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3 years ago

Find a quadratic function that includes the set of values below.

1 answer:

3 0

Plug in points to general form of quadratic function:
y=ax²+bx+c

(0,7)
7 = c
(2,13)
13 = 4a +2b + c
(4,3)
3 = 16a + 4b + c

Now solve the system of equations in two unknowns.

Substitute the value of 7 for c in the second equation:
13 = 4a + 2b + 7
6 = 4a + 2b
3 = 2a + b
b = 3 - 2a

Substitute this into third equation:
3 = 16a + 4(3-2a) + 7
3 = 16a + 12 - 8a + 7
3 = 8a + 19
-16 = 8a
a = -2

b = 3-2a = 3 - 2(-2) = 7

a = -2, b =7. c = 7
The quadratic function is y= -2x² + 7x +7

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The table displays the number of students in each grade at Richmond High School who will or will not be attending the amusement

Pani-rosa [81]

Answer:

$P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\$

Step-by-step explanation:

We are given a joint probability table.

There are four different graders in a school

1. Grade Ninth

2. Grade Tenth

3. Grade Eleventh

4. Grade Twelfth

Field trip refers to the students who will attending the amusement park field trip.

No field trip refers to the students who will not be attending the amusement park field trip.

We want to find out the probability that the selected student is an eleventh grader given that the student is going on a field trip.

$P( eleventh\: \: |\: \: FT)= \frac{P( eleventh\: \: and \: \: FT)}{P(FT)}$

Where P(eleventh and FT) is the probability of students who are in eleventh grade and will be going to field trip

$P(eleventh\: and \: FT) = \frac{13}{92} \\\\P(eleventh \: and \: FT) = 0.1413$

Where P(FT) is the probability of students who will be going to field trip

$P(FT) = \frac{12}{92} + \frac{9}{92} + \frac{13}{92} + \frac{19}{92}\\\\P(FT) = 0.1304 + 0.0978 + 0.1413 + 0.2065\\\\P(FT) = 0.576 \\\\$

So the required probability is

$P( eleventh\: \: |\: \: FT)= \frac{P( eleventh\: \: and \: \: FT)}{P(FT)} \\\\P( eleventh\: \: |\: \: FT)= \frac{0.1413}{0.576} \\\\P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\$

6 0

3 years ago

Find F(-2) F(x)=5^x A=1/25 B=1/10 C=-10 D=-25

kati45 [8]

F(-2) when F(x)=5^x is 1/25

7 0

3 years ago

The ratio of angles angles A:B:C is 5:4:3 . find measure of angle A and B And C

mr Goodwill [35]

Answer:

A=75

B=60

C=45

Step-by-step explanation:

5+4+3=12

every triangle is equal to 180 so we divide

180/12=15

then we multiply each angle by 15

5*15

4*15

and 3*15

don't forget to check your work by adding the answers together to get 180

8 0

2 years ago

You buy x bottles of soda for $1.50 using a gift card that you got as a reward for getting good grades

nadya68 [22]

Answer:

$0\leq x \leq 10$

Step-by-step explanation:

The function is $f(x)=15-1.50x$ where x is the number of bottles of soda.

The domain means the set of "allowed" x values.

Also, f(x) means the amount of money left, which cannot be less than 0. So we put 0 into f(x) and solve for x:

$f(x)=15-1.5x\\0=15-1.5x\\1.5x=15\\x=\frac{15}{1.50}\\x=10$

This means the highest number of bottles you can buy is 10. So the domain is anything from 0 to 10. You can buy 0 until highest 10 bottles. Hence the domain is

$0\leq x \leq 10$

4 0

3 years ago

What is 10k+-1=4k+-43 and how?

azamat

10k+(-1)=4k+(-43)
10k-1=4k-43
Subtract 45 from both sides and add 1 to both sides:
6k=-42
Divide by 6 on both sides
k= -7

3 0

3 years ago