What is 3/4 divided by 1/8? SHOW your reasoning.

How do I evaluate 564÷24 with a fraction or decimal

Butoxors [25]

564/24 equals to 47/2 or 23.5

4 0

3 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

The distance traveled by a certain vehicle varies directly to the amount of fuel the vehicle consumes. The vehicle traveled 90 m

olga_2 [115]

Answer:

The vehicle covers 126 miles on 7 gallons of fuel.

Step-by-step explanation:

Given:

The distance traveled is directly proportional to the amount of fuel.

For $F$ gallons of fuel distance traveled $D$ miles can be given as:

$D$ ∝ $F$

$D=kF$

where $k$ is constant of proportionality.

The vehicle covers $D=90$ miles on $F=5$ gallons.

So

$90=k(5)$

Dividing both sides by 5.

$\frac{90}{5}=\frac{k(5)}{5}$

$18=k$

∴ $k=18$

When $F=7$ gallons

$D=(18)(7)$

$D=126$ miles

∴ The vehicle covers 126 miles on 7 gallons of fuel.

4 0

2 years ago

Sheila is building an addition to a house. The points E(- 1 1/2, -2 1/2), F(4 1/2, -2 1/2), G(4 1/2, 3 1/2), and H (9-1 1/2, 3 1

Helga [31]

Answer:

24 units

Step-by-step explanation:

8 0

2 years ago

Can you please explain this?

Leni [432]

Answer:

The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.

Step-by-step explanation:

Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. $s_{1} = -s_{2}^{-1}$ )

Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:

(3,5)-(1,1) and (0, 2)-(5, 12)

To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate. That will give us a valid Δx and Δy to get the slope.

In the first pair, 3 > 1, so we'll subtract the second point from the first:

$s = \Delta y / \Delta x\\s = \frac{5 - 1}{3 - 1}\\s = 4/2\\s = 2$

So the first pair of vectors describe a line with a slope of 2. Let's look at the other pair:

$s = \Delta y / \Delta x\\s = (12 - 2) / (5 - 0)\\s = 10 / 5\\s = 2$

That also gives us a slope of 2, meaning that the two lines are parallel.

This same process will need to be done for the other three questions. We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image. For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.

6 0

3 years ago