Sum of the 15 two elements subset of $\{1,2,3,4,5,6} = ( N-1) (N)(N+1)/2
Three elements....two at time (1,2) (1,3) (2,3)....sum = 12
Four elements .... two at a time (1,2) (1,3) (1,4) (2,3) (2,4) (3,4) .....sum = 30
Five elements....two at a time (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)
Note that for N elements taken 2 at a time....the pattern of sums seems to be
= (N-1)(N)(N+1) / 2
For taking 6 elements taking 2 at a time the sum should be
=(5)(6)(7) /2
=210 /2
=105
Therefore, total sum of those 15 sums of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$ = 105
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the planning board members for a city are debating whether to build a new municipal parking garage. the parking garage would be funded by the revenue the city collects from its existing parking meters. since the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200. a random sample of 35 days was selected, and the parking revenue collected in dollars was recorded. based on previous research, the board members assume that the population standard deviation is $196. the board conducts a one-mean hypothesis at the 1% significance level, to test whether the mean daily parking revenue is greater than $1,200.
The required hypothesis for the given data of the problem is
Null hypothesis H₀: μ=$1200 , n = 35
Alternate hypothesis Hₐ : μ > 145
What is tailed test?In statistics, a two-followed test is a technique wherein the basic region of a dissemination is two-sided and tests whether an example is more noteworthy or under a scope of values. It is utilized in invalid speculation endlessly testing for measurable importance.
According to question:We have,
the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200
So, Null hypothesis H₀: μ=$1200 , n = 35
Then, Alternate hypothesis Hₐ : μ > 145
Standard deviation = $196
Thus, It is right tailed hypothesis.
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When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
How many hours for one pipe to fill the pool? How many hours for the other pipe to fill the pool?
One pipe takes 6 hours to fill the pool and the other takes 12 hours.
Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.
Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:
4(1/x + 1/y) = 1
You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.
So, Pipe A, working for t hours, fills half the pool:
t(1/x) = 1/2
And Pipe B, working for 9 - t hours, fills half the pool:
(9-t)(1/y) = 1/2
You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):
4(1/x + 1/y) = 1
t(1/x) = 1/2
(9-t)(1/y) = 1/2
Solve for t in that second equation, then plug it into the third equation:
t(1/x) = 1/2
t = x(1/2)
t = x/2
(9 - x/2)(1/y) = 1/2
Now you've got a system of two equations:
4(1/x + 1/y) = 1
(9 - x/2)(1/y) = 1/2
Solve for y in the second equation, then plug that into the first equation:
(9 - x/2)(1/y) = 1/2
(9 - x/2) = y(1/2)
2(9 - x/2) = y
18 - x = y (this is a really nice-looking form of that equation; we'll use it again later)
4(1/x + 1/y) = 1
4(1/x + 1/(18-x)) = 1
4/x + 4/(18-x) = 1
(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1
(4(18-x) + 4x)/(x(18-x)) = 1
4(18-x) + 4x = x(18-x)
72 - 4x + 4x = 18x - x2
72 = 18x - x2
x2 - 18x + 72 = 0
(x - 6)(x - 12) = 0
x - 6 = 0 OR x - 12 = 0
x = 6 OR x = 12
So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.
When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.
These cases are equivalent, since the original problem makes no distinction between the pipes.
Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.
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on your desk, there is a very special die with a prime number p of faces, and you throw this die once. show that no two events a and b can be independent unless either a or b is the whole sample space or the empty set.
We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.
A sample space can be defined as the set of all possible outcomes of any experiment.
We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅} (i)
This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)
Using the values of (i) and (ii), we get -
= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.
= p|C|=|A||B|.
From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|. if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.
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6y-5=7
what is y hdhfhdjshbdhdj
Answer: Y=2
Step-by-step explanation:
a town’s january high temperatures average 36°f with a standard deviation of 10°, while in july the mean high temperature is 74° and the standard deviation is 8°. in which month is it more unusual to have a day with a high temperature of 55°? explain.
