By using operations on integers, it can be calculated that
Difference between the amount of memory allocated by char*arr[3] on the intel ia 32 versus the intel x86-64 is 12 bytes
What is operation on integers?
At first it is important to know about integers
Integers are those numbers without any fractional part. Integers can be positive or negative and zero is also an integer.
The operation on integers are
Addition
Suppose there are numbers and the sum of those numbers has to be calculated. For this addition is used
Subtraction
To find the difference between two integers, subtraction is used
Multiplication
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers
Division
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This problem can be solved using operation on integers
On Intel IA 32, the address is 32 bit or 32 [tex]\div[/tex] 8 = 4 bytes
On Intel x86 - 64, the address is 64 bit or 64 [tex]\div[/tex] 8 = 8 bytes
On an array of size 3,
On Intel IA 32, the address is 4 [tex]\times[/tex] 3 bytes = 12 bytes
On Intel x86 - 64, the address is 8 [tex]\times[/tex] 3 bytes = 24 bytes
Difference between the address = 24 - 12 = 12 bytes
Difference between the amount of memory allocated by char*arr[3] on the intel ia 32 versus the intel x86-64 is 12 bytes
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Complete Question
how many bytes difference will there be in the amount of memory allocated by the following code on the intel ia 32 versus the intel x86-64?
char*arr[3]
consider a blackbody of surface area a that cools down with time according to the time-dependent tem- perature function t(t)
The blackbody surface area cools down the area according to time dependent temperature (t)
Radiation that is incident on an object is partially absorbed and partially reflected. At thermodynamic equilibrium, the rate at which an object absorbs radiation is the same as the rate at which it emits it.
Therefore, a good absorber of radiation - any object that absorbs radiation, is also a good emitter. A perfect absorber absorbs all electromagnetic radiation incident on it; such an object is called a blackbody.
The temperature (T) of the object that emits radiation, or the emitter, determines the wavelength at which the radiated energy is at its maximum. For example, the Sun, whose surface temperature is in the range between 5000 K and 6000 K, radiates most strongly in a range of wavelengths about 560 nm in the visible part of the electromagnetic spectrum. The body, when at its normal temperature of about 300 K, radiates most strongly in the infrared part of the spectrum.
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How many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram?.
If there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.
We need to find how many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram. This can be calculated by using unitary method.
There are 2. 2 pounds in 1 kilogram,
We need to find the kilograms are there in 4. 21 pounds
If there are 2. 2 pounds in 1 kilogram,
Then, 1 pound is 1/2.2 kilogram
1 pound = 0.4545
4.21 pound is (1/2.2) 4.21 kilogram
4.21 pound is 1.91 kilogram.
Therefore, if there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.
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These expressions are equivalent. True or False?
2x−3(x−4) = 5x+12
the answer is -6x and the equation is equivalent
Translate the phrase -19y and 20y is -6 into an algebraic equation.
Answer:
-19y+20y=-6
Step-by-step explanation:
and means plus so its would be -19y+20y
is=equal sign so -19y+20y=-6
After __ hour, Evelyn and her friends are __ miles from shore
for point (1,4)
After 1 hour, Evelyn and her friends are 4 miles from shore.
for point (3,12)
After 3 hour, Evelyn and her friends are 12 miles from shore.
If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively, then the formula for the mean absolute deviation over a range of forecasted values isA) MAD t 1 t 1 B) MAD At C) MAD t 1 At-Ft D) MAD t 1
The correct option is A. The formula for the mean absolute deviation over a range of forecasted values is MAD t 1 t 1.
