Answers
Answer:
Proofs provided below
Step-by-step explanation:
[tex]\bold {\text{Prove } (a + b)^2 = a^2 + 2ab + b^2}}[/tex]
[tex]\\\\\implies (a + b)^2 = (a+b) \times (a+b)\\\\\implies (a + b)^2 = a \times (a+b) +b \times (a+b)\\\\\implies (a + b)^2 = a \times a + a \times b + b \times a + b \times b\\\\\implies (a + b)^2 = a^2+ab+ba+b^2\\\\\implies (a + b)^2 = a^2+ab+ab+b^2 \;\;\;\;\text{ since ab = ba}\\\\\implies (a+b)^2 = a^2+2ab+b^2\\\\[/tex]
[tex]\bold{\text{Prove } a^2-b^2 \,=\, (a+b)(a-b)\\\\}[/tex]
1. Add and subtract ab to LHS
[tex]\implies a^2-b^2 = a^2-b^2-ab+ab\\\\\implies a^2-b^2 = a^2-ab+ab-b^2\\\\[/tex]
2. Factorize the above expression
[tex]\implies a^2-b^2 = a(a-b)+b(a-b)\\\\\implies a^2-b^2 = (a-b)(a+b) \;\;\;\; \text{since (a-b) is a common factor in RHS }[/tex]
∴ (a² - b²) = (a - b) (a + b)
[tex]\bold{\text{Prove $\dfrac{\sqrt{3}+1}{\sqrt{3}-1}$= $2+\sqrt{\ensuremath{3}}$}}\\[/tex]
[tex]\text{1. Multiply LHS by $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$}\\\\\implies $\dfrac{\sqrt{\text{}3}+1}{\sqrt{3}-1}$ \times $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$ \\\\[/tex]
[tex]\implies \dfrac{ (\sqrt{3} + 1)(\sqrt{3}-1) }{(\sqrt{3} - 1)(\sqrt{3}-1) }\\\\[/tex]
Numerator is
[tex](\sqrt{3} + 1)(\sqrt{3}-1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\\\\[/tex]
Denominator is
[tex](\sqrt{3}-1)^2 = (\sqrt{3})^2 - 2\cdot \sqrt{3} \;\cdot 1 + (-1)^2\\\\= 3 - 2 \sqrt{3} + 1\\\\= 4 - 2 \sqrt{3}\\\\[/tex]
So LHS becomes
[tex]\dfrac{2}{4 - 2\sqrt{3}} \\\\[/tex]
Dividing numerator and denominator by 2 yields
[tex]\dfrac{2}{4 - 2\sqrt{3}} = \dfrac {1}{2 - \sqrt{3}}[/tex]
Multiply numerator and denominator by [tex]{2-\sqrt {3}}[/tex]
[tex]$\dfrac{1\cdot(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3)}}$[/tex]
[tex]=$\dfrac{\ensuremath{2}+\sqrt{3}}{2^{2}-(\sqrt{3)^{2}}}=$$\dfrac{\ensuremath{\ensuremath{2}+\sqrt{3}}}{4-3}=\ensuremath{2}+\sqrt{3}$[/tex]
Hence Proved
Related Questions
According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
Answers
a) Probability of receiving no e-mails during an hour = 0.0067
b) Probability of receiving at least three e-mails during an hour = 0.8754
c) Expected number of e-mails received during 15 minutes = 1.25
d) Probability that no e-mails are received during 15 minutes = 0.2865
Given that five emails are typically received every hour. If X represents the number of emails received in an hour, then X is poisoned with the given parameter, λ = 5.
⇒ P (X = x) = [tex]\frac{e^{ -x} X^{x}}{x!} = \frac{e^{-5} 5^{x}}{x!}[/tex]
(a) Likelihood of not receiving any emails for an hour = p (x = 0)
= (e⁻⁵5⁰) / 0! = (e⁻⁵ * 1) / 1 = e⁻⁵ = 0.00674 ≈ 0.0067
(b) Likelihood of receiving three or more emails in a single hour P(x ≥ 3)
= 1 - [P (x < 3) = 1 - [P(x = 0) + P(x = 1) + P(x = 2)]
= 1 - [(e⁻⁵5⁰) / 0! + (e⁻⁵5¹) / 1! + (e⁻⁵5²) / 2!]
