Answer:
Step-by-step explanation:
Given that:
[tex]f_x = \dfrac{x^2}{a^7-x^7}[/tex]
[tex]= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}[/tex]
[tex]= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}[/tex]
since [tex]\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)[/tex]
Then, it implies that:
[tex]\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}[/tex]
[tex]\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}[/tex]
Compute ????×????, where ????=????−2????+5????, ????=2????+????+3????. (Write your solution using the standard basis vectors ????, ????, and ????. Use symbolic notation and fractions where needed.)
Given: ????=????−2????+5????
and ????=2????+????+3????
To find: We need to find the value of ????×????
Solution: Here given,
????=????−2????+5????
and ????=2????+????+3????
Therefore, solving these two we have, ????=0
So,????×????=0
What is the inverse of function f? f(x)=10/9+11
Answer:
Option D is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = 10/9 X + 11
Let f(X) be "y".
y = (10/9) X + 11
Interchange "X" and "y".
x = (10/9) y + 11
or, 9x = 10y + 99
or, y = (9x-99)/10
Therefore, f'(X) = (9x-99)/10.
Hope it helps!
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
Which point represents the unit rate?
A
B
C
D
Answer:
Point C represents the unit rate
Step-by-step explanation:
Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score
Answer:
Mean scores.
Step-by-step explanation:
The golf player will score in the first round, according to these scores the golf player scores can be predicted. The golf player can perform high in first round but he may score lesser in the second round due to stress or mental pressure. The scores can be predicted taking mean of the scores and adding standard deviation to it.
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
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
Julie and Mona know that that Earth’s average distance from the Sun is approximately 93 million miles and it takes 1 year to complete an orbit of the Sun. A new asteroid has been discovered orbiting the Sun at an average distance of 1,488 million miles. How long will it take for the asteroid, in Earth years, to complete one orbit of the Sun.
Answer:
16 years
Step-by-step explanation:
Given that :
Earth's distance from sun = 93 million miles
Number of years to complete an orbit = 1 year
Average orbiting distance of new asteroid = 1488 million miles
Number of years to complete an orbit = x
93,000,000 Miles = 1
1488000000 miles = x
Cross multiply :
93000000x = 1488000000
x = 1488000000 / 93000000
x = 16 years
Period taken to orbit the sun = 16 years
Answer: 64 Earth years...
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]
can anyone help with this please !!!!
Answer:
"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
Step-by-step explanation:
Let be the following system of linear equations:
[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)
[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)
[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)
1) We eliminate [tex]y[/tex] by adding (1) and (2):
[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]
[tex]6\cdot x +2\cdot z = 24[/tex] (4)
2) We eliminate [tex]y[/tex] by adding (1) and (3):
[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]
[tex]9\cdot x -4\cdot z = 36[/tex] (5)
Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
A little help?? It’s trig
Answer:
12 [tex]\pi[/tex] = 37.699 f/s
Actually, the more interesting question
would have been how fast is the ball going in MPH?
25.7 MPH
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2 [tex]* \pi * 1.2[/tex]
C = 2.4 [tex]\pi feet[/tex]
C (per second) = (5)(2.4 [tex]\pi feet[/tex])
C(per second) = 12 [tex]\pi[/tex] = 37.699 f/s
In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?
Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
If 3 3/4m of cloth was used for one suit, how many suits can be made with 30m cloth
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
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
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
A rectangular prism has a volume of 60cm^3. What could the length, width and
height be? Explain how you know. "Recall, the formula for the volume of a prism
is V=lwh.
Can you guys help
One number is 1/4 of another number. The sum of the two numbers is 5. Find the two numbers. Use a comma to separate your answer
Answer: 1, 4
Step-by-step explanation:
Number #1 = xNumber #2 = [tex]\frac{1}{4} x[/tex][tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]
Number #1 = x = 4Number #2 = [tex]\frac{1}{4} x[/tex] = [tex]\frac{1}{4} *4=\frac{4}{4} =1[/tex]Find the value of x in each case
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
Adam borrowed $5,600 from the bank. The bank charges 4.2% simple interest each year.
Which equation represents the amount of money in dollars, x, Adam will owe in one year, if no payments are made?
x=5,600+5,600(42)(12)
x=5,600+5,600(0.042)(1)
x=5,600+5,600(42)(1)
x=5,600+5,600(0.042)(12)
Answer:
[tex]x = 5600 + 5600 * 0.042 * 1[/tex]
Step-by-step explanation:
Given
[tex]P = 5600[/tex] -- Principal
[tex]R = 4.2\%[/tex] -- Rate
[tex]T = 1[/tex] -- Time
Required
The amount (x) to be paid
This is calculated as:
[tex]x = P + I[/tex]
Where:
[tex]I = PRT[/tex]
So, we have:
[tex]x = 5600 + 5600 * 4.2\% * 1[/tex]
Express percentage as decimal
[tex]x = 5600 + 5600 * 0.042 * 1[/tex]
(c) is correct
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
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
write the equation of the line shown in the graph above in slope-intercept form
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.
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a standard deviation of 118. Determine the 26th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
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.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that [tex]\mu = 1262, \sigma = 118[/tex]
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.643 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.643*118[/tex]
[tex]X = 1186[/tex]
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -1.96*118[/tex]
[tex]X = 1031[/tex]
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 1.96*118[/tex]
[tex]X = 1493[/tex]
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.675*118[/tex]
[tex]X = 1182[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 0.675*118[/tex]
[tex]X = 1342[/tex]
IQR:
1342 - 1182 = 160
. A small home business is set up with an investment of Birr 1,000,000 for equipment. The business manufactures a product at a cost of Birr 60 per unit. If the product sells for Birr 140, how many units must be sold before the business breaks even?
Answer:
12,500
Step-by-step explanation:
P = R-E
b.e.p : P=0
R=E
140x = 1000000 + 60 x
80x = 1000000
x=12,500
The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test them out. A number of the club's fastest swimmers performed a 50m freestyle swim in a regular spandex bodysuit and in a Speedo Fastskin suit. The table below summarizes their times in seconds.Swimmer Spandex Speedo Fastskin1 31.1 29.12 28.9 30.43 31.4 32.04 34.9 31.75 27.7 28.26 36.7 32.97 33.3 28.68 30.8 26.2Perform a t-test for dependent means to determine if there is a difference between the regular spandex suit and the Fastskin bodysuit in terms of performance.t = _____df = _____Critical value of t = _____ (use alpha = 0.05)Would you reject the null hypothesis?
Answer:
T = 2.215
df = 7
Critical value = 2.364
Fail to reject the null
Step-by-step explanation:
Swimmer __Spandex __Speedo Fastskin__ d
1 __________31.1 _______29.1 __ 2
2_________ 28.9 ______30.4 __ -1.5
3_________ 31.4 ______ 32.0 __ - 0.6
4_________ 34.9 ______31.7 __ 3.2
5 _________27.7 ______28.2 __ - 0.5
6_________ 36.7 _____ 32.9 ___ 3.8
7 _________ 33.3 _____28.6 ___ 4.7
8_________ 30.8 _____26.2 ___ 4.6
The mean difference = Σd / n
2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6
μd = Σd / n = 15.7 / 8 = 1.9625
Sd = standard deviation of difference = 2.5065 (using calculator)
H0 : μd = 0
H1 : μd ≠ 0
The test statistic:
T = μd / (Sd/√n)
T = 1.9625 / (2.5065/√8)
T = 2.2145574
The degree of freedom, df = n - 1 = 8 - 1 = 7
Using a Pvalue calculator :
α = 0.05
Critical value, Tcritical = 2.364 (T distribution table)
Since Test statistic < Critical value
we fail to reject H0 ;
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
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
9514 1404 393
Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
