1.) Four teachers bought an old boat for $60.
The first teacher paid one-half of the sum of the amounts paid by the other teachers.
The second teacher paid one-third of the sum of the amounts paid by the other teachers.
The third teacher paid one-fourth of the sum of the amounts paid by the other teachers.
How much did the fourth teacher pay?

2.) What is the smallest number of coins that you need so that you can give exact change for any amount from 1 cent to 99 cents?

Show your work please. Any improper answers will be reported and removed- thanks!
:) Have fun!

Answers

Answer 1

For problem number 1:-
1)Let's assume the payment which each one of them paid are A,B,C, and D, for the 1st, 2nd, 3rd and 4th respectively.
so the total payment is the sum of all of them
A+B+C+D= 60 ----->(eq 1)
The 1st paid 0.5 of the sum of the other teachers payments
A= 0.5 (B+C+D) ---->(eq 2)

The 2nd paid 1/3 of the others payment
[tex] B= \frac{A+C+D}{3}[/tex] ------>(eq 3)

The 3rd paid 1/4 of the others payment
[tex] C = \frac{A+B+D}{4} [/tex] ---->(eq 4)
we have now 4 equations in 4 unknowns.

From equation 1 and 2 :-
----------------------------------
By multiplying (eq 2) by 2 and substitute in (eq 1)
2 A = B+C+D (sub in eq 1)
A+ 2A =60
then 3A= 60
then A =$20 (The first teacher's payment)

From equations 1 and 3 :-
------------------------------------
By multiplying (eq 3) by 3
3B = A+C+D (sub in eq 1)
B+3B=60
4B=60
B= $15 (The second teacher's payment)

From equations 1 and 4:-
------------------------------------
By multiplying (eq 4) by 4
then 4 C=A+B+D (sub in eq 1)
4C+ C = 60
5C=60
C= $6 (The third teacher's payment)

By substituting the values of A,B and C in (eq 1).
20 + 15 + 6 + D=60
41+ D =60 (By subtracting both sides by 41)
D = $19.(The forth teacher's payment)

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2)unfortunately i don't your coins cuz im not american :D

Related Questions

HELP PLEASE HELP HELP

Answers

[tex]( \sqrt{x} )^5=(x^{ \frac{1}{2} })^5=x^{ \frac{1}{2}*5 }=x ^{\frac{5}{2} }[/tex]

The answer is D

helppppppppppppppppppppppppppppp

Answers

For this case, you must rewrite the expression correctly.
We have then:
2 (16x ^ 3y) ^ (1/3) + 4 (54x ^ 6y ^ 5) ^ (1/3)
We then have to use properties of exponents:
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2y ^ (5/3))
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2 * y * y ^ (2/3))
We rewrite:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
Answer:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
option 1

what Is the product? 4n/4n-4*n-1/n+1

Answers

Answer:

n/(n+1) . . . . n ≠ 1

Step-by-step explanation:

As written, there is no product. There is ony the sum ...

[tex]4\dfrac{n}{4}-4n-\dfrac{1}{n}+1[/tex]

With appropriate parentheses, this becomes the product of rational functions ...

... (4n)/(4n-4)·(n-1)/(n+1)

[tex]=\dfrac{4n(n-1)}{4(n-1)(n+1)}=\dfrac{n}{n+1}[/tex]

_____

At n=1, the product has a "hole" where the denominator of the original expression is zero, so the expression is undefined. Hence the domain of the product must be restricted to n≠1 (as well as n≠-1).

If the circumference of a circle is 11inches, which is closest to its area?a.380 square inchesb.95 square inchesc.17 square inchesd.35 square inches

Answers

C=2 pi r and 11=2*3.14*r
11=6.28*r
r=1.75
A=pi r^2
A=3.14* (1.75)^2=9.625
this number is closer to 17 square inches

Solve for x in the equation x2+20x+100=36

Answers

The answer is:
[tex] x = - 64 \div 22 = -2.909091[/tex]
But if x2 was supposed to be x^2 then the answer is:
[tex]x = - 4.-16[/tex]

Answer:

x = -4 and x = -16.

Step-by-step explanation:

We have the equation,

[tex]x^{2}+20x+100=36[/tex]

i.e. [tex]x^{2}+20x+64=0[/tex]

As the solution of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].