Forecasting is the method of creating predictions primarily based on past and gift information. Later these can be compared (resolved) against what occurs. for example, a company would possibly estimate their sales in the next yr, then examine it in opposition to the real results. Prediction is similar, but the more preferred time period. Forecasting would possibly confer with particular formal statistical methods using time series, pass-sectional or longitudinal information, or as an alternative to less formal judgmental strategies or the manner of prediction and resolution itself. utilization can range among regions of application:
for example, in hydrology, the phrases "forecast" and "forecasting" are sometimes reserved for estimates of values at sure unique future instances, at the same time as the term "prediction" is used for extra widespread estimates, consisting of the wide variety of times floods will arise over an extended duration.
chance and uncertainty are vital to forecasting and prediction; it's miles generally taken into consideration as an excellent practice to indicate the diploma of uncertainty attached to forecasts. in any case, the information ought to be updated in order for the forecast to be as accurate as possible. In a few instances, the information used to are expecting the variable of the hobby is itself forecast
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The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.002. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.96 for a person with the disease and 0.01 for a person without the disease. The proportion of adults for which the test would be positive is
The probability of contracting an illness is 0.0475.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is .According to our question-
D: The patient has the illness
ND: the individual without the disease
TD: The results of the test show the patient has the illness.
P(D) will therefore equal 0.001 since only 0.001 of the population is affected by the disease.
P(ND) = 0.991
Because the test successfully identifies a patient with the condition 99% of the time, P(TD/D) = 0.99.
P(TD/ND) = 0.02 because the test indicates that a healthy person contracts the disease 2% of the time.
We are seeking for P(D|TD) and P(ND|TD), respectively.
According to the Bayes formula, 0.00099/0.00099+0.01982 = 0.00099/0.02081 = 0.0475 = (0.99*0.001)/(0.99*0.001)+(0.02*0.991)
And, \s = 1 - \s = 1 - 0.0475 \s = 0.9525
Therefore,
The likelihood of having an illness is 0.0475.
The likelihood of not having any sick people is 0.9525.
Hence, The probability of contracting an illness is 0.0475.
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A local tennis club has an annual tournament to raise money. they allow a total of 128 players to enter. each round eliminates half the players. how many players will be left after 5 rounds?
The total of 4 players left after 5 rounds.
Given information,
Given that a neighborhood tennis club holds a fundraising competition every year. A total of 128 players are permitted to enter. In each round, half the participants are eliminated.
The function will be written as,
[tex]F(x) = 128e^x[/tex]
To know how many players left after 5 rounds,
Round 1 ⇒ 128/2 = 64
Round 2 ⇒ 64/2 = 32
Round 3 ⇒ 32/2 = 16
Round 4 ⇒ 16/2 = 8
Round 5 ⇒ 8/2 = 4
Hence, 4 players will be left after 5 rounds.
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PLEASE HELP ASAP .................... I will mark brainiest.
Answer:
x>3
Step-by-step explanation:
the answer is x>3 because I took this test in class
Alan has a guessing game on his computer.
He estimates that the probability of winning each game is 0.35
Alan decides to play 20 of these games.
How many of these games should he expect to win?
Answer:7
Step-by-step explanation:
100/20 = 5
35/5 = 7
what is 4 1/3 multplyed by 6?
Answer:
26!
Step-by-step explanation:
let's firstly convert the mixed fraction to improper fraction.
[tex]\stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{3}\cdot 6\implies \cfrac{13}{3}\cdot \cfrac{6}{1}\implies \cfrac{13}{1}\cdot \cfrac{6}{3}\implies \cfrac{13}{1}\cdot\cfrac{2}{1}\implies \text{\LARGE 26}[/tex]
An engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78 Does this data suggest that the population mean strength of the components differs from 50? Set up an appropriate hypothesis test to answer this question.
The population mean strength of the components differs from 50 is 0.304.
In the given question, an engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78
We have to check does this data suggest that the population mean strength of the components differs from 50 and we have to set up an appropriate hypothesis test to answer this question.
Sample size n = 30
Claim : The population mean strength of the components differs from 50.
Null and alternative hypothesis:
H(0): μ = 50
H(A): μ≠50
As the population standard deviation is unknown (not given) , t-test can be used .
Test Statistic :
t = (X-μ)/(S/√n)
To find the sample mean we find the average of the given sample.
