You have a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2-10, a jack, a queen, a king, and an ace.
You select one card at random from the deck. Let A be the event that the randomly selected card is a diamond and let B be the event that the card is a king. Based on this information, answer the following questions.
Answer:
[tex]P(A) = \dfrac{1}{4}\\P(B) = \dfrac{1}{13}\\P(A \cap B) = \dfrac{1}{52}\\P(A/B) = \dfrac{1}{4}\\P(A/B) = P(A)\\[/tex]
A and B are not independent events.
Step-by-step explanation:
Total number of possibilities is 52 (Total number of cards in the deck).
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
For event A, number of cases possible for a card to be diamond = 13
[tex]P(A) = \dfrac{13}{52} \\\Rightarrow P(A) = \dfrac{1}{4}[/tex]
For event B, number of cases possible for a card to be a king = 4
[tex]P(B) = \dfrac{4}{52} \\\Rightarrow P(B) = \dfrac{1}{13}[/tex]
For the event, [tex]A \cap B[/tex], the card is a king and diamond, only one case is possible.
Because there is only one card for king of diamond.
[tex]P(A \cap B) = \dfrac{1}{52}[/tex]
Formula for P(A/B):
[tex]P(A/B) = \dfrac{P(A \cap B)}{P(B)}[/tex]
[tex]\Rightarrow \dfrac{\dfrac{1}{52}}{\dfrac{1}{13}}\\\Rightarrow \dfrac{1}{4}[/tex]
Yes, P(A) is same as P(A/B).
Here, A and B are not independent events because they have a common case i.e. a king is there which is of diamond in the deck.
Answer:
1/4
1/13
1/52
Yes, events a and b are independent events
pls help pls its hard ....
Answer:
(1,5)
Step-by-step explanation:
plug in the x and y values to see if they are equal in the equation. If not, then you know the answer is wrong.
Answer: if you need help ask
Step-by-step explanation:
First you start by finding a problem
Next you ask someone to help you with the problem, simple :)
Dr. Barber needs to pay her employees $15.00 an hour. If she has five
technicians and they each worked 25 hours, how much money in total will Dr.
Barber pay all of the technicians?
Answer:
$1,875
Step-by-step explanation:
$15.00 per hour (multiply by hours)
per technician (multiply by technicians)
so: 15x25=375 then 375x5=1,875
Answer:
$1875
Step-by-step explanation:
First, let's find how many hours the technicians worked
She has 5 technicians, and the each worked 25 hours
We can multiply 5 and 25 to find the total number of hours
5*25=125
Now we know that the technicians worked 125 hours altogether. Now, we need to find how much money that is.
They worked 125 hours, and they are paid $15 per hour
We can multiply 125 and 15 to find the cost
125*15=1875
So, Dr. Barber will pay the technicians $1875 in total
Karen has a coupon for $1.52 off any
candy related item. She decides to buy
a package of 9 chocolate bars that
normally costs $10.25. If Karen uses
her coupon, what will the price per
chocolate bar be?
—
Enter
Answer:
$8.73 per package of candy bars
Step-by-step explanation:
10.25 - 1.52=
please help asap, will mark brainlest. Thanks
Answer:
2.
4x^2 + 4 - 5x + x - 2x^2 + 8
= (4x^2 - 2x^2) + (x - 5x) + (4 + 8)
= 2x^2 - 4x + 12
=> D is correct
3.
2x^2 + 6x - 7x + 8 - 3x^2 + 1
= (2x^2 - 3x^2) + (6x - 7x) + (1 + 8)
= -x^2 - x + 9
=> C is correct
4.
B is correct (4 and 3)
Hope this helps!
:)
Find the GCF for each pair of monomials. 1. 14n2, 35n4 2. 21n3, 18n2 3. 7n2, 9
Answer:
[tex](1)7n^2\\(2)3n^2\\(3) 1[/tex]
Step-by-step explanation:
(1) [tex]14n^2, 35n^4[/tex]
[tex]14n^2=2 X 7 X n^2\\35n^4=5 X 7 Xn^2Xn^2\\$Therefore, the GCF of 14n^2$ and 35n^4$ is 7Xn^2=7n^2[/tex]
(2)[tex]21n^3, 18n^2[/tex]
[tex]21n^3=3 X 7 X n^2 X n\\18n^2 =3 X 6 X n^2\\$Therefore, the GCF of 21n^3$ and 18n^2$ is 3Xn^2=3n^2[/tex]
(3) [tex]7n^2, 9[/tex]
The two terms are co-prime. Therefore their GCF is 1.
answer with work pls !!
