Solution :
Given :
[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]
1. Cumulative distribution function
[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]
[tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]
[tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]
[tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]
[tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]
[tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]
[tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]
2. Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]
[tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]
[tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]
[tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]
[tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]
[tex]$=\frac{1}{450} [4608 - 252]$[/tex]
= 17.2857
Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]
Answer:
[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
Step-by-step explanation:
[tex] (2 + i) \div (1 - 4i) = [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]
[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]
[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]
[tex] = \dfrac{2 + 9i - 4}{17} [/tex]
[tex] = \dfrac{-2 + 9i}{17} [/tex]
[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
what are the following proof triangle LMN equals triangle OPQ
Answer:
D. SSS
Step-by-step explanation:
Was given to us that the corresponding sides are congruent so is SSS.
Side Side Side Theorem tells us that if am the sides of a triangle are having the same measurement with the corresponding sides of another triangle then the two triangles are congruent.
the time it takes a runner to complete a race is inversely related to the speed of the runner if a runner can complete a race in 40 minutes while running at 8 mph how long will it take the runner to complete the race running at 9 mph t
stuck on this problem
Answer:
B
Step-by-step explanation:
When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.
B is the Answer
Answer:
c. switch the x-values and y-values in the table
Step-by-step explanation:
For any table or graph reflection over the line y=x
The rule is (x,y) ----> (y,x)
f(x) is reflected over the line y=x, so the coordinates of f(x) becomes
(-2,-31) becomes (-31,-2)
(-1,0) becomes (0,-1)
(1,2) becomes (2,1)
(2,33) becomes (33,2)
As per the rule, we switch the x-values and y-values in the table
For reflection over the line y=x , the coordinate becomes
(-31,-2)
(0,-1)
(2,1)
(33,2)
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.
Answer:
the operating characteristics have been solved below
Step-by-step explanation:
we have an average of 10 minutes per customers
μ = mean service rate = 60/10 = 6 customers in one hr
the average number of customers that are waiting in line
mean arrival λ = 2.5
μ = 6
[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]
= 6.25/21
= 0.2976
we calculate the average number of customers that are in the system
[tex]L=Lq+\frac{2.5}{6}[/tex]
= 0.2976+0.4167
= 0.7143
we find the average time that a customer spends in waiting
[tex]Wq=\frac{0.2976}{2.5}[/tex]
= 0.1190 hours
when converted to minutes = 0.1190*60 = 7.1424 minutes
[tex]0.1190+\frac{1}{6}[/tex]
=0.2857
probability that arriving customers would wait for the service
= 2.5÷6 = 0.4167
Sketch the graph of y = 2(x – 2)2 and identify the axis of symmetry
Answer:
x = 2
Step-by-step explanation:
The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
simplify 6 x + 3y /3
Answer:
6x + y
Step-by-step explanation:
6x + 3y/3
6x + y
Answer:
6x + y
Step-by-step explanation:
6x + 3y / 3
cancel 3y by 3
6x + y
Geometry Oddsseseyware
Restaurants sales totaled $38,676 for the week your customer count was $7,325 what did the average customer spend for the week
On a map of a town, 3 cm represents 150 m. Two points in the town are 1 km apart. How far apart are the two points on the map?
Answer:
5000 km
Step-by-step explanation:
We are given that
3 cm represents on a map of a town=150 m
Distance between two points=1 km
We have to find the distance between two points on the map.
3 cm represents on a map of a town=150 m
1 cm represents on a map of a town=150/3 m
1 km=1000 m
1 m=100 cm
[tex]1km=1000\times 100=100000 cm[/tex]
100000 cm represents on a map of a town
=[tex]\frac{150}{3}\times 100000[/tex] m
100000 cm represents on a map of a town=5000000 m
100000 cm represents on a map of a town
=[tex]\frac{5000000}{1000} km[/tex]
100000 cm represents on a map of a town=5000 km
Hence, two points are separated by 5000 km on the map.
Х/10 is between 1/5
and 0.6. What could the value of x be?
Answer:
2 < x < 6
Step-by-step explanation:
x/10
1/5 = 2/10
.6 = 6/10
2 < x < 6
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
What is the rate of change of the line on the graph
Answer:
A. ¼
Step-by-step explanation:
Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:
Where,
[tex] (4, 1) = (x_1, y_1) [/tex]
[tex] (-4, -1) = (x_2, y_2) [/tex]
Plug in the values
Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]
= [tex] \frac{-2}{-8} [/tex]
= [tex] \frac{1}{4} [/tex]
Rate of change = ¼
if y = k where k is a constant and y =24 when x =6 what is the value of y when x= 5
Answer:
20
Step-by-step explanation:
y=kx
24=6k
k=4
y=4*5=20
What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answer:
The length of MN is 4
Choose B
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
A(n) _____ is an expression that uses variables to state a rule.
plz help asap
Answer:
A FORMULA is an expression that uses variables to state a rule.
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 12 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 11.5.
