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3 years ago

What polynomial has roots of −5, −4, and 1

Mathematics

1 answer:

vredina [299]3 years ago

8 0

Answer:

Step-by-step explanation:

The question continues with these options:

a. x3 − 8x2 − 11x + 20

b. x3 − x2 + 22x + 40

c. x3 + x2 − 22x − 40

d. x3 + 8x2 + 11x − 20

A cubic in equation (x+5)(x+4)(x-1) or on a graph that crosses at -5, -4, and 1. Multiply the factors out to find the equation.

$(x+5)(x+4) = x^2+5x+4x+20=x^2+9x+20$

$(x-1)(x^2+9x+20)\\x^3-x^2+9x^2-9x+20x-20\\x^3+8x^2+11x-20$

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The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken

agasfer [191]

33.3..........................................

3 0

3 years ago

Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, seq

MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.

Now we have everything in order to replace into formula (1):

$30.9-1.97\frac{7.5}{\sqrt{174}}=29.780$

$30.9+1.97\frac{7.5}{\sqrt{174}}=32.020$

So on this case the 95% confidence interval would be given by (29.780;32.020)

The value 29.6 is not contained on the interval calculated.

5 0

3 years ago

(pls fast) A scale drawing of a kitchen is shown below. The scale is 1 : 20.

viktelen [127]

Answer:

6 2/3 ft by 8 1/3 ft

Step-by-step explanation:

So the room will be 80 inches by 100 inches

( 1 inch ----> 20 inches

so 4 inches ----> 80 inches )

8 0

3 years ago

Read 2 more answers

The diagonal of a TV set is 13 inches long. It’s length is 7 inches more than the height. Find the dimensions of the TV set.

alukav5142 [94]

Answer: The length is 12 inches while the height is 5 inches

Step-by-step explanation: It the Television has a diagonal of 13 inches, and a height of H inches, then the length would be (H + 7) inches. It’s length is 7 inches more than the height. At this point we can draw up a right angled triangle with the hypotenuse as 13 (diagonal side) and the other two sides as H and (H + 7)

Then we can apply the Pythagoras theorem which states that

AC^2 = AB^2 + BC^2

(Where AC is the hypotenuse and AB and BC are the two other sides)

Hence,

13^2 = H^2 + (H + 7)^2

169 = H^2 + (H^2 + 14H + 49)

169 = 2H^2 + 14H + 49

By collecting like terms we now have

169 - 49 = 2H^2 + 14H

120 = 2H^2 + 14H

By re-arranging all terms on one side of the equation, we arrive at

2H^2 + 14H - 120 = 0

Divide all sides by 2

H^2 + 7H - 60 = 0

To solve the quadratic equation, we now factorize and we have,

H^2 + 12H - 5H - 60 = 0

(H + 12) (H - 5) = 0

Therefore

Either H + 12 = 0 OR

H - 5 = 0

Hence, Either H = -12 or H = 5

The dimension can not be a negative value so we shall take h equals 5.

Having calculated the height of the television as 5 inches, the length which was given as H + 7 can now be calculated as

Length = H + 7

Length = 5 + 7

Length = 12

Therefore, the length of the Television is 12 inches and the height is 5 inches

4 0

3 years ago

What’s is 2 1/2 divided 1/3

Marat540 [252]

Answer:

7 $\frac{1}{2}$

Step-by-step explanation:

$2\frac{1}{2} *$ the reciprocal of $\frac{1}{3}$

To find reciprocal, flip the top and the bottom.

So $\frac{1}{3}$ would be $\frac{3}{1}$ .

Multiply like normal.

6 0

3 years ago