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Leya [2.2K]
3 years ago
9

The Scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. Response times are normally distr

ibuted with a standard deviation of 1 minute. Would a sample of 18 fire calls with a mean response time of 4 minutes 30 seconds provide sufficient evidence to show that the goal is not being met at α = .01?
Mathematics
1 answer:
IgorC [24]3 years ago
3 0
<h2><u>Answer with explanation</u>:</h2>

Let \mu be the population mean.

As per given , we have

H_0:\mu \leq4\\\\ H_a: \mu >4

Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.

Also, population standard deviation is given \sigma=1 , so we perform one-tailed z-test.

Test statistic : z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

, where \mu = Population mean

\sigma = Population standard deviation

n= sample size

\overline{x} = Sample mean

For n= 18 , \overline{x}=4.50 , \sigma=1 , \mu =4, we have

z=\dfrac{4.5-4}{\dfrac{1}{\sqrt{18}}}\approx2.12

P-value (for right tailed test): P(z>2.12) = 1-P(z≤ 2.12)  [∵ P(Z>z)=1-P(Z≤z)]\

=1- 0.0340=0.9660

Decision : Since P-value(0.9660) > Significance level (0.01), it means we are failed to reject the null hypothesis.

[We reject null hypothesis if p-value is larger than the significance level . ]

Conclusion : We do not have sufficient evidence to show that the goal is not being met at α = .01 .

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SVEN [57.7K]

Using the pythagorean theorem, the value of x would be eight. The equation of Pythagorean is

a^2 + b^2 = c^2

(C is the hypotenuse. Hypotenuse being the length of 10) Applying the lengths leaves us with the equation

36 + x^2 = 100.

You then subtract 36 from 100 to get X alone on the opposite side of the equation.

X^2 = 64

Lastly, you take the square root of 64. Therefore, the final answer will be eight.

4 0
3 years ago
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HELP ME PLEASE HELP ME HELP ME PLEASE
riadik2000 [5.3K]

Answer:

<h2>     no, because the remainder is 126</h2>

Step-by-step explanation:

if x+3 is a factor, then -3 is a root of expression, and the remainder would be 0

calculating remainder:

-3(-3)^3+6(-3)^2+6(-3)+9=-3\cdot(-27)+6\cdot9-18+9=\\\\=81+54-9=126

4 0
3 years ago
Jane brought x shirts for $20 each and y skirts for $25 each she spent $210 in all. which equation represents this situation 2
miv72 [106K]

Answer:

Part A

20x + 25y = 210 --> D.

Part B

If jane purchased exactly 4 shirts she must have purchased Exactly ___ skirts. (round to the nearest tenth)

20*4 + 25y = 210 --> y = 5.2

is it possible for jane to purchase exactly 4 shirts? ____(yes or no)

no, because she can't buy 5.2 skirts.

5 0
3 years ago
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7 times the number of cookies in the jar plus 5 more from the tray is 54. How many cookies are in the jar?
Digiron [165]

Answer:

The number of cookies in the jar is 7.

If we include the 5 cookies from the tray in the jar the total number of cookies would be 5 + 7 = 12

Step-by-step explanation:

<em>Consider the number of cookies in the jar as 'x'. Hence the equation formed would be:-</em>

7(x) + 5 = 54

7x + 5 = 54

7x = 54 - 5

7x = 49

x = \frac{49}{7}

x = 7

The number of cookies in the jar is 7.

If we include the 5 cookies from the tray in the jar the total number of cookies would be 5 + 7 = 12

<em>Hope this helps.</em>

8 0
3 years ago
Keith started saving for retirement at age 45 with plans to retire at age 70. He invested an average of $500 per month in variou
saveliy_v [14]
500×((1+0.06÷12)^(12×25)−1)÷(0.06÷12)
=346,496.98
8 0
3 years ago
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