Four balls of wool will make 8 knitted caps.How many balls of wool will Malcolm need if he wants to make 6 caps, (how would you do in ratio table)

Answers

Answer 1

Answer: Well one ball of wool makes 2 knitted caps so 3 balls of wool are needed to make 6 knitted caps

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Number 7 please help

Answers

7) Draw a quadrilateral with 1 pair of parallel side. What special quadrilateral have you drawn?

Properties of a quadrilateral:
1) has four sides or edges
2) has four vertices or corners
3) interior angles add up to 360°

US definition: A trapezoid is a quadrilateral that has 1 pair of parallel sides.
UK definition: A trapezium is a quadrilateral that has 1 pair of parallel sides.

John, Sally, and Natalie would all like to save some money. John decides that itwould be best to save money in a jar in his closet every single month. He decides
to start with $300, and then save $100 each month. Sally has $6000 and decides
to put her money in the bank in an account that has a 7% interest rate that is
compounded annually. Natalie has $5000 and decides to put her money in the
bank in an account that has a 10% interest rate that is compounded continuously.

How much money have after 2 years?

How much money will sally have in 10 years?

What type of exponential model is Natalie’s situation?

Write the model equation for Natalie’s situation

How much money will Natalie have after 2 years?

How much money will Natalie have after 10 years

Answers

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

$b=\$300$

$y=100x+300$

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

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

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

$A=P(1+(r)/(n))^(nt)$

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

$P=\$6,000\n r=7\%=0.07\nn=1$

substitute in the formula above

$A=6,000(1+(0.07)/(1))^(1*t)\n A=6,000(1.07)^(t)$

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

$P=\$5,000\nr=10\%=0.10$

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

If a sweater sells for $ 48 after a 25 % markdown what was the original price

Answers

If a sweater sells for $ 48 after a 25 % markdown then the original price

is $64.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Let the original price of the sweater be p dollars.

After a 25% markdown, the sweater sells for $48, which means the customer pays 75% of the original price:

75% of p = $48

Converting the percentage to a decimal:

0.75p = $48

Solving for the originalprice:

p = $48 / 0.75

p = $64

Therefore, the original price of the sweater was $64.

To learn more on Percentage click:

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The original orice was $60
How? Well you just have to multiply $48 by 25% (or 0.25) and you get 12.00. Finally you add that to $48 and you get $60

What is 32.60 rounded to the nearest tenth

Answers

that would be 32.6 32.60 and 32.6 are exactly the same just like 1635 and 01635 are the same number

You just round the ten in the nearest place value

How do you solve this?

Answers

Interest equals principle (the amount that you had to begin with) times the rate (the rate if interest) times the time (usually in years)

ms ruiz planted 14 flowers in 3 pots.she planted 4 flowers in one pot and split the rest equally between the other 2 pots write and solve an equation to find the number of flowers ms ruiz planted in eaxh of 2 pots

Answers

So, Ms. Ruiz has 14 flowers. If she put 4 flowers in 1 pot, she has 10 flowers left. If she splits the rest evenly, she gets 5 flowers each. Let's make this into an equation: 14=2x+4. In other words, 14 flowers equals x flowers in one pot, plus x flowers in another pot, plus 4 flowers in another pot. (Note that 2x=x+x: 2x is another way of writing that out.) Now, we solve using inverse operations: 14-4=2x+4-4. 10=2x. 10/2=2x/2. x=5.

Answer: 14=2x+4; x=5

Your answer should be 14=2x+4 ; x=5

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