The density functions of U1, U2 and U3 can be calculated as fU1(u) = 2(2 - (u+1)), 0 < u < 1, 0, elsewhere; fU2(u) = 4/u2, 0 < u < 1, 0, elsewhere; and fU3(u) = 2/√u, 0 < u < 1, 0, elsewhere.
The method of transformation is used to find the density functions of U1, U2 and U3 when given the probability density function of a random variable Y. The equation for the transformation of a random variable Y to U is U = g(Y), where g is a function of Y. To find the density functions of U1, U2 and U3, we need to first calculate the derivatives of U1, U2 and U3 with respect to Y, which are given by dU1/dY = 2, dU2/dY = -1/2 and dU3/dY = 2Y. Then, the density functions of U1, U2 and U3 can be calculated using the formula fU(u) = fY(g-1(u)) * |dg-1/du|, where fU(u) and fY(y) denote the density functions of U and Y, respectively, and g-1 is the inverse of g. For U1, U2 and U3, g-1(u) is y = (u+1)/2, y = 2/u and y = √u, respectively. Therefore, the density functions of U1, U2 and U3 can be calculated as fU1(u) = 2(2 - (u+1)), 0 < u < 1, 0, elsewhere; fU2(u) = 4/u2, 0 < u < 1, 0, elsewhere; and fU3(u) = 2/√u, 0 < u < 1, 0, elsewhere.
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The graph of the exponential function f is shown. Find f(-7)
The value of f(-7) from the graoh is 1/128
How to determine unknown point on exponential graphExponential function typically refers to the positive-valued function of a real variable, although it can be extended to complex numbers or generalized to other mathematical objects like matrices.
From the given graph, we need to determine then value f(-7). The function f(-7), is the equivalent value on the y-axis if the value of x is -7.
The standard exponential equation is y = ab^x
Using the coordinate points (0, 1) and (-2, 4), the resulting equations are:
1 = ab^0
4 = ab^-2
From equation 1, a = 1
4 = b^-2
b^2 = 1/4
b = 1/2
The exponential function will be y = (1/2)^x
f(-7) = (1/2)^-7
f(-7) = 1/128
Hence the resulting value of f(-7) is 1/128
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please save me ASAP !
Answer:
40h = e
Step-by-step explanation:
40 x 11 = 440
A radio-controlled helicopter sells for $20, but needs a lithium battery that costs 25% of that price. A sales tax of 6% will be added to the cost of both items. What is the total cost of the helicopter, battery and tax? Complete the explanation.
Answer:
$26.50
Step-by-step explanation:
Helicopter is $20.
The battery is 25% of 20.
25% of 20
= .25 • 20
= 5
The battery will be $5.
The total purchase will be 20 + 5, that is,
$25
Calculating the tax:
6% of $25
= .06 • 25
= 1.5
Add the tax onto the total.
$25 + $1.50
= 26.50
The helicopter, battery and tax all adds up to $26.50
Suppose X has a Poisson distribution with a mean of 7. Determine the following probabilities. Round your answers to four decimal places (e.g. 98.7654) (a) P(X= 1)i (b) PIXs 2)=i (c) PIX= 4)- (d) PIX-8)
The probabilities are obtained as -
a) P(X = 1) = 0.006377
b) P(X ≤ 2) = 0.0296075
c) P(X = 4) = 0.091137
d) P(X = 8) = 0.130251
What is Poisson Distribution?
The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.
The mean of the Poisson distribution is given by λ.
The cumative distribution function is -
P(X = π) = (e^(-λ)λ^π) / π!, where π = 0,1,2,...
a) So, putting π = 1, λ = 7 in the above formula -
P(X = 1) = (e^(-7)7^1) / 1!
P(X = 1) = (0.000911 × 7) / 1
P(X = 1) = 0.006377
Therefore, the value is P(X = 1) = 0.006377.
b) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = (e^(-7)7^0) / 0! + (e^(-7)7^1) / 1! + (e^(-7)7^2) / 2!
P(X ≤ 2) = 0.000911 + 0.006377 + 0.022319
P(X ≤ 2) = 0.0296075
Therefore, the value is P(X ≤ 2) = 0.0296075.
c) So, putting π = 4, λ = 7 in the above formula -
P(X = 4) = (e^(-7)7^4) / 4!
