Water flows into a tank according to the rate F(t) = t+6/1+t, and at the same time empties out at the rate E(t) = ln(t+2)/t+1, with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes. You must show your setup but can use your calculator for all evaluations.
Answer:
12.29minutes
Step-by-step explanation:
The net flow rate = flow in - flow out = F(t) - E(t) = t+6/1+t - ln(t+2)/t+1 = [(t + 6) - ln(t+2)]/(t+1)
So, the amount of water present in the tank at time, t is A = net flow rate × time = [(t + 6) - ln(t+2)]/(t+1) × t = t[(t + 6) - ln(t+2)]/(t+1)
At t = 10 minutes,
A = t[(t + 6) - ln(t+2)]/(t+1)
A = 10[(10 + 6) - ln(10+2)]/(10+1)
A = 10[16 - ln12]/11
A = 10[16 - 2.485]/11
A = 10[13.515]/11
A = 135.15/11
A = 12.29 minutes
circumference of circle whose radius is 7cm
Answer:
43.98 cm
Step-by-step explanation:
[tex]C=2\pi r[/tex] where r is the radius
Plug the radius 7 cm into the equation as r
[tex]C=2\pi (7)\\C=14\pi \\C=43.98[/tex]
Therefore, the circumference of the circle is approximately 43.98 cm.
I hope this helps!
if we have 10 slices of sandwiches and each 2 person take one how many slices do we still have..its easy
guys i have 5 min left plz
Answer:
both are wrong
Step-by-step explanation:
raj's mistake: he did not multiply -2 by -5a/4
antonia's mistake: she went from -4a/4 to a which is wrong because -4/4 is -1.
what are systems of equations and inequalities definitions?
Answer:
A system of equations is a set of equations with the same variables. A system of inequalities is almost exactly the same, except you're working with inequalities instead of equations. To solve such a system, you need to find the variable values that will make each inequality true at the same time.
Step-by-step explanation:
Hope this helps. :D
Find the area of the shape
Answer:28.5
Step-by-step explanation:
A ping-pong ball rolls forward 6 meters to the right, and bounces backward 3 meters to the left. It traveled a total displacement of.
Answer:
a displacement of 3 meters.
Step-by-step explanation:
you move 6 meters to the right, then 3 meters to the left
6 - 3 = 3
displacement is the distance away from the starting point
The ball traveled a total displacement of 3m.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
<------------6m----------------->
Ball ____________________
Ball_________
<------3m------>
Distance traveled by the ball.
= 6 m + 3m
= 9 m
Displacement is the shortest distance traveled by the ball.
= 6 - 3
= 3m
Thus,
Displacement is 3m.
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Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the j$ fare among the 3 of them. Angela also paid a $5, tip. How much did Angela pay in total?
Answer:
[tex]$\frac{j}{3}+5$[/tex]
Step-by-step explanation:
It is given Angela shared a cab with her 2 friends.
Total number of people = 3
Total fare = j $
Tip paid by Angela = $ 5
The total fare was equally divided by the 3 friends.
So, fare paid by angle = [tex]$\frac{j}{3}$[/tex]
Total money paid by Angela is = fare + tip
= [tex]$\frac{j}{3}+5$[/tex]
Buying one movie ticket online costs $16.50. Two tickets cost $30.50. Assuming that the relationship is linear, what is the recursive formula? (remember recursive formula is An = An-1 + d)
1. An = A1 + (n - 1) +30.50
2. An = An-1 + 14 where A1 = 16.50
3. A20 = 231
4. An = 30.5 + 16.50
Answer:
c(n)= 14n+2.50
Step-by-step explanation:
Have a good day
The value of 23 + 33
Answer:
56 hope it helps....
hhcxxghjo9
Answer:
2^3 + 3^3 = 35
Step-by-step explanation:
You can simply use a calculator on your PC, phone, tablet, or macbook. If you just add 2 to the 3rd power and 3 to the 3rd power then you'd get 35. I'm sorry I'm not really good at math but I just wanted to give you a simpler way to do this problem considering it is not too hard to solve.
George scored 70, 92, 70, 90, and 95 on five physics tests. The mean, median, and mode of his scores are given below. Mean = 83.4 median = 90 mode = 70 Which value best describes George's scores? Explain.
Answer:
mean; the average of George's scores is the mean = 83.4
Step-by-step explanation:
The value that best describes George's scores is the mean that has a value of 83.4.
What is the mean?
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number. The mean makes use of all the data in the data set.
Mean = sum of the numbers / total number
(70+ 92 + 70 + 90 + 95) / 5 = 83.4.
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Help Me! I will mark Brainliest!
Answer: Paper clip is 1 2/8 inch and Pushpin is 7/8 inch and last one the scissors is 3 2/3 inches. I’m not sure
Azul used a number cube with the numbers 1-6 in a simulation. He assigned 1-4 as the favorable outcome and 5-6 as the unfavorable outcome. What situation could this represent.
Answer:b
Step-by-step explanation:
Answer:
the answer is the top right if confused then it's the one with the fraction 2/3
Step-by-step explanation:
i got it right on i ready quiz.
In 1978, the amount of earnings required to earn one Social Security credit was $250. Thirty years later, in 2008, this amount was $1,150. What was the percent increase in the amount required to earn a credit, over this 30-year span? Use a percent sign .
Answer:
the percentage increase is 360%
Step-by-step explanation:
The computation of the increase in percentage is shown below;
Given that
SOcial security credit as on 1978 is $250
And, the social security tax as on 2008 is $1,150
Now based on the above information
The percentage increase is
= ($1,150 - $250) ÷ ($250)
= 360%
Hence, the percentage increase is 360%
How many pairs of glasses can we make
with the foil beads, and how many foil
beads will be left over?
