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Rashid [163]
3 years ago
8

Need help to write equations for 5, 6 & 7

Mathematics
1 answer:
Softa [21]3 years ago
3 0
6)
A quadratic function has the form
y = ax^2 + bx + c

Use point (3, 5) in the equation above:

5 = a(3^2) + 3b + c
5 = 9a + 3b + c
9a + 3b + c = 5     Equation 1

Use point (4, 3) in the equation above:

3 = a(4^2) + 4b + c
16a + 4b + c = 3    Equation 2

Use point (5, 3) in the equation above.

5 = a(5^2) + 5b + c
25a + 5b + c = 5       Equation 3.

Now solve the system of equations of equations 1, 2, and 3 to find the coefficients, a, b, and c.

9a + 3b + c = 5
16a + 4b + c = 3
25a + 5b + c = 5

Subtract the first equation from the second equation.
Subtract the second equation from the third equation.
You get
7a + b = -2
9a + b = 2

Subtract the first equation above from the second equation to get.
2a = 4
a = 2

Substitute:
7a + b = -2
7(2) + b = -2
b = -16

9a + 3b + c = 5
9(2) + 3(-16) + c = 5
18 - 48 + c = 5
c - 30 = 5
c = 35

The equation in standard form is

y = 2x^2 - 16x + 35

We can find it in vertex form:

y = 2(x^2 - 8x) + 35

y = 2(x^2 - 8x + 16) + 35 - 32

y = 2(x - 4)^2 + 3
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5 0
2 years ago
This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot,
Vlad [161]

Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

Conditional Probability

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • P(A \cap B) is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem:

  • Event A: Person has the flu.
  • Event B: Person got the flu shot.

The percentages associated with getting the flu are:

  • 20% of 30%(got the shot).
  • 65% of 70%(did not get the shot).

Hence:

P(A) = 0.2(0.3) + 0.65(0.7) = 0.515

The probability of both having the flu and getting the shot is:

P(A \cap B) = 0.2(0.3) = 0.06

Hence, the conditional probability is:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.515} = 0.1165

0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.

To learn more about conditional probability, you can take a look at brainly.com/question/14398287

7 0
2 years ago
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