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3 years ago

What is a set- builder notation?

Mathematics

1 answer:

patriot [66]3 years ago

5 0

Answer:

set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.

Step-by-step explanation:

You might be interested in

The first four terms of a sequence are \text{3, -6, 12, -24}. Write an explicit formula for this sequence, where n is any term n

steposvetlana [31]

Answer:

see explanation

Step-by-step explanation:

The terms form a geometric sequence with n th term

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

r = $\frac{a_{2} }{a_{1} }$ = $\frac{a_{3} }{a_{2} }$ = ......

r = $\frac{-6}{3}$ = $\frac{12}{-6}$ = - 2 and a = 3, hence

$a_{n}$ = 3 $(-2)^{n-1}$ ← explicit formula

3 0

3 years ago

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they

Lunna [17]

Answer:

The mechanic who worked 5 hours charged $115 per hour, the one who worked 15 hours charged $120 per hour.

Step-by-step explanation:

x = rate of mechanic who worked 5 hours

y = rate of mechanic who worked 15 hours

Then

x + y = 235

5x + 15y = 2375

Just solve these 2 equations above for x and y.

x + y = 235 ⇒ x = 235 - y

Substitute into second equation to find y.

5(235 - y) + 15y = 2375

1175 - 5y + 15y = 2375

10y = 1200

y = 1200/10 = 120

x = 235 - y = 235 - 120 = 115

5 0

2 years ago

Please helpppp it has to do with P(A U B)

Katyanochek1 [597]

$P(A)=0.5$ , $P(B)=0.6$ , $P(A\cup B)=0.8$

We find the probability of intersection using the inclusion/exclusion principle:

$P(A\cap B)=P(A)+P(B)-P(A\cup B)=0.3$

By definition of conditional probability,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.3}{0.6}=0.5$

For $A$ and $B$ to be independent, we must have

$P(A\cap B)=P(A)\cdot P(B)$

in which case we have $0.3=0.5\cdot0.6$ , which is true, so $A$ and $B$ are indeed independent.

Or, to establish independence another way, in terms of conditional probability, we must have

$P(A\mid B)\cdot P(B)=P(A)\cdot P(B)\implies P(A\mid B)=P(A)$

which is also true.

7 0

3 years ago

a rectangle consists of two identical squares with a common side. The perimeter of the rectangle is 27 inches. Find its area

sammy [17]

Answer:

40.5 square inches

Step-by-step explanation:

Rectangle consists of two identical squares.

So, if the sides of square = x,

Then, Width of rectangle = x &

Length of rectangle = x +x = 2x

Perimeter of rectangle = 27 inches

2*(length + width) = 27

2*( 2x + x) = 27 {Combine like terms]

2* 3x = 27

6x= 27 {Divide both sides by 6}

x = 27/6

x = 4.5

Width = x = 4.5 inches

Length = 2x = 2*4.5 = 9 inches

Area of rectangle = length *width

= 4.5 *9

= 40.5 square inches

3 0

3 years ago

Read 2 more answers

John Johnson’s gross pay for this week is $520.95. He is single and claims one withholding allowance. What amount will be withhe

Ivan

Answer:

amount which will be withheld from John's pay for federal income tax this week is $54

Step-by-step explanation:

It is given that John Johnson's gross pay for a week is $520.95,

From table it is clear that his gross pay ( $520.95) lies between at least 520 but less than 530 category.

and he claimed one withholding allowance, therefore John Johnson has to pay $54 for federal income tax.

I hope this answer will help you

8 0

3 years ago