The double number line shows that 111 pound of chocolate costs \$4$4dollar sign, 4.

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

There are five wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be atta

docker41 [41]

Answer:

Number of Possible Sequence = 5 x 4 x 3 x 2 x 1 = 120 ways

Please give 5-star rating

3 0

2 years ago

What are scientific figures?

Nikolay [14]

Sig Figs, as they are also known, are important only in Science. But there are three ways you can determine how many sig figs there are. Non-Zero digits are sig figs. Any zeros between two sig figs are significant. (EX: 7008) And, lastly, A final zero(s) in a decimal are significant. (EX: 0.76540800) Last two zeros are significant.

8 0

3 years ago

Why is it necessary to use the absolute value of the difference when finding the distance on a number line, but not necessary wh

padilas [110]

Remember that the distance on a number line is given by the formula: $d=|x_{2}-x_{1}|$
where
$d$ is the distance between the points.
$x_{2}$ is the second point in the number line.
$x_{1}$ is the first point in the number line.
Now, suppose we are trying to find the distance between the points -1 and -5; our first point is -1, so $x_{1}=-1$ , and our second point is $-5$ , so $x_{2}=-5$ . Suppose we are going to find the distance between the two point without using absolute value:
$d=x_{2}-x_{1}$
$d=-5-(-1)$
$d=-5+1$
$d=-4$
Look what we have here, a negative distance! Since distances cannot be negative, we must use absolute value to always get postie distances between two point on a umber line:
$d=|x_{2}-x_{1}|$
$d=|-5-(-1)|$
$d=|-5+1|$
$d=|-4|$
$d=4$

Now, the distance between two coordinates on a plane is given by the formula: $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$
$where$
$d$ is the distance between the two coordinates
$(x_{1},y_{2})$ are the coordinates of the first point
$(x_{2},y_{2})$ are the coordinates of the second point
Notice that $(x_{2}-x_{1})^2$ and $(y_{2}-y_{1})^2$ are squared, so it doesn't matter if we get a negative distance because a negative number raised to an even power (like 2) is always positive; therefore we don't need absolute value in this case because we won't ever get a negative distance.

7 0

3 years ago

Every week, Enrique walks one mile each day for 4 days of the week. He can usually walk one mile in about 14 to 16 minutes.

Snezhnost [94]

Answer:

512

Step-by-step explanation:

Beacuse 4x3 =32 32 x 16 =512

8 0

3 years ago

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