Sharon has a patio in the shape of a rectangle

A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total?

attashe74 [19]

Answer:

There are 256 ways in total.

There are 56 possible outcomes contain exactly three heads.

The possible outcomes contain at least three heads is 219.

The possible outcomes contain the same number of heads and tails are 70.

Step-by-step explanation:

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

Therefore the total number of ways are:

$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^8=256$

Hence, there are 256 ways in total.

Part (b) contain exactly three heads?

We want exactly 3 heads, therefore,

n=8 and r=3

According to the definition of combination: $\binom{n}{r}=\frac{n!}{r!(n-r)!}$

$\binom{8}{3}=\frac{8!}{3!(5)!}=56$

Hence, there are 56 possible outcomes contain exactly three heads.

Part (c) contain at least three heads?

For 3 heads: $\binom{8}{3}=\frac{8!}{3!(5)!}=56$

For 4 heads: $\binom{8}{4}=\frac{8!}{4!(4)!}=70$

For 5 heads: $\binom{8}{5}=\frac{8!}{5!(3)!}=56$

For 6 heads: $\binom{8}{6}=\frac{8!}{6!(2)!}=28$

For 7 heads: $\binom{8}{7}=\frac{8!}{7!(1)!}=8$

For 8 heads: $\binom{8}{8}=1$

Now add them as shown:

56+70+56+28+8+1=219

Hence, the possible outcomes contain at least three heads is 219.

Part (d) contain the same number of heads and tails?

Same number of heads and tails means that the value of r=4.

Therefore,

$\binom{8}{4}=\frac{8!}{4!(4)!}=70$

Hence, the possible outcomes contain the same number of heads and tails are 70.

6 0

3 years ago

Please Answer <br> If each quadrilateral below is a rectangle, find the missing measures

denpristay [2]

To solve for YW and VX I would use the Pythagorean Theorem. Add 19^2 to 31^2. Your answer should come out to be 1322. Now, find the square root of 1322. Due to the fact that it is not a perfect square, I would round this number. I am not sure if you were given a decimal place to round to, so I will just give you the full number (36.35932) Also, both diagonals are congruent, so ZX would just be half of 36.35932. Again, round the where you are asked to round.

6 0

3 years ago

Write an equation in standard form for the line that goes through (5,-3) with a slope of 2/5

KATRIN_1 [288]

Answer:

y = 2/5x - 5

Step-by-step explanation:

y = 2/5x - 5

(If you go to desmos.com you can graph any equation. It really helps. I'm doing similar things in class, I use it all the time.)

3 0

3 years ago

Please help it’s the last question I have left until I can turn this in please answer ASAP if possible

telo118 [61]

Answer:

i cant see

Step-by-step explanation:

5 0

3 years ago

Solve the inequality. 9x − 4 > 95

SOVA2 [1]

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

9*x-4-(95)≥0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1 Pull out like factors :

9x - 99 = 9 • (x - 11)

Equation at the end of step

1

:

STEP

2

:

2.1 Divide both sides by 9

Solve Basic Inequality :

2.2 Add 11 to both sides

x ≥ 11

Inequality Plot :

2.3 Inequality plot for

9.000 X - 99.000 ≥ 0

One solution was found :

x ≥ 11

Step-by-step explanation:

3 0

3 years ago