Suppose that from a standard deck, you draw three cards without replacement. What is the expected number of spades that you will draw
Answer: The expected number of spades that you will draw is 0.751 spades
Step-by-step explanation:
The expected value can be calculated as:
∑xₙ*pₙ
Where xₙ is the n-th event, and pₙ is the probability of that event.
First, let's count the possible events and calculate the probability for each one.
x₀ = drawing 0 spades.
Out of 52 cards, we have only 13 spades, then 52 - 13 = 39 are not spades.
Then the probability of not drawing a spade in the first draw is:
p1 = 39/52
In the second draw we will have a card less than before in the deck (so we have 38 cards that are not spades, and 51 cards in total), then the probability of not drawing a spade is:
p2 = 38/51
And with the same reasoning, in the third draw the probability is:
p3 = 37/50
The joint probability for this event will be:
p₀ = p1*p2*p3 = (39/52)*(38/51)*(37/50) = 0.413
Second event:
x₁ = drawing one spade.
Let's suppose that in the first draw we get the spade, the probability will be:
p1 = 13/52
In the second draw, we get no spade, then the probability is:
p2 = 39/51
in the third draw we also get no spade, the probability is:
p3 = 38/50
And we also have the case where the spade is drawn in the second draw, and in the third draw, then we have 3 permutations, this means that the probability of drawing only one spade is:
p₁ = 3*p1*p2*p3 = 3*(13/52)(39/51)*(38/50) = 0.436
third event:
x₂ = drawing two spades:
Let's assume that in the first draw we do not get a spade, then the probabilities are:
p1 = 39/52
p2 = 13/51
p3 = 12/50
And same as before, we will have 3 permutations, because we could not draw a spade in the second draw, or in the third, then the probability for this case is:
p₂ = 3*p1*p2*p3 = 3*( 39/52)*(13/51)*(12/50) = 0.138
And the last event:
x₃ = drawing 3 spades.
The probabilities will be:
p1 = 13/52
p2 = 12/51
p3 = 11/50
And there are no permutations here, so the joint probability is:
p₃ = p1*p2*p3 = (13/52)*(12/51)*(11/50) = 0.013
Now we can calculate the expected value:
EV = 0*0.413 + 1*0.436 + 2*0.138 + 3*0.013 = 0.751
The expected number of spades that you will draw is 0.751 spades
Simplify 8 over negative 3 divided by negative 4 over 9.
−8
−6
6
8
Answer:
The answer is 6. Hope this helped :D
(100 points if answered) (attatched screenshot) Algebra II need question 1 and 2
A large pot of water is heating up on a stove at a constant rate. After three minutes of heating it had a temperature of 100 ℉. After nine minutes of heating the temperature was at 148 ℉. Let T be the temperature and n be the number of minutes. Write a linear equation for T in terms of n.
Answer:
Given function:
y=9.5x+62.1
We have to find the number of minutes x, when y=138.1°F
Put value of y in function.
138.1=9.5x+62.1
Subtract 62.1 from both sides.
76=9.5x
Divide both sides by 9.5.
8=x
or
x=8 minutes
Answer: After 8 minutes the temperature of water will be 138.1°
Step-by-step explanation:
Answer:
T= 8n+76
Step-by-step explanation:
First you need to find the average rate of change:
( 3, 100)
(9,148)
Subtract:
148-100= 48
9-3= 6
Then divide them:
48/6=8
This is your slope, now we must find our y- intercept by using the formula
y= mx+b:
y=mx+b
Plug in what you know:
y= 8x+b
To find your y-intercept use one of the 2 points above, either (3,100) or (9,148)
Plug in your x's and y's into your almost complete equation:
100= 8(3)+b
Then solve to get b:
You should get b=76
Hope this helps
Linden Middle School has 480 students. The number of students is increasing by 5% next year
How many students will there be? (Please do step by step)
Answer:
Please do step by step)
hope I gave
If two rectangles are similar, what is the length of side x? Give your answer to one decimal place. Rectangle 1: A = 13.4ft B = 4.6ft Rectangle 2: A = 87.1 ft B = x
Answer:
x = 29.9 ft
Step-by-step explanation:
Given:
Rectangle 1 ≈ Rectangle 2
In Rectangle 1
A = 13.4 ft
B = 4.6 ft
In Rectangle 1
A = 87.1 ft
B = x ft
Find:
Value of x
Computation:
Rectangle 1 ≈ Rectangle 2
So,
13.4 / 4.6 = 87.1 / x
x = [(87.1)(4.6)] / 13.4
x = 29.9 ft
32. Sinead bought 2 shirts for $15.82 each and a pair of shoes for $42.37. If she
paid for the items with a $100 bill, how much change did she receive?
