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
Which situation represents an example of a non-proportional relationship?
A. A restaurant charges $1.75 for each soft drink.
B. A cell phone company charges customers 10 cents per text sent or received.
C. A gym charges a membership fee of $50, plus a monthly charge of $20 per month.
D. A dog walker charges $10 to walk one dog for 30 minutes.
Option c is the correct answer. A gym charges a membership fee of $50, plus a monthly charge of $20 per month.
What is a proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. That constant is known as the "constant of proportionality".
So a non-proportional relationship is basically a line that does not cross the origin of a graph. So using the linear exhaustion of a line, y=mx+b, a proportional relationship would be something along the lines of y=mx+0 because b, which is the w intercept is 0. I
Having said that, here is the equation for a line:
a) would be y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y-intercept). This means this is a
b) would be y=0.10x (because it is only charging per amount of texts, and nothing else, there is again no b value, so the y-intercept is 0, crossing the origin). (THIS IS ALSO NOT THE ANSWER)
c) y=20x+50 (x is the number of months, which then determine the amount of money you spend at the gym based on how many months you go there. Plus, you have to add in the cost of the gym membership as well, being 50$. So, in this case, because 50 is being added to the 20x, the b value or y-intercept would be 50.
To know more about proportional relationships follow
https://brainly.com/question/28777033
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This graph shows the rate of a scuba diver’s ascent to the surface. What does the y-intercept of the graph represent?
Answer: The scuba diver was 35 meters below the surface of the water at the start of the ascent.
Step-by-step explanation:
−9.76d − (−12.81d) = 8.54
Answer:
d = 2.8
Step-by-step explanation:
−9.76d − (−12.81d) = 8.54
~Simplify
−9.76d + 12.81d = 8.54
~Combine like terms
3.05d = 8.54
~Divide 3.05 to both sides
d = 2.8
Best of Luck!
HELPPPPP HURRYYYYYY FASTTTT
Answer:
A.
Step-by-step explanation:
A slope is 2
B slope is -1/2
hope this helps :3
if it did pls mark brainliest
Rewrite in simplest terms: 9(-6r – 3) + 2(r +9)
Answer:
I think its 'r= 15/7=0.467'
Step-by-step explanation:
What is the solution to 2(x-4)=16
Answer:
x=12
Step-by-step explanation:
A ticket to see your favorite baseball team costs $43.76. That price decreases by $0.33 for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses games. What is the price of a ticket after the team loses games?
Answer:
C=$0.33L-$43.76
I hope this is good enough:
Here is a diagram that describes the cups of green and white paint in a mixture. Select ALL the statements that accurately describe this diagram.
Answer:that’s the answer enjoy
Step-by-step explanation:
4b + 3 = 2b + 13 Can someone please help me with this problem
Answer:
b = 5
Step-by-step explanation:
[tex]4b - 2b = 13 - 3 \\ 2b = 10 \\ b = 5[/tex]
45% of overnight campers reported feeling homesick their first night away.If 90 campers felt homesick, how many total campers were there?
p+7-p2 = 18; 7 + p-p2 = 18
Addition Property
Distribution Property
Commutative Property
Associative Property
Answer:
Commutative Property
Step-by-step explanation:
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.
What are the first three terms of the Arithmetic Sequence an = 11 – 3(n – 1)?
Answer:First three terms: 11,20,29 .
Step-by-step explanation:
Write a systems of equations. tn=a+(n−1)d. sn=n2 (2a+(n−1)d). So,. 110=11+(n−1)d 726=n2(22+(n−1)d).
I hope this is right
help please i only have 10 mins left
ill give brainliest!!!
the fair has a total of 90 rides. 30% of the rides are considered kiddie rides. How many of the fair rides Are not kiddie rides?
Answer:
63
Step-by-step explanation:
70 percent aren't so multiply 90 by 7/10
what is the slope of y = -x + 7
Answer:
slope m = - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 7 ← is in slope- intercept form
with slope m = - 1
A teacher wrote this expression on the board (-6)(2)+(-8+4)
Answer:
The answer is -16
Step-by-step explanation:
Help pls it would be much appreciated need it asap
Answer:
( 6, -3 )
Step-by-step explanation:
How much does one slice of pumpkin pie cost if there are 8 servings per pie?
