Answer:
Tom:
initial money = $ 39000
% increased per annum = 2.9%
money gained per annum = 39000 * 2.9/100 = $1131
Allen:
initial money = $ 39000
% increased per annum = 5.7 %
money gained per annum = 39000 * 5.7/100 = $2223
Allen has $ (2223 - 1131) = $ 1192 more than Tom
The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.
Answer:
a
The null hypothesis is [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]
The alternative hypothesis [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]
b
The 95% confidence interval is [tex]27.475 < \mu < 37.925[/tex]
Step-by-step explanation:
From the question the we are told that
The population mean is [tex]\mu = 35.1 \ million \ shares[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = 32.7 \ million\ shares[/tex]
The standard deviation is [tex]\sigma = 14.6 \ million\ shares[/tex]
Given that the confidence level is [tex]95\%[/tex] then the level of significance is mathematically represented as
[tex]\alpha = 100-95[/tex]
[tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]
[tex]E = 5.225[/tex]
The 95% confidence interval confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]
[tex]27.475 < \mu < 37.925[/tex]
When you enter the Texas Turnpike, they give you a ticket showing the time and place of your entry. When you exit, you turn in this ticket and they use it to figure your toll. Because they know the distance between toll stations, they can also use it to check your average speed against the turnpike limit of 65 mph. On your trip, heavy snow limits your speed to 40 mph for the first 120 mi. At what average speed can you drive for the remaining 300 mi without having your ticket prove that you broke the speed limit?
Answer:
87 mph
Step-by-step explanation:
Total distance needed is 120 mi + 300 mi and that is 420 mi.
Driving at 65 mph means that it would take
420 / 65 hours to reach his destination.
6.46 hours .
at the first phase, he drove at 40 mph for 120 mi, this means that it took him
120 / 40 hours to complete the journey.
3 hours.
the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of
6.46 - 3 hours = 3.46 hours.
300 mi / 3.46 hours => 86.71 mph approximately 87 mph
Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit
Yiadom is y
years now.
What would be
his age in the next ten
years.
Answer:
(y+10 ) years
Step-by-step explanation:
If Yiadom is y years now.
Then after 10 years, his anew age will be = (y+10) yrs
what number should be added to -5/8 to get -3/2
Answer:
-7/8
Step-by-step explanation:
-5/8+x=-3/2
x= -3/2+5/8=-12/8+5/8= -7/8
How can you add, subtract and multiply with decimals
Lets Take two decimals 1.01 and 2.32
Addition:-
[tex]\\ \sf\longmapsto 1.01+2.32[/tex]
[tex]\\ \sf\longmapsto \dfrac{101}{100}+\dfrac{232}{100}[/tex]
[tex]\\ \sf\longmapsto \dfrac{333}{100}[/tex]
[tex]\\ \sf\longmapsto 3.33[/tex]
Subtraction:-
[tex]\\ \sf\longmapsto 2.32-1.01[/tex]
[tex]\\ \sf\longmapsto \dfrac{232}{100}-\dfrac{101}{100}[/tex]
[tex]\\ \sf\longmapsto \dfrac{131}{100}[/tex]
[tex]\\ \sf\longmapsto 1.31[/tex]
Multiplication:-
[tex]\\ \sf\longmapsto 1.01\times 2.32[/tex]
[tex]\\ \sf\longmapsto \dfrac{101}{100}\times \dfrac{232}{100}[/tex]
[tex]\\ \sf\longmapsto \dfrac{23432}{10000}[/tex]
[tex]\\ \sf\longmapsto 2.3432[/tex]
Determine the slope of the line passing through the points (0,-3) and (3,-11).
Answer:
-3/8
Step-by-step explanation:
Hey there!
Well to find the slope with 2 points “(0,-3) and (3,-11)”, we’ll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
Plug in the given points.
[tex]\frac{-11 - - 3}{3-0}[/tex]
-11 + 3 = -8
3 - 0 = 3
Slope = -8/3
Hope this helps :)
If y = 4x -2, what are possible inputs and outputs of the function?
