V(t), left parenthesis, t, right parenthesis models the number of visitors in a park as a function of the outside temperature t (in degrees Celsius).
Look at picture posted below.
t 18 20 37
------------------------
v(t) 10 18 46
When does the number of visitors in the park increase faster?
Choose 1 answer:
(A). Between outside temperatures of 181818 degrees Celsius and 202020 degrees Celsius
(B). Between outside temperatures of 202020 degrees Celsius and 272727 degrees Celsius
(C).The number of visitors increases at the same rate over both intervals
Answers
Answer:
The number of visitors increases at the same rate over both intervals
Step-by-step explanation:
The unit rate at which the number of visitors in the park increases over a given temperature interval is called the average rate of change, or ARCARCA, R, C.
To find the average rate of change of a function over an interval, we need to take the total change in the function value over the interval and divide it by the length of the interval.
Hint #22 / 3
We are asked to compare the rates at which the number of visitors increases over the interval between an outside temperature of 181818 degrees Celsius and 202020 degrees Celsius, and over the interval between an outside temperature of 202020 degrees Celsius and 272727 degrees Celsius. These correspond to the domain intervals [18,20][18,20]open bracket, 18, comma, 20, close bracket and [20,27][20,27]open bracket, 20, comma, 27, close bracket.
Let's calculate the average rate of change of VVV over those intervals:
ARC_{[18,20]}ARC
[18,20]
A, R, C, start subscript, open bracket, 18, comma, 20, close bracket, end subscript ARC_{[20,27]}ARC
[20,27]
A, R, C, start subscript, open bracket, 20, comma, 27, close bracket, end subscript
\begin{aligned} \dfrac{V(20)-V(18)}{20-18}&=\dfrac{18-10}{2}\\\\&=\dfrac{8}{2}\\\\&=4\end{aligned}\quad
20−18
V(20)−V(18)
=
2
18−10
=
2
8
=4
\begin{aligned} \dfrac{V(27)-V(20)}{27-20}&=\dfrac{46-18}{7}\\\\&=\dfrac{28}{7}\\\\&=4\end{aligned}
27−20
V(27)−V(20)
=
7
46−18
=
7
28
=4
Hint #33 / 3
The average rate of change over the interval [18,20][18,20]open bracket, 18, comma, 20, close bracket is the same as the average rate of change over the interval [20,27][20,27]open bracket, 20, comma, 27, close bracket.
Therefore, the number of visitors increases at the same rate over both intervals.
Using the average rate of change, it is found that the correct option is:
(A) Between outside temperatures of 18 degrees Celsius and 20 degrees Celsius.
The rate of change of a function is given by the change in the output divided by the change in the input.
When the temperature changes from 18 to 20 degrees, the number of visitors increase from 10 to 18, thus, the rate of change is:
[tex]r = \frac{18 - 10}{20 - 18} = \frac{8}{2} = 4[/tex]
When the temperature changes from 20 to 37 degrees, the number of visitors increase from 18 to 46, thus, the rate of change is:
[tex]r = \frac{46 - 18}{37 - 20} = \frac{28}{17} = 1.65[/tex]
First case has higher rate of change, thus, option A is correct.
A similar problem is given at https://brainly.com/question/20732437
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Answers
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A store sells new video games for $25 each. Used video games sell for $10 each. Jacob is buying 3 new video games and x used video games. Which equation can be used to find y, the total price Jacob must pay in dollars?
Answers
Answer:
[tex]y = 75 + 10x[/tex]
Step-by-step explanation:
Given
New Video Games
[tex]Cost = \$25[/tex]
[tex]Number = 3[/tex]
Used Video Games
[tex]Cost = \$10[/tex]
[tex]Number = x[/tex]
Required
Determine the amount spent (y)
First, we need to determine the total spent on new games
1 new game = $25
3 new games will be: 3 * $25
Next, we determine the total spent on old games
1 used game = $10
x used games will be: x * $10
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Courtney walked from her house to the beach at a constant speed of 444 kilometers per hour, and then walked from the beach to the park at a constant speed of 555 kilometers per hour. The entire walk took 222 hours and the total distance Courtney walked was 888 kilometers.
Answers
Answer:
I suppose that each number is repeated 3 times, the actual question is:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Now, remember the relation:
Distance = Speed*Time
Let's define:
D1 = distance between Courtney's house and the beach.
D2 = distance between the beach and the park.
T1 = time that it took the first walk.
T2 = time that it took the second walk.
We know that the total distance Courtney walked is 8km, then:
D1 + D2 = 8km.
And we also know that the entire walk took 2 hours, then:
T1 + T2 = 2h.
We also have the equations:
D1 = 4km/h*T1
D2 = 5km/h*T2.
