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oksano4ka [1.4K]
3 years ago
15

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

Mathematics
1 answer:
vredina [299]3 years ago
8 0

Answer:

D

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.

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