Answer: 27.3 %
Step-by-step explanation:
There are 8 blue and 3 red marbles in the bad so total is 11 marbles
We just need to take 3 divided by 11, then timed 100 and will get the percent of 27.27, or I round up to 27.3%
Graph the opposite of − 7 on the number line.
Answer:
Positive seven.
Step-by-step explanation:
Go past zero to normal seven.
Answer:positive 7
Step-by-step explanation:
let x represent the sum of the first 25 positive odd integers. let $y$ represent the sum of the next 25 positive odd integers. what is the value of y-x?
By using the concept of arithmetic series, it can be calculated that
y - x = 1250
What is arithmetic series?
Arithmetic series are those series whose difference between two consecutive terms are same.
The odd integers forms an arithmetic series
For the sum of first 25 odd integer
First odd integer = 1
25th odd integer = 49
Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625
x = 625
For the sum of first 50 odd integers
First odd integer = 1
50th odd integer = 99
Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500
Sum of next 25 odd integers = 2500 - 625 = 1875
y = 1875
y - x = 1875 - 625 = 1250
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to log on to a certain computer account, the user must type in a -letter password. in such a password, no letter may be repeated, and only the lower case of a letter may be used. how many such -letter passwords are possible? (there are letters in the alphabet.)
There are 358,800 different ways that a 4-letter password might be used.
Explain the term permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.For the stated question-
To make a four-letter password with no repeating letters and just lowercase letters;Every letter from A -Z (or 26) can be used as the initial letter for the computer account.Apart from the first letter again for second letter, we can select any letter between A and Z.Whatever letter from A to Z is available for selection, with the exception of the first and second letters again for third letter.For the fourth letter, we might select any letter between A and Z besides the first, second, and third letters.
SO;
Number of possible combinations for 4-letter passwords
= 26 × 25 × 24 × 23
= 358,800
Thus, there are 358,800 different ways that a 4-letter password might be used.
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The complete question is-
To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible.
automobile repair costs continue to rise with the average cost now at $367 per repair.† assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. answer the following questions about the cost of automobile repairs. what is the probability that the cost will be between $250 and $470?
The probability that the cost will be between $250 and $470 is 0.7354.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
Automobile repair costs continue to rise with the average cost now at $367 per repair.†
Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.
We have to find the probability that the cost will be between $250 and $470.
P( 250 < x < 470 ) = P( x <470 ) - P( x < 250 )
P( x < 470 ) = NORMDIST( 470 , 367, 88, 1 ) = 0.8272
P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183
P( 250 < x < 470 ) = 0.8272 - 0.09183 = 0.7354
P( 250 < x < 470 ) = 0.7354
Hence, the probability that the cost will be between $250 and $470 is 0.7354.
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suppose that, as in exercises 5.11 and 5.79, y1 and y2 are uniformly distributed over the triangle shaded in the accompanying diagram. (–1, 0) (1, 0) (0, 1) y1 y2 a find cov(y1, y2). b are y1 and y2 independent? (see exercise 5.55.) c find the coefficient of correlation for y1 and y2. d does your answer to part (b) lead you to doubt your answer to part (a)? why or why not?
Using the definition of covariance, Cov(Y(1)Y(2))= 0. From the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2)). So, it can be concluded that Uncorrelated variables need not be independent.
Given joint probability function of Y(1) and Y(2), is
p(Y(1)*Y(2)) = 1/3, for (y(1)*y(2)) = (- 1, 0), (0, 1), (1, 0)
So Y(1), takes random variable -1,0,1.
And Y(2) takes random variable 0,1.
Y(2)|Y(1) -1 0 1
0 1/3 0 1/3
1 0 1/3 0
From the table:
The marginal probability function of Y(1) is;
P(Y(1)=y(1)) = ∑P(Y(1)=y(1)), y(1)= -1,0,1. That is;
Y(1)=y(1) -1 0 1
P(Y(1)=y(1)) 1/3 1/3 1/3
From the definition of expectation,
E[y(1)]= [tex]\Sigma_{y_{1}}[/tex] y(1)P(Y(1)=y(1))
E[y(1)]= -1(1/3)+0(1/3)+1(1/3)
E[y(1)]= -1/3+0+1/3
E[y(1)]= 0
The marginal probability mass function of y(2) is
P(Y(2)=y(2)) = ∑P(y(1)y(2)), y(2)= 0,1. That is;
Y(2)=y(2) 0 1
[tex]P_{Y(2)}[/tex](y(2)) 2/3 1/3
Now E[y(2)]= [tex]\Sigma_{y_{2}}[/tex] y(2)P(Y(2)=y(2))
E[y(2)]= 0(2/3)+1(1/3)
E[y(2)]= 1/3
And
E[y(1)y(2)]= [tex]\Sigma_{y_{1}}\Sigma_{y_{2}}[/tex] y(1)y(2)P(y(1)y(2))
E[y(1)y(2)]= -1(0)(1/3)+0(1)(1/3)+1(0)(1/3)
E[y(1)y(2)]= 0
From the definition of covariance.
The Cov(Y(1)Y(2))= E[Y(1)Y(2)]-E[Y(1)E[Y(2)]
Cov(Y(1)Y(2))= 0-1/3 (0)
Cov(Y(1)Y(2))= 0
The Cov(Y(1)Y(2))=0, implies that the two variables are uncorrelated. But from the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2))
Hence, it can be concluded that Uncorrelated variables need not be independent.
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Subtract.
(2/9v) − (−1/3v + 5/9)
Answer:
5(v-1)/9
Step-by-step explanation:
(2/9v) - (-1/3v + 5/9)
To find the opposite of -1/3v + 5/9, find the opposite of each term.
2/9v - (-1/3v) - 5/9
The opposite of -1/3v is 1/3v.
2/9v + 1/3v - 5/9
Combine 2/9v and 1/3v to get 5/9v
5/9v - 5/9
A garden has 8 rows of plants. each row has 12 tomato plants and 3 bean plants. how many more tomato plants than bean plants are in the garden?
Answer: 72
Step-by-step explanation: because 8 x 12 = 96 and 3 x 8 = 24
96 - 24 = 72
To participate in a baeball league, the required equipment for each player i a glove, a hat, and a pair of cleat. A glove cot $50. 95 , a hat cot $20. 95 , and a pair of cleat cot $25. 95. What i the total cot for a team of 10 player?
The total cost for a team of 10 player in a baseball league is $978.5.
Explain the term unitary method?By using the unitary technique, we may calculate the price of a specific unit from the values of several other units, and then we can use this value to assess the cost of the necessary number of units.For the stated question,
The cost of each equipment for each player is-
glove = $50. 95 hat = $20. 95 pair of cleat = $25. 95Thus,
Total cost for each player = $50. 95 + $20. 95 + $25. 95
Total cost for each player = $97.85
Total number of player in a baseball league = 12
Total cost for team = 10 x $97.85
Total cost for team = $978.5
Thus, the total cost for a team of 10 player in a baseball league is $978.5.
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Sam and Rohan's families are driving to Chicago, Illinois, from Orlando, Florida. Sam's
family is driving a direct route of 1,157 miles at 65 mph. Rohan and his family are driving
through Charlotte, North Carolina and will drive 1,250 miles at 70 mph.
1.
2.
At this rate, how many hours will it take Sam's family to get to Chicago, Illinois?
(Round your answer to the tenths place. )
How many hours will it take Rohan's family to arrive in Chicago, Illinois? (Round
your answer to the tenths place. )
(1) It will take 17.8 hours for Sam's family to get to Chicago, Illinois .
(2) Rohan's family will take 17.9 hours to arrive in Chicago, Illinois .
In the question ,
it is given that ,
For Sam's Family ,
total distance to be covered is = 1157 miles ,
the average speed is given to be = 65 mph .
By the formula of Speed , Distance and Time ,
we get ,
65 = 1157/t
t = 1157/65
t = 17.8 hours .
For Rohan's family ,
total distance to be covered is = 1250 miles ,
the average speed is given to be = 70 mph ,
By the formula of Speed , Distance and Time ,
we get ,
70 = 1250/t
t = 1250/70
t = 17.9 hours
Therefore , Sam's family will take 17.8 hours and Rohan's family will take 17.9 hours .
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need help quickly its due in 30
Answer: Alternate exterior angles --> 1,8 and 2,7
Vertical angles --> 2,3 and 5,8
Corresponding angles --> 1,5 and 2,6
Alternate interior angles --> 3,6 and 4,5
#3 Mia has $50 on a gift card to her favorite *
coffee shop. Each time she visits the coffee
shop she spends $3.75 on her favorite drink.
Write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card
a test for a certain drug has a 0.1% probability of producing a false positive. if a company hired 500 drug-free employees, what is the probability of obtaining at least 1 false positive?
The probability of obtaining at least 1 false positive if the number of employees is 500 is 0.5
Probability
In the statistics concept, the probability refers the possible number of way of happening the particular event.
Given,
A test for a certain drug has a 0.1% probability of producing a false positive.
Here we need to find the probability of obtaining at least 1 false positive if a company hired 500 drug-free employees.
In the given question, we have the following values,
=> number of employees = 500
=> Probability of false positive = 0.1%
So, the probability of obtaining at least 1 false positive is calculated as,
=> 500 x 0.1/100
=> 5 x 0.1
=> 0.5
Therefore, the probability of obtaining at least 1 false positive is 0.5.
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assume that the helium porosity level (measured in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75. how large a sample size is necessary if the width of the 95% interval for the true average porosity level is to be 0.40
A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40
Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes.
Sample sizes may be chosen in several ways:
Using experience – small samples, though sometimes unavoidable, can result in wide confidence intervals and risk of errors in statistical hypothesis testing.Using a target variance for an estimate to be derived from the sample eventually obtained, i.e., if a high precision is required this translates to a low target variance of the estimator.Using a target for the power of a statistical test to be applied once the sample is collected.Using a confidence level, i.e. the larger the required confidence level, the larger the sample size.Given in the question:
A sample size of n is needed.
n is found when M = 0.4.
95% Central interval
Z = 1.96
M = z × σ /√n
⇒ 0.40 = 1.96 × 0.75 /√n
⇒ 0.40√n = 1.96 ×0.75
⇒ √n = 1.96 ×0.75/0.40
⇒ (√n)² = (1.96 ×0.75 / 0.40 )²
⇒ n = 14.6
Rounding up 14.6
n = 15
The sample size of 15 is needed.
Thus, A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40
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uppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour. (a) choose the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour.
Tn the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂
What are alternative hypotheses?An assertion used in statistical inference experiments is known as the alternative hypothesis.
It is indicated by Ha or H1 and runs counter to the null hypothesis.
Another way to put it is that it is only a different option from the null.
An alternative theory in hypothesis testing is a claim that the researcher is testing.
The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge.
According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.
So, the new production method supposedly lowers the mean operating cost per hour.
The following are the hypothesis when comparing the average production costs of the new production method (μ₁) with the old production method (μ₂):
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
Therefore, in the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂
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if a woodworker builds 3/7 chair in 3/4 hour, how long does it takes the woodworker to build 1 chair
Answer:
it would take him 4/7 of an hour
Step-by-step explanation:
help me out please
answers:
-2/3
3/2
-3/2
2/3
Answer:
Step-by-step explanation:
Chose 2 points (-3,6) and (0,8)
Using slope formula; m=( y2 - y1 ). / ( x2 -x1)
m=(8-6)/(0+3) = 2/3
slope 2/3 and y intercept is 8 because the line cuts the y axis at (0,8)
the equation of the line is: y=2/3(x) + 8
A family buys a studio apartment for $200,000. They pay a down payment of $20,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would a $90,000 down payment be?
Answer:
A. 20,000 is 10% of 200,000, so the percentage of the purchase price is 10%.
B. 90,000 is 45% of 200,000, so the percentage of the 90,000 down payment is 45%.
describe the sampling distribution for the sample mean by naming the model and telling its mean and standard deviation.
Mean and standard deviation for the sample distribution is in the main body.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
sample Mean
Population mean =mu = ∑ xi /N
Mu represents pop mean
∑xi = the sum of all scores in the dataset
sample mean is the average score of a sample on a given variable and is represented by
x bar = ∑ xi /N
SE.M(Sample error of the Mean) is
=σ/√n
standard deviation is
σ = √∑(xi - υ)²/N
hence the formula for each of terms is as follows.
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PLEASE HELP
Which values of a, b, and c correctly represent the answer in simplest form?
a = 1 b= 5 c= 9
a = 10 b =18 c=1
a =9 b =5 c=1
a =1 b =10 c=18
The values of a, b and c in the mixed fractions are 1, 5 and 9 respectively.
How to simplify fractions?The fractions are mixed fractions . let's convert it to improper fraction be we simplify its.
A mixed fraction is a whole number and a proper fraction combined. Improper fractions are defined as fractions for which the numerator is greater than the denominator.
Therefore, let's solve the fractions as follows:
[tex]3\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
[tex]3\frac{1}{2} = \frac{7}{2}[/tex]
[tex]2\frac{1}{4} = \frac{9}{4}[/tex]
Therefore,
[tex]\frac{7}{2} (\frac{4}{9} ) = \frac{28}{18} = 1\frac{10}{18} = 1\frac{5}{9}[/tex]
Hence,
a = 1
b = 5
c = 9
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7 cups to 20 ounces ratio
Answer:7:20
Step-by-step explanation:
6 balls are drawn with replacement from a bag containing 7 red balls and 3 black balls. (round your answers to five decimal places.)
(a) Find the probability that 2 of the balls will be red. (b) Find the probability that all 6 balls will be black. (c) Find the probability that at least 4 of the balls will be black.
Step-by-step explanation:
"with replacement". that means any pulled ball is returned into the bag, and we have the full 7+3 = 10 balls to pull from every time.
remember, a probability is always
desired cases / totally possible cases
(a) 2 back will be red. I understand this, that exactly 2 balls will be red (not fewer, not more).
to get exactly 2 red balls we get 2 red balls and 4 black balls.
the probability for such a single event is
7/10 × 7/10 × 3/10 × 3/10 × 3/10 × 3/10 = 49×81/1000000 =
= 0.003969
because the probably to get a red ball (one from 7 out of 10) is 7/10.
the probability to get a black ball is 3/10.
how many different such single events are possible ?
as many as there are combinations to pick 2 out of 6 :
C(6, 2) = 6! / (2! × (6-2)!) = 6! / (2 × 4!) =
= 6×5 / 2 = 3×5 = 15
so, the probability to get exactly 2 red balls is
15 × 0.003969 = 0.059535 ≈ 0.05954
(b)
the probability of all 6 balls being black is
3/10 × 3/10 × 3/10 × 3/10 × 3/10 × 3/10 =
= 3⁶/1000000 = 0.000729 ≈ 0.00073
(c)
"at least 4 black balls" means exactly 4, or exactly 5, or exactly 6 balls are black.
that means we need to calculate all 3 probabilities and add them (non-overlapping "or"-cases means addition of probabilities, "and" cases mean multiplication as above).
to get exactly 4 black balls (= 4 black balls and 2 red balls) is the same as (a) : 0.059535
to get exactly 5 black balls (= 5 black balls and 1 red ball) in one specific constellation is
3⁵/10⁵ × 7/10 = 243×7/1000000 = 0.001701
and we have C(6, 5) possible constellations
C(6, 5) = 6! / (5! × (6-5)! = 6! / 5! = 6
the total probability to get exactly 5 black balls is
6 × 0.001701 = 0.010206
to get exactly 6 black balls is (b) : 0.000729
the probability to get at least 4 black balls is
0.059535 + 0.010206 + 0.000729 =
= 0.07047
a jury pool consists of 30 people, 16 men and 14 women. compute the probability that a randomly selected jury of 12 people is all male.
The probability that a randomly selected jury of 12 people is all male is 2.01 × 10⁻⁵ .
In the question ,
it is given that ,
total number of people in the jury pool is 30 people ,
the total number of men in the jury pool is = 16 ,
total number of women in the jury pool is = 14 ,
So , 12 members can be selected from 30 people in ³⁰C₁₂ ways ,
So , total number of ways = ³⁰C₁₂ = 86493225 ways
and 12 male can be selected from 16 men in ¹⁶C₁₂ ways
= ¹⁶C₁₂ = 1820.
So , the probability of selecting 12 men is = 1820/86493225
= 0.00002104211
≈ 2.01 × 10⁻⁵
Therefore , the required probability is 2.01 × 10⁻⁵ .
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A high school. Asket ball team is selling 10$ dollar raffle tickets as part of a fund raising program the first prize is a trip to the bahamas find the average amount per game
The Expected Value to the player for one play of the game is - 7.784.
Define Expected Value.In probability theory, the weighted average is expanded upon by the expected value. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the anticipated value.
Price of raffle ticket= $10
First price= $5460
Second prize= $496
Remaining 18 prize= $100
$0 for the remaining tickets= 3500-20=3480 tickets
When winning the 1st prize, the winnings = $5460−$10=$5450.
When winning the 2nd prize, the profit= $496−$10=$486.
When winning the other 18 prizes, the profit= $100−$10=$90.
When there is no winning, the loss= $0
The probability is calculated by dividing the number of likely outcomes by the total number of outcomes:
P(X=5450)= 1/3500
P(X= 486)= 1/3500
P(X= 90)= 18/3500
P(X= -10)= 3480/3500
The product of each alternative and its probability equals the expected value, which is added up:
E(X)= ∑ xP(x)
= 5450 * [tex]\frac{1}{3500}[/tex] + 486 * [tex]\frac{1}{3500}[/tex] + 90 * [tex]\frac{18}{3500}[/tex] + (-10) * [tex]\frac{3480}{3500}[/tex]
= [tex]\frac{-27224}{3500}[/tex]
= - 7.784
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A rectangular pan has a length that is the width. The total area of the pan is 432 in. 2. What is the width of the cake pan?.
Using the area formula, we know that the width of the pan is 18 inches.
What is the area?An area is a unit of measurement used to describe a region's size on a flat or curved surface.
While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
So, the width of the pan will be:
We know that:
The length of a rectangular pan is exactly 4/3 the width.
The pan's total surface area is 432in².
Formula: Area = 432 = length*width = w*4w/3
Now, calculate the width as follows:
Formula: Area = 432 = length*width = w*4w/3
4w^2/3 = 432
w^2 = 432*3/4 = 324
w = 18
Therefore, using the area formula, we know that the width of the pan is 18 inches.
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Complete question:
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan
Answer: B. 18 in
Step-by-step explanation:
You will get this answer using the Area formula, which is A-lw
Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?
a. Explain what 120 represents, and how it relates to the cows and chickens.
b. Explain what 48 represents, and how it relates to the cows and chickens.
c. Setup a system, of two equations, to help you solve this riddle.
d. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.
Answer:
a. 120 represents the total number of cow legs and chicken legs
b. 48 represents the total number of cow heads and chicken heads
c. System:
Let x = number of cows
Let y = number of chickens
1. 2x + 4y = 120
2. x + y = 48
d. I am going to use substitution for this problem
Step 1: Solve for y in the equation x + y = 48
1. x + y = 48 → y = -x + 48
Step 2: Substitute -x + 48 for y in 2x + 4y = 120
2. 2x + 4(-x + 48) = 120
Step 3: Solve for x
3. 2x - 4x + 184 = 120 → -2x + 184 = 120 → -2x = -64 → x = 32
Step 4: Sustitute 32 for x in x + y = 48
4. (32) + y = 48
Step 5: Solve for y
5. y = 16
Number of chickens on the farm (y) = 16
Number of cows on the farm (x) = 32
Step-by-step explanation:
All of it is above :)
HELP PLEASE, I’ll give points and mark brainliest
One diagonal of a rhombus is decreasing at a rate of 777 centimeters per minute and the other diagonal of the rhombus is increasing at a rate of 101010 centimeters per minute. At a certain instant, the decreasing diagonal is 444 centimeters and the increasing diagonal is 666 centimeters. What is the rate of change of the area of the rhombus at that instant (in square centimeters per minute)?.
At that point, the area of the rhombus is changing at a rate of -1 cm²/min (measured in square centimeters per minute).
What is rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the form of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. The graphic below illustrates some examples of rhombuses in everyday objects, like a diamond, a kite, an earring, etc.
Here,
The area of a rhombus is given in terms of its diagonal lengths x and y,
A = (1/2)xy
A' = (1/2)(x'y +xy')
A' = (1/2)((-7 cm/min)(6 cm) +(4 cm)(10 cm/min))
A' = (1/2)(-42 cm²/min +40 cm²/min)
A' = -1 cm²/min
The rate of change of the area of the rhombus at that instant (in square centimeters per minute) is -1 cm²/min.
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i have 5 marbles numbered 1 through 5 in a bag. suppose i take out two different marbles at random. what is the expected value of the product of the numbers on the marbles? answer as a decimal to the nearest tenth.
The expected value of the product of the numbers on the marbles is
6.
Given:
There are 5 marbles numbered 1 through 5 in a bag.
Suppose if two different marbles are taken out at random.
what is the expected value of the product of the numbers on the marbles = ?
5C 2 = 10
So we have ten possible sums
1 + 2 = 3 2 + 3 = 5 3 + 4 = 7 4 + 5 = 9
1+ 3 = 4 2 + 4 = 6 3 + 5 = 8
1 + 4 = 5 2 + 5 = 7
1 + 5 = 6
Expected value =
3 * Prob of occurence + 4 * Prob of occurence + 5*Prob of occurence + 6 * Prob of occuence +7 * Prob of occurence + 8 * Prob of occurence + 8 * Prob of occurence
3 (1/10) + 4(1/10) + 5(2/10) + 6(2/10) + 7 (2/10) + 8 (1/10) + 9(1/10) =
3/10 + 4/10 + 10/10 + 12/10 + 14/10 + 8/10 + 9/10 =
60/10
= 6
Hence we get the required answer.
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lacy draws a '10' from a standard deck of 52 cards. without replacing the first card, she then proceeds to draw a second card and gets a '4'. are these events independent? input yes or no
Determine the probability of drawing a spade and then a club without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
The first two events are not independent, with a probability P = 0.00603
The second pair of events is independent, and the probability is P = 0.0625
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a spade card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a 10 card at first is:
P = 4/52 (because there are 4 10's and a total of 52 cards).
The probability of drawing a 4's after is:
Q = (4/51)
The joint probability is the product of the individual probabilities, this will give: p = P*Q = (4/52)*(4/51) = 0.00603
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a spade is:
P = 13/52
Now we replace the spade card drawn.
The probability of drawing a club will be:
Q = 13/52
The joint probability is:
p = P×Q = (13/52)² = 0.0625
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Enlarge the triangle by scale factor -3 with centre (3,3)
The triangles when enlarged by a scale factor of 3 the final image is at the coordinates: (7, 3), (5, 3), and (7, 7)
How to find the coordinates of the imageThe coordinates of the preimage are
(5, 3), (4, 3), and (5, 5)
translate to the origin
= (5 - 3, 3 - 3), (4 - 3, 3 - 3), and (5 - 3, 5 - 3)
= (2, 0), (1, 0), and (2, 2)
dilate about the origin
2 * { (2, 0), (1, 0), and (2, 2) }
(4, 0), (2, 0), and (4, 4)
translate back to usual position
(4 + 3, 0 + 3), (2 + 3, 0 + 3), and (4 + 3, 4 + 3)
(7, 3), (5, 3), and (7, 7)
Therefore the image is at (7, 3), (5, 3), and (7, 7)
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