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Zigmanuir [339]
3 years ago
6

Describe a situation that could be modeled with the ratio 4:1

Mathematics
2 answers:
aleksklad [387]3 years ago
7 0
In a lybrary there are books. The ratio for the science books to science fiction books is 4:1.  How many books of science fiction are if in total are 36.000 books?
Nookie1986 [14]3 years ago
5 0
The American infantry is outnumbered by the Chinese infantry by 4:1
You might be interested in
Help me. The graph of a polynomial with unknown a is given. Write a polynomial
Xelga [282]

Answer:

f(x)=\dfrac{7}{20}\left(x+2\right)^{2}\left(x-1\right).

Step-by-step explanation:

If a graph touches the x-axis at x=c, then (x-c) is a factor of function.

From the given graph it is clear that the graph of function intersect x-axis at x=1 and touch the x-axis at x=-2.

It means (x-1) and (x+2) are not factors of given function but power of (x+2) must be 2.

So, the required function is

f(x)=a(x+2)^2(x-1)    ...(1)

where, a is a constant.

From the given figure it is clear that the graph passes through the point (-4,-7). So, substitute x=-4 and f(x)=-7 in the above function.

-7=a(-4+2)^2(-4-1)

-7=a(-2)^2(-5)

-7=-20a

\dfrac{7}{20}=a

Substitute a=\dfrac{7}{20} in (1).

f(x)=\dfrac{7}{20}(x+2)^2(x-1)

Therefore, the required function is f(x)=\dfrac{7}{20}(x+2)^2(x-1).

6 0
3 years ago
Graph y=-2/3x-3 i need help quick
timurjin [86]

Answer: just get gud at math lol

Step-by-step explanation: no

5 0
3 years ago
Mary wants to join a gym.
Leya [2.2K]

Answer:

It would take five months for the total cost of the gyms to be equal.

Step-by-step explanation:

5 0
2 years ago
John, Sally, and Natalie would all like to save some money. John decides that it
brilliants [131]

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) \$2,700

Part 5) Is a exponential growth function

Part 6) A=6,000(1.07)^{t}

Part 7) \$11,802.91

Part 8)  \$6,869.40

Part 9) Is a exponential growth function

Part 10) A=5,000(e)^{0.10t}    or  A=5,000(1.1052)^{t}

Part 11)  \$13,591.41

Part 12) \$6,107.01

Part 13)  Natalie has the most money after 10 years

Part 14)  Sally has the most money after 2 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

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) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

so

2\  years=2(12)=24\ months

For x=24 months

substitute in the linear equation

y=100(24)+300=\$2,700

Part 5) 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 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) 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 8) How much money will Sally have after 2 years?

For t=2 years

substitute  the value of t in the exponential growth function

A=6,000(1.07)^{2}=\$6,869.40

Part 9) 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 10) Write the model equation for Natalie’s situation

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

see Part 9)

Part 11) 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 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

A=5,000(e)^{0.10*2}=\$6,107.01

Part 13) 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

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0
3 years ago
Lucy collects data from a random sample of seventh-graders. Out of 40 respondents, 7 attend after-school programs. Of the 200 se
Shalnov [3]

Answer:

35

Step-by-step explanation:

For every 40 students, you add 7

Ratio:

Students : Students in afterschool programs

40:7

80:14

120:21

160:28

200:35

8 0
2 years ago
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