So
X = 34 + 54 + 73 + 38 + 89 + 52 + 75 + 33 + 50 + 39 + 42 + 42 + 40 + 66 + 72 + 85 + 28 + 71 + 52 + 47 + 41 + 36 + 33 + 38 + 49 + 51 + 55 + 63 + 72 + 78/ 30
X = 53.267
Now finding the standard deviation using the excel.
SD = 17.1101
To find the SD we use the formula =STDEV(B1:C15)
Now putting the value in the formula of Test Statistic
t = (X-μ)/(S/√n)
t = (53.267-50)/(17.1101/√30)
After solving:
t=1.046
P-value :
As the alternative hypothesis H(A) is of not equal to type , this is two tailed test.
Degrees of freedom = n-1 = 30 -1 = 29
df =29
Using Excel function , =TDIST( t , df , number of tails )
=TDIST( 1.046 , 29 , 2 )
=0.304201657
Rounding to three decimal places
= 0.304
P-value = 0.304
Hence, the population mean strength of the components differs from 50 is 0.304.
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in macroland there is $12,000,000 in currency. the public holds 60% of the currency and banks hold the rest as reserves. if banks' desired reserve/deposit ratio is 25.0 percent, deposits in macroland equal and the money supply equals .
If banks' desired reserve/deposit ratio is 25.0 percent, deposits in macro land are $28800000 and the money supply is $36000000
The deposit ratio is the rate sum of money (stores) that commercial banks must not loan out or invest, the reserve ratio is as a rule fixed by the central banks to control inflation and the volume of cash in circulation inside a given country in a particular time.
Initial bank deposit= 60% of 12000000 = 7200000, The reserve/deposit will calculate as follows (25.0 /100%)=0.25 and If banks desired to keep 25.0 it deposit ratio will be : 1/0.25*7200000= 28800000
So the money supply will be the desired deposited :
=28800000+ 7200000 =36000000
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What are the roles of political parties at the national state and local levels ?.
A political party is made up of people who band together to run the government, win elections, and shape public policy. Currently, the two major parties in Congress are the Democratic and Republican.
The actions of the parties?Political parties act as a conduit between the governed and the ruling class. They educate the public, arouse inspiration, and pique interest in and engagement in public affairs. Their main duty is to suggest candidates for elected office.
What is self-annuncement?Self-annuncation, in which a candidate for office only declares their candidacy, is the earliest method of nominating in American politics.
The national chairman, a national committee, the national convention, and two congressional campaign committees make up the party's overall organizational structure. The party is decentralized at the state level, and state legislation generally determines how it is structured.
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A rectangle has a height of 10 and length of 8. the unshaded regions inside the rectangle include a rectangle with length of 5 and height 2, a triangle with base of 4 and height of 8, and a square with side lengths of 4. all other regions are shaded. tara is playing a party game in which a tiny ball is dropped into a rectangular box. to win the game, she must guess where the ball will stop. what should she guess to maximize her chances of winning? which word describes the likelihood of the ball stopping in a square or rectangular shaped area?
Answer:
shaded area
unlikely
Step-by-step explanation:
She should guess a shaded portion of a rectangle that has a height of 10 and a length of 8 to maximize her chances of winning. The unlikely word describes the likelihood of the ball stop.
First, we need to find the areas of all the regions.
The area of the shaded rectangle = Length x Breadth = 10 x 8 = 80 square units
Area of unshaded rectangle = Length x Breadth = 5 x 2 = 10 square units
Area of unshaded triangle = 1/2 x base x height = 1/2 x 4 x 8 = 32/2 = 16 square units
Area of unshaded square = Side^2 = 4^2 = 16 square units
The area difference between the shaded and unshaded areas = The area of the shaded rectangle - (Area of unshaded rectangle + Area of unshaded triangle + Area of the unshaded square)
The area difference between the shaded and unshaded areas = 80 - (10 + 16 + 16)
The area difference between the shaded and unshaded areas = 80 - 42 = 38
As we see that the area of the shaded region is 38 more than the unshaded region so to maximize her chances of winning she should guess the shaded region or area.