PLEASE ASAP
graph
-1
Answer:
on a graph paper draw the coordinate plane and locate -1 and draw a horizontal line
Step-by-step explanation:
Find the Surface Area of the Square Pyramid
Step 1:
Step 2:
Step 3:
Step 4: *
(20 Points)
Step-by-step explanation:
Step 1: Set up the formula for the surface area of a regular pyramid.
SA = [tex]\frac{p*h}{2} + B[/tex]
where :
SA equals the total surface area of the pyramid, p equals the perimeter of the base, h equals the slant height of the pyramidB equals the area of the base.Step 2: Plug the perimeter of the base into the formula
you can calculate the perimeter by multiplying the length of one edge by the number of edges.
Step 3: plug the value of the slant height into the formula (it is not the perpendicular height)
Step 4: find the area of the base (depend on the shape of the base)
Hope it will find you well.
What is 25 percent of 48?
Answer:
12
Step-by-step explanation:
Divide 48 into 4 parts
Answer:
(25:100)*48=
(25*48):100=
1200:100=12
Answer=12
What is the value of x?
A.2
B.3
C.6
D.7
Answer:
A
Step-by-step explanation:
Given 2 secants from a point outside the circle.
Then the product of the external part and the entire secant of one secant is equal to the product of the external part and the entire secant of the other secant, that is
(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)
(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides
x² + 13x + 12 = x² + 9x + 20 ← subtract x² + 9x from both sides
4x + 12 = 20 ( subtract 12 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2 → A
Jennifer, Kate, and Lucy line up in random order for basketball practice. What is the probability that the girls will line up from front to back in alphabetical order of their names?
A• 1/3
B• 1/6
C• 2/3
D• 1/4
Answer:
1/6, because there is only one way it's possible and there are 6 outcomes.
Step-by-step explanation:
What is the value of |–2|?
A- 1
B- –2
C- 0
D- 2
Answer:
D) 2
Step-by-step explanation:
Absolute values are never negative, so B is wrong. Absolute value is the distance from zero, in this case, 2.
a pool is in the shape of a rectangular prism holds 1800 cubic feet of water. the pool is 6 feet deep and 10 feet wide. what is the length of the pool in yards
Answer:
Step-by-step explanation:
length = 1800 / 6/10 = 30 ft long = 10 yard
Solve for x. Describe the steps taken to find the solution.
3( 4x - 3) + 8 = 2x + 10x -1
Answer:
see below
Step-by-step explanation:
3( 4x - 3) + 8 = 2x + 10x -1
Distribute
12x - 9 +8 = 2x+10x -1
Combine like terms
12x - 1 = 12x - 1
Subtract 12x from each side
12x - 1 -12x = 12x - 1-12x
-1 = -1
This is true for all values of x
x = all real numbers
Answer:
All real numbers are solutions.
Step-by-step explanation:
3 ( 4x - 3 ) +8 = 2x + 10x - 1 Example 1:
12x - 9 + 8 = 12x - 1 3 ((4*1) -3) + 8 = (2*1) + (10*1) - 1
- 12x = -12x 3 ((4) - 3) + 8 = (2) + (10) - 1
-9 + 8 = -1 ( 12 - 9 ) + 8 = 12 - 1
-1 = -1 3 + 8 = 12 - 1
Example 2 11 = 11
3 ((4*6) - 3) + 8 = (2*6) + (10*6) - 1
3 ((24) - 3) + 8 = (12) + (60) - 1
72 - 9 + 8 = 72 - 1
72 - 1 = 72 - 1
71 = 71
Graph f(x) = x+1 What kind of function is it? Describe the graph.
This is a linear function with a slope of 1 and a y-intercept at one.
Answer:
Linear function
because this kind of graph use line using the slope and y-intercept or two points
slope 1
y-intercept 1
x | y
0 | 1
1 | 2
I need help with this please ASAP!!!!
Answer:
C, 9.4
Step-by-step explanation:
Solve.
3(1−2)<3
Please I need help
I will give brainlyest!!
Answer:
-3<3
Step-by-step explanation:
youre welcome
Answer:
45
Step-by-step explanation:
WIll give brainliest help!!!
