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Suppose that instead of using natuarl logarithma to compute b, we use logarithms with the base 10 and define b=(log r)/(log 2). Does this change the value of b?

Answers

Answer 1

Answer:

Answer:

Yes it changes the value of b.

Step-by-step explanation:

Natural log is log with base e = 2.71828.

$ln(2)=log_(e)(2)=0.693\n\nwhere as\n\nlog_(10)(2)=0.301\n$

From this we can conclude that value b when calculated with log to base 10 instead of natural log, value of b will change.

Question:

After an 80% reduction, you purchase a new sofa on sale for $108. What was the original price?

Detailed Answer:

To find the original price, we need to determine what the 80% reduction represents in terms of the original price. If the sale price is 80% of the original price, then we can set up the equation: sale price = 0.2 * original price. We know the sale price is $108, so we can solve for the original price by dividing both sides of the equation by 0.2: original price = $108 / 0.2 = $540. Therefore, the original price of the sofa was $540.

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5. One teacher and 23students visit a zoo. The teacher
pays $12 and each student pays
$9. Use the expression 12 + 23 x
9 to find how much money they
pay in all.

Answers

Answer: 396

Step-by-step explanation:

A meteorologist is studying the speed at which thunderstorms travel. A sample of 10 storms are observed. The mean of the sample was 12.2 MPH and the standard deviation of the sample was 2.4. What is the 95% confidence interval for the true mean speed of thunderstorms?

Answers

Answer:

The 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].

Step-by-step explanation:

Given information:

Sample size = 10

Sample mean = 12.2 mph

Standard deviation = 2.4

Confidence interval = 95%

At confidence interval 95% then z-score is 1.96.

The 95% confidence interval for the true mean speed of thunderstorms is

$CI=\overline{x}\pm z*(s)/(√(n))$

Where, $\overline{x}$ is sample mean, z* is z score at 95% confidence interval, s is standard deviation of sample and n is sample size.

$CI=12.2\pm 1.96(2.4)/(√(10))$

$CI=12.2\pm 1.487535$

$CI=12.2\pm 1.488$

$CI=[12.2-1.488, 12.2+1.488]$

$CI=[10.712, 13.688]$

Therefore the 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].

According to a poll, 76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education is one of the top issues facing California. Find the error bound. (Round your answer to three decimal places.)

Answers

Answer:

The error bound is 3.125%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the zscore that has a pvalue of $1 - (\alpha)/(2)$ .

For this problem, we have that:

A sample of 506 California adults.. This means that $n = 506$ .

76% of California adults (385 out of 506 surveyed) feel that education is one of the top issues facing California. This means that $\pi = 0.76$

We wish to construct a 90% confidence interval

So $\alpha = 0.10$ , z is the value of Z that has a pvalue of $1 - (0.10)/(2) = 0.95$ , so $z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.76 - 1.645\sqrt{(0.76*0.24)/(506)} = 0.7288$

The upper limit of this interval is:

$\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.76 + 1.645\sqrt{(0.76*0.24)/(506)} = 0.7913$

The error bound of the confidence interval is the division by 2 of the subtraction of the upper limit by the lower limit. So:

$EBM = (0.7913 - 0.7288)/(2) = 0.03125$

The error bound is 3.125%.

If ST=19 and S lies at -4 , where could T be located?

Answers

Answer:

15 or -23

Step-by-step explanation:

I think you probably already turned this in but in case you haven't:

ST = 19 means that line segment ST is 19 units long. If we know that S is at -4, then T has to be 19 units away from -4, right?

So there's two directions we could go.

Add 19 to -4 to get 15, so T could be at 15. (If there's a line drawn between -4 and 15, it would be 19 units long.)

But the line could go left, towards negative infinity, too. So if we subtract 19 from -4, we'd get -23. T could also be at -23. (If there's a line drawn between -4 and -23, it would also be 19 units long. There's no such thing as a negative length.)

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a moving truck charges $250 to rent a truck and $0.40 for each mile driven. mr.lee paid a total of $314. which equation can be used to find m, the number of miles he drove the moving truck?