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3 years ago

What are the roots of the equation? x2−x−42=0 Enter your answers in the boxes.

Mathematics

1 answer:

Levart [38]3 years ago

8 0

Answer:

x = 7 x = -6

Step-by-step explanation:

x^2−x−42=0

Factor

What two numbers multiply to -42 and add to -1

-7*6 = -42

-7+6 = -1

(x-7) (x+6) =0

Using the zero product property

x-7 =0 x+6 =0

x = 7 x = -6

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A paraboloid container is being filled with fluid at the rate of 4.5 cubic feet per minute. At what rate is the level of fluid c

docker41 [41]

Answer:

2.62 ft./min

Step-by-step explanation:

Just took the test.

7 0

3 years ago

What is the slope of the line that passes through the points (5, 2) and (3,-1)?

oksano4ka [1.4K]

Slope = -4/5

to calculate the slope m use the gradient form

m = y2 -y1
————
x2 - x1

let (x1, y1) = (3,1) and (x2, y2) = (-2, 5)

m = 5 - 1 4
———- = ——-
-2 - 3 -5

= - 4/5

3 0

3 years ago

A radar gun was used to record the speed of a swimmer (in meters per second) during selected times in the first 2 seconds of a r

Natalka [10]

Trapezoidal is involving averageing the heights
the 4 intervals are
[0,4] and [4,7.2] and [7.2,8.6] and [8.6,9]

the area of each trapezoid is (v(t1)+v(t2))/2 times width

for the first interval
the average between 0 and 0.4 is 0.2
the width is 4
4(0.2)=0.8

2nd
average between 0.4 and 1 is 0.7
width is 3.2
3.2 times 0.7=2.24

3rd
average betwen 1.0 and 1.5 is 1.25
width is 1.4
1.4 times 1.25=1.75

4th
average betwen 1.5 and 2 is 1.75
width is 0.4
0.4 times 1.74=0.7

add them all up
0.8+2.24+1.75+0.7=5.49

5.49
t=time
v(t)=speed
so the area under the curve is distance
covered 5.49 meters

8 0

3 years ago

Andy randomly selects an outfit to go to school. He can choose from 4 shirts: blue stripes, red stripes, black or white stripes.

denpristay [2]

Answer:

B and D

Step-by-step explanation:

The probability that Andy chooses a striped shirt and a pair of blue shorts is:

$\frac{3}{4} * \frac{1}{3} = \frac{3}{12} = \frac{1}{4}$

The probability that Andy chooses a striped shirt and pair of tan or plaid shorts is:

$\frac{3}{4} * (\frac{1}{3} + \frac{1}{3}) = \frac{6}{12} = \frac{1}{2}$

5 0

3 years ago

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