Click on the solution set below until the correct one is displayed.

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

8 0

Answer: Second Option

(Point in Quadrant I)

Step-by-step explanation:

The solution to a system of linear equations is the point where the two lines intersect.

Note that in this case we have two lines with different slope . By definition, if two lines have different slopes and are contained in the same plane, then there will always be an intersection between them at some point in the plane.

Looking at the image, you can see that the lines get closer as x and y increase. Then they will intercept in the first quadrant.

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15 points! The data set shows the weights of pumpkins, in pounds, that are chosen for a photograph in a farming magazine. The re

vladimir2022 [97]

Answer:

Step-by-step explanation:

a). Mean of the given data set = $\frac{32+28+18+40+22}{5}$

= 28

b). x $x-\overline{x}$ $(x-\overline{x})^2$

32 32-28 = 4 16

28 28 - 28 = 0 0

18 18 - 28 = -10 100

40 40 - 28 = 12 144

22 22 - 28 = -6 36

$\sum({x-\overline x})^2$ = 296

c). Standard deviation = $\sqrt{\frac{\sum (x-\overline{x})^2}{n}}$

= $\sqrt{\frac{296}{5} }$

= 7.69

d). Mean of the new set of weights = $\frac{32+33+34+35+36}{5}$

= 34

Since mean of the data set is more close to each data, standard deviation will be less than the deviation given in part (c).

7 0

3 years ago

Let n be a positive integer and define [n] to be the set of the first n positive integers. That is, [n] = {1, 2, 3, . . . , n}.

yaroslaw [1]

Answer: There are $2^{n-1}$ ways of doing this

Hi!

To solve this problem we can think in term of binary numbers. Let's start with an example:

n=5, A = {1, 2 ,3}, B = {4,5}

We can think of A as 11100, number 1 meaning "this element is in A" and number 0 meaning "this element is not in A"

And we can think of B as 00011.

Thinking like this, the empty set is 00000, and [n] =11111 (this is the case A=empty set, B=[n])

This representation is a 5 digit binary number. There are $2^5$ of these numbers. Each one of this is a possible selection of A and B. But there are repetitions: 11100 is the same selection as 00011. So we have to divide by two. The total number of ways of selecting A and B is the $2^{5-1} = 2^4$ .