Task: Use the following situation to answer Parts A and B Instructions At noon, a tank contains 100 gallons of water. The table shows the input and output of water from pipes A, B, and C. The pipes begin operating simultaneously at noon. A B C Pipe Flow IN (gallons per minute) a (2) = 172 6(2) = 80 Flow OUT (gallons per minute) c (2)=30r Complete each of the 2 activities for this Task. Activity 1 of 2 Let T (2) represent the amount of water in the tank x minutes after all of the pipes A, B, and C are opened. Which of the following functions represents T (x)? O A T (2) = 100 + a(z) +b(2) - c(x) OCT (x) = 100 + a (x) +b(2) + c(2) OBT () = a (x) + b() +(2) ODT (2) = a (x) +b(x) - c(:) Activity 2 of 2 Using the equation, after how many minutes will the tank be empty?
Answers
Answer:
1. Option C2. NeverStep-by-step explanation:
Refer to attached for the table and clearer version of the question
As per table A and B pipes feed the tank and C is the outlet
Considering initial volume of 100 gallons, the amount of water in the tank after x minutes is:
T(x) = 100 + a(x) + b(x) - c(x), this is option C.We can calculate when tank is going to be empty:
0 = 100 + 25x + 10x - 30x0 = 5x + 1005x = -100x = -20Since we got negative number, the tank is not going to be empty when all 3 pipes are open.
The function which represent T (x) for the tank which contains 100 gallons of water and input and output of water from pipes A, B, and C is,
[tex]T(x)=100+a(x)+b(x)-c(x)[/tex]
The tank will not be empty when all the three pipes are in operation.
What is a function?If we have two sets A and B as:
[tex]A = \{a_1, a_2, ... \}\\B = \{b_1, b_2, ... \}[/tex]
Then, function
[tex]f:A \rightarrow B[/tex]
is a connection of elements of A to B such that one element of A is connected to only single element of B, and not many.
The connected pairs are then written as:
[tex]\{(a_i_1,b_j_1), (a_i_2, b_j_2), ... \}[/tex]
Under the function f.
The table shows the input and output of water from pipes A, B, and C.
Pipe A B C
Flow In (gallons/minute) a(x)=25x b(x)=10x
Flow Out (gallons/minute) c(x)=30x
The pipes begin operating simultaneously at noon. Let T (2) represent the amount of water in the tank x minutes after all of the pipes A, B, and C are opened.
At noon, a tank contains 100 gallons of water. In the above table A and B shows the inlet of water while C shows the out let of the water.
So, 100, A and B added in the function while C will be subtracted as,
[tex]T(x)=100+a(x)+b(x)-c(x)[/tex]
Thus, the function in option C represents T (x).
Now use this equation, to find the number of minutes for the tank be empty. For this equation, the equation equal to zero as,
[tex]T(x)=100+25x+10x-30x[/tex]
[tex]0=100+25x+10x-30x\\-100=5x\\x=-20[/tex]
This negative value of x tells that if all the three pipes are open, the tank is never become empty completely.
Thus, the function which represent T (x) for the tank which contains 100 gallons of water and input and output of water from pipes A, B, and C is,
[tex]T(x)=100+a(x)+b(x)-c(x)[/tex]
The tank will not be empty when all the three pipes are in operation.
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Related Questions
(x + 8)(x-8)
answer choices
A x2 + 8x + 64
B x²-64
C x² + 64
x2 + 16X - 64
Answers
Step-by-step explanation:
we know the formula(x^2-y^2)=(x+y)(x-y)
so (x+8)(x-8)=x^2-8^2=x^2-64
so the right answer is B
Graph the line of the slope of 1/4 and includes the point (0,2)
Answers
Answer:
I'm on Edulastic.com taking a 100 Q test and this question is on it!
Step-by-step explanation:
Imao im fgging confused
The graph of the required line [tex]\bold{y=\frac{x}{4}+2}[/tex] is given below.
