A science museum charges an admission fee of $10 per adult and $6 per child. If the museum had 2,000 visitors on a particular day and the total collection was $18,800, how many adults and children visited the museum?

Answers

Answer 1
a = adult
c = child

10a + 6c = 18,800
a + c = 2,000

In the second equation, subtract c from both sides.

a = 2000 - c

Put this into the first equation.

10(2000 - c) + 6c = 18800

Multiply everything in the parenthesis by 10.

20,000 - 10c + 6c = 18,800

Combine like terms.

20,000 - 4c = 18,800

Subtract 20,000 from both sides.

-4c = -1,200

Divide -4 on both sides.

c = 300

Put this into the second equation.

a + 300  = 2,000

Subtract 300 from both sides.

a = 1,700

Hope this helps!

Related Questions

Given: Lines a and b are parallel and line c is a transversal. Prove: 2 is supplementary to 8 What is the missing reason in the proof?

Answers

Corresponding Angles Postulate I think...

Answer:

your answer is: A

Step-by-step explanation:

corresponding angles theorem.

You are enclosing a rectangular garden with 60 feet of ornamental fencing. the area of the garden is 200 square feet. what are the dimensions of the​ garden?

Answers

The perimeter is equal to 60 feet and has the formula:

Perimeter = 2 l + 2 w

60 = 2 l + 2 w

 

The area is equal to 200 square feet and has the formula:

Area = l w

200 = l w

 

Rewriting area in terms of l:

l = 200 / w

 

Combining this with the perimeter formula:

60 = 2 (200 / w) + 2 w

60 = 400 / w + 2 w

Multiplying all by w:

60 w = 400 + 2 w^2

Dividing by 2 and rearranging:

w^2 – 30 w = - 200

Completing the square:

(w – 15)^2 = - 200 + (-15)^2

(w – 15)^2 = 25

w – 15 = ±5

w = 10, 20

 

Hence the dimensions of the garden is 10 feet by 20 feet

Final answer:

The width and length of the rectangular garden, given an area of 200 square feet and a total available perimeter of 60 feet, are 10 feet and 20 feet respectively.

Explanation:

To solve this problem, we can use the formula for the area of a rectangle, which is length × width = area, and the perimeter of a rectangle, which is 2(length + width) = perimeter. We know the total perimeter available (which is the ornamental fencing) is 60 feet and the area is 200 square feet.

Let's denote the length of the rectangle as L and the width as W. We can then set up these two equations:

2L + 2W = 60L × W = 200

We can simplify the first equation to get L + W = 30 and then isolate either L or W to substitute into the area equation. Let's isolate L to get L = 30 - W.

We then substitute this into the area equation to get: (30 - W)W = 200. Solving this quadratic equation, the possible solutions are W=10 and W=20. However, if W=20, that would leave 0 feet for the length, which is not possible. Therefore, we have W=10 and L=20.

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Use the formula to evaluate the series 3+6+12+24+48+96

Answers

multiplication by 2.
I do not know the formula you need to sue but the answer is 189.

Ms. Harris is stocking up on dry-erase markers for the upcoming school year. She used 56 dry-erase markers last year and plans to use at least that many for next year. The number of markers in each box is two more than three times the number of boxes she purchased for this upcoming school year.

Which of the following inequalities can be used to determine b, the number of boxes she purchased.

Answers

for plato users the answer is D

Answer:

[tex]3b^2+2b\geq 56[/tex]

Step-by-step explanation:

Here, b represents the number of boxes she purchased for this upcoming school year,

Also,  The number of markers in each box is two more than three times the number of boxes she purchased for this upcoming school year.

⇒ The number of marker in each box = 3b+2

Now, the total number of marker = Number of boxes × Number of marker in each box

[tex]=b\times (3b+2)[/tex]

[tex]=3b^2+2b[/tex]

Since, she plan to use at least 56 marker in the upcoming year,

That is, the total number of marker ≥ 56

[tex]\implies 3b^2+2b\geq 56[/tex]

Which is the required inequality that shows the given situation.

Could someone check to see if I'm doing this right please? Will give brainiest. (Picture attached)

Answers

yes so far you are doing it correctly

You're doing great! Rational numbers have an end or repeat, Irrational do not.

Which linear inequality is represented by the graph?

A) y > 2/3x - 2

B) y < 2/3x + 2

C) y > 2/3x + 1

D) y < 2/3x - 1

I NEED THE ANSWER ASAP ‼️

Answers

D) y < 2/3x - 1 is the answer you are looking for this is because the negative one if your y intercept and the 2/3 is your slope this makes the line and the sign draws the shading down with a dotted line.

A theater has 500 seats. Three-fourths of the seats are filled. How many seats are filled?

