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3 years ago

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You just bought a dog and you want to put a fence up in your backyard so Fido doesn't run away. One side of the yard needs 20 fe

et of fence, another 50 feet of fence, and 2 sides needs 75 feet of fence. How much fence do you need to enclose your yard?

1 answer:

DENIUS [597]3 years ago

7 0

Answer:

170 feet

Step-by-step explanation:

add 75+75+20

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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

4 years ago

Read 2 more answers

P(A) = 20%. P(B) = 50%. P(BIA) = P(B). What is P(A and B)?

8_murik_8 [283]

Answer:

P(A and B) = 0.1 = 10%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question, we have that:

$P(A) = 0.2, P(B|A) = 0.5$

What is P(A and B)?

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(A \cap B) = P(B|A)*P(A) = 0.5*0.2 = 0.1$

P(A and B) = 0.1 = 10%

8 0

3 years ago

If you can help tyyyy :))))

Tanzania [10]

Answer: it should be 5+3+4+11=23

Step-by-step explanation: when you look for the volume you add all the numbers. hope it helps :)

plz mark as branlist

3 0

3 years ago

the base of a pyramid is a square with 5 lines of 5cm the slant height of each lateral face of the pyramid is 6 cm what is the s

il63 [147K]

Answer:

105.97

Step-by-step explanation:

5 0

3 years ago

The exterior angles of a quadrilateral have measures of $72\degree,\ 58\degree,\ 2x\degree,$ and $3x\degree$ . Find the value of

kiruha [24]

Answer:

46degrees

Step-by-step explanation:

The sum of angles of exterior angles of a quadrilateral is 360 degrees

Hence;

72 + 58+2x+3x = 360

130 + 5x = 360

5x = 360-130

5x = 230

x =230/5

x = 46 degrees

Hence the vale of x is 46degrees

4 0

3 years ago