On comparing, a = 1, b = 20, c = 64.

So, the solution is,

[tex]x=\frac{-20\pm \sqrt{(20)^{2}-4\times 1\times 64}}{2a\times 1}[/tex].

i.e. [tex]x=\frac{-20\pm \sqrt{400-256}}{2}[/tex].

i.e. [tex]x=\frac{-20\pm \sqrt{144}}{2}[/tex].

i.e. [tex]x=\frac{-20\pm 12}{2}[/tex].

i.e. [tex]x=\frac{-20+12}{2}[/tex] and [tex]x=\frac{-20-12}{2}[/tex].

i.e. [tex]x=\frac{-8}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex].

i.e. x = -4 and x = -16

Thus, the solution of the given equation is x = -4 and x = -16.

The equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.
According to to the model, what is the best estimate of the cost for towing a car 22 miles.

A. $24.75
B $46.25
C $104.50
D $124.50

Answers

The answer to the question is D

Answer: $124.50

Step-by-step explanation:

We are given that the equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.

To find the best estimate of the cost for towing a car 22 miles., we substitute x= 22 in the above equation, we get

Cost of towing a car 22 miles=[tex]y=4.75(22)+20=[/tex]

[tex]\rightarrow\ y=104.50+20=124.50[/tex]

Therefore, the best estimate of the cost for towing a car 22 miles = $124.50

Ninas car exponentially depreciates at a rate of 7 percent per year. If nina bought the car when it was 6 years old for 12000, what was the original price of the car

Answers

the original price of the car would be $17,040 brand new
hope this helps

Answer:

[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]

And solving for the initial amount [tex] A_o[/tex] we got:

[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]

So then the original price for the car would be approximately 18263.539$

Step-by-step explanation:

For this case we can use the exponential model given by:

[tex] A(t) = A_o e^{bt}[/tex]

Where:

[tex]A_o[/tex] represent the initial amount for the car

[tex]b=-0.07[/tex] represent the exponential growth/decay rate

t represent the number of years. With t =0 at the begin

After 6 year we have that t =6, and we know this condition:

[tex] A(6) = 12000[/tex]

So then we can use the exponential model formula and the condition given and we have this:

[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]

And solving for the initial amount [tex] A_o[/tex] we got:

[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]

So then the original price for the car would be approximately 18263.539$

jake plans to use a ramp to make it easier to move a piano out of the back of his truck the back of the truck is 33 inches tall and the ramp is 65 inches long. what is the horizontal distance from the end of the ramp to the back of the truck

Answers

check the picture below.

Answer:

56 inches is the horizontal distance from the end of the ramp to the back of the truck.

Step-by-step explanation:

Height of the back of the truck =33 inches

Length of the ramp = 65 inches

Length of the end of ramp to the back of the truck =?

In triangle ABC:

AB = 33 inches

BC = ?

AC = 65 inches

[tex]AB^2+BC^2=AC^2[/tex] (Pythagoras theorem)

[tex](33 inches)^2+(BC)^2=(65 inches)^2[/tex]

BC = 56 inches

PLEASE HELP I NEED THE ANSWER TO THIS ASAP. YOU JUST NEED TO MATCH EACH THING ON THE LEFT TO ITS CORRECT ANSWER ON THE RIGHT.
Match the following items.

Complete the proof for Theorem 3-13. (if you dont know what this theorem is i added a picture that explains it so you can help)

Answers

The only thing is with this one... I don't have an image showing where angles 1 2 3 4 are.

But I'll give it a try:

1) l // m ___ Given

2) <1 = <3 ___ if parallel lines, then corresponding angles (<s) are equal

3) <2 = <3 ___ Vertical <s are equal

4) <1 = <2 ___ Substitution

The complete proof of the theorem in chronological order is;

GivenIf lines are ∥, corresponding angles are equal.Vertical angles are equalSubstitution

How to complete a proof?

The proof that when a transversal cut two parallel lines, alternate angles are equal.

Statement: l ∥ m

Reason: Given

Statement: m ∠ 1 = m ∠ 3

Reason: If lines are ∥, corresponding angles are equal.

