Algebra II : Radical Expressions. Instructions: Rationalize each denominator.

Answers

Answer 1

Answer: remember multiplying something by 1 doesn't change the value

also √x times √x=x

rationalize means get rid of the square root at thebottom

basically, if the bottom is x√n then multiply the whole fraction by (x√n)/(√n) to rationalize it, then simlify by finding ones

also remember the thingummy you need for problems 6, 9 and 10
(a-b)(a+b)=a^2-b^2

and remember
$\sqrt{ (x)/(y) } = ( √(x) )/( √(y) )$

1. $( √(3) )/( √(7) )$
multply by $( √(7) )/( √(7) )$
$( √(21) )/(7)$

2. $\sqrt{ (1)/(11) } = ( √(1) )/( √(11) )$ multply by $( √(11) )/( √(11) )$
$( √(11) )/(11)$

3. 2/(∛3)
multiply by (∛3)/(∛3)
(2∛3)/3

4. $\sqrt{ (14x)/(y^(2)) } = ( √(14x) )/( y√(5) )$ multply by $( √(5) )/( √(5) )$
$( √(70x) )/(5y)$

5. ∛(4/(9x^2))=(∛4)/(∛(9x^2))
multiply by (∛(9x^2))/(∛(9x^2))
(∛(36x^2))/(9x^2)

6. multiply top and bottom by (1+√3)/(1+√3)
(8+8√3)/(1^2-(√3)^2)=(8+8√3)/(1-3)=(8+8√3)/ (-2)=-4-4√3

7. so tired, answer is $\frac{6 \sqrt[3]{4xy^(2)} }{4x^(2)y^(2)}$

8. multiply tp and bottom by (√x-3)/(√x-3)
((-2√x)+6)/(x-9)

9. multiply by (√a+√b)/(√a+√b)
$(a+ √(ab) )/(a+b)$

10 multiply top an bottom by $( √(2)+ √(6) )/( √(2)+ √(6) )$
result
$(12+3 √(12) )/(-8)$

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The following contingency table shows opinion about global warming (nonissue vs. serious concern) among registered voters, broken down by political party affiliation (Democratic, Republican, and Independent). Use the table to answer a) through c) below. Opinions on Global Warming Nonissue Serious Concern Total 500 500 200 1200 Democratic 80 Political Party Republican 300 Independent110 490 42 200 90 Total 710 a) What is the probability that a randomly selected registered voter who is a Republican believes that global warming is a serious issue? 0.400 (Round to three decimal places as needed.) b) What is the probability that a randomly selected registered voter is a Republican given that he or she believes global warming is a serious issue? 0.167(Round to three decimal places as needed.)

Answers

Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter

What is Probability?

Probability is the branch of mathematics that deals with the quantification of uncertainty. It is the likelihood of an event happening, expressed as a number between 0 and 1. Probability is used to infer the likelihood of outcomes based on past data and current conditions. Probability is important in decision-making, risk management, and finance.

The probability of a randomly selected registered voter being a Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter who is a Republican believing that global warming is a serious issue, because there are more total registered voters who believe that global warming is a serious issue than there are registered Republicans who believe that global warming is a serious issue. This means that the probability of a randomly selected registered voter being a Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter who is a Republican believing that global warming is a serious issue, because there are more total registered voters who believe that global warming is a serious issue than there are registered Republicans who believe that global warming is a serious issue.

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No, political party affiliation and opinion on global warming are not independent because the probability of a randomly selected registered voter being a Republican is not the same for both "nonissue" and "serious concern" opinion on global warming.

What is Probability?

Probability is the branch of mathematics that deals with the quantification of uncertainty. It is the likelihood of an event happening, expressed as a number between 0 and 1. Probability is used to infer the likelihood of outcomes based on past data and current conditions. Probability is important in decision-making, risk management, and finance.

No, they are not independent. This is because the probability of a Republican being selected given that they believe global warming is a serious issue is not equal to the probability of a Republican being selected regardless of opinion on global warming (0.400 vs 0.167). This implies that there is a higher probability of a Republican being selected if they believe global warming is a serious issue.

To know more about probability click-
brainly.com/question/24756209
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–3(t − 17) = 6 whats the answer

Answers

Answer:

t = 15

–3(t − 17) = 6

Step-by-step explanation:

1. Distribute the –3 to the terms inside the parentheses:

–3 * t + 3 * 17 = 6

2. Simplify:

–3t + 51 = 6

3. Next, we want to isolate the variable t by getting rid of the constant term. To do this, we can subtract 51 from both sides of the equation:

–3t + 51 - 51 = 6 - 51

This simplifies to:

–3t = -45

4. Now, to solve for t, we need to isolate the variable. Since –3t means –3 times t, we can divide both sides of the equation by –3:

–3t / –3 = -45 / –3

This simplifies to:

t = 15

So, the solution to the equation –3(t − 17) = 6 is t = 15.

okay i got the first one down what about this one GUYS PLEASE HELP BECAUSE I HAVE TO BE SOMEWHERE AND IF I DONT GET THIS THEN I CANT GO PLEEEAASEE REEEEEEE

Answers

Answer:

Step-by-step explanation:

Bob and James are finishing the roof of a house =. Working alone, Bob can shingle the roof in 10 hours. James can shingle the roof in 16 hours. How long will it take them working together to shingle the roof? Round your answer to the nearest hundredth if necessary.A) 13 hours
B) 26.67 hours
C) 6.15 hours
D) 0.04 hours

Answers

Bob can do a tenth of the roof in an hour
James can do a sixteenth in an hour

Bob can do 16/160 of the roof in an hour
James can do 10/160 of the roof in an hour

Together they do 26/160 of the roof in an hour
160/26 = 6.15 (to 2 d.p.)

Which is a counterexample for the conditional statement shown?If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.

any fraction with a denominator of O

any fraction with a numerator of O

any fraction with a positive numerator and a negative denominator

any fraction with a negative numerator and a positive denominator

Answers

Answer: It is c

Step-by-step explanation: Im doing the test and did some research.

But if you are seweing this on 9/22/2020 please wait for me to put the confirmed answer in the comments.

Answer:

It's c

Step-by-step explanation:

If each person takes up 2.25 square feet of space, how many people can fit into an area that is 15 feet by 30 feet?A) 17
B) 40
C) 88
D) 200

Answers

D is the answer Multiply 15 times 30 and divide by 2.25

Answer:

Step-by-step explanation:

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Two functions, y = |x - 3| and 3x + 3y = 27, are graphed on thesame set of axes. Which statement is true about the solution to thesystem of equations?(1) (3,0) is the solution to the system because it satisfies the equationy = |x - 3|.(2) (9,0) is the solution to the system because it satisfies the equation3x + 3y = 27.(3) (6,3) is the solution to the system because it satisfies both equations.(4) (3,0), (9,0), and (6,3) are the solutions to the system of equationsbecause they all satisfy at least one of the equations.