Answers

375 seats are filled
Three-fourths or 3/4 of the seats are taken out of the 500 would be 3/4 = 0.75 or 75% of the seats taken out of the 500 seats in total. 
500 / 75% or 500 * 0.75 = 375 

So, your answer would be that 75% of the seats were taken out of the total of 500 seats. Which would be 375 seats were taken out of 500 seats in total.

Hope this helps. 

~ ShadowXReaper069


Four doughnuts and 4 coffees cost $12. The cost of the 4 coffees is half the cost of the 4 doughnuts. What is the cost of each coffee?

Answers

The cost of each coffee is $1.05

Which of the following is important in a two-column proof?

A.) a list of all theorems
B.) staircase Logic
C.) order
D.) detailed explanations for each step

Answers

It's C because if it's not in order then it wouldn't make sense and it would be wrong.

A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid. T. A. =

Answers

Answer:

[tex](24\sqrt{3}+72)\text{ square unit}[/tex]

Step-by-step explanation:

Since, the area of a regular hexagon is,

[tex]A=\frac{3\sqrt{3}}{2}a^2[/tex]

Where, a is the side of the hexagon,

Here, the base of the pyramid is a regular hexagon having side length,

a = 4 unit,

Thus, the base area of the pyramid is,

[tex]A_B=\frac{3\sqrt{3}}{2}(4)^2[/tex]

[tex]=\frac{48\sqrt{3}}{2}[/tex]

[tex]=24\sqrt{3}\text{ square unit}[/tex]

Now, the lateral face of the pyramid is a triangle having base = 4 unit and height = 6 unit,

Also, a hexagonal pyramid has 6 triangular faces,

So, the total lateral area of the pyramid is,

[tex]A_L=6\times \frac{1}{2}\times 4\times 6[/tex]

[tex]=\frac{144}{2}[/tex]

[tex]=72\text{ square unit}[/tex]

Hence, the total area of the pyramid is,

[tex]T.A.=A_B+A_L[/tex]

[tex]=(24\sqrt{3}+72)\text{ square unit}[/tex]

Answer:

[tex]24\sqrt3+72[/tex] Square units

Step-by-step explanation:

We are given that a pyramid which has a regular hexagonal base.

Side length of hexagonal base=Base of triangular face=4 units

Height of triangle=6 units

We have to find total area of the pyramid.

The total area of pyramid=[tex]A_B+A_L[/tex]

Where [tex]A_B[/tex]=Base area

[tex]A_L[/tex]=Lateral area

Area of hexagonal base=[tex]\frac{3\sqrt3}{2}a^2[/tex]

Where a= Side length

Now, area of hexagonal  base=[tex]\frac{3\sqrt3}{2}(4)^2=24\sqrt3[/tex] square units

Area of triangular face=[tex]\frac{1}{2}\times base\times height=\frac{1}{2}\times 6\times 4=12[/tex] square units

In pyramid , there are 6 triangular faces.

Therefore, lateral area of pyramid=[tex]6\times 12=72[/tex] square units

Substitute the values in the given formula then, we get

Total lateral area of given pyramid=[tex]24\sqrt3+72[/tex] Square units

The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x − 4 The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.

Answers

13

You can find this by simply adding the y intercepts of both functions.
Thus 9+4 = 13

Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,-4,-13...
Imran said the formula is g(n)=14-9(n-1)
Aubrey said the formula is g(n)=14-9n
Which one of them is right?
Just Irman
Just Aubrey
Both
Neither


PLEASE HELP ASAP!!!

Answers

Answer with Step-by-step explanation:

An explicit formula for the sequence

14,5,-4,-13...

given by Imran  is g(n)=14-9(n-1)

and by Aubrey is g(n)=14-9n

We have to determine who is right

g(n)= 14-9n

g(1)=14-9

    = 5

Hence, formula given by Aubrey is wrong

g(n)=14-9(n-1)

g(1)=14-9(0)=14

g(2)=14-9(1)=5

g(3)=14-9(2)= -4

g(4)=14-9(3)= -13

Hence, formula given by Imran is correct

Hence, correct option is:

Just Imran

Answer:

Only Imran

Step-by-step explanation:

This graph shows the costs of purchasing two types of laundry detergent.
Which statement is true?


a.) Detergent A is less expensive than Detergent B.

b.) Detergent B is less expensive than Detergent A.

c.) Detergent A and Detergent B cost about the same.

Answers

The the answer would be B

Answer:

the other person is correct

Step-by-step explanation:

Which physical property is shown by scratching one material with another? malleability
viscosity
conductivity
hardness

Answers

Malleability is the ability to be turned into thin wires (Incorrect) 
Viscosity is how thick or thin the substance is (Incorrect) 
Conductivity is the ability of the substance to pass electric current (Incorrect) 
Hardness is how easy it is to peel off or scratch a material with another (Correct) 

The physical property would be hardness. 

