1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
WINSTONCH [101]
3 years ago
12

Which equations apply the distributive property? Select each correct answer. 70⋅2.028=(70⋅1)+(70⋅0.02)+(70⋅0.008)70⋅2.028=(70⋅1)

+(70⋅0.02)+(70⋅0.008) −2.5⋅0.6⋅5.8=−2.5⋅5.8⋅0.6−2.5·0.6·5.8=−2.5·5.8·0.6 −1.5⋅(6⋅1.25)=(−1.5⋅6)⋅1.25−1.5⋅(6⋅1.25)=(−1.5⋅6)⋅1.25 (0.7⋅0.7)+(0.7⋅0.9)+(0.7⋅0.2)=0.7⋅(0.7+0.9+0.2)(0.7⋅0.7)+(0.7⋅0.9)+(0.7⋅0.2)=0.7⋅(0.7+0.9+0.2)
Mathematics
1 answer:
Advocard [28]3 years ago
8 0
I think is the first one
You might be interested in
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)

Since X and Y are independent, Cov(X,Y)=0

=Var(X)+Var(Y)

Therefore as required:

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

7 0
3 years ago
Help with number 4 please?
LekaFEV [45]
10 because 7 x 3 = 21 and 7 + 3 = 10 so your answer is 10
5 0
3 years ago
Read 2 more answers
There are 12 students who wish to enroll in a particular course. there are only five seats left in the classroom. how many diffe
siniylev [52]
792 is the answer

(12*11*10*9*8)/5!=792
5 0
3 years ago
A pharmacist has 18% bleach solution. How much of this solution and how much water must be mixed together to make 10 liters of a
kkurt [141]
X = the amount of water to add
10 - x = amount of 18% bleach to add

.18(10-x)= .12 x 10
1.8 -.18x =1.2
-.18x = -.6
x = 3 1/3 liters water
therefore 6 2/3 liters bleach

4 0
3 years ago
Converting from vertex to standard form
stich3 [128]

Answer:

Step-by-step explanation:

y = (x+1)² - 3

 = (x²+2x+1)-3

 = x²+2x-2

:::::

y = (x-2)² + 3

 = (x²-4x+4) + 3

 = x²-4x+7

6 0
3 years ago
Other questions:
  • The area of a rectangle is 270 square feet. The ratio of the width to length is 5:6. Find the length and width
    10·1 answer
  • What is the height of this relation: <br> h= -0.3d² + 1.2d + 1.5
    11·1 answer
  • Find the inverse of the function y = x2 - 12.
    12·1 answer
  • Need help with #5 please explain
    11·1 answer
  • If a circle garden has a diameter of 60 feet and there’s a sidewalk 18 feet from the center, how long is the sidewalk?
    13·1 answer
  • Help me plsssss I am failing in this class pls give me step by step
    10·2 answers
  • If two angles and an included side of one triangle are equal in measure to the corresponding angles and side of another triangle
    12·1 answer
  • They currently give me 15 euros a week, but I have convinced my parents to raise it for me by 12%. What will be my weekly money
    14·2 answers
  • 2-6² +4 2<br><br>please help it's review for my finals ​
    8·2 answers
  • Ratio of girls to boys is 2:3. How many boys if there are 56 girls?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!