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4 years ago

How many one-to-one correspondences are there between two sets with 6 elements each?

Mathematics

2 answers:

WINSTONCH [101]4 years ago

3 0

Answer:

6 * 5 * 4 * 3 * 2 * 1, i.e. 6! or 720. Of course, since both sets have the same number of elements, you can't have one-to-one without being onto, aka a surjection, so “one to one correspondence” is the right term (or bijection—merci, M.

Hope it helps >3!

timama [110]4 years ago

3 0

Answer:

Step-by-step explanation:

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You might be interested in

Rachel has a bag containing 3 red marbles, 5 purple marbles, and 10 blue marbles.

tankabanditka [31]

Answer:

5/18, 13/18

Step-by-step explanation:

The basic probability of anything is Specific Outcome / Total Outcomes

The specific outcome here is pulling a purple marble. We see there are 5 purple marbles therefore there are 5 ways to get them. The total outcomes are the total number of marbles which is 18. Therefore, the answer is 5/18

The complement of a probability is 1 minus the original probability, so, it would be 1 - 5/18 here getting us 13/18 as the answer.

7 0

3 years ago

Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make s

tatyana61 [14]

Answer:

Part A

We note that the vertices of a triangle are formed by three non colinear points, which are A(3, 3), B(6, 6), C(9, 3)

The image of the reflection of a point (x, y) across the x-axis is (x, -y)

Therefore, the image of the triangle are; A'(3, -3), B'(6, -6), and C'(9, -3)

The characteristics of the transformation includes;

1) The dimensions of the preimage and image triangles are the same (rigid transformation)

2) The image is the representation of the inverted (upside down) of the preimage

3) The x-values of the image and the preimage are the same, while the y values are equal in magnitude but opposite in sign

Part B

Please find attached the drawing of the triangle ΔABC, ΔA'B'C' and the lines from A and and A' to the reflecting line, the x-axis

Based on the above characteristics, the perpendicular line drawn from A to the reflecting line(the x-axis and the line drawn from A' to the x-axis are equal in length and they intersect at the same point on the x-axis

Part C

Given that the x-axis values of B and B' and the magnitudes of the y-axis values of B and B' are the same, we have that the length of the perpendicular lines from B and B' will have equal length and point of intersection on the x-axis

Therefore, the same characteristics is seen when a line segment connecting B with the reflecting x-axis and then a line B' with the reflecting line is drawn

Step-by-step explanation:

7 0

3 years ago

What is y when 8=2y-10x

Naddika [18.5K]

Answer:

Y = 9

Step-by-step explanation:

2Y (with Y having a value of 9) would be equal to 2 x 9 which would give you 18

then you take the 18 and subtract 10x

which would give you 8x with the x not being relevant in your case (maybe)

8 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h a

Arada [10]

Answer:

Volume of the sphere is 66.67r/h

Step-by-step explanation:

Hello,

Volume of a sphere = ⁴/₃πr³

Volume of a cylinder = πr²h

The volume of the cylinder = 50ft³

But the cylinder and sphere both have the same radius and height

Volume of a cylinder = πr²h

50 = πr²h

Make r² the subject of formula

r² = 50/πh

Volume of a sphere = ⁴/₃πr³

Put r² into the volume of a sphere

Volume of a sphere = ⁴/₃π(50/πh)r

Volume of a sphere = ⁴/₃ × 50r/h

Volume of a sphere = ²⁰⁰/₃ r/h

Volume of a sphere = 66.67r/h

The volume of the sphere is 66.67r/h

7 0

4 years ago

A farmer has 144 feet of fencing to use to create a rectangular enclosure for his pigs. He decides to use the wall of his barn a

andreyandreev [35.5K]

Answer:

The farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.

Step-by-step explanation:

The question tests the applications of differential calculus. We are informed that the farmer will use the wall of his barn as one side of the enclosure implying that the 144 feet of fencing will only be used to form the three remaining sides of the rectangular enclosure.

If we let x denote the width of this rectangular enclosure to be formed, then its length will be 144-2x since we shall be having two sides each measuring x and the total length of the fencing is 144. 2x will be used on the width leaving 144-2x for the length since one side of the length is formed by the wall.

If we let A denote the area of the rectangular enclosure, then;

A = x(144 - 2x)

since the area of a rectangle is simply the product of the length and the width. We open the brackets;

A = 144x - 2x^2

Clearly, the Area is a function of the width that is A is the dependent variable while x is the independent one.

At the maximum area, the slope of the tangent to the curve 144x - 2x^2 is 0. Therefore, we differentiate the given function of x with respect to x then set the resulting expression to 0 to determine x that will maximize A;

dA/dx = 144 - 4x

We set this expression to 0 and solve for x;

144 - 4x = 0

144 = 4x

x = 36

Therefore, the farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.

5 0

3 years ago