= 1 - [0.00674 + 0.03369 + 0.08422]
= 1 - 0.12465
= 0.87535 ≈ 0.8754
(c) The number of emails that should be received in the next 60 minutes = an hour's worth of emails on average = 5
As a result, the anticipated quantity of emails received in 15 minutes = 5 / 4 = 1.25
(d) Number of emails received on average every 15 minutes = Number of emails that should be received in the next 15 minutes = 1.25
Let X represent how many emails were received in 15 minutes. X then proceeds with a parameterized Poisson distribution, λ = 1.25
⇒ P (x = X) = [tex]\frac{e^{-x} X^{x} }{x!} = \frac{e^{-1.25}1.25^{x} }{x!}[/tex]
The likelihood that no emails will be received during the next 15 minutes = [tex]\frac{e^{-1.25}* (1.25)^{0} }{0!} = \frac{e^{-1.25}*1 }{1} = e^{-1.25} = 0.2865[/tex]
COMPLETE QUESTION: According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?
b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.
c. What is the expected number of e-mails received during 15 minutes (to 2 decimals)?
d. What is the probability that no e-mails are received during 15 minutes (to 4 decimals)?
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Order -9, -8, 15, 0 from greatest to least
Answers
15, 0, -8, -9
Negatives go backwards
Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?
Answers
Answer:
Josie can by 4 dish sets.
Step-by-step explanation:
Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?
can be represented by equation:
35d + 10 = 150
subtract 10 from both sides:
35d + 10 - 10 = 150 - 10
35d = 140
divide both sides by 35:
35d/35 = 140/35
d = 4
Josie can by 4 dish sets.
check:
35(4) + 10 = 150
During an experiment, the temperature of a liquid, in degrees Celsius, is given by the function t(m)= -0.2m+6, where m is the number of minutes since the experiment began.
Which graph correctly shows this function?
Answers
The graph of the linear function t(m) = -0.2m + 6 is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change of the linear function.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis, and can also be interpreted as the initial value of the function.In this problem, the function is defined by:
t(m) = -0.2m + 6.
Hence:
The slope is of m = -0.2.The intercept is of b = 6.To graph the function, we have to consider the constraint that the time cannot be negative, hence the domain is:
t ≥ 0.
Thus, the graph is given by the image at the end of the answer.
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How would I answer and what would be the answer?
Answers
Given the exression:
[tex]\frac{x-1}{x+4}-\frac{4x-11}{x+4}[/tex]Let's solve the expression and identify the error.
Since both expressions have the same denominator, let's combine the numerators:
[tex]\frac{(x-1)-(4x-11)}{x+4}[/tex]Apply distributive property:
[tex]\begin{gathered} \frac{x-1-4x-(-11)}{x+4} \\ \\ \frac{x-1-4x+11}{x+4} \end{gathered}[/tex]Combine like terms in the numerator:
[tex]\begin{gathered} \frac{x-4x-1+11}{x+4} \\ \\ \frac{-3x+10}{x+4} \end{gathered}[/tex]The error in the problem was that distributive property was not applied when the numerators were combined.
ANSWER:
[tex]\frac{-3x+10}{x+4}[/tex]Janet has $50 in a savings account that earns 10% annually the interest is not compounded how much interest will she earn in the next three years
Answers
When Janet has $50 in a savings account that earns 10% annually, the interest is $15.
How to calculate the interest?It should be noted that the interest is the extra amount that's given for keeping money for a specified period of time. Interest is the payment of a sum over and above the original amount owed by a lender or deposit-taking financial institution to a depositor or lender, at a set rate.
The formula for calculating interest is given as:
Interest = PRT / 100
where P = Principal. = $50
R = rate = 10%
T = Time = 3
Interest = PRT / 100
Interest = (50 × 10 × 3) / 100.
Interest = 1500 / 100
Interest = $15
The interest is $15.
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find slope of the line that passes through each pair of points 4,3 -1,6
Answers
Answer:
Formula for slope is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.
