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3 years ago

Paul makes 3 5/6 dozen cookies. He gives each of his friends 1/6 dozen cookies.

1 answer:

7 0

If he gives ALL of the cookies away..

3 5/6 = 6/6 + 6/6 + 6/6 + 5/6

6+6+6+5 = 23

Paul has 23 friends. (if he takes 1/6, then he has 22)

hope this helps

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Elena runs for 28 seconds and finishes at 250 seconds what is her velocity please explain

ExtremeBDS [4]

Answer:

The velocity is 8.93 meters/second.

Step-by-step explanation:

It is given that Elena runs for 28 seconds and finishes at 250 meters.

Here the displacement is 250 meters and the time is 28 seconds.

We know that $V=\dfrac{\text{Displacement}}{\text{Time}}$

Substitute displacement = 250 and time = 28 in above formula.

$V=\dfrac{250}{28}$

$V\approx 8.93$ meters/second

Hence, the velocity is 8.93 meters/second.

5 0

3 years ago

triangle MNO is an equilateral triangle with sides measuring 16 units What is the height of the triangle?

fiasKO [112]

see the attached figure to better understand the problem

we know that

The equilateral triangle has three equal sides

in the equilateral triangle ABC

$AB=BC=AC=16 units$

the height of the triangle is the segment BD

in the right triangle BCD

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

solve for BD

$BD^{2}=BC^{2}-DC^{2}$

substitute the values

$BD^{2}=16^{2}-8^{2}$

$BD^{2}=192$

$BD=\sqrt{192}\ units$

therefore

<u>the answer is</u>

the height of the triangle is $\sqrt{192}\ units$

7 0

3 years ago

Read 2 more answers

Solve the differential. This was in the 2016 VCE Specialist Maths Paper 1 and i'm a bit stuck

Nimfa-mama [501]

$\sqrt{2 - x^{2}} \cdot \frac{dy}{dx} = \frac{1}{2 - y}$
$\frac{dy}{dx} = \frac{1}{(2 - y)\sqrt{2 - x^{2}}}$

Now, isolate the variables, so you can integrate.
$(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}$
$\int (2 - y)\,dy = \int\frac{dx}{\sqrt{2 - x^{2}}}$
$2y - \frac{y^{2}}{2} = sin^{-1}\frac{x}{\sqrt{2}} + \frac{1}{2}C$

$4y - y^{2} = 2sin^{-1}\frac{x}{\sqrt{2}} + C$
$y^{2} - 4y = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} - 4 = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} = 4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C$

$y - 2 = \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$
$y = 2 \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$

At x = 1, y = 0.
$0 = 2 \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$
$-2 = \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0$
$\therefore 2 = \sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 = 4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C$
$0 = -2sin^{-1}\frac{1}{\sqrt{2}} - C$
$C = -2sin^{-1}\frac{1}{\sqrt{2}} = -2\frac{\pi}{4}$
$C = -\frac{\pi}{2}$

$\therefore y = 2 - \sqrt{4 + \frac{\pi}{2} - 2sin^{-1}\frac{x}{\sqrt{2}}}$

6 0

3 years ago

What is the 89,420 divided by 27

disa [49]

The answer is 3311.851851851852

8 0

3 years ago

Read 2 more answers

Damian works after school. Each

nadya68 [22]

Answer:

f(x) = 12x = 10

Step-by-step explanation:

We need a linear equation in the slope-intercept form.

y = mx + b

where y = total pay, m = hourly salary, x = number of hours worked, and b = y-intercept, or initial value

Let's look in the table.

1 hour: $22

2 hours: $34

The difference in pay between 1 hour and 2 hours is $34 - $22 = $12.

The difference in time between 1 hour and 2 hours is 1 hour.

In 1 hour he earns $12. That means the slope is 12.

We know he earns $22 for working a total of 1 hour.

Start at 1 hour and $22 on the table.

Subtract 1 hour from 1 hour to get 0 hours.

Subtract $12 form $22 to get $10.

That means for 0 hours he gets $10. b = 10

The equation is

y = 12x + 10

In function form, we have:

f(x) = 12x = 10

5 0

2 years ago