Answer:
a. With replacement
1/2197
b. Without replacement
1/5,525
Step-by-step explanation:
Okay, here is a probability question.
The key to answering this question is by knowing the number of aces in a deck of cards.
There is 1 ace per suit, so there is a total of 4 aces per deck of cards.
So, mathematically the probability of picking an ace would be;
number of aces/ total number of cards = 4/52 = 1/13
a. Now since the action is with replacement; that means that at any point in time, the total number of cards would always remain 52 even after making our picks.
So the probability of picking three aces with replacement would be;
1/13 * 1/13 * 1/13 = 1/2197
b. Without replacement
what this action means is that after picking a particular card, we do not return the picked card to the deck of cards.
For the first card picked, we will be having a total of 4 aces and 52 total cards.
So the probability of picking an ace would be 4/52 = 1/13
For the second card picked, we shall be left with selecting an ace out of the remaining 3 aces and the total remaining 51 cards
So the probability will be 3/51 = 1/17
For the third and last card to be picked, we shall be left with picking 1 out of the remaining 2 aces cards and out of the 50 cards left in the deck.
So the probability now becomes 2/50 = 1/25
Thus, the combined probability of picking 3 aces cards without replacement from a deck of cards will be;
1/13 * 1/17 * 1/25 = 1/5,525
Using the binomial and the hypergeometric distribution, it is found that the probabilities are:
a) 0.0005 = 0.05%.
b) 0.0002 = 0.02%.
Item a:
With replacement, hence the trials are independent, and the binomial distribution is used.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.For this problem:
In a deck, there are 52 cards, of which 4 are Aces, hence [tex]p = \frac{4}{52} = 0.0769[/tex]3 cards are drawn, hence [tex]n = 3[/tex].The probability is P(X = 3), then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.0769)^{3}.(0.9231)^{0} = 0.0005[/tex]
0.0005 = 0.05% probability.
Item b:
Without replacement, hence the trials are not independent and the hypergeometric distribution is used.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
Deck of 52 cards, hence [tex]N = 52[/tex].4 of the cards are Aces, hence [tex]k = 4[/tex].3 cards are drawn, hence [tex]n = 3[/tex].The probability is also P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,52,3,4) = \frac{C_{4,3}C_{48,0}}{C_{52,3}} = 0.0002[/tex]
0.0002 = 0.02% probability.
To learn more about the binomial and the hypergeometric distribution, you can take a look at https://brainly.com/question/25783392
PLEASE HELP
Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity.
Answer:
h,k,i,m,g,l
Step-by-step explanation:
I did all the work and i(x) limt should = -.25 and k(x) =0 but it said it was wrong. f(x) and j(x) cant be used, so my guess is to switch i(x) and k(x)
The answer is given in the image below.
Do all functions have limits?One of the fundamental standards of calculus is limits (limits of a function); it offers the fee of a function at a particular factor called limit. Limits are used to calculate the exact vital of the function. Not all functions include limits. A few functions no longer have any restrictions as the variable has a tendency to infinity.
What are examples of nonfunctions?The equations y = ± x and x 2 + y 2 = 9 are examples of non-function due to the fact there is at least one -price with or greater -values.
Learn more about Limits here: https://brainly.com/question/251701
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subtract c from 7, then divide b by the result
Answer:
[tex]\frac{7-c}{b}[/tex]
Answer:
[tex]\frac{7 -c}{b}[/tex]
Step-by-step explanation:
Subtract c from 7 : 7 - c
Then the result is divide by b : [tex]\frac{7 -c}{b}[/tex]
|10-11| = simplify the expression
Answer:
1
Step-by-step explanation:
Let's ignore the absolute value signs for a moment.
We have the expression [tex]10-11[/tex]. We know that if we subtract 10 from 10 we get 0, so if we subtract 11 from 10 we must get -1.
However, there is an absolute value sign. This means that whatever number is inside it has to be converted to a positive number.