Answer:
d
Step-by-step explanation:
Answer:
C. 35
Step-by-step explanation:
7/40=x/200
200/40 x 7=35
Help pleaseeeeeeeeeeeeee
Theoretically, on a number cube, each side has an equal chance. There are 6 sides, and 2 is one of the sides, so then you subtract 1/6, which would leave you with 5/6.
D. 5/6
A flagpole casts a shadow that is 25 feet long. A signpost near the flagpole is 3 feet tall, and it casts a shadow that is 5 feet long. How tall is the flagpole?
Answer:
The ratio of shadow should be kept, then we have: x/25 = 3/5
=> x = 25 x 3/5 = 15
=> The flagpole is tall 15 feet
Hope this helps!
:)
Answer:
15 feet
Step-by-step explanation:
Length : shadow
3 : 5
X : 25
X/25 = 3/5
X = 25 × 3/5
X = 15
please help:)))))))))))))
Answer: The area is 103.5
Step-by-step explanation: The question becomes very simple once you know how to split this object into objects that you most likely know how to solve the area of. In truth, if you split the shapes in triangles and rectangles, you would find 4 rectangles and a triangles. Once you have solved the area of all of them, you would just have to add. How I solved it goes like this. I added 22.5 as the triangle, 35 as a rectangle, 2 as another rectangle, 18 as another rectangle, and 26 as the final rectangle.(take note that these numbers are the areas of the split shapes) If you added correctly, you would get 103.5
PLS HELP THIS IS A LOT OF PIONTS SO BE FAST
Answer:
see below
Step-by-step explanation:
distance = rate * time
meters Edgar ran= e*t
meters Mathieu ran = m*t
Difference in meters per second is the difference in rates= m-e
Number of seconds = time = t
Answer:
this took like forever but there u go
Step-by-step explanation:
distance = rate * time
meters Edgar ran= e*t
meters Mathieu ran = m*t
Difference in meters per second is the difference in rates= m-e
Number of seconds = time = t
7. For a period of time, an island's population of rabbits grows at a rate proportional to its population. If the
population doubles every 17 years and the current population is 196, what will the population be 45 years from
now?
can someone help me with this? i’m desperate
Answer:
The answer is 784
Step-by-step explanation:
You divide 17 from 45 it will equal 2.647 years technically 2 year that the population has doubled.
You multiply 196 by 2 and do that a second time to get 784.
PLZ HELP it's LITERALLY THE LAST QUESTIOOOON
Answer:
b
Step-by-step explanation:
325,310,289,288,285,285,285,280,273. the mean of the set is 290 pounds what is the mean absolute deviation of the data set,to the nearest whole number
Answer:
276
Step-by-step explanation:
Which binomial is a factor of the quadratic trinomial x2 − 7x + 12? A. (x + 2) B. (x − 6) C. (x + 3) D. (x − 4)
Answer:
D
Step-by-step explanation:
To factor a quadratic you need to think about what adds up to the b coefficient (the number in front of b) and multiplies to the constant. 3 and 4 do these, but you also know that you have -7 instead of positive 7. A negative times a negative is equal to a positive, which you can do (x-3)(x-4) to equal your quadratic trinomial.
6³=216. Using exponents, write three more expressions whose value is 216.
I don't understand. Please help.
Answer:
36
Step-by-step explanation:
reverse the number
Please send help I really need your help
Answer:
#4: 4 hits
Step-by-step explanation:
At first, you are given the ratio 1/37 which you can scale to 148 by dividing and multiplying both by. So you divide 148/37 to reach 4 and then multiply 4 by 1 to find out that about four hits will prbably be made.
Answer:
the answer for number four is four and number five is 39
I am not sure about number 5 plz check somebody.
Step-by-step explanation:
The three friends drove to a park that had batting cages and pitching machines that tossed the balls to the batter automatically. Rameck took his place, ready to bat. "Keep your hands together," George shouted from the other side of the fence. "Bend your knees a little," Sampson offered. "I've watched the Yankees for years," Rameck said, ignoring both of them. "Baseball is easy!” The machine pitched the first ball. Rameck swung with a powerful twist. He missed. The second ball erupted from the machine. Rameck swung again. He missed it by a mile. A third ball came. He swung and missed that one, too. The balls kept coming. Rameck kept swinging. And missing. —We Beat the Street, Sampson Davis et al, Using the drop-down menus, identify the correct sequence of events. First: Second: Third:
Answer:
first B,second A, third C on edg
Step-by-step explanation:
Answer:
answer is D
Step-by-step explanation:
