The linear equation that models the school’s graduating class size (y) in terms of the year (x) after 2015 is given as y = 24x + 257
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
Let y represent the graduating class size in terms of the year (x) after 2015.
Kyle’s older brother’s class had 257 students when he graduated in 2015. That is (0, 257)
In 2018, and his class has 329 students, That is (3, 329)
The linear equation is calculated using (0, 257) and (3, 329):
y - 257 = [(329 - 257)/(3 - 0)](x - 0)
y - 257 = 24x
y = 24x + 257
The linear equation is given as y = 24x + 257
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noah is running a portion of a marathon at a constant speed of 6 miles per hour.
The miles he ran in 4/3 hours at a constant speed of 6 miles per hour is 8 miles.
What is the average speed?The average speed is the ratio of total length traveled to total time taken to travel that length. Average speed is the total distance travelled per time.
Average speed = the total distance / total time
Given that Noah's average speed is 6mph
From the above formula, to determine miles run is average speed x time
The Total miles he ran in 1 hour = 6 x 1 = 6 miles
Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles
Total miles he ran in 1 and 1/3 hours = 6 x 4/3 = 8 miles
The formula for the total time: total distance / average speed
The Time it took Noah to run 1 and 1/2 miles = 3/2 ÷ 6 = 1/4
Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2
Time it took Noah to run 4 and 1/2 miles = 9/2 ÷ 6 = 3/4
The miles he ran in 4/3 hours at a constant speed of 6 miles per hour is 8 miles.
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The complete question is
Noah is running a portion of a marathon at a constant speed of 6 mph. Complete the table to predict how long it would take him to run different distances at that speed and how far he would run in different time intervals.
Time in hours Miles traveled at 6mph
1.
1/2
1 1/3
1 1/2
9
4 1/2
3x - 4y ≥ 12 slope intercept form
A chicken soup recipe calls for 13 cups of chicken stock. How much is this in quarts?Write your answer as a whole number or a mixed number in the simplest form. Include the correct unit in your answer.
ANSWER
[tex]3\frac{1}{4}qt[/tex]EXPLANATION
We want to find how much chicken stock will be needed in quarts.
To convert a value from cups to quarts, we have to divide it by 4.
Therefore, the amount of chicken stock needed, in quarts, is:
[tex]\begin{gathered} \frac{13}{4} \\ \Rightarrow3\frac{1}{4}qt \end{gathered}[/tex]That is the answer.
The undergraduate library at State U tends to have 33.4 students enter every hour during normal operation. Over the next two hours, what is the probability at least 75 students arrive at the library?
The probability that at least 75 students arrive at the library is 0.1440.
How to calculate the probability?From the information, the undergraduate library at State U tends to have 33.4 students enter every hour during normal operation.
The expected number of students for the two hours will be:
= 2 × 33.4
= 66.8
The probability that at least 75 students arrive at the library will be:
P(x >= 75) = 1 - P(x <= 74)
This will be looked at in the distribution table
= 1 - 0.8560
= 1.440
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Brian's final exam in math had two parts. He had a total of 60 minutes to complete the entire exam. He spent 15 minutes on Part 1 of the exam. Write and solve an equation to show how much time he had left to complete Part 2.
m over 15 equals 60; m = 900 minutes
m − 15 = 60; m = 75 minutes
15 + m = 60; m = 45 minutes
15m = 60; m = 4 minutes
Answer:
15 + m = 60; m = 45 minutes
Step-by-step explanation:
Hello!
According to the question He had a total of 60 minutes to complete the entire exam. He spent 15 minutes on Part 1 of the exam. how much time he had left to complete Part 2.
Let's make an equation where the time spent on part 1 which is 15 + m which is minutes remaining for part 2 is equal to Total minutes which is 60 minutes
So, if we put it together;
15 + m = 60
So, let's solve for m
15 + m = 60
Substract 15 from both sides
15 - 15 + m= 60 - 15
m = 45
So, the equation is 15 + m = 60 and he had 45 minutes of time remaining to complete part 2.
Factor 16cd − 56c2d.
--------------------------------
Show your work.