P(X = 4) = (0.000911 × 2401) / 24
P(X = 4) = 0.091137
Therefore, the value is P(X = 4) = 0.091137.
c) So, putting π = 8, λ = 7 in the above formula -
P(X = 8) = (e^(-7)7^8) / 8!
P(X = 8) = (0.000911 × 5764801) / 24
P(X = 8) = 0.130251
Therefore, the value is P(X = 8) = 0.130251.
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Given the preimage ABC, describe a sequence of transformations that produces the
image A'B'C'.
Answer:
Step-by-step explanation:
Sorry I don’t know
a cylindrical tank is 18 feet high with a diameter of 8.5 feet. if the tank is filled to the top, how many gallons will it hold
I believe its 44,880
A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row. If a person is aiming to park in first row, what is his probability in decimal form of getting a parking spot?
The probability in decimal form of getting a parking spot is, 0.2
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row.
Hence, Total parkin spots = 9 + 15 + 21
= 45
And, Number of spots in first row = 9
Thus, The probability in decimal form of getting a parking spot when a person is aiming to park in first row is,
⇒ 9 / 45
⇒ 1/5
⇒ 0.2
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Use an equation to find the value of k so that the line that passes through (k,4) and (3,-2) has a slope of m=-1
K=
Step-by-step explanation:
trfg gh fg gyfggr d vd f fvy e ht4gjgdgdhdggygggg
why did brainly get me so up someone help
Answer:
we on top
Step-by-step explanation:
Answer:
Step-by-step explanation:
you gotta be kidding me right now b r u h. Aint no way bro is posting this hahahha get it i guess
2-1=1 explain how you get 1
Answer:
Step-by-step explanation:
you take away 1 from 2 and that leaves you with 1
Answer:
Let's say I have two apples. You want one too! I give you one, and how many do I have left? 1
What I am explaining here is that if you take one away from two, it becomes one.
Translate this sentence into an equation. The sun of 15 and Delia’s age is 65. Use the variable d to represent Delia’s age
The translation of the sentence 'The sum of 15 and Delia’s age is 65'
is 15 + d = 65.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The age of Delia be 'd'.
Therefore, The equation for the statement 'The sum of 15 and Delia’s age is 65' can be expressed as,'
15 + d = 65.
d = 65 - 15.
d = 50.
So, The age of Delia is 50 years.
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In 2008, the per capita consumption of soft drinks in Country A was reported to be 18.88 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.88 gallons and a standard deviation of 4 gallons. Complete parts (a) through (d) below.
a. What is the probability that someone in Country A consumed more than 15 gallons of soft drinks in 2008?
b. What is the probability that someone in Country A consumed between 5 and 9 gallons of soft drinks in 2008?
c. What is the probability that someone in Country A consumed less than 9 gallons of soft drinks in 2008?
d. 99% of the people in Country A consumed less than how many gallons of soft drinks?
On solving the provided question, we can say that Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\ = 0.9645 and Probability(5<x<9) = P(x<9) - P(x<5) = 0.0101 and P(x<9) = 0.0106
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\
= 0.9645
Probability(5<x<9) = P(x<9) - P(x<5)
= 0.0101
P(x<9) = 0.0106
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IS THIS CORRECT PLEASE HELP MEEEEEEEEEE
The following statements are either true or false;
Chemicals in the environment can cause mutation - TrueDifferences in characteristics within a specie is known as variation - TrueFossils cannot be dated - FalseIf an organism cannot adapt fast enough, they may become extinct - TrueOrganisms evolve because of natural selection - True What is mutation?Mutation can be defined as the altering or the change in the DNA sequence or arrangement of a cell.
variation can be defined as any difference between cells, organisms, or groups of organisms of any species caused by genetic differences or environmental factors.
Fossils refers to the remains of plants and animals whose bodies were buried in sand, mud, seas, lakes and rivers over a long period of time.
Therefore, the statement Fossils cannot be dated is false because fossils can be dated to upto 10,000 years ago.
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Select the expression that matches subtract three from 4/9 of 20
Answer: The answer is D
Alexa plans to join a members-only speaker series for $50. As a member, she will pay just $12.50 for each event she attends. Alexa has budgeted $100 to become and member and attend these events. How many events can she afford to attend?
Answer:
4 events
Step-by-step explanation:
you divide 12.50 by 50 then you get 4
At first, Mrs. Hanrahan's students thought that a linear model might describe the relationship between a pendulum's length and its period pretty well. After fitting a least-squares regression model to data, they decided that a better model be available. Perform this analysis yourself, and explain why the students didn't favor the linear model.
