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hodyreva [135]
3 years ago
7

It takes three identical water pumps 8 hours to fill a pool.

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
4 0
10 hours and 40 minutes
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What is the growth factor of the exponential function
Deffense [45]

Answer:

the answer is 5

Step-by-step explanation:

4 0
3 years ago
You deposit $20,000 in an account that pays 7.77% annual interest. Find the balance after 2 years when the interest is compounde
Mademuasel [1]

Answer:

The account balance after 24 months will be $23,092.70

Step-by-step explanation:

Given data

P= $20,000

r= 7.77%= 0.077

t= 2 years

A= ?

n= 24

The compound interest formula is

A= P(1+t)^t

Inserting our values to solve for A we have

A= 20000(1+\frac{0.077}{24} )^2^*^2^4\\\\A= 20000(1+0.003 )^2^*^2^4\\\\A= 20000(1.003 )^2^*^2^4\\\A= 20000(1.003 )^4^8\\\A= 20000*1.15463517818\\\A= 23092.7035636\\\A= 23,092.70

5 0
3 years ago
three notebooks and 4 binders are $9.00. two notebooks and 4 binders cost $8.00. how much does a binder cost?
Goryan [66]
$1.50 (please mark brainliest)
4 0
2 years ago
Given congruent triangles ΔRST ΔLMN where MN = 33, LN = 54, and RT = 4x+6 . Find the value of x
Scilla [17]

Answer:

x=12

Step-by-step explanation:

We know that both triangles are congruent meaning corresponding parts are equal. We know that line LN=54 and that RT=LN meaning that RT also equals 54. With that information we can simply subtract 6 from 54 to get 48 then divide by 4 to get  12. Hope this helps!

7 0
3 years ago
John, Sally, and Natalie would all like to save some money. John decides that it would be best to save money in a jar in his clo
Radda [10]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) y=100x+300

Part 3) \$12,300

Part 4) Is a exponential growth function

Part 5) A=6,000(1.07)^{t}  

Part 6) \$11,802.91  

Part 7) Is a exponential growth function

Part 8) A=5,000(e)^{0.10t}    or  A=5,000(1.1052)^{t}  

Part 9)  \$13,591.41

Part 10) Natalie has the most money after 10 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

m=\$100\ per\ month

The y-intercept or initial value is

b=\$300

so

y=100x+300

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

y=100x+300

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

10 years=10(12)=120 months

For x=120 months

substitute in the linear equation

y=100(120)+300=\$12,300

Part 4) What type of exponential model is Sally’s situation?

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

P=\$6,000\\ r=7\%=0.07\\n=1  

substitute in the formula above

A=6,000(1+\frac{0.07}{1})^{1*t}  

A=6,000(1.07)^{t}  

therefore

Is a exponential growth function

Part 5) Write the model equation for Sally’s situation

A=6,000(1.07)^{t}  

see the Part 4)

Part 6) How much money will Sally have after 10 years?

For t=10 years

substitute  the value of t in the exponential growth function

A=6,000(1.07)^{10}=\$11,802.91  

Part 7) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

A=P(e)^{rt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

P=\$5,000\\r=10\%=0.10  

substitute in the formula above

A=5,000(e)^{0.10t}  

Applying property of exponents

A=5,000(1.1052)^{t}  

therefore

Is a exponential growth function

Part 8) Write the model equation for Natalie’s situation

A=5,000(e)^{0.10t}    or  A=5,000(1.1052)^{t}

see Part 7)

Part 9) How much money will Natalie have after 10 years?

For t=10 years

substitute

A=5,000(e)^{0.10*10}=\$13,591.41

Part 10) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

4 0
3 years ago
Read 2 more answers
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