The manager of a theater wants to know whether the majority of its patrons were adults or children. one day 5100 tickets were sold in the receipts totaled $22,210. The adult admission is $5.50, and the children’s admission is $3.50. How many adult patrons were there?
Answer:
x= 2,180
x= number of adult tickets sold
Step-by-step explanation:
First, we need to establish the system of equations:
x= number of adult tickets sold
y= number of children tickets sold
5.5x + 3.5y = 22,210
x + y = 5,100
Now, we isolate one variable in a formula and substitute its value in the other:
x= 5,100 - y
5.5*(5,100 - y) + 3.5y= 22,210
28,050 - 5.5y +3.5y = 22,210
2y= 5,840
y= 2,920
x= 5,100 - 2,920
x= 2,180
The shadow of a 60 foot pole is a 100 feet long. What is the angle of evaluation from the end of the shadow to the top of the pole?
Answer:
θ = 36.86°
Step-by-step explanation:
Given that,
The shadow of a 60 foot pole is a 100 feet long.
We need to find the angle of elevation from the end of the shadow to the top of the pole.
Height, h = 60 foot
Hypotenuse, H = 100 feet
Using trigonometry to find it.
[tex]\sin\theta=\dfrac{\text{Height}}{\text{Hypotenuse}}\\\\\sin\theta=\dfrac{60}{100}\\\\\theta=\sin^{-1}(\dfrac{60}{100})\\\\\theta=36.86^{\circ}[/tex]
So, the angle of elevation is 36.86 degrees.
A diagram of a new competition swimming pool is shown. If the width of the
pool is 25 meters, find the length of the actual pool. (Round to the nearest
tenth)
47m at least I think it is
Given f(x) = x^3 + kx + 2, and x + 1 is a factor of f(x), then what is the value of
k?
Answer:
k = 1
Step-by-step explanation:
Given that,
[tex]f(x) = x^3 +kx + 2[/tex]
If (x+1) is a factor of (x), we need to find the value of k.
Using remainder theorem to find it.
Put (x+1) = 0
x = -1
Put x = -1 in equation below.
[tex]x^3 + kx + 2=0\\\\(-1)^3+k(-1)+2=0\\\\-1-k+2=0\\\\1-k=0\\\\k=1[/tex]
So, the value of k is 1.
The formula for the volume of a sphere is given below and the relationship between the radius r and the diameter d is r=d/2. Find the EXACT volume of the sphere in terms of the diameter d. Be sure to fully simplify the expression
Answer:
for the volume of the sphere its answer is 4πr³/3 which when converted to diameter will be 2(4πr³/3) as r=diameter/2 so diameter =2r
Answer:
4πr³/3
Step-by-step explanation:
When converted to diameter will be 2(4πr³/3) as r=diameter/2 so diameter =2r
If 2x+y=10 and y=3x find the value of both x and y
Given ΔPQR and ΔSTU, what is m∠Q?
Given that ΔPQR and ΔSTU are similar triangles, m∠Q = 64°.
Similar TrianglesThe ratios of the corresponding sides of similar triangles are always equal to each other, that is, the corresponding sides are proportional.Also, corresponding angles of two similar triangles are congruent.Thus:
ΔPQR and ΔSTU are similar because:
PQ/ST = PR/SU = QR/TU = 3.5
Therefore,
m∠Q = 180 - 70 - 46
m∠Q = 64°
Thus, given that ΔPQR and ΔSTU are similar triangles, m∠Q = 64°.
Learn more about similar triangles on:
https://brainly.com/question/2644832
Find the sum of the expressions .
8+x-13+n(3-x) =
Answer: =−nx+3n+x−5
Step-by-step explanation:
does anyone understand this i never get it
Answer: 18
Step-by-step explanation:
6 ÷ 2 = 3
162 ÷ 54 = 3
The constant ratio is 3
6 × 3 = 18
Hope I helped!
Please help ASAP !!
Answer: surface area is 215.27; volume is 297.1
Step-by-step explanation:
you have to find the radius first, c = 2(pi (3.14))r, the formula for surface area is 4(pi(3.14)r^2, the formula for volume is 4/3(3.14(pi))r^3
Someone answer this for me. I will give u branily whoever right.
Step-by-step explanation:
21x+72+105+78=360
21x=105
x=5
Write an equation for the line that passes through (−10,3) and whose slope is undefined. Give an answer in standard form.
Answer:
y=-10x+3
Step-by-step explanation:
The slope is -10
4x+8≥5(3-x)
solve with steps pleaseee!
Answer:
[tex]x >\ or\ =\ \frac{7}{9}[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\4x+8>\ or =\ 5(3-x)\\Hence,\\We\ can\ treat\ inequality\ in\ the\ same\ way\ we\ do\ for\ solving\ equalities.\\Hence,\\4x+8>\ or\ =\ 5(3-x)\\By\ simplifying\ the\ RHS,\\4x+8 >\ or\ =\ 15-5x\\Hence,\\Adding\ (+5x)\ to\ the\ LHS\ and\ RHS,\\4x+8+(5x) >\ or\ =\ 15-5x+(5x)\\Simplifying,\\5x+4x+8 >\ or\ =\ 15+(5x-5x)\\9x+8 >\ or\ =\ 15\\Adding\ (-8)\ to\ both\ LHS\ and\ RHS,\\9x+8+(-8) >\ or\ =\ 15+(-8)\\Simplifying,\\9x+(8-8) >\ or\ =\ 7\\[/tex]
[tex]9x >\ or\ =7\\x >\ or\ =\ \frac{7}{9}[/tex]
Step-by-step explanation:
4x+8≥5(3-x)
4x+8≥15-5x
adding 5x on each term
4x+5x+8≥15-5x+5x
9x+8≥15
subtract each term by 8
9x+8-8≥15-8
9x≥7
dividing each term by 9
9x/9=7/9
x≥7/9
is your answer
What is the measurement of the indicated central angle. 6 pi. R=15
Answer:
r=12
Step-by-step explanation:
r=12
circumference of arc = theta/360*2πr=3π given
Pi cancels
theta/360*2*12=3
theta*6/90=3
theta*3/45=3
3 cancels,45 to the other side
theta=45 degrees
This should do it :)
Work out the area of the triangle.