The relationship between pendulum length and period is nonlinear. As the period is dependent on the square root of the length.
To anatomize this relationship, the scholars would need to gather data on pendulum length and period, also fit a regression model.However, the residuals from the model would be erratically distributed around zero, If the relationship is direct.
If the relationship is nonlinear, the residuals would parade a pattern, indicating that a direct model is not the swish fit. In this case, a nonlinear model analogous as the square root of pendulum length would give a better fit for the data. The scholars probably set up that the residuals from the direct model were not erratically distributed, hence they didn't favor the direct model.
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Suppose that 3 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 53 cm.
(a) How much work is needed to stretch the spring from 41 cm to 45 cm? (Round your answer to two decimal places.)
_____ J
(b) How far beyond its natural length will a force of 30 N keep the spring stretched? (Round your answer one decimal place.)
_____ cm
a ) Work is needed to stretch the spring from 41 cm to 45 cm is 0.58J
b ) 1445 cm far beyond its natural length will a force of 30 N keep the spring stretched.
A spring has a spring constant k,
It takes force kx to extend the spring's length.
A spring stretched length x has energy kx²/2.
Work of 3J gave the spring energy k(53-36)²/2.
Therefore,
3 = k(53-36)²/2
k = 6/289 N/cm
Work is needed to stretch the spring from 41 cm to 45 cm
At 41 cm the spring has energy k(41-36)²/2.
At 45 cm the spring has energy k(45-36)²/2.
The extra energy is given by,
(6/289)(45-36)²/2 - (6/289)(41-36)²/2
= (6/289) * 81/2 - (6/289) * 25/2
= 243/289 - 75/289
= 168/289
= 0.58J
Work is needed to stretch the spring from 41 cm to 45 cm is 0.58J
The natural length will a force of 30 N keep the spring stretched,
30 = kx
x = 30/k
= 1445 cm
1445 cm far beyond its natural length will a force of 30 N keep the spring stretched.
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Two items are omitted from each of the following summaries of balance sheet and income statement data for two proprietorships for the year 2022, Greene’s Goods and Solar Enterprises.
Greene’sGoods
SolarEnterprises
Beginning of year:
Total assets
$110,000
$129,000
Total liabilities
85,000
(c)
Total owner’s equity
(a)
80,000
End of year:
Total assets
160,000
180,000
Total liabilities
120,000
50,000
Total owner’s equity
40,000
130,000
Changes during year in owner’s equity:
Additional investment
(b)
25,000
Drawings
37,000
(d)
Total revenues
220,000
100,000
Total expenses
175,000
60,000
The missing amounts are a) $79,000, b) $22,000, c) $51,000, d) $15,000 and e) $6,000.
We have,
The theory used in this question is the basic accounting equation which states that Assets = Liabilities + Equity.
This equation can be used to determine the missing amounts in the summaries of Greene's Goods and Solar Enterprises.
Step 1: Start with the beginning of year data for Greene's Goods. We know that the Total Assets = $110,000, Total Liabilities = $85,000 and that the Total Owner's Equity is missing. We can use the basic accounting equation to solve for Total Owner's Equity.
Assets = Liabilities + Equity
110,000 = 85,000 + Equity
Equity = 25,000
Step 2: Now look at the ending of year data for Solar Enterprises. We know that the Total Assets = $180,000, Total Liabilities = $50,000 and that the Total Owner's Equity is missing. We can use the basic accounting equation to solve for Total Owner's Equity.
Assets = Liabilities + Equity
180,000 = 50,000 + Equity
Equity = 130,000
Step 3: Lastly, look at the changes in owner's equity for each proprietorship. For Greene's Goods, we know that Additional Investment = $7,000 and Drawings = $37,000. We can use the basic accounting equation to solve for the missing amount.
Change in Equity = Additional Investment + Drawings
Change in Equity = 7000 + 37000
Change in Equity = $44,000
For Solar Enterprises, we know that Additional Investment
= $25,000 and Drawings = $15,000.
We can use the basic accounting equation to solve for the missing amount.
Change in Equity = Additional Investment + Drawings
Change in Equity = 25000 + 15000
Change in Equity = $40,000
Therefore, the missing amounts are:
a) $79,000
b) $22,000
c) $51,000
d) $15,000
e) $6,000
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kenneth wants to solve the system of equations shown below he made two
tables showing the value if y for different values of x
The solutions to the system of equations are the values of x for which f(x) and g(x) have the same value according to the table.