Answer:
we conclude that population mean is not 11.5
Step-by-step explanation:
The hypothesis :
H0 : μ = 11.5
H1 : μ ≠ 11.5
The test statistic :
(xbar - μ) ÷ (s/√(n))
Test statistic = (12 - 11.5) ÷ (2/√(16))
Test statistic = (0.5) ÷ (2 ÷ 4)
Test statistic = 0.5 / 0.5
Test statistic = 1
The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15
Pvalue = 0.333
Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Answer:
4
Problem:
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Step-by-step explanation:
One approach would be to plug in the choices and see.
If n=1, then we have m^2-1=9.
This would give m^2=10 after adding 1 on both sides. There is no integer m when squared would give us 10. ( Square root of 9 is a decimal )
If n=16, then we would have m^2-256=9.
This would give m^2=265 after adding 256 on both sides. There is no integer m when squared would give us 265. ( Square root of 265 is a decimal )
If n=9, then we would have m^2-81=9.
This would give m^2=90 after adding 81 on both sides. There is no integer m when squared would give us 90. ( Square root of 90 is a decimal )
If n=4, then we would have m^2-16=9.
This would give m^2=25 after adding 16 on both sides. There is an integer m when squared would give us 25. ( Square root of 25 is a 5)
hello can anyone help with this?
Answer:
<2 and <13 are alternate exterior angles.
In simple form, alternate exterior angles are the opposite angle on the opposing parallel line. So, to make you understand better, <4 and <15 are alternate exterior angles.
Hope this helps :D
what is the difference between the products of the digits in 425 and the sum of the digits in the numeral 92784
Answer: 10
Step-by-step explanation:
4 x 2 x 5 = 40
9 + 2 + 7 + 8 + 4 = 30
40 - 30 = 10
= 10
Can someone help me out?
Answer:
Terms:
-5x4-x-1Like Terms:
-5x and -x4 and -1Coefficients:
The coefficient of -5x is -5.The coefficient of -x is -1.Constants:
4-1You simplify the expression by combining like terms:
-5x + 4 - x - 1 = -6x + 5
(7b - 4) + (-2b + a + 1) = 7b - 4 - 2b + a + 1 = 5b + a - 3
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 73% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA test until the first pass. (Assume the trials are independent).
(a) What is the probability that Cathy passes the CPA test on the first try?
(b) What is the probability that Cathy passes the CPA test on the second or third try?
Answer:
The responses to these question can be defined as follows:
Step-by-step explanation:
For point a:
[tex]\to P(1) = 0.73[/tex]
For point b:
[tex]\to P(2\ or\ 3) = P(2) + P(3)[/tex]
[tex]= 0.27 \times 0.73 + 0.27\times 0.27\times0.73\\\\=0.1971+0.1971\times 0.27\\\\=0.1971+0.053217\\\\=0.250317[/tex]
the campus bookshop sells exercise books and textbooks, where, the total cost of 10 exercise books and 2 textbooks is $1400.00. One also finds the total cost of 3 textbooks and 30 exercise books is $3000. Then determine the price of 1 exercise book?
Answer:
The price of 1 exercise book is $122.45.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the price of one exercise book.
y is the price of one textbook.
Total cost of 10 exercise books and 2 textbooks is $1400.00.
This means that:
[tex]10x + 2y = 1400[/tex]
Since we want x:
[tex]2y = 1400 - 10x[/tex]
[tex]y = 700 - 5x[/tex]
One also finds the total cost of 3 textbooks and 30 exercise books is $3000.
This means that:
[tex]3x + 30y = 3000[/tex]
Since [tex]y = 700 - 5x[/tex]
[tex]3x + 30(700 - 5x) = 3000[/tex]
[tex]3x + 21000 - 150x = 3000[/tex]
[tex]147x = 18000[/tex]
[tex]x = \frac{18000}{147}[/tex]
[tex]x = 122.45[/tex]
The price of 1 exercise book is $122.45.
Young invested GH150,000 and 2.5% per annum simple interest. how long will it take this amount to. yield an interest of GH11,250,00
Answer: 3 years
Step-by-step explanation:
Interest is calculated as:
= (P × R × T) / 100
where
P = principal = 150,000
R = rate = 2.5%.
I = interest = 11250
T = time = unknown.
I = (P × R × T) / 100
11250 = (150000 × 2.5 × T)/100
Cross multiply
1125000 = 375000T
T = 1125000/375000
T = 3
The time taken will be 3 years
Prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
Please help!! How do I solve for x?
The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.
2(x-3) = x + 6
Simplify:
2x -6 p x + 6
Add 6 to both sides
2x = x + 12
Subtract x from both sides:
X = 12
The answer is B) 12
SOMEONE PLS HELP ME I WILL MAKE U BRAINLIST ! In a survey sample of 83 respondents, about 30.1 percent of the samplework less than 40 hours per week. What is the estimated standard error for the group of respondents who work 40 hours or more per week?
(*round to two decimal places)
Answer:
Answer = √(0.301 × 0.699 / 83) ≈ 0.050
A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)
Step-by-step explanation:
√(0.301 × 0.699 / 83) ≈ 0.050
We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of as . A confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351). is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.
Hope this answer helps you :)
Have a great day
Mark brainliest
How do I make people brainliest
Answer:
you have to wait until two people answer then you click their answer to make them brainliest
Step-by-step explanation:
i dont know
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