Answer:
probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)
=194/285 or 0.6807.
Step-by-step explanation:
The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.
The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.
Hence
|E'| = C(14,3)
= 14×13×12/3!.
Therefore probability P(E')
= |E'|/|S|
= (14×13×12)/(20×19×18)
= (14×13×2)/(20×19×3)
=(7×13)/(5×19×3)
= 91/285.
Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.
The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities
a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?
Solution :
a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= [tex]$(1-0.75)^3 \times 0.75$[/tex]
= 0.01171875
b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
[tex]$E(X)=\frac{k}{p}$[/tex]
[tex]$=\frac{6}{0.75}$[/tex]
= 8
So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]
[tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]
= 1.6330
The work of a student to solve a set of equations is shown:
Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z
Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3
In which step did the student first make an error?
Step1
Step 2
Step 3
Step 4
Step 2
−2y = 15 − 2z
should be
−2y = -30 + 4a
Help! I need help with these two questions (10 points each!)
Answer:
see image...
the (x-h) shifts the curve left right (east west)
and the +k at the end shifts it up/down (north/south)
Step-by-step explanation:
Find the largest factor of 2520 that is not divisible by 6.
if for men working for hours for 4 days complete for unit of work then how many unit of work will be completed by two men working for two hours per day?
The 2 men working for 2 hours per 2 days will complete 1/2 unit of work. This is calculated by using the proportions formula.
What is the formula for calculating equal proportions?The formula for the given proportions is,
a: b = c: d
⇒ a/b = c/d
⇒ ad = bc
In this way, the required variable is calculated.
Calculation:For the given question, the proportion we can write
M1 × H1 × D1: M2 × H2 × D2 = W1: W2
⇒ M1 × H1 × D1 × W2 = M2 × H2 × D2 × W1
Where M1 = 4; H1 = 4; D1 = 4; M2 = 2; H2 = 2; D2 = 2 and W1 = 4
We need to calculate W2 - required units of work
So, on substituting,
M1 × H1 × D1 × W2 = M2 × H2 × D2 × W1
⇒ 4 × 4 × 4 × W2 = 2 × 2 × 2 × 4
⇒ 64 × W2 = 32
⇒ W2 = 32/64
∴ W2 = 1/2
Thus, the required units of work are 1/2.
So, 2 men working for 2 hours for 2 days will complete 1/2 unit of work.
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Disclaimer: The given question is incomplete. Here is the complete question.
Question: If 4 men working for 4 hours for 4 days complete 4 units of work then how many unit of work will be completed by two men working for two hours per 2 days?
This table shows how many male and female students attended two different
movies.
What is the probability that a randomly chosen person from this group is male
and attended an action movie?
Round your answer to two decimal places.
Action
Drama
Total
Mala
105
124
229
Female
99
151
250
Total
204
275
479
A. 0.11
B. 0.43
Ο Ο Ο Ο
C. 0.22
D. 0.52
Answer:
Male & action movie among a group of total 479
Step-by-step explanation:
We only choose male from action movie category so:
p = 105/ 479 = 0.22
The probability that a randomly chosen person from this group is male and attended an action movie will be 0.22. Then the correct option is C.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
This table shows how many male and female students attended two different movies.
Action Drama Total
Mala 105 124 229
Female 99 151 250
Total 204 275 479
Then the probability that a randomly chosen person from this group is male and attended an action movie will be
Favorable event = 105
Total event = 479
Then the probability will be
P = 105 / 479
P = 0.219
P ≈ 0.22
Then the correct option is C.
More about the probability link is given below.
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Solve for X: A=2B/x+3
the answer is 2B divided by A minus 3
Question 3 of 10
Which angle in ABC has the largest measure?
2
С
A
B.
C.
D. Cannot be determined
Answer:
Step-by-step explanation:
C
heSellsSeaShells is an ocean boutique offering shells and handmade shell crafts on Sanibel Island in Florida. Find the price SheSellsSeaShells should charge to maximize revenue if p(x)=160−2xp(x)=160−2x, where p(x)p(x) is the price in dollars at which xx shells will be sold per day.
Answer:
it's too much for me im a child u know
Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
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Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
I need to know the answer ASAP thank you
Answer:
Step-by-step explanation:
From a club of 24 people, in how many ways can a group of four members be selected to attend a conference?
Answer:
255,024
Step-by-step explanation:
24 x 23 x 22 x 21
24 options for the first member
23 options for the second member
22 options for the third member
21 options for the last member
Which best describes the process of selecting a cluster sample?
Clusters that each represent the population are sampled from such that no two members of the same cluster are included in the sample.
Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample.