Then we have a system of equations:
D1 + D2 = 8km
T1 + T2 = 2h
D1 = 4km/h*T1
D2 = 5km/h*T2.
To solve this, first let's replace equations 3 and 4 in the first equation:
4km/h*T1 + 5km/h*T2 = 8km
Now we have only two equations left:
4km/h*T1 + 5km/h*T2 = 8km
T1 + T2 = 2h
Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:
T1 = 2h - T2.
Replacing this in the first equation gives:
4km/h*(2h - T2) + 5km/h*T2 = 8km
Now let's solve this for T2.
8km - 4km/h*T2 + 5km/h*T2 = 8km
8km + 1km/h*T2 = 8km
1km/h*T2 = 0
from this, we have T2 = 0
This would mean that T1 = 2h.
Then:
D1 = 4km/h*2h = 8km.
T2 = 0
D2 = 5km/h*0 = 0.
This happens because the numbers in the problem were not well thought.
You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.
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Answers
Answer:
Step-by-step explanation:
The explicit formula for a GP is expressed as
Tn = ar^{n-1}
a is the first term
n is the number of terms
r is the common ratio
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a3 = ar^3-1
a3 = ar^2 = 36
ar^2 = 36
a(6)^2 = 36
36a = 36
a = 1
Get the nth term
Tn = 1(6)^{n-1}
Tn = 6^{n-1}
b) If a6 = 64 and r = 2
a6 = ar^6-1
a6 = ar^5 = 64
ar^5 = 64
a(2)^2 = 64
4a = 64
a = 16
Get the nth term
Tn = 16(2)^{n-1}
Tn = 16*(2^n/2)
Tn = 8(2^n)
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Step-by-step explanation:
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12 minutes
Answer:
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Step-by-step explanation:
If the rate of the plane is -450 meters per minute, then you have to use the "division" operation in order to know how much time it takes for the plane to reach an altitude of -5,400 meters.
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It will take 12 minutes for the plane to reach an altitude of -5,400 meters.
Let's check:
-450 meters x 12 minutes = -5,400 meters
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Answers
Answer:
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Step-by-step explanation:
2y - 2x = 8
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
You would need 13.5 2/3 cups.
Step-by-step explanation:
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27÷3=9
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Answers
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270
Step-by-step explanation:
Evaluate for a=3, b=2 and c=10.
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Answers
Answer:
49
Step-by-step
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Answer:
49
Step-by-step explanation:
Step 1:
a = 3; b = 2; c = 10 Given
Step 2:
[tex](c-a)^{b}[/tex] Equation
Step 3:
[tex]( 10 - 3)^{2}[/tex] Input values
Step 4:
( 7 ) ² Parentheses
Answer:
49
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Answers
Answer:
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Step-by-step explanation:
Answer:
19.2
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Step-by-step explanation:
A logo is drawn inside a rectangle.
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Answers
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Step-by-step explanation:
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James is a journalist with an annual income of $85,350. James has to pay an income tax of 8%. What is the amount of income tax in dollars and cents that James has to pay? 7.13A
Answers
Answer: $6828
Step-by-step explanation:
James annual income = $85350
Income tax = 8%
The amount of income tax in dollars and cents that James has to pay will be calculated by multiplying the income tax by his annual income. This will be:
= 8% × $85350
= 8/100 × $85350
= 0.08 × $85350
= $6828
Select all polynomials that have (x – 3) as a factor.
Answers
In other words, everything but choice B
==========================================================
Explanation:
You could use polynomial long division or synthetic division to check each answer. The shorter route of the two options is synthetic division
There's a much faster way that doesn't involve complicated division. Recall that if (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
------------------------------------------------
Here's a fairly short proof:
Consider a polynomial q(x) such that
p(x) = (x-k)q(x)
which shows that (x-k) is a factor of p(x). We don't need to worry about what q(x) actually is since it will go away effectively.
If we plug x = k into the p(x) function, we get
p(x) = (x-k)q(x)
p(k) = (k-k)q(k)
p(k) = 0*q(k)
p(k) = 0
------------------------------------------------
How is this useful? Well we can note that the factor (x-3) is in the form (x-k) where k = 3.
So the idea is to plug x = 3 into each of the four functions and see which result in 0. If we get 0 as an output, then we have a factor. Otherwise, it's not a factor.
-------------------------------------------------
Plug x = 3 into the first function
A(x) = x^3 - 2x^2 - 4x + 3
A(3) = 3^3 - 2(3)^2 - 4(3) + 3
A(3) = 0
This shows (x-3) is a factor of the function A(x)
------------------------------------------------
Repeat for the second function
B(x) = x^3 + 3x^2 - 2x - 6
B(3) = 3^3 + 3(3)^2 - 2(3) - 6
B(3) = 42
We don't get an output of 0, so (x-3) cannot be a factor of B(x)
-----------------------------------------------
Now onto the third function
C(x) = x^4 - 2x^3 - 27
C(3) = 3^4 - 2(3)^3 - 27
C(3) = 0
So (x-3) is a factor of C(x)
----------------------------------------------
Finally the last function
D(x) = x^4 - 20x - 21
D(3) = 3^4 - 20(3) - 21
D(3) = 0
Therefore (x-3) is a factor of D(x) as well.