Statement: m ∠ 2 = m ∠ 3

Reason: Vertical angles are equal

Statement: m ∠ 1 = m ∠ 2

Reason: Substitution

Therefore, alternate exterior angles are equal when a transversal cut two parallel lines,

Answers

No, because the coin has 2 sides so it mostly likely wont let on heads them 20 times. Hope i helped u :)

Yes, it is possible, but very unlikely. There is two sides to a dice, so the probability of heads is 1/2 each time. (1/2)^20 would make the probability very low. So: Yes it is possible but no is is not likely.

What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth.

Answers

The answer to this is 80.47.

Answer:

80.47

Step-by-step explanation:

This is correct! :D

A chef has less than 25.8 pounds of rice. She takes out 5 pounds to use during the day and stores the rest in containers. Each container has 2.5 pounds of rice. Let x represent the number of containers. What is the maximum number of containers the chef will be able to fill with rice? 13 12 8 7

Answers

The answer should be eight. Hope this helps! :)

The chef has less than 25.8 pounds of rice.

She takes out 5 pounds to use during the day and stores the rest in containers.

Quantity of rice stored = 25.8 - 5 = 20.8 pounds

Each container can store 2.5 pounds of rice.

Let x represent the number of containers.

The number of containers that can be filled = 20.8/2.5 = 8.32

So, the maximum number of containers the chef will be able to fill with rice is 8

For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answers

1. Area of the first figure;
Area of the quarter circle = 1/4 πr²
= 1/4π 12²
= 36π cm²
Area of the triangle = 1/2×base×height
= 1/2 × 12×12
= 72 cm²
Thus the area of the region
= (36π-72) cm²

2. Perimeter of the first figure
The length of the arc AC is 2πr/4
= 2π×12/4
= 6π cm
the length of line AC
√(12² +12²) = 16.97
Thus the perimeter of the figure
= (6π+16.97) cm

3. The are of figure 2
Area of the semi circle πr²/2
= 12²π/2 = 72π cm²
The area of the square
= 24 × 24 =576 cm²
Area of the semi circle = 72 π cm²
Thus the area of the part of the square
= (576-72π) cm²
total area
72π +576-72π
= 576 cm²

4. Perimeter of figure 2
The length of arc AD = (2πr)/2
= 2π×12/2 = 12π cm
but length of arc AD is equal to that of arc BC
Thus arc BC = 12πcm
Therefore, total perimeter
= 12π +12π +24 +24
= (24π +48) cm

Answer:

The perimeter of the first figure is [tex]6\pi +12\sqrt{2}[/tex]

Step-by-step explanation:

Besides that, they got everything right.

Please solve these for me. I need them for a quiz.

Answers

4a)

I'm going to use the Substitution method

c = 160 + 67t
55 + 82t = 160 + 67t .... replace c with 55+82t; solve for t
55 + 82t - 55 = 160 + 67t - 55
82t = 67t + 105
82t - 67t = 67t + 105 - 67t
15t = 105
15t/15 = 105/15
t = 7

Use t = 7 to find that
c = 160 + 67t
c = 160 + 67*7
c = 629
You can use the other equation as well to get the same answer for c.

It takes 7 months for the cost to be the same. That cost is $629

===========================================================
4b)

I'm going to use the Elimination method

Subtract the equations to get
x+y = 20
x-4y = -15
-----------
0x+5y = 35

If 5y = 35, then y = 7 after we divide both sides by 5

Plug y = 7 into the first equation and solve for x
x+y = 20
x+7 = 20
x+7-7 = 20-7
x = 13

So x = 13 and y = 7 are the solutions

Max exercises 13 hours a week while Sasha exercises 7 hours a week
===========================================================
4c)

I'm going to use the Substitution method

x = price for one adult ticket (in dollars)
y = price for one student ticket (in dollars)

Fact #1
4 adult tickets + 2 student tickets = 64 dollars
4x + 2y = 64

Fact #2
3 adult tickets + 3 student tickets = 60 dollars
3x + 3y = 60
3(x + y) = 60
3(x + y)/3 = 60/3
x + y = 20
x + y-x = 20-x ... subtract x from both sides
y = 20 - x

Plug that into the first equation
4x + 2y = 64
4x + 2(y) = 64
4x + 2(20-x) = 64 ... replace y with 20-x; solve for x
4x + 40-2x = 64
2x + 40 = 64
2x + 40-40 = 64-40
2x = 24
2x/2 = 24/2
x = 12

Use x = 12 to find y
y = 20 - x
y = 20 - 12
y = 8

In summary, x = 12 and y = 8, which means...
One adult ticket costs $12
One student ticket cost $8

If the radius of the circle is doubled, by what number is the circumference multiplied?