Slope = (6 - 3)÷(- 1 - 4)
= -3/5
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
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hihihihihiihiihihihihihihhi
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Please Help
this is math, PLEASE HELP
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A statement of order that shows the relation of the in-town speed limit to the highway speed limit is that the in-town speed limit is less than or equal to 30 and the highway speed limit is less than or equal to 60.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
The rules for writing an inequality.In Mathematics, these four rules are generally used to write an inequality:
When the arrow points to the right on a number line, the inequality is either (≥ or >).When the arrow points to the left on a number line, the inequality is either (≤ or <).The circle/dot on a number line should be filled when the inequality symbol is (≥ or ≤).The circle/dot on a number line should not be filled when the inequality symbol is (> or <).Now, we would apply the aforementioned inequality rules to write the solution to the compound inequality shown in the graph above:
30 ≤ x ≤ 60.
In conclusion, x represent the speed limit for in-town and highway.
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pls help with geometry 9th-grade honors
Answers
The measures of the internal angles of the triangle are given as follows:
Angle A: 55º.Angle B: 90º.Angle C: 35º.What is the sum of the internal angles of a triangle?
A triangle is composed by three internal angles, and the sum of it's measures is of 180º.
In the context of this problem, the measures are given as follows:
Angle A: 3x + 10.Angle B: 6x.Angle C: 2x + 5.Considering that the sum is of 180º, we can build an equation to solve for x as follows:
3x + 10 + 6x + 2x + 5 = 180
11x + 15 = 180
11x = 165
x = 165/11
x = 15
Hence the measures of the angles are given as follows:
Angle A: 3(15) + 10 = 55º.Angle B: 6(15) = 90º.Angle C: 2(15) + 5 = 35º.More can be learned about the sum of the internal angles of a triangle at https://brainly.com/question/25215131
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The measure of the angles are;
m∠ A = 55 degreesm∠ B = 90 degreesm∠ C = 35 degreesHow to determine the value of each angleIt is important to note that the sum of angles in a triangle is supplementary.
Also, supplementary angles are defined as pair of angles that sum up to 180 degrees.
Two angles are termed supplementary when they add up to give 180 degrees.
Since, we have that the sum of the interior angles of a triangle are supplementary, then,
Angle A + Angle B + Angle C = 180 degrees
Given the values as;
m∠ A = 3x + 10m∠ B = 6xm∠ C = 2x + 5Now, put or substitute the values into the formula
3x + 10 + 6x + 2x + 5 = 180
collect like terms
3x + 6x + 2x = 180 - 15
Add or subtract like terms
11x = 165
Make 'x' the subject by dividing both sides by the coefficient of x, we have;
11x/11 = 165/11
Find the quotient
x = 15
But we have to find the angles by substituting the value of x
m∠ A = 3x + 10 = 3(15) + 10 = 55 degrees
m∠ B = 6x = 6(15) = 90 degrees
m∠ C = 2x + 5 = 2(15) + 5 = 35 degrees
Hence, the angles are 55 degrees, 90 degrees and 35 degrees respectively.
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Need help with Stats homework, Picture has been uploaded of the question
Answers
Solution:
Given that a livestock company reports that the mean weight of a group of young steers is 1123 pounds with a standard deviation of 84 pounds, this implies that
[tex]\begin{gathered} \mu=1123 \\ \sigma=84 \\ \end{gathered}[/tex]A) Percentage of steers that weigh over 1300 pounds.
Step 1: Evaluate the z score value.
The z score value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\Rightarrow sample\text{ value} \\ \mu\Rightarrow mean\text{ value} \\ \sigma\Rightarrow standard\text{ deviation of the sample} \end{gathered}[/tex]In this case, x equals 1300.
Thus, the z score value is evaluated as
[tex]\begin{gathered} z=\frac{1300-1123}{84} \\ \Rightarrow z=2.107142857 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh over 1300 pounds.
Using the normal distribution table, we have
thus,
[tex]\begin{gathered} Pr(z>1300)=0.0175525991947 \\ \end{gathered}[/tex]The percentage of young steers that weigh over 1300 pounds is thus evaluated as
[tex]\begin{gathered} 0.0175525991947\times100 \\ =1.7552991947\% \\ \approx1.8\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]B) Percentage of steers that have weights under 1050 pounds.
