Simplify: sin8x cos3x + cos8x sin3x

A random survey was taken in Centerville. People in twenty-five homes were asked how many cars were registered to their househol

Ulleksa [173]

In order to find the mean, you first count how many numbers are there. Then, you add all numbers together and divide them by the total of numbers. In this case, you would add (1+2+1+0+3+4+0+1+1+1+2+2+3+2+3+2+1+4+0+0+2+2+1+1+1), which equals to 40. The total of numbers is 25. You divide 40 by 25, and it would get you 1.6. Therefore, your mean is 1.6.

To calculate the median, you list the numbers from least to greatest, and find the middle number. The list for this survey would be 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4. The middle number of this list is 1, therefore, your median is 1.

The mode is simply the number that appears the most in this list. There are 4 zeroes, 9 ones, 7 twos, 3 threes, and 2 fours. The most in this list would be 1, because there are 9 of them. Your mode is 1.

Mean - 1.6
Median - 1
Mode - 1

Answer: A. 1.6, 1, 1

8 0

2 years ago

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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

1 year ago

I need help plz ...i need this done by today !!!!

Deffense [45]

5. At First Street Elementary School, about 18% of the 610 students ride bicycles to school. About how many students ride bicycles to school?

Since 100% is equal to 610 students

Then 18% is equal to X students

Results X students = 18%*610students/100% = 109.8 students. As it does not make sense to split students, we have to round up to the nearest unit. Then we have 110 students. That would be approximately 18.03%, that rounded to the nearest unit is approximately 18%.

Answer 5) 110 students ride bicycles to school.

6. Write a proportion and answer each question using the conversion factor 1 inch = 2.54 centimeters.

a) Don is 67 inches tall. How many centimeters tall is he?

Since 1 inch is equal to 2.54 centimeters

Then 67 inches will be X centimeters

Results X cm = 67in * 2.54cm/1in = 170.18 centimeters

Answer 6a) Don is 170.18 centimeters tall.

b) Amira's pencil is 13.5 centimeters long. How many inches long is it?

Since 2.54cm is equal to 1inch

Then 13.5cm will be X inches

Results X inches = 13.5cm * 1in/2.54cm ≈ 5.315 approximately 5.32 inches

Answer 6b) Amira's pencil is approximately 5.32 inches long.

7. Use dimensional analysis to convert 60 miles per hour to feet per second. Remember that there are 5,280 feet in 1 mile.

Since 1 mile is equal to 5,280 feet

Then 60 miles will be X feet

Results X feet = 60 miles * 5,280 feet/1 mile = 316,800 feet

Since there are 3,600 seconds in 1 hour

316,800 feets per hour = 316,800 feets/hour x 1hour/3,600secs = 88 feet/sec

Answer 7) 60 miles per hour are converted to 88 feets per second

Hope this helps!

$\textit{\textbf{Spymore}}$

6 0

1 year ago

The hypotenuse of a 45 -45 -90 triangle measures 128 cm what is the length of one leg of the triangle

erma4kov [3.2K]

This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.

4 0

2 years ago

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Given: m∠AEB = 45° ∠AEC is a right angle. Prove: Ray E B bisects ∠AEC. 3 lines extend from point E. A horizontal line extends to

Marta_Voda [28]

Answer:

RIGHT Angle Addition Postulate.

Step-by-step explanation:

Applying the RIGHT Angle Addition Postulate gives m∠AEB + m∠BEC = m∠AEC. Applying the substitution property gives 45° + m∠BEC = 90°. The subtraction property can be used to find m∠BEC = 45°, so ∠BEC ≅ ∠AEB because they have the same measure. Since Ray E B divides ∠AEC into two congruent angles, it is the angle bisector.

3 0

1 year ago

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