Please make this quick

1. While solutions to the general quintic equation in terms of radicals are impossible to obtain, they do exist. Prove that the

Marta_Voda [28]

Answer:

Step-by-step explanation:

Given is a function as $x^5-3x+1$

Equating to 0 we have equation

If the function f(x) has x intercepts then the solutions are real

Let us use remainder theorem and change of signs rule

f(0) = 1>0

f(-1) = -1+3+1=3

f(-2) = -32+6+1<0

This implies there is a real root between -1 and -2.

f(1) = -1

Since f(0) and f(1) have different signs, there exists a real root between 0 and 1.

f(2) = 32-6+1>0

Since f(1) and f(2) have different signs there exists a real root between 1 and 2.

Thus there are definitely three real solutions as

one between -1 and 0, one between 0 and 1, and third between 1 and 2.

3 0

4 years ago

Read 2 more answers

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65

erma4kov [3.2K]

Answer:

Probability that the sample average is at most 3.00 = 0.98030

Probability that the sample average is between 2.65 and 3.00 = 0.4803

Step-by-step explanation:

We are given that the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation 0.85.

Also, a random sample of 25 specimens is selected.

Let X bar = Sample average sediment density

The z score probability distribution for sample average is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 2.65

$\sigma$ = standard deviation = 0.85

n = sample size = 25

(a) Probability that the sample average sediment density is at most 3.00 is given by = P( X bar <= 3.00)

P(X bar <= 3) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{3-2.65}{\frac{0.85}{\sqrt{25} } }$ ) = P(Z <= 2.06) = 0.98030

(b) Probability that sample average sediment density is between 2.65 and 3.00 is given by = P(2.65 < X bar < 3.00) = P(X bar < 3) - P(X bar <= 2.65)

P(X bar < 3) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{3-2.65}{\frac{0.85}{\sqrt{25} } }$ ) = P(Z < 2.06) = 0.98030

P(X bar <= 2.65) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{2.65-2.65}{\frac{0.85}{\sqrt{25} } }$ ) = P(Z <= 0) = 0.5

Therefore, P(2.65 < X bar < 3) = 0.98030 - 0.5 = 0.4803 .

8 0

4 years ago

Help please I don’t know the answer

andrew-mc [135]

Answer:

$16,534.95

Step-by-step explanation:

To compute interest on loans, we use the compounded interest equation. We use the equation $A=P(1+\frac{r}{n})^{nt}$ where

P is the principle or starting value

A is the total amount after interest and a period of time

r is the rate at which interest gathers as a decimal

t the time in years

n is the number of times compounded in a year.

For this problem, we know P=$8000, r=19%=0.19, t=4 years and n=2. We substitute into the formula and simplify to find the total amount A.

$A=P(1+\frac{r}{n})^{nt}\\A=8000(1+\frac{0.19}{2})^{2(4)}\\A=8000(1+0.095)^{8}\\A=16,534.95$

8 0

4 years ago

Gcf of 6x^3, 8x^5, 10x^7

Art [367]

Answer: 2x^3

Step-by-step explanation: Find the prime factors of each term in order to find the GCF (Greatest Common Denominator).

Hope this helps you out! ☺

5 0

3 years ago

Express 13.57g in higher and lower units

Liula [17]

13.57g expressed in higher and lower units is; 0.01357kg and 13570mg.

<h3>Higher and lower units:</h3>

According to the questions;

The ground unit given is grams (g).

To convert to higher units, we can divide by 1000; so that we have;

13.57/1000 = 0.01357kg

To convert to higher units, we can divide by 1000; so that we have;

13.57×1000 = 13570mg.

Read more on higher and lower units:

brainly.com/question/2555957

4 0

3 years ago