A tank contains 22 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water begun draining and let v represent the volume of water in the tank. Write a formula that expresses y in terms of t .
Answers
Answer:
V= 22-2t
Step-by-step explanation:
I guess the alphabet should be v instead of y. So I am working using v
The rate at which water is draining from the tank is 2gallons/hour. This is the rate of water removal from the tank. So after an hour, 2 × 1= 2 gallons would have drained. After 5 hours, 2×5 =10 gallons would have drained
Therefore to obtain the amount of water in gallons that have been removed from the tank, you will multiply the rate by the time in hours after which the draining started.
Amount (gallons) =2×t
The amount of water remaining in the tank will be obtained by subtracting the amount of water drained after some hour (2×t) from the initial amount of water in the tank (22)
Therefore, the amount of water present in the tank (v)= 22-2t or 2(11-t) gallons
Final answer:
The formula to express volume of the water v in terms of time t is v = 22 - 2t, where 22 is the initial volume and 2t represents the rate at which the water is draining.
Explanation:
This problem is a mathematical representation of a real-world scenario using a linear equation. The volume of water v in the tank can be represented in terms of time t through the equation v = 22 - 2t. This equation illustrates the initial volume of water in the tank (22 gallons) and accounts for the constant rate at which the water is draining (2 gallons per hour).
When time t = 0 (meaning no time has passed since the water started draining), the volume of water v = 22 (the initial volume). As time increases, the volume gradually decreases at a rate of 2 gallons per hour, represented by the term -2t.
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1/8 + 1/10 + 1/12 + 1/4
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Answers
Reece needs to add 3 treatments to the fish tank.
How to determine How many treatment does Reece need to add
First, we need to calculate the volume of the fish tank in cubic meters.
Volume = Length × Width × Depth
Volume = 1.8 m × 0.6 m × 0.5 m (converting 50 cm to meters by dividing by 100)
Volume = 0.54 m³
Now, we can calculate how many treatments Reece needs to add using the given ratio of 5 ml per 0.18 m³.
Number of treatments = Volume of tank / Volume per treatment
Number of treatments = 0.54 m³ / 0.18 m³
Number of treatments = 3 treatments
Therefore, Reece needs to add 3 treatments to the fish tank.
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Answer:
15 ml
Step-by-step explanation:
Find the volume of the tank which is 1.8m*0.6m*0.5m=0.54m^3
For every 0.18m^3,5ml of treatment is added,what of 0.54m^3
(0.54m^3*5ml)/(0 18m^3)=15ml
Answers
145.50 - 129.75 = 15.75
The shop made £15.75 in one hour.
B. Confidence Level: 95%; Confidence Interval: 40 to 50
C. Confidence Level: 68%; Confidence Interval: 43 to 47
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Answers
ConfidenceLevel: 95%; Confidence Interval: 42 to 48. Then the correct option is D.
How to interpret the confidence interval?
Suppose the confidence interval at P% for some parameter's values is given by x ± y.
That means that the parameter's estimated value is P% probable to lie in the interval
[x - y, x + y]
Four research teams each used a different method to collect data on how fast a new iron skillet rusts.
Assume that they all agree on the sample size and the sample mean (in days).
Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.
Then we have
48 - 42 = 6
Then we have
6/2=3
3 is smallest
Then the correct option is D.
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Answer:
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Step-by-step explanation:
48-42=6
6/2=3
3 is smallest
I tested A and got it incorrect so D is the awnser
Answers
Answer:
28.6m
Step-by-step explanation:
this question is very incomplete. it requires a number of assumptions to give an answer. the main one - where is Bryan located relative to Anna ? I assume diametrically on the opposite side of the kite. because he has the steeper angle, it is clear that he is nearer to the kite.
so, I guess, we have to add his distance to the kite to her distance to the kite to get the distance between her and him.
but he could be on any point on a circle around the kite to have the same viewing angle, and we would have no clue about where on that circle.
as the other extreme alternative, he could be on the same line to the kite as Anna. and then we would have to subtract his distance from her distance.
but again, we assume he is exactly on the other side of the kite.
anyway, each person creates a right-angled triangle with the kite:
there is the direct line of sight as the base line or Hypotenuse (c).
there is the line on the ground from the person to the point on the ground directly under the kite as one side.
there is the line representing the height of the kite above ground as the other side. we let this start at the height of the eyes of the watching person.
and we assume that both persons are of the same height (so the height of the kite relative to their eyes is the same for both).
let's start with Anna.
the side a of Anna's triangle is
a = 20m
angle between a and c = 44 degrees
we know the angle between a and b is 90 degrees.
therefore the angle between b and c = 180-90-44 = 46 degrees.
now we use the law of sines :
a/sin(bc) = b/sin(ac) = c/sin(ab)
we know sin(ab) = sin(90) = 1
20/sin(46) = b/sin(44)
b = 20×sin(44)/sin(46) = 19.31... m = height of the kite
now to Bryan.
now we know his b (height of the kite) = 19.32... m
his angle between a and c is 66 degrees.
his angle between a and b is also 90 degrees.
therefore his angle between b and c = 180-90-66 = 24 degrees.
19.31/sin(66) = a/sin(24)
a = 19.31×sin(24)/sin(66) = 8.6 m
based on our assumption that they are standing opposite from each other in relation to the kite their distance is
20 + 8.6 = 28.6m
maximum; –10
b
minimum; –10
c
maximum; 2
d
minimum; 2
Answers
The function f(x) = 4x² – 16x + 6 has a minimum value is –10 when the value of x is 2. Then the correct option is B.
What is differentiation?
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given below.
Differentiate the function, then we have
The value of x will be
Then again differentiate the function, if the value comes negative then maxima and if the value is positive then minima.
Then the function is minimum at 2.
More about the differentiation link is given below.
Answer:
minium:-2................
Answers
Answer:
A) (3,-2)
Step-by-step explanation:
A) (3,-2)