A customer goes to a bank and gets change for a $100 bill. The change is to be in $1, $5, and $10 bills. There were four times as many $5 bills as $10 bills. If there are 25 bills in all, how many are $5 bills?

Answer:

a.  71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

b.  23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

c. 99840π lb/ft-s²∫₀⁶rdr

Step-by-step explanation:

.(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.

The work done, W = ∫mgdy where m = mass of cylindrical tank = ρA([5 + 4] - y) where ρ = density of water = 62.4 lb/ft³, A = area of base of tank = πd²/4 where d = diameter of tank = 12 ft.( we add height of the tank + the height of point above the tank and subtract it from the vertical point above the base of the tank, y to get 5 + 4 - y) and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdy

W = ∫ρA([5 + 4] - y)gdy

W = ∫ρA(9 - y)gdy

W = ρgA∫(9 - y)dy

W = ρgπd²/4∫(9 - y)dy

we integrate W from  y from 0 to 5 which is the height of the tank

W = ρgπd²/4∫₀⁵(9 - y)dy

substituting the values of the other variables into the equation, we have

W = 62.4 lb/ft³π(12 ft)² (32 ft/s²)/4∫₀⁵(9 - y)dy

W = 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

.(b) Write down an integral for the fluid force on the side of the tank

Since force, F = ∫PdA where P = pressure = ρgh where h = (5 - y) since we are moving from h = 0 to h = 5. So, P = ρg(5 - y)

The differential area on the side of the tank is given by

dA = 2πrdy

So.  F = ∫PdA

F = ∫ρg(5 - y)2πrdy

Since we are integrating from y = 0 to y = 5, we have our integral as

F = ∫ρg2πr(5 - y)dy

F = ∫ρgπd(5 - y)dy    since d = 2r

substituting the values of the other variables into the equation, we have

F = ∫₀⁵62.4 lb/ft³π(12 ft) × 32 ft/s²(5 - y)dy

F = 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

.(c) How would your answer to part (a) change if the tank was on its side

The work done, W = ∫mgdr where m = mass of cylindrical tank = ρAh where ρ = density of water = 62.4 lb/ft³, A = curved surface area of cylindrical tank = 2πrh  where r = radius of tank, d = diameter of tank = 12 ft. and h =  height of the tank = 5 ft and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdr

W = ∫ρAhgdr

W = ∫ρ(2πrh)hgdr

W = ∫2ρπrh²gdr

W = 2ρπh²g∫rdr

we integrate from r = 0 to r = d/2 where d = diameter of cylindrical tank = 12 ft/2 = 6 ft

So,

W = 2ρπh²g∫₀⁶rdr

substituting the values of the other variables into the equation, we have

W = 2 × 62.4 lb/ft³π(5 ft)² × 32 ft/s²∫₀⁶rdr

W = 99840π lb/ft-s²∫₀⁶rdr

Answer:

11 or 2, it depends on how you think abt it

Answer:

2

Deedederffetfrerggrrrggtrrttt

Answer:

acute triangle

Step-by-step explanation

MRK ME BRAINLIEST PLZZZZZZZZZZZZZZZZZZZZ

Answer:

30=6j

j=5

hope it helps .......

Answer:

πr2

Step-by-step explanation:

Answer:

i think the answer is

Step-by-step explanation:

πr^2

Answer:

10!

Step-by-step explanation:

Because 40*10= 4

and we all know 4/10=40 so there you go! Go succeed!

Answer: 5/6

Step-by-step explanation:

If you chose \(\frac{5}{6}\) foot, you are correct. If you chose 10 feet, you forgot to convert inches to feet. If you chose 1 foot, you thought that there were 10 inches in a foot. If you chose \(\frac{1}{10}\)foot, you wrote 1 over the number of inches because you were unsure how to write fractions in terms of feet.

Answer:

A

Step-by-step explanation:

Answer:

it is A because the shape is the same and is just facing a different way

Step-by-step explanation:

Answer:

D.They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.

