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3 years ago

Which two numbers add up to -19 and multiply to make 35

Mathematics

1 answer:

iris [78.8K]3 years ago

4 0

x+y = -19
x*y = 35

x=-19-y
(-19-y)y = 35
y^2 +19y +35 = 0
y = -2.066965626
therefore x=35/y = -16.93303437

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A professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their class

KIM [24]

Answer:

We conclude that seniors skip more than 2% of their classes at 0.01 level of significance.

Step-by-step explanation:

We are given that a professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their classes.

He randomly samples a group of seniors and out of 2521 classes, the group skipped 77.

Let p = percentage of seniors who skip their classes.

So, Null Hypothesis, $H_0$ : p $\leq$ 2% {means that seniors skip less than or equal to 2% of their classes}

Alternate Hypothesis, $H_A$ : p > 2% {means that seniors skip more than 2% of their classes}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of seniors who skipped their classes = $\frac{77}{2521}$

n = sample of classes = 2521

So, test statistics = $\frac{\frac{77}{2521} -0.02}{{\sqrt{\frac{\frac{77}{2521}(1-\frac{77}{2521})}{2521} } } } }$

= 3.08

The value of the test statistics is 3.08.

Now at 0.01 significance level, the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical value of z as 2.3263 < 3.08, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that seniors skip more than 2% of their classes.

6 0

3 years ago

Find two numbers whose difference is 154 and whose product is a minimum.

Serggg [28]

Y - x = 154
let z = xy = x(154 + x) = x^2 + 154x

we need to find the minimum value of z

z' = 2x + 154 which = zero for minm or maxm value

x = -77 and y = 154 -77 = 77

so the 2 numbers are -77 and 77

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3 years ago

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Arisa [49]

Answer: 6

Steps:
7 + 11 + 0 = 18
18/3 = 6

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A triangle has an angle that measures 115°. The other two angles are in a ratio of 2:11. What are the measures of those two angl

schepotkina [342]

One angle of a triangle is 115 degrees.
The sum of the remaining angles is therefore 180-115=65°
If they are in a ratio of 2:11, then the smaller angle is 65*(2/(2+11))=10°
the larger angle is 65*(11/(2+11))=55°.
Check: 10+55=65°=180-115° ok.
Answer: the measures of the remaining angles are 10 and 55°

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3 years ago

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gtnhenbr [62]

Answer:

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Step-by-step explanation:

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2 years ago

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