Answer: It's B.
Step-by-step explanation: I took the test.
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?
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.
Learn more about the function here;
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Please help i will give brainliest
Can you use the same multiplication fact to find 4x60 and 3x80
Answer:
Yes you can
Step-by-step explanation:
I need help math is a pain
Answer:
The answer is A because A has 9 zeroes behind 3.5
14. Solve and check the solution .2x + 1/3 =
4/3*
O X = 1/3
O X = 1/2
[tex]2x + \frac{1}{3} = \frac{4}{3} [/tex]
[tex]2x = \frac{4}{3} - \frac{1}{3} [/tex]
[tex]2x = \frac{3}{3} [/tex]
[tex]2x = 1[/tex]
[tex]\color{hotpink}x = \frac{1}{2} [/tex]
Therefore , the correct option is :-
[tex]\color{yellow}\mapsto\color{teal}x =\color{magenta} \frac{1}{2} [/tex]
Please Help Due Soon!
y = 1/3x +b
1 = 1/3(9) +b
1 = 3 +b
subtract 3 from both sides
-2 = b
y = 1/3x - 2The graph and the table show 2 different bicycle riders. Each rider travels at a constant speed. Compare the speeds of the two riders.
Answer:
C
Step-by-step explanation:
Round off to the highest place value of 5658
Answer:
6000
Step-by-step explanation:
You want to make the 5 a 6 and zero's for the rest. You make the five a six because if the number is 5 or higher you bump it up one number, if it is 4 or lower you don't need to bump it up or down. I hope this helps!
Place values is the value of a digit in relation to its position
5658 approximated to the highest place value is 6000
The number is given as:
[tex]\mathbf{Number = 5658}[/tex]
The number is in thousands; so, the highest place value is thousands
This means that the number must be approximated to thousands.
When 5658 is approximated to the nearest thousands, the approximated value is:
[tex]\mathbf{Approximated = 6000}[/tex]
Hence, 5658 approximated to the highest place value is 6000
Read more about place values at:
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Paige mows 1/4 acre in 1/2 hour. How many acres does Paige mow per hour? Paige mows acre per hour.
Answer:
Paige mows 1/2 acre per hour
Step-by-step explanation:
1/4=.25
1/2=.5
.25*2=.50
.50*2= 1
In a recent car study, 55% of the cars tested failed the safety test. If 231 cars failed the test. How many cars were tested.?
Answer:
420 Cars were tested
Step-by-step explanation:
231×100÷55=420
Mary loves to read. She reads almost everyday! On Monday, she read for 145 minutes . On Tuesday and Wednesday, she read for 459 minutes. How many minutes total has she read so far this week?
Answer:
604 minutes
Step-by-step explanation:
145+459=604
A student uses the following steps to prove the sine sum identity. The proof is incorrect. Which steps is incorrect
Answer:
4
Step-by-step explanation:
The incorrect step is Step 4, cos (π/2 -x) cos(-y) + sin (π/2 -x)sin(-y), the correct option is C.
What is Trigonometric Identity?Trigonometric Identities are based on the trigonometric ratios used to solve Trigonometric equations.
The steps used to solve the trigonometric identity are :
Step 1 : sin(x+y)
Step 2: cos ((π/2) - (x+y))
Step 3 : cos ( (π/2 -x) -y)
Step 4 : cos (π/2 -x) cosy + sin (π/2 -x)siny
Step 5: sinxcosy+cosxsiny
Therefore,the correct step is cos (π/2 -x) cosy + sin (π/2 -x)siny and not cos (π/2 -x) cos(-y) + sin (π/2 -x)sin(-y) , the incorrect step is Step 4.
The complete question is attached with the answer.
To know more about Trigonometric Identity
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A tennis racket is normally priced at 90.00 is on for 30% off. What is an expression for the sale price of the racket,
Answer:
90×0.7
Step-by-step explanation:
I think this is the correct answer.
100-30=70
70=0.7
Rectangle A is enlarged to create Rectangle B.