It is more unusual to have a high temperature of 55 degrees in July because the month's z-score is 2.375 standard deviations from its mean.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. Standard deviation is significant because it enables consumers to evaluate risk. Think about an investing strategy with a 10% average yearly return.
Here,
Calculations are attached in image.
A high temperature of 55 degrees is particularly rare since July's z-score is 2.375 standard deviations outside of its mean.
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Help please!! I need this answer!!
Answer: Store B and C sell at a lower unit price.
Step-by-step explanation:
Store B: $3.48/3 = $1.16 per pound.
Store C: $3.80/4 = $0.95 per pound.
write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have
The expression that represents the orders is 12 * (5 + 3.5)
Another expression is 12 * 8.5 The total order is 102How to determine the expression for Sean's purchase?From the question, we have the following parameters that can be used in our computation:
Number of cupcakes in a box = 12Number of boxes ordered for his sister’s graduation party = 5Number of boxes ordered for the Variety Show party = 3.5The above parameters mean that:
Expression for Sean's purchase = Number of cupcakes in a box * (Number of boxes ordered for his sister’s graduation party + Number of boxes ordered for the Variety Show party)
Substitute the known values in the above equation, so, we have the following representation
Expression for Sean's purchase = 12 * (5 + 3.5)
Hence, the expression is 12 * (5 + 3.5)
A different expressionIn (a), we have
Expression = 12 * (5 + 3.5)
Evaluate the sum
Expression = 12 * 8.5
Evaluate
Expression = 102
This means that the total number of box is 102
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Complete question
A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean orders.
Write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have
in a lecture hall containing 100 people, you consider whether or not there are three people in the room who share the same birthday. explain how to calculate this probability exactly, using the same assumptions as in our previous analysis.
The probability of three people who share the same birthday is 0.6459.
Let us consider that A₀ be the event that everyone in the room has a distinct birthday. Let Ai be the event that pairs of people share a birthday. Then the probability we are interested in is
P(at lest three people share a birthday) = 1 - P(A₀) - ∑ P(Ai)
where there are n people in the lecture hall.
First we note that P(A₀) is in the book and is
P(A₀) = (365Cn)n!/365^n.
Now we will compute P(Ai).
For i = 1,
P(A₁) = (365) × [tex]\frac{(nC2)(365-1Cn-2)(n-2)!}{365^{n} }[/tex]
For i = 2,
P(A₂) = [tex]\frac{(365C2)(nC2)(n-2C2)(365-2Cn-4)(n-4)!}{365^{n} }[/tex]
This generalizes for i pairs of people sharing i distinct birthdays
P(Ai) = (365Ci)πj=1toi(n-2j+2C2)(365-iCn-2i)(n-2i)!/([tex]365^{n}[/tex])
Substituting all values into the equation and putting in n = 100, we can compute a value for this probability.
Therefore we get,
P(at least 3 people share a birthday)0.6459.
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if gallup wishes to use a 95% confidence interval, compute the minimum number of american adults that they need to survey to ensure that the error bound, under no circumstances, is more than 0.01 before conducting the experiment?
the minimum number of american adults that they need to survey to ensure that the error bound is 16,867 with sample size
The sample size of a study is the number of subjects or observations that are included.Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.
The minimum sample size required to get a 95% confidence interval with an error bound of 0.01 is 16,867. This can be calculated using the formula:
n = (1.96 / 0.01)2 = 16,867.
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a population doubles in size every 15 years. assuming exponential growth, find the (a) annual growth rate (b) continuous growth rate
The annual growth rate is 4.73 %
The continuous growth rate is 4.62 %
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
Let us assume:
The initial amount of 1, so results are 2.
