In one day a movie theater collected $4275 from 675 people. The price of admission is $7 for an adult and $5 for a child. How many adults and how many children were admitted to the movie theater that day?
To find the number of adults and children admitted to the movie theater, we set up two equations based on the admission costs and total number of attendees. Solving these equations revealed that there were 450 adults and 225 children.
Explanation:The question involves a system of equations where we are required to determine the number of adults and children who were admitted to the movie theater given the total revenue and total number of attendees.
Let's denote the number of adults by A and the number of children by C. Given the price of admission is $7 for an adult and $5 for a child, we can represent the total revenue with the equation:
7A + 5C = 4275
Also, considering the total number of people is 675, we have another equation:
A + C = 675
To solve these equations, we'll use the substitution or elimination method:
From the second equation, express C in terms of A:Therefore, there were 450 adults and 225 children admitted to the movie theater that day.
If f(x) = 7 + 4x and g(x)= 7x, what is the value of (f/g)(5)
The value of [tex](\frac{f}{g})(5)[/tex] is [tex]\frac{27}{35}[/tex]
Explanation:
Given that [tex]f(x)=7+4x[/tex] and [tex]g(x)=7x[/tex]
The value of [tex](\frac{f}{g})(5)[/tex]:
The value of [tex](\frac{f}{g})(5)[/tex] can be determined by substituting x = 5 in the functions f(x) and g(x) and then dividing the terms, we get, the value of [tex](\frac{f}{g})(5)[/tex]
Thus, we have,
[tex](\frac{f}{g})(5)=\frac{f(5)}{g(5)}[/tex]
Substituting the value of x = 5 in the functions f(x) and g(x), we get,
[tex](\frac{f}{g})(5)=\frac{7+4(5)}{7(5)}[/tex]
Simplifying the terms, we have,
[tex](\frac{f}{g})(5)=\frac{7+20}{35}[/tex]
Adding the terms in numerator, we have,
[tex](\frac{f}{g})(5)=\frac{27}{35}[/tex]
Thus, the value of [tex](\frac{f}{g})(5)[/tex] is [tex]\frac{27}{35}[/tex]
A square is inscribed in a circle. If the area of the square is 49 square units, what is the radius of the circle?
a
√2/7 unit
b
(7√2)/2 units
c
7√2units
d
14√2 units
Answer:
B
Step-by-step explanation:
If it is inscribed in the circle that means all four corners of the square are touching the circle
so therefore the diagonal of the square is the diameter of the circle
the side lengths of the square as you know is 7 units ([tex]\sqrt{49[/tex]) the length of the diagonal is [tex]7\sqrt{2}[/tex] heres how I know
If you cut the square in half through the centre diagonally you will get a right isosceles triangle, using the pythagorus theorum
[tex]7^2+7^2=C^2\\49+49=C^2\\98=C^2\\\sqrt{98}=C\\C=7\sqrt{x}[/tex]
Now we have the diameter
it's just half of that, so the answer is B
For a square inscribed in a circle, the length of the diagonal of the square equals the diameter of the circle. Given the area of the square is 49 units, the length of a side is 7 units, and thus the diagonal (or diameter of the circle) is 7√2 units. Therefore, the radius of the circle is half of the diameter, which is (7√2)/2 units.
Explanation:In this question, we need to determine the radius of a circle in which a square is inscribed. The square has an area of 49 square units. In a square inscribed in a circle, the diameter of the circle is equal to the diagonal of the square. Thus, if 'a' is the length of a side of the square, the length of the diagonal, which is the diameter of the circle, is 'a√2'.
Given that the area of the square is 49 units, 'a^2=49' or 'a=7' units. Therefore, 'a√2' = '7√2' units. As this is the diameter, the radius of the circle is half of the diameter thus, it equals '(7√2)/2' units. Which means option b '(7√2)/2' units is the correct answer.
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at a farm 15 of the 20 chicken are hens what percent of the chicken in the farms hens
Answer: 75 percent of the chicken are hens.
