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
KATRIN_1 [288]
3 years ago
15

A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolled togethe

r, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray. S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.) The event that the numbers showing face up are the same. E =___________.
Mathematics
1 answer:
Nikitich [7]3 years ago
7 0

Answer:

E = {11, 22, 33, 44, 55, 66}

Step-by-step explanation:

There 36 total possible outcomes when rolling two dice together. Since there are six different numbers, in only six of those outcomes the numbers showing face up are the same. Therefore, the probability of the number showing face up being the same is 1/6. The set that represents this event is.

E = {11, 22, 33, 44, 55, 66}

You might be interested in
F(x) = x^2. What is g(x)?
fredd [130]

Good evening ,

Answer:

B. g(x)= -x² - 4

___________________

Step-by-step explanation:

The graph of g is downward facing then we must have (-) before the x²

Since, The vertex of parabola g is on point (0 ,-4) then we have to subtract 4.

:)

3 0
3 years ago
A bag contains 30 lottery balls numbered 1-30 a ball is selected replaced then another is drawn find each probability
iogann1982 [59]
#1) 5/20
#2) 7/300
#3) 3/50
#4) 5/20

Explanation
For #1:
There are 15 even numbers out of 30.  Since it is replaced before drawing the second ball, there will be 15 odd numbers out of 30.  This gives us
15/30(15/30) = 225/900 = 5/20.

For #2:
There is 1 7 out of 30; then there are 14 numbers greater than 16 out of 30:
1/30(14/30) = 14/900 = 7/300

For #3:
There are 6 multiples of 5 out of 30; then there are 9 prime numbers out of 30:
6/30(9/30) = 54/900 = 3/50

For #4:
There are 15 even numbers out of 30; then there are still 15 even numbers out of 30:
15/30(15/30) = 225/900 = 5/20
7 0
3 years ago
Read 2 more answers
Y'ALL PLEASE HELP ME I REALLY NEED HELP !!!!
Anvisha [2.4K]
C should be correct since AB and XY are in the same places
6 0
3 years ago
Find the absolute maximum and minimum values of the following function on the specified region R.
yan [13]

Answer:

Step-by-step explanation:

Since it is said that the region R is a semicircular disc, we asume that the boundaries of the region are given by -2\leq x \leq 2, 0\leq y \leq \sqrt[]{4-x^2}. First, we must solve the optimization problem without any restrictions, and see if the points we get lay inside the region of interest. To do so, consider the given function F(x,y). We want to find the point for which it's gradient is equal to zero, that is

\frac{dF}{dx}=9y=0

\frac{dF}{dy}=9x=0

This implies that (x,y) = (0,0). This point lays inside the region R. We will use the Hessian criteria to check if its a minimum o r a maximum. To do so, we calculate the matrix of second derivates

\frac{d^2F}{dx^2} = 0 = \frac{d^2F}{dy^2}

\frac{d^2F}{dxdy} = 9 = \frac{d^2F}{dydx}

so we get the matrix

\left[\begin{matrix} 0 & 9 \\ 9 & 0\end{matrix}\right]

Note that the first determinant is 0, and the second determinant is -9. THis tell us that the point  is a saddle point, hence not a minimum nor maximum.  

Since the function is continous and the region R is closed and bound (hence compact) the maximum and minimum must be attained on the boundaries of R. REcall that when -2\leq x \leq x and y=0 we have that F(x,0) = 0. So, we want to pay attention to the critical values over the circle, restricting that the values of y must be positive. To do so, consider the following function

H(x,y, \lambda) = 9xy - \lambda(x^2+y^2-4) which consists of the original function and a function that describes the restriction (the circle x^2+y^2=4), we want that the gradient of H is 0.

Then,

\frac{dH}{dx} = 9y-2\lambda x =0

\frac{dH}{dx} = 9x-2\lambda y =0

\frac{dH}{d\lambda} = x^2+y^2-4 =0

From the first and second equation we get that

\lambda = \frac{9y}{2x} = \frac{9x}{2y}

which implies that y^2=x^2. If we replace this in the restriction, we have that x^2+x^2 = 2x^2 = 4 which gives us that x=\pm \sqrt[]{2}. Since we only care for the positive values of y, and that y=\pm x, we have the following critical points (\sqrt[]{2},\sqrt[]{2}), (-(\sqrt[]{2},\sqrt[]{2}). Note that for the first point, the value of the function is

F(\sqrt[]{2},\sqrt[]{2}) = 9\cdot 2 =18

as for the second point the value of the function is

F(-\sqrt[]{2},\sqrt[]{2}) = 9\cdot -2 =-18.

Then, the point (\sqrt[]{2},\sqrt[]{2}) is a maximum and the point (-(\sqrt[]{2},\sqrt[]{2}) is a minimum.

6 0
3 years ago
This question is based on the circle graph below, which shows how an electrical contracting company divides its monthly income.
Alona [7]
We have to see the circle graph I guess
5 0
2 years ago
Read 2 more answers
Other questions:
  • 25 students are asked to line up in lines of 5 students. How many lines will there be?
    11·2 answers
  • The formula
    13·1 answer
  • What is the answer to 4/5+1/2? what is the answer
    6·2 answers
  • What is bigger 1.5km or 1400m
    15·3 answers
  • What is the image point of (-2,-7)(−2,−7) after a translation right 4 units and down 2 units?
    15·1 answer
  • Find the remainder when f(x) is divided by (x - k).
    7·2 answers
  • Suppose that y varies directly with x
    8·1 answer
  • Please help me I don’t understand this
    8·1 answer
  • Please help me with this please ​
    12·1 answer
  • -3=x+5 what I need to do with a negative and positive number?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!