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2 years ago

Round 7.4304909778 to the nearest millionth.

Mathematics

1 answer:

diamong [38]2 years ago

6 0

Answer:

7.430491

Step-by-step explanation:

Round the number based on the sixth digit. That is the millionth.

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Prove the following with Euler's formula to write e^itheta and e^-itheta in terms of sine and cosine. Then subtract them.

kirill115 [55]

Euler's formula tells us that

$e^{i\theta}=\cos\theta+i\sin\theta$
$e^{-i\theta}=\cos\theta-i\sin\theta$

Suppose we subtract the two. This eliminates the cosine terms.

$e^{i\theta}-e^{-i\theta}=i\sin\theta-(-i\sin\theta)=2i\sin\theta$

Divide both sides by $2i$ and you're done.

8 0

2 years ago

A new car is purchased for 17900 dollars. The value of the car depreciates at 13% per year. What will the value of the car be, t

Hatshy [7]

17,900 * (1 -0.13)^7 = 6752.86 . . . . dollars

7 0

2 years ago

a group of girls bought 72 rainbow hairbands ,144 brown and black hairbands and 216 bright colored hairbands .what is the larges

Nitella [24]

Answer:

Step-by-step explanation:

We are assuming that all girls in the group bought the same number of items.

Therefore, we need to find the highest common factor of 72, 144 and 216.

HCF

72 = 2 * 2 * 2 * 3 * 3

144 = 2 * 2 * 2 * 2 * 3 * 3

216 = 2 * 2 * 2 * 3 * 3 * 3

The product of the emboldened numbers is the highest common factor.

That is:

2 * 2 * 2 * 3 * 3 = 72

Therefore, the largest possible number of girls in the group is 72.

5 0

2 years ago

Among all monthly bills from a certain credit card company, the mean amount billed was $465 and the standard deviation was $300.

Fynjy0 [20]

Answer:

0.02% probability that the average amount billed on the sample bills is greater than $500.

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.

In this problem, we have that:

$\mu = 465, \sigma = 300, n = 900, s = \frac{300}{\sqrt{900}} = 10$ .

What is the probability that the average amount billed on the sample bills is greater than $500?

This probability is 1 subtracted by the pvalue of Z when $X = 500$ . So

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

$Z = \frac{500 - 465}{10}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998.

So there is a 1-0.9998 = 0.0002 = 0.02% probability that the average amount billed on the sample bills is greater than $500.

8 0

2 years ago

Kate recorded what she ate for breakfast every day for six months. Her findings are shown in the graph below. A bar graph titled

Amiraneli [1.4K]

Answer: The correct answer is option B: 19%

Step-by-step explanation: The bar graph according to the question has the following set of data;

Cereal ----------34

Eggs and Bacon ----------21

Pastries ----------39

Bagels ----------48

Waffles ----------38

The total from this set of data is 180 (that is the summation of all the observed data). The portion taken up by cereals can be derived as follows;

Cereal = (34/180) x 360

Cereal = 68 degrees

Note that we have used degrees as the unit since the data would be transferred to a pie chart. Hence on the pie chart it occupies 68 degrees of the entire 360 degrees.

In order to find out what percentage this represents we can now express 68 degrees as a percentage as follows;

Cereal = (68/360) x 100

Cereal = 18.8888888

Cereal ≈ 19

Therefore cereal occupies 19 percent of the pie chart.

8 0

2 years ago

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