Hope I helped :) 

hardness        is the answer for sure

Point A is between points M and C. If MC = 3x+6, find the measure of each segment.

Answers

if A is between M and C, then AM + AC = MC

2x + 8 + 3x + 6 = 7x
5x + 14 = 7x
14 = 7x - 5x
14 = 2x
14/2 = x
7 = x

AM = 2x + 8.......2(7) + 8 = 22
AC = 3x + 6.......3(7) + 6 = 27
MC = 7x............7(7) = 49







Find the common difference for the sequence shown 1/4,5/16,3/8

Answers

common difference for the sequence = 1/16

cause
1/4 = 4/16
and
3/8 = 6/16

so
4/16 + 1/16 = 5/16
5/16 + 1/16 = 6/16

What is the solution to the system of equations?

2x – y = 7

y = 2x + 3

(2, 3)
(2, 7)
no solution
infinite number of solutions

Answers

Consider


2x – y = 7

y = 2x + 3


Subst. 2x+3 for y in the first equation: 2x - (2x + 3) = 7


This boils down to 0 + 3 = 7, which simply is not true and can never be true.


Thus, this system of equations has no solution.


Answer:

The system of x and y is no solutions.

C is correct

Step-by-step explanation:

Given: System of equation

[tex]2x-y=7[/tex]

[tex]y=2x+3[/tex]

We have system of equation and to solve for x

Using substitution method to solve for x and y

Substitute y=2x+33 into 2x-y=7

[tex]2x-(2x+33)=7[/tex]

[tex]2x-2x-33=7[/tex]

[tex]-33\neq 7[/tex]

-33 is not equal to 7.

We didn't get the value of x.

No solution for x and y

Hence, The system of x and y is no solutions.

Some of the steps in the derivation of the quadratic formula are shown. Step 4: Step 5: Step 6: Step 7: Which best explains why the expression cannot be rewritten as during the next step? Negative values, like −4ac, do not have a square root. The ± symbol prevents the square root from being evaluated. The square root of terms separated by addition and subtraction cannot be calculated individually. The entire term b2 − 4ac must be divided by 2a before its square root can be determined.

Answers

Answer:c

Step-by-step explanation:

The answer is the square root of terms separated by addition and subtraction cannot be calculated individually.

To find expression cannot be rewritten as during the next step and explain.

What is expression?

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

The statement that best explains why the expression cannot be rewritten as during the next step is that the square root of terms separated by addition and subtraction cannot be calculated individually.

So, the square root of terms separated by addition and subtraction cannot be calculated individually.

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Write an equation of the line passing through the point A(2, 0) that is parallel to the line y = 3x−5 .

Answers

Hello,

In order for lines to be parallel to each other, they need to have the same slope. So, let's plug in the points and slope for point-slope form.

The equation for point-slope form is: y-y1 = m (x-x1)

Let's plug in the points into the equation. 
y-5 = m (x-0), and then let's plug in the slope for "m" : y-5 = 3 (x-0).

After plugging the numbers in, the equation is simplified to y-5 = 3 (x-0). Then distribute the 3 to the parenthesis. y-5 = 3x. To get y by itself, you need to add 5 to both sides. After that, the equation parallel to that equation is: y = 3x + 5.

Hope this helps! =)

The equation of the line passing through the point A (2, 0) that is parallel to the line y = 3x - 5 is y = 3x - 6.

To find the equation of a line parallel to the line y = 3x - 5 and passing through point A (2, 0), we can use the fact that parallel lines have the same slope.

The given line has a slope of m = 3. Therefore, any line parallel to it will also have a slope of m = 3.

Now, using the point-slope form of the equation of a line, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where m is the slope of the line and [tex](x_1, y_1)[/tex] is a point on the line, we can substitute the values we know:

For point A (2, 0):

[tex]x_1[/tex] = 2

[tex]y_1[/tex] = 0

Slope m = 3

The equation becomes:

y - 0 = 3 (x - 2)

y = 3x - 6

This line has the same slope as the given line, y = 3x - 5, and passes through the point A (2, 0). Therefore, it is parallel to the given line and passes through the given point.

What is the intersection of planes ADE and BEA?

a.) Plane BED
b.) Plane ABC
c.) Line BD
d.) Line AE

Answers

The correct answer is D.) Line AE

Answer:

d.) Line AE

Step-by-step explanation:

We have been given a diagram. We are asked to find the intersection of planes ADE and BEA.

Upon looking at our given diagram, we can see that both planes intersect only at two points that are point A and E respectively.