Step-by-step explanation:

Type 2 error results in a statistical analysis when a false null is incorrectly accepted.

The hypothesis Given :

H0: p = 0.6

HA: p > 0.6

The null in this context is that, the percentage of members who wants a name change is 60% ; while the alternative is that more than 60% wants a name change.

In this context, accepting a false null means Making a conclusion that exactly 60% wants a name change while it is actually FALSE.

Answer:

[tex]x < -4[/tex]

[tex]-4 > x[/tex]

Step-by-step explanation:

Given

Description of number line

Range: -6 to 2

Open circle on -4

Left shaded

Required

Select the number line

From the question, we understand that the left side of the number line is shaded.

This means that the inequality is [tex]\le[/tex] or [tex]<[/tex]

Also, the open circle on -4 means that we discard [tex]\le[/tex].

So, the inequality is:

[tex]x < -4[/tex]

The opposite of the above inequality is:

[tex]-4 > x[/tex]

Answer:

A, D.  

Step-by-step explanation:

good luck with edge :)

Answer: 7.1835091

Step-by-step explanation:

Answer:

610m^2

Step-by-step explanation:

break the polygon into two rectangles as shown in attachment

I have labeled the new length A

A = 50 - 18

A = 32 m

area of rectangle 1 = l x w

= 5 x 32

= 160m^2

area of rectangle 2 = l x w

= 18 x 25

= 450 m^

area of polygon = rectangle 1 + rectangle 2

= 160 + 450

= 610m^2

Answer:

c cylinder

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: Possibly -4

Step-by-step explanation:

But wait for others to check I’m not fully sure

Answer:

scale = 1 in: 5 ft

         = 1inch x 5 5/8  = 5.625

              5 ft x 5 5/8    28.125 ft

The actual height of the house is 28.125 ft

Answer:

x + 2y - 5 = 0

Step-by-step explanation:

We can see that , the graph passes through (0,2.5) and (5,0) . Therefore the ,

We can use the intercept form of equation as ,

=> x/a + y/b = 1

=> x/5 + y/2.5 = 1

=> x + 2y/5 = 1

=> x + 2y = 5

=> x + 2y -5 = 0 .

This equation can be verified by plotting the graph .[ Refer to attachment ]

Answer:

3/2

Step-by-step explanation:

Answer:

[tex] \frac{3}{2} [/tex]

9514 1404 393

Answer:

  x = 60

Step-by-step explanation:

The angle x is half the sum of the intercepted arcs:

  x = (40 +80)/2

  x = 60

Answer:

Step-by-step explanation:

Tan(theta) = Sin(theta) / cos(theta)

1/4 = sin(theta) / sqrt(1 - sin^2(theta) )    Cross multiply

sqrt(1 - sin^2(theta)) = 4*sin^2(theta)      Square both sides.

1 - sin^2(theta) = 16 * sin^4 (theta)         Transfer the left side to the right side.

0 = 16 sin^4(theta) + sin^2(theta) - 1

Use the quadratic formula to find a value for sin^2(theta)

a = 16

b = 1

c = - 1

I'll leave solving the quadratic to you.

There are two answers

sin^2(theta)= .22069

The other root is - 0.28 which you cannot use.

Sin(theta) = +/- 0.4698

Cos(theta) is < 0 in quads 2 and 3

So sin(theta) is positive in quad 2

and sin(theta) is minus in quad 3

Answer:

[tex]x < - 7[/tex]

the answer is option C

Answer:

Your solution is (-1, 1).

Step-by-step explanation:

-2x = 8 - 6y

-15x = 21 - 6y

Let's solve this through elimination.

Right away I can see that our y-values are the same. We want to eliminate one variable at a time, so let's make one of the -6y's a positive by multiplying each term in the equation by -1.

-15x = 21 - 6y

-1(-15x = 21 - 6y)

15x = -21 + 6y

Now we have a new equation in our system.

-2x = 8 - 6y

15x = -21 + 6y

Now, eliminate by performing each action given by the terms.

-2x = 8 - 6y

15x = -21 + 6y

___________

13x = -13

Divide both sides by 13 to isolate x.

x = -1

Now that we know x, plug it back into one of the original equations to find y.

-2x = 8 - 6y

-2(-1) = 8 - 6y

Multiply.

2 = 8 - 6y

Subtract 8 from both sides.

-6 = -6y

Divide both sides by -6.

y = 1

Your solution is (-1, 1).

Check your answer by plugging both values into one of the original equations.

-15x = 21 - 6y

-15(-1) = 21 - 6(1)

Multiply.

15 = 21 - 6

Add 6 to both sides.

15 = 15

Your answer is correct.

Hope this helps!

Answer:

(-1,1)

Step-by-step explanation:

-2x = 8 -6y *

-15x = 21 - 6y

Solve for -6y:

-6y = -8 - 2x *

-15x = 21 - 6y

Substitute the given value of 6y into second equation, you get:

-15x = 21 -8 - 2x

Solving this equation for x gets you:

x = -1

Substitute this value (x = -1) into the equation (-6y = -8 - 2x):

-6y = -8 - 2x (-1)

This provides y:

y = 1

Answer:

65m = 6500 Cm.

Step-by-step explanation:

Answer:

The answers are given in the pictures. One of them was an opinionated question, so you can just put whatever you want there. I put my opinion just in case.

Step-by-step explanation:

Answer:

Due to the higher margin of error, the 1st analyst will have a wider interval.

Step-by-step explanation:

Width of a confidence interval:

The width of a confidence interval is twice its margin of error, meaning that the sample with the largets margin of error will be wider.

1st analyst:

Margin of error of 0.85, so width of 0.85*2 = 1.7

2nd analyst:

Margin of error of 0.7, so width of 0.7*2 = 1.4

Which analyst will have a wider interval?

Due to the higher margin of error, the 1st analyst will have a wider interval.

Answer:

45

Step-by-step explanation:

9 × 3 = 27

started with 72

72 - 27 = 45

Note: I had to write FA in that order, and not the other way around, due to the filter.

Part 1

There are 2 answers and they are

------------------

Explanation:

For any of the answer choices we are involving the following segments

So we're only involving four segments. They are paired up to form fractions which are then set equal to one another. Notice how segment FA is smaller than AB, and how they correspond together. Going from FA to AB means go from small to big. If we write the ratio FA/AB, then can think of it as small/big.

Also note that FG is smaller than BC, and both segments also correspond as they are both going downhill from left to right. So we can write FG/BC to set equal to the first fraction we set up.

Overall, the proportion FA/AB = FG/BC is one valid answer.

The other valid answer is AB/FA= BC/FG. This equation is formed by applying the reciprocal to both sides of the first equation mentioned.

We can rule out choice 1 because FA/AB is small/big, but BC/FG is big/small. The two don't match up. Choice 4 is ruled out because AB does not correspond to FG.

=====================================================

Part 2

------------------

Explanation:

Through similar ideas mentioned in part 1, we can form this proportion

FA/AB = AG/AC

we have the format small/big = small/big

We are given these values either in word form or through the diagram

Plug in those given values and isolate AG

FA/AB = AG/AC

15/45 = AG/81

15*81 = 45*AG .... cross multiply

1215 = 45AG

45AG = 1215

AG = 1215/45 .... divide both sides by 45

AG = 27

Segment AG is 27 inches long.

Answer:

Sand

Step-by-step explanation:

120kg = (4 + 3 + 1) units = 8 units

1 unit = 120 ÷ 8 = 15kg

Calculating required quantities:

Cement: 4 units = 4(15) = 60kg

Sand: 3 units = 3(15) = 45kg

Gravel: 1 unit = 1(15) = 15kg

Comparing these values to those given in the question, he is short of sand.

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Exact Form:

z=0,7√8

Decimal Form:

z=0,1.34590019…

Hope this helps!

Have a great day!

- Hailey : )