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3 years ago

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

Mathematics

2 answers:

Rashid [163]3 years ago

4 0

Answer:

Step-by-step explanation:

Taking the quiz rn trust on this <3

nexus9112 [7]3 years ago

3 0

Hello:
the equation is : y = ax+b
the slope is a : a×(-3/2) = -1......( perpendicular to a line with a slope of -3/2)
a = 2/3 y=(2/3)x+b
the line that passes through (-2, -2) : -2 = (2/3)(-2)+b
b = -2/3
 the equation is : y = (2/3)x-2/3

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You buy 6 apples at $0.49/apple, 1 gallon of milk at $3.48/gallon, and 2 loaves of bread at $1.49/loaf. How much was your total

Makovka662 [10]

Answer:

Your total purchase was $9.40

Step-by-step explanation:

6 x 0.49 = 2.94

1 x 3.48 = 3.48

2 x 1.49 = 2.98

2.94 + 3.48 + 2.98 = 9.4

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2 years ago

Find Mean, Median, mode and range. Round to the nearest tenth.

stiv31 [10]

Answer:

Mean = 26.24

Median = 27

Mode = 32

Range = 38

Step-by-step explanation:

Plotting the original data from leaf plot

$9,11,12,12,14,17,25,25,27,32,32,32,33,35,41,42,47$

Finding Mean:

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$\mu=\frac{446}{17}$

= 26.24

Therefore, the range = 26.24.

Finding Median:

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

So, the median is 27 .

Finding Mode:

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

We see that the mode is 32.

Finding Range:

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

The lowest value is 9.

The highest value is 47.

The range = 47 - 9 = 38

4 0

2 years ago

Let X and Y be discrete random variables. Let E[X] and var[X] be the expected value and variance, respectively, of a random vari

Ulleksa [173]

Answer:

(a) $E[X+Y]=E[X]+E[Y]$

(b) $Var(X+Y)=Var(X)+Var(Y)$

Step-by-step explanation:

Let X and Y be discrete random variables and E(X) and Var(X) are the Expected Values and Variance of X respectively.

(a)We want to show that E[X + Y ] = E[X] + E[Y ].

When we have two random variables instead of one, we consider their joint distribution function.

For a function f(X,Y) of discrete variables X and Y, we can define

$E[f(X,Y)]=\sum_{x,y}f(x,y)\cdot P(X=x, Y=y).$

Since f(X,Y)=X+Y

$E[X+Y]=\sum_{x,y}(x+y)P(X=x,Y=y)\\=\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y).$

Let us look at the first of these sums.

$\sum_{x,y}xP(X=x,Y=y)\\=\sum_{x}x\sum_{y}P(X=x,Y=y)\\\text{Taking Marginal distribution of x}\\=\sum_{x}xP(X=x)=E[X].$

Similarly,

$\sum_{x,y}yP(X=x,Y=y)\\=\sum_{y}y\sum_{x}P(X=x,Y=y)\\\text{Taking Marginal distribution of y}\\=\sum_{y}yP(Y=y)=E[Y].$

Combining these two gives the formula:

$\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y) =E(X)+E(Y)$

Therefore:

$E[X+Y]=E[X]+E[Y] \text{ as required.}$

(b)We want to show that if X and Y are independent random variables, then:

$Var(X+Y)=Var(X)+Var(Y)$

By definition of Variance, we have that:

$Var(X+Y)=E(X+Y-E[X+Y]^2)$

$=E[(X-\mu_X +Y- \mu_Y)^2]\\=E[(X-\mu_X)^2 +(Y- \mu_Y)^2+2(X-\mu_X)(Y- \mu_Y)]\\$Since we have shown that expectation is linear$\\=E(X-\mu_X)^2 +E(Y- \mu_Y)^2+2E(X-\mu_X)(Y- \mu_Y)]\\=E[(X-E(X)]^2 +E[Y- E(Y)]^2+2Cov (X,Y)$