30 grams equals how many milligrams

A back contains 120 marbles some are red and the rest are black They are 19 red marbles for every black marble How many red marb

egoroff_w [7]

Answer:

6.3 ?

Step-by-step explanation:

4 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

Plz I need it now I am stuck

vredina [299]

Answer:

116

Step-by-step explanation:

5 0

2 years ago

Three boxes have a total weight of 640 pounds. Box A weights twice as much as Box B. Box C weight 30 pounds more than Box A. How

Zarrin [17]

Answer:

A: 244 pounds

B: 122 pounds

C: 274 pounds

Step-by-step explanation:

We have A+B+C = 640; A=2B; C=A+30. Substituting the last into the first gives ...

A + B + (A +30) = 640

2A +B = 610 . . . . . . . . . . . . subtract 30

Substituting the second into this equation gives ...

2(2B) +B = 610

B = 610/5 = 122 . . . . . divide by 5

A = 2B = 244 . . . . . . . .find A from B

C = A+30 = 274 . . . . . find C from A

Box A weighs 244 pounds; box B weighs 122 pounds; box C weighs 274 pounds.

4 0

3 years ago

4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.

artcher [175]

Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.

Two lines that intersect at right angles are perpendicular.

A. The statement is not reversible.

B. Yes; if two lines intersect at right angles, then they are perpendicular.

C. Yes; if two lines are perpendicular, then they intersect at right angles.

D. Yes; two lines intersect at right angles if (and only if) they are perpendicular.

Your Answer would be (D)

Yes; two lines intersect at right angles if (and only if) they are perpendicular.

REF: 2-3 Biconditionals and Definitions

6 0

3 years ago

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