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skad [1K]
3 years ago
11

One angle of atriangle measures 12 degrees. the second angle's measurements is five times the third. what is the measure of the

third angle
Mathematics
1 answer:
andrezito [222]3 years ago
8 0
28 degrees. This is because the first angle is 12 degrees, the third is x degrees and the second is 5x. You know that in a triangle the angles add up to 180 degrees so 12 + 5x + x = 180. Then you get 6x =168 and x =28 degrees. (**x being the thrid angle**)
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Answer:

(a) <em>H₀</em>: <em>μ</em> = 10 vs. <em>Hₐ</em>: <em>μ</em> < 10.

(b) The level of significance is 0.05.

Step-by-step explanation:

A new system is used to reduce the time customers spend waiting for teller service during peak hours at a bank.

A single mean test can be used to determine whether the waiting time has reduced.

(a)

The hypothesis to test whether the new system is effective or not is:

<em>H₀</em>: The mean waiting time is 10 minutes, i.e. <em>μ</em> = 10.

<em>Hₐ</em>: The mean waiting time is less than 10 minutes, i.e. <em>μ</em> < 10.

(b)

The information provided is:

\bar x=9.5\\s=2.2\\n=70

Compute the test statistic value as follows:

t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{9.5-10}{2.2/\sqrt{70}}=-1.902

The test statistic value is <em>t</em> = -1.902.

Compute the <em>p</em>-value of the test as follows:

p-value=P(t_{n-1}

               =P(t_{69}1.902)\\=0.031

The null hypothesis will be rejected if the <em>p</em>-value of the test is less than the significance level (<em>α</em>).

The <em>p</em>-value obtained is 0.031.

To reject the null hypothesis the value of <em>α</em> should be more than 0.031.

The most commonly used values of <em>α</em> are: 0.01, 0.05 and 0.10.

So, the least value of <em>α</em> at which we can conclude that the wait times have decreased is, <em>α</em> = 0.05.

Thus, the level of significance is 0.05.

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