Let x be the percent in decimal form
Growth rate per year:
[tex]1(1+x)^{15} = 2[/tex]
Take ln on both the sides
[tex]ln((1+x)^{15}) = ln(2)[/tex]
15*ln(1+x) =0 .693
ln(x+1) = 0.693/15
ln(x+1) = 0.04621
Take anti ln on both the sides
x+1 = 1.0473
x = 1.0473 - 1
x = .0473
x =4.73 % annual growth rate
Continuous growth rate:
[tex]1*e^{15x} = 2[/tex]
[tex]ln(e^{15x}) = ln(2)[/tex]
15x*ln(e) = ln(2)
ln(e) = 1
15x =0.693
x =0 .693/15
x = .0462
x = 4.62 %
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the residual is defined as the difference between the actual and predicted, or fitted values of the response variable. group of answer choices false true
The Residual is defined as the difference between the actual and predicted, or fitted values of the response variable. This statement is true.
Linear regression is a statistical tool that determines how well a straight line fits a set of paired data. The straight line that best fits that data is called the least squares regression line. This line can be used in a number of ways. One of these uses is to estimate the value of a response variable for a given value of an explanatory variable. Related to this idea is that of a residual.
Residuals are obtained by performing subtraction. All that we must do is to subtract the predicted value of y from the observed value of y for a particular x. The result is called a residual.
The formula for residuals is straightforward:
Residual = observed y – predicted y
It is important to note that the predicted value comes from our regression line. The observed value comes from our data set.
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To test the effectiveness of a liquid supplement that is supposed to help forgetful people with their memory, 400 college students are recruited for a study and divided into two groups. Group A with 250 students receives the supplement, while group B with 150 students receives some colored water. Neither group is told what they received. After several weeks, they are given a memory test. This study can best be described as: . a census a controlled placebo experiment a survey using quota sampling a survey using simple random sampling the placebo effect
This study can be best described as Controlled Placebo Experiment
What is a Controlled Placebo Experiment?
A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.
According to the given question:
This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.
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a research study reported that 10% of the people who are given a certain drug experience dizziness.if 15 people are selected at random, find the probability that none of them experience dizziness when given the drug.
Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .
10% of the people experiences dizziness.
Probability that a random patient experiences dizziness = 0.1
Probability that the person does not experience dizziness = 0.9
Now this is in the form of a binomial distribution such that the probability is given by:
Sample = 15
P = 0.1
P' =0.9
Required probability :
= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)
= 1 × 0.1⁰ × 0.9¹⁵
= 0.20589...
≈ 0.206
Hence the required probability is approximately 0.206 .
The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.
If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.
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a laboratory supply company produces graduated cylinders, each with an internal radius of 222 inches and an internal height between 7.757.757, point, 75 inches and 888 inches. what is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?
One possible volume of a graduated cylinder produced by the company is 98 cubic inch.
The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object. An object with a larger volume would occupy more space.
The volume of a cube can be found by multiplying the edge length three times. For instance, if the length of an edge of a cube is 4, the volume will be 4³. The formula to calculate the volume of a cube is given as,
Volume of a cube = s³, where 's' is the length of the side of the cube.
Given in the question:
Radius of cylinder = 2 inches.
Height of the cylinder = 7.75 to 8 inches.
We know that,
Volume of Cylinder = πr²
For minimum Volume 7.75 :
Volume = πr²× 7.75
= 3.14 × 4 × 7.75
= 97.34 cubic inches.
For maximum volume 8.00 inches
Volume = πr² × 8
= 3.14 × 4 × 8
= 100.81
Therefore, the possible volume could be between 97.34 cubic inches and 100.81 cubic inches.
Thus, the volume is 98 cubic inches.
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can someone help me really quick
(please Explain how you know this is correct)
The answer is $12.50
You can see on the graph that if the weight is 20 pounds, it will cost $10. We are looking for how much it will cost to ship a 25 pound package. It can’t be $20.00 either.
hope this helps!
Give me Brainliest please!
help me for math..........
Answer:
A) -20
Step-by-step explanation:
[tex]4y(4y-4)-4(-4y+5+4y^2)\\\\16y^2-16y + 16y-20-16y^2\\\\-20\\[/tex]
Morgan and her children went into a grocery store and she bought $10
worth of peaches and mangos. Each peach costs $1 and each mango
costs $2. She bought a total of 8 peaches and mangos altogether.
Graphically solve a system of equations in order to determine the
number of peaches, a, and the number of mangos, y, that Morgan
bought.