Slope point form of equation of line: -An equation of line with slope m and passing through point (p, q) is:
(y - q) = m × (x - p)
We have been given the slope of the line m = 1/4,
and a point (p, q) = (0, 2)
Using the slope-point form equation of line would be,
⇒ (y - 2) = 1/4 × (x - 0)
⇒ (y - 2) = 1/4(x)
⇒ y = x/4 + 2 ...............................(1)
So, the equation of the line is [tex]y=\frac{x}{4} +2[/tex].
To plot the line we need at least two coordinate points.
We have been given a point (0, 2).
We need to find another point.
Substitute x = -4 in equation (1),
⇒ y = (-4)/4 + 2
⇒ y = -1 + 2
⇒ y = 1
So, another point on the line would be (-4, 1).
Now, we plot points (0, 2) and (-4, 1) on coordinates plane.
Then the graph of the line [tex]\bold{y=\frac{x}{4}+2 }[/tex] is as shown in figure.
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Please help me i dont understand
Answers
the triangle is 4
the circle is 6
Answer:
5
4
6
.........................
Joe buys lunch at a local cafe for 8.60 if she leaves a 15% tip how much does she spend at the cafe
Answers
Answer:
dhvbhdvhdhddjbd
Step-by-step explanation:
Molly has three pairs of shoes. 1 cost $40, 2 cost $20, and 3 cost $25, if she got 50% off for all shoes, what price was each shoe?
Answers
Answer:
20, 10, 12.50
Step-by-step explanation:
You roll two dice. The first dice shows a ONE and the other dice rolls under the table and you cannot see it. Now, what is the probability that both dice show one?
Answers
how many faces does the dice have? I'm gonna assume it had six faces.
Answer:
1/6
Step-by-step explanation:
since the dice has one 1 on it and it cannot be seen
5. (01.07A MC)
Which number line best shows the position of ? (5 points)
J7
HHHH +
-4 -3
-1 0 1 2
+
4
-2
3
3
7
HHH H
-4 -3 -2 -1 0 1 2 3
+
4
7
HH
-4
-3 -2
-1 0 1 2
3
4
-
OL
7
t. +
3 4 5
-5 -4
-3 -2
-1 0 1 2
Answers
Answer:
if u could include a photo it may help more ..thanks
Math
What is the number of solutions in this system?
No solution
Infinitely many solutions
One solution
Answers
Answer:
should be Infinitely many solutions
Step-by-step explanation:
johanna prepares a mixture of salad mixed with mayonnaise carrots cucumber lettuce and cheese. what type of mixture divine salad is? why do you think so?
Answers
Answer:
johanna prepares a mixture of salad mixed with mayonnaise carrots cucumber lettuce and cheese. what type of mixture divine salad is? why do you think so
Mary has a bag with 80 pieces of candy. She gives ¼ of her candy to John and 10% to Lisa. How much more candy did she give to John then Lisa?
Answers
Answer:
12 pieces
Step-by-step explanation:
80 pieces of candy
1/4 is 25% or 20 pieces of candy
10% would be 8 pieces of candy
subtract the two. Your answer is 12
Answer:
He had 14 more pieces
Step-by-step explanation:
So 80/4 is 20 pieces. So we know John has 20. Now she has 60 left since 80-20 is 60. Now 10 percent of 60 would be 6 pieces. We can subtract 6 from 20 to find out how many more pieces John had. 20-6 is 14. So John had 14 more than Lisa
the abbreviation for the constant change in a graph or table?
Answers
Answer:
ROC
Step-by-step explanation:
ROC. rate of change
On a table or graph, the constant change is same as the unit rate, rate of change or slope, which can be denoted as m.
Constant change on a graph or table simply refers to the rate of change of the output (y) over the change in input (x).
Constant change in a graph or table is the same as the unit rate or the slope value which is dented by the letter m.
