MATHEMATICS COLLEGE

Divide the following polynomial.

(x^2 - 4) (x - 1)

Answers

Answer 1
Answer:

(x2 + x + 2) • (x - 2)

—————————

x - 1
Answer 2
Answer:

x-1 is the answer!!!!! :)

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Answers

Answer:

it is 68

Step-by-step explanation:

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.) (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX = (e) In a sample of 90 children, what is the probability that none has a food allergy?

Answers

Answer:

a) P(X ≤ 3) = 0.9946

P(X < 3) = 0.9639

b) P(X ≥ 4) = 0.0054

c) P(1 ≤ X ≤ 3) = 0.5313

d) E(X) = 0.75

σX = 0.84

e) P(X=0) = 0.0099

Step-by-step explanation:

We have x: number in the sample who have a food allergy. As the sample is of n=15 and p=0.05, we have:

X \sim Bin(15, 0.05)

a) We have to determine P(X ≤ 3) and P(X < 3)

We can calculate P(X ≤ 3) as the sum of P(0), P(1), P(2) and P(3).

P(x\leq 3)=\sum_(k=0)^3P(k)\n\n\nP(x=0) = \binom{15}{0} p^(0)q^(15)=1*1*0.4633=0.4633\n\nP(x=1) = \binom{15}{1} p^(1)q^(14)=15*0.05*0.4877=0.3658\n\nP(x=2) = \binom{15}{2} p^(2)q^(13)=105*0.0025*0.5133=0.1348\n\nP(x=3) = \binom{15}{3} p^(3)q^(12)=455*0.0001*0.5404=0.0307\n\n\nP(x\leq 3)=0.4633+0.3658+0.1348+0.0307=0.9946

P(x<3) can be calculated from the previos result as:

P(x<3)=P(X\leq3)-P(3)=0.9946-0.0307=0.9639

b) We can calculate P(X ≥ 4) as:

P(X\geq4)=1-P(X<4)=1-P(X\leq3)=1-0.9946=0.0054

c) We can calculate P(1 ≤ X ≤ 3) as:

P(1 \leq X \leq 3)=P(1)+P(2)+P(3)=0.3658+0.1348+0.0307=0.5313

d) The expected value of a binomial variable is the product of the sample size n and the probability of success p:

E(X)=np=15*0.05=0.75

The standard deviation is calculates as:

\sigma_x=√(np(1-p))=√(15*0.05*0.95)=√(0.7125) =0.84

e) In this case, the sample size is n=90.

We can calculate the probability that none has a food allergy as:

P(x=0) = \binom{90}{0} p^(0)q^(90)=0.95^(90)=0.0099

What is 35.5% of $210,000?

Answers

Answer:

$74,550

Step-by-step explanation:

What the measure of a interior angle of a six sided figure

Answers

Answer:

120 degrees.

Step-by-step explanation:

If it is a regular 6 sided figure then each interior angle is 180 - (360/6)

= 120 DEGREES.

Find the scale factor of the line segment dilation. AB: endpoints (-6, -3) and (-3,-9) to A'B': endpoints at (-2, -1) and (-1, -3). A) -1/3 B) 1/3 C) 3D) -3

Answers

we know that the endpoints of AB are

\begin{gathered} (x_1,y_1)=\mleft(-6,-3\mright) \n (x_2,y_2)=(-3,-9) \end{gathered}

and the distance formula is given by

d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}

By substituying these points, we have that

d=\sqrt[]{(-3-(-6))^2+(-9-(-3))^2}

which is equal to

\begin{gathered} d=\sqrt[]{(-3+6)^2+(-9+3)^2} \n d=\sqrt[]{3^2+(-6)^2} \end{gathered}

then

\begin{gathered} d=\sqrt[]{9+36} \n d=\sqrt[]{45} \n d=\sqrt[]{9\cdot5} \n d=\sqrt[]{9}\cdot\sqrt[]{5} \n d=3\sqrt[]{5}\ldots..(A) \end{gathered}

On the other hand, if

\begin{gathered} (x_1,y_1)=(-2,-1) \n (x_2,y_2)=(-1,-3) \end{gathered}

similarly to the previous case, the distance between the endpoint for A'B' is

d=\sqrt[]{(-1-(-2))^2+(-3-(-1))^2}

which is equal to

\begin{gathered} d=\sqrt[]{(-1+2)^2+(-3+1)^2} \n d=\sqrt[]{1^2+(-2)^2} \n d=\sqrt[]{1+4} \n d=\sqrt[]{5}\ldots..(B) \end{gathered}

Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.

Then, the answer is B.

If bd = 7x - 10, BC= 4x - 29, and cd
= 5x - 9, find each value

Answers

Answer:

BD = 88

BC = 27

CD = 61

Explanation:

Given that,

BD = 7x - 10

BC= 4x - 29

CD = 5x - 9

Here we assume BD is a line segment and C is a point lies between B & D.

BD = BC + CD

7x - 10 = 4x - 29 + 5x - 9

Now combine like terms

7x - 10 = 4x + 5x - 29 - 9

7x - 10 = 9x - 38

Move 7x from left hand side to right hand side

-10 = 9x - 7x - 38

-10 = 2x - 38

Add 38 both the side

-10 + 38 = 2x - 38 + 38

28 = 2x

Divide by 2 both the side

x = 14

Now put the value of x and find the length of BD, CD, BC

BD = 7x - 10 = 7*14 - 10 = 98 - 10 = 88

BC= 4x - 29 = 4*14 - 29 = 56 - 29 = 27

CD = 5x - 9 = 5*14 - 9 = 61

That's the final answer.

I hope it will help you.

The value of the expression will be:

BD = 88

BC = 27

CD = 61

How to solve the expression

Given that,

BD = 7x - 10

BC= 4x - 29

CD = 5x - 9

Here we assume BD is a line segment and C is a point lies between B & D.

BD = BC + CD

7x - 10 = 4x - 29 + 5x - 9

Now combine like terms

7x - 10 = 4x + 5x - 29 - 9

7x - 10 = 9x - 38

Move 7x from left hand side to right hand side

-10 = 9x - 7x - 38

-10 = 2x - 38

Add 38 both the side

-10 + 38 = 2x - 38 + 38

28 = 2x

Divide by 2 both the side

x = 14

Now put the value of x and find the length of BD, CD, BC

BD = 7x - 10 = 7*14 - 10 = 98 - 10 = 88

BC= 4x - 29 = 4*14 - 29 = 56 - 29 = 27

CD = 5x - 9 = 5*14 - 9 = 61

Learn more about expressions

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