Step 1: Evaluate the z score value.
Thus, we have
[tex]\begin{gathered} z=\frac{1050-1123}{84} \\ =-0.869047619 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would have weights under 1050 pounds.
Using the normal distribution table, we have
thus,
[tex]Pr(z<1050)=0.192410542709[/tex]Thus, the percentage of young steers that would have weight under 1050 pounds is evaluated as
[tex]\begin{gathered} 0.192410542709\times100 \\ =19.2410542709\% \\ \approx19.2\%(\text{ 1 decimal place\rparen} \end{gathered}[/tex]C) Percentage of young steers that weigh between 1000 and 1200 pounds.
Step 1: Evaluate the z score value.
[tex]\begin{gathered} z_1=\frac{1000-1123}{84} \\ =-1.464285714 \\ z_2=\frac{1200-1123}{84} \\ =0.9166666667 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh between 1000 and 1200 pounds.
Using the normal distribution table, we have
thus, we have
[tex]Pr(1000Thus, the percentage of young steers that weigh between 1000 and 1200 pounds is evaluated as[tex]\begin{gathered} 0.748783381404\times100 \\ =74.8783381404\% \\ \approx74.9\% \end{gathered}[/tex]Suppose that 15% of the time Danny goes swimming twice a week, 35% of the time he goes swimming once a week, and 50% of the time he doesn't go swimming at all in a given week. What is the expected value for the number of times Danny goes swimming during a week?
Answers
The expected value for the number of times Danny goes swimming during a week is 0.65.
Given that:-
Percentage of time Danny went swimming twice a week = 15 %
Percentage of time Danny went swimming once a week = 35 %
Percentage of time Danny doesn't go swimming at all in a given week = 50%
The expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.
Hence, based on the data given in the question, we can write,
Expected value n how many times Danny will go to swimming in a week = 15 %*2 + 35 % * 1 + 50 % *0 = 0.3 + 0.35 + 0 = 0.65
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4. Solve the quadratic equation x² = 16.
Answers
[tex]x^2=16\\\sqrt{x^2}=\sqrt{16}\\x=\lm+/-4[/tex]
x = 4, x = -4
hope this helps!
x=4,-4
Jacob and Diego are racing to see who can get his community service hours for scouting completed first. Jacob, who has already completed 50 hours, plans to volunteer for 5 hours per week going forward. Diego hasn't started yet, but plans to dedicate 6 hours per week to his volunteer project from now on. Before too long, the boys will be tied, with the same number of volunteer hours. How long will that take?
Answers
Number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
As given in the question,
Let number of weeks be represented by a variable x.
Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.
Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.
For Jacob and Diego to tie in the race, their volunteer hours should be equal. Translating this into a linear algebraic equation,
6x = 5x+50
=> 6x-5x = 50
=> x = 50
Therefore, number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
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A member of a book club wishesto purchase two books from aselection of eight booksrecommended for a certainmonth. In how many ways canshe choose them?Note: Crnn!r!(n-r)!
Answers
From a total of 8 books, she has a choice of 2 in 28 different ways.
What is permutation and combination ?When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.
The member must select 2 books from a group of 8 books in the scenario that is provided. It is not important what sequence you select your books in. If a member chooses books A and B or books B and A, for instance, she is choosing the same books from the list of available titles (A,B,C,D,E,F,G, and H). By extension, this is a problem of combinations since the order of the selections is irrelevant in this situation.
Eight books, two at a time, must be combined to produce
The general formula of combination is :
[tex]nC_{r} = \frac{n!}{r!(n-r)!}[/tex]
Using the values of n=8 and r=2, we get:
[tex]8C_{2}[/tex] = [tex]\frac{8!}{2!(8-2)!}[/tex]
=28
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Find the measure of <1, <2, and <3.
Answers
The measure of the angles for the given parallel lines are-
∠1 = 100°∠2 = 80°∠3 = 100°What is defined as the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair always is 180°. These angles are also referred to as supplementary angles. The adjacent angles include those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
The set of parallel lines are given;
Thus,
∠1 + 80 = 180 (linear pair)
∠1 = 100°
Now, two set of parallel line form a parallelogram.
Thus, in parallelogram opposite angles are equal.