Answer:
The number of peaches and the number of mangos that Savannah bought
are 4 and 10 respectively.
The variable use to write the equation is x and it is the number of peaches
Savannah and her children bought
let
the number of peaches Savannah and her children bought = x
Therefore
the number of mangoes Savannah and her children bought = x + 6
The total worth of what they bought = $22
Therefore,
1.75x + 1.50(x + 6) = 22
1.75x + 1.50x + 9 = 22
3.25x + 9 = 22
3.25x = 22 - 9
3.25x = 13
x = 13 / 3.25
x = 4
Therefore,
number of peaches bought = 4
number of mangoes bought = 4 + 6 = 10
Step-by-step explanation:
Answer: 6 Peaches and 2 Mangos
Step-by-step explanation: If one peach is worth $1 and one mango is worth $2, to get $10 used you need to buy 6 peaches and 2 mangos since 2 + 2 = 4 and 6 + 4 = 10
Which of these relations is a function?
The relation that is a function is the graph (d)
How to determine the function?From the question, we have the graphs to represent the given parameters that can be used in our computation
We are to find out which of them represents a function
For a graph to represent a function, the graph must pass the vertical line test
This means that a line drawn from the x-axis must touch the graph at most once
So, we draw these lines and attach the graphs (see attachment)
The graph that pass the vertical line test is graph d
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7x3/4=7 true or false
Answer:
false
Step-by-step explanation:
7*3 / 4 = 7
21 / 4 = 7
5.25 ≠ 7
Could you please give me brainliest? Thanks!
Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)
It takes Bob 125.0633 seconds to cover the entire track.
Let the time taken by Bob to cover the track be x sec
Let the distance of the track be y m
Akira covers the whole track in 95 seconds
hence, his speed is y/95 m/s
Similarly, Bob's speed is y/x m/s
He has traveled to the Easternmost point in 22 seconds. Hence to meet Akira, he has to run for 4 more seconds.
In that time he will cover a distance of 4y/95 m
Similarly, in 26 seconds, Bob will cover
26 y/x m/s
Now Akira has started from the Northernmost point, and we all know that the distance between the Easternmost and Northernmost points of the track will be 1/4th of the whole track length.
Hence,
4y/95 + 26y/x = y/4
or, y(4/95 + 26/x) = y/4
or, 4/95 + 26/x = 1/4
or, (4x + 2470)/95x = 1/4
or, 4x + 2470 = 95x/4
or, 16x + 9880 = 95x
or, 79x = 9880
or, x = 125.0633 seconds
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If x = 6, what y? Please help
Answer: I think the answer is 2
Step-by-step explanation:
The smaller of the two shapes is 12, and the larger of the two shapes is 16,
I found that the difference between the two is 4 (or 16 - 12 =4). If x = 6 and the difference is 4, then subtract 4 from 6 and the answer will come out to be 2
16-12=6-4
y=2
PLS HELP 50 pnts!!!!!!! giving brainliest!!! 1-4 (find the slope)
-attached pic
-unacceptable answers will result in 2 reports (2 warnings and the max is 3 then you will be banned)
Answer:
1) slope = 1/2 2) slope= -1 3)slope= 1/2 4) 5/4
Step-by-step explanation:
if you want y intercpt form
1) y=1/2x
2)y= -x-3
3) y= 1/2x-3.5
4) y= 5/4x - 1
Given: Triangle ABC is isosceles with A as the vertex angle and segment AD bisects segment BC,
Prove: Segment AD bisects angle BAC.
Answer:
PAy Attention Triangle
Step-by-step explanation:
Triangle ABC is isolated True
Calculate the cfse for a d^3 system in an octahedral field in units of ∆_o. In other words, do not enter "∆_o" with your answer. For example, if your answer is −0. 8∆_o, then enter "−0. 8. "
The magnetic moment of an octahedral complex with CFSE=0.8Δo and weak field ligands can take the form of Q.
