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2 years ago

Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)

Mathematics

1 answer:

Debora [2.8K]2 years ago

6 0

a) Step 3 is correct. You can apply the log to both sides, as long as the log base is the same.

b) Step 4 is incorrect. The expression $\log_3(27)$ should simplify to 3, and not 9. This is because 3^3 = 27. Recall that $b^x = y$ is equivalent to $\log_{b}(y) = x$ . Based on that, we can say $3^3 = 27$ is equivalent to $\log_3(27) = 3$

So the final answer should be x = 3

If we check this with the original equation, then we have

7*3^x = 189

7*3^3 = 189

7*27 = 189

189 = 189

So the answer is confirmed.

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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

What is the average (arithmetic mean) of 34, 43, 17 and 67?

Sonja [21]

The average is 40.25

5 0

2 years ago

Read 2 more answers

A company buys paper clips at the rate of $7.50 per box for the first 10 boxes, $5.50 per box for the next 10 boxes, and $3.50 p

BlackZzzverrR [31]

Answer:

46 boxes

Step-by-step explanation:

First 10 boxes can be bought for $7.5*10=75$
Next 10 boxes can be bought for $5.5*10=55$

So for a total of 20 boxes, the cost is $75+55=130$

We have remaining $221-130=91$

Each additional box costs 3.5, so for 91 dollars, we can get:

$\frac{91}{3.5}=26$ boxes

So, total $10+10+26=46$ boxes can be bought for $221.00

5 0

2 years ago

A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the l

iren [92.7K]

Answer:

0.2611

Step-by-step explanation:

Given the following information :

Normal distribution:

Mean (m) length of time per call = 3.5 minutes

Standard deviation (sd) = 0.7 minutes

Probability that length of calls last between 3.5 and 4.0 minutes :

P(3.5 < x < 4):

Find z- score of 3.5:

z = (x - m) / sd

x = 3.5

z = (3.5 - 3.5) / 0.7 = 0

x = 4

z = (4.0 - 3.5) / 0.7 = 0.5 / 0.7 = 0.71

P(3.5 < x < 4) = P( 0 < z < 0.714)

From the z - distribution table :

0 = 0.500

0.71 = very close to 0.7611

(0.7611 - 0.5000) = 0.2611

P(3.5 < x < 4) = P( 0 < z < 0.714) = 0.2611

3 0

2 years ago

Polygon ABCD is a parallelogram, and <img src="https://tex.z-dn.net/?f=m" id="TexFormula1" title="m" alt="m" align="absmiddle" c

djyliett [7]

Polygon ABCD is a parallelogram
m<ABC = m<ADC = 127

360 - 2(127) = 360 - 254 = 106

m<BCD = m<BAD = 106/2 = 53
P = 2(10 + 5) = 2(15) = 30

answer
The perimeter of the parallelogram is 30 units, and m<BCD is 53°

6 0

2 years ago

Read 2 more answers