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kiruha [24]
2 years ago
11

Describe the steps you would use to factor 2x3 + 5x2 – 8x – 20 completely. Then state the factored form.

Mathematics
2 answers:
WARRIOR [948]2 years ago
5 0
The polynomial 2x^3 + 5x^2-8x-20 may have solutions which are the divisors of -20, therefore -20 has the following divisors: \pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20.
If x=1, then 2\cdot1^3 + 5\cdot1^2-8\cdot1-20=-20\neq 0,
if x=-1, then 2\cdot(-1)^3 + 5\cdot(-1)^2-8\cdot(-1)-20=-9\neq 0,
if x=2, then 2\cdot2^3 + 5\cdot2^2-8\cdot2-20=0, then x=2 is a solution and you have the first factor (x-2). 
If x=-2, then 2\cdot(-2)^3 + 5\cdot(-2)^2-8\cdot(-2)-20=0, then x=-2 is a solution, so you have the second factor (x+2).
Since x-2 and x+2 are two factors of 2x^3 + 5x^2-8x-20 , then the polynomial x^2-4 is a divisor of 2x^3 + 5x^2-8x-20 and dividing the polynomial 2x^3 + 5x^2-8x-20 by x^2-4 you obtain 
 2x^3 + 5x^2-8x-20=(x-2)(x+2)(2x+5).











Nikolay [14]2 years ago
5 0
You have the polynomial 2x³+5x²-<span>8x-20=0
 To factor you must apply the steps shown below:
 1. Form two groups and factor the Greatest Common Factor of both groups, which are x</span>² and 4<span>
 x</span>²(2x+5)-4(2x+5)=0
<span> 2. Combine both groups to obtain a monomial:
 (x</span>²-4)(2x+5)=0
 3. Factor (x²-4)<span> by Difference of squares:
 (x-2)(x+2)(2x+5)=0
 4. Then you obtain the following result:
 x=2
 x=-2
 x=-5/2 
 It can be factor by using the Greatest Common Factor and the Difference of squares.
 </span>
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Answer:

Thirty-two percent of fish in a large lake are bass. Imagine scooping out a simple random sample of 15 fish from the lake and observing the sample proportion of bass. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.

A.  The standard deviation is 0.8795. The 10% condition is met because it is very likely there are more than 150 bass in the lake.

B. The standard deviation is 0.8795. The 10% condition is not met because there are less than 150 bass in the lake.

C. The standard deviation is 0.1204. The 10% condition is met because it is very likely there are more than 150 bass in the lake.

D. The standard deviation is 0.1204. The 10% condition is not met because there are less than 150 bass in the lake.

E. We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 150 bass in the lake

The answer is E.

6 0
2 years ago
Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they canno
tensa zangetsu [6.8K]
<h2>Answer with explanation:</h2>

As per given , we have

\hat{p}=0.48   , n=331

Critical value for 90% Confidence interval : z_{\alpha/2}=1.645

a) Confidence interval :

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

0.48\pm (1.645)\sqrt{\dfrac{0.48(1-0.48)}{331}}\\\\\approx 0.48\pm0.02746\\\\=(0.48-0.02746,\ 0.48+0.02746)\\\\=(0.45254,\ 0.50746)

Hence, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot a ord it : (0.45254,\ 0.50746)

b) Margin of error : E=1.5%=0.015

Formula for sample size : n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2

For p =0.48 , we  have

n=0.48(1-0.48)(\dfrac{1.645}{0.015})^2=3001.88373333\approx3002

Hence, the required sample size to survey = 3002

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2 years ago
In a survey of a town, 56% of residents own a car, 21% of residents now a truck, and 4% of residents own both a car and a truck.
Vesna [10]
The conditional probability is 80
4 0
2 years ago
The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write and
notsponge [240]

Answer:

4.65\leq x\leq 5.35

Step-by-step explanation:

Let the actual width of belt be x

we are given that the ideal width of safety belt strap is 5 cm

So, Difference between actual and ideal = (x-5)cm

We are also given that An actual width can vary by at most 0.35 cm.

So, The difference between actual and ideal width should be less than or equal to 0.35 cm

So, |x-5|\leq 0.35

We know

x-5\leq 0.35 and x-5\geq -0.35

x\leq 0.35+5 and x\geq -0.35+5

x\leq 5.35 and x\geq 4.65

So, 4.65\leq x\leq 5.35

Hence the range of acceptable widths is 4.65\leq x\leq 5.35

8 0
2 years ago
Suri made 6 gallons of lemonade to sell at her lemonade stand. in one day she sold 2/3 of the lemonade. how much lemonade did sh
Zina [86]
I hope this helps you

7 0
2 years ago
Read 2 more answers
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