How to obtain the solution to the system of equations?When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.
At these intersections point, the functions have the same numeric value, which are the points looked at to find the solution on a table.
From the table given by the image presented at the end of the answer, the solutions are given as follows:
x = 1, as both f(x) and g(x) have a numeric value of 14 at x = 1.x = 9, as both f(x) and g(x) have a numeric value of 6 at x = 9.Missing InformationThe problem is incomplete, hence the solution was given in general terms, with an example problem solved.
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What is the smallest integer value for IK for which parallelogram IJKL will have an obtuse angle at J ? A. 12 B. 13 C. 14 D. 15
The smallest integer value for IK is (c) 14
How to determine the smallest integer valueFrom the question, we have the following parameters that can be used in our computation:
The parallelogram
The value of IK can be calculated as
IK^2 = 5^2 + 12^2 - 5 * 12cos(J)
IK^2 = 169 - 60cos(J)
If J is obtuse, then cos(J) is a negative value,
This means that IK^2 must be greater than 169 and therefore IK must be greater than 13.
The smallest integer value greater than 13 is 14,
So your answer is (c). IK = 14
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Morgan is shipping boxes at a package center. She is shipping x small boxes that weight 2 pounds each and y large boxes that weigh 10 pounds each. She is shipping 17 boxes altogether and the combined weight of all the boxes she ships is 74 pounds. Write an equation in standard form to model this scenario.
A system of equations in standard form to model this scenario include the following:
2x + 10y = 74.
x + y = 17.
How to write the system of equations for this system?In order to write a system of linear equations that could be used to model the situation and determine the number of small boxes shipped and the number of large boxes shipped, we would assign variables to the number of small boxes that were shipped, the number of large boxes that were shipped respectively as follows:
Let the variable s represent the number of small boxes.Let the variable l represent the number of large boxes.Next, we would translate the word problem into system of linear equations as follows:
Since x small boxes weigh 2 pounds each and y large boxes weigh 10 pounds each and all the boxes she ships is 74 pounds;
2x + 10y = 74.
Additionally, she is shipping 17 boxes altogether;
x + y = 17.
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A fully inflated professional basketball has a circumference of 78 centimeters. What is the radius of a circular cross section through the center of the ball? use 3.14 for pi?
A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.
what is circle ?A circle is created when almost every point there in plane that is a specific distance away from another point does so (center). As a conclusion, it is a curve made up of segments that are spaced from each other in the plane. It is rotationally homogeneous about the centre in anyway angles. All pair of points in the grid that make up a circle are evenly spaced away from the "centre" and create a closed, two-dimensional object. A specular parity line is generated by a line that passes through circle. It is rotationally symmetric about just the centre at all angles.
given
The football's circumference is 12.42 cm.
Football's circumference is 78 cm.
The formula for the football's circumference is C = 2pir
= 78 r
= 78/2pi r
= 12.42 cm.
A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.
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Yemi sold 100 books at ₦4.25each for a publishing company that gives 12%commission. how many commission would he get
The amount of commission Yemi gets is, ₦51
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
Yemi sold 100 books at ₦4.25 each,
So,
the total sales revenue is,
⇒ 100 x ₦4.25
⇒ ₦425
The publishing company gives a 12% commission on sales,
So, Yemi's commission would be,
⇒ 12/100 x ₦425
⇒ ₦51
Therefore, Yemi would get a commission of ₦51.
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Deandre rented some movies and video games last month. He did the same this month. The table below shows the number of movies and video games he
rented each month. It also shows the total cost (in dollars).
A) the picture…
B)How much did it cost(in dollars) to rent each movie and each video game?
Rental cost for each movie:?
Rental cost for each video game:?
Answer:
Step-by-step explanation:
We can find the rental cost for each movie and each video game by dividing the total cost by the number of movies and video games rented, respectively.
For the movies:
Rental cost for each movie = Total cost of movies rented / Number of movies rented
= $33 + $24 = $57
= $57 / 6 = $9.50 per movie
For the video games:
Rental cost for each video game = Total cost of video games rented / Number of video games rented
= $18 + $24 = $42
= $42 / 4 = $10.50 per video game.
suppose that a is an upper bound for the set S and that there is a sequence of elements xn that exists in S such that xn-->a. Prove that a is the least upper bound.
a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.
What is the difference between the least upper bound and upper bound?
