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3 years ago

Given the set definitions below, find X Y. X = {100, 200} Y = {1,2}

1 answer:

4 0

The Cartesian product of two sets can be defined as the following: the set of all possible pairs where the 1st coordinate is an element of the 1st set and the 2nd coordinate is the element of the 2nd set. This has an obvious generalization for n sets (the cartesian product has then n coordinates).
Let us pick now all the pairs that have 100 as their first coordinate. We then have 2 choices for the 2nd coordinate, 1 and 2. Hence, the 2 pairs are: (100,1), (100,2). Similarly, if 200 is the first coordinate, the pairs are (200,1), (200,2).
These 4 pairs are the cartesian product (we have 4 pairs =2 elements from X* 2 elements from Y) .
It helps to remember that the cartesian product has as many elements as the product of the number of elements of each set.

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Find solution to the system of linear equations. 5x1 + x2 = 0 , 25x1 + 5x2 = 0

Zigmanuir [339]

Answer:

the system of equation has infinite solution

Step-by-step explanation:

$5x_1 + x_2 = 0$ , $25x_1 + 5x_2 = 0$

Solve the first equation for x_2

Subtract 5x1 on both sides

$5x_1 + x_2 = 0$

$x_2 =-5x_1$

Now substitute -5x1 on second equation

$25x_1 + 5x_2 = 0$

$25x_1 + 5(-5x_1)= 0$

$25x_1-25x_1= 0$

0=0

So the system of equation has infinite solution

5 0

3 years ago

Read 2 more answers

David found and factored out the GCF of the polynomial 80b4 – 32b2c3 + 48b4c. His work is below. GFC of 80, 32, and 48: 16 GCF o

BlackZzzverrR [31]

Answer: The correct statements are

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

David applied the distributive property.

Step-by-step explanation:

GCF = Greatest common factor

1) GCF of coefficients : (80,32,48)

80 = 2 × 2 × 2 × 2 × 5

32 = 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

GCF of coefficients : (80,32,48) is 16.

2) GCF of variables :( $b^4,b^2,b^4$ )

$b^4$ = b × b × b × b

$b^2$ = b × b

$b^4$ =b × b × b × b

GCF of variables :( $b^4,b^2,b^4$ ) is $b^2$

3) GCF of $c^3$ and c: c is not the GCF of the polynomial. The variable c is not common to all terms, so a power of c should not have been factored out.

4) $80b^4-32b^2c^3+48b^4c$

$=16b^2(5b^2-2c^3+3b^2c)$

David applied the distributive property.

7 0

3 years ago

Read 3 more answers

The test scores of a geometry class are given below. 90, 75, 72, 88, 85 The teacher wants to find the variance for the class pop

ella [17]

The data given as a whole would be called ungrouped data. Now to get the variance, you will need the formula:

s^2= Σ(x-mean)^2
n

x = raw data
mean = average of all data
n = no. of observations
s^2 = variance

Now we do not have the mean yet, so you have to solve for it. All you need to do is add up all the data and divide it by the number of observations.

Data: 90, 75, 72, 88, 85 n= 5
Mean=Σx
n
Mean = 90+75+72+88+85 = 410 = 82
5 5

The mean is 82. Now we can make a table using this.

The firs column will be your raw data or x, the second column will be your mean and the third will be the difference between the raw data and the mean and the fourth column will be the difference raised to two.

90-82 = 8
8^2 =64

75-82 = -7
-7^2 =49

72-82 = -10
-10^2=100

88-82=6
6^2 = 12

85-82=3
3^2=9

Now you have your results, you can now tabulate the data:

x mean x-mean (x-mean)^2
90 82 8 64
75 82 -7 49
72 82 -10 100
88 82 6 36
85 82 3 9

Now that you have a table, you will need the sum of (x-mean)^2 because the sigma sign Σ in statistics, means "the sum of."

64+49+100+36+9 = 258

This will be the answer to your question. The value of the numerator of the calculation will be 258.

6 0

4 years ago

ASK YOUR TEACHER Two streets meet at an 84° angle. At the corner, a park is being built in the shape of a triangle. Find the are

Alla [95]

Answer:

22,203 ft^2

Step-by-step explanation:

The area of a triangle with angle ∅ and two sides a and b is;

Area A = 1/2 × absin∅ ......1

The park is in the shape of a triangle, with two sides and an angle given;

Given;

a = 190 ft

b = 235 ft

∅ = 84°

Substituting the values into equation 1;

Area of the park;

A = 1/2 × 190 × 235 × sin84°

A = 22,202.70131409 ft^2

A = 22,203 ft^2 (to the nearest whole number)

Area of the park is 22,203 ft^2

3 0

3 years ago

60 min is 20%of blank min

enot [183]

Answer:

20% of the number is 60.

100% of the number is therefore (100/20) x 60 = 5 x 60 = 300

Step-by-step explanation:

Explanation:

No further explanation required really!

4 0

4 years ago