4 cm<br>7 cm<br>2 em<br>10 cm<br>9 cm

You deposit $800 into an account that earns simple annual interest. After 2 years. the account balance is $900.

asambeis [7]

Answer: 6.25%

Step-by-step explanation:

3 0

3 years ago

There are 50 students in a calculus class. The amount of time needed for the instructor to grade a randomly chosen midterm exam

natta225 [31]

Answer:

14.46% probability that the instructor can finish grading in 4 and a half hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n values from a distribution, the mean is $n\mu$ and the standard deviation is $s = \sqrt{n}\sigma$

In this problem, we have that:

$\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843$

What is the probability that the instructor can finish grading in 4 and a half hours

Four and half hours is 4.5*60 = 270.

So this probability is the pvalue of Z when X = 270.

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

By the Central Limit Theorem

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

$Z = \frac{270 - 300}{28.2843}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

14.46% probability that the instructor can finish grading in 4 and a half hours

8 0

3 years ago

Adam dropped a rubber ball from a window 40 ft above the sidewalk the ball always bounces half of the height that it drops how f

sergij07 [2.7K]

Answer:

The ball will reach a height of 5 ft by the 4th time.

Step-by-step explanation:

The initial height of the ball is 40 ft, when it bounces from the floor once the height will be 20 ft, the second time it'll be 10 ft, and so on. The sequence that can represent the maximum height of the ball after each bounce is:

{40, 20, 10,...}

This kind of sequence is called a geometric progression, in this kind of progression the next number is related to the one before it by the product of a constant called ratio, in this case 1/2. To calculate a specific position in this sequence we only need the ratio and the first number, using the formula below:

a_n = a*r^(n-1)

Where n is the position we want to know, a is the first number and r is the ratio. In this case we have:

a_4 = 40*(1/2)^(4-1) = 40*(1/2)^3 = 40/8 = 5

The ball will reach a height of 5 ft by the 4th time.

6 0

4 years ago

You are making numbers to hang outside the classrooms in your school.

Oksanka [162]

Answer:

0- 11 times

1,2,3,4,5,6,7,8,9- 12 times

5 0

3 years ago

Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 3.

Rudik [331]

Where is the image ??

7 0

3 years ago

Read 2 more answers

4 cm7 cm2 em10 cm9 cm​

4 cm7 cm2 em10 cm9 cm