The factorised form of the algebraic expression 16cd − 56c²d as given in the task content is; 8cd (2 - 7c).
What is the factorised form of the expression 16cd − 56c²d?It follows from the task content that the factorised form of the expression; 16cd − 56c²d as given is to be determined.
Since the given expression is;
16cd − 56c²d
First, each of the terms can be factored as follows;
16cd = 2 × 2 × 2 × 2 × c × d
56c²d = 2 × 2 × 2 × 2 × 7 × c × c × d
Therefore, since the factors which are common to both terms as follows; 2 × 2 × 2 × c × d = 8cd.
Therefore the factorised form of the expression is;
8cd (2 - 7c).
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To rent a car for a trip, 4 friends are combining their money. The
table shows the amount of money that each puts in. One expression for their
total amount of money is 137+b+212 +c. Use a Commutative Property to
find equivalent expressions.
Use pencil and paper. If they need $700 to rent a car, find at least two
different pairs of numbers that friends B and D must put in.
Friend
A
B
C
D
Travel Fund
Amount (dollars
137
212
с
Which expressions below are equivalent to 137 +b +212 + c by a Commutative Property? Select all that apply.
Answer: 1049
Step-by-step explanation:
SOMEONE PLEASE HEP. determine if these triangles are similar and choose the correct postulate.
Answer:
C). Or SAS~with 3/2 proportionate sides.
Step-by-step explanation:
You can tell because the similar angle shows which sides should be proportional to the other on the corresponding triangle, and of those sides, 6/4 = 10.5/7
Easily simplifying to 3/2 both times to find the rate at which the side lengths where changed.
Hope this helps.
Use what you know about domain to select all of the following functions that could be the one graphed.
Using transformations, the functions that could represent the one graphed are given as follows:
y = sqrt(x) - 3.y = sqrt(x) - 1.What is a transformation?A transformation is when a function undergoes a change in it's definition. Depending on the type of the transformation, the function can keep the same orientation, same side lengths, and so on.
In the context of this problem, the function kept the same orientation, it just changed it's position, hence the type of transformation that the function underwent was a translation.
The possible translations are given as follows:
Translation down, changing the range.Translation up, changing the range.Translation left, changing the domain.Translation right, changing the domain.The domain of the graphed function is given by:
x ≥ 0.
Which is the same domain as the parent square root function, given as follows:
y = sqrt(x).
From the graph, the function was translated down a units, changing it's range, hence the function has the following format:
y = sqrt(x) - a.
Hence the first two options can be correct, either with a = 1 or with a = 3. The last two options change the range but not the domain, hence they are incorrect.
What is the missing information?The image at the end of the answer gives the complete problem.
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Please help me with this question thank you
As given by the question
There are given that the expression
[tex]22=\frac{a}{5}[/tex]Now,
Multiply by 5 on both side of the equation
So,
[tex]\begin{gathered} 22=\frac{a}{5} \\ 22\times5=\frac{a}{5}\times5 \\ 22\times5=a \\ 110=a \end{gathered}[/tex]Hence, the value of a is 110.
write an equation to describe the relationship between w and z w: | 18 | 45 | 81z: | 2 | 5 | 9
Notice that the values for w are multiples of 9, and their respective factor is expressed on the values of z. Therefore, the equation to describe the relationship between w and z is w=9z
Calculate the expected value of the scenario.
Expected value:
[tex]E(x)=\Sigma(x_i*p(x_i))[/tex]For the given scenario:
[tex]E(x)=(1*0.25)+(2*0.38)+(3*0.03)+(4*0.16)+(5*0.18)[/tex][tex]E(x)=0.25+0.76+0.09+0.64+0.9[/tex][tex]E(x)=2.64[/tex]Then, the expected value is 2.64In your book copy and complete the image below work out the what number replaces then ? to simpfly the ratio 8:12
Answer:
2:3
Step-by-step explanation:
Calculate the pay for the following day of a weekly time card given a wage of $14.50/hr. Name Week of: SI Morning lo Out Monday | 08:15 12:15 Afternoon In Out 13:00 17:30 pay = $[?] Round your answer to the nearest hundredth. Can you please just give me the direct answer for the pay cause I don't have mutch time to answer this problem.
