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solniwko [45]
3 years ago
9

Mega Movies hosted a film premiere on Friday night. They charged $8 for adults and $5 for children. Ninety-two adults and childr

en attended, and $688 was made in ticket sales. How many children and how many adults went to the film premiere?
A.
16 children; 76 adults
B.
13 children; 79 adults
C.
10 children; 82 adults
Mathematics
1 answer:
zmey [24]3 years ago
4 0

Answer:

Step-by-step explanation:

a + c = 92.....c = 92 - a

8a + 5c = 688

8a + 5(92 - a) = 688

8a + 460 - 5a = 688

3a = 688 - 460

3a = 228

a= 228/3

a = 76 <==== adults

a + c = 92

76 + c = 92

c = 92 - 76

c = 16 <=== children

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HELPPPP 100 points if you help!!!!
nignag [31]

Answer:

Part A)

Chorus:

c(t)=15(1.12)^t

Band:

b(t)=2t+30

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

c(t)=a(r)^t

Where <em>a</em> is the initial population and <em>r</em> is the rate of change.

We will substitute 15 for <em>a </em>and 1.12 for <em>r</em>. Hence:

c(t)=15(1.12)^t

This represents the number of people in the chorus after <em>t</em> years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

b(t)=mt+b

And by substitution:

b(t)=2t+30

This represents the number of people in the band after <em>t</em> years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

c(9)=15(1.12)^9\approx41.59\approx41

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

b(9)=2(9)+30=48

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for <em>t</em>. So:

15(1.12)^t=2t+30

Unfortunately, it is impossible to solve for <em>t</em> using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0
3 years ago
A race car can go around the track 48 times in 8 minutes how many times can the race car go around per minute
BARSIC [14]

Answer:

Step-by-step explanation:

6

cause you take 48/8 equals 6

hope this heps:)

8 0
3 years ago
Write an expression that can be used to multiply 6 x 198 mentally? please answer thanks!
valkas [14]
-6 x 2 + 6 x 200. Since you want to find out 6 multiplied by 198 the easiest way (for me) would be to round it and then substract 12 since 200-198 is equal to 2 and 6 x 2 is equal to 12

3 0
3 years ago
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Write down the gradient of the<br> line with equation y = 5X-8
k0ka [10]

Answer:

Let X be 2

Now,

y = 5*2 - 8

or, y= 10-8

or, y =2

Hope this will help please mark me as <em>brainlest.</em>

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True or false !!!<br><br> T or F
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Tan x = opp/adj

For angle C, opp = 4, and 3 = adj, so

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