-1 as a positive number is +1, or just 1.
Hope this helped!
The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown.
5x2 + 27x = 14 − 13x
5x2 + 40x = 14
5(x2 + 8x) = 14
Which is the best step to do next to solve the equation by completing the square?
Answer:
Step-by-step explanation:
Give the equation 5x² + 27x = 14 − 13x, we are to write the steps needed to solve for x using the completing the square method.
Step 1: Rewrite the equation in a quadratic form by first adding 13x to both sides of the equation.
5x² + 27x +13x= 14 − 13x+13x
5x² + 40x = 14
Step 2: factor out the common constant in the left hand side of the equation.
5(x²+8x) = 14
Step3: The next step to take is to divide through by the the value of 5 to have;
5(x²+8x)/5 = 14/5
x²+8x = 14/5
Step 4: complete the square of the equation at the left hand side by adding the square of half of the coefficient of x to both sides i.e {1/2(8)}² which is 4²
x²+8x +4² = 14/5+4²
x²+8x +16 = 14/5+16
(x+4)² = 94/5
Step 5: Taking the square root of both sides
√(x+4)² = ±√94/5
x+4 = ±√94/5
Step 6: subtract 4 from both sides
x+4-4 = ±√94/5 - 4
x = ±√94/5 - 4
Hence the solution to the equation using completing the square method is x = -4±√94/5
Answer:
5(x2 + 8x + 16) = 94
Step-by-step explanation:
PLEASE HELP How can a company use a scatter plot to make future sale decisions
Answer:
From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.
Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).
Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).
Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.
A
Find the value of x. Your answer must be exact.
30
9
Answer:
x = 9√3Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use tan
tan∅ = opposite/ adjacent
From the question
The opposite is 9
The adjacent is x
Substitute the values into the above formula
That's
[tex] \tan(30) = \frac{9}{x} [/tex]
[tex]x \tan(30) = 9[/tex]
Divide both sides by tan 30
[tex]x = \frac{9}{ \tan(30) } [/tex]
We have the final answer as
x = 9√3Hope this helps you
look at picture and solve
Answer:
79°
Step-by-step explanation:
PQO is straight angle with measure of 180°
the given angles' sum makes 101° and we need 79 to complete it to 180° therefore the angle STQ = 79°
what is the length of DI? A 1.4 B 4.4 C 5.6 D 17.6
[tex]\dfrac{DI}{DR}=\dfrac{DE}{DZ}\\\\\dfrac{DI}{6+2.8}=\dfrac{3}{6}\\\\6DI=26,4\\DI=4,4[/tex]
Part 1: You work 4 hours and earn $36. What is your earning rate (dollars per hour)?
Answer:
9 dollars per hour
Step-by-step explanation:
36/4=9
Answer:
9
Step-by-step explanation:
4 hours : $36
1 hour : $ x
we need to find x so,
4 hours ÷ 4 = 1 hour
1 : $
since we have divided 4 by 4,
we need to do that to 36 aswell
36 ÷ 4 = 9
1 hour : $9
Use the concept of slope to find t such that the three points are collinear. (-8,5) (0,t) (2,-1)
Answer:
t = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Since the points are collinear they lie on the same line.
Thus the slopes between any of the 3 points are equal.
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (2, - 1)
m = [tex]\frac{-1-5}{2+8}[/tex] = [tex]\frac{-6}{10}[/tex] = - [tex]\frac{3}{5}[/tex]
Repeat using
(x₁, y₁ ) = (- 8, 5 ) and (x₂, y₂ ) = (0, t) and equate to previous m
m = [tex]\frac{t-5}{0+8}[/tex] = [tex]\frac{t-5}{8}[/tex] = - [tex]\frac{3}{5}[/tex] ( cross- multiply )
5(t - 5) = - 24 , that is
5t - 25 = - 24 ( add 25 to both sides )
5t = 1 ( divide both sides by 5 )
t = [tex]\frac{1}{5}[/tex]
The school's square parking lot has an
area of 3025 ft2. What is the length of each
side of the parking lot?
