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kifflom [539]
3 years ago
12

Simplify, following the order of operations: 23 + 5 × 10 ÷ 2 – 33 + (11 – 8)

Mathematics
1 answer:
ANEK [815]3 years ago
7 0
The order of operations is parentheses, exponents, multiply and divide, add and subtract
put the things being multiplied and divided in parentheses
23+(5 *10/2)-33+(11-8)
solve the things in the parentheses
23+(25)-33+(3)
then combine the terms
18
You might be interested in
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
Avary wanted to buy a gold necklace that cost $578. She pain an initial amount of $128 and agreed to pay the rest in monthly ins
serg [7]

Answer:

75 each month

Step-by-step explanation:

578-128=450

450/6=75

7 0
2 years ago
A road is 4 cm long on the map. Find the actual length of the road.
Usimov [2.4K]

The distance between two cities is

75

k

m

s

.

Explanation:

As a road of

4

c

m

.

on road map indicates a road of length equal to

30

k

m

.

Each

c

m

.

on map indicates

30

4

=

7.5

k

m

s

.

Hence a distance of

10

c

m

.

between two cities on the map indicates

7.5

×

10

=

75

k

m

s

7 0
3 years ago
Suzy fills a 1 pint thermos with milk each day for lunch how many times will she be able to fill her thermos with 1/2 gallon of
pogonyaev
1 gallon is 8 pints....so 1/2 gallon = 4 pints

she fills a 1 pt thermos with milk each day......how many times will she be able to fill her thermos with 1/2 gallon (or 4 pints) of milk ?

if she fills a 1 pint thermos each day....and she has 4 pints of milk, then she will be able to fill her thermos 4 times <===
6 0
4 years ago
The diameter of the base of the cone measures 8 units. The height measures 6 units. What is the volume of the cone?
Maslowich
V = \pir^2h/3

V = 3.14 x 4^2 x 6/3       (remember r is 1/2 of the diameter)
V = 3.14 x 16 x 2
V = 100.5
3 0
3 years ago
Read 2 more answers
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