I need help on my homework Number 8. Part A and Part B

I need help in this please! thank you so much!

Anna35 [415]

Answer:

C) p(x) has a zero between x=2 and x=4

Step-by-step explanation:

For a polynomial p(x), $p(a)=R$ means that, when p(x) is divided by $x-a$ , the remainder is $R$ .

This is called the remainder theorem

Therefore $p(2)=1$ , $p(4)=-1$ means that when p(x) is divided $x-2$ and $x-4$ is 1 and $-1$ respectively.

Also the Intermediate value theorem says that, if p(a) and p(b) have opposite signs then there is a certain $c$ on $(a,b)$ where $f(c)=0$ i.e there is a zero between $a$ and $b$

Therefore the correct answer is C

5 0

3 years ago

Luis solves the following system of equations by elimination.

Komok [63]

The value of s is 11

5 0

3 years ago

Determine algebrically if f(x)=4x³-5x is odd or even function

Gelneren [198K]

Answer:

Odd function

Step-by-step explanation:

So to see if a function is odd or even we need to plug in a negative x for x, so f(-x)=4(-x)^3-5(-x). This produces -4x^3+5x, which is the exact opposite of the original equation, so it is an odd function. If it were even, then the signs of the coefficients would be the same as the original function.

4 0

2 years ago

The Iditarod sled dog race extends 1049 miles from Anchorage to Nome. If a musher is twice as far from Anchorage as from Nome, h

Alexxandr [17]

262 and a quarter miles

5 0

3 years ago

Read 2 more answers

A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi

Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

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 normal distributions 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.

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 the sum of n values of a distribution, the mean is $\mu \times n$ and the standard deviation is $\sigma\sqrt{n}$

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that $\mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300$

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 20000}{300}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0

2 years ago