$25.99
$10.17
$74.01
$41.81
15.82x2=31.64
31.64+42.37=74.01
100-74.01=25.99
Sinead received $25.99 for change.
Answer:
Sinead received $25.99 for change.
Step-by-step explanation:
A man travels 320 miles in 8 hours. If he continues at the same rate, how many miles will he
travel in the next 2 hours?
Answer: 80 miles
Step-by-step explanation:
320miles/8hours= 40mph
40mph=xmiles/2hrs
40*2= 80 miles
What’s three more than seventeen?
Write the slope-intercept form of the equation of the line through the given point and slope.
Point: (1, -3)
Slope: -4
Answer:
y=-4x+1
Step-by-step explanation:
Graph (1,-3)
Go down 4 over one/ up left one
Get y-intercept
Then BOOM you got it
Answer:
y = -4x + 1
Step-by-step explanation:
We are given that a line has a slope of -4 and a point (1, -3).
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept.
As we are already given the slope, we can immediately plug its value into the equation.
Substitute -4 as m in the equation.
y = -4x + b
Now we need to find b.
As the equation passes through the point (1, -3), we can use its values to help solve for b.
Substitute 1 as x and -3 as y.
-3 = -4(1) + b
Multiply.
-3 = -4 + b
Add 4 to both sides
1 = b
Substitute 1 as b in the equation.
y = -4x + 1
Topic: writing the equation of the line (slope-intercept form)
See more: https://brainly.com/question/22448557
More than half of the students were excited about the project. In fact, were excited. If 10 students were not
excited about the project. how many students were excited?
Answer:1/2 divided by 10
Step-by-step explanation:
convert 53 yards per hour into inches per day
1 yard = 36 inches.
53 yards per hour x 36 inches per yard = 1908 inches per hour.
1 day = 24 hours.
1908 inches per hour x 24 hours = 45,792 inches per day.
pls help me with the math test will give the first person who answers brainliest answers and points
write the expression for 100 less than the sum of 3 and x
Answer:
3 + x < 100
3 + x - 3 < 100 - 3
x < 97
Step-by-step explanation:
A friend told Sandy that absolute value makes everything positive so Sandy wrote the equation |x-6|=5 as x+6=5. Do you agree with the statement, or with what Sandy did to the equation? Explain your answer.
help please :)))))(
Answer:
6 hours :))))))
Step-by-step explanation:
Answer:
3 or 4 I think
Step-by-step explanation:
I think this because if u find the red candles unit rate it's 9 and 9×4 is 36 but the thing is the other one is 12 12×4 is 48 but then if u do 12×3 it's 36. The rest don't work so 3 or 4 hours. But if someone else has a different answers do not put mines because I have no clue but I think it's that because of that reason.
Subtract 8 feet from 9 yards, 1 foot.
A. 6 yards, 2 feet
B. 7 yards, 1 foot
C. 6 yards, 1 foot
D. 1 yard, 1 foot
Answer: B
Step-by-step explanation:
I knew I would have 1 foot left so that made sure it wasn’t A then I knew that it the answer had to be in yards so I convert 8 feet into yards which becomes 2.7 so it’s not three which makes I’m not C. So 9 yards minus 2.7 yards would equal the answer B
Answer:
your answer should be A let me know
Step-by-step explanation:
A
Which relationship between x and y in the equation shows a proportional relationship?
y=3x
y=5(r+3)
y=x-2
y=5x +3
Answer:
Y=3x
Step-by-step explanation:
Proportional relationships always have multiplication or division
Find the equation of the line that passes through the points:
(-2, 4) and (1, 10)
Step-by-step explanation:
y=mx+ C
to find m (slope )
m= 10 _ 4 / 1- ( -2 )
m = 6 / 3 = 2
( I,10 ) Satisfy eq.
10 =2 x I + C
C= 5
. so, equation of Line is \
y= 2x +5
PLZ HELP ME WITH THIS!?!? I WILL MARK BRAINLIEST!!!
Answer: can it be a bit clearer pls?
