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3 years ago

What type of logarithm do you need to use when solving exponential equations?

1 answer:

3 0

How To: Given an exponential equation in which a common base cannot be found, solve for the unknown. Apply the logarithm of both sides of the equation. If one of the terms in the equation has base 10, use the common logarithm. If none of the terms in the equation has base 10, use the natural logarithm..

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What is 13.8÷10 and a half

KengaRu [80]

The answer is 1.314

hope it helps

8 0

3 years ago

Read 2 more answers

Graph the line with slope 7 and y-intercept -7

poizon [28]

Given :-

To graph the line with slope 7 and y intercept -7.

To Find :-

The graph of the line .

Solution :-

Here since the slope of the line is 7 and y intercept is -7 , we can use the slope intercept form of the line to find the equation of the line . The slope intercept form of the line is ,

$\longrightarrow$ y = mx + c

On putting the respective values ,

$\longrightarrow$ y = 7(x) + (-7)

$\longrightarrow$ y = 7x - 7

For the graph see attachment .

6 0

2 years ago

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

Notice that the margin of error decreases when the sample size increases.

4 0

3 years ago

What’s 50/4 as a decimal?

bearhunter [10]

Answer:

Hello, Your answer will be "12.5"

Step-by-step explanation:

To write 50/4 as a decimal you have to divide numerator by the denominator of the fraction.

We divide now 50 by 4 what we write down as 50/4 and we get 12.5 Hope That Helps!

5 0

3 years ago

Read 2 more answers

The power P of a jet of water is jointly proportional to the cross sectional area A and to the cube ofthe velocity V. (a) Write

anastassius [24]

Answer:

a) $P=kAV^3$

b) 54

Step-by-step explanation:

If one quantity, A, is jointly proportional to other 2 quantities (B & C), we can write proportionality equation as:

$A=k*B*C$

Where

k is the proportionality constant

Now, for this problem, P is jointly proportional to A and CUBE OF V, so we can write:

$P=kAV^3$

Now velocity, V, is triples, which means it becomes 3V

Also, cross sectional area, A, is doubled, which means it becomes 2A

Let's put these into formula and see the difference:

$P=kAV^3\\P=k(2A)(3V)^3\\P=k(2A)(27V^3)\\P=(2*27)kAV^3\\P=54kAV^3$

So, power is multiplied by a factor of 54. Power becomes 54 times if Area is doubled and velocity is tripled ( as seen ).

8 0

3 years ago