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3 years ago

Determine the x and y intercepts

Mathematics

1 answer:

kakasveta [241]3 years ago

5 0

Answer:
x-intercepts: (2,0), (4,0)
y-intercepts: (0,-8)

Explanation:
To find the x intercept(s), you must compute where y=0. So solve 0= -x^2 + 6x - 8. So, the x intercepts are: (2,0) and (4,0) since the solutions to the mentioned equation are x=2 and x=4. To find the y intercept(s) compute what is y when x=0. In this case, when x=0, y=-8. So the only y intercept is (0,-8).

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No, we don't have sufficient evidence to support the claim that the doors are either too long or too short.

Step-by-step explanation:

We are given that a lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used.

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Let $\mu$ = population mean length of doors.

So, Null Hypothesis, $H_0$ : $\mu$ = 2058.0 millimeters {means that the mean length of doors is 2058.0 millimeters}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 2058.0 millimeters {means that the doors are either too long or too short}

The test statistics that will be used here is One-sample t-test statistics because we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = 2043.0 millimeters

s = sample standard deviation = 25.0 millimeters

n = sample of doors = 11

So, the test statistics = $\frac{2043.0-2058.0}{\frac{25.0}{\sqrt{11} } }$

= -1.989

The value of t-test statistics is -1.989.

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Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean length of doors is 2058.0 millimeters.

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