The Crystal Field Stabilization Energy for a (d3 metal in both forms must be determined in order to provide an answer. The chosen geometry will be the one with the greatest stabilization. The Crystal Field Stabilization Energy is therefore CFSE = -0.8 x 4/9 Δo = -0.355 Δo for tetrahedral d3.
The octahedral d7 complex [Co(CN)64-] is also CN—a strong field ligand. Because of its (t2g)6(eg)1 orbital occupancy, it possesses one unpaired electron. The CFSE in this instance is −(6)(25)ΔO+(1)(35)ΔO+P=−95ΔO+P.
The [Ti(H2O)6]3+ complex's crystal field stabilization energy (CFSE), measured in kJ/mol. The first absorption maximum for the transition, according to CFT, is at 20,3000 cm-1.
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help plsssssssssssssss
Answer:
multiplication property of equality
8(t+2) -3(t-4=6(t-7)+8
Answer: T-62
Step-by-step explanation: i think this is correct
The solution is, the value we get, t = 62.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
8(t+2) -3(t-4)=6(t-7)+8
or, 8t + 16 -3t +12 = 6t - 42 +8
or, 5t + 28 = 6t - 34
or, t = 62
Hence, The solution is, the value we get, t = 62.
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the execution of the commandselect cname from customer where age < 30 and age > 40will produce the following number of rows:
The given command "select cname from customer where age < 30 and age > 40" will produce 4 rows according to the database table.
What is database?A database in computing is a structured collection of data that is electronically accessible and stored. Large databases are housed on computer clusters or cloud storage, whilst small databases can be kept on a file system. A database is a collection of data that has been organized to make it simple to maintain and update. Data records or files containing information, including as sales transactions, customer information, financial data, and product information, are often aggregated and stored in computer databases. A database is a planned gathering of data. They enable the manipulation and storage of data electronically. Data administration is made simple by databases. Let's use a database as an example. A database is used to store information about people, their phone numbers, and other contact information in an online telephone directory.
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The base of a triangle is four more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.
The height of the triangle is
centimeters.
(Simplify your answer. Type an exact answer, using radicals as needed.)
The height of the triangle would be 5.63 cm.
What is the area of the triangle?
For a given triangle of height 'h' and the base is 'b' then the area of the triangle is
A = 1/2 Base * Height
Given data:
Base of the triangle = 2*height of the triangle + 4
b = 2h + 4
Area = 43 square centimeters
By using the area of the triangle,
A = 1/2 *b * h
43 = 1/2(2h + 4)*h
86 = 2h²+4h
Simplifying this, we get
h² + 2h - 43 = 0
Solving this, we get
h = 5.63 and h = -7.63
Height cannot be a negative value so h = 5.63
Hence, the height of the triangle would be 5.63 cm.
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carols buys 3 gallons of juice for a party. What is greatest number of cups of juice he can Surve
Answer:
24
Step-by-step explanation:
the answer is 24 because 3 gallons can definitely do more then 16 it also depends on how much water the cups can hold.
In cooking class, Lupita and Jacob each make a mixture of basil and oregano. Lupita uses 2 tsp basil for every 3 tsp oregano. Jacob uses 4 tsp basil for every 5 tsp oregano. Lupita says the two mixtures will taste the same. Jacob says his will have a stronger basil taste than Lupita’s. Who is correct? Explain.
Using ratio and proportions, Jacob has mixture with stronger basil taste
Ratios and ProportionRatio can be defined as a comparison between two or more numbers that shows their sizes in relation to each other. A ratio often compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Proportion can be defined as equality of two ratios. Two equivalent ratios are always in proportion. Proportion is an equation or statement that shows that the two ratios or fractions are equivalent.
In this case, we can compare the ratio and determine which will have a stronger basil taste.
Lupita mixed 2 tsp of basil for 3tsp of oregano
The ratio of basil to oregano = 2/3 = 0.67
Jacob mixed 4 tsp of basil for 5 tsp of oregano
The ratio of basil to oregano = 4/5 = 0.8
Comparing the ratios, Jacob ratio is higher compared to Lupita and makes Jacob have the strong basil taste.
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