Answers

circumference is also doubled (multiplied by 2)

Answer:

The number by which the circumference is multiplied is:

Step-by-step explanation:

We know that the circumference of the circle in terms of the radius r is given by:

[tex]\text{Circumference}=2\pi r[/tex]

Now, if the radius is doubled.

i.e.

[tex]r'=2r[/tex]

Hence, the circumference of the new circle is given by:

[tex]\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)[/tex]

i.e.

[tex]\text{Circumference of new circle}=2\times \text{Circumference of original circle}[/tex]

The constant by which the circumference is multiplied is: 2

Your team gets an ice sculpture in the shape of a basketball. It has a radius of 12 inches. What is the volume of the ice? Use 3.14 for pi. Round your answer to the nearest hundredth.

Answers

The answer is 7234.56 inches cubed. The equation to find the volume of a sphere is 4/3*pi*r^3.

The equation would be 4/3 * 3.14 * 12^3.

4/3 * 3.14 * 1728

4/3 * 5425.92

7234.56

What is 6/7 as a recurring decimal?

Answers

this is not actually a recurring decimal when you divide 6 by 7, you get .85714286

The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse

Answers

Consider the attached figure. All the triangles shown are similar, so

CB/CA = CD/CB
30/50 = projection/30
projection = 30^2/50
projection = 18

Simplify (3x − 5) − (5x + 1).

−2x + 6

−2x − 6

2x − 6

2x + 6
can you please work this out for me?
thank you verymuch.

Answers

we have been asked to simplify

[tex] (3x-5)-(5x + 1) [/tex]

To Simplify this, we will first open the parenthesis, as below

[tex] (3x-5)-(5x + 1)=3x-5-5x-1\\
\\
\text{take the like terms together and simplify we get}\\
\\
(3x-5)-(5x + 1)=3x-5x-5-1\\
\\
(3x-5)-(5x + 1)=-2x-6\\
\\

[/tex]

Hence the simplified expression is -2x-6

Answer:

-2x-6

Step-by-step explanation:

The perimeter of the rectangle is 34 cm. Find the value of x.

A. 2

B. 17

C. [tex] \frac{34}{33} [/tex]

D. 20

Answers

2(3x + 11) = 34
3x + 11 = 34/2
3x + 11 = 17
3x = 17 - 11
3x = 6
x = 6/3
x = 2

look at the pictures bellow

Answers

The answer is C.
C=-2

which figures can be precisely defined by using only undefined terms? check all that apply
1) angle
2) arc
3) circle
4) line segment
5) parallel lines

Answers

i think it is answer choices 1, 3, 4, and 5

Please help out with this question! Thanks :)

Answers

On the horizontal line P=6, it looks like the values W=10, 11, 12 may be in the doubly-shaded region. We know that each of those will give a purchase of at least 16 fruits, but we don't know if the budget constraint is met with 12 watermelons. You'd have to check prices to make sure.

If 11 is among the choices, that is the answer I'd choose.

A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.

Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.

Answers

The confidence interval would be 90% Probability that mean lies between 74% and 86% is 90% Prob( 74 <= X-bar<= 86) = 0.9 So the confidence interval is [74, 86] with 90% confidence that the actual population mean lies inside the interval. The error margin would be 6%. In 9 out of 10 the confidence interval for similar samples of seniors will have the true mean of the population of senior scores.

Simplify. −5x4(−3x2+4x−2)
1:−8x^6−x^5−7x^4
2:15x^8−20x^4+10
3:15x^6−20x65+10x64
4:−15x^8−20x^5+10x^4

Answers

The answers my dear friends is 15x^6-20x^5+10x^4

Answer:

[tex]15x^{6}-20x^{5}+10x^4)[/tex]

Step-by-step explanation:

We have been given an expression [tex]-5x^4(-3x^2+4x-2)[/tex] and we are asked to simplify our given expression.

We will use distributive property [tex]a(b+c)=a*b+a*c[/tex] to simplify our given expression.