Constant rate of change, unite rate, and slope can be denoted as m of a graph or table.
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The random variables X and Y are jointly continuous, with a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,otherwise, where c is a normalizing constant. For x∈[0,0.5] , the conditional PDF fX|Y(x|0.5) is of the form axb . Find a and b .
Answers
Answer:
The value of a and b are 8 and 1 respectively
Step-by-step explanation:
[tex]f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 , \text{otherwise}\end{matrix}\right.[/tex]
[tex]\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1\\\\c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1\\\\\frac{c}{2}\int_{0}^{1}x\left ( 1-y^2\right )\text{dx}=1\\\\\frac{c}{2}\int_{0}^{1}(x-x^3)\text{dx}=1\\\\\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1\\\\\frac{c}{2}\left [ \frac{1}{2}-\frac{1}{4} \right ]=1\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1\\\\c=8[/tex]
Conditional pdf of [tex]f_{x,y}(x|0.5)[/tex]
[tex]f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}[/tex]
Normalizing pdf of 1
[tex]f_{y}y=\int_{0}^{y} 8yx \text{dx}[/tex]
[tex]f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\\f_{y}y=4y(y^2)\\f_{y}y=4y^3\\f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}=\frac{2x}{0.25}=8x[/tex]
We are given that PDF [tex]f_{x|y}(x|0.5)[/tex] is of the form [tex]ax^b[/tex]
So, on comparing 8x with [tex]ax^b[/tex]
So, a = 8 , b = 1
So, the value of a and b are 8 and 1 respectively
The resulting value of a and b given the conditional PDF of fX|Y(x|0.5) is mathematically given as
a = 8 , b = 1 .
What are the values of a and b?Question Parameters:
a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,
For x∈[0,0.5]
the conditional PDF fX|Y(x|0.5)
Generally, the equation for the function of (x,y) is mathematically given as
[tex]f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 ,\end{matrix}\right.[/tex]
Therefore
[tex]\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1[/tex]
[tex]c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1[/tex]
[tex]\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1[/tex]
[tex]\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1[/tex]
C=8
Where, the conditional PDF fX|Y(x|0.5)
[tex]f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}[/tex]
We have
[tex]f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\[/tex]
[tex]f_{y}y=4y^3[/tex]
[tex]f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}[/tex]
f_{x|y}(x|0.5)=8x
In conclusion. with the pdf in the form of ax^2
8x comparing ax^b
The value of a = 8 , b = 1 .
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Laura had 192 dollars to begin with. She just spent b dollars. Using b, write an expression for the number of dollars she has left
Answers
Answer:
$192-$b
Step-by-step explanation:
If Laura had $192 and she spent $b, the expression is $192-$b. Hope it helps!
The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch.
Answers
Answer:
what is the answerrrrrrrStep-by-step explanation:
Is 8(3x+2) and 4(6x÷4) equivalent?
Answers
Answer:
x= - 8/9
Step-by-step explanation:
Don’t understand this question
Answers
not positive but pretty sure
Which lines are perpendicular to the line y - 1 = {(x+2)? Check all that apply.
Oy + 2 = -3(x - 4)
Oy- 5 = 3(x + 11)
Oy=-3x -
5
y y = 1x-2
=
3x + y = 7
Answers
Answer: A C E
Step-by-step explanation:
y = -1x-2 is the perpendicular line of the given line y - 1 = {(x+2).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The product of slope of perpendicular lines will be equal to minus one.
y-1=x+2 the line has a slope of +1.
The slope of the perpendicular line will be -1.
y = -1x-2 is the perpendicular line of the given line y - 1 = {(x+2).
Hence, y = -1x-2 is the perpendicular line of the given line y - 1 = {(x+2).