Answer:
A = 12.92
Step-by-step explanation:
Base x Height x 1/2
3.4 x 7.6 = 25.84
26.52 x 1/2 = 12.92
Hope this helps :)
Subtract. Simplify (or reduce) your answer, if necessary.
2 1/5 - 5/6 =
Answer:
2 1/5 - 5/6 = 41/30
Step-by-step explanation:
Turn the denominator to be the same because if the denominator is not the same so you can't subtract neither can you add.
Next find the least common multiple of both denominator (5, and 6) and ask yourself what time the denominator would give you the least common multiply you got.
1/5 x 6/6 = 6/30 and 5/6 x 5/5 = 25/30
Your expression now would be 2 6/30 - 25/30
You can't subtract 6 from 25 so you have to turn the proper fraction into a improper fraction
2 6/30 = 2 x 30 + 6 = 66/30. 25/30 = 0 x 0 + 25 = 25/30.
Your new expression would be:
66/30 - 25/30
Now you can subtract 66 - 25 and you get 41
Therefore the correct answer is 41/30 you can not simplify the answer because the numerator is a odd number and the denominator is a even number.
Subtract $987.59 from $1,581.06.
The difference is?
A. $593.47
B. $603.47
C. $693.47
D. $694.47
Answer
A=1,597.06
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
(1.5,1)
Step-by-step explanation:
what is the value of x when x:3=2.13
Answer:
The other dude was wrong :( the answer is 6.39
Step-by-step explanation:
I took the test on K12
The artist realizes she has 49 ounces left . How many ounces of blue does she need to add
2 ounces of blue paint to every 7 ounces of yellow
Answer:
hwope this helps ＼(=^‥^)/’`
Step-by-step explanation:
f(x) = -x^2
Find f(3)
Answer:
9
Step-by-step explanation:
f(x) = -x^2
f(3) = -3^2
f(3) = 9
I will give brainiest to whoever answers correctly !!
Answer:
26275
Step-by-step explanation:
if simple interest its just .017*25000 which is 1 year then multiply by 3 and add to 25000
a florist can creat 16 bouquets of flowers during an 8-hour workday. how many bouguets can the florist creat per hour what is the unit rate
Answer:2 per hour
Step-by-step explanation:16 divided by 8 equals 2 making it 2 per hour
Answer:
A florist can create 2 bouquets of flowers per hour
Step-by-step explanation:
16/8 = 2
Hamda and Layla get paid per project.
Hamda is paid a project fee of AED 25 plus AED 10.50 per hour.
Layla is paid a project fee of AED 18 plus AED 14.25 per hour.
Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.
Show your steps
Answer:
The company will pay 24.75h+43 AED if they hire both workers.
Step-by-step explanation:
Given that:
Project fee of Hamda = AED 25
Per hour charges = AED 10.50
Let,
h be the number of hours
y = 10.50h + 25
Project fee of Layla = AED 18
Per hour charges = AED 14.25
y = 14.25h + 18
Total amount to hire both.
Total cost = y+y
Total cost = 10.50h+25+14.25h+18
Total cost = 24.75h+43
Hence,
The company will pay 24.75h+43 AED if they hire both workers.
30% of what number is 150? A. 500 B. 50 C. 45 D. 200
Answer:
500
Step-by-step explanation:
.
Answer:
A. 500
Step-by-step explanation:
We know that it can't be B. or C. since it has to be greater than 150, so (I know this isn't the way to do it) bet is you try multiplying your leftover answers you have by .3 you would see that 200 times .3 is 60, so that isn't it but 500 times .3 is 150!
I hope this helps and you have a great day! :)
32 POINTS! *URGENT*
When Pizza Paradise first opened their business in 2010, they decided on a price for their large cheese pizza. After their first full year in business, they decided they would increase the price at a constant rate each year for four years. The new price in 2011, after their first increase, was $7.75. The price in 2014 was $10.00.
What is the slope!
Answer:
The price in 2010 was $7. every year the price went up $0.75 slope should be 0.75x
Step-by-step explanation:
Answer:
lol i had the same question
Step-by-step explanation:
slope is 2 and contains the point (5,-7)
write the equation of a line
Answer:
y = 2x - 17
Step-by-step explanation:
y = mx + b
m = 2
y = 2x + b
Plug in (5, -7) for x & y.
-7 = 2(5) + b
-7 = 10 + b
Subtract 10 from both sides.
-17 = b
y = 2x - 17
Check work.
-7 = 2(5) - 17
-7 = 10 - 17
- 7 = -7
Your answer is correct.
which statement is true about the function f(x) = -√-x?
what is the product of 4.35 and 0.95
EMERGENCY IF you dont know the answer do not answer IT
Answer:
[tex]x^2+11x+24[/tex]
Step-by-step explanation:
The area of a rectangle is given by [tex]l\cdot w[/tex]. Plugging in our given values, we get:
[tex]A=(x+3)(x+8)=x^2+8x+3x+24=\fbox{$x^2+11x+24$}[/tex].
This is a polynomial in standard form [tex]\checkmark[/tex]
Answer:
x^2 + 11x + 24
Step-by-step explanation:
x times x is x^2
x times 8 is 8x
x times 3 is 3 x
8 times 3 is 24
add it all together and its x^2 + 11x + 24