Answer:
The answer is 55ftStep-by-step explanation:
Since the school's parking lot is a square,
Area of a square = l²
where l is the length of one side
From the question
Area = 3025ft²
We have
3025 = l²
Find the square root of both sides
l = √3025
l = 55ft
The length of each side of the parking lot is 55ft
Hope this helps you
Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?
Answer:
Step-by-step explanation:
The most likely quantity is centimetres.
The second option can be inches.
Hope this helps
plz mark it as brainliest!!!!!!!!!
Identify the domain of the function shown in the graph.
A. x is all numbers.
B. X20
O C. 0
D. x<0
Answer:
[tex]\boxed{ x \geq 0}[/tex]
Step-by-step explanation:
Hey there!
Well we can cross out A. x is all real numbers because,
it’s not it only has all the positive numbers.
B. Is correct because the domain is every number greater than or equal to 0.
x ≥ 0
Hope this helps :)
The domain of the graph of a function is x ∈ [0, ∞) or x ≥ 0 option (B) x ≥ 0 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
A function is shown in the graph which is plotted on the two-dimensional coordinate plane.
From the graph, we can see the graph of a function exists in the first quadrant only and it is increasing.
The interval in which the graph exists is [0, ∞)
or
The domain of a graph of a function is:
x ≥ 0
Thus, the domain of the graph of a function is x ∈ [0, ∞) or x ≥ 0 option (B) x ≥ 0 is correct.
Learn more about the function here:
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Question
De acuerdo con la experiencia de una empresa dedicada al desarrollo de software, para realizar un proyecto mediano se requieren seis programadores para finalizarlo en 21 días. Teniendo en cuenta que la relación entre el número de programadores y el número de días necesarios para el desarrollo es inversa, la cantidad de programadores que se deben contratar para finalizar el proyecto en 14 días es nueve.
Answer:
u should put his is English and then translate it to read it
equation y = (2x)/(x-1), how do I get -0.5 as the x intercept ???
Answer:
( 0,0) is the x intercept
Step-by-step explanation:
y = (2x)/(x-1),
To find the x intercept set y = 0 and solve for x
0 = (2x)/(x-1)
Multiply by x-1 on each side assuming x does not equal 1
0 = 2x
x = 0
The x intercept is 0
( 0,0) is the x intercept
3-2y-1+5x^2-7y+7+4x^2
Answer: Hi!
The only thing we can do to simplify the equation is combine like terms.
5x^2 + 4x^2 = 9x^2
-2y - 7y = -9y
3 - 1 + 7 = 9
Our equation now looks like this:
9x^2 - 9y + 9
We have nothing left to simplify, so we're done!
Hope this helps!
Jon wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor
is
oft by 3 1 ft. Find the area the carpet needs to cover. •!
12
4
5
tiled floor
Entar
Answer:
321/8 ft^2
Step-by-step explanation:
The whole area is 49/4 × 5 = 245/4 ft^2
The area of tiled floor is 13/2 × 13/4 = 169/8
245/4 - 169/8 we need to equalise the bottom of fraction to subtract so
2/2 × 245/4 = 490/8
490/8 - 169/8 = 321/8 ft^2
what is the prime factorization of 430
Answer:
[tex]\huge \boxed{430=2 \times 5 \times 43}[/tex]
Step-by-step explanation:
Using factor tree,
Answer:
[tex]\large\boxed{2, 5, 43}[/tex]
Step-by-step explanation:
430
/ \
215 2
The 2 cannot be factorized anymore, so I will put a small box around it.
430
/ \
215 [tex]\boxed{2}[/tex]
/ \
43 5
5 and 43 cannot be factorized any smaller.
430
/ \
215 [tex]\boxed{2}[/tex]
/ \
[tex]\boxed{43}[/tex] [tex]\boxed{5}[/tex]
The prime factorization is the numbers in the boxes, which are 2, 5, and 43.
