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12 Explain A bag includes one number card each for the numbers 1-25. Each of

Alex

Answer:

Let us say the domain in the first case, has the numbers. And the co-domain has the students, .

Now for a relation to be a function, the input should have exactly one output, which is true in this case because each number is associated (picked up by) with only one student.

The second condition is that no element in the domain should be left without an output. This is taken care by the equal number of students and the cards. 25 cards and 25 students. And they pick exactly one card. So all the cards get picked.

Note that this function is one-one and onto in the sense that each input has different outputs and no element in the co domain is left without an image in the domain. Since this is an one-one onto function inverse should exist. If the inverse exists, then the domain and co domain can be interchanged. i.e., Students become the domain and the cards co-domain, exactly like Mario claimed. So, both are correct!

8 0

3 years ago

In 1987, 522 comma 000 people worked in the air transportation industry. In 2003, the number was 480 comma 000. (a) Find a li

umka2103 [35]

Answer:

the linear equation is :

y= -2625x+5737875

and 440000 employees will be in year 2271

Step-by-step explanation:

in order to find the linerar equation let us first convert the given data into (x,y ) co-ordinates i.e

x1= 1987 y1= 522,000

and

x2= 2003, y2 = 480000

according to two point form:

$y-y1 = (y2-y1) \frac{x-x1}{x2-x1}$

In this example we have x1=1987 , y1=522000 , x2=2003 and y2=480000. So,

$y - 522000 = \frac{480000-522000}{2003-1987} (x-1987)\\y- 522000 = -2625(x-1987)\\y- 522000= -2625x+5215875\\\\y= -2625x+5737875$

now to find the year when there will be 440000 employs working , we simply put y= 440000 in the above derived equation

$440000= -2625x+ 5737875\\\\2526x = 5737875 -440000\\2526x = 5736555\\x= \frac{5736555}{2526} \\x= 2271$

7 0

3 years ago

Margarita is 15 years older than Silvia the sum of their ages is 41

Nimfa-mama [501]

One of them is 13 and the other is 28

3 0

3 years ago

Read 2 more answers

15. A band expects to have 16 songs on their next

stepladder [879]

Answer:

There will be 13 songs in the final album.

Step-by-step explanation:

i) number of songs expected = 16 songs

ii) the band wrrites 62.5% more

therefore the band writes $16 \times ( 1 + 0.625) = 16 \times 1.625 = 26$ songs

iii) During the editing process 50% of the songs are removed.

Therefore there will be in the final album = $( 1 - 0.5) \times 26 = 0.5 \times 26 = 13$ songs.

8 0

3 years ago

Find the other two vertices of a square with one vertex (0, 0) and another vertex (4, 2). Can you find another answer?

Margarita [4]

It is given that two vertices of square are (0,0) and (4,2).

Now the problem is that you haven't given that whether these two vertices are adjacent vertices or opposite vertices of the square.

1. By Supposing that these two are adjacent vertices of Square

The third vertex will be at (-4,2) which lies in third quadrant.

Suppose the coordinate of fourth vertex be (x,y).

Mid point of line joining (4,2) and (-4,2) is{ [4+(-4)]/2,(2+2)/2} is (0,2).

Mid point of line joining (x,y) and (0,0) is (x/2,y/2).

Since diagonals of square bisect each other,

∵ x/2=0

⇒x=0

and

y/2=2

⇒y=4

So, The Coordinate of fourth vertex is (0,4).

Now coming back to second condition if these are two opposite vertex of Square.

Let the third coordinate be (a,b).

Length of diagonal= $\sqrt{(4-0)^2+(2-0)^2}=\sqrt20=2\sqrt5$

Now,let side of Square be A.

Then length of Diagonal of square =√2 A

⇒√2 A=2√5

⇒A =√10

As third vertex is (a,b).

Using distance formula

a² + b²=10 -------------(1)

(a-4)²+ (b-2)²=10 --------------(2)

Solving expression (1) and (2), we get

⇒a²+ b²=(a-4)² +(b-2)²

⇒2a + b =5

⇒b=5-2a

Putting the value of b in (1),we get

⇒a² +(5-2a)²=10

⇒a²+25+4a²-20a =10

⇒5a²-20a+15=0

⇒a² - 4a + 3=0

Splitting the middle term,we get

⇒(a-3)(a-1)=0

⇒a=3 ∧ a=1

we get b=5-2×1=3 and b=5-2×3=5-6=-1

So,the other vertex are (1,3) and(3,-1).

3 0

3 years ago