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2 years ago

George has 1/3 pan of brownies.He eats 1/4 of them.What fraction did George eat?

Mathematics

1 answer:

Evgen [1.6K]2 years ago

5 0

Answer:

1/12

Step-by-step explanation:

You want to find the compatible numbers with the common denominator so you want to multiply by ones until you get something with the same denominator. In this case it's 12, 1/3 x 4 = 4/12 and 1/4 x 3 = 3/12, Then subtract. Therefore you get your answer 1/12

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Mrs. Stevens wants to have $18,000 in the bank in 3 years. If she deposits $9500 today at 4% compounded quarterly for 3 years, h

serg [7]

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\qquad 
\begin{cases}
A=\textit{current amount}\\
P=\textit{original amount deposited}\to &\$9500\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, 4 quarters a year}
\end{array}\to &4\\

t=years\to &3
\end{cases}$

so.. if she deposits a principal of 9,500 today, compounding quarterly for 3 years, she'll have A amount

how much additional amount? well, 18,000 - A

7 0

2 years ago

Read 2 more answers

Colin is painting figurines. He spends 20 minutes painting each figurine. After painting for 60 minutes, he still has 9 more fig

miss Akunina [59]

Answer:

$f(t) = -0.05t +12$

Step-by-step explanation:

To solve this problem we must pay attention to the following data supplied:

- f It is the number of figurines that remain to be painted.

- t amount of time, in minutes, that Colin spends painting

- Colin takes 20 minutes painting each figurines.

- After painting 60 min, he still has 9 figurines left. f (60) = 9

If he takes 20 minutes painting 1, it means that in 60 minutes he has painted 3 and he has 9 left.

Then, at the beginning he has 9 +3 figurines to be painted.

$f (0) = 3 + 9\\f (0) = 12$

With these two points we can find the function:

If m is the slope of the line, then:

$m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{9-12}{60-0}\\\\m = -0.05\\\\f (t) = -0.05t + c$

Where by definition $c = f(0) = 12$

Finally the formula is:

$f(t) = -0.05t +12$

3 0

2 years ago

Read 2 more answers

The total distance in centimeters that a toy robot moves varies directly with the time in seconds the toy robot moves a total di

kobusy [5.1K]

Answer:

Hey there!

The robot moves 63 cm in 9 seconds. Then in 1 second, it moves 7 cm.

If it goes 49 cm, it will take 7 seconds.

Let me know if this helps :)

4 0

2 years ago

Conservation of Species A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sol

JulijaS [17]

Answer:

The turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

Ten years after the conservation measures are implemented the population will be 3260 turtles.

Step-by-step explanation:

To find the rate of growth of the turtle population at any time <em>t</em> you need to find $N'(t)$

$\frac{d}{dt}N(t)=\frac{d}{dt}(2t^3+3t^2-4t+1000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dt}(2t^3)+\frac{d}{dt}(3t^2)-\frac{d}{dt}(4t)+\frac{d}{dt}(1000)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\N'(t)=6t^2+6t-4$

In particular, when t = 2 and t = 6, we have

$N'(2)=6(2)^2+6(2)-4=32\\\\N'(6)=6(6)^2+6(6)-4=248$

so the turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

The turtle population at the end of the tenth year will be

$N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260 \:turtles$

3 0

2 years ago

Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number

Masja [62]

Answer:

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y² = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m by √512 m

5 0

2 years ago