[tex]\large\boxed{2, 5, 43}[/tex]
Hope this helps :)
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If the formatting is not showing up correctly, please refer to the images of my answer below instead.
divide 1725 by 102 show work please
Answer:
16.91176471
Step-by-step explanation:
1725÷102
= 16.91176471
What property is 21+(36+19)
Answer:
76
Step-by-step explanation:
21+(36+19)
21+(55)
21+55
=76
Answer:
The identity property
Step-by-step explanation:
I took it on Egd.
If f(x) = 3х2 +1 and g(x) = 1-х, what is the value of (f-g)(2)?
12
14
оооо
36
38
Answer:
( f - g)(2) = 14Step-by-step explanation:
f(x) = 3x² + 1
g(x) = 1 - x
To find (f - g)(2) first find (f - g)(x)
To find (f - g)(x) subtract g(x) from f(x)
That's
(f - g)(x) = 3x² + 1 - ( 1 - x)
(f - g)(x) = 3x² + 1 - 1 + x
(f - g)(x) = 3x² + x
To find ( f - g)(2) substitute 2 into (f - g(x)
That's
( f - g)(2) = 3(2)² + 2
( f - g)(2) = 3(4) + 2
( f - g)(2) = 12 + 2
We have the final answer as
( f - g)(2) = 14Hope this helps you
Find the distance between points K(−1, −3) and L(0, 0). Round to the nearest tenth.
Answer:
d = √10
Step-by-step explanation:
[tex]K(-1, -3) , L(0, 0).\\\\d=\sqrt{((x_2-x_1)^2+ (y_2-y_1)^2) } \\\\x_1 =-1\\\\y_1 =-3\\\\x_2 =0\\\\y_2 =0 \\\\d = \sqrt{(0-(-1))^2+(0-(-3))^2}\\\\ d = \sqrt{(0+1)^2+(0+3)^2}\\\\ d = \sqrt{(1)^2 + (3)^2}\\\\ d = \sqrt{1 + 9}\\\\ d = \sqrt{10} \\[/tex]
Answer:
[tex]\huge\boxed{|KL|=\sqrt{10}\approx3.2}[/tex]
Step-by-step explanation:
METHOD 1:The formula of a distance between two points (x₁; y₁) and (x₂; y₂):
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have K(-1; -3) and L(0; 0). Substitute:
[tex]|KL|=\sqrt{(0-(-3))^2+(0-(-1))^2}=\sqrt{3^2+1^2}=\sqrt{9+1}=\sqrt{10}}[/tex]
METHOD 2:Look at the picture.
We have the right triangle with the legs 3 and 1.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
substitute:
[tex]3^2+1^2=|KL|^2\\\\|KL|^2=9+1\\\\|KL|^2=10\to|KL|=\sqrt{10}[/tex]
Sams building a suspension bridge for the playground at the elementary school I needed some chain-link and some rope he bought a total of 80 feet of materials and The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135 how much of each did he buy
Answer:
Amount of material for chain link = 30 feet
Amount of material for rope = 50 feet
Step-by-step explanation:
Let the amount of chain link = X
The amount of rope be represented by Y
He bought a total of 80 feet of materials
Hence we have:
X + Y = 80 ....... Equation 1
Y = 80 - X
The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135
X × $2 + Y × $1.50 = $135
2X + 1.5Y = 135 ......Equation 2
Substitute 80 - X for Y in Equation 2
2X + 1.5(80 - X) = 135
2X + 120 - 1.5X = 135
Collect like terms
2X - 1.5X = 135 - 120
0.5X = 15
X = 15/0.5
X = 30 feet
Substitute 30 feet for X in Equation 1
X + Y = 80 ....... Equation 1
30 + Y = 80
Y = 80 - 30
Y = 50 feet
Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet
Evaluate the expression 5^3
Answer: Five to the power of three (5*5*5) is equal to 125.
