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3 years ago

PLEASE HELP 12 POINTS

Mathematics

1 answer:

Assoli18 [71]3 years ago

3 0

Answer:

5:5 (first box, pencils to pens)

7:3 (second box, coloured pencils to crayons)

The probability of picking a pen (1st box): 5/10

The probability of picking a crayon (2nd box): 3/10

Probability of picking both: 5/10*3/10 = 15/100

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Triangle WXY has coordinates W(1, 5), X(1, 1), and Y(5, 1). Which of the following sets of points represents a dilation of trian

timofeeve [1]

The correct answer for the question shown above is the second option, the option B, which is: B. W'(2, 10), X'(2, 2), Y'(10, 2)
The explanation is shown below: As you can see, the original triangle has the following coordinates W(1, 5), X(1, 1), and Y(5, 1); the triangle must be dilated by a common scale factor, so if you analize the option B, you can notice that the triangle was dilated by a scale factor of 2.

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3 years ago

The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

yanalaym [24]

Answer:

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of y = eˣ, y = 0, x = 0, and x = 1. Each cross-section perpendicular to the x-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each x value. So, we integrate from x = 0 to x = 1.

The area for an equilateral triangle is given by:

$\displaystyle A=\frac{\sqrt{3}}{4}s^2$

Where s is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at x is simply y, which is eˣ.

Therefore, our volume is:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx$

Substitute:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx$

Evaluate the integral. Simplify:

$\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx$

Integrate using u-substitution:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)$

Evaluate:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)$

Therefore, the volume of the solid is:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)$

Our answer is A.

3 0

3 years ago

Read 2 more answers

What is the volume of a rectangular cube that has 5yd, 3yd and another 3yd

iVinArrow [24]

Answer:45cm³

Step-by-step explanation:

Volume=l×b×h

5×3×3=45

3 0

3 years ago

Which is the measure of the angle shown on the protractor?

Alex73 [517]

The measure of the angle should be 170° as this angle looks like an obtuse angle.

Hope that helps!

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3 years ago

14x50 help I need it in words

DanielleElmas [232]

Answer and Step-by-step explanation:

Fourteen times fifty.

The number 14 is said as fourteen, and the number 50 is said as fifty. The X represents the multiplication symbol, in which it is used to multiply terms together.

Fourteen times fifty equals seven hundred.

14 x 50 = 700

#teamtrees #PAW (Plant And Water)

I hope this helps!

4 0

3 years ago