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2 years ago

Please select the best answer from the choices provided A B C D

Mathematics

2 answers:

SSSSS [86.1K]2 years ago

6 0

ANSWER

The correct answer is D.

$\sum_{n=1} ^{6} (n - 3) = ( - 2) + ( - 1) + (0) + (1) + (2) + (3) = 3$

EXPLANATION

The given expression is

$\sum_{n=1} ^{6} (n - 3)$

The symbol means summation.

So we need to substitute

$n=1,n=2,n=3,n=4,n=5, \:and\:n=6$

into the formula and add all to get,

$\sum_{n=1} ^{6} (n - 3) = (1 - 3) + (2 - 3) + (3- 3) + (4 - 3) + (5 - 3) + (6 - 3)$

We simplify to obtain,

$\sum_{n=1} ^{6} (n - 3) = ( - 2) + ( - 1) + (0) + (1) + (2) + (3) = 3$

The correct answer is D

SIZIF [17.4K]2 years ago

5 0

the answer is D simply................

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

Part 2) $y=100x+300$

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Part 7) $\$11,802.91$

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Part 9) Is a exponential growth function

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Part 14) Sally has the most money after 2 years

Step-by-step explanation:

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

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x ---> the time in months

The linear equation in slope intercept form

y=mx+b

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$m=\$100\ per\ month$

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$b=\$300$

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John’s situation is modeled by a linear equation

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

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

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

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

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

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

$A=P(e)^{rt}$

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substitute in the formula above

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

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$A=5,000(1.1052)^{t}$

therefore

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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

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