Answer:
How am I supposed to know, you're not telling me any information.
i need help i forgot how to multiply decimals
Stack the numbers on top of each other so the decimals are lined up. Get rid of the decimals and then multiply. Put the decimal point back in directly under where it was before
In the figure, m∠2=55⁰ and m∠4=85⁰ . Find the measures of ∠1 and ∠3 .
Step-by-step explanation:
Angle 1= Angle 4 (Vertically Opposite Angles)
Angle 3= Angle 2 (Vertically Opposite Angles)
Therefore,
Angle 1= 85 degree
Angle 3= 55 degree
Hope this Helps
The measure of angle ∠1 and angle ∠3 will be 85° and 55°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
In the figure, ∠2 = 55° and ∠4 = 85°.
Angle ∠1 and angle ∠4 are vertically opposite angles. Then we have
∠1 = ∠4
∠1 = 85°
Angle ∠2 and angle ∠3 are vertically opposite angles. Then we have
∠3 = ∠2
∠3 = 55°
The measure of angle ∠1 and angle ∠3 will be 85° and 55°, respectively.
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A salesperson sells $2700 in merchandise and earns a commission of $513.
Find the commission rate. Write your answer as a percentage.
Answer:
1.9%.
Step-by-step explanation:
Help me it’s just median range and meseurement of a square
Sharon is buying a circular rug for her room. The diameter of the rug is 8 feet which measurement is closest to the area of the rug in square feet
Answer:
50.24 feet²
Step-by-step explanation:
Given that:
Diameter of circular rug = 8 feets
To obtain the area of the circular rug, we use the formula for the Area of a circle = πr²
A = πr²
r = Radius of circle = diameter / 2 = 8 /2 = 4 feets
Area of circular rug = π * 4²
Area of circular rug = 3.14 * 16 = 50.24 feet²
Carly is 8/11 the height of her mother, 2/3 the height of her father, 3/4 the height of her older sister, and 5/6 the height of her older brother. Carly is 48 inches tall.
What is the height of the Carly father?
HELP ME PLEASE
Pls helppp my last question and my last of point. This is veryyy important
Answer:
kids
Step-by-step explanation:
don't need to do much math, just compare the differences between the numerators and denominators of 22/35 and 18/42
22 portions out of 35 is a lot closer to 100% than 18 portions out of 42 (it's not even 50%)
I need this done please
Answer:
I think is going to be c because we can see with the dot plot and according of the reading is going to be c
Answer:
C
Step-by-step explanation:
The mean for store 1 is 2.9 while the mean for store 2 is 2.0
What is the perimeter of this
polygon?
A
3 cm
9 cm
B 3 cm
If the tangent is drawn from the outside of the circle. Then the length of the tangents will be same. Then the perimeter is 30 cm.
What is the perimeter of a triangle?Let the triangle be ABC. Then the perimeter of the triangle will be
Perimeter = AB + BC + CA
Now,
We know that if the tangent is drawn from the outside of the circle. Then the length of the tangents will be same.
Then the completed diagram is given below.
Hence, We get;
The perimeter of the graph of figure is,
P = 3 + 3 + 3 + 3 + 9 + 9
P = 30 cm
Thus, The perimeter of the graph of polygon is,
P = 30 cm
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A horse’s heart rate is about 36 beats per minute. If the horse's heart has beaten 189 times how many minutes have passed by.
Answer:
5.25 mins
Step-by-step explanation:
189/36 = 5.25.
Don't download/ clikc on any links they are hackers.
please help with the question below
Answer:
I’m not sure but I. Think it’s a I guess
Step-by-step explanation:
Give the values of a, b, and c from the standard form of the equation (2x + 1)(x - 2) = 0.
A. a = 3, b = 1, c = -1
B. a = 2, b = 5, c= -2
C. a = 2, b = -3,c = -2
Given:
The equation is:
[tex](2x+1)(x-2)=0[/tex]
To find:
The values of a, b and b from the standard form.
Solution:
The standard form of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex] ....(i)
We have,
[tex](2x+1)(x-2)=0[/tex]
In can be rewritten as
[tex]2x(x)+(2x)(-2)+(1)(x)+(1)(-2)=0[/tex]
[tex]2x^2-4x+x-2=0[/tex]
[tex]2x^2-3x-2=0[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=2,b=-3,c=-2[/tex]
Therefore, the correct option is C.
Which of the following measurements could be the three side lengths of a right triangle?
4 cm, 5 cm, 9 cm
12 cm, 20 cm, 25 cm
18 cm, 24 cm, 30 cm
2 cm, 3 cm, 5 cm
Answer:
18 cm, 24 cm, 30 cm
Step-by-step explanation:
30² = 18² + 24²
900 = 324 + 576
900 = 900
solve for x. round your answer to the nearest tenth
Trigonometry
Answer:
63.5°
Step-by-step explanation:
Reference angle = x°
Opposite = 17
Hypotenuse = 19
Apply the trigonometric function, SOH:
[tex] sin(x) = \frac{Opp}{Hyp} [/tex]
Substitute
[tex] sin(x) = \frac{17}{19} [/tex]
[tex] x = sin^{-1}(\frac{17}{19}) [/tex]
x = 63.474648° ≈ 63.5° (nearest tenth)
more than 1 correct answer, help!
Answer:
Select 1, 4 and 5
The slope is -1/10
The x intercept is 100
The y intercept shows the initial amount on the card in dollars