If the circumference of a circle is doubled, how does the diameter of the circle change?

HELP PLEASE!!! I need help with 94 if you could show the steps that would be very helpful!

aksik [14]

A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:

n!/((n-r)!r!)

In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.

5!/((5-1)!1!) = 5!/(4!*1!) = (5*4*3*2*1)/(4*3*2*1*1) = 5

5!/((5-2)!2!) = 5!/(3!2!) = (5*4*3*2*1)/(3*2*1*2*1) = 10

5!/((5-3)!3!) = 5!/(2!3!) = (5*4*3*2*1)/(2*1*3*2*1) = 10

5!/((5-4)!4!) = 5!/(1!4!) = (5*4*3*2*1)/(1*4*3*2*1) = 5

Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.

Now we add together the combinations

1 + 5 + 10 + 10 + 5 + 1 = 32 choices combinations to discard.

The answer is 32.

-------------------------------

Note: There is also an equation for permutations which is:

n!/(n-r)!

Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.

We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.

I hope this helps! If you have any questions, let me know :)

7 0

3 years ago

Adjust the equation so the line passes through the points. Y=x+1

lapo4ka [179]

Answer:

Slope=

2.000

=1.000

x−intercept=

−1

1

=−1.00000

y−intercept=

1

=1.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(x+1)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-x-1 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-x-1 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.00000

y-intercept = 1/1 = 1.00000

Calculate the X-Intercept :

When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x=-1.00000

x-intercept = 1/-1 = -1.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - 1.000 = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 2.000/2.000 = 1.000

Geometric figure: Straight Line

1. Slope = 2.000/2.000 = 1.000

2. x-intercept = 1/-1 = -1.00000

3. y-intercept = 1/1 = 1.00000

3 0

3 years ago

Given that f(x) = x² +8x+3 and g(x) = -x-7, which of the following is true?

Valentin [98]

B and C make sense to me.

4 0

3 years ago

Carol used 114 cups of flour in 2 muffins. How many cups of flour are needed to make 12 similar muffins?

son4ous [18]

Answer:

7 1/2 cups

Step-by-step explanation:

If Carol uses 1 1/4 cups of flour for 2 muffins, then she will need to repeat this conversion 6 times since she wants to make identical 12 muffins in all.

So, 1 1/4 * 6 = 7 1/2

Therefore, she needs 7 1/2 cups of flour

Hope that helps! :)

7 0

3 years ago

Jada paints a circular table that has a diameter of 44 inches. What is the area of the table? Round to the nearest whole number!

Elza [17]

Answer: 1521

Step-by-step explanation: use the equation pi times radius square. Your radius is always going to be half your diameter so you'll use 22 instead. Then plug that I'm and you should get 1520.53 rounded would be 1521.

5 0

3 years ago

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