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2 years ago

Determine the number of subsets of 3,4,5,6,7,8,9,10,11,12,13,14,15

Mathematics

1 answer:

lbvjy [14]2 years ago

3 0

Answer:

8192

Step-by-step explanation:

The number of subsets of an n-element set is 2^n.

Your set has 13 elements, so has 2^13 = 8192 subsets.

This count includes the empty set and the full set.

You might be interested in

(2x³+11x²+5)-(x³-2x²+2)<br>

SOVA2 [1]

Answer:x^3+13x^2+3

Step-by-step explanation:

(2x^3+11x^2+5)-(x^3-2x^2+2)

Clearing brackets

2x^3+11x^2+5-x^3+2x^2-2

Collect like terms

2x^3-x^3+11x^2+2x^2+5-2

x^3+13x^2+3

3 0

2 years ago

An 8 by 19 ft wall has three 4 by 5ft windows. The area of three windows is what percent of the area of the entire wall

sergij07 [2.7K]

Area of the wall = 8 x 19 = 152 ft square
Area of the window = 4 x 5 = 20 ft square
Area of 3 windows = 20 x 3 = 60 ft square
The percent area of 3 windows from area of the wall = 60/152 or approximately .395 or 39.5%

6 0

2 years ago

Am I correct <br> 2017 -1846= 171<br> 2017-1781= 236<br> 1847-1781=65 yrs difference

Anit [1.1K]

Yes for the first one, yes for the second one, and yes for the third one although your subtraction equation had the wrong year (its not 1847 its 1846) but the answer was right, 65.

5 0

2 years ago

Density is calculated by dividing the mass by volume. A student measures the mass of an 8 cm3 object as 12.9g. What is the densi

andrew11 [14]

Answer: D

Density= mass/volume

12.9g/8cm3= 1.6 g/cm3

5 0

2 years ago

Jennifer serves the volleyball to Marsha with an upward velocity of 10.5 ft/s. The ball is 5 feet above the ground when she stri

Katarina [22]

Answer:

0.98 seconds

Step-by-step explanation:

We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.

<h3>motion equation</h3>

The general form of the equation of height for ballistic motion is ...

$h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}$

The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.

For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...

h(t) = -16t² +10.5t +5

<h3>reaction time</h3>

Marsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...

a = -16
b = 10.5
c = 5

The solution is ...

$t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}$

The positive solution is ...

t ≈ 0.976327 ≈ 0.98

Marsha has about 0.98 seconds to react before the volleyball hits the ground.

_____

<em>Additional comment</em>

After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.

4 0

1 year ago