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2 years ago

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Classify the number 85 in as many groups on the Venn diagram as possible. A) rational B) irrational C) rational, integer D) rati

onal, integer, whole

1 answer:

Mazyrski [523]2 years ago

4 0

aAnswer:

aStep-by-step explanation:

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Suppose Johnny invests $41,745 into an account, which has been earning interest for many years and he now has a total of $39,974

Tcecarenko [31]

The interest means the amount that adds up to your previous capital that you invest in the past. If you invest an amount of money and get an interest revenue out of it, the amount of your capital will be increased, not decreased.

7 0

2 years ago

Computer upgrades have a nominal time of 80 minutes. samples of five observations each have been taken, and the results are as l

Goshia [24]

The answer:
<span>the upper and lower control limits (uclim and lclim) for mean formula is

for the mean chart
uclim= x+A2xR
where x = sum(of the value) / number of each value
and for
lclim=</span>x+A2xR
<span>
R is the range such that R= Xmax - Xmin

in the case of the sample 1: S1
the data are:
79.2 78.8 80.0 78.4 81.0

the mean is x1 = (</span>79.2 + 78.8 + 80.0 + 78.4 + 81.0) / 5= 79.48
<span>its range is R 1= 81.0 -78.4 = 2.6

we can do the same method for finding the mean chart and range for all samples
</span>S2: x2=<span> 80.14 , R2=2.3
</span>S3: x3= 80.14 , R3=1.2
S4: x4= 79.60 , R4=1.7
S5: x5= 80.02 , R5=2.0
S6: x6=80.38 , R6=1.4
<span>
therefore the average value is X= sum( x1+x2+...+x6) / 6 = 79.96
and R=sum(R1+R2+...+R6)/6=1.87
finally
range chart uclim =D4xR=3.95 and lclim is always equal to 0, because D3=0

we can say that the process is not in control.

</span>

3 0

2 years ago

Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

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".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are df=n-1=48-1=47

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that $z_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$530-2.01\frac{70}{\sqrt{48}}=509.692$

$530+2.01\frac{70}{\sqrt{48}}=550.308$

So on this case the 95% confidence interval would be given by (509.592;550.308)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

Assuming that $\hat \sigma =s$

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (b) we got:

$n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523$

So the answer for this case would be n=523 rounded up to the nearest integer

3 0

2 years ago

The table shows the side length and approximate area of an octagonal stop sign.

Ann [662]

Area = (# of sides * side length^2) / [4 * tan (180/n)]
area = (8 * x^2) / 4 * tan (22.5)
area = 8 x^2 / (4 * 0.41421)
area = 8 x^2 / <span> <span> <span> 1.65684 </span> </span> </span>
area = 4.828 x^2

So, it seems the correct answer is the first one.

5 0

2 years ago

Read 2 more answers

Suppose the following are the city driving gas mileages of a selection of sport utility vehicles (SUVs). 19, 20, 19, 20, 18, 21,

nikdorinn [45]

Answer:

Step-by-step explanation:

The mean of the gas mileages is 317÷16=19.8125

317 is the sum total of all the figures and 16 is the number of figures in the distribution

Standard deviation is the square root of the variance and the variance is the mean of all squared deviations

The 16 squared deviations are

7.9102(×2) + 3.2852(×2) + 0.6602(×3) + 0.0352(×4) + 1.4102(×3) + 10.1602 + 17.5352 = 56.4382

56.4382÷16 = 3.5274

This is the Variance. The standard deviation is herefore √3.5274 =1.878 ~ 1.88 (to 2 decimal places)

(B) Chebyshev's inequality predicts that 75% of the selection will fall within 2 standard deviations of the mean

2×1.88=3.76

19.8125-3.76 = 16.05

19.8125+3.76= 23.57

The gas mileages are between 16.05 and 23.57

(C) the actual % of SUV models of the sample that fall in the above range is (15/16 × 100) = 93.75%

(D) the empirical rule gives the more accurate prediction

5 0

2 years ago