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3 years ago

The number a exceeds the number b by 50 percent. By what percent is the number b smaller than the number a?

Mathematics

1 answer:

inna [77]3 years ago

5 0

Answer:

33 1/3 percent smaller

Step-by-step explanation:

The number a exceeds the number b by 50 percent.

a = b + b*.5

a = b(1.5)

Divide by 1.5

a/1.5 = b

2/3a =b

We want to find (a-b)/a to find the percent decrease

(a-2/3a)/a *100percent

(1/3a)/a* 100 percent

1/3 * 100 percent

33 1/3 percent smaller

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4x + 5 = 25 x = 2 x = 5 x = 2 x = 7

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Hi there!

Answer:

$\huge\boxed{x = 5}$

4x + 5 = 25

Subtract 5 from both sides:

4x + 5 - 5 = 25 - 5

4x = 20

Divide both sides by 4:

4x/4 = 20/4

x = 5.

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Step-by-step explanation:

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Read 2 more answers

Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answe

wariber [46]

Answer:

(a)

$A\ u\ (B\ n\ C) = \{a,b,c\}$

$(A\ u\ B)\ n\ C = \{b,c\}$

$(A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}$

$(A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)$

(b)

$A\ n\ (B\ u\ C) = \{b,c\}$

$(A\ n\ B)\ u\ C = \{b,c,e\}$

$(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}$

$A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)$

(c)

$(A - B) - C = \{a\}$

$A - (B - C) = \{a,b,c\}$

They are not equal

Step-by-step explanation:

Given

$A= \{a,b,c\}$

$B =\{b,c,d\}$

$C = \{b,c,e\}$

Solving (a):

$A\ u\ (B\ n\ C)$

$(A\ u\ B)\ n\ C$

$(A\ u\ B)\ n\ (A\ u\ C)$

$A\ u\ (B\ n\ C)$

B n C means common elements between B and C;

So:

$B\ n\ C = \{b,c,d\}\ n\ \{b,c,e\}$

$B\ n\ C = \{b,c\}$

So:

$A\ u\ (B\ n\ C) = \{a,b,c\}\ u\ \{b,c\}$

u means union (without repetition)

So:

$A\ u\ (B\ n\ C) = \{a,b,c\}$

Using the illustrations of u and n, we have:

$(A\ u\ B)\ n\ C$

$(A\ u\ B)\ n\ C = (\{a,b,c\}\ u\ \{b,c,d\})\ n\ C$

Solve the bracket

$(A\ u\ B)\ n\ C = (\{a,b,c,d\})\ n\ C$

Substitute the value of set C

$(A\ u\ B)\ n\ C = \{a,b,c,d\}\ n\ \{b,c,e\}$

Apply intersection rule

$(A\ u\ B)\ n\ C = \{b,c\}$

$(A\ u\ B)\ n\ (A\ u\ C)$

In above:

$A\ u\ B = \{a,b,c,d\}$

Solving A u C, we have:

$A\ u\ C = \{a,b,c\}\ u\ \{b,c,e\}$

Apply union rule

$A\ u\ C = \{b,c\}$

So:

$(A\ u\ B)\ n\ (A\ u\ C) = \{a,b,c,d\}\ n\ \{b,c\}$

$(A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}$

The equal sets

We have:

$A\ u\ (B\ n\ C) = \{a,b,c\}$

$(A\ u\ B)\ n\ C = \{b,c\}$

$(A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}$

So, the equal sets are:

$(A\ u\ B)\ n\ C$ and $(A\ u\ B)\ n\ (A\ u\ C)$

They both equal to $\{b,c\}$

So:

$(A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)$

Solving (b):

$A\ n\ (B\ u\ C)$

$(A\ n\ B)\ u\ C$

$(A\ n\ B)\ u\ (A\ n\ C)$

So, we have:

$A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d\}\ u\ \{b,c,e\})$

Solve the bracket

$A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d,e\})$

Apply intersection rule

$A\ n\ (B\ u\ C) = \{b,c\}$

$(A\ n\ B)\ u\ C = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ \{b,c,e\}$

Solve the bracket

$(A\ n\ B)\ u\ C = \{b,c\}\ u\ \{b,c,e\}$

Apply union rule

$(A\ n\ B)\ u\ C = \{b,c,e\}$

$(A\ n\ B)\ u\ (A\ n\ C) = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ (\{a,b,c\}\ n\ \{b,c,e\})$

Solve each bracket

$(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}\ u\ \{b,c\}$

Apply union rule

$(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}$

The equal set

We have:

$A\ n\ (B\ u\ C) = \{b,c\}$

$(A\ n\ B)\ u\ C = \{b,c,e\}$

$(A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}$

So, the equal sets are:

$A\ n\ (B\ u\ C)$ and $(A\ n\ B)\ u\ (A\ n\ C)$

They both equal to $\{b,c\}$

So:

$A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)$

Solving (c):

$(A - B) - C$

$A - (B - C)$

This illustrates difference.

$A - B$ returns the elements in A and not B

Using that illustration, we have:

$(A - B) - C = (\{a,b,c\} - \{b,c,d\}) - \{b,c,e\}$

Solve the bracket

$(A - B) - C = \{a\} - \{b,c,e\}$

$(A - B) - C = \{a\}$

Similarly:

$A - (B - C) = \{a,b,c\} - (\{b,c,d\} - \{b,c,e\})$

$A - (B - C) = \{a,b,c\} - \{d\}$

$A - (B - C) = \{a,b,c\}$

They are not equal

4 0

3 years ago

"if the standard deviation of a group of 20 scores is 15, what is the variance?"

DerKrebs [107]

We have been given that the standard deviation of a group of 20 scores is 15 and we are asked to find variance.

Since we know variance is square of standard deviation. In order to find out the variance of the given data we have to take the square of 15.

$\text{ Variance}=\sigma^{2}\\
=15^{2}=225$

Therefore, our variance is 225.

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3 years ago