(-1) - 3y = -8
-2 - 3y = -8
-3y = -6
y = 2

x= -1, y = 2

(-1,2)

Check:
2(-1)-3*2=-8 -----> - 2 - 6 = -8 ----> -8 = -8 True
9x+2y=-5 -------> 9(-1) +2*2 = -5 ------> - 5 = -5 True

So, solution is (-1,2).

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4 years ago

A lot of 100 semiconductor chips contains 20 that are defective. (a) two are selected, at random, without replacement, from the

borishaifa [10]

Given: all selections are without replacement
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note that D and N are complementary.
x=undefined event
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4 years ago

A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A

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Answer: C

Step-by-step explanation:

Given:

Sample size (n) = 50

x = 12

$\widehat{\mathbf{p}}=\frac{\mathbf{x}}{n}=\frac{12}{50}=0.24$

Confidence level = 90%

α = 1 − 0.90 = 0.10

α/2 = 0.05

$\text { Critical value }\left(z_{c}\right)=z_{\frac{\alpha}{2}}=z_{0.05}=1.6449$

(from standard normal table)

90% Confidence interval is,

$\begin{aligned}&\text { Confidence interval }=\widehat{\mathbf{p}} \pm z_{c} \times \sqrt{\frac{\hat{\mathbf{p}}(1-\hat{\mathbf{p}})}{n}} \\&\text { C. I }=0.24 \pm 1.6449 \times \sqrt{\frac{0.24(1-0.24)}{50}} \\&\text { C. I }=0.24 \pm 1.65 \times \sqrt{\frac{0.24(1-0.24)}{50}}\left\end{aligned}$

Therefore, 90% confidence interval for the true proportion of sophomores who favour the adoption of uniforms is C

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3 years ago