Which graph represents -9x+4y≤8

3. What are the roots of the polynomial y = x³ - 8?

zzz [600]

Step-by-step explanation:

x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

Cube root of x^3 is x.

Cube root of 8 is 2

So

a=x

b= 2.

$(x - 2)( {x}^{2} - 2x + 4)$

Set these equations equal to zero

$x - 2 = 0$

$x = 2$

${x}^{2} - 2x + 4 = 0$

If we do the discriminant, we get a negative answer so we would have two imaginary solutions,

Thus the only real root is 2.

If you want imaginary solutions, apply the quadratic formula.

$1 + i \sqrt{ 3 }$

and

$1 - i \sqrt{3}$

4 0

1 year ago

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose pe

soldier1979 [14.2K]

Using the normal distribution, it is found that:

a) 0.8599 = 85.99% probability that x is more than 60.

b) 0.1788 = 17.88% probability that x is less than 110.

c) 0.6811 = 68.11% probability that x is between 60 and 110.

d) 0.0643 = 6.43% probability that x is greater than 125.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

In this problem:

The mean is of 87, thus $\mu = 87$ .
The standard deviation is of 25, thus $\sigma = 25$ .

Item a:

This probability is 1 subtracted by the p-value of Z when X = 60, thus:

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

$Z = \frac{60 - 87}{25}$

$Z = -1.08$

$Z = -1.08$ has a p-value of 0.1401.

1 - 0.1401 = 0.8599

0.8599 = 85.99% probability that x is more than 60.

Item b:

This probability is the p-value of Z when X = 110, thus:

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

$Z = \frac{110 - 87}{25}$

$Z = 0.92$

$Z = 0.92$ has a p-value of 0.8212.

1 - 0.8212 = 0.1788.

0.1788 = 17.88% probability that x is less than 110.

Item c:

This probability is the p-value of Z when X = 110 subtracted by the p-value of Z when X = 60.

From the previous two items, 0.8212 - 0.1401 = 0.6811.

0.6811 = 68.11% probability that x is between 60 and 110.

Item d:

This probability is 1 subtracted by the p-value of Z when X = 125, thus:

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

$Z = \frac{125 - 87}{25}$

$Z = 1.52$

$Z = 1.52$ has a p-value of 0.9357.

1 - 0.9357 = 0.0643.

0.0643 = 6.43% probability that x is greater than 125.

A similar problem is given at brainly.com/question/24863330

7 0

3 years ago

Heights of adult males are known to have a normal distribution. a researcher claims to have randomly selected adult males and me

8090 [49]

Answer:

The sum of the probabilities is greater than 100%; and the distribution is too uniform to be a normal distribution.

Step-by-step explanation:

The sum of the probabilities of a distribution should be 100%. When you add the probabilities of this distribution together, you have

22+24+21+26+28 = 46+21+26+28 = 67+26+28 = 93+28 = 121

This is more than 100%, which is a flaw with the results.

A normal distribution is a bell-shaped distribution. Graphing the probabilities for this distribution, we would have a bar up to 22; a bar to 24; a bar to 21; a bar to 26; and bar to 28.

The bars would not create a bell-shaped curve; thus this is not a normal distribution.

3 0

3 years ago

Read 2 more answers

What’s the range of ()=−4|−2|−3

Tpy6a [65]

Answer:

4

Step-by-step explanation:

4 0

3 years ago

2. What is the approximate value of b in the triangle below?

s344n2d4d5 [400]

Answer:

d) 17.6

Step-by-step explanation:

Use the law of Sines

SinA/a=SinB/b=SinC/c

6 0

3 years ago