∠1 = °∠3 = 100°
So, ∠3 = 100°
And, ∠2 = 80° (opposite angle of 80)
Thus, the measure of the angles are calculated.
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a final exam in math 160 has a mean of 73 with standard deviation 7.2. if 22 students are randomly selected, find the probability that the sample mean of their test scores is less than 75
Answers
The probability is that the mean of their test scores is less than 70.
What is probability?
A probability is a number that reflects tha chance of particular event will occur.
Sol-
As per the question given-
Mean = 73
Standard daviation=7.2
Number of students randomly selected =22
Let's take n number for experiment of outcomes.
The number of favorable outcomes can be denoted by x.
The formula to calculate the probability is -
probability = favorable
Outcomes/total outcomes =x/n
The number of standard daviation form the mean is called z.
Z = (x-¥)/€
Z=(75-73)(7.2/√22)
Z= -37.0582965
P(z<-37.05)
= 37.05
There for the probability is 37.05.
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Darius runs with an acceleration of 21 m/s2 and has a force of 400N. Calculate his mass.
Answers
we can use the formula
[tex]F=m\times a[/tex]where F is the force, m the mass and a the acceleration
now, replacing
[tex]400=m\times21[/tex]then solve for m
[tex]\begin{gathered} m=\frac{400}{21} \\ \\ m=19.05 \end{gathered}[/tex]the mass is 19.05Kg
Newton had 15 baseball cards. Today he bought 3 packs of baseball cards. Now he has a total of 45 baseball cards. Write and solve an equation to determine how many baseball cards were in each pack
Answers
Answer:
15 I did 15+15+15 or 15x3 and it equals 45
Step-by-step explanation:
Brainliest?
15
Divide 45 by 3 because newton has 15 base ball cards and each card has fifteen card in each pack
match the angle to its corresponding visual representation
Answers
1) Alternate interior angles
2) Corresponding angles
3) Alternate exterior angles
4) Same-side interior angles
5) Vertical angles (angles opposite of each other)
Describe the rate of change for the function f (x)=[tex]\sqrt{x}[/tex]
Answers
The rate of change is [tex]\frac{1}{2\sqrt{x} }[/tex]
What is rate of change ?The link between one quantity changing in respect to another is given by the rate of change formula.can be used to calculate the rate of change from y coordinates to x coordinates (x2 - x1 ). The rate of change m for a linear function is written as y=mx+b in the slope-intercept form for a line, whereas the rate of change for a function is written as (f(b)-f(a))/b-a. It is said that the rate at which one quantity changes in relation to another is known as the rate of change function. The amount of change in one item is simply divided by the comparable amount of change in another when calculating the rate of change.
Given that : The function f (x)=[tex]\sqrt{x}[/tex]
f (x)=[tex]\sqrt{x}[/tex]
[tex]f^{'} x = \frac{1}{2\sqrt{x} }[/tex]
The rate of change is [tex]\frac{1}{2\sqrt{x} }[/tex]
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If a= -2, b= -4, and C=5,
evaluate c-(a+b)
Answers
A metal sculpture has a total volume of 1250 cm³ and a mass of 9.2 kg.
Work out its density, in grams per cubic centimetre (g/cm³).
Give your answer to 2 d.p
Answers
Answer:
7.36 g/cm3
Step-by-step explanation:
Density = mass ÷ volume
Mass in grams = 9200g
Volume in cm3 = 1250cm3
9200 ÷ 7850 = 7.36
7.36 is already in 2 d.p.
Una masa de 2,0 kg está unida al extremo de una cuerda de 5,0 m. La masa se mueve en una trayectoria circular sobre una superficie horizontal sin rozamiento. Si la resistencia a la rotura de la cuerda es 40 N, la máxima velocidad lineal con la que se puede hacer girar la masa sin que se rompa la cuerda es aproximadamente
Answers
La maxima velocidad lineal de la masa con la que se puede girar la masa es igual a 40 newtons.
¿Cuál es la velocidad lineal máxima permitida por la masa en movimiento circular uniforme?
En este problema tenemos el caso de una masa (m), en kilogramos, conectada a una cuerda y que experimenta un movimiento circular uniforme, en donde la partícula