Probability percentage of the shaded rectangle = 80/122 x 100 = 65.57%
Probability percentage of an unshaded rectangle = 10/122 x 100 = 8.20%
Probability percentage of an unshaded triangle = 16/122 x 100 = 13.11%
Probability percentage of an unshaded square = 16/122 x 100 = 13.11%
The unlikely word describes the likelihood of the ball stopping in a square or rectangular-shaped area because one is shaded and unshaded and the other is only unshaded. So, both are having different probabilities because of shape, area, and portion.
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explanation+answer please
Answer:
-1
Step-by-step explanation:
if the input is 4 you just go through the cycles
4 then subtract 7
4-7
-3
Then divide by 3
-3/3
-1
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A box holds fewer than 200 apples. either 2, 3, 4, 5, or 6 children could evenly share these apples. how many apples could be in the box?
The number of apples that could be in the box is 180
How to determine the number of apples that could be in the box?From the question, we have the following parameters that can be used in our computation:
Number of apples = Fewer than 200
Children that can share the apples evenly = 2, 3, 4, 5, or 6 children
This means that the number of apples that could be in the box can be a multiple of 2, 3, 4, 5, or 6
Also, the number must be less than 200
The highest number less than 200 that is a multiple of 2, 3, 4, 5, or 6 is 180
Hence, the possible number of apples is 180
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Answer:
Multiples of 60 under 200!
Step-by-step explanation:
What does dilated by a scale factor of 3 mean?.
a deck of cards contains red cards numbered 1,2,3,4, blue cards numbered 1,2,3,4,5,6 and green cards numbered 1,2,3,4,5,6,7,8,9. if a single card is picked at random, what is the probability that the card is blue? give your answer as a fraction.
if a single card is picked and if it is blue card then the probability is 6 / 19 .
What is probability ?Probability means possibility of happening of event, it varies from 0 to 1.
Generally it helps us in determining odds of this situation. Probability expresses that situation.
Probability is defined as the the number of favourable outcomes to the total number of outcomes.
Red Cards = 1, 2, 3, 4
Blue Cards = 1, 2, 3, 4, 5, 6
Green Cards= 1, 2, 3, 4, 5, 6, 7, 8, 9.
Now,
Total number of cards = 19
P ( Blue card ) = [tex]\frac{Number of blue cards}{Total number of cards}[/tex]
= 6 / 19
Hence, if a single card is picked and if it is blue card then the probability is 6 / 19 .
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there are three different cars that you could buy. they differ in initial cost, annual operating costs, and life. your minimum acceptable rate of return is 14%. use the ror method to select the best alternative.
You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%
Given,
There are three different cars that you could buy. They differ in initial cost, annual operating costs, and life. Your minimum acceptable rate of return is 14%. Use the ROR method to select the best alternative.
Alternative A B C
Initial Cost 10,000 8,000 5,000
Annual Cost 1,000 1,500 1,500
Life 8 years 8 years 5 years
Here,
Rate of Return of car A = (10,000 - 1000 x 8) / 100 = 2000/100 = 20%
Rate of Return of car B = (8,000 - 1500 x 8) / 100 = -4000/100 = -40%
Rate of Return of car B = (5,000 - 1500 x 5) / 100 = -2500/100 = -25%
That is,
You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%
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Construct the lowest-degree polynomial given the zeros below. Then, choose the intervals that contain the coefficients of the polynomial in the form x3 + bx? + cr + d. -4 + 4i and 4 I A. b€ (-2.3, 2.2),c € (-3, 10), and d € (-22, -15] B. be[-2.3, 2.2),c € (-14, -6), and d € [11, 19] C. be[-5.4, -1],ce 1-3, 10), and d e [123, 134] D. 6 € (2.1, 5.3],c el-3, 10), and d e f-138, -126] E. None of the above.
Option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].
