Write an equation for this model and solve for x. х = 3 x = -3 x = 4 x = -4

Rolling a 3 or rolling an odd number on a six sided die. Is it mutually exclusive or non-mutually exclusive? Give one reason.

Cerrena [4.2K]

Answer:

Non-mutually exclusive

Step-by-step explanation:

both events can happen simultaneously... 3 is an odd number, events A and B have a common outcome.

It would be mutually exclusive if event A was rolling a 4 and event B was rolling an odd number.

7 0

3 years ago

Read 2 more answers

Find the coefficient of the x7y2term in the binomial expansion of (x+y)^9

statuscvo [17]

Answer:

36

Step-by-step explanation:

first, see the formula in the attached picture.

now, by applying that formula we get :

the coefficient of the x7y2 is :

9C7 = 36 (you can either use a calculator or just the algebraic formula)

8 0

2 years ago

In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9. Is

Oksi-84 [34.3K]

Answer:

When both the conditions hold true, F is prime.

Step-by-step explanation:

AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

AB

+ CD

--------

EF

1st condition, B and D are consecutive.

Adding B and D gives us F.

Possible values can be (F being the unit value after adding not considering the carry over):

B + D = F

1+2=3

2+3=5

3+4=7

4+5=9

5+6=1

6+7=3

7+8=5

8+9=7

Here F is not prime (because 9 is not prime).

Now, let us consider the 2nd condition as well.

i.e. C = 8

For the following

AB

+ CD

--------

EF

C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.

So, E = 8 + 1 = 9

Now, B and D are consecutive and can not be 1, 8 or 9.

So, possible values are:

B + D = F

2 + 3 = 5

3 + 4 = 7

Here F is prime.

So, when both the conditions hold true, F is prime.

3 0

2 years ago

The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?

borishaifa [10]

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\dfrac{3-2}{4-2}=\dfrac{1}{2}$

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

$m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}$

We have the equation:

$\dfrac{-3}{x-2}=\dfrac{1}{2}$ cross multiply

$(1)(x-2)=(-3)(2)$

$x-2=-6$ add 2 to both sides

$x=-4$

<h3>Answer: x = -4.</h3>

7 0

2 years ago

Solve the equation 6x + 3y = 15 for y. What does y equal if x = 2? If x = 5?

horsena [70]

6(2)+3y=15
12+3y=15
-12 -12
3y=3
3y/3 3/3
y=1

6(5)+3y=15
30+3y=15
-30 -30
3y=-15
3y/3 -15/3
y= -5

4 0

2 years ago

Read 2 more answers