If the sides of two similar triangles are in the ratio of 3:5, find the ratio of their areas.
Ratio of areas of similar triangles is 9 : 25.
Solution:
Given data:
Ratio of sides of two similar triangles = 3 : 5
To find the ratio of areas of the triangles:
We know that,
In two triangles are similar, then the ratio of their area is equal to the square of the ratio of their sides.
[tex]$\text{Ratio of areas} = \frac{\text{Area of triangle 1}}{\text{Area of triangle 2} }[/tex]
[tex]$=\left(\frac{3}{5}\right) ^2[/tex]
[tex]$=\frac{9}{25}[/tex]
Ratio of areas of similar triangles is 9 : 25.
Answer:
16
:
81
Explanation:
Scale factor for the sides of these triangles.
k
=
4
9
.
Therefore the ratio of area will be:
k
2
=
Area Triangle A
Area triangle B
k
2
=
(
4
9
)
2
=
16
81
In the early 1990s, the group was approached by film director Spike Lee to compose a song for his upcoming biopic on the life of Malcolm X.
Read the passage underlined (3).There may be a mistake in punctuation, capitalization, or spelling. If you find a mistake, choose the answer that corrects the mistake. If there is no mistake, choose ‘Correct as is.’
A) Correct as is.
B) In the Early 1990s, the group was approached
C) In the early 1990s the group was approached
D) In the early 1990s, the group, was approached
Answer: A
Step-by-step explanation: that’s the answer
Answer:
A
Step-by-step explanation:
Graph each function.
Answer:
Step-by-step explanation:
We can recognize that the parent function for all of these graphs is going to be y=x^2. What this means is that we can graph y=x^2 and then apply transformations to it to get to all of these new graphs.
1. y = -x^2 + 5
We can see that the coefficient of the x^2 term is negative which tells us that the graph will now open downwards.
We also know that we are adding 5 on the outside of the argument which means it affect vertical shift. Therefore, we will be moving 5 units up.
2. y = x^2 - 4
We can see that the only change made to this equation is subtracting 4 on the outside of the squared part of the equation. Again, this signifies vertical movement, but since it's negative we will be moving the entire y = x^2 graph down 4 units.
3. y = -x^2 - 1
What do you notice about this graph?
- negative coefficient
- subtracting 1 outside of the argument
What do these mean?
- negative coefficient: opens downwards
- subtracting 1: move entire y = x^2 graph down 1 unit
A tea vendor gives samples of tea in cone shaped cups. The cups have a diameter of 4 inches and a height of 5 inches. If there are about 0.55 fluid onces in one cubic inch, how many fluid ounces of tea will one sample hold? Round to the nearest tenth
One sample cup will hold 11.51 ounces of fluid.
Step-by-step explanation:
Diameter of cone shaped cup = 4 inches
Radius = [tex]\frac{Diameter}{2}=\frac{4}{2}=2\ inches[/tex]
Height of cup = 5 inches
Volume of cone = [tex]\pi r^2 \frac{h}{3}[/tex]
Putting values
Volume of cone = [tex]3.14*(2)^2*\frac{5}{3}\\[/tex]
Volume of cone = [tex]3.14*4*\frac{5}{3}=\frac{62.8}{3}[/tex]
Volume of cone = 20.93 inches cubed
Amount of fluid in one cubic inch = 0.55 ounces
Amount of fluid in 20.93 cubic inches = 0.55*20.93 = 11.51 ounces
One sample cup will hold 11.51 ounces of fluid.
