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▹ Answer
1/2k - 3/5
▹ Step-by-Step Explanation
2/5k - 3/5 + 1/10k
Collect like terms:
2/5k + 1/10k = 1/2
Final Answer:
1/2k - 3/5
Hope this helps!
CloutAnswers ❁
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Answer:
1/2k - 3/5
Step-by-step explanation:
Hey there!
Well the only fraction needed to combine are,
2/5 and 1/10.
To add them we need to make 2/5 have a denominator of 10.
To do that we multiply 5 by 2.
5*2 = 10
What happens to the denominator happens to the denominator.
2*2 = 4
Fraction - 4/10
4/10 + 1/10 = 5/10
5/10
simplified
1/2
1/2k - 3/5
Hope this helps :)
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
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
find the value of x, circles and angles
Answer:
x = 50
Step-by-step explanation:
When two secants intersect in the interior of a circle, the angles formed are the average of the arc an angle and its vertical intercept. In this case, our angle, 73, should be the average of x and 96. We can translate this to an equation and solve:
[tex]\frac{x+96}{2} = 73[/tex]
x + 96 = 146
x = 50
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]
The number of values of xx in the interval [0,5π][0,5π] satisfying the equation 3sin2x−7sinx+2=03sin2x-7sinx+2=0 is/are
Answer:
6
Step-by-step explanation:
Given, 3sin2x−7sinx+2=03sin2x-7sinx+2=0
⇒(3sinx−1)(sinx−2)=0⇒3sinx-1sinx-2=0
⇒sinx=13 or 2⇒sinx=13 or 2
⇒sinx=13 [∵sinx≠2]⇒sinx=13 [∵sinx≠2]
Let sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα
now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)
⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]
Hence, required number of solutions are 6
Nick needs one more class to complete his schedule. There are 5 writing classes, 3 history classes, and 4 mathematics classes that can fit into his schedule. If Nick chooses a class at random, what is the probability that he chooses a history class? Give your answer as a fraction.
Answer:
1/4
Step-by-step explanation:
Probability = 3/(5+3+4)
= 3/12 or 1/4
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.
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
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]
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
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.
Store's Card Major Credit Card
Sample size 64 49
Sample mean $140 $125
Population standard deviation $10 $8
A point estimate for the difference between the means is:________
a. 18
b. 265
c. 15
d. 2
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.find the surface area of the cylinder
Answer
50.24
Step-by-step explanation:
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
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.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
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.
A 20-foot ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 5√15 feet up the tree. Use tangent to find the angle created between the ladder and tree. Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.
Answer:
14.5°
Step-by-step explanation:
The sketch results in an angle of depression problem.
In this case, the opposite side of the triangle formed is 5 ft
The hypotenuse side is 20 ft
The adjacent side is the [tex]5\sqrt{15}[/tex] ft
Using tangent θ = opp/adj
tangent θ = 5/[tex]5\sqrt{15}[/tex] = [tex]\frac{1}{\sqrt{15} }[/tex] = 0.258
θ = [tex]tangent^{-1}[/tex] 0.258 = 14.5°
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
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.
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
The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:\
Answer: Expected value
Step-by-step explanation: The expected value of a random variable refers to a predicted variable which is obtained from the summation of the product of all possible values and the probability of occurrence of each value. The expected values gives the mean or average possible value over the cause of a certain experiment or scenario. It is thus the probability weighted average of all possible values or outcomes of an experiment.
The expected value could be represented mathematically as thus;
E(x) = [Σ(x * p(x)]
Where x = all possible values or outcomes of x;
p(x) = corresponding probability of each x value.
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 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
What is the volume of a cone below?
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
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:
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
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.