The probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
To calculate the probability of drawing three balls from a box containing six white balls, five red balls, and four blue balls, we need to consider two scenarios: with replacement and without replacement.
(i) With replacement:
When each ball is replaced after it is drawn, the total number of balls remains the same for each draw. Therefore, the probability of drawing a specific color on each draw remains constant.
The probability of drawing a blue ball on each draw is 4/15, the probability of drawing a red ball is 5/15, and the probability of drawing a white ball is 6/15 (assuming all colors are equally likely to be drawn).
To find the probability of drawing a blue, red, and white ball consecutively, we multiply the probabilities together since the events are independent:
P(Blue, Red, White) = (4/15) * (5/15) * (6/15) = 120/3375
(ii) Without replacement:
When the balls are not replaced after being drawn, the total number of balls decreases for each subsequent draw. This affects the probability of each color being drawn on subsequent draws.
For the first draw, the probability of drawing a blue ball is 4/15, a red ball is 5/15, and a white ball is 6/15.
For the second draw, the probability of drawing a blue ball is 3/14, a red ball is 5/14 (as one blue ball is already drawn), and a white ball is 6/14.
For the third draw, the probability of drawing a blue ball is 2/13, a red ball is 4/13 (as two blue balls and one red ball are already drawn), and a white ball is 6/13.
To find the probability of drawing a blue, red, and white ball consecutively without replacement, we multiply the probabilities together:
P(Blue, Red, White) = (4/15) * (5/14) * (6/13) = 120/2730
Therefore, the probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
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HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 142825
Step-by-step explanation:
If \(t\) is the number of years, then the population is \(P(t)=100000(1.02)^t\).
Setting \(t=18\). \(P(18)=100000(1.02)^{18} \approx 142825\).
The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 30 hours. 1 day 24 hours 12 hours 12 hours 1 and 1 over 4. days 1 and 1 over 2. days 1 and 3 over 4. days 2 days
Answer:
12 hours + 12 hours and 1 over 4
or 12 + 13 + 1/4 / 6 hours
Step-by-step explanation:
this is true since 1/4 of a day is 6 hours and 30 hours is equivalent to 24 hours plus 6 extra hours..
Answer:
HOURS AND HOURS WHIC IS EQUAL TO 24 WHICH MEANS 1 X 4 IS 4 SO THE ANSWER IS 42
Step-by-step explanation:
Rolle's Theorem Let be function that satisfies the following hypothesis: - f is continuous on [a,b]; - f is differentiable on (a,b); - f(a)=f(b): Then there is number c: a
Rolle's theorem can be applied on f(x) = x^2 - 5x + 6 in (2, 3).
The given function x^2 - 5x + 6 is a polynomial function, hence it is continuous in the interval [2, 3].
Differentiating f(x),
f ' (x) = 2x -5, which is differentiable in (2, 3).
f(2) = (2)^2-5(2)+6 = 0
f(3) = (3)^2-5(3)+6 = 0
Hence, f (2) = f (3)
All the hypothesis of Rolle's theorem are satisfied.
Then there exists a number c ∈ (2, 3):
f ' (x) = 0
2x - 5 = 0
x = 5/2 ∈ (2, 3).
The question is incomplete, the complete question is:
Rolle's Theorem: Let f be a function that satisfies the following hypothesis: -
- f is continuous on [a,b];
- f is differentiable on (a,b);
- f(a)=f(b):
Then there is number c: c ∈ (a, b), f ' (c) = 0.
Verify whether Rolle's theorem can be applied on f(x) = x^2 - 5x + 6 in the interval (2, 3).
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Your dad has made a drink for you, using 1.5 ounces of rum and 2.5 ounces of Coke. Your mom scolds your dad and says that drink is too strong. She insists your dad pour in some more Coke until the mixed drink is only 20% rum. How many ounces of Coke should your dad add?
Answer:
Dang bro that mom gotta chill
Step-by-step explanation:
Answer:If you answered YES to these questions, then this is the article for you! ... Awaken your inner bartender by adding different garnishes to this cocktail! Fill up a cup halfway with ice; 1.5 ounces of gin; Top it off with seltzer ... Ginger ale can be used, but be careful not to make the drink too sweet. Campari soda
Step-by-step explanation:
Write an expression for "the quotient of z and 4
Answer:
z/4
Step-by-step explanation:
you divide the numerator by the denominator
Answer:
z/4 is the answer
please brainliest me
Step-by-step explanation:
and can me divide which is also (/)
PEMDAS Simplify using order of operations.
7 + 3 x 5
Answer: 22
Step-by-step explanation:
3 times 5 then add 7
Help help help help help help help help
help what is 383 plus 727 minus 71 plus 8181 times 2 divided by 6 rounded to the nearest tenth to the tenth power help hurry!!
Solve for z. -10 = 5z + 5
Answer: -2
:)
Step-by-step explanation:
The equation x^2+y^2+3x-2y=0 is an example of ?
The equation x^2+y^2+3x-2y=0 is an example of ?
We can say that this equation is the circle equation.
\(\begin{gathered} \mleft(x-a\mright)^2+\mleft(y-b\mright)^2=r^2,\mathrm{\: with\: a\: radius\: r,\: centered\: at}\: \mleft(a,\: b\mright) \\ \end{gathered}\)Using the form standard equation circle equation:
\(\mleft(x-\mleft(-\frac{3}{2}\mright)\mright)^2+\mleft(y-1\mright)^2=\mleft(\frac{\sqrt{13}}{2}\mright)^2\)Therefore,
\(\mleft(a,\: b\mright)=\mleft(-\frac{3}{2},\: 1\mright)\)and
\(r=\frac{\sqrt{13}}{2}\)Answer: The given equation is an example of the circle equation.
Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
I NEED HELP PLEASE IM IN A TEST RN IF YOU GIVE ME THE CORRECT ANSWER I WILL GIVE U 70 PONITS
Sara and Ashton both have the same number of comic books after 10 months
How to determine when they both have the same number of books?From the question, we have the following parameters that can be used in our computation:
Sara
Initial = 12 comic books
Books at the fourth month = 20
Ashton
Initial = 2 comic books
Books each month = 3
The equations can be represented as
Total number of books = Initial + Books each month * Number of months
Rewrite as
y = Initial + Books each month * x
For Ashton, the equation is
y = 2 + 3x
For Sara, we have
y = 12 + Books each month * Number of months
So, we have
20 = 12 + Books each month * 4
This gives
Books each month = 2
So, the equation is
y = 12 + 2x
Substitute y = 2 + 3x in y = 12 + 2x
2 + 3x = 12 + 2x
Evaluate the like terms
x = 10
This means that
Number of months = 10
Hence, the number of months is 10
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Complete question
Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.
Calculate when they both have the same number of books
Please help me with 1-4. I will give an Brainly and a bunch of extra points.
Answer: 1. {a, b, c, d, e}
2. {a, b, d}
3. {c, f, g, h}
4. {a, c}
Step-by-step explanation:
1. AUC ==> Means take all parameters from A and C.
A+C=
{a, b, c, d}+{a, e}={a, b, c, d, e}
2. B∩A ==> Means take the common parameters from B and A
B: {b, e, a, d}
A: {a, b, c, d}
Both B and A have a, b, and d.
So answer is {a, b, d}.
3. B' is every parameter that isn't in B
Reminder: B={b, e, a, d}.
All parameters: {a, b, c, d, e, f, g, h}
Remaining Parameters(B'): {c, f, g, h}
4. A-B∩C'
First, let's find C'.
C' is every parameter that isn't in C.
Reminder: C={a, e}
All parameters: {a, b, c, d, e, f, g, h}
Remaining Parameters(C'): {b, c, d, f, g, h}
Then lets find B∩C'
B: {b, e, a, d}
C': {b, c, d, f, g, h}
Both B and C' have b and d, so B∩C' is {b, d}
A-{b, d}=
{a, b, c, d}-{b, d}={a, c} ==> Answer for 4
Answer:
\(\sf 1) \quad \sf A \cup C = \{a, b, c, d, e\}\)
\(\sf 2) \quad B \cap A = \{a, b, d\}\)
\(\sf 3) \quad B' = \{c, f, g, h \}\)
\(\sf 4) \quad A -(B \cap C') = \{a, c \}\)
Step-by-step explanation:
Set Notation
\(\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}\)
Given sets:
U = {a, b, c, d, e, f, g, h}A = {a, b, c, d}B = {b, e, a, d}C = {a, e}Therefore:
Universal set = {a, b, c, d, e, f, g, h}B' = not in B = {c, f, g, h}C' = not in C = {b, c, d, f, g, h}Question 1
\(\begin{aligned}\sf A \cup C & = \sf \{a, b, c, d\} \cup \{a,e\}\\& = \sf \{a, b, c, d, e\}\end{aligned}\)
Question 2
\(\begin{aligned}\sf B \cap A & = \sf \{b, e, a, d\} \cap \{a, b, c, d\}\\& = \sf \{a, b, d\}\end{aligned}\)
Question 3
\(\begin{aligned}\sf B' & = \rm U - \sf B\\& = \sf \{a, b, c, d, e, f, g, h \}-\{b, e, a, d\}\\& = \sf \{c, f, g, h \}\end{aligned}\)
Question 4
\(\begin{aligned}\sf A -(B \cap C') & = \sf \{a, b, c, d \}- \left( \{b, e, a, d \} \cap \{b, c, d, f, g, h \} \right)\\& = \sf \{a, b, c, d \}- \{b, d \} \\& = \sf \{a, c \}\end{aligned}\)
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Please anwser this is all the points I have :)
Check the picture below.
so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?
\(\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2\)
Answer: Large
Step-by-step explanation: Hope it helps Good luck!!!
PLease guys help!!!
Ice has ________ energy.
1. mechanical
2. cold
3. heat
Answer:
ice has kinetic enery
Step-by-step explanation:
Ice has heat energy
The length of a rectangular piece of land is 60 yards more than two times its width. The perimeter is 540 yards. Find its dimensions.
According to the problem the length of the land is 60 yards more than two times the width, in a math expression this would be:
\(\text{l = 2}\cdot w+60\)Where "l" is length and "w" is width. The perimeter of a rectangle is twice the length plus twice the width. Therefore:
\(2\cdot l+2\cdot w\text{ = 540}\)Applying the first expression we can isolate one variable as shown below.
\(\begin{gathered} 2\cdot(2\cdot w+60)+2\cdot w\text{ = 540} \\ 4\cdot w+120+2w=540 \\ 6\cdot w=540-120 \\ 6\cdot w=420 \\ w=\frac{420}{6} \\ w=70 \end{gathered}\)The width is 70 yards. We can use the first expression to find the length.
\(\begin{gathered} l\text{ = 2}\cdot70+60 \\ l=140+60 \\ l=200 \end{gathered}\)The length is 200 yards.
X is inversely proportional to y, and x = 18 when y = 4. Write an equation relating the two
Answer:
\(xy=72\)
Step-by-step explanation:
If x is inversely porportionaly to y, then for some constant k,
\(x = \frac{k}{y}\\xy=k\)
Since y is 4 when x = 18, k is equal to 4*18=72, so the equation is:
\(xy=72\)
suppose that the length of a certain rectangle is 7 meters less than four times its width. The perimeter of the rectangle is 46 meters. find the length and width of the rectangle.
The answer to the given question is length is 17m and width is 6m
Given that a rectangle's length is 7 meters less than its width.
And also given the perimeter of the rectangle is 46 meters.
We know that the rectangle's perimeter is twice the sum of its length and width.
l - length of the rectangle
w - width of the rectangle
P - perimeter of the rectangle
Then we have P = 2 × (l + w)
Given that a rectangle's length is 7 meters less than its width.
⇒ l = 4 × w - 7
Given the perimeter of the rectangle is 46 centimeters.
⇒ 2 × ( l + w) = 46
⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)
⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)
⇒ 5w - 7 = 23
⇒ 5w = 23 + 7
⇒ 5w = 30
⇒ w = 6 (dividing both sides by 5)
Using the width value in the length equation, we get
l = 4 × 6 - 7
⇒ l = 24 - 7
⇒ l = 17
Therefore, The rectangle is 17 meters in length and 6 meters in width.
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True or false question need help
A 587.5 kg crate is dragged across an ice covered lake. The box accelerates at a speed of 0.08 m/s. What is the force used to move the crate?
The force used to move the crate across an ice covered lake is 47 N. N refers to Newtons.
Given parameters:
Rate of acceleration of the box = 0.08m/s²
Mass of the body = 587.5 kg
Unknown:
Force of the box = ?
The force applied on a body is push or pull on it to move it in a specific direction. Force causes the motion of a body.
Mathematically, force is expressed as the product of mass and acceleration;
Force = mass x acceleration
Input parameters and solve for force;
Force = 587.5 x 0.08
Force = 47
Force = 47 N
The Force of the box is 47 N
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4 1/15 divided by 3.1 PLEASE HELP
Answer:
1.31182795699
Step-by-step explanation:
Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.
The probability that the third largest observation in the sample is less than 0.7 is 0.2401 = 24.01%.
How do we calculate?The sample size n = 5,
Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.
Probability that X₃ is less than 0.7:
Since X₃ is the third largest observation = (X₁ and X₂) < 0.7.
The probability that X₃ is less than 0.7 is (0.7)² = 0.49.
The Probability that X₁ and X₂ < or equal to 0.7 is found as:.
The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.
We then get the product of both cases:
Probability = 0.49 * 0.49 = 0.2401
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A scientist has two solutions what she has labeled solution a and solution b each contains salt she knows that solution a is 60% salt and solution b is 85% salt she wants to obtain 70 ounces of a mixture that is 80% salt how many ounces of each solution should she use
Solving a system of equations we can see that:
She needs to use 56 oz of the 85% solution.She needs to use 14 oz of the 60% solution.How many ounces of each solution should she use?We can use the variables:
x = mass of the 60% solution.
y = mass of the 85% solution.
We can write a system of equations.
x + y = 70
x*0.6 + y*0.85 = 70*0.8
We can isolate x on the first equation to get:
x = 70 - y
Replace that in the other one:
(70 - y)*0.6 + y*0.85 = 70*0.8
Now we can solve this for y.
y*0.25 = 70*0.8 - 70*0.6
y = 14/0.25 = 56
Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.
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Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
Snow flake
A.
No
B.
Yes; 3 lines of symmetry
C.
Yes; 6 lines of symmetry
D.
Yes; 12 lines of symmetry
The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.
How many lines of symmetry does a snowflake have ?Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.
So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided
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10cm 3mm - 4.8cm
I do not understand that well can someone please help no need to explain
Answer:
60mm or 6cm
Step-by-step explanation:
108mm - 48mm = 60mm
does anyone want to HELP me please
Answer:
x = 12
Step-by-step explanation:
We will be using pythagoras theorem.
Therefore, we will have: \(a^{2}\) + \(x^{2}\) = \(13^{2}\)
Moreover, we have: \(a^{2}\) = \(4^{2} + 3^{2}\) => \(a^{2}\) = 25
=> 25 + \(x^{2}\) = 169
=> \(x^{2}\) = 144 => x = \(\sqrt{144}\) = 12
A summary of the two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metropolis, Ltd MTP 17.95 18.25 18.28
Suburbia, Inc SBR 5.63 4.98 5.25
Suppose you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks and by how much?
Day 2 is the best by $13.00.
Day 3 is the best by $13.00.
Day 2 is the best by $2.45.
Day 3 is the best by $2.45.
The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.
Given are the closing prices of two stocks in three days.
If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,
Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25
If the stock is sold in day 2,
Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25
Profit = $1435.25 - $1448.25 = -$13
If the stock is sold in day 3,
Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7
Profit = $1450.7 - $1448.25 = $2.45
The profit is more for day 3 than day 2.
Hence it is best to sell on day 3 by $2.45.
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At birthday Party girls ate 7 3/4
pizzas and the boys ate 2 1/2 pizzas. How many pizzas were eaten at my party?
Answer:
10 1/4
Step-by-step explanation:
2 1/2 = 5/2
5/2 (2/2)= 10/4
7 3/4 = 31/4
10/4+31/4=41/4
41/4 = 10 1/4
Cisca, 12 years old, is three times as old as Catherine. How old will she be when she's twice as old as Catherine?
Step-by-step explanation:
Divide 12 by 3 to determine Catherine's age.
\(12 \div 3 = 4\)
Catherine is 4 years old when Cisca is 12 years old.
Let's identify when Cisca will be twice as old as Catherine by representing the ages per future years.
Year 1: 13, 5
Year 2: 14, 6
Year 3: 15, 7
Year 4: 16, 8
Year 5: 17, 9
Year 6: 18, 10
In 4 years, Cisca will be twice as old as Catherine.
Her age is 16.
She would be 4 years
Calculation of ageAge of Catherine = X
Age of Cisca = 12yrs = 3x
Therefore X = 12/3= 4 years.
Actual age of Catherine = 4 years.
Twice ( 2x) age of Catherine = 2×4= 8
Therefore, she will be 4 years to be twice as old as Catherine
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Complete the table of values for the equation 4x + 2y =64
The completed table of values for the equation 4x + 2y = 64 is provided .
To complete the table of values for the equation 4x + 2y = 64, we can assign different values to x and solve for y. Let's choose a range of values for x and calculate the corresponding values of y.
Table of Values:
x y
0 32
4 28
8 24
12 20
16 16
20 12
24 8
28 4
32 0
To find the values of y, we substitute each x-value into the equation and solve for y. For example, when x is 0, we have 4(0) + 2y = 64, which simplifies to 2y = 64 and y = 32. Similarly, for x = 4, we have \(4(4) + 2y = 64\), which simplifies to \(16 + 2y = 64\) and\(y = 28.\)
By continuing this process for the remaining values of x, we can complete the table of values for the equation 4\(x + 2y = 64.\)
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Which graph show y is less than or equal to 3x-4?
The graph that shows that y is less than or equal to 3x - 4 is plotted and attached
how to plot the graphThe graph is plotted by forming a table of value, then tracing eaching point in the table and marking the points of intersection of the x and y
The points intersections later joined with a line
The table of value is formed for x = -2, 0, and2
y ≤ 3x - 4
for x = -2, y ≤ 3 * -2 - 4 = -10
for x = 0, y ≤ 3 * 0 - 4 = -4
for x = 2, y ≤ 3 * 2 - 4 = 2
table of value
x y
-2 -10
0 -4
2 2
The graph is attached, the line is a solid line since the inequality is less than or "equal to". The shading is below because it is less than
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