An upper bound of a set S of real numbers is any real number that is greater or equal to all numbers in S. A lower bound is any which is less than or equal to all numbers in S. A least upper bound is an upper bound that is less than or equal to all upper bounds.
To prove that a is the least upper bound (LUB) of the set S, we need to show that a satisfies two conditions:
a is an upper bound of S, meaning that for every element x in S, x <= a.
If there is another upper bound b for S, then a <= b.
First, we already know that a is an upper bound of S because it is given that a is an upper bound of the set S.
Next, suppose there is another upper bound b for S such that b > a. Then, since the sequence xₙ converges to a, there exists a positive integer N such that for all n >= N, xₙ is arbitrarily close to a, meaning that |xₙ - a| < (b - a)/2. This means that xₙ < b for all n >= N, which contradicts the assumption that b is an upper bound of S, since xₙ is an element of S and xₙ < b.
Therefore, a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.
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what is 4+4?????????????????????????????????????
Answer:
Step-by-step explanation:
uhhhhh 8 lol
The vector [-14,-7,19] is a linear combination of vectors [-3,-3,-3] and [10,9,-10] if and only if the matrix equation Ax = b has a solution x where A = [? ?] and b = [?] [? ?] [?] [? ?] [?]T
A = [[-3, 10], [-3, 9], [-3, -10]], b = [-14, -7, 19] Ax = b's matrix equation has a solution in the form of T. x.
Only if the matrix equation Ax = b has a solution x is the vector [-14,-7,19] a linear combination of the vectors [-3,-3,-3] and [10,9,-10]. The vector [-14,-7,19] must be transposed for this to hold true, and A must be the matrix of coefficients of the linear combination of the two vectors. As a result, A is a 3x2 matrix and its formula is as follows: A = [[-3, 10], [-3, 9], [-3, -10]], and b = [-14, -7, 19]T. The vector [-14,-7,19] is a linear combination of the two vectors [-3,-3,-3] and [10,9,-10] if there is a solution x to the matrix equation Ax = b.
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Which of the following problems would NOT have a solution? Group of answer choices 10 divided by 2. 10 divided by 5. 10 divided by 0. 0 divided by 10.
10 divided by 0 problem would NOT have a solution.
Given:
a. 10 divided by 2
b. 10 divided by 5
c. 10 divided by 0
d. 0 divided by 10
We know that ,
Integer divided by an integer is an integer
Therefore (a) and (b) will have a proper solution
We also know that ,
Zero divided by anything is Zero
Therefore (d) also have a unique answer that is zero
Now , We know that
Any numeric value divided by Zero tends to infinity .
Hence, 10 divided by 0 problem would NOT have a solution.
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the average of senators in the 108th congress was 61 years, if the standard deviation was 15 years find the z-scores corresponding to the oldest and youngest senators of age 86% and 41. round z scores to two decimal places.
Therefore , the solution of the given problem of test statistic comes out to be rounding to two decimal places, the z-score is -0.26.
What is the test statistic?The Z-statistic, which demonstrates that the ordinary ordinary neutral hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the variable results show that you got a 2.5 R t. (also Z-value). The p-value for this Z-value is 0.0124.
Here,
To find the z-scores corresponding to the oldest and youngest senators of age 86% and 41%, respectively, we can use the standard normal distribution formula:
z = (x - μ) / σ
where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
For the oldest senators of age 86%, we can find the corresponding z-score as follows:
z = (x - μ) / σ
z = (0.86 - 0.5) / 0.3413
z = 1.055
Rounding to two decimal places, the z-score is 1.06.
For the youngest senators of age 41%, we can find the corresponding z-score as follows:
z = (x - μ) / σ
z = (0.41 - 0.5) / 0.3413
z = -0.264
Rounding to two decimal places, the z-score is -0.26.
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The digit in the units place of a 2 digit number is 4 times the digit in the tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.
A. 28B. 32C. 15D. 25
The number in question is 28.
To make solving this problem easier, we need to consider the number.
Let the number is ab.
So that,
4 × a = b
4a = b
We spread the numbers on the options.
28
(4 × 2 = 8) → True
32
(4 × 3 = 2) → False
15
(4 × 1 = 5) → False
25
(4 × 2 = 5) → False
We prove what number of 28 is when the digits is reversed to be greater than 54.
28 ⇄ 82
It is proved that the number 82 is greater than the number 54.
So, the number in question is 28.
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