An urn contains 3 red and 7 black balls. (a) You randonly draw the balls out one by one without replacement. What is the probability that the last red ball was the 8th ball out? (b) Player A and B withdraw balls from the urn consecutively until the first red ball is selected. Find the probability that A selects the first red ball. (A draws the first ball, then B, ans so on. There is no replacement of the balls drawn.)
Answers
The probability of Drawing balls one by one without replacement until the last red ball is reached is 0.0357 and the probability of players A and B taking turns drawing balls until the first red ball is selected is 40%.
(a) To calculate the probability that the last red ball is drawn on the 8th draw, we consider the favorable outcomes where the first 7 draws result in black balls and the 8th draw is a red ball. The probability of drawing a black ball on the first draw is 7/10, then 6/9 for the second draw, and so on. Therefore, the probability is (7/10) * (6/9) * (5/8) * (4/7) * (3/6) * (2/5) * (1/4) * (3/7) = 0.0357, approximately.
(b) In the second situation, we need to determine the probability of player A selecting the first red ball. Player A draws first, and there are three possible outcomes: A selects a red ball on the first draw, A selects a black ball and B selects a black ball, or A selects a black ball and B selects a red ball. The probability of A selecting a red ball on the first draw is 3/10. If A selects a black ball, the urn now contains 3 red and 6 black balls, and the probability of B selecting a black ball is 6/9. If A selects a black ball and B selects a red ball, the probability is (7/10) * (3/9) = 0.2333. Therefore, the overall probability of A selecting the first red ball is 3/10 + (7/10) * (3/9) = 0.4, or 40%.
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Related Questions
The expression 36 divided 6 • 2+1 is equal to
A.13
B.4
C.2
D.18
15 points for the question
Answers
The dual-energy x-ray absorptiometry (dexa) is the gold standard measurement for body composition. (gold standard = most accurate form of measurement) true false
Answers
The DEXA is the most accurate form of body composition measurement.
What is an x-ray?
An X-ray is a rapid and painless technique which is commonly used to generate images of the internal parts of a human body. It is a very effective and convenient way of looking for bone damages and other problems.
Explanation
The statement 'the dual-energy x-ray absorptiometry (DEXA) is the gold standard measurement for body composition is true. Here, the gold standard means the most accurate form of measurement.
Hence, the given statement is true.
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O points
Solve for x. Your answer will be of the form ##°
Answers
Answer:
x = 59
Step-by-step explanation:
Here, we want to get the value of x
To do this, we use an important arc-angle relationship
we have this as:
x = (36 + 82)/2
x = 59
The breadth of a box is two third of its length and height is one third of its length. if the volume of box is 48m³, find the area of the base of the box.
Answers
Answer:
Step-by-step explanation:
To find the area of the base of the box, we need to determine the length, breadth, and height of the box. We can set up a system of equations to represent the given information:
breadth = 2/3 * length
height = 1/3 * length
volume = length * breadth * height
Substituting the second equation into the third equation, we get:
volume = length * breadth * (1/3 * length)
= length^2 * (2/3) * (1/3)
= (2/9) * length^2
= 48
= 2^4 * 3
Solving for length, we find that length = 6. Plugging this value back into the first equation, we find that breadth = 4.
Therefore, the area of the base of the box is length * breadth = 6 * 4 = 24 square meters.
if a fair coin comes up heads five times in a row, then the probability that it will come up heads on the next flip is
Answers
The probability that it will come up heads on the next flip is still 0.5 (or 50%), regardless of the previous five consecutive heads or any previous outcomes.
The probability of flipping a fair coin and getting heads is always 0.5 (or 50%) because the coin has no memory of previous flips.
Each flip of a fair coin is an independent event, meaning the outcome of one flip does not affect the outcome of subsequent flips.
Even if a fair coin has come up heads five times in a row, the probability of getting heads on the next flip remains 0.5 (or 50%).
The previous outcomes do not influence the outcome of the next flip. Each flip is a separate event with an equal chance of heads or tails.
The probability of the coin coming up heads on the next flip is still 0.5 (or 50%), regardless of the previous five consecutive heads or any previous outcomes.
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PLEASE HELP! Will give brainleasit
Answers
Answer:
Step-by-step explanation:
7. 2/5
8. 3/5
9. 2/5
10. 2/5
Answer:
Number 7: 2/5 chance or 40%
Number 8: 4/5 or 80% chance
Number 9: 2/5 chance
Number 10: 2/5 chance
Step-by-step explanation:
For each one, you put the total number of polygons at the bottom of the fraction or the denominator and the number of how many of them answer the question as the numerator.
Triangle abc gets translated and reflected prove its congruent to a"b'c"
A. AA postulate
B. HL Postulate
C.ASA throem
D.SSA Theroem
Answers
Answer: the answer is b
Step-by-step explanation: since i helped can i have brainlist please it would be greatly apperacited. :D
PLEASE LAST ONE HELP!!!
Answers
Answer:
JKN and ONK
Step-by-step explanation:
Hope this helps :)
2.1Simplifying Expressions: Problem 1 (1 point) Simplify the following expression. 6- 4(x - 5)-
Answers
The simplified expression is 26 - 4x.
To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.
6 - 4(x - 5)
First, distribute -4 to the terms inside the parentheses:
6 - 4x + 20
Now, combine like terms:
(6 + 20) - 4x
Simplifying further:
26 - 4x
Therefore, the simplified expression is 26 - 4x.
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imagine tossing a fair coin 3 times. what is the sample space for this chance process what is the assignment of probabilities to outcomes in this sample space
Answers
a) Sample space is {HHH, HHT.HTH,THH,TTT,TTH,THT,HTT}.
b) The assignment of probabilities to outcomes in this sample space is 1/8.
Define probability.By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are just two outcomes when you flip a coin: either it comes up heads or tails.
Given,
(A) What is the scope of this random process' sample space?
There are three possible results from tossing a coin three times.
The sample area connected to the specified random process is:
S = {HHH, HHT.HTH,THH,TTT,TTH,THT,HTT}
(b) How are outcomes in this sample space assigned probabilities?
Since there are eight possible outcomes in the sample space supplied, and we are aware that a fair coin is tossed three times, As a result, the likelihood of every event listed in the provided sample space is the same. Thus, we have:
Probability = 1/8
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Ms. Adams needs to make 50 ml of 15% saline solution. However, she only has bottles of 7.5% and 20% solution. How many milliliters of each does she need to mix?
Answers
Answer: 20 mL of 7.5% solution and 30 mL of 20% solution
Step-by-step explanation:
Let the amount of 7.5% solution in mL be \(x\) and the amount of 20% solution in mL be \(y\).
Then, we know that \(x+y=50\) (from the total amount) and that \(0.075x+0.20y=50(0.15)\) from the concentration.
\(x+y=50 \implies y=50-x\\\\\therefore 0.075x+0.20(50-x)=50(0.15)\\\\0.075x+10-0.20x=7.5\\\\-0.125x=-2.5\\\\x=20\\\\\implies y=50-20=30\)
minimize f(x) = |x+3| + x^3 S.t. x sum [-2, 6]
Answers
Minimization of f(x) = |x+3| + x^3 at the endpoints (-2 and 6) the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}
within the given interval.
To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.
First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:
|x+3| =
x+3 if x+3 >= 0
-(x+3) if x+3 < 0
Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.
Case 1: x+3 >= 0
In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3
Case 2: x+3 < 0
In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3
Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.
Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.
Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.
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Round 8250 to the nearest hundred.
Answers
Answer:
8300
Step-by-step explanation:
i believe it is 8300 but if im wrong let me know
HELP PLEASE NO LINKSSS
Answers
Answer:
Step-by-step explanation:
multiply the botom olf the pick by the side of the pink and then add all the side of the blue
Write a quadratic function f whose zeros are 3 and 10
Answers
Answer:
\(f(x) = {x}^{2} - 13x + 30\)
Step-by-step explanation:
A quadratic equation may be expressed as a product of the two binomials. The roots of the equations are 3 and 10, so the factors are (x-3) and (x-10).
f(x) = (x-3)(x-10)
f(x) = x^2 - 13x + 30
During one hour of running, Jeff can run 5.5 miles. The number of miles Jeff runs and the number of hours are in a proportional relationship. This is represented by y=5.5x .
Answers
Answer:
can you plz show a pic of the page ...
Step-by-step explanation:
3. prove that if : → and : → are bijective functions then is a bijective function.
Answers
We can prove that the f:A → B and g: B → C composition of these two bijective functions is also bijective.
To prove that the composition of two bijective functions is also a bijective function, we need to show that it is both injective (one-to-one) and surjective (onto).
Let f: A → B and g: B → C be bijective functions.
To show that the composition function h: A → C is injective, we assume that h(x₁) = h(x₂) for some x₁, x₂ ∈ A. Since h(x) = g(f(x)), we have g(f(x₁)) = g(f(x₂)). Since g is injective, it follows that f(x₁) = f(x₂). And since f is also injective, we can conclude that x₁ = x₂. Therefore, h is injective.
To show that h is surjective, let y ∈ C. Since g is surjective, there exists b ∈ B such that g(b) = y. Similarly, since f is surjective, there exists a ∈ A such that f(a) = b. Thus, h(a) = g(f(a)) = g(b) = y. Hence, h is surjective.
Therefore, the composition function h = g ∘ f is bijective.
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What is 38,050,000 expressed in scientific notation?
O A. 3.805 x 108
O B. 0.3805 x 108
O C. 0.38 x 10-8
O D. 3.805 x 107
Answers
Answer:
I think it is 3.805 × 10 to the 7th power
Step-by-step explanation:
Hope this helps!
Answer should be B/0.3805 x 108
Step-by-step explanation:
if I'm wrong please tell me and I will try to correct it :)
From the diagram shown, find the measurement of the indicated angle.
Answers
Answer:
x = 50°
Step-by-step explanation:
The three angles of any triangle always add up to 180°. Here, we have a 40° and a right angle. Right angles are always 90°.
To find the value of x, find the sum of the two other angles.
90 + 40 = 130°
Since we know that all angles add to 180, we can conclude the following:
x + 130 = 180
x = 50°
Hope this helps
please help with this math problem
Answers
Answer: x is 55
hard to explain sorry
How do i do this. Im mad lost
Answers
Answer:
x-int: (8/3, 0)
y-int: (0, -32/3)
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
x-intercept is the x-value when y = 0
y-intercept is the y-value when x = 0
Step 1: Write equation
2x - 1/3 = 1/2y + 5
Step 2: Subtract 5 on both sides
2x - 16/3 = 1/2y
Step 3: Multiply 2 on both sides
4x - 32/3 = y
Step 4: Rewrite
y = 4x - 32/3
Step 5: Find x-int
0 = 4x - 32/3
32/3 = 4x
x = 8/3
(8/3, 0)
Step 6: Find y-int
y = 4(0) - 32/3
y = 0 - 32/3
y = -32/3
(0, -32/3)
BRAINLIEST!!! Correct and fastest answer!
Answers
Answer:
whats the question?????
Step-by-step explanation:
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
Referring to Scenario D.1, assume that an optimal serving contains 0.89 ounces of chicken
and 0.52 ounces of tomatoes. Which of the following statements is BEST?
The serving costs about 20 cents.
The serving costs about 30 cents
The serving costs about 50 cents.
The serving costs about 40 cents.
Answers
the BEST statement is: The serving costs about 40 cents.
To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.
Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:
Cost of chicken =\(0.89 ounces * $0.40/ounce\)
Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)
Total cost = Cost of chicken + Cost of tomatoes
Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)
Total cost =\($0.356 + $0.0416\)
Total cost ≈\($0.3976\)
Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.
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PLS PLS i need step by step please and undefined numbers to be shown please THANK YOU!
Answers
1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.
x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.
2) The given expression is:
(5-2x)/(x+2) + x^2/(x^2-4) - 5
To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:
[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]
Expanding the brackets and simplifying, we get:
(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]
This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.
(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.
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Find the equation of the line parallel to the line y = 4x – 2 that passes through the point (1, 5).
Answers
Answer:
4x-y+1=0
Step-by-step explanation:
here,given equation of a line id
4x-y-2=0.. eqn(i)
equation of any line parallel to line (i) is
4x-y+k=0...eqn(ii)
since, the line(ii) passes through (1,5)[replacing x=1 and y=5 in eqn(ii), we get]
4*1-5+k=0
or, 4-5+k=0
or,-1+k=0
•°•k=1
substituting the value of k=1 in eqn(ii),
4x-y+1=0 is the required equation of the line.
Select all of the following statements that are true.
All real numbers are natural numbers.
All whole numbers are integers.
All integers are whole numbers.
All natural numbers are rational numbers.
All irrational numbers are dense.
DONE
Answers
Answer:
All whole numbers are integer
All natural numbers are rational numbers
Step-by-step explanation:
Answer:
2, 4, 5
Step-by-step explanation:
edge 2021 :)
Which expression represents the model?
Answers
9*1/6
Step-by-step explanation:
1= 6/6 and there are 9 boxes so multiply 9*1/6
Desperate
please Hurry
Question Down Below
Answers
Answer:
4
Step-by-step explanation:
\(\frac{17 + 9}{4}\)
\(\frac{16}{4}\)
\(4\)
Answer:
1/2
Step-by-step explanation:
7 - 9 = 2
2/4 simplify to 1/2
(Its also hard to tell if that's supposed to be a plus sign or a minus sign so Im not completely sure if this is right)
you want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size if the margin of error . please choose the correct answer from the following choices, and then select the submit answer button. answer choices
Answers
The needed sample size Smaller if the margin of error .
Given,
In the question:
This question in the form of: Fill in the blanks.
So, You want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size_____ if the margin of error.
Hence, The answer is smaller the margin of error.
Let's Know:
What is Confidence level?
The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.
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Some one help on this
Answers
Answer:
C
Step-by-step explanation: