MATHEMATICS COLLEGE

Suppose a parabola has vertex (-3, 7) and also passes through the point (-2, 11). Write the equation of the parabola in vertex form.​

Answers

Answer 1
Answer:

Answer:

f(x)=4(x-(-3))+7

Step-by-step explanation:

vertex form= f(x)=a(x-h)^2 +k

vertex= (h,k)

x=-2

f(x)=11

plug in all the variables

11=a(-2-(-3))^2 +7

simplify the right side

11=a(1)^2+7

11=a+7

subtract 7

4=a

equation= f(x)=4(x-(-3))+7

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Is this relationship proportional or not and give at least proof. Time: 1, 2, 3, 4, 5, 10 Pages: 65,130,195,260,325,650 ​

Answers

A relationship is proportional if the ratio between the output and the input is constant:

y=kx \iff (y)/(x) = k

In your case, we have

(65)/(1) = (130)/(2) = (195)/(3) = (260)/(4) = (325)/(5) = (650)/(10) = 65

This means that it takes the reader one unit of time to read 65 pages. So, after 2 units of time, he reads 130 pages, and so on.

S = the team's scoreg = the number of goals a team has scored
Which of the variables is independent and which is dependent?

Answers

Answer:

s would be the dependent variable, and g the independent.

Step-by-step explanation:

Whatever the score is, it would depend on how many goals the team has scored.

Throughout the US presidential election of 2012, polls gave regular updates on the sample proportion supporting each candidate and the margin of error for the estimates. This attempt to predict the outcome of an election is a common use of polls. In each case below, the proportion of voters who intend to vote for each candidate is given as well as a margin of error for the estimates. Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll. (Assume the candidate who gets more than of the vote wins.)

Answers

Answer:

1.) We cannot say for certain which candidate will win. But A has a statistical edge.

2.) We can say certainly that candidate A will win the election; albeit with a not so big margin.

3.) Candidate A will win this election based on the results of the final poll's before the election.

4.) We cannot say for certain which candidate will win. But A has a statistical edge.

The reasons are explained below.

Step-by-step explanation:

Confidence interval expresses a range of values in the distribution where the true proportion or mean can be found with some level of confidence.

Confidence Interval = (Sample Mean or Proportion) ± (Margin of error)

1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5%

The confidence interval for candidate A

(54%) ± (5%) = (49%, 59%)

The confidence interval for candidate B

(46%) ± (5%) = (41%, 51%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1%

The confidence interval for candidate A

(52%) ± (1%) = (51%, 53%)

The confidence interval for candidate B

(48%) ± (1%) = (47%, 49%)

Here, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. So, candidate A wins this one, easily; albeit with a close margin though.

3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2%

The confidence interval for candidate A

(53%) ± (2%) = (51%, 55%)

The confidence interval for candidate B

(47%) ± (2%) = (45%, 49%)

Here too, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. Hence, statistics predicts that candidate A wins this one.

4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10%

The confidence interval for candidate A

(58%) ± (10%) = (48%, 68%)

The confidence interval for candidate B

(42%) ± (10%) = (32%, 52%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

Hope this Helps!!!

An object is translated by (x-2, y-6). If one point in the pre-image has the coordinates (-3, 7), what would be the coordinates of its image? (-1,7) O (-5,1) O(-9,5) O (-1, 13)​

Answers

Answer:(-5,1)

Step-by-step explanation:! X= -3 so -3-4= -7, Y= 7 so 7+2=9, So the coordinates will be (-7,9) I hope that I could help you

If f(x)=2x-3 find the following
f(7)=
f(-2)=
f(-4)=

Answers

The value of f(7) ,f(-2) and f(-4) will be 11 , -17 and -31 respectively.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given,

f(x)=2x-3

f(7) so put x = 7

f(7) = 2(7) - 3

f(7) = 11

Now,

f(-2) so put x = -2

f(-2) = -2×7-3

f(-2) = -17

Now,

f(-4) so put x = -4

f(-4)= -4×7-3

f(-4) = -31

Hence,The value of f(7) ,f(-2) and f(-4) will be 11 , -17 and -31 respectively.

For more about the function,

brainly.com/question/23712366

#SPJ2

Step-by-step explanation:

f(x)=2x-3

now,

f(7)=2× 7-3

=14-3

=11

f(-2)='-2×7-3

= -14-3

b= -17

f(-4)= -4×7-3

= -28-3

= -31

The mass of Box A and Box B is 0.6 kg. The mass of Box A and Box C is 1.3 kg.Box C is 3 times as heavy as Box B. Find the mass of Box A.
​

Answers

Answer:

A=0.25

B=0.35

C=1.05

Step-by-step explanation:

1. A+B=0.6

2. A+C=1.3

3. C=3B

2 subtract 1:

  • C-B=0.7

3 substituted:

  • 3B-B=0.7
  • B=0.35
  • C=0.7+0.35=1.05
  • A=0.6-0.35=0.25
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