Members of a population are ordered by some characteristic, and then a cluster sample is formed by selecting every kth member.
Members of a population are separated into clusters based on a characteristic important to the study and a random sample is selected from each cluster.
Answer:
"Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample"
Step-by-step explanation:
In cluster random sampling, "the population is divided, usually geographically, into groups that generally have the same size. A certain number of groups are randomly chosen, and every individual in the chosen groups are chosen for the sample."
In accord with this logic, the second choice, "Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample" seems to be correct.
NOTE: This may not be the correct answer. I am simply basing my answer on the definition I have learnt.
Answer:
B
Step-by-step explanation:
Hey guys not good at math please help
Answer:
3/2
Step-by-step explanation:
Recall that slope is y2 - y1 / x2 - x1.
Excellent. The question provides us with two points: (2,4) and (0,1). We can insert these two points into our equation.
Slope = (4 - 1) / (2 - 0) = 3 / 2.
Hope this helps!
Answer:
3/2
Step-by-step explanation:
(0,1) and (2,4)
(y2-y1)/(x2-x1)
= (4-1)/(2-0)
=3/2
Answered by GAUTHMATH
A heating pad takes 8,827 Watts during each time it is turned on. If you only use it for 43 minutes, how much CO2 was created? Round to 1 decimal.
Answer:
6.3 Kwhr
Step-by-step explanation:
Given :
Power = 8827 watts
Time in minutes = 43 minutes
To obtain the amount of CO2 that was created :, which is the energy :
Recall
Energy = power * time
Energy in kw/hr = (8827/100) * (43/60)
Energy = 8.827 * 0.7166666
Energy = 6.326 Kwhr
Plz help
Need answers ASAP
Answer:
1. cube
2. square pyramid
4. cone
5. cube
The median age (in years) of the U.S. population over the decades from 1960 through 2010 is given by
f(t) = −0.2176t3 + 1.962t2 − 2.833t + 29.4 (0 ≤ t ≤ 5)
where t is measured in decades, with t = 0 corresponding to 1960.
(a) What was the median age of the population in the year 1970?
(b) At what rate was the median age of the population changing in the year 1970?
(c) Calculate f ''(1).
Considering the given function, we have that:
a) 28.31 years.
b) 0.3382 years a decade.
c) 2.6184.
What is the function?The median age of the U.S. population in t decades after 1960 is:
f(t) = -0.2176t³ + 1.962t² - 2.833t + 29.4.
1970 is one decade after 1960, hence the median was:
f(1) = -0.2176 x 1³ + 1.962 x 1² - 2.833 x 1 + 29.4 = 28.31 years.
The rate of change was is the derivative when t = 1, hence:
f'(t) = -0.6528t² + 3.924t - 2.933
f'(1) = -0.6528 x 1² + 3.924 x 1 - 2.933 = 0.3382 years a decade.
The second derivative is:
f''(t) = -1.3056t + 3.924
Hence:
f''(1) = -1.3056 x 1 + 3.924 = 2.6184.
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Which sequence is arithmetic?
O 2, 6, 18, 54, ...
O 3, 6, 12, 24, ...
O 11, 14, 17, 20, ...
O 7, 11, 13, 18, ...
Answer:
11, 14, 17, 20, ...
Step-by-step explanation:
An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.
terms are there. Divide 51 into three parts in AP so that the largest exceeds the smallest by 10.
The first three terms of the Arithmetic Progression are 12, 17 and 22.
For an ARITHMETIC PROGRESSION, AP ;
First term = a
Second term = a + d
Third term = a + 2d
Where, d = common difference ;
If third term exceeds smallest by 10 ;
Third term - first term
a + 2d - a = 10
2d = 10
d = 10/2
d = 5
Sum of the three terms :
a + (a + d) + a + 2d = 51
3a + 3d = 51
d = 5
3a + 3(5) = 51
3a + 15 = 51
3a = 51 - 15
3a = 36
a = 12
The AP would be:
First term, a = 12
Second term, a + d = 12 + 5 = 17
Third term = a + 2(d) = 12 + 10 = 22
Therefore , the first three terms of the AP are :
12, 17 and 22
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The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms. Statistical analysis of the output suggests that the resistances can be approximated by a normal distribution with known standard deviation of 0.005 ohms. We are interested in testing the hypothesis that the resistors conform to the specifications.
Requied:
a. Determine whether a random sample of 10 resistors yielding a sample mean of 0.152 ohms indicates that the resistors are conforming. Use alpha = 0.05.
b. Calculate a 95% confidence interval for the average resistance. How does this interval relate to your solution of part (a)?