Ingredients
• Pumpkin 15oz can ($1.50 for 15oz can)
2 eggs ($2.59 for one dozen)
• 1 tsp pumpkin pie spice ($5.99 for 1.12oz Jar =
approx.6tsp)
• Evaporated Milk 14oz can ($1.25 for 14oz can)
• Pillsbury Pie Crust ($3.79 for two crusts)
Show Your Work Here:
Answer:
$0.76 per serving of pumpkin pie
Step-by-step explanation:
the total cost of the ingredients needed to prepare a pumpkin pie = $1.50 + ($2.59 / 6) + ($5.99 / 6) + $1.25 + ($3.79 / 2) = $6.075
if we cut 8 servings per pie, then the cost per serving = total cost of the pie / number of servings = $6.075 / 8 = $0.759375 ≈ $0.76 per serving of pumpkin pie
We want to find the cost of each slice of a pie given that we know the price of the ingredients that we use to make the whole pie. We will see that the cost of a single slice is $0.75.
First, we must get the cost of the whole pie. We have:
$1.50 for the 15oz can of PumpkinWe know that 12 eggs cost $2.59, then 2 eggs cost: (2/12)*$2.59 = $0.43.We know that 1.12 oz of pie spice costs $5.99, and we use only one teaspoon of this, remember that: 1tsp = 0.167 oz, Then the cost of 1tsp of pie spice is: (0.167 oz)/(1.12 oz)*$5.99 = $0.89.$1.25 for the 14oz can of evaporated milk.One pie crust, we know that two of them cost $3,79, then only one costs: $3.79/2 = $1.90The total cost is then:
C = $1.50 + $0.43 + $0.89 + $1.25 + $1.90 = $5.97
Now we know the total cost of the pie, and it has 8 slices, then each slice costs: $5.97/8 = $0.75
If you want to learn more, you can read: https://brainly.com/question/20005135
Which of the following best defines an output? (4 points)
An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
An output is a special type of relation for which there is a rule that pairs each input with exactly one output.
An output is a set of ordered pairs in which no y-value repeats.
Answer:
An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
Usually, output refers to the dependent value of a function rule.
It is also correct that the y coordinate of ordered pairs, graphed points, and in a function table.
Answer:
An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph best disfines an output because an input can have multiple outputs like
x y
4 5
3 5
6 5
but a function cannot have the same input with different outputs like
this example shows what is not a function
x y
3 5
3 6
4 79
4 64
this is not a function
Step-by-step explanation:
PLEASEEEE HELPPP ME this is due today!!!
find the value of x pls help
Answer: 90 degrees
Step-by-step explanation:
It is a right angle which means it is 90 degrees. Plz mark me brainliest
At a farmer’s market, two vendors sell fresh milk. One vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. Which is the better deal? Explain your reasoning.
Answer:
The second vendor because when you purchase 6 liters, it costs less to get it from the second vednor.
Step-by-step explanation:
Compare the price at 6 liters.
3.80(3)= $11.40
$2.70(4)= $10.80
The daily cost of hiring a superhero, y, to work x hours of saving people
can be modeled using a linear function. The superhero charges a fixed
cost of $100 plus an additional $50 per hour. The superhero works a
maximum of 10 hours per day. For one day of work, what is the range of
the function for this situation? *
Answer:
$600
Step-by-step explanation:
50x10=$500
500+100=$600
Q1.is the given value of the variable , s, a solution to the inequality?s > -2.25; s = -2.21.yes 2.no
Q2.which value of the variable is a solution of the inequality?t > -7
1. -9
2. -8
3. -7
4. -6
Answer:
- 6
Step-by-step explanation:
;)
PLEASE SOLVE ITS QUICK
Solve | X +6| = 16
Answer:
|x| = 10
should be your answer
Which graph has a slope of 4/5 ?
Answer:
quadratic
Step-by-step explanation:
maybe you can try searching in google
whats the slope to this
Answer:
-14/15
Step-by-step explanation:
Part 5
I have done some of these but I feel unthanked I am going to continue to give pts. These points are for the females because they are strong and smart and good. We men deserve more women like you all. please take these pts. <3
Haha
I appreciate it I guess.
The original Ferris wheel, designed by George Ferris in 1892 for the World’s Columbian Exposition in Chicago, had a radius of 125 feet. What was the circumference of the original Ferris wheel?
Answer:
Step-by-step explanation:
The answer is 250 pi
Answer:
r
Step-by-step explanation:
