A scale drawing of a playground is shown below.
PLAYGROUND
2.5 in.
KEY
1 in. = 40 ft.
3 in.
1 in.
4.5 in.
Using this scale, what is the area, in square feet, of the playground?
540 square feet
450 square feet
440 square feet
380 square feet
Answers
Related Questions
Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. (The same conditions as in the previous problem). After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank.
(a) Find the concentration, in kilograms per liter, of salt in the tank after 10 min. [Hint: Let A denote thenumber of kilograms of salt in the tank at t minutes after the process begins and use the fact that rate of increase in A = rate of input - rate of exit.
(b) After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank. What will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops?
Answers
Answer:
(a) 0.288 kg/liter
(b) 0.061408 kg/liter
Step-by-step explanation:
(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute
The mass of salt exiting the tank per minute = 5 × (5 + x)/500
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
Δ/dt = x - 5 × (5 + x)/500
The increase, in mass, Δ, after an increase in time, dt, is therefore;
Δ = (x - 5 × (5 + x)/500)·dt
Integrating with a graphing calculator, with limits 0, 10, gives;
Δ = (99·x - 5)/10
Substituting x = 1 gives
(99 × 1 - 5)/10 = 9.4 kg
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)
∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter
(b) With the added leak, we now have;
Δ/dt = x - 6 × (14.4 + x)/500
Δ = x - 6 × (14.4 + x)/500·dt
Integrating with a graphing calculator, with limits 0, 20, gives;
Δ = 19.76·x -3.456 = 16.304
Where x = 1
The increase in mass after an increase in = 16.304 kg
The total mass = 16.304 + 14.4 = 30.704 kg
The concentration of the salt in the tank then becomes;
Concentration = 30.704/500 = 0.061408 kg/liter.
Calculating the salt concentration per liter of water we will find:
(a) [tex]0.288 kg/liter[/tex]
(b) [tex]0.061408 kg/liter[/tex]
The mass of salt entering the tank per minute:
[tex]X= (0.2)( 5) = 1 kg/minute[/tex]
The mass of salt exiting the tank per minute:
[tex]\frac{5 * (5 + x)}{500}[/tex]
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
[tex]\frac{\Delta}{dt} = \frac{x - 5 * (5 + x)}{500}[/tex]
The increase, in mass, Δ, after an increase in time, dt, is therefore;
[tex]\Delta = (x - 5 * (5 + x)/500)dt[/tex]
Integrating with a graphing calculator, with limits 0 at 10, gives;
[tex]\Delta = (99X - 5)/10[/tex]
Substituting x = 1 gives:
[tex](99)( 1 - 5)/10 = 9.4 kg[/tex]
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank). The concentration of the salt and water in the tank after 10 minutes:
[tex](5 + 9.4)/500 = (14.4)/500 = 0.288[/tex]
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter.
(b) With the added leak, we now have;
[tex]\frac{\Delta}{dt} = \frac{ (x - 6 ) (14.4 + x}{500} \\\Delta = \frac{(x - 6)(14.4 + x)}{500} dt[/tex]
Integrating with a graphing calculator, with limits 0 at 20, gives;
[tex]\int\limits^{20} _0 {\frac{(x - 6)(14.4 + x)}{500} dt}[/tex]
Where x = 1:
[tex]\Delta = 19.76(1) -3.456 = 16.304[/tex]
The increase in mass after an increase in = 16.304 kg. The total mass:
[tex]16.304 + 14.4 = 30.704 kg[/tex]
The concentration of the salt in the tank then becomes;
[tex]30.704/500 = 0.061408 kg/liter[/tex]
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3b) Two pizzas are made to the same dimensions. The only difference is that
Pizza 1 is cut into pieces at 30° angles and Pizza 2 is cut at 45° angles. They are
sold by the slice. The slices for Pizza 1 sell for $1.45/slice and the slices for Pizza 2
sell for $1.75/slice. What is the difference in total sales between Pizza 2 and Pizza
1?
Answers
Step-by-step explanation:
$0.30 because they only sell 30 cents less/more than each other
The teacher separated her group of 28 students into 2 groups. One group has 4 more than twice as many students as the other group. How many students are in each group?
Answers
Answer:
one group has 12. one has 16. 12 + 16 = 28. 16 is 4 more than 12
Which difference is closest to 12?
A. 89−1112
B. 67−19
C. 1516−38
D. 35−611
Answers
Answer:
b
The rest are at least 500 numbers away from 12
Step-by-step explanation:
If f(1) = 1, what is f(3)?
Answers
Answer:
would be 3
Step-by-step explanation:
if 1 is 1 ,3 would be 3 ;-;
(-2,-4) and (6,7)
Need help show steps too
Answers
Answer:
Step-by-step explanation:
period
PLZ HELP !!!!!!
28x+36y=2520 Write this in slope intercept form or graph!!
Answers
Answer:
y= -7/9 x+70
Step-by-step explanation:
28x+36y=2520
36y=-28x+2520
y= -7/9 x+70
Solve for n 3m+2n=8 how do you do theseee?
Answers
HELP PLEASE!!!
I’ll give brainlest
Answers
2\3n = -12 what value of n makes this equation true
Answers
Answer:
-0.055555555555556
Step-by-step explanation:
(-16t - 2)(t - 5) is the same as 10+78t-16t^2 but in factored form. Explain how you know,
basically help me convert the factored form into the standard form
Answers
Answer:
10+78t-16t^2
Step-by-step explanation:
(-16t-2)(t-5)
-16t × t= -16t²
-16t × -5=80t
-2 × t= -2t
-2 × -5=10
-16t²+80t-2t+10= -16t^2+78+10
Every Friday, Jesse puts $3 into his piggy bank. is it discrete or continuous?
Answers
Answer:
I would think continuous if she does it constantly every friday night
Step-by-step explanation:
Answer:
continuious
Step-by-step explanation:
Covert 45 1/2 % to a fraction
Answers
A pet store was selling 2 lizards for
$14.48. If they ended up selling 6
lizards, how much money would they
have earned?
Answers
Answer:
43.44
Step-by-step explanation:
If they are selling 2 lizards for 14.48 you would divide
14.48 by two which is 7.24.
This means the lizards are 7.24 each.
7.24x6 is 43.44
Answer:
$43.44
Step-by-step explanation:
If two lizards are worth $14.48, then you just need two multiply the cost by three.
Give 5 reasons explaining why math is your favorite subject.
Give 5 reasons why you dont like math.
Give 5 areas that math can help you now or in the future.
Answers
Answer:Math is important
Step-by-step explanation:
It could help you get into collage and get a good job and with that you could start your life.
Answer:
1.)
I love working with numbers
I love math because of what a challenge it is
I love math because I can become a engineer
I love math because I can also become a doctor with it
I love math because it is useful
2.)
I don't like math because of the word problems
I don't like math because it sometimes gets too easy
I don't like math because I usually have to help others
I don't like math because people call me a nerd
I don't like math because it makes me explain in words
3.)
when your in the store and it helps you with knowing how much your spending
lets you know about if the discount in the store is really good or bad
helps you with becoming certain things when you grow up
it will help you with most of your jobs
Will help others if you know it, you can share your knowledge
Step-by-step explanation:
brainlist pls :>
When I graph the inequality symbol > should it be a open or closed
circle on the number line?
Answers
Answer:
It should be open.
Step-by-step explanation:
Hope this helped!
I need some help on this problem.
Answers
Answer:
It would be <XWY & <UTW.
9
show questions
Carol feeds her bird the same amount of food every day. Over the past 7 days, her bag of bird
food has decreased by 1 cups.
Answers
Answer: 1/7 of a cup
Step-by-step explanation:
7x=1 x=food per day
divide 7 from both sides
7 / 7x = 1 /7
x = 1/7
Find the cos of angle c
A.3/5
B.6/5
C.5/3
D.1
Answers
Simplify the expression
Answers
Answer:
B
Step-by-step explanation:
Express your answer as a polynomial in standard form.
f(x) = 3x² + 4x – 7
g(x) = 2x – 11
Find: g(f(x))
Answers
Answer:
g(f(x)) = 6x^2 + 8x - 25
Step-by-step explanation:
So, first we have to substitute f(x) into the place of x in the g(x). This will be shown as g(f(x)) (which is what we need to solve). Next, we have to substitute 3x^2 + 4x - 7 into the place of x in 2x - 11. We do this because we had to substitute f(x) into the place of x in g(x).
So this is how your equation should look, and then solve:
g(f(x)) = 2(3x^2 + 4x - 7) - 11
g(f(x)) = 6x^2 + 8x - 14 - 11
g(f(x)) = 6x^2 + 8x - 25 < ---- This is your answer
Hope this helps!
