Answers
Answer:
(a) [tex]P" = (-4,-3)[/tex]
(b) [tex](x,y) \to (4,-8)[/tex]
Step-by-step explanation:
Given
[tex]P = (4,3)[/tex]
Solving (a): Reflect across x and y-axis.
Reflection across x-axis has the following rules
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]P' = (4,-3)[/tex]
Reflection across y-axis has the following rules
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]P" = (-4,-3)[/tex]
Hence, the new point is: (-4,-3)
Solving (b): Rx . Do,2 (2,4)
[tex]R_x \to[/tex] reflect across the x-axis
Reflection across x-axis has the following rules
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex](2,4) = (2,-4)[/tex] ---- when P is reflected across the x-axis
[tex]D_{o,2} \to[/tex] dilate by a scale factor of 2
The rule is:
[tex](x,y) \to 2 * (x,y)[/tex]
So, we have
[tex](x,y) \to 2 * (2,-4)[/tex]
Open bracket
[tex](x,y) \to (4,-8)[/tex]
Related Questions
Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random answer generator to determine which of true or false would be the correct answer for each quiz question, but his internet is not working. Instead, he writes each possible answer combination on a small slip of paper, folds each paper in half, and then places them in a box. Without looking, he draws one of the slips of paper.
Use what you know about counting methods and set operations to answer the following questions.
After grading the quizzes, Mr. Montes decides that his students could use some additional practice with the concepts tested. He writes a take-home assignment for his students. The assignment starts with two true or false questions and then has 3 multiple choice questions. The multiple choice questions each have 4 answer options, only 1 of which is correct. Luckily, Mr. Montes’ internet is working when he writes the quiz and he is able to use a random answer generator.
After grading the take-home assignments, Mr. Montes randomly selects 5 take-home assignments to analyze. He considers the student’s responses to the three multiple choice questions, which are as shown.
Student 1: Student 2: Student 3: Student 4: Student 5:
{C, A, C} {C, B, B} {C, B, C} {C, B, A} {C, A, A}
Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she randomly selected answers without reading any of the questions. Suppose that you wanted to find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you would use a permutation or a combination?
1. The correct responses for the multiple choice questions are, in order, C, B, and A. If Set 1 represents the subset of these students who answered C for number 1, Set 2 represents the subset of these students who answered B for number 2, and Set 3 represents the subset of students who answered A for number 3, find each of the following. Explain what each notation means in context of this scenario.
a. Set 1 ∩ Set 2
b. Set 2 ∪ Set 3
c. The complement of Set 1
2. Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she randomly selected answers without reading any of the questions. Suppose that you wanted to find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you would use a permutation or a combination?
Answers
Answer:
There are 4 questions to answer here and the answers are given below:
1. COMBINATION
2. SET 2
3. {S2, S3, S4, S5}
4. { } OR ∅
Step-by-step explanation:
The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.
The assignment has 5 questions in all. The options for each question are listed below and separated by commas:
1. True, False
2. True, False
3. A, B, C, D
4. A, B, C, D
5. A, B, C, D
Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.
QUESTION 1
If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?
ANSWER TO QUESTION 1
You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.
QUESTION 2
Find "Set 1 ∩ Set 2" and explain the notation in the sentence.
ANSWER TO QUESTION 2
First list out relevant information:
- The correct answers to questions 3, 4 and 5 are respectively C, B, A
- The universal set consists of five students: S1, S2, S3, S4, S5 hence
Ц = {S1, S2, S3, S4, S5}
Next, enlist the elements of each defined set
Set 1: {S1, S2, S3, S4, S5} Set 2: {S2, S3, S4} Set 3: {S4, S5}
Note: Set 1 is equal to the universal set.
Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.
In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.
If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:
The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.
So the answer to question 2 is
Set 1 ∩ Set 2 = Set 2
QUESTION 3
Find "Set 2 ∪ Set 3" and explain the notation in the sentence.
ANSWER TO QUESTION 3
The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.
So, Set 2 union Set 3 = {S2, S3, S4, S5}
As earlier stated, Student 4 isn't appearing twice in the new set.
QUESTION 4
Find the ' of Set 1 and explain the notation in this sentence.
ANSWER TO QUESTION 4
The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.
Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!
Set 1 ' Ц = { } or ∅
where the empty bracket symbol and the slashed zero symbol represent null set.
Kudos!
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answers
Answer:
3.2 hours
Step-by-step explanation:
12 workers * 4 hours = 48 worker hours
15 workers * x hours = 48 worker hours
48 /15 =3.2 hours
Answer:
3 hours and 12 minutes.
Step-by-step explanation:
12 Workers complete a job in 4 hours
1 worker complete a job 12 × 4 = 48
15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵
= 3 hours + 1/5 × 60 minutes = 3 hours 12 minutes.
do the two trapezoids in the figure appear to be similar? why or why not?
Answers
Answer:
The answer is D cuz two if the corresponding angles are congruent.
Player Productions theatre finds that their ticket sales for Friday night performances (number of tickets sold) is given by the function h , where h ( t ) measures the number of tickets sold, and where t is the play length (measured in hours). Regal Theatre found that their ticket sales for Friday nights performances can be modeled by the function, g , where g (t)= 1.6h(t + 0.25).
Required:
How do the ticket sales for Friday night perfomances at Player Productions compare to the ticket sales for a Friday night perfomance at Regal Theatre?
Answers
Answer:
Regal Theatre makes 1.6 times more than Player Productions when they have 0.25 hours longer productions
Step-by-step explanation:
Given
[tex]h(t) \to[/tex] player production theatre
[tex]g(t) \to[/tex] regal theatre
Where:
[tex]g(t) = 1.6h(t + 0.25)[/tex]
Required
Compare both functions
We start from the bracket
[tex]t + 0.25[/tex]
The + in [tex]t + 0.25[/tex] means longer hours of production
So:
[tex]t + 0.25[/tex] means 0.25 hours longer that player productions
[tex]g(t) = 1.6h(t + 0.25)[/tex] can be rewritten as:
[tex]g(t) = 1.6 * h(t + 0.25)[/tex]
The above means 1.6 times player production when they have 0.25 longer hours.
One book is 4cm thick, find out how many such books can be placed in a space of 53cm.
Answers
Then getting the answer 13.25. Since we can’t have (.25 cm) of a book we can fit 13 whole books
1. Plot the following points by hand or using an online graphing calculator. What is the function that best fits the points?
(0, 3), (1, 6), (2, 12), (3, 24)
•Linear
•Exponential
•Quadratic
Answers
Please help me with this on the image
Answers
Answer:
a) Obtuse angle b) Reflex angleYou have collected data about the average response time of participants in your study. You are delighted to find that the variable is normally distributed. More than half your respondents take longer than 16 seconds to respond and one third take less than 12 seconds to respond. What is the median response time of your participants
Answers
Answer:
15
Step-by-step explanation:
It's 15 because it would be the median (middle) between 16 and 12 if there was more variability in 16 seconds.
Write a quadratic equation in standard form that has two solutions, 9 and -2
(the leading coefficient must be 1.)
Answers
x^2 + 2x -9x -18 = 0
x^2 - 7x - 18 = 0
Find the length of the segment indicated. circles 4
Answers
I need more information, comment on my "answer".
Simplify the following expression by using these values:
m = −6; n = 2; p = 4
[tex]-3m^{2}[/tex]+4n-p
Answers
Hi there!
Given the expression below:-
[tex] \large{ - 3 {m}^{2} + 4n - p}[/tex]
We are also given these three values below:
m = -6n = 2p = 4Simply substitute these values in:-
[tex] \large{ - 3 {( - 6)}^{2} + 4(2) - 4}[/tex]
Any negative numbers squared would result in positive.
[tex] \large{ - 3(36) + 8 - 4} \\ \large{ - 108 + 4} \\ \large \boxed{ - 104}[/tex]
Hence, the answer is -104 when substituting values in the expression.
Let me know if you have any questions!
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-3m}\mathsf{^2}\large\textsf{ + 4n - p}\\\large\textsf{= -3(-6)}\mathsf{^2}\large\textsf{ + 4(2) - 4}\\\\\large\textsf{(-6)}^2\\\large\textsf{= (-6)(-6)}\\\large\textsf{= \bf 36}\\\\\large\textsf{= -3(36) + 4(2) - 4}\\\\\large\text{-3(36)}\\\large\textsf{= \bf -108}\\\\\large\textsf{= -108 + 4(2) - 4}\\\\\large\textsf{4(2)}\\\large\textsf{= \bf 8}\\\\\large\textsf{= -108 + 8 - 4}\\\\\large\textsf{-108 + 8}\\\large\textsf{= \bf -100}\\\\\large\textsf{-100 - 4}\\\large\text{ = \bf -104}[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \boxed{\bf -104}}}}\huge\checkmark[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Use a half-angle identity to find the exact value of cos 15
Answers
Answer:
It's too short. Write at least 20 characters to explain it well.
A particular variety of watermelon weighs on average 22.4 pounds with a standard deviation of 1.36 pounds. Consider the sample mean weight of 64 watermelons of this variety. Assume the individual watermelon weights are independent.
Required:
a. What is the expected value of the sample mean weight?
b. What is the standard deviation of the sample mean weight?
c. What is the approximate probability the sample mean weight will be less than 22.02?
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
Answers
Answer:
a) 22.4 pounds.
b) 0.17 pounds.
c) 0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d) c = 22.62
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Average 22.4 pounds with a standard deviation of 1.36 pounds.
This means that [tex]\mu = 22.4, \sigma = 1.36[/tex]
Consider the sample mean weight of 64 watermelons of this variety.
This means that [tex]n = 64, s = \frac{1.36}{\sqrt{64}} = 0.17[/tex]
a. What is the expected value of the sample mean weight?
By the Central Limit Theorem, 22.4 pounds.
b. What is the standard deviation of the sample mean weight?
By the Central Limit Theorem, 0.17 pounds.
c. What is the approximate probability the sample mean weight will be less than 22.02?
This is the p-value of Z when X = 22.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{22.02 - 22.4}{0.17}[/tex]
[tex]Z = -2.235[/tex]
[tex]Z = -2.235[/tex] has a p-value of 0.0127.
0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
This is the 90th percentile, that is, [tex]X = c[/tex] when z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{c - 22.4}{0.17}[/tex]
[tex]c - 22.4 = 1.28*0.17[/tex]
[tex]c = 22.62[/tex]
Please help im new and i need help!
Please help me if you onlw the answers please!!
Answers
9514 1404 393
Answer:
a) 2.038 seconds
b) 5.918 meters
c) 1.076 seconds
Step-by-step explanation:
For the purpose of answering these questions, it is convenient to put the given equation into vertex form.
h = -4.9t² +9.2t +1.6
= -4.9(t² -(9.2/4.9)t) +1.6
= -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²
= -4.9(t -46/49)² +290/49
__
a) To find h = 0, we solve ...
0 = -4.9(t -46/49)² +290/49
290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9
√(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds
The ball takes about 2.038 seconds to fall to the ground.
__
b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:
290/49 m ≈ 5.918 m
The maximum height of the ball is about 5.918 m.
__
c) We want to find t for h ≥ 4.5.
h ≥ 4.5
-4.9(t -46/49)² +290/49 ≥ 4.5
Subtracting 290/49 and dividing by -4.9, we have ...
(t -46/49)² ≥ 695/2401
Taking the square root, and adding 46/49, we find the time interval to be ...
-√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49
The difference between the interval end points is the time above 4.5 meters. That difference is ...
2√(695/2401) ≈ 1.076 . . . . seconds
The ball is at or above 4.5 meters for about 1.076 seconds.
__
I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.
_____
Additional comment
I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.
"Vertex form" for a quadratic is ...
y = a(x -h)² +k . . . . where the vertex is (h, k) and 'a' is a vertical scale factor.
In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)
Find m
a 24.7
b 79.2
c 68.3
d 57.4
e 46.5
f 80.1
g 35.6
Answers
Answer:
68.3 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan I = opp side / adj side
tan I = sqrt(82) / sqrt(13)
tan I = sqrt(82/13)
Taking the inverse tan of each side
tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))
I = 68.2892
Rounding to the nearest tenth
I = 68.3 degrees
PLS HELP! What is the mistake made below in solving x2 – 12x + 10 = 0 using the completing the square method?
x2 – 12x + 10 = 0
x2 – 12x + (- 6)2 = - 10 + (- 6)2
x2 – 12x + 36 = 26
(x – 6)(x – 6) = 26
x – 6 = √26
x = 6 + √26
Answers
Answer:
Step-by-step explanation:
Everything is correct. But you forgot to add
x = 6 - square root of 26. The answer is
x = 6 + square root of 26 or
x = 6 - square root of 26
at a local college, four sections of economics are taught during the day and two sections are taught at night. 85 percent of the day sections are taught by full-time faculty. 30 percent of the evening sections are taught by full-time faculty. if jane has a part-time teacher for her economics course, what is the probability that she is taking a night class
Answers
Answer:
Hence The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher) = 0.6999.
Step-by-step explanation:
Probability(full-time teacher/ day ) = 0.85
Probability(part-time teacher/ day ) = 1- 0.85 = 0.15
Probability(full-time teacher/ night) = 0.30
Probability(part-time teacher/ night) = 1 - 0.30 = 0.70
total no of section = 4+2 = 6
P(jane has part time teacher) = P(jane is from day section)*Probability(part-time teacher/ day )+P(jane is from night section)*Probability(part-time teacher/ night)
= (4/6)(0.15)+(2/6)(0.70) = 0.33
P(jane has part time teacher and she is taking night class ) = P(jane is from night section)*Probability(part-time teacher/ night) = (2/6)(0.70) = 0.23
According to Bayes theorem :
The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)
= 0.23/0.33
= 0.6999
I need help so what’s 6 divide by 2(1+2)=
Answers
Answer:
9
Step-by-step explanation:
Divide 6 by 2:
3(1+2)
Add 1 and 2:
3 x 3
Multiply 3 by 3:
3 x 3 = 9
Answer:
1
Step-by-step explanation:
6
------
2(1+2)
6
-----
2(3)
6
-----
6
1
how many degrees are there in the angle made by the heart hand and the minute hand of a clock when it is 9 o'clock
Answers
both angles are 90 degrees
How much would $200 invested at 5% interest compounded monthly be
worth after 9 years?
Answers
9514 1404 393
Answer:
$313.37
Step-by-step explanation:
The compound interest formula is used to find that value.
A = P(1 +r/12)^(12t)
P compounded monthly at annual rate r for t years.
A = $200(1 +0.05/12)^(12·9) ≈ $313.37
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
Answers
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?
Answers
Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.
Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:
y = 4x + 7.75
Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.
A study examined the relationship between having a baccalaureate degree and passing a cultural competency exam among a group of 987 randomly selected registered nurses at your hospital. The researchers report that more registered nurses with a baccalaureate degree passed the cultural competency exam (OR 1.54, 95% CI 0.98-1.79). Interpret this information.
Answers
Answer:
More nurses with a baccalaureate degree is estimated to pass the exam but this was not a significant difference.
Step-by-step explanation:
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Answers
Answer: Megan's at 3 inches per week
Answer: D (Megan's at 2.5 inches per week)
Step-by-step explanation: Its right.
A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.
Answers
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
Learn more about z-score here:
brainly.com/question/13793746
#SPJ5
The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh more than 15.6 ounces
Answers
Answer:
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 15.0 ounces and a standard deviation of 0.2 ounces.
This means that [tex]\mu = 15, \sigma = 0.2[/tex]
What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?
This is 1 subtracted by the p-value of Z when X = 15.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.6 - 15}{0.2}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a p-value of 0.9987.
1 - 0.9987 = 0.0013
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
Identify the decimals labeled with letters A B and C on the scale
Answers
Answer:
A. 37.39 B. 37.41 C. 37.27
I need help asap with this question
Answers
In a trapezoid, the midline is the average of the two bases.
PW = (YZ + TM) / 2
29 = (23 + 11x + 2) / 2
58 = 23 + 11x + 2
58 = 25 + 11x
11x = 33
x = 3
Hope this helps!
An urn contains 12 balls, five of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls
Answers
The expected value of the distribution of the number of selected red balls is 0.795.
What is the expected value?The expected value of the distribution is the mean or average of the possible outcomes.
There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.
In this case, the possible outcomes are 0, 1, 2, or 3 red balls.
To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.
The probability of selecting 0 red balls is :
[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].
The probability of selecting 1 red ball is :
[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].
The probability of selecting 2 red balls is
[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]
The probability of selecting 3 red balls is
[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]
The expected value is then :
[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]
To learn more about the expected value of the distribution click here:
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please help me with geometry
Answers
Answer:
x = 8
Step-by-step explanation:
Set 2x + 3 = 3x - 5
Solve for x
x = 8
