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3 years ago

What is the definition of the union of two mathematical sats ,A and B

Mathematics

1 answer:

Zepler [3.9K]3 years ago

5 0

Set contain all the elements present in both the sets.

<u>Step-by-step explanation:</u>

Definition:

The union of two mathematical sets can be defined as the set that consists of all the elements present in both the sets without the repetition of elements.

Consider, A and B be the sets.

A = {1,7,5,6,0}

B = {2,3,4,5,6}

U is the symbol of union of sets, so A U B = {1,2,3,4,5,6,7,0}

Here 5 and 6 are the elements present in both the sets, so written only once in the set of A U B.

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Two certificates of deposit pay interest that differ by 3%. Money invested for one year in the first CD earns $240 interest. The

Soloha48 [4]

a = interest rate of first CD

b = interest rate of second CD

and again, let's say the principal invested in each is $X.

$\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\$

$\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft$

$\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft$

3 0

3 years ago

What is the factored form of 3x^2 + 23x - 36?

alex41 [277]

The factored form is (3x-4)(x+9)

6 0

4 years ago

Will someone plz help me this us due and I am confused

mihalych1998 [28]

Hey there! I would love to help you.

Question 1: In both questions, we have to find the repeating decimal as a fraction. There is a specific way to find the fraction given a repeated decimal. In our equation, our variable x will represent the fraction.

x=0.272727....

If you know how too solve systems of equations by elimination, we need to to do something similar to eliminate all of the repeating parts so we can solve for x.

We need to make this a number greater than zero but line up the digits so that we can eliminate every single repeating digit.

To do this, we move the digit as many times to the right as there are digits that repeat. In this case, there are two repeating digits, so we multiply the whole equation by 100.

100x=27.2727...

Now, we can subtract the first equation from the second so that the repeating parts are removed and we can then solve for x and find our fraction.

99x=27

Now, we solve for x.

x=27/99

Now we subtract this from the first fraction.

11/6-27/99= 1 37/66

To make this into a repeating decimal, we just divide the numerator by the denominator.

1.560606060...

As we can see, the 60 is repeating, so the answer is the second option on the first one.

Question 2: In this case, we have two repeating decimals. Let's solve for them both. Because we have a digit after the decimal that does not repeat, we need to move it before we subtract.

10x=4.090909...

We need to line up the decimals, and in this case we need to multiply by 1000.

990x=409.090909...

Now we subtract...

990x=405

We solve...

x=9/22

Now we do the other one.

10x=6.81818181...

We multiply by 100 to line up the decimals for subtraction.

1000x=681.8181....

We subtract...

990x=675

x=15/22

Now, we add our fractions.

24/22 or 1 2/22

Now we turn it back into a repeating.

24/22= 1.09090909...

For this question, select the second option.

I hope this helps!

7 0

3 years ago

Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling ga

Serga [27]

Answer:

The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this question:

$\mu = 152, \sigma = 14.5$