how many elements must a set have if the number of proper subsets of the set 1/2 of the total number of subsets of the set?

Answers

Answer 1

Answer: A proper subset of a set A is a subset that is strictly contained in A and excludes at least one member of A. The empty set is also a proper subset of any nonempty set.
So there is only 1 element that a set must have if the number of proper subsets is 1/2 of the total number of subsets.
For example: A = { 4 }
Proper subset : { } ( 1 )
All subsets: { } , { 4 } ( 2 )
1 = 1/2 * 2
Answer: 1 element.

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In scientific notation, 330 is written?

Answers

3.3 x 10^2

When you convert a number to scientific notation, you have to move the decimal right or left so that the whole number falls between 1 and 10. You then "describe" what you would multiply by to get the original number by multiplying by 10^x. x is the number of decimal places you moved. If you move the decimal to the left, it will be a positive exponent. If you move the decimal to the right it will be a negative exponent. Here are some examples...

10,000 = 1 x 10^4
0.0001 = 1 x 10^-4

Which angle corresponds to 1/6 of a circle?

Answers

Answer:

$(1)/(6)$ of a circle makes 60° angle.

Step-by-step explanation:

There are 360° in one full rotation or we can say that one circle has 360 degrees.

If a circle has 360°, $(1)/(6)$ of a circle is equal to

$(1)/(6)$ × 360 = 60°

If you divide a circle into 6 equal parts each would be of 60°.

= 60 + 60 + 60 + 60 + 60 + 60 = 360

$(1)/(6)$ of a circle makes 60° angle.

The angle that corresponds to 1/6 of a circle is 60 degrees

Which angle corresponds to 1/6 of a circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The distance between any point of the circle and the center is called the radius.

A full circle has an angle 360 degrees. The angle that corresponds to 1/6 of a circle will be:

1/6 * 360 = 60 degrees

Therefore, the angle that corresponds to 1/6 of a circle is 60 degrees.

Learn more about circle on:

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Solve the following quadratic by factoring1) x²+5x+6=0
2) x²+10x+21=0
3) x²+8x+15=0
4) x²+9x+14=0
5) x²-2x35=0

Answers

Answer:

Step-by-step explanation:

To solve these quadratic equations by factoring, you need to find two numbers that multiply to the constant term (the number without x^2) and add up to the coefficient of the linear term (the number with x). Here are the solutions for each of the equations:

1. x² + 5x + 6 = 0

We need two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.

So, we can factor the equation as (x + 2)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 2 = 0 => x = -2

x + 3 = 0 => x = -3

So, the solutions are x = -2 and x = -3.

2. x² + 10x + 21 = 0

We need two numbers that multiply to 21 and add up to 10. The numbers are 7 and 3.

So, we can factor the equation as (x + 7)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 7 = 0 => x = -7

x + 3 = 0 => x = -3

So, the solutions are x = -7 and x = -3.

3. x² + 8x + 15 = 0

We need two numbers that multiply to 15 and add up to 8. The numbers are 5 and 3.

So, we can factor the equation as (x + 5)(x + 3) = 0.

Now, set each factor equal to zero and solve for x:

x + 5 = 0 => x = -5

x + 3 = 0 => x = -3

So, the solutions are x = -5 and x = -3.

4. x² + 9x + 14 = 0

We need two numbers that multiply to 14 and add up to 9. The numbers are 7 and 2.

So, we can factor the equation as (x + 7)(x + 2) = 0.

Now, set each factor equal to zero and solve for x:

x + 7 = 0 => x = -7

x + 2 = 0 => x = -2

So, the solutions are x = -7 and x = -2.

5. x² - 2x - 35 = 0

To factor this equation, we need two numbers that multiply to -35 and add up to -2. The numbers are -7 and 5.

So, we can factor the equation as (x - 7)(x + 5) = 0.

Now, set each factor equal to zero and solve for x:

x - 7 = 0 => x = 7

x + 5 = 0 => x = -5

So, the solutions are x = 7 and x = -5.

Question answer now please

Answers

A certain clock requires a weight lifted up once a day. The weight provides the energy that allows the clock to keep running. Identify the transformation of that powers a grandfather clock.

What is the volume and surface area of a sphere if the diameter is 7.5 feet?

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The volume of a sphere is expressed as the four thirds of the product of pi and the cube of its radius. The surface area, on the other hand, is expressed as four times the product of pi and the square of its radius. Radius is half the diameter. Calculations are as follows:

V = 4/3 X (πr^3) = 4/3 X (π x 3.75^3) =220.89 ft^3
SA = 4πr^2 = 4 x π x 3.75^2 = 176.71 ft^2

The sales tax on a digital camera is $7.15. What is the sales tax rate?

Answers

You just have to find out the percent 7.15 is of 105. To do that, you set up a proportion with x as the percentage:

$(7.15)/(105)=(x)/(100)$

Then, cross multiply to get:

$(7.15)/(105)=(x)/(100)\n715=105x\n105x/105=715/105\nx=6.810$

So, the sales tax rate was 6.8%.

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