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3 years ago

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A person invests 10000 dollars in a bank. The bank pays 4.75% interest compounded semi-annually. To the nearest tenth of a year,

how long must the person leave the money in the bank until it reaches 19200 dollars?

1 answer:

hjlf3 years ago

8 0

Answer:

Step-by-step explanation:

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It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minute

Molodets [167]

Answer:

10.38% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 410 minutes.

99.55% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 410 minutes

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mildly obese

Normally distributed with mean 375 minutes and standard deviation 68 minutes. So $\mu = 375, \sigma = 68$

What is the probability (±0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 410 minutes?

So $n = 6, s = \frac{68}{\sqrt{6}} = 27.76$

This probability is 1 subtracted by the pvalue of Z when X = 410.

$Z = \frac{X - \mu}{s}$

$Z = \frac{410 - 375}{27.76}$

$Z = 1.26$

$Z = 1.26$ has a pvalue of 0.8962.

So there is a 1-0.8962 = 0.1038 = 10.38% probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 410 minutes.

Lean

Normally distributed with mean 522 minutes and standard deviation 106 minutes. So $\mu = 522, \sigma = 106$

What is the probability (±0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 410 minutes?

So $n = 6, s = \frac{106}{\sqrt{6}} = 43.27$

This probability is 1 subtracted by the pvalue of Z when X = 410.

$Z = \frac{X - \mu}{s}$

$Z = \frac{410 - 523}{43.27}$

$Z = -2.61$

$Z = -2.61$ has a pvalue of 0.0045.

So there is a 1-0.0045 = 0.9955 = 99.55% probability that the mean number of minutes of daily activity of the 6 lean people exceeds 410 minutes

6 0

4 years ago

The sum of 5 consecutive odd numbers is 135 what is the second number in this sequence

hoa [83]

Step-by-step explanation:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

5·x + 20 = 135

5·x = 115

x = 23

So the sequence is

23, 25, 27, 29, 31

The second number is 25.

Do you agree?

6 0

3 years ago

Which of the following threats to biodiversity is a result of plants and animals introduced to an ecosystem where they are not n

Dahasolnce [82]

Invasive Species since they were brought into a habitat that they were not originally in.

3 0

3 years ago

Read 2 more answers

Jim is running on a trail that is 5/4 of a mile long. How many miles has he run so far?

vekshin1

1 mile and 1/4 of a mile

6 0

4 years ago

The part of a cylindrical soup can that is covered by the label is 8.5 cm tall and has a diameter of 6.5 cm. What is the area of

julia-pushkina [17]

Answer:

$180.4~cm^2$

Step-by-step explanation:

<u>Surface Area</u>

The surface area of a cylinder of height h and radius r is given by:

$A=2\pi rh$

It only covers the lateral side of the cylinder. If both the top and the bottom sides are to be included, then:

$A=2\pi rh+2\pi r^2$

The label will cover only the lateral side of the soup can that has a height of h=8.5 cm and a diameter of 6.5 cm. We need to calculate the radius which is half of the diameter r=6.5 cm / 2 = 3.25 cm.

Now we calculate the side area of the can:

$A=2\pi (3.25)(8.5)$

$A=173.6~cm^2$

We need to add the 0.8 cm overlap to the total area already calculated. This overlap has 0.8 cm of width and 8.5 cm of height, so this overlap area is:

$A_o= 0.8*8.5=6.8~cm^2$

The total area of the label is:

$A=173.6~cm^2+6.8~cm^2=180.4~cm^2$

The area of the label is $\mathbf{180.4~cm^2}$

5 0

3 years ago