30. The table below shows the average temperature of a lake in months since April in a certain year. Find
the equation for the curve of best fit using a quadratic model, then predict the average temperature of
the lake during December of the same year. Round all answers to the nearest hundredth.
Month
Temp (°F)
April
59
May
68
June
71
July
78
August
74
1

Answer:

The temperature, in December is 47 °F

Step-by-step explanation:

The given data for the temperature are;

Month             [tex]{}[/tex]         Temp (°F)

April                   [tex]{}[/tex]          59

May               [tex]{}[/tex]               68

June             [tex]{}[/tex]                71

July                  [tex]{}[/tex]             78

August              [tex]{}[/tex]            74

Let x represent the month, and f(x) = y represent the temperature, we have;

y = a·x² + b·x + c

When x = 1, we have, f(1) = a·1² + b·1 + c = 59

f(1) = a + b + c = 59...(1)

When x = 2, we have, f(2) = a·2² + b·2 + c = 68

f(2) = 4·a + 2·b + c = 68...(2)

When x = 3, we have, f(3) = a·3² + b·3 + c = 71

f(3) = 9·a + 3·b + c = 71...(3)

When x = 4, we have, f(4) = a·4² + b·4 + c = 78

f(3) = 16·a + 4·b + c = 78...(4)

When x = 5, we have, f(5) = a·5² + b·5 + c = 74

f(3) = 25·a + 5·b + c = 74...(5)

Subtracting equation (3) from equation (5), we get;

25·a + 5·b + c - (9·a + 3·b + c) = 74 - 71

16·a + 2·b = 3...(6)

Subtracting equation (1) from equation (2), we get;

4·a + 2·b + c - (a + b + c) = 68 - 59

3·a + b = 9...(7)

Multiply equation (7) by 2 and substract from equation (6) gives;

16·a + 2·b - 2 × (3·a + b) = 3 - 2 × 9

16·a + 2·b - 6·a - 2·b = 3 - 2 × 9

16·a - 6·a + 2·b  - 2·b = 3 - 2 × 9 = -15

10·a = -15

a = -15/10 = -1.5

a = -1.5

From, 3·a + b = 9, we have;

3 × (-1.5) + b = 9

b = 9 + 4.5 =13.5

b = 13.5

From, a + b + c = 59, we have;

-1.5 + 13.5 + c = 59

c = 59 - (-1.5 + 13.5) = 47

c = 47

The quadratic equation becomes, y = a·x² + b·x + c = -1.5·x² + 13.5·x + 47

f(x) = y = -1.5·x² + 13.5·x + 47

For December, we have, x = 9, and f(x) = -1.5×9² + 13.5×9 + 47 = 47

The temperature, in December = 47 °F

Find the equation of the following set of points. Then give the slope of a line
Perpendicular to the found equation.
{(1, 6), (3,-4)}

Diane earns $14,500 a year. She pays 11% of her gross income for federal, state, and local taxes. She is taxed at the FICA rate of 7.65%. She has 3.5% of her income withheld for personal deductions. She is paid biweekly. What is her net pay for each pay period? Round to nearest cent.

Find the area of the shaded region.

Can someone help me with this math problem

PLEASE HELP ME!!! I WILL GIVE BRAINLIEST TO CORRECT ANSWER!!

Suppose there are 360 students in the seventh grade at the middle school the table shows the favorite outdoor activities for a random of seventh graders from the schoolBased on the responses from the start of the survey about how many of the 360 students will be expected to choose kickball.

Peyton spent $15.05 on 7 gallons of gas for her car. Jamal is buying the same gasoline,
but only has $8.60 to spend. How many gallons of gas can Jamal buy. Explain
your reasoning.

How do I multiply 24 times 18

PLS HELP

What is John's average test scores?

97%, 42%, 76%, 85%, 18%, 100%
pls help

Consider the equation: 3x + 1 – 9 = 3(x + 2) + n.

Give a value of n so that the equation has no solutions.

Explain why you are correct.

If 30 sets of goggles are ordered, how many total items should the surf shop order?

Help please please!!!!!

MARY is making pillows for her new office. She bought 2 1/2 yards of fabric. Her
total cost was $17. What was the cost per yard?

HELP ME PLZ

these two polygons are similar​

how do i find angle 1 without angle 2 and only the 70?

Find the slope of the line y=1/6+3/2

» Which expression shows 35 + 15 written as a product of two factors?

Please some answer this I need help!! What is A b g h j d c f e k?

Consider the line 4x+2y=-7.

What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line?

You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. Let x = the number of short sleeved shirts and let y = the number of long sleeve shirts.
Write an equation to model the situation.
Graph the equation.

I need help plz someone help me

HELP !
CLICK ON THE PHOTO FOR THE QUESTION. ALOT OF POINTS GIVEN.

Brainlest to whoever can tell me what pi stands for

A person rents a moving truck for the day. There is an initial fee of 20$ and an additional 0.25$ every mile driven. Write the equation represent cost, C(m), as a function of the number of miles traveled, m.
C(m)=___________

Given:15y+7=12-20y prove:y=1/7 (I just need the prove thanks)

Which diagram shows the correct electron configuration for fluorine (F)?

A group of five short lines. The first line has an up and a down arrow above it and is labeled 1 s below. The second line has an up and a down arrow and is labeled 2 s. The third and fourth lines each have an up and a down arrow; the fifth line has an up arrow . The third, fourth, and fifth lines are bracketed with the label 2 p.

A group of five short lines. the first line has an up and a down arrow, and is labeled 1 s. The second has an up and a down arrow and is labeled 2 s. The third has an up and a down arrow, the fourth has an up, a down, and an up arrow, and the fifth has no arrow. The third, fourth, and fifth lines are bracketed and labeled 2 p.

A group of five short lines. The first line has an up, a down, and an up arrow and is labeled 1 s. The second line has an up, a down, and an up arrow and is labeled 2 s. The third, fourth, and fifth lines all have up arrows, and are bracketed with the label 2 p.

The medians of ADEF are DK, EL, and FJ. They meet at a single point M.
(In other words, M is the centroid of ADEF.)
Suppose ML = 9, MJ=8, and DK = 24.
Find the following lengths.
Note that the figure is not drawn to scale.

Given the following points, find the equation of the line. Then state the slope of a line
parallel to the found equation.
(4,-2) (6,5)

Giving brainlest and ALL OF THE answers are can and cannot

6. Determine the value of x and y in the diagram below.
Show how you determined the value of x and y using Algebra