Exit ticket help please
Answers
Answer:
The answer is B
Step-by-step explanation:
I am learning the same thing somehow
⚠️⚠️marking brainliest⚠️⚠️
It’s a math question :((
Answers
Answer:
slope: 3 y-intercept: 9
Step-by-step explanation: 19-10 is 9, and 6-3 is 3 9/3 is 3.
28-19 equals 9. 19-10 is 9, so 9 fills out that blank beside 10.
Answer:
slope is 3 and in the blank goes 1. and y intercepts line at y=1
What is the image of (-5, 6) after a reflection over the line y = -2
Answers
Answer:
I'm pretty sure it would be (5,6)
Step-by-step explanation:
Reflecting a point over the Y-axis would change the x-coordinate, but not the y-coordinate
123476870975 divide by 5
Answers
Answer: 24695374195
Step-by-step explanation: did you really need this?
Write sec 325° in terms of the secant of'a positive acute angle.
Answers
Answer:
sec35°
Step-by-step explanation:
sec325° = sec(360 - 325)° = sec35°
The secant of a positive acute angle of sec 325° = sec 35° = 1.22077
What are Trigonometric Ratios?
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios.The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given data ,
The trigonometric ratio is = sec 325°
Now , to express the ratio in terms of a positive acute angle , we take the four quadrants of the graph and express the angle in the first quadrant.
And , 325° lies on the 4th Quadrant , where all cosines and secants are positive.
Therefore , sec 325° = sec ( 360° - 35° )
= sec ( 35° )
=1.22077
Hence , the secant of a positive acute angle of sec 325° = sec 35° = 1.22077
To learn more about trigonometric ratio click :
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need help pease its due at 11;59pm today explian
Answers
Answer:
65
Step-by-step explanation:
you add all the numbers inside.
80+35= 115
You have to make sure it equals to 180 to find angle 1.
Therefore, 180-115=65.
A rectangle has a length that is 4 ft more
than its width. What are the length and
width of the rectangle if the rectangle has
a perimeter of 48 ft?
Answers
Answer:
length = 14 width = 10
Step-by-step explanation:
48/4=12
10+10+14+14=48
Length = L = 14 ft
P = perimeter = 48 ft
Explanation:
P rectangle = 2L+ 2W
L = W + 4
P = 48
Substitute into formula:
P rectangle = 2L + 2W
48 = 2( W + 4 ) + 2W
48 = 2W + 8 + 2 W
48= 4W + 8
48 - 8 = 4W
40 = 4W
W = 40/4 = 10
W = 10
The rectangle has a length that is 4 ft more than its width : L = W + 4
Substitute : L = 10 + 4 = 14
L = 14 ft
I hope this help!!!
what is the answer a, b, c, or d
Answers
Answer: Choice B
(-2, 5)
==================================================
Explanation:
The original system is
[tex]\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}[/tex]
Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations
[tex]\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}[/tex]
Now add straight down
The x terms add to -4x+3x = -1x = -x
The y terms add to 3y+(-3y) = 0y = 0
The terms on the right hand sides add to 23+(-21) = 2
We end up with the equation -x = 2 which solves to x = -2
Now use this to find y. You can pick any equation with x,y in it
----------------
-4x+3y = 23
-4(-2)+3y = 23
8+3y = 23
3y = 23-8
3y = 15
y = 15/3
y = 5
Or
x-y = -7
-2-y = -7
-y = -7+2
y = -5
y = 5
Either way, we get the same y value.
So that's why the solution is (x,y) = (-2, 5)
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. Without
looking, what is the probability that Fiona pulls out a marble that is not white?
Answers
Answer:
85%
Step-by-step explanation:
The probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
What is the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event.
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. The total number of marbles in the bowl is,
[tex]n=5+2+10+3\\n=20[/tex]
The number of white balls in the bowl is 3. Thus, the probability that Fiona pulls out a marble that is white, is,
[tex]P=\dfrac{3}{20}[/tex]
The probability that Fiona pulls out a marble that is not white is,
[tex]P^{-1}=1-\dfrac{3}{20}\\P^{-1}=\dfrac{20-3}{20}\\P^{-1}=\dfrac{17}{20}[/tex]
Thus, the probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
Learn more about the probability here;
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