2. Solve each equation and check your solution.
a.-3w - 4= w + 3
b. 3(3 – 3x) = 2(x + 3) - 30
c. 1/(2 + 4) – 6 = 2 (5 – 2)
Answer:
1. Solution
-3w-w=3+4
-4w=7
Therefore,w= -7/4
Step-by-step explanation:
2. Solution
3(3-3x)=2(x+3)-30
9-9x=2x+6-30
9+40-6=2x+9x
43=11x
Therefore, x=43/11
#Hope it helps u
Find the value of M. (please answer)
Answer:
M = 70
Step-by-step explanation:
Supplementary Angles = 180
180 - 110 = 70
Also linear pairs = 180.
m=70 degrees
I hope that helps you :)
The product of 2 and the sum of 5 is 8
Answer:26
Step-by-step explanation:
2x(8+5)
2x13=26
I think i know but I probably have it wrong, will give Brainliest
Answer:
164 square feet
164 ft^2
Step-by-step explanation:
Base: 10 × 4 = 40 (×2 = 80)
Front/back face: 10 × 3 = 30 (×2 = 60)
Left/right face: 3 × 4 = 12 (×2 = 24)
Add: 80 + 60 + 24 = 164
Damon buys lumber worth $562. He gets 20% contractor discount. The sales tax is 6%. his credit card gives him 2% off. How much does he pay?
Answer:
$467.05
Step-by-step explanation:
The price is $562
First, 20% off of that:
562 - 20% of 562 = 562 - 0.2(562) = $449.60
Second, he has to pay 6% tax on this amount, so:
6% = 6/100 = 0.06
449.60 + 0.06*449.60 = $476.58
He won't be paying this amount, because paying through credit card will give him 2% discount on this, so:
476.58 - 0.02(476.58) = $467.05
Final Price: $467.05
The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the sum of the first 100 even natural numbers?
Answer:
1) 200
2) 10100
3) less than
explanation:
just did it :))
The sum of the first 100 even natural numbers will be 10,100.
What is the sum of an arithmetic sequence?Let a₁ be the first term, L be the last term, n be the number of terms, and d be a common difference.
Then the sum of the arithmetic sequence will be
S = (n / 2)[a₁ + L]
S = (n/2) [2a + (n − 1) d]
The arithmetic sequence is given below.
2, 4, 6, 8, 10, .....
The first term is 2 and the common difference is 2. Then the sum of the first 100 even natural numbers will be
S = (100/2) [2 x 2 + (100 − 1) x 2]
S = 50 [4 + 99 x 2]
S = 50 [4 + 198]
S = 50 [202]
S = 10,100
The sum of the first 100 even natural numbers will be 10,100.
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I ONLY HAVE A LITTLE TIME ANS NEED HELP!!!!! can someone explain this to me
Answer:
x = 92
Step-by-step explanation:
[tex]\frac{x}{46} =\frac{78}{39}[/tex]
I did big side over small side, proportions.
Cross Multiply.
39x = 3,588
divide by 39x
x = 92
Answer:
92
Step-by-step explanation:
These triangles are similar because they share a common angle and two pairs of sides in the same ratio.
Sides of the bigger triangle are double of those of the smaller triangle
46+46 = 92
Y= 4.6, 13.9, 21.6, ????
Option B: 13.9 is the value of y
Explanation:
Given triangle is a right angled triangle.
The legs of the triangle are 8 and y.
The hypotenuse of the triangle is x.
And the angle opposite to y is 60°
We need to determine the value of y.
Let us find the value of y using the tangent formula.
The formula for tan is given by
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Since, we know that [tex]\theta = 60^{\circ[/tex] , [tex]opp=y[/tex] and [tex]adj=8[/tex]
Substituting these values in the formula, we get,
[tex]tan \ 60^{\circ}=\frac{y}{8}[/tex]
Multiplying both sides by 8, we have,
[tex]8\times tan \ 60^{\circ}=y[/tex]
Substituting the value of [tex]\tan 60^{\circ}[/tex] , we get,
[tex]8\times 1.732=y[/tex]
Simplifying, we have,
[tex]13.856=y[/tex]
Rounding off, we get,
[tex]13.9=y[/tex]
Thus, the value of y is 13.9
Hence, Option B is the correct answer.
ASSIGNMENTS
COURSES
Assignment - 4. Ratios, Rates, and Unit Rates
Attempt 1 of 2
Decide which unit rate is greatest and explain why using complete sentences.
