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4 years ago

Which of the following equations is equivalent to log(y) = 5.112

Mathematics

2 answers:

Alecsey [184]4 years ago

7 0

Answer: y=10^5.112

Step-by-step explanation:

A P E X

belka [17]4 years ago

3 0

We are given the following equation:

$log(y)=5.112$

When a log is written without a base it is understood that its base is 10. So we can also write the above equation as:

$log_{10}(y)=5.112$

In order to transform logarithmic equation to exponential equation we move the base of log to other side of the equation and place the values on the other side in its exponent. So the above equation becomes:

$y= 10^{5.112}$

Thus, option b gives the correct answer

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You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence

Alla [95]

Answer:

$122 \leq \mu \leq 138$

The 95% confidence interval would be given by (122;138)

And the correct interpretation for this case is:

c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

Step-by-step explanation:

Previous concepts

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 % where by 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".

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

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(0.025,24)".And we see that $t_{\alpha/2}=2.06$

Now we have everything in order to replace into formula (1), for this case we got:

$122 \leq \mu \leq 138$

The 95% confidence interval would be given by (122;138)

And the correct interpretation for this case is:

c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

6 0

3 years ago

chubhunter [2.5K]

Answer is 143. See picture for explanation

4 0

3 years ago

Enter an expression into each box to create a true equation 30x + __=6(__+7)

slava [35]

30x + 42 = 6(5x + 7) you can understand it now

3 0

2 years ago

A snack mix recipe calls for 2 1/5 cups of grapes and 1/4 cup of cheese. Skyler wants to make the same recipe using 1 cup of che

Sophie [7]

Answer:

8.8

Step-by-step explanation:

You multiply by 4

4 0

3 years ago

Read 2 more answers

A cylindrical tank has a radius of 15 ft. and a height of 45 ft. How many cubic feet of water can the tank hold?

vladimir1956 [14]

The formula to solve for this would be pi(r^2)xheight. Essentially what this formula does is it takes the are of the base (pi x r^2) and multiplies it by the height of the cylinder to find how many times the base can stack on itself until it reaches the top. This formula of base are times height works for all prisms with two bases. Here are the steps to solve:

1) plug in the values
- pi(15^2) x 45

2) solve for the base area of one of the circles
- pi(15^2)=225pi

3) multiply the base area by the height
- 225pi x 45 = 10,125pi

4) final answer: the tank can hold 10,125pi cubic feet of water

4 0

3 years ago