As we can see in the card, on Monday the worker clocked in at 08:15 and clocked out at 12:15. This means they worked 4 hours.
They then clocked in at 13:00 and clocked out at 17:30. This means they worked for 4 and a half hours.
Since they earn a wage of $14.50/h, they earned:
[tex](4+4.5)\cdot14.50=8.5\cdot14.50=123.25.[/tex]So that day they earned $123.25
Who knows answer to this?
An individual with $36,000 in taxable
income pays $970 for the 10% tax
bracket, and $3,156 for the 12% bracket.
What is the overall federal income tax
payment for this individual?
A. $32,900
C. $4,126
B. $2,136
D. $3,656
The federal income tax is levied against the yearly profits of people, companies, and other legal entities. The overall federal income tax payment of this individual will be $4126.
What is federal Income tax?The federal income tax is levied against the yearly profits of people, companies, and other legal entities. Federal income taxes are due on all compensation, including salaries, monetary gifts from employers, business profits, tips, winnings from gaming, bonuses, and unemployment benefits.
Income taxes are levied by the federal government and the majority of states in the US. Income taxes, which may be incurred as income increases, are produced by applying a tax rate to taxable income, which is the total income less allowable deductions.
The overall federal income tax payment of this individual exists $970 + $3,156 = $4126.
The taxable income of the individual will be $4126.
Therefore, the correct answer is option C. $4,126.
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Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of
(fx)=1 / 1/2
and the x axis between x=2 and x=5.
Volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.
As given,
Volume of solid of revolution formed by rotating about the x-axis region between the graph of f(x)= x /2:
Volume = π∫[f(x)]²dx
⇒Volume =π∫(x/2)²dx
⇒Volume =(π/4)∫x²dx
⇒Volume =(π/4) (x³/3)
=(π/12)(x³)
x axis between x=2 and x=5
Volume =(π/12)(125-8)
=117π/12 unit³
Therefore, volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.
The complete question is:
Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of
f(x)= x /2
and the x axis between x=2 and x=5.
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Add (7x^3-2x^2-5x+6) and (2x^3+3x^2-x-1)
Answer:
(9x^3+x^2-6x+5) is the answer to algebra equation
Identify the parent function for the function g (x) = x + 4 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.Linear; translation up 4 unitsConstant; translation up 4 unitsLinear; translation down 4 unitsConstant; translation down 4 units
linear; translation up 4 units
Explanation:The given function is:
g(x) = x + 4
This is of the form:
y = mx + c
where m is the slope and c is the y-intercept
Therefore, g(x) is a linear function
The parent function is:
g(x) = x
g(x) = x + 4 means that the function is translated up 4 units
find the difference between 289.6 and 99.9
Answer:
189.7
Step-by-step explanation:
Hope it helps! =D
please please help me out
.
[tex]Pr(x)=\sum_{x\mathop{=}0}^nnC_x\times p^x\times q^{n-x}[/tex][tex]x=0,\text{ n=43, p=}\frac{1}{124},\text{ q=1-}\frac{1}{124}=\frac{123}{124}[/tex][tex]Pr(x=0)=43C_0\frac{}{}\times(\frac{1}{124})^0\times(\frac{123}{124})^{43}=0.71[/tex]For the soccer team fundraiser, you carn 5 points
for every $3 you raise. If Tyson carned 85 points,
how much money did he raise?
Answer:
He raised 51 dollars
Step-by-step explanation:
If for every 5 points he raised 3 dollars he would have raised 51 dollars because he had 85 points.
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
The coordinates of point A are (-2,5). The coordinates of point B are (3,5). Which expression represents the distance, in units, between A and B?