• 12 apples for $4
• 21 apples for $8
• 35 apples for $14
• 45 apples for $16
WRITER
Answer:
3 apples per $ is the greatest unit rate when someone buy 12 apples for $4, because we are able buy more apples with this rate for the same price.
Step-by-step explanation:
As we know that unit rate can be calculated by dividing the two quantities having different units.
For example, Madrid has been champions 10 times in 30 seasons,
i.e. 10 champions / 30 seasons = 0.33 champions per season
and
Barcelona has been champions 5 times in 30 seasons.
i.e. 5 champions / 30 seasons = 0.16 champions per season
Thus, the champion rate for Real Madrid is greater than the champion rate for Barcelona. It means, Real Madrid has been a better team.
Now, let us check and answer the question.
12 apples for $4 means:12 apples / $4 = 3 apples per $
21 apples for $8 means:21 apples / $8 = 2.62 apples per $
35 apples for $14 means:35 apples / $14 = 2.5 apples per $
45 apples for $16 means:45 apples / $16 = 2.81 apples per $
From the above calculations and observation, we can conclude that 3 apples per $ is the greatest unit rate when someone buy 12 apples for $4.
This unit rate is the greatest because we are able buy more apples with this rate for the same price.
In other words, the rate is cheaper than the unit rate of the rest, because can buy more apples with this rate for the same price.
What is the area of this trapezoid?
Check the picture below.
[tex]\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases}\\ h=height\\[-0.5em] \hrulefill\\ a=12\\ b=15\\ h=16 \end{cases}\implies A=\cfrac{16(12+15)}{2}\implies A=216[/tex]
Decrease 620 by 10%
Answer:
682
Step-by-step explanation:
620, percentage decreased by - 10% (percent) of its value = 682
you deposit $1600 in an account. The annual interest rate is 5% for 3 years. How much
interest will you earn on the money?
Answer: $240
Step-by-step explanation:
Simple interest= Principal x Rate x Time
Where P= 1600, R= 5% = 0.05, T=3
= 1600 x 0.05 x 3
$240
0) Rodney had $60 to spend on sports equipment. After buying 6 footballs, he had $7.50. How
much did each football cost?
Answer:
$8.75
Step-by-step explanation:
He had $60 to spend on sports equipment.
He bought 6 footballs and was left with $7.50
First get the amount used in buying all the footballs
That’s
$60 - $7.50 = $52.5
He bought the 6 balls for $52.5
Therefore, amout paid for each football will be amount spent in buying the footballs divided by number of footballs bought
That’s
$52.5/6 = $8.75
Each football cost $8.75
The solution to an inequality is 5≤x<9. What is the smallest value of x that will make the original inequality true?
Answer:
5
Step-by-step explanation:
It is given that the solution to an inequality is
[tex]5\leq x<9[/tex]
It means the original inequality is true for any values of x which is greater than or equal to 5 and less than 9.
We need to find the smallest value of x that will make the original inequality true.
[tex]5\leq x\text{ and }x<9[/tex]
Therefore, smallest value of x is 5 that will make the original inequality true.
JL has coordinates J(-6, 1) and L(-4,3).
Find the coordinates of the midpoint.
Answer:
The coordinates of the mid-point of JL are (-5 , 2)
Step-by-step explanation:
If point (x , y) is the mid-point of a segment whose end-points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], then [tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ JL is a segment
∵ The coordinates of J are (-6 , 1)
∴ [tex]x_{1}[/tex] = -6 and [tex]y_{1}[/tex] = 1
∵ The coordinates of L are (-4 , 3)
∴ [tex]x_{2}[/tex] = -4 and [tex]y_{2}[/tex] = 3
Lets use the rule above to find the mid-point of JL
∵ [tex]x=\frac{-6+-4}{2}=\frac{-10}{2}[/tex]
∴ x = -5
∴ The x-coordinate of the mid-point is -5
∵ [tex]y=\frac{1+3}{2}=\frac{4}{2}[/tex]
∴ y = 2
∴ The y-coordinate of the mid-point is 2
∴ The coordinates of the mid-point of JL are (-5 , 2)
Final answer:
The coordinates of the midpoint of the segment with endpoints J(-6, 1) and L(-4,3) are obtained by averaging the x and y coordinates of the endpoints, resulting in (-5, 2).