Hope this helps!
Answer:
125
Step-by-step explanation:
[tex]5^3=\\\\5*5*5=\\\\25*5=\\\\\boxed{125}[/tex]
GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Three stores have the same tablet computer on sale. The regular price of the tablet is $150. Store A is offering the tablet on sale at 15% off the regular price. Store B is offering a $25 coupon to be deducted from the regular price. Store C is offering a rebate of $20.00 to purchasers. Store D has the tablet on sale for $120.00. Which store is offering the tablet at the lowest cost?
A. Store A
B. Store B
C. Store C
D. Store D
Show ALL work please! <3
Answer: Store D
Step-by-step explanation:
Store A - 15% off:
$150 times 15/100 = 22.5
$150 - $22.50 = $127.50 so the price at store A is $127.50
Store B - $25 coupon
$150 - $25 = $125 so the price at store B is $125
Store C - $20 rebate
$150 - $20 = $130 so the price at store B is $130
Store D - $120
$120 is the lowest so the answer is Store D
Answer:
[tex]\Large \boxed{\mathrm{Store \ D}}[/tex]
Step-by-step explanation:
Store A is offering the tablet on sale at 15% off the regular price.
150 × (1 - 15%) = 127.5
Store B is offering a $25 coupon to be deducted from the regular price.
150 - 25 = 125
Store C is offering a rebate of $20.00 to purchasers.
150 - 20 = 130
Store D has the tablet on sale for $120.00.
Store D is offering the tablet at the lowest cost.
Question is in the pic I really suck at this stuff can I get some help plssssss
Answer:
see below
Step-by-step explanation:
The hypotheses is the if part of the statement ( after the if)
hypotheses: it is January
The conclusion is the then part of the statement ( after the then)
conclusion there is snow
3 x 19 x 14 + 18 ÷ 2
Answer:
807Step-by-step explanation:
[tex]3 \times 19 \times 14 + 18 \div 2 \\ PEDMAS \\ (3 \times 19 \times 14 )+ 9 \\ = 798 + 9 \\ [/tex]
[tex] = 807[/tex]
Answer:
408
Step-by-step explanation:
3x19= 57
57x14= 798
798 + 18= 816
816/ 2= 408
solve for x 3x - 4 = 3x - 10
Answer:
no solution
Step-by-step explanation:
3x - 4 = 3x - 10
Subtract 3x from each side
3x-3x - 4 = 3x-3x - 10
-4 = -10
This is never true so there is no solution
Answer:
Step-by-step explanation:
I think you might have copied down the problem incorrectly.
If you try and solve this problem by moving the variables onto one side and the constants onto the other, you get:
3x-4=3x-10
+10 +10
3x+6=3x
-3x -3x
6=0 (which is FALSE)
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Jorge finds that 56% of his 75 classmates like salsa music and 80% of his 60 relatives like salsa music. How many more of Jorge's relatives,as compared to his classmates, like salsa music?
Answer:
6 more
Step-by-step explanation:
Find 56% of 75 first
75/x=100/56
(75/x)*x=(100/56)*x
75=1.78571428571*x
(1.78571428571) to get x
75/1.78571428571=x
42=x
x=42
Then Find 80% of 60
60/x=100/80
(60/x)*x=(100/80)*x
60=1.25*x
60/1.25=x
48=x
x=48
Subtract 48 by 42
=6
Practice Writing Composite Functions Given: f(x) = x - 7 and h(x) = 2x + 3 Write the rule for h(f(x)).
Answer:
h(f(x)) = 2x - 11Step-by-step explanation:
f(x) = x - 7
h(x) = 2x + 3
To find h(f(x)) substitute f(x) into h(x) that's replace every x in h(x) by f(x)
That's
h(f(x)) = 2(x - 7) + 3
h(f(x)) = 2x - 14 + 3
We have the final answer as
h(f(x)) = 2x - 11Hope this helps you