We can also see that the line AE is a common side of both planes, therefore, line AE is the intersection of planes ADE and BEA.

It costs $3 to bowl a game and $2 for shoe rental. a. Complete the table for the cost of up to 5 games.

Answers

The answer to this is $26

One nanometer is about 0.00000003937 of an inch. what is this number in scientific notation?

Answers

0.00000003937 = 3,937 * 10^-8

The scientific notation of  0.00000003937  is 3.397 x [tex]10^{-8}[/tex]

what is scientific notation?

A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less. So, we utilise scientific notation to clearly describe extremely large or extremely small integers.

Given  number:

0.00000003937

Now, to make the number in standard form we have to write the number in 10 raise to power.

So, 0.00000003937

= 3.397 x [tex]10^{-8}[/tex]

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Find (x - 6)2

a. x2 + 12x + 36

b. x2 - 12x + 36

c. x2 + 6x + 36

s. x2 - 6x + 36

Answers

its 4-6=2 its easy because just keep useing numbers until the become two


The answer is b if the question is (x-6)^2 and NOT (x-6)2

(x-6)^2= 2x +12x +36

A wise man once said “200 reduced by twice my age is 42” What is his age ?

Answers

Is age is x

2x-200=42 

2x=242

x=121

He is 121 years old. 

Hope this helped!!
If you have any questions, let me know!:)
200⁻2x= 42
200-42=158
158÷2=
79 

A cashier always starts the day with $60 in pennies, nickels, dimes, and quarters. She begins with five times as many pennies as quarters, and the number of nickels and dimes are both twice the number of quarters. How many pennies does she start with?

6 pennies
26 pennies
100 pennies
500 pennies

Answers

6 ........................................................I think

500 pennies

500 pennies= $5
1/5 of 500 is 100 quarters, which is $25 
There are 2x as many dimes an nickels are there are quarters, so 200 dimes (which is $20) and 200 nickels is $10.

5 + 25 + 20 + 10 = $60

The width of the rectangle shown below is 8 inches (in.). The length is 3 feet (ft.). What is the area of the rectangle in square inches?

Answers

convert feet to inches 3 feet=36 inches.
8*36=288 inches squared

Answer:

3 feet = 36 inches...

THEN

8 x 36 = 288 inches squared!

Step-by-step explanation:

hope this helped

An airplane traveled 1,991.25 kilometers at an average speed of 885 kilometers per hour. How long did it take for the airplane to travel this distance? hours and minutes

Answers

This trip would take 2 hours and 15 minutes, since 1,991.25/885=2.25. This means it would take two hours and 25/100 (1/4) of an hour. 1/4 of an hour is 15, so you add 15 minutes to 2 hours.

Answer:

It took 2 hours and 15 minutes for the airplane to travel 1,991.25 Km

Step-by-step explanation:

In order to find the time, you need to use the fact that average speed = distance traveled/time taken, the problem gives you that the distance traveled is equal to 1,991.25 Km and the average speed is 885 Km/h.

So, you use these values to find the time taken as follows:

[tex]time = \frac{distance}{speed}=\frac{1991.25 km}{885 \frac{km}{h}} = 2.25 h[/tex]

2.25 is a number made by two parts: integer-part and fractional-part.

The integer-part is equal to 2 hours.

The 0.25 is the fractional-part and corresponds to the minutes. 0.25 in fraction is [tex]0.25 = \frac{1}{4}[/tex], the hour has 60 minutes, so when you divided by  [tex]\frac{1}{4}[/tex] you the get 15 minutes.


PLEASE HELP 

Write the linear inequality shown in the graph. The gray area represents the shaded region.


y ≤ –3x + 5


y ≥ –3x + 5


y ≥ –3x – 5


y ≤ –3x – 5

Answers

Its A, all y-values are less than -3x+5. also consider root by setting -3x+5=0

x=5/3 is positive so its the first one

Answer:

[tex]y\leq-3x+5[/tex]

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area below the solid line (the gray area)

The slope of the solid line is negative

The y-intercept of the solid line is positive

The equation of the solid line is equal to [tex]y=-3x+5[/tex]

therefore

the equation of the inequality is equal to

[tex]y\leq-3x+5[/tex]

does this table represent a function?why or why not?
x:4,7,8,8,10
y:0,5,5,8,9

Answers

No, x can't repeat. So this is not a function because two 8s. 

Which of the following is the solution set of the given equation?
14 + 8m = 14 - 3m - 5m

A.) Ø
B.) {0}
C.) {all reals}

Answers

c.) {all reals}, letter c is the answer because : 14+8m=22 and than when you add 14+3m+5m=22 , you need to change the soustraction in addition.
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