The remainder theorem will be used to identify the polynomial that has a remainder of zero when divided by (x - 3)
The polynomials that have 0 as a factor are;
(C) C(x) = x⁴ - 2·x³ - 27(D) D(x) = x⁴ - 20·x - 21Reason:
According to the remainder theorem, we have;
The remainder following the division of a polynomial, by (x - a) is P(a)
Therefore, (x - 3) is a factor of the polynomial P(x) where P(3) = 0
For option (A), we have; A(x) = x³ - 2·x² - 4·x + 3
The remainder when (x³ - 2·x² - 4·x + 3) is divided by (x - 3) is therefore;
A(3) = 3³ - 2 × 2² - 4 × 2 + 3 = 14
Therefore, (x - 3) is not a factor of A(x) = x³ - 2·x² - 4·x + 3
For option (B), we have;
B(x) = x³ + 3·x² - 2·x - 6
The remainder when B(x) is divided by (x - 3) is therefore;
B(3) = 3³ + 3×3² - 2×3 - 6 42
Therefore, (x - 3) is not a factor of B(x) = x³ + 3·x² - 2·x - 6
For option (C), we have;
C(x) = x⁴ - 2·x³ - 27
The remainder when C(x) is divided by (x - 3) is therefore;
C(3) = 3⁴ - 2×3³ - 27 = 0
Therefore;
(x - 3) is a factor of C(x) = x⁴ - 2·x³ - 27For option (D), we have;
D(x) = x⁴ - 20·x - 21
The remainder when D(x) is divided by (x - 3) is given as follows;
D(3) = 3⁴ - 20×3 - 21 = 0
Therefore;
(x - 3) is a factor of D(x) = x⁴ - 20·x - 21Learn more here:
https://brainly.com/question/11456067
Plz help will make brainiest.
Answers
The first two are correct for sure, the last one I’m pretty sure is also correct.
What is an equation of the line that passes through the points (-2,7) and (1, -8)?
Put your answer in fully reduced form.
Answers
What happens when we multiply conjugates
together?
Answers
The coach fare to a theme park costs $21 for 3 people, what would be the cost for 6 people?
A) $42 B) $63 C) $140
Answers
Answer:
42
Step-by-step explanation:
You add 21 twice because 3 is half of 6
Answer:
A - 42
Step-by-step explanation:
21 x 2 = 42
3 x 2 = 6
Write as an exponent with the base of b:
[tex]bb^{m}[/tex]
Answers
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[tex]b. {b}^{m} = {b}^{1 + m} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
A group of friends were working on a student film. They spent all their budget on props and costumes. They spent $693 on props, and 45% of the total budget on costumes. What was the total budget for their student film?
Answers
Answer:
The total budget is $1260
Step-by-step explanation:
Given
[tex]Props = \$693[/tex]
[tex]Costumes = 45\%[/tex]
Required
Determine the total budget
Since all budgets was spent on Props and Costumes only.
We have that.
[tex]\%Props + \%Costumes = 100\%[/tex]
[tex]\%Props + 45\%= 100\%[/tex]
[tex]\%Props= 100\% -45\%[/tex]
[tex]\%Props= 55\%[/tex]
In other words, 55% was spent on Props
Let the total budget be x, we have:
[tex]55\% * x = \$693[/tex]
Make x the subject
[tex]x = \$693/55\%[/tex]
[tex]x = \$1260[/tex]
Hence, the total budget is $1260
Factor Completely
f(x)= x^4 - 2x^3 - 3x^2 + 2x + 2
Answers
Decide if each statement about the expression 7f + 15 - 2g is true or false.
The expression contains 2 terms.
Answers
Answer:
FALSEStep-by-step explanation:
The statement "The expression contains 2 terms." is false because the expression contains 3 terms: 7f, 15 and -2g
The given statement "expression contains 2 terms" is false, Because it contains three terms of which two are the variable and one is a constant.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
The expression is,
7f + 15 - 2g
The given expression contains 2 terms.
A term is a single expression, a single integer (positive or negative), and a single variable (a letter), or a number of variables that have been multiplied but never added or canceled are all acceptable.
The given statement is false because it reported only two terms but there are more than two terms.
Thus, the given statement "expression contains 2 terms" is false Because it contains three terms of which two are the variable and one is a constant.
Learn more about the equation here,
https://brainly.com/question/10413253
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