Here, we are given a polynomial of the form [tex]x^{3}[/tex] + b[tex]x^{2}[/tex] + cx + d
The zeroes of the polynomial are ( -4 + 4i ) and 4
The third root of the cubic equation will be (-4 - 4i) which is the conjugate of (-4 + 4i)
This means that for x = ( -4 + 4i ), ( -4 - 4i ) and 4, the polynomial is equal to 0.
Further, the sum of zeroes of a cubic equation
= -(coefficient of [tex]x^{2}[/tex] )/(coefficient of [tex]x^{3}[/tex])
Thus, -4 + 4i + 4 - 4 - 4i = -b
b = 4
Similarly, the sum of the product of zeroes taken 2 at a time = c
⇒ (-4 + 4i)(-4- 4i) + 4(-4 + 4i) + 4(-4- 4i) = c
c = 16 -16[tex]i^{2}[/tex] - 16 + 16i - 16 - 16i
c = 16 + 16 - 32
c = 0
Further, product of zeroes = -d
-d = (-4 + 4i) (-4- 4i) 4
d = -(16 + 16i - 16i -16[tex]i^{2}[/tex]) 4
d = -(16 + 16)4
d = -128
Thus, we get that option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].
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What is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle ABC?.
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
Given,
Triangles ABC and A'B'C' are similar
For ABC;- (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, 2)
For A'B'C' ;- (x₁, y₁) = (-4, -1) and (x₂, y₂) = (1, -1)
We have to find the scale factor of the dilation;
Here,
Find the distance AB and distance A'B' with the formula
Distance, d = [tex]\sqrt{(y_{2} -y_{1})^{2} +(x_{2} -x_{1} )^{2} }[/tex]
Then,
a) Distance of AB
d AB = [tex]\sqrt{(2-2)^{2}+(2-0)^{2} }[/tex]
d AB = [tex]\sqrt{0^{2} +2^{2} }[/tex]
d AB = √4
Distance of AB = 2 units
b) Distance of A'B'
d A'B' = [tex]\sqrt{(-1+1)^{2} +(1+4)^{2} }[/tex]
d A'B' = [tex]\sqrt{0^{2} +5^{2} }[/tex]
d A'B' = √25
Distance of A'B' = 5 units
Now,
Scale factor;
Scale factor = Distance of AB / Distance of A'B'
Scale factor = 5/2
Scale factor = 2.5
Therefore,
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
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Unless specified, all approximating rectangles are assumed to have the same width.
Evaluate the upper and lower sums for f(x) = 6 - x², -2 ≤x≤ 2,
with n = 2, 4, and 8. Illustrate each case with a sketch similar to the figure shown below. (Round your answers to two decimal places.)
The upper sum is 24 and the lower sum is 8 for the given function
f(x) = 6 - x², -2 ≤x≤ 2.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given,
f(x) = 6 - x²
-2 ≤x≤ 2
When n=2, partition of interval -2, 0, 2
When x=-2, f(-2)=6-4
f(-2)=2
x=0, f(0)=6-0
f(0)=6
x=2, f(2)=6-4
f(2)=2
Upper sum= M₁S₁+M₂S₂
=6(2)+6(2)
=24
Lower sum=m₁ s₁+m₂ s₂
=2(2)+2(2)
=8
Therefore, upper sum=24 and lower sum= 8
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How do you solve linear systems using linear combinations?.
a system of two linear equations is solved by combining the two equations to eliminate one of the variables.
Using the linear combination method, a system of two linear equations is solved by combining the two equations to eliminate one of the variables. Once one of the variables is eliminated, an equation with only one variable is left, e.g., 2x=2, and it is very simple to see that in this case, x=1
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your subject-matter expert tells you that her most likely estimate to complete her task is 40 hgours. the task starts on thrusday, january 20, at 8 a.m.
The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.
Given that,
Your subject-matter expert informs you that she believes it will take her 40 hours to finish the work. The project begins on January 20 at 8 a.m. The staff only works throughout the weekdays, eight hours a day.
We have to find when will the assignment be completed.
