Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=9−x, y=3x−3, and x=0 about the y-axis.

Katie invested $33,750 at 11.17% compounded continuously.

ser-zykov [4K]

Answer:

Katie's account balance in 10 years will be $3,769,875

Step-by-step explanation:

you multiply the amount of money you invest by the percentage, and the amount of years.

EX: $33,750 × 11.17% × 10= $3,769,875

5 0

2 years ago

The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of vi

baherus [9]

Answer: 2185

Step-by-step explanation:

Let p be the proportion of visitors are campers.

Given : The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state.

The prior proportion of visitors are campers : p=0.35

Allowable error : E= 2%= 0.02

We know that the z-value for 95% confidence = $z_c=1.96$

Then by Central Limit Theorem , the required sample size would be :

$n=p(1-p)(\dfrac{z_{c}}{E})^2$

$\Rightarrow\ n=0.35(1-0.35)(\dfrac{1.96}{0.02})^2\\\\ n= 0.35(0.65)(9604)$

Simply , we get

$n=2184.91\approx2185$ [Rounded to the next whole number.]

Hence, the smallest sample size to estimate the population proportion of campers =2185

7 0

2 years ago

A one story home has a total square footage of 1,200. If 900sq ft of the home has a basement, and 300 sq ft has a slab foundatio

anastassius [24]

Answer:

it has 1200

Step-by-step explanation:

because 900+300=1200

8 0

1 year ago

Read 2 more answers

A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mea

uysha [10]

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

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 size n, the mean is $\mu*n$ and the standard deviation is $s = \sqrt{n}*\sigma$

In this question:

$n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250$

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

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

By the Central Limit Theorem

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

$1.28 = \frac{X - 6328125}{11250}$

$X - 6328125 = 1.28*11250$

$X = 6342525$

The 90th percentile for the distribution of the total contributions is $6,342,525.

3 0

2 years ago

Suppose that we wish to expand (x + y + z)17. what is the coefficient of x 2 y5z10

Delvig [45]

We use the trinomial theorem to answer this question. Suppose we have a trinomial (a + b + c)ⁿ, we can determine any term to be:

[n!/(n-m)!(m-k)!k!] a^(n-m) b^(m-k) c^k

In this problem, the variables are: x=a, y=b and z=c. We already know the exponents of the variables. So, we equate this with the form of the trinomial theorem.

n - m = 2
m - k = 5
k = 10

Since we know k, we can determine m. Once we know m, we can determine n. Then, we can finally solve for the coefficient.

m - 10 = 5
m = 15

n - 15 = 2
n = 17

Therefore, the coefficient is equal to:

Coefficient = n!/(n-m)!(m-k)!k! = 17!/(17-5)!(15-10)!10! = 408,408

6 0

2 years ago