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Dmitrij [34]
2 years ago
15

4.

Mathematics
1 answer:
Svetach [21]2 years ago
5 0

Answer:

A. b2 – 4ac = 0

Step-by-step explanation:

Hey user☺☺

Option a is correct

Because the graph has only one solution.

As the graph touches the x-axis at one point that means that it will have only one solution for x. But we know that a quadratic equation has two solutions. So the graph will have two equal solution and therefore the discriminant will be 0.

Hope this will help☺☺

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A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writin
Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

<u><em>Let </em></u>\mu<u><em> = true average writing lifetime under controlled conditions</em></u>

So, Null Hypothesis, H_0 : \mu \geq 10 hr   {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, H_A : \mu < 10 hr    {means that the true average writing lifetime under controlled conditions is less than 10 hr}

<u>The test statistics that is used here is one-sample t test statistics;</u>

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

where, \bar X = sample mean

             s = sample standard deviation

             n = sample size of pens = 18

          n - 1 = degree of freedom = 18 -1 = 17

<u>Now, the decision rule based on the critical value of t is given by;</u>

  • If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then <u>we will not reject our null hypothesis</u> as it will not fall in the rejection region.
  • If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then <u>we will reject our null hypothesis</u> as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

<em>Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

<em>Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

<em>Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is more than the critical value of t as  -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0
2 years ago
Solve the equation: -9h - 6 +12h + 40 =22
Anettt [7]

h = -4

Hope this helps! :)

~Zane


3 0
3 years ago
a 24 ft ladder is leaning against a 20 ft building, what is the distance between the bottom of the ladder and the base of the bu
madreJ [45]
The distance at the base is 4 feet. Hope this helps.
4 0
2 years ago
Kala, Deandre, and Eric have a total of $119 in their wallets, Kala has $6 more than Deandre. Eric has 3 times what kala has. Ho
Tomtit [17]
Deandre = x
Kala = x + 6
Eric = 3(x+6)
x + x + 6 + 3(x+6) = 119
2x + 6 + 3x + 18 = 119
5x + 24 = 119
5x = 95, x = 19
Deandre has $19
Kala has 19 + 6 = $25
Eric has 3(25) = $75
4 0
2 years ago
What is the percent change from 68 miles to 42.5 miles
Arte-miy333 [17]
The answer -35.5 Hope this helps you


5 0
3 years ago
Read 2 more answers
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