Upon distributing [tex]-5x^4[/tex] we will get,

[tex](-5x^4*-3x^2)+(-5x^4*4x)-(-5x^4*2)[/tex]

Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,

[tex](15x^{4+2})+(-20x^{4+1})-(-10x^4)[/tex]

[tex](15x^{6})+(-20x^{5})-(-10x^4)[/tex]

[tex]15x^{6}-20x^{5}+10x^4)[/tex]

Therefore, our given expression simplifies to [tex]15x^{6}-20x^{5}+10x^4)[/tex].

The original price of sn item is $25, but after the discount, you only have to pay $18.50. what is the discount (as a percent)?

Answers

The first thing that you have to do is subtract 18.5 from 25. Then you do 6.5/25 and that equals 0.26. To get a percentage you multiply that by 100. You get 26%

The discount is 26%.

What is Discount?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

Given:

Marked price = $25

Selling price = $18.50

So,

Discount = MP - SP

Discount = 25-18.50

Discount = 6.50

Now,

D% = D/MP *100

D% = 6.5 /25*100

D% = 26%

Hence, the discount percent is 26%.

Learn more about discount here:

https://brainly.com/question/3541148

#SPJ2

Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−3x+12y=−6x+2

Select the correct answer from the drop-down menu.

Answers

The slope of (y=-3x+12) is -3 while the slope of (y=-6x+2) is -6. Therefore, it's Inconsistent.
Coincident is one line on the graph
Consistent is two parallel lines

Answer:

The given system of equations is inconsistent.

Step-by-step explanation:

We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.

[tex]y=-3x+12...(1)[/tex]

[tex]y=-6x+2...(2)[/tex]

Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.

Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.

Now let us check slope of given lines.

Upon dividing equation (2) by 2 we will get,

[tex]y=-3x+1...(2)[/tex]

We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.

Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.

Which rule describes a translation that is 8 units to the right and 2 units up?

Answers

we know that

when we speak of right or left we refer to the x axis
x positive --------------> right
x negative--------------> left

when we speak of up or down we refer to the y axis
y positive --------------> up
y negative--------------> down

therefore

the rule is
(x,y)---------> (x+8, y+2)

The answer is

x, y (x + 8, y + 2)

Easy Geometry! Easy Geometry! Easy Geometry!

Answers

Answers:

b. Linear Pair
c. Definition of supplementary
d. Substitution; Combine like terms
e. Division Property of Equality
f. Definition of Right Angle
g. Definition of Perpendicular
=========================================

Further Explanations:

b. A linear pair is simply a result of cutting a straight angle into two pieces. They are adjacent and supplementary (add to 180 degrees)

c. If two angles are supplementary then they add to 180. This is simply a definition to memorize.

d. The "m < 2" is replaced with "m < 1" through the substitution property. This is possible because of statement (a) on the first line of the proof. The teacher has also combined like terms. Technically this step would require its own line.

e. Think of this as 2x = 180 solving to x = 90. The step done here is dividing both sides by 2, which uses the division property of equality. Alternatively you can use the multiplication property of equality to multiply both sides by 1/2 = 0.5

f. If an angle is 90 degrees, then by definition it is considered a right angle. This is another thing you memorize.

g. Also to be memorized is the fact that if two segments form a right angle, then they are considered perpendicular segments. The upside down T symbol means "perpendicular to"

Answer:

b) Linear Pair

c) Definition of supplementary

d) Substitution; Combine like terms

e) Division Property of Equality

f) Definition of Right Angle

g) Definition of Perpendicular

The area of a playground is 204 yards squared the width of a playground at 5 yards longer than its length whats the length and the width of the playground

Answers

w= width= L+5
L= length
Area= 204

Area= LW
204 square yards= LW
substitute w=L+5 for w
204= (L)(L+5)
204= L^2 + 5L
subtract 204 from both sides
0= L^2 + 5L - 204
factor
0= (L+17)(L-12)

0= L+17
-17= L

0= L-12
12 yards= L

WIDTH
Since the area cannot be a negative number, we'll use L=12 to find the width.

w=L+5
w=12+5
w=17 yards

CHECK:
204=(12)(17)
204=204

ANSWER: The length is 12 yards and the width is 17 yards.

Hope this helps! :)

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