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2k=18. find the value of k
Answers
because 18/2 is 9
Answer:
Step-by-step explanation:
18 divided by 2 would be 9 so k=9
Solve two-step equations
2 = 4s + –10 i need it ASAP
Answers
Answer:
s=3
Step-by-step explanation:
Answer:
s=3
Step-by-step explanation:
simplify the equation to the form, which is simple to understand
and then move all terms containing s to the left and all other terms to the right!
7th grade math help me plzzzz
Answers
Answer:
B.
Step-by-step explanation:
Answer:
0.05 per ounce
Step-by-step explanation:
5.20 per 40 is 0.13 per ounce
whereas
2.70 per 15 is 0.18 per ounce
Helpppppppppppppppppppppppppppppppppppp
Answers
pls look at the picture attached! i need help
Answers
it is 9 aahh it says to short well 3 times 9 is 27 then minus 17 is less than 13
Answer:
v <= 10
(-infinity, 10]
Step-by-step explanation:
3v - 17 <= 13
+17 +17
3v <= 30
3v/3 30/3
v <= 10
(-infinity, 10]
Which statement about -8 and
-12 is true?
Answers
Answer:they are both neagtive numbers.
Step-by-step explanation:
they say it right in front of you.
Lin rode her bike 2 miles in 8 mins. She rode at constant speed. Complete the table to show the time it took travel different distances at this speed
Answers
Answer:
4, 1
Step-by-step explanation:
If you take 2, 8 and make it a ratio you get 2 : 8.
Then you turn 2 : 8 into 1 : 4. That is your answer for a mile.
For the other answer, you want to divide 2 by 8.
(Hope this helps) :)
15,420 divided by 20 =
Answers
Answer:
771
Step-by-step explanation:
Question 1
Manipulate the base area and the height of the pyramid, setting different values for each. Record the base dimensions, height, and the exact
volume for two kinds of pyramids: one with a square base and one with a rectangular base. Also calculate the decimal value of each volume, and
verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answers
Answer:
Step-by-step explanation:
89.95 DVD player; 5% discount
Answers
Answer:
The answer is $85.45 after the 5% discount
Damien left his house at time Zero and drove to the store, which is 12 blocks away, at a speed of 6 blocks per minute. then he stopped and went into the store for 5 minutes. from there, he drove in the same direction at speed of 2 blocks per minute until he got to the bank, which is 12 blocks away from the store. he stopped at the bank for 2 minutes. then he drove home at a speed of 6 blocks every minute. make a graph of showing the number of blocks away from home that Damien is x minutes after he leaves his house, until he gets back home.
Answers
Answer:It take her 20 minutes, but I dont know how to graph yet, so I can only tell you that xx=20
A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says, “The snail was traveling faster because it went a greater distance.”
Answers
Answer:
Mai is wrong since both travel the same distance in the same amount of seconds
Step-by-step explanation:
3 centimeters in 3 seconds is 1 centimeter a second for the slug
6 centimeters in 6 seconds is 1 centimeter a second for the snail
so both travel the same distance
Answer:
No, she is wrong. They are both going the same pace.
Step-by-step explanation:
3 centimer divided by 3 is 1. 1 cm a second. 6 centimeters didvided by 6 is 1.
1 cm a second. Hence they are both going the same speed. If you don't understand anything comment and ill explain more. Please heart and 5 stars and brainlest if you don't mind
what is the 12
th term rule of the linear sequence 13 7 1 -5 -11
Answers
Answer:
-53, f(n) = -6(n-1) + 13
Step-by-step explanation:
given the equation to this linear/arithmetic sequence for the nth term: f(n) = -6(n-1) + 13
f(12) = -6(12-1) + 13
f(12) = -6(11) + 13
f(12) = -66 + 13
f(12) = -53
*substitute and simplify*
______________
f(n) = f(1) + d(n-1)
given f(1) = 13, f(2) = 7, and f(3) = 1
7-13 = 1-7 = -6 = d
= f(1) + d(n-1)
f(1) = 13 so
the equation must be f(n) = 13 - 6(n-1) or -6(n-1) + 13