The distance expression of the number of units between points A and B is √[(-2 - 3)^2 + (5 - 5)^2]
How to determine the expression of the distance between A and B?From the question, we have the following parameters:
The coordinates of point A are (-2,5). The coordinates of point B are (3,5).This means that
A = (-2, 5)
B = (3, 5)
The distance between the points is calculated as
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Where
A = (x1, y1) = (-2, 5)
B = (x2, y2) = (3, 5)
Substitute the known values in the above equation
So, we have
Distance = √[(-2 - 3)^2 + (5 - 5)^2]
The question does not imply that the we simplify the above expression
So, we leave the expression unsimplified
Hence, the expression of the distance between A and B is √[(-2 - 3)^2 + (5 - 5)^2]
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simplify the expression -1/3x-12+1/2x-2
Answer:
Step-by-step explanation:
x-84/6
Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is V = 3/4pi r^3 and its surface
area is 4pi r². Determine the rate at which the surface area is changing with respect to time when r = 40 cm.
(Use symbolic notation and fractions where needed.)
Answer:
The rate at which the surface area is changing with respect to time when r = 40 cm is 22400π cm²/min
Not sure if you want it in absolute values since the question says use symbolic notation but if so, multiplying by π gives 70371.675 cm²/min
Step-by-step explanation:
[tex]\text {Volume of a sphere of radius r is given by }\\\\ \text {$V = \dfrac{3}{4}\pi r^3$}[/tex]
The surface area of a sphere of radius r is given by:
[tex]\\S = 4\pi r^2\\[/tex]
The rate of change of surface area is given by
[tex]\dfrac{dS}{dt} = \dfrac{d}{dt}\left(4\pi r^2\right)}\\\\\dfrac{dS}{dt} = 4 \pi \dfrac{d}{dt}\left( r^2\right)}\\\\\\\dfrac{d}{dt}(r^2) = 2r\dfrac{dr}{dt}\\\\\\[/tex]
[tex]\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}[/tex]
We are given that [tex]\text{$\dfrac{dr}{dt}$}[/tex] = 70 cm/min and asked to find rate of change of S when r = 40 cm
Substituting these values into the equation for [tex]\dfrac{dS}{dt}[/tex]
[tex]\dfrac{dS}{dt} = 8 \pi \cdot 40 \cdot 70\\\\\\\\\dfrac{dS}{dt} = 22400 \pi \;cm^2/min[/tex]
In absolute values
D
Let a be a number such that 15 < a < 50, and let b be
a number such that 40 < b < 70. Which of the
following represents all possible values of a - b?
A. -55 < a - b < 10
B. 20
C. -55 < a - b <-20
D. -25 < a - b < 10
Answer:
A
Step-by-step explanation:
Please see no 17 attached.
To convert the number given in base 7 to a bse 10 number we follow the procedure shown, that is, we need to multiply each number by the appropiate power of seven (given by their position) and then add them, then we have that:
[tex]\begin{gathered} 21603_{\text{seven}}=(2\times7^4)+(1\times7^3)+(6\times7^2)+(0\times7^1)+(3\times7^0) \\ 21603_{\text{seven}}=5442_{\text{ ten}} \end{gathered}[/tex]Therefore:
[tex]21603_{\text{seven}}=5442_{\text{ ten}}[/tex]WHAT IS GCF OF 35 AND 28 TELL ME WITH MULTIPLES
Answer:
i think it is 7 but not sure
Step-by-step explanation:
GCF of 28 and 35 is the largest possible number that divides 28 and 35 exactly without any remainder. The factors of 28 and 35 are 1, 2, 4, 7, 14, 28 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 28 and 35 - prime factorization, Euclidean algorithm, and long division.
Question
Consider the function f(x) = 4x² +9 for x ≤ 0.
What is the domain of f-1(x)? Write your answer in interval notation.
Provide your answer below:
The domain of f⁻¹(x) is (9,∞).
The function we have is
f(x) = 4x² + 9 for x ≤ 0
Now, let us find the inverse of the function f(x),
To find the inverse of f(x),
Replacing f(x) with f(y)
f(y) = 4y² + 9
Now the equation is,
x = 4y² + 9
y² = (x-9)/4
y = √(x-9)/2
The inverse of f(x) is,
f⁻¹(x) = √(x-9)/2
The domain of √(x-9)/2 can be found as,
(x-9)>0
x>9
The domain of f⁻¹(x) is (9,∞).
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