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skad [1K]
3 years ago
13

a runner ran at a rate of 0.12 mile per minute for 50 minutes on Monday, Wednesday ,and Friday. on Saturday and Tuesday the runn

er ran 0.14 mile per minute for 60 minutes and on Sunday the runner ran 0.08 mile per minute for 1 hour 30 minutes.what was the total mileage the runner covered during the week
Mathematics
1 answer:
masya89 [10]3 years ago
4 0

Answer: 42 miles


Step-by-step explanation: For Monday, Wednesday, and Friday you would multiply 0.12, 50, and 3, and get 18 miles.

For Saturday and Tuesday multiply 0.14, 60, and 2 and get 16.8

For Sunday, multiply 0.08 and 90 and get 7.2 then add your answers together to get 42


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A publisher wants to estimate the mean length of time (in minutes) all adults spend reading newspapers. To determine this estima
liq [111]

Answer:

a)  \bar X=9.07

b) The 95% confidence interval is given by (8.197;9.943)  

c) m=2.14 \frac{1.580}{\sqrt{15}}=0.873

d)  3 possible ways

1) Increasing the sample size n.  

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

Step-by-step explanation:

Notation and definitions  

n=15 represent the sample size  

\bar X= 9.07 represent the sample mean  

s=1.580 represent the sample standard deviation  

m represent the margin of error  

Confidence =95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Part a: Find the point estimate of the population mean.

The point of estimate for the population mean \mu is given by:

\bar X =\frac{\sum_{i=1}^{n} x_i}{n}

The mean obteained after add all the data and divide by 15 is \bar X=9.07

Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. The degrees of freedom are given by:  

df=n-1=15-1=14  

We can find the critical values in excel using the following formulas:  

"=T.INV(0.025,14)" for t_{\alpha/2}=-2.14  

"=T.INV(1-0.025,14)" for t_{1-\alpha/2}=2.14  

The critical value tc=\pm 2.14  

Part c: Calculate the margin of error (m)  

First we need to calculate the standard deviation given by this formula:

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}

s=1.580

The margin of error for the sample mean is given by this formula:  

m=t_c \frac{s}{\sqrt{n}}  

m=2.14 \frac{1.580}{\sqrt{15}}=0.873  

Part b: Calculate the confidence interval  

The interval for the mean is given by this formula:  

\bar X \pm t_{c} \frac{s}{\sqrt{n}}  

And calculating the limits we got:  

9.07 - 2.14 \frac{1.580}{\sqrt{15}}=8.197  

9.07 + 2.14 \frac{1.580}{\sqrt{15}}=9.943  

The 95% confidence interval is given by (8.197;9.943)  

Part d: How can we reduce the margin of error?

We can reduce the margin of error on the following ways:

1) Increasing the sample size n.  

2) Reducing the variability. If we have more data probably we will have less variation.

3) Lower the confidence level. Because if we have lower confidence then the quantile from the t distribution would belower and tthe margin of error too.

3 0
3 years ago
Le: Convert an interest rate of 12% p.a. compounded monthly to an interest
stellarik [79]

9514 1404 393

Answer:

  12.1204%

Step-by-step explanation:

The nominal annual rate is 4 times the effective quarterly rate:

  (1 +0.12/12)^3 = 1.030301

so the effective quarterly rate is 3.0301%.

The equivalent annual rate compounded quarterly is 12.1204%.

8 0
2 years ago
What is the square root of 4
atroni [7]
Square root of a number is 2 numbers that multiply to get 4 that are the same
first find the factors

4=2 times 2
then find the doubles and write only one from each pair
√4=2

so if you had a number like 36 then
36=2 times 2 times 3 times 3
the doubles are 2 and 3 so
√36=2 times 3=6


square root of 4 can be 2 or -2
5 0
3 years ago
Read 2 more answers
Help me out please, thanks
aev [14]

Hello!

f(x) = x² + 12x <=>

<=> a = 1, b = 12 <=>

<=> x = -12/2×1 <=>

<=> x = -6 <=>

<=> f(-6) = -36 <=>

<=> (-6; -36)

Good luck! :)

8 0
3 years ago
Please help in this!
vovikov84 [41]

Step-by-step explanation:

Correct option is C)

41−

21+

19−

9

=

41−

21+

19−3

=

41−

21+

16

=

41−

21+4

=

41−

25

=

41−5

=

36

=6

4 0
2 years ago
Read 2 more answers
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