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Naddik [55]
3 years ago
8

Yesterday, Jack drove 43.5 miles. He used 11 gallons of gasoline. What is the unit rate for miles per gallon?

Mathematics
1 answer:
Alexxx [7]3 years ago
4 0

Answer:

the unit rate for miles per gallons = 3.95 miles

Step-by-step explanation:

Let x be the unit rate for miles per gallon.

Given:

Jack drove 43.5 miles. He used 11 gallons of gasoline.

Find the unit rate for miles per gallon?

Jack used 11 gallons of gasoline for 43.5 miles.

11 gallons = 43.5 miles

The unit rate for miles per gallon is

unit rate of gallons = total miles divided by total used gallons of gasoline

x=\frac{43.5}{11}

x=3.95miles

Therefore, the unit rate for miles per gallons is 3.95 miles.

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After how many years will £6,000.00 yield a simple interest of £900.00 at 3%​
PilotLPTM [1.2K]

Answer:

add 1 Century to divide £6 000 000

7 0
3 years ago
Read 2 more answers
F. Use the information above to find 345 + 15. Explain your thinking.
8090 [49]

Answer:

360

Step-by-step explanation:

ikaw na ang mag step by step niyan paki barainlest

6 0
3 years ago
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
3 (x+2)+9&lt;6(x-3) solve the inequality and write the solution using interval notation​
Darya [45]

Answer:

(11, ∞).

Step-by-step explanation:

3 (x+2)+9<6(x-3)

3x + 6 + 9 < 6x - 18

-3x < -18 - 6 - 9

-3x < -33

x > 11       (Note the inequality flips as we are dividing by a negative value).

6 0
2 years ago
Can someone help me solve x
evablogger [386]

Answer:6

Step-by-step explanation:solve the equation, you know that it equals 90 because the angle is 90

so 16x-6=90

+6 both sides

16x=96

divided by 16 both sides to isolate x

x=6

4 0
3 years ago
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