Step-by-step explanation:
What’s the answer to this radical function
Step-by-step explanation:
We have,
[tex]f(x) = - 2 \sqrt[3]{x + 7} [/tex]
Taking limit,
[tex] \lim _{x \rarr \infty } f(x) \\ = \lim _{x \rarr \infty } - 2 \sqrt[3]{x + 7} [/tex]
If x approaches to positive infinity,
this implies f(x) approaches to negative infinity
what is a preimage and image of triangle in a translation
Answer:
translation to what language?
Step-by-step explanation:
9514 1404 393
Explanation:
The preimage is the original triangle, the figure before any transformation is done to it.
The image is the result of applying a transformation to the preimage.
__
When the transformation is translation, the image is congruent to the preimage, but is located in a different place. It is not rotated or reflected if the only transform is translation.
Hurry please
I need the answer to this one in 2 minutes
Answer:
125
Step-by-step explanation:
45 ÷9=5
5² or 5×5=25
25×5=125
Hope this helps!
Answer:
I THINK ITS
Step-by-step explanation:
5x(2025 ÷81)
5x25
125
15 people are expected for a dinner. Three ounces of corn serves one person. A can of corn is nine ounces. How many cans of corn should be bought for the dinner?
Answer:
there should be 5 cans of corn! hope This Helps
Step-by-step explanation:
Answer:
The answer is 5
Step-by-step explanation: You have to multiply the amount of people by the servings a person gets (15*3), you then divide that by the amount of ounces a can has (45/9) the result is 5.
a principle orders t-shirts and wants to check some of them to make sure they were printed properly. she opens the closet 2 of the 10 boxes of shirts and checks every shirt in those 2 boxes. what type of sampling is this?
Answer:
Cluster random sampling
Step-by-step explanation:
What type of correlation does the scatter plot show?
A. Positive
B. Negative
C. Cannot tell
D. None
Colin loves to eat tuna salad for lunch. His mom is always looking for a bargain on 12-ounce cans of tuna. Today, his local grocery store is offering 4 cans of Sea Star tuna for $3.28 and 2 cans of Ocean's Best tuna for $1.88. Which brand is the better deal?
Answer:
Local Grocer store's offer is the better deal
Step-by-step explanation:
In order to calculate which is the better bargain, we need to find out how much each deal is charging for the individual can of tuna. We calculate this by dividing the total of the offer by the number of cans of tuna it includes like so...
Local: $3.28 / 4 = $0.82 per can
Ocean's Best: $1.88 / 2 = $0.94 per can
Therefore, we can see that the Local Grocer store's offer is the better deal since it is selling you each can at 0.82 cents compared to the 0.94 cents that Ocean's Best is charging per can.
Answer:
It's seastar
Step-by-step explanation: tbh I put in seastar as an answer on ixl and got it correct but if you want to know what you have to all you need to do is divide price by amount and the one with less is the better option for example if you have a 4 pack for $4.56 you would do $4.56/4 price always goes first remember that! :D
Which graph can be used to solve the equation 2^x-1=x+2?
Answer:
Bottom Left
Step-by-step explanation:
I found the graph. All you needed to do was switch the red and blue line. I put a screenshot of the correct answer on I-Ready as well as the graph I had found.
The system of equations needed to solve the given equations is . Thus, the correct graph is the top-right graph. Its plotted below.
How to find the system of equations needed to solve an equation?An equation usually consists of equality of two mathematical expressions. Let it be [tex]A = B[/tex]. If we take them to be equal to third variable, then:
[tex]A = B = C[/tex] type of equation is obtained.
We can then take it as system of two equations as:
[tex]A = C\\B = C[/tex]
Solution to this system will give us the solution to the considered equation
For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs.
For the given case, we are given that:
[tex]2^x-1=x+2[/tex]
Taking these two mathematical expression equal to 'y', we get:
[tex]2^x-1=x+2 = y[/tex]
or
[tex]y = 2^x - 1\\and\\y= x+2[/tex]
Plotting these two functions on the X-Y plane, the common point of these curves is the common value which can satisfy both the equations simultaneously, and thus, being the solution to the considered system of equations.
Thus, the solutions are those two points that are intersections of those two curves.
Learn more about solution of a system of an equation here:
https://brainly.com/question/13722693
which statement is true regarding the graphed functions?
Answer:
if -2 refers to the y-intercept "f(-2)=g(-2)" would be correct
HELP URGENT !!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
P（x）=x³-5x²+4x-3
D（x）=x-1
Answer:
hope this helps.
btw I used synthetic decision method