Explanation:
To find the coordinates of the midpoint of a segment with endpoints J(-6, 1) and L(-4,3), you use the midpoint formula which is ((x1 + x2)/2, (y1 + y2)/2). In this case, x1 is -6, x2 is -4, y1 is 1, and y2 is 3. Plugging these into the formula, we get the midpoint coordinates ((-6 - 4)/2, (1 + 3)/2) which simplifies to (-5, 2). Therefore, the midpoint of JL is at the coordinates (-5, 2).
what is the perimeter of this tile 6in 2in
Answer:
16 inches
Step-by-step explanation:
The perimeter of the tile is 16 inches. The perimeter of a shape is the total length of all of its sides added together.
In this case, the tile has two sides that are 6 inches long and two sides that are 2 inches long.
To find the perimeter, we can add all of the side lengths together:
Perimeter = 6 inches + 6 inches + 2 inches + 2 inches
Perimeter = 16 inches
Therefore, the perimeter of the tile is 16 inches.
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Is 4/6 greater than 1/2
Yes because you have to convert the answers to 8/12 to 6/12
1/2 is not greater than 4/6 and the answer to the question "Is 1/2 greater than 4/6?" is no.
An engineer drew the graph of a new tire on a coordinate plane. The equation of the tire was x^2+y^2-26y=0. How many feet will the tire roll in 100 complete revolutions. If necessary, round your calculations to the nearest hundredths, and your final answer to the nearest whole number. Complete the explanation (look at picture)
Answer:
Mr. Z ?
Step-by-step explanation:
Which function has the given properties below? The domain is the set of all real numbers. One x-intercept is (StartFraction pi over 2 EndFraction, 0 EndFraction). The maximum value is 3. The y-intercept is (0, –3).
Answer:
y = -3cosx
Step-by-step explanation:
Let me rewrite your question:
One x-intercept is ( pi/2 , 0) so we know that it is a trigonometric function such as cosine that has x-intercept (pi/2,0). The maximum value is 3, it means the amplitude must be 3: y = 3 cos x The y-intercept is (0,-3), means when x =0, y will equal to negative 3 (-3) then it is the function y = -3cosx,So y = -3cosx is the function has the given properties
Line segment CD is 5 inches long. if line segment CD is dilated to form line segment C'D' with a scale factor of 0.6, what is the length of line segment C'D'.
Answer:
3 inches
Step-by-step explanation:
5 inches * 0.6 scale factor = 3 inches
Answer:
3 inches
Step-by-step explanation:
Which method would be the most simplest way to solve the system? 7x+5y=19
-7x-2y=-16
Answer:
14x+3y=3
Step-by-step explanation:
Answer:
The answer is elimination and the equation evaluated would be (2,1)
Step-by-step explanation:
Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.
Weights of eggs: 95% confidence; n=53, /x =1.34 oz, standard deviation = 0.58 oz
A.) (0 pts) 0.13 oz
B.) (0 pts) 0.02 oz
C.) (1 pts) 0.16 oz
D.) (0 pts) 0.36 oz
Answer: option c
Step-by-step explanation:
margin of error = critical value × s/√n
Where s = sample standard deviation = 0.58, n = 53
The critical value = 1.96 ( this is the critical value for a two test test corresponding to a level of significance of 5%)
By substituting the parameters, we have that
Margin of error = 1.96×0.58/√53
Margin of error = 1.96 × 0.0796
Margin of error = 0.156 ~ 0.16
Answer:
0.16 oz
Step-by-step explanation: