Answer: 203,280
Step-by-step explanation:
Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.
Number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.
Total number of ways to do this: [tex]^{11}C_9\times ^{12}C_2\times^{8}C_3[/tex]
[tex]=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280[/tex]
hence , this can be done in 203,280 ways.
6 is what percentage of 10?l
Answer:
Hello! The answer will be below!
Step-by-step explanation:
The answer is 60, steps will be below....
Steps:
6 divided by 10
=0.6
And than we do (0.6 x 100)%
Which will give us 60%
Hope this helps! :)
⭐️Have a wonderful day!⭐️
There are five questions listed below. Each question includes the quantity 22. Match
the 22 in each question on the left to which part of the problem it represents on the right
-- the base, percent, or amount. Some answer options on the right will be used more
than once.
What percent of 22 is 3?
percent
22 is what percent of 164?
base
What is 4% of 22?
amount
8 is 22% of what number?
What is 5% of 22?
Using concepts of percentage,
3 is 16.63% of 22.
22 is 13.41% of 164.
0.88 is 4% of 22.
8 is 22% of 36.36.
1.1 is 5% of 22.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Let 3 be x% of 22.
[tex]=\frac{x}{100} *22 = 3\\\\=x = \frac{3*100}{22} = 13.63%[/tex]
3 is 13.63% of 22.
Let 22 be y % of 164.
[tex]=\frac{y}{100} *164 = 22\\\\=y = \frac{22*100}{164} = 13.41%[/tex]
13.41% of 164 is 22.
4% of 22 = 0.88
[tex]\frac{4}{100}*22 = 0.88[/tex]
Let 8 is 22% of z.
[tex]\frac{22}{100}*z = 8\\ \\z = \frac{8*100}{22} = 36.36[/tex]
5% of 22 = 1.1
[tex]\frac{5}{100}*22 = 1.1[/tex]
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Sam weights 51kg. What is this weight to the nearest stone?. Use this conversion, 1kg= 2.2 pounds and 14 pounds= 1 stone
Sam's weight to the nearest stone is equal to 8.0 stone.
Given the following data:
Sam's weight = 51 kg.1 kg = 2.2 pounds.14 pounds = 1 stone.To determine Sam's weight to the nearest stone:
How to convert the units of measurement.In this exercise, you're required to determine Sam's weight to the nearest stone. Thus, we would convert his weight in kilograms to pounds and lastly to stone as follows:
Conversion:
1 kg = 2.2 pounds.
51 kg = [tex]51 \times 2.2[/tex] = 112.2 pounds.
Next, we would convert the value in pounds to stone:
14 pounds = 1 stone.
112.2 pounds = X stone.
Cross-multiplying, we have:
[tex]14X = 112.2\\\\X=\frac{112.2}{14}[/tex]
X = 8.01 ≈ 8.0 stone.
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A lottery ticket has a grand prize of $31 million. The probability of winning the grand prize is .000000018. Determine the expected value of the lottery ticket.
Answer:
$0.558
Step-by-step explanation:
The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:
Win $31 millionWin $0Then our expected value can be calculated as:
[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]
Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm). 59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = 61.81 Correct: Your answer is correct. cm s = 10.64 Correct: Your answer is correct. cm (ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada. (a) What is the level of significance? 0.100 Incorrect: Your answer is incorrect. State the null and alternate hypotheses. H0: μ = 66; H1: μ 66 H0: μ ≠ 66; H1: μ = 66 H0: μ < 66; H1: μ = 66 Incorrect: Your answer is incorrect.
Answer:
We conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
Step-by-step explanation:
We are given that slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm.
A random sample of avalanches in spring gave the following thicknesses (in cm);
X: 59, 51, 76, 38, 65, 54, 49, 62, 68, 55, 64, 67, 63, 74, 65, 79.
Let [tex]\mu[/tex] = true mean slab thickness in the Vail region
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 66 cm {means that the mean slab thickness in the Vail region is the same as that in the region of Canada}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 66 cm {means that the mean slab thickness in the Vail region is different from that in the region of Canada}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean thickness = [tex]\frac{\sum X}{n}[/tex] = 61.81 cm
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 10.64
n = sample of avalanches = 16
So, the test statistics = [tex]\frac{61.81-66}{\frac{10.64}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex]
= -1.575
The value of t-test statistics is -1.575.
Now, at a 1% level of significance, the t table gives a critical value of -2.947 and 2.947 at 15 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
A runner can run 3 miles in 18 minutes. At this rate, how many miles can he run in 54
minutes?
6
9
12
I
18
Answer:
9 miles
Step-by-step explanation:
54 divided by 18
=
3.
3 x 3 (miles per 18 min)
=
9 miles
Answer:
9 miles in 54 minutes
Step-by-step explanation:
Create proportions
Do it miles:minutes
In this case it would be
3:18
Then divide both sides of the proportion by three to get
1 : 6
or the statement "It takes the runner 6 minutes to run a mile."
Now create another proportion
x: 54
If he can run a mile in 6 minutes,
he can run x miles in 54 minutes.
In this case divide 54 and 6 to get 9 miles in 54 minutes.
Hope this helps!
Simplify the expression:
– 10x + – 4 – 8 + 7x
Answer:
-3x-12
Step-by-step explanation:
-10x-4-8+7x
-3x-4-8
-3x-12
Answer:
-3x-12
Step-by-step explanation:
– 10x + – 4 – 8 + 7x
Combine like terms
-10x +7x -4-8
-3x -12
Using the information regarding proportion of snoring events, choose the correct conclusion for this hypothesis test. H0:p=0.35 ; Ha:p>0.35 The p-value for this hypothesis test is 0.03. The level of significance is α=0.05
Select the correct answer below:
a. There is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.
b. There is NOT sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.
c. There is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 5%.
d. There is NOT sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 5%.
Answer:
Option A
Step-by-step explanation:
With the following data, H0:p=0.35 ; Ha:p>0.35 The p-value for this hypothesis test is 0.03. The level of significance is α=0.05.
Since the p value (0.03) is less than alpha (0.05), we will reject the null hypothesis and conclude that there is sufficient evidence to conclude that the proportion of snoring events compared to other events during a sleep study is more than 35%.
Solve the equation for x 5x-(4x-1)=2 A 1/9 B -1 C -1/9 D 1
Answer:
D
Step-by-step explanation:
Which of the following algebraic expressions represents the statement given below?
A number is increased by five and squared.
A. x+5²
В.
x²+5
c. ° +5
D. (x+5)
Answer:
Let the number be x
The statement
A number is increased by five is written as
x + 5
Then it's squared
So we the final answer as
(x + 5)²Hope this helps
Eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 63% have an emergency locator, whereas 89% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.) (a) If it has an emergency locator, what is the probability that it will not be discovered? (b) If it does not have an emergency locator, what is the probability that it will be discovered?
Answer:
a) P(B'|A) = 0.042
b) P(B|A') = 0.625
Step-by-step explanation:
Given that:
80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered
Of the aircraft that are discovered, 63% have an emergency locator,
whereas 89% of the aircraft not discovered do not have such a locator.
From the given information; it is suitable we define the events in order to calculate the probabilities.
So, Let :
A = Locator
B = Discovered
A' = No Locator
B' = No Discovered
So; P(B) = 0.8
P(B') = 1 - P(B)
P(B') = 1- 0.8
P(B') = 0.2
P(A|B) = 0.63
P(A'|B) = 1 - P(A|B)
P(A'|B) = 1- 0.63
P(A'|B) = 0.37
P(A'|B') = 0.89
P(A|B') = 1 - P(A'|B')
P(A|B') = 1 - 0.89
P(A|B') = 0.11
Also;
P(B ∩ A) = P(A|B) P(B)
P(B ∩ A) = 0.63 × 0.8
P(B ∩ A) = 0.504
P(B ∩ A') = P(A'|B) P(B)
P(B ∩ A') = 0.37 × 0.8
P(B ∩ A') = 0.296
P(B' ∩ A) = P(A|B') P(B')
P(B' ∩ A) = 0.11 × 0.2
P(B' ∩ A) = 0.022
P(B' ∩ A') = P(A'|B') P(B')
P(B' ∩ A') = 0.89 × 0.2
P(B' ∩ A') = 0.178
Similarly:
P(A) = P(B ∩ A ) + P(B' ∩ A)
P(A) = 0.504 + 0.022
P(A) = 0.526
P(A') = 1 - P(A)
P(A') = 1 - 0.526
P(A') = 0.474
The probability that it will not be discovered given that it has an emergency locator is,
P(B'|A) = P(B' ∩ A)/P(A)
P(B'|A) = 0.022/0.526
P(B'|A) = 0.042
(b) If it does not have an emergency locator, what is the probability that it will be discovered?
The probability that it will be discovered given that it does not have an emergency locator is:
P(B|A') = P(B ∩ A')/P(A')
P(B|A') = 0.296/0.474
P(B|A') = 0.625
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7
====================================================
Explanation:
Here's our sample space
{1,2,3,4,5,6,7,8,9,10}
This is the set of all possible outcomes.
We see that {1,3,5,7,9} are odd. We have 5 odd numbers out of 10 total. The probability of getting an odd number is therefore 5/10 = 1/2. Let A = 1/2 as we'll use it later.
After we select the first card and put it back (or replace it with a copy), the stack of cards is the same as before we made that first selection. So the sample space hasn't changed. The set of values greater than 7 is {8,9,10}. We have 3 items in here out of 10 total. The probability of getting a value larger than 7 is 3/10. Let B = 3/10.
Multiply the values of A and B to get the answer
A*B = (1/2)*(3/10) = 3/20
This represents the probability of getting an odd number on the first selection, and a second card that is larger than 7. This only applies if a replacement is made on the first card. Otherwise, 3/10 would be different.
A recent study found that toddlers who have a diet high in processed foods may have a slightly lower IQ later in life. The conclusion came from a long-term investigation of 14,000 people whose health was monitored at 3,4,7, and 8 years of age.
a) One analysis found that of the 4000 children for which there were complete data, there was a significant difference in IQ between those who had had "processed" (i.e., junk) food and those who followed health-conscious diets in early childhood. Is this an experiment? Why or why not?
b) Discuss at least two explanatory factors that could conceivably confound the relationship between diet and IQ.
Answer:
A) it is not an experiment it is an observational study/analysis
B) i)Foods high in fats and sugar affects IQ (ii)Foods that contain the required classes of food affects IQ positively
Step-by-step explanation:
A) An analysis carried out on 400 children using the data derived from the long term investigation can not be said to be an experiment but an observational analysis this is because the complete data has been provided already from the long term investigation already. hence it can only be observed
B ) i) foods high in fats and sugar affects The IQ of children later in life as seen from the results of the observational study that children whom had processed foods had a significant negative difference in IQ when compared with children who had health-conscious diets
ii) following health conscious diets early in childhood will have a positive effect on one's IQ later in life .
i
dont
get
this
help
rn
Answer:
6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.
Step-by-step explanation:
Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.
How many different lists containing the numbers 1, 4, 5, 8, 17, 21, and nothing else are there in which each odd integer appears before any even integer?
Answer:
4! * 2! = 48
Step-by-step explanation:
In general you have 6 elements so there are 6! = 6*5*4*3*2*1 lists in total, now, you have to think about the second condition, an odd integer has to appear before any even integer. Therefore odd integers go first, and since there are 4 odd integers, there are 4! possible lists, and since there are two even integers there are 2! lists, so in total you have 4! * 2! lists
Please help ASAP! Do not understand how to conduct problem!
Answer:
AB =-4 24 25
-5 15 15
BC= -5
4
10
2BC = -10
8
20
THE Operation AB -2BC cannot be performed because the unequality of the arrays
Step-by-step explanation:
AB=first row (3*2)+(1/2*0)+(5*-2), (3*-4)+(1/2*2)+(5*7), (3*0),(1/2*0),(5*5)
Second row ((1*1)+(-1*0)+(3*-2),(1*-4)+(-1*2)+(3*7), (1*0)+(-1*0)+(3*5)
AB =-4 24 25
-5 15 15
BC =FIRST ROW (1*1)+(-4*2)+(0*0)
SECOND ROW (0*1)+(2*2)+(0*0)
THIRSD ROW (-2*2)+(7*2)+(5*0)
BC= -5
4
10
2BC = -10
8
20
THE Operation AB -2BC cannot be performed because the unequality of the arrays
determining probability of events. please help!
Answer:
23/90
Step-by-step explanation:
55/90 + 12/90 = 67/9090 - 67 = 2323/9023/90 balls are green or white
i hope this helps!
Here is a sample distribution of hourly earnings in Paul's Cookie Factory:
Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15
Frequency 16 42 10
The limits of the class with the smallest frequency are:_________
A) $6.00 and $9.00.
B) $12.00 and up to $14.00.
C) $11.75 and $14.25.
D) $12.00 and up to $15.00.
Answer:
The correct answer is:
$12.00 and up to $15.00 (D)
Step-by-step explanation:
Let us arrange the data properly in a tabular format.
Hourly Earnings($) 6 - 9 9 - 12 12 - 15
Frequency 16 42 10
The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.
From the frequency table above the following observations can be made:
Highest frequency = 42 (hourly earnings of $9 - $12)
smallest frequency = 10 ( hourly earnings of $12 - $15)
This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority
John is a quarterback. This year, he completed 350passes, which is 70%of all the passes he's attempted this year.
How many passes has John attempted this year?
Answer:
500
Step-by-step explanation:
350/70%=500
If I set my alarm to read 8:10 when it is really 8:00 (i.e., it is 10 minutes fast) and the alarm goes off each day when it reads 8:10, it will be ___________ but not ___________.
Answer:
If I set my alarm to read 8:10 when it is really 8:00 (i.e., it is 10 minutes fast) and the alarm goes off each day when it reads 8:10, it will be reliable but not valid.
Step-by-step explanation:
If I set my alarm to wake me earlier than I need to be woken, it might be in order to give me enough time to adjust to the alarm, and be awake enough to get out of bed before the normal time I need to be out of bed. This method is very reliable, as there is a very little probability of me waking up late, since I have a 10 minutes head start everyday to get out of bed. The problem is that this method is not valid, since I now actually wake earlier than I am supposed to. The extra 10 minutes can actually lead to a disorientation with time.
Linda, Reuben, and Manuel have a total of $70 in their wallets. Reuben has $10 more than Linda. Manuel has 2 times what Linda has. How much does each have? Amount in Linda's wallet: $ Amount in Reuben's wallet: $ Amount in Manuel's wallet:
Answer:
Linda has $15Reuben has $25Manuel has $30Step-by-step explanation:
Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.
Linda has $15
Reuben has $25 . . . . . . $10 more than Linda
Manuel has $30 . . . . . . twice what Linda has
Give the null and alternative hypotheses in symbolic form that would be used in a hypothesis test of the following claim:
The mean time between "clicks" of the second hand on a particular clock is not 1 second.
a. H0: = 1 vs. H1: 1
b. H0: p = 1 vs. H1: p 1
c. H0: = 1 vs. H1:
d. none of these
Answer:
Step-by-step explanation:
The null hypothesis is usually the default statement. The alternative is the opposite of the null and usually tested against the null hypothesis
In this case study,
The null hypothesis in would be that the mean time between clicks of the second hand on a particular clock is 1 second. In symbolic form it would be u = 1
The alternative hypothesis would be that the mean time between clicks of the second hand on a particular clock is 1 not second. In symbolic form, it would be: u =/ 1
If the code for CAB is DEK, what is the code for BED?
Answer:
CIM
Step-by-step explanation:
C is the 3rd letter of the alphabet, A is the 1st, and B is the 2nd.
CAB = 3,1,2
Repeating for DEK:
DEK = 4,5,11
Comparing:
4−3 = 1
5−1 = 4
11−2 = 9
BED = 2,5,4, so adding the corresponding numbers:
2+1 = 3
5+4 = 9
4+9 = 13
So the code is CIM.
The code for BED is CIM. A further explanation is below.
As we know that,
"C" is the third letter of the alphabet"A" is the first letter of the alphabet."B" is the Second letter of the alphabet.then,
→ CIB = 3, 1, 2
Same as above,
→ DEK = 4, 5, 11
By comparing the values, we get
[tex]4-3 =1[/tex][tex]5-1 =4[/tex][tex]11-2 =9[/tex]Same as above,
→ BED = 2, 5, 4
then,
[tex]2+1=3[/tex][tex]5+4 =9[/tex][tex]4+9 =13[/tex]Thus the above approach is appropriate.
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Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4
Answer:
Step-by-step explanation:
We can solve each inequality apart and then see the possible solution sets.
Consider the inequality 4x+8 < -16. If we divide by 4 on both sides, we get
x+2 < -4. If we substract 2 on both sides we get x<-6. So the solution set for this inequality is the set of real numbers that are less than -6 (lie to the left of the point -6).
Consider 4x+8>4. If we divide by 4 on both sides we get x+2>1. If we substract 2 on both sides we get x>-1. So the solution set for this inequality is the set of real numbers that are bigger than -1 (lie to the right of the point -1).
So, for us to have 4x+8<-16 or 4x+8>4 we must have that either x <-6 or x>-1. So the solution set for the set of inequalities is the union of both sets, that is
[tex](\-infty, -6) \cup (-1,\infty)[/tex]
Which two statements describe domestic stocks? They are directly affected by exchange rate fluctuations. They are always traded in local currency. They are likely to be unfamiliar to investors. They are based in the investor’s country of residence. They form an important part of foreign trade.
Answer:
They are based in the investor’s country of residence
They are always traded in local currency.
Step-by-step explanation:
Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.
These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.
Answer
They are based in the investor’s country of residence
They are always traded in local currency.
Step-by-step explanation:
Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.
These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
The cycle times for a truck hauling concrete to a highway construction site are uniformly distributed over the interval 50 to 70 minutes.
Required:
What is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes?
Answer:
The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes, should be 1 / 3.
Step-by-step explanation:
It is known that the cycle times for a truck hauling concrete is uniformly distributed over a time interval of ( 50, 70 ). If c = cycle time, according to the question the probability that the cycle exceeds 65 minutes, respectively exceed 55 minutes should be the following - ' [tex]Probability( c > 65 | c > 55 )[/tex]. '
_____
[tex]f( c ) = \left \{ {{1 / 20,} \atop {0}} \right. \\50< c<70 - ( elsewhere )[/tex]
We know that the formula for Probability( A | B ) is P( A ∩ B ) / P( B ),
[tex]P( c > 65 | c > 55 ) =[/tex] [tex]P( c > 55[/tex] ∩ [tex]c > 65 )[/tex] / [tex]P( c > 55 )[/tex],
And now we come to the formula [tex]P( a < c < b )[/tex] = [tex]\int\limits^{70}_{65} {f(x)} \, dc[/tex]. Substitute known values to derive two solutions, forming a fraction that represents the probability we desire.
[tex]P( 65<c<70) = \int\limits^{70}_{65} {f(y)} \, dy\\ = \int\limits^{70}_{65} {(1/20)} \, dy\\ \\= 0.25[/tex]
-------------------------------------
[tex]P( 55<c<70) = \int\limits^{70}_{55} {f(y)} \, dy\\ = \int\limits^{70}_{65} {(1/20)} \, dy\\ \\= 0.75[/tex]
Take 0.25 over 0.75, 0.25 / 0.75, simplified to the fraction 1 / 3, which is our solution.
_____
Probability: 1 / 3
Find dw/ds using the appropriate Chain Rule for w=y^3-4x^2y where x=e^s and y=e^t, and evaluate the partial derivative at s=-3 and t=5 . Round your answer to two decimal places.
Answer:
-2.95
Step-by-step explanation:
Given the functions w=y^3-4x^2y where x=e^s and y=e^t, to get dw/ds, we will use the chain rule for composite functions as shown;
dw/ds = dw/dx*dx/ds + dw/dy*dy/ds
dw/dx = -8xy
dx/ds = e^s
dw/dy = 3y²-4x²
dy/ds = 0 (since there are no s variable in the function)
Substituting the differentials into the formula above;
dw/ds = -8xy(e^s) + 3y²-4x²(0)
dw/ds = -8xy(e^s)
Substituting s = -3 and t = 5 into the resulting function;
dw/ds = -8(e^s)(e^t)(e^s)
dw/ds = -8(e^2s)(e^t)
dw/ds = -8(e^-6)(e^5)
dw/ds = -8*0.00248*148.413
dw/ds = -2.945 ≈ --2.95 (to 2 dp)
Which results only in a horizontal compression of Y = by a factor of 6?
Answer:
Y = 6*y
Step-by-step explanation:
We have Y = b * y by a factor of 6.
That is, b = 6.
now, to find what results only in a horizontal compression of y = b * y by a factor of 6.
By transformation rule, the function would be a horizontal compression f (a * x) if a> 1.
Therefore, knowing the above, the answer would be:
Y = 6 * y