Rectangle A measures 4.1 cm by 5.2 cm.
Rectangel B measures 12.3 cm by 15.6 cm.
What is the scale factor?
Answer:
itz 5
Step-by-step explanation:
i took quiz
Marissa spent $56 at the flea market. She spent 1/4 of her money for
lunch. How much did Marissa spend on lunch?
Answer:
she spent $14
Step-by-step explanation:
1/4=0.25
0.25 x 56= 14
need help plz can someone please help
Answer:
D
Step-by-step explanation:
Answer:
d. 40
Step-by-step explanation:
If a room has 28 people in it, how many people Are in a room 14 times it’s size?
Answer:
392
Step-by-step explanation:
times 28 by 14 and youll get 392 - may i get brainliest :)
Answer:
392 people would be in the room
Step-by-step explanation:
you do 8 times 4 which is 32 then you multiply 8 times 10= 80 add them together 112, then multiply 20 times 4= 80, finally 10 time 20=200 add all together it equals 392
During the 2004 senatorial campaign in a large southwestern state, illegal immigration was a major issue. One of the candidates argued that illegal immigrants made use of educational and social services without having to pay property taxes. The other candidate pointed out that the cost of new homes in their state was 20–30% less than the national average due to the low wages received by the large number of illegal immigrants working on new home construction. A random sample of 5,500 registered voters was asked the question, "Are illegal immigrants generally a benefit or a liability to the state’s economy?" The results were as follows: 3,500 people responded "liability," 1,500 people responded "benefit," and 500 people responded "uncertain."
a. What is the population of interest?
b. What is the population from which the sample was selected?
c. Does the sample adequately represent the population?
d. If a second random sample of 5,000 registered voters was selected, would the results be nearly the same as the results obtained from the initial sample of 5,000 voters? Explain your answer.
Answer:
a
The population of interest is the registered voters , this is because it is the population from which the sample size is selected from.
b
The population is the registered voters of the large southwestern state
c
Well this does not adequately represent the population because this sample where selected from only the registered voters of the large southwestern state and not the whole country
d
Yes the result will be nearly the same because
Both samples are selected from the same population The size of the sample selected is sufficiently large to approximate the populationStep-by-step explanation:
From the question we are told that
The sample size is n = 5,500
Considering question a
What is the population of interest
The population of interest is the registered voters , this is because it is the population from which the sample size is selected from.
Considering question b
What is the population from which the sample was selected
The population is the registered voters of the large southwestern state
Considering question c
Does the sample adequately represent the population
Well this does not adequately represent the population because this sample where selected from only the registered voters of the large southwestern state and not the whole country
Considering question d
Yes the result will be nearly the same because
Both samples are selected from the same population The size of the sample selected is sufficiently large to approximate the populationWhat is (21/6) * (-3 3/4)? :
Answer:
...
Step-by-step explanation:
...
what is the ratio of 6 to 26 expressed as a fraction in simplest from?
Answer:
8 : 5
simple math
Jasmine wrote a number that is the opposite of -3. What
number did Jasmine write?
0 1/3
3
0
-3
Answer:
3
Step-by-step explanation:
This is because its the opposite.
Jasmine would write 3.
Hope this helps!!
Answer:
c
Step-by-step explanation:
Which of the following are polynomials?
What value of x makes this equation true?
0.5x – 8= 0.2x + 7
Based on experience, Farmer Fern knows that 15% of her eggs will be damaged in
route to the stores. In a sample of 100 eggs, what is the probability that less than
13% will be damaged?
Answer: 0.2877
Step-by-step explanation:
Given : The proportion of eggs will be damaged in route to the stores = 15% = 0.15
Sample size = 100
Let p be the probability of her eggs will be damaged.
The probability that less than 13% will be damaged is given by :-
[tex]P(p<0.13)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}<\dfrac{0.13-0.15}{\sqrt{\dfrac{0.15\times(1-0.15)}{100}}})[/tex]
[tex]=P(z<-0.56)[/tex]
[tex]=1-P(z<0.56)\\\\= 1-0.7123\\\\= 0.2877[/tex]
Hence, the required probability = 0.2877
Which graph matches the exponential function f(x) = 2(1.5)x?
Answer: its nit the 3rd one i just took the test
Step-by-step explanation:
Find the value of the missing angles ?
Help please for question
Last year a sports team made $2,000,000 in profit, and this year it increased its profits
to $2,500,000. How much money was made on food sales in both years based on how
the sports team makes its profits:
• Programs: 15%
• Food: 40%
• Souvenirs: 25%
• Tickets: 20%
1,000,000
2,500,000x0.4 (40 as a decimal) = 1,000,000
Can someone help me ASAP
Answer:
the y intercept is -4 and the slope is 1
Step-by-step explanation:
Point A is at (-2, 4) and point M is at (2.5, 3.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
Coordinates of point B: (7, 3)
Step-by-step explanation:
Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),
let [tex] A(-2, 4) = (x_2, y_2) [/tex]
[tex] B(?, ?) = (x_1, y_1) [/tex]
[tex] M(2.5, 3.5) = (\frac{x_1 +(-2)}{2}, \frac{y_1 +(4)}{2}) [/tex]
Rewrite the equation to find the coordinates of B
[tex] 2.5 = \frac{x_1 - 2}{2} [/tex] and [tex] 3.5 = \frac{y_1 + 4}{2} [/tex]
Solve for each:
[tex] 2.5 = \frac{x_1 - 2}{2} [/tex]
[tex] 2.5*2 = \frac{x_1 - 2}{2}*2 [/tex]
[tex] 5 = x_1 - 2 [/tex]
[tex] 5 + 2 = x_1 - 2 + 2 [/tex]
[tex] 7 = x_1 [/tex]
[tex] x_1 = 7 [/tex]
[tex] 3.5 = \frac{y_1 + 4}{2} [/tex]
[tex] 3.5*2 = \frac{y_1 + 4}{2}*2 [/tex]
[tex] 7 = y_1 + 4 [/tex]
[tex] 7 - 4 = y_1 + 4 - 4 [/tex]
[tex] 3 = y_1 [/tex]
[tex] y_1 = 3 [/tex]
Coordinates of point B: (7, 3)
Answer:
Coordinates of point B: (7, 3)
Step-by-step explanation:
Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),
Rewrite the equation to find the coordinates of B
Coordinates of point B: (7, 3)
Within six (6) weeks, four (4) colleagues in your department will make an important project. After the project, they were given Php100,000.00 as prize. Give the following amount of contribution each of their member exerted in making the project. How should the prize be divided to the members?
• Member A has made 25% of the total project.
• Member B has made 40% of the total project.
• Member C has made 25% of the total project.
• Member D has made 10% of the total project.
and why did you come up with your decision?
Answer:
The prize is p100,000.00, and we can define this as the 100%.
Now, we could say:
"Each member receives the same percentage of the price as the total percentage of the project that he/she did"
Then:
Member A did 25% of the total project.
Then he gets an amount X.
X = 25%
p100,000.00 = 100%
We can solve this system for X as:
X = (25%/100%)*p100,000.00 = p25,000.00
Now we can use the samme aproach for the other members:
Member B did 40% of the total project:
Then he gets an amount X.
X = 40%
p100,000.00 = 100%
X = (40%/100%)*p100,000.00 = p40,000.00
Member C did 25% of the total project.
Then he gets an amount X.
X = 25%
p100,000.00 = 100%
X = (25%/100%)*p100,000.00 = p25,000.00
Member D did 10% of the total project.
Then he gets an amount X.
X = 10%
p100,000.00 = 100%
X = (10%/100%)*p100,000.00 = p10,000.00
Now, we also could divide the price evenly between the four members:
p100,000.00/4 = p25,000.00
So they all get the same amount, but i think that the actual solution to this problem is the other one.