Answer:
a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Step-by-step explanation:
Question a:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.
At the null hypothesis, we test if this is the average resistance, that is:
[tex]H_0: \mu = 0.15[/tex]
We are interested in testing the hypothesis that the resistors conform to the specifications.
At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:
[tex]H_1: \mu \neq 0.15[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.15 is tested at the null hypothesis:
This means that [tex]\mu = 0.15[/tex]
Sample mean of 0.152, sample of 10, population standard deviation of 0.005.
This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]
[tex]z = 1.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.
Looking at the z-table, z = -1.26 has a p-value of 0.1038.
2*0.1038 = 0.2076
The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
Question b:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.
The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.
The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Help me please and thank you
Answer:
Option C is correct
Step-by-step explanation:
[tex]log( {10}^{3} )[/tex]
Use logarithm rules to move 3 out of the exponent.[tex]3 \: log \: (10)[/tex]
Logarithm base 10 of 10 is 1.[tex]3×1[/tex]
Multiply 3 by 1.[tex]3[/tex]
Hope it is helpful....Which of the following is the graph of…
Answer:
A
Step-by-step explanation:
Try graphing the function on desmos
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
both angles are 90 degrees
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
Quick Test
7. After 12% discounts, the price of a car is RM 44,000. What is the original price?
A. RM 52,800
B. RM 38,720
C. RM 49,280
D. RM 50,000
8. Find the interest on RM 2,800 if the rate is 5% for 4 years.
A. RM 500
B. RM 660
C. RM 460
D. RM 560
9. Find the net price of an item with a list price of RM 80.00 and a trade discount of 12%
A. RM 69.50
B. RM 57.70
C. RM 70.50
D. RM 70.40
10. The price of a hard drive is RM 215. If Andrew is given 6% discounts, find the mark down
amount.
A. RM 202.10
B. RM 86.00
C. RM 129.00
D. RM 12.90
Answer:
number 7 the answer is 50,000
Solve for x then measure to find A
Answer:
[tex]125 \: \: degrees[/tex]
Step-by-step explanation:
As the 2 lines are parallel
<A = <B ( Alternative Angles)
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = 20[/tex]
[tex]<A = 6x + 5 \\ = 6 \times 20 + 5 \\ = 120 + 5 \\ = 125[/tex]
<A=6x+5
=6×20+5
=120+5
=125
<B=4x+45
=4×20+45
=80+45
=125
it is alternate angle they are equal each other
<A = < B
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20 \\ \\ [/tex]
tìm m để đồ thị hàm số y=x^4-2mx^2+1 cắt trục hoành tại 4 điểm phân biệt
Answer:
Step-by-step explanation:
Tìm cc
Henry bought 2 kilograms of chicken for a family dinner. After dinner, only 61.5 grams were left. How much chicken was eaten, in kilograms?
Answer:
1.9385 kg
Step-by-step explanation:
Given :
Total kilogram of chicken = 2 kilograms
Amount left after dinner = 61.5 gram
Recall :
1000 grams = 1 kilogram
Hence,
61.5 grams = x kg
x = (61. 5 / 1000) = 0.0615 kg
Hence,
Amount eaten = Total chicken - amount left
Amount eaten = (2 - 0.0615) kg
Amount eaten = 1.9385 kg
Help? I need to simplify
Answer:
x=0
Step-by-step explanation
I think that's what you're looking for :l/
Manish writes the functions g(x)= 3 sqrt -x - 72 and h(x) = -(x + 72)^3
Which pair of expressions could Manish use to show that g(x) and h(x) are inverse functions?
Answer:
[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]
Step-by-step explanation:
Given
[tex]g(x) = 3\sqrt x - 72[/tex]
[tex]h(x) = -(x +72)^3[/tex]
Required
Show that they are inverse functions
For g(x) and h(x) to be inverse, then:
[tex]g(h(x)) = h(g(x))[/tex]
We have:
[tex]g(x) = 3\sqrt x - 72[/tex]
Replace x with h(x)
[tex]g(h(x)) = 3\sqrt{h(x)} - 72[/tex]
Substitute value for h(x)
[tex]g(h(x)) = 3\sqrt{-(x +72)^3} - 72[/tex]
Similarly;
[tex]h(x) = -(x +72)^3[/tex]
Replace x with g(x)
[tex]h(g(x)) = -(g(x) +72)^3[/tex]
Substitute value for g(x)
[tex]h(g(x)) = -(3\sqrt x - 72 +72)^3[/tex]
Recall that:
[tex]g(h(x)) = h(g(x))[/tex]
So:
[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]
Its c
explanation:
on edge