We know that,
This simple table explains the answer
Thursday, January 20, at 4 p.m. - 8 hours worked
Friday, January 21, at 4 p.m. - 16 hours worked
Monday, January 24, at 4 p.m. - 24 hours worked
Tuesday, January 25, at 4 p.m. - 32 hours worked
Wednesday, January 26, at 4 p.m. - 40 hours worked
Therefore, The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.
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in a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that group of answer choices the estimated mean of y is 2 when x1 equals zero. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant. the relationship between x1 and y is significant. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, without regard to x2.
In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that B. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant
What is a multiple regression?Multiple regression is a statistical technique for examining the relationship between a single dependent variable and a number of independent variables. The goal of multiple regression analysis is to use known independent variables to predict the value of a single dependent variable.
Multiple regression predicts the value of one dependent variable by taking into account the values of the available multiple independent variables. For example, suppose a researcher decides to study the performance of students at a school over time.
In this case, the correct option is B.
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Which special segments go through a midpoint?.
Bisectors are the special segments that pass through the mid point of the lines or line segments.
A bisector is the line, line segment or ray that intercepts and/or divided lines or line segments into two equal line segments and thus passes through the midpoint of the given line segment or line segments.
There can be infinite bisector for one particular line or line segment at multiple angles.
The bisector that intercepts and/or cuts a line in half, passes through the midpoint when it is perpendicular (making an angle of 90°) to the line segment is known as the Perpendicular Bisector.
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How do you know if a system has one solution or infinitely many?.
If you try to solve an equation and receive a variable or a number equal to itself, the problem has an unlimited number of solutions.
There are an infinite number of solutions to the equation system when two lines coincide with the same y-intercept. If the slope and y-intercept of the two lines coincide, they actually belong to the same line. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). When the two lines that make up a linear system cross each other once, the system has a single solution. When the two lines are identical, as in the cases of y=x+3 and 2y=2x+6, a linear system has several (infinite) solutions. When the lines never cross (i.e., they are parallel and have the same slope), a linear system cannot be solved.
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let v be a finite-dimensional vector space. let t : v !v be a linear transformation. if for each eigenvalue of t , the geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.
The geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.
The word "nilpotent" is missing from the title, rather confusing, since being nilpotent is easily seen to be the only possible obstruction against being diagonalisable for a rank 1 operator. After all, by rank-nullity this implies the nullity equals n−1, and this is (by definition) the dimension of the eigenspace for 0. Also Im(T) is always T-stable, so being of dimension 1 its nonzero vectors are eigenvectors, and if this is for a nonzero eigenvalue λ, then the eigenspaces for 0 and for λ are complementary, and so T is diagonalisable.
So the only thing that can go wrong is that the nonzero vectors of Im(T) are eigenvectors for 0, but then clearly T2=0 so T is nilpotent.
It would have been a bit more fun if instead of T not being nilpotent it had been given that T has nonzero trace. Since 0 is a root of the characteristic polynomial χT with multiplicity at least n−1 (which is its geometric multiplicity), the "final" root of χT equals the sum of all its roots, which is the trace of T. This is also the eigenvalue of nonzero vectors in Im(T), and as we have seen it is zero if and only if T is nilpotent if and only if T is not diagonalisable.
Hence the answer is the geometric multiplicity is equal to the algebraic multiplicity, then t is diagonalizable.
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BBQ Corp. had a 3:1 stock split ratio. Pre-split the company had 1.35 Million outstanding shares at a price of $72.45 per share.
What is the price per share of BBQ Corp. stock post-split?
The price per share of BBQ Corp. after there has been a stock split, or post - split, is $24. 15
How to find the price after a stock split?When there is a stock - split, then each of outstanding shares that a company has, is divided into a number of shares that is determined by the stock split ratio.
The price of the individual shares are also divided into the same ratio as the shares.
This means that the price per share for BBQ Corp. post - split is:
= Price per share before split / 3
= 72. 45 / 3
= $24. 15
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