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2 years ago

6

Mary has a pink dress, a blue dress, and a yellow dress. She has a black pair of shoes and a white pair. How many dress and shoe

outfits can she make?

1 answer:

Yanka [14]2 years ago

8 0

There are two ways to solve this.
The first way is logically.
Mary can
-wear a pink dress with black shoes -wear a pink dress with white shoes
-wear a blue dress with black shoes -wear a blue dress with white shoes
-wear a yellow dress with black shoes - wear a yellow dress with white shoes

Count them up, and you'll get six combinations!

Another way is simply mathematically, which is easier in my opinion.

3 (different colored dresses) × 2 (different colored shoes) = 6 (combos)

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Drag the expressions to the table to show whether the product is less than 3/4, greater than 3/4, or equal to 3/4.

KiRa [710]

A fraction 3/4 is called greater than 3/4 if,

Numerator > denominator,

Otherwise it is less than 3/4 ,

$\frac{1}{3} \times \frac{3}{4}=\frac{1}{4}$

$\begin{aligned}&\frac{5}{2} \times \frac{3}{4}=\frac{15}{8} \\&\because 8 < 15 \\&\Longrightarrow \frac{5}{2}\times \frac{3}{4} < 3/4 \\&\frac{7}{7} \times \frac{3}{4}=\frac{3}{4} \\&\because 3 < 4 \\&\Longrightarrow \frac{3}{4} \times \frac{3}{4} = 1 \\& \frac{9}{7} \times \frac{3}{4}=\frac{27}{28} \\&\because 28 > 27 \\&\Longrightarrow \frac{5}{5} \times \frac{3}{4} > \frac{3}{4} \end{aligned}$

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which meaning "to break," is the source of the English term "fraction." The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions were first written in India with one number above the other, but without a line. The line used to divide the numerator and the denominator was only added by Arabs.

To learn more about fraction brainly.com/question/10354322

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1 year ago

Select the correct statements that correspond to the question. Thank you!

lions [1.4K]

I’m pretty sure it’s B :))

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2 years ago

Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks

Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

It is estimated that 25% of these tanks leak.

This means that $p = 0.25$

15 tanks chosen at random

This means that $n = 15$

a.What is the expected number of leaking tanks in such samples of 15?

$E(X) = np = 15*0.25 = 3.75$

b.What is the probability that fewer than 3 tanks will be found to be leaking?

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134$

$P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668$

$P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361$

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

$\mu = E(X) = np = 2000*0.25 = 500$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.25*0.75} = 19.36$

This probability is 1 subtracted by the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{600 - 500}{19.36}$

$Z = 5.16$

$Z = 5.16$ has a pvalue of 0.

0% the probability that at least 600 of these tanks are leaking

4 0

3 years ago

You get in an elevator and go up 4 floors. You exit on the 12th floor. What floor did you get on the elevator

MissTica

Answer: 8th floor

Explanation:

6 0

3 years ago

Read 2 more answers

8) HELP PLEASE ILL GIVE BRAINLIEST!! Find the median of the set of data.(Remember to put the

crimeas [40]

The median is 7.

——————————

Arrange data in numerical order

1 3 3 6 8 10 10 15

Total number are 8, N = 8

Take the middle two numbers 6 and 8 and take their average

6+8/2 = 14/2 = 7

Therefore the median is 7.

3 0

2 years ago