Complete the ordered pairs:
(0, __)
(-2, __)
(___, 14)
(___, -14)
Graph the data, what type of function is it?
Answer:
(0,-2), (-2,-10), (4,14), (-3,-14)
Step-by-step explanation:
y(0)=-2, y(-2)=-10, y(x) = 14 so x=16/4=4, y(x) = - 14, x=-12/4=-3.
If X = 4 and y = -2, the value of 1/2 xy^2 is
Answer:
[tex]8[/tex]
Step-by-step explanation:
Note that 1/2 xy^2 is, by order of operations, read as [tex]\frac12xy^2[/tex]. If this is not what was intended in the question then please amend it according order of operations.
Plugging the values [tex]x=4[/tex] and [tex]y=-2[/tex] gives
[tex]\frac12xy^2=\frac12(4)(-2)^2=\frac12(4)(4)=\frac12(16)=8[/tex]
I need all the steps
Answer:
ig
Step-by-step explanation:
[tex](9-\sqrt{-8} )- (5 + \sqrt{-32} ) \\(9-5) + (-\sqrt{-8}- \sqrt{-32} )\\4 - \sqrt{-8} -\sqrt{-32} \\4-2i\sqrt{2} -4i\sqrt{2} \\4-6i\sqrt{2}[/tex]
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 6.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.0 minutes.
Answer: P(X<6) = 0.3085 or 30.85%
Step-by-step explanation: Determine, first, z-score:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
x is a random variable for time a student takes to find a spot, in this case, x=6:
[tex]z = \frac{6-6.5}{1}[/tex]
z = -0.5
Using z-score table, find z-score:
P(X<6) = P(z< -0.5)
P(X<6) = 0.3085
Probability of finding a parking spot in less than 6 minutes is approximately 30.85%.
Given these four points: A(3, 3), B(−5, 7), C(2, 11), and D(9, −2), find the coordinates of the midpoint of line segments AB and CD.
Midpoint formula: (x1 + x2)/2 , (y1 + y2)/2
Midpoint AB = (3 +-5)/2, (3 + 7)/2 = -2/2 , 10/2 = (-1,5)
Midpoint CD = (2 +9)/2, (11 + -2)/2 = (11/2,9/2)
What is the eighth term in the sequence 4, 8, 12, 16, 20…?
Answer:
32
Step-by-step explanation:
The pattern is multiples of 4
The 8 term will be the 8 multiple of 4
4 * 8 = 32
Answer:
32
Step-by-step explanation:
We are adding 4 each time
an = a1+d(n-1)
an = 4+4(n-1)
we want the 8th term
a8 = 4+4(8-1)
a8 = 4+4(7)
a8 = 4+28
a8 = 32
The daily production of electronic motors at a certain factory averaged 120 with a variance of 100. The fraction of days that will have production levels between 100 and 140 assuming doubt about the normality of the data is
On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M? (–10, 0) (–6, 2) (0, –6) (8, –10)
Answer:
The point that lies on the line parallel to line KL would be ( 8, - 10 )
Step-by-step explanation:
Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).
Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.
Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),
( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3
Slope of respective Parallel line : - 2 / 3,
Another point on Parallel line : ( 8, - 10 )
How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.
( y₂ - y₁ ) / ( x₂ - x₁ ),
( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3
And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.
Answer:
D
Step-by-step explanation:
A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
= 18.2 miles per hour
Step-by-step explanation:
Speed = distance / time
=82 miles / 4.5 hours
=18.22222222 miles per hour
Rounding
= 18.2 miles per hour
Answer:
Given that
Distance = rate × time
82 = r × 4½
r = 18.2 mph
i need help really bad
Answer:
see explanation
Step-by-step explanation:
If f(x) and [tex]f^{-1}[/tex] are inverse functions, then
f([tex]f^{-1}[/tex])(x) = x
Thus substitute x = [tex]f^{-1}[/tex] (x) into f(x)
f([tex]\frac{x+6}{5}[/tex] )
= 5 ([tex]\frac{x+6}{5}[/tex] ) - 6
= x + 6 - 6
= x
Thus f(x) and [tex]f^{-1}[/tex] (x) are inverse functions
What is the equation of the following graph?
Answer:
y=0.5x + 5
Step-by-step explanation:
The points are (0,5) and (-10,0)
to find the slope do
0-5/-10-0 = 5/10 = 1/2 = 0.5
next plug one of the points into point slope formula
y-y1=m(x-x1)
lets use the point (-10,0)
y1=0
x1= -10
m= 0.5
y-0=0.5(x- -10)
y = 0.5(x+10)
distribute the 0.5
y=0.5x+5
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
I just answered it
Step-by-step explanation:
You are an assistant director of the alumni association at a local university. You attend a presentation given by the university’s research director and one of the topics discussed is what undergraduates do after they matriculate. More specifically, you learn that in the year 2018, a random sample of 216 undergraduates was surveyed and 54 of them (25%) decided to continue school to pursue another degree, and that was up two percentage points from the prior year. The Dean of the College of Business asks the research director if that is a statistically significant increase. The research director says she isn’t sure, but she will have her analyst follow up. You notice in the footnotes of the presentation the sample size in the year of 2017 was 200 undergraduates, and that 46 of them continued their education to pursue another degree.
There is a short break in the meeting. Take this opportunity to answer the dean’s question using a confidence interval for the difference between the proportions of students who continued their education in 2018 and 2017. (Use 95% confidence level and note that the university has about 10,000 undergraduate students).
Answer:
(0.102, -0.062)
Step-by-step explanation:
sample size in 2018 = n1 = 216
sample size in 2017 = n2 = 200
number of people who went for another degree in 2018 = x1 = 54
number of people who went for another degree in 2017 = x2 = 46
p1 = x1/n1 = 0.25
p2 = x2/n2 = 0.23
At 95% confidence level, z critical = 1.96
now we have to solve for the confidence interval =
[tex]p1 -p2 ± z*\sqrt{((1-p1)*p1)/n1 + ((1-p2)*p2/n2}[/tex][tex]0.25 -0.23 ± 1.96*\sqrt{((1 - 0.25) * 0.25)/216 + ((1 - 0.23) *0.23/200}[/tex]
= 0.02 ± 1.96 * 0.042
= 0.02 + 0.082 = 0.102
= 0.02 - 0.082 = -0.062
There is 95% confidence that there is a difference that lies between - 0.062 and 0.102 on the proportion of students who continued their education in the years, 2017 and 2018.
There is no significant difference between the two.
what is Collatz conjecture?
Is Collatz conjecture always true?
What so special about 3x+1 ?
Answer:
Step-by-step explanation:
The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.
Simply put it says
if a number is even, divide by 2If a number is odd, multiply by 3 and add1. or 3x + 1The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.Try 5
It's odd so triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2. You get 22 is even. Divide by 2. You get 11 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.
Take 15It's odd. Triple it and add 1. That gives 46.46 is even. Divide by 223 which is odd. Triple it and add 1 = 7070 is even. Divide by 2. 3535 is odd. Triple and add 1. 106 which is even53 which is odd. Triple it and add 1. You get 160160 is even. Divide by 2. You get 8080 is even Divide by 2. You get 4040 is even. Divide by 2. You get 2020 is even. Divide by 2. You get 1010 is even. Divide by 2. You get 55 is odd. Triple it and add 1. You get 1616 is even. Divide by 2. You get 88 is even. Divide by 2. You get 44 is even. Divide by 2.. You get 2.2 is even. Divide by 2. You get 11 is odd and you are in the loop because you get 4 which you have already done.A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes. Data are below:
Treatment 1: 63, 54, 69, 50, 72
Treatment 2: 45, 60, 40, 56
Treatment 3: 31, 40, 45, 25, 23, 28
Required:
a. Calculate 90% confidence intervals for all pairwise comparisons of treatment means using the uncorrected method. Create a letter code table to summarize your results, then interpret the results in context.
b. Now calculate 90% confidence intervals for all pairwise comparisons using the Bonferroni correction. Create a letter code table, and interpret your results in context. Do any of the results differ from part (a)?
Answer:
the answer is A
Step-by-step explanation: i have calculated this problom
find the surface area of the cylinder
Answer
50.24
Step-by-step explanation:
Consider the following binomial experiment: A study in a certain community showed that 6% of the people suffer from insomnia. If there are 10,300 people in this community, what is the standard deviation of the number of people who suffer from insomnia?
Answer:
The standard deviation is [tex]\sigma = 24.10[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of those that suffer from insomnia is p = 6% = 0.06
The sample size is n = 10300
Generally the proportion of those that do not suffer from insomnia is mathematically represented as
[tex]q = 1-p[/tex]
substituting values
[tex]q = 1 -0.06[/tex]
[tex]q = 0.94[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{n * p * q }[/tex]
substituting values
[tex]\sigma = \sqrt{ 10300 * 0.06 * 0.94 }[/tex]
[tex]\sigma = 24.10[/tex]
Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is 24.10
Recall :
[tex] standard \: deviation, σ = \sqrt{n \times \: p \: (1 - p)} [/tex] p = probability of success = 6% = 0.061 - p = 1 - 0.06 = 0.94Sample size, n = 10300Substituting the values into the equation :
[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: (1 - 0.06)} [/tex]
[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: 0.94} [/tex]
[tex] standard \: deviation, σ = \sqrt{580.92} = 24.10[/tex]
Hence, the standard deviation is 24.10.
Learn more : https://brainly.com/question/15929089
The probability density function for random variable W is given as follows: Let x be the 100pth percentile of W and y be the 100(1 – p)th percentile of W, where 0
Answer:
Step-by-step explanation:
A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).
X = 100pth percentile of W
Y = 100(1-p)th percentile of W
Expressing Y as a function of X;
Y = 100(1-p)th = 100th - 100pth
Recall that 100pth is same as X, so substitute;
Y = 100th - X
where 100th = hundredth percentile of W and X = 100pth percentile of W
a number is divisible by 10 if it has ____ in ones place .
Answer:
A number is divisible by 10 if it has a zero in ones place.
Step-by-step explanation:
We know that 10= 2 x 5 .So to be divisible by 10 we have to be divisible by both 2 and 5As we know ,Numbers divisible by 2 are even numbers and numbers divisible by 5 if it has a zero or a five in ones place . From that, we have A number is divisible by 10 if it has a zero in ones place.Solving a word problem with three unknowns using a linear...
Rachel, Trey, and Deshaun sent a total of 98 text messages during the weekend. Trey sent 4 times as many messages as Deshaun. Rachel sent 10 fewer
messages than Deshaun. How many messages did they each send?
Number of text messages Rachel sent:
221
Х
?
Answer:If Rachel texted 221 text messages, then Deshaun texted 231 text messages, and Trey texted 924 text messages.
Step-by-step explanation:
221+10=231, 321 times 4 equal 924
pls give answer
write down the literal coefficient of the monomial
Answer:
-2
Step-by-step explanation:
The coefficient of a term is literally the constant place before a variable. So in this monomial:
-2xy^2z^3
The coefficient would be -2.
Cheers.
i will rate you brainliest
Answer:
Option (3)
Step-by-step explanation:
For a geometric progression,
[tex]a,ar,ar^{2},ar^3.........a(r)^{n-1},a(r)^n[/tex]
First term of the progression = a
Common ratio of each successive term to the previous term = r
Recursive formula for geometric progression will be,
[tex]a_1=a[/tex]
And [tex]a_{n}=a_{n-1}(r)[/tex]
Following this rule for the G.P. given in the question,
[tex]a_1=4[/tex]
[tex]a_n=-1.5a_{n-1}[/tex]
Therefore, from the recursive formula,
Common ration 'r' = -(1.5)
Option (3) will be the correct option.
what is the definition of a sequence
Answer:
the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.
Step-by-step explanation:
Find Term 20 for the sequence a= 4 6 8 10......
4,6,8,10 are in A.P
a=4d=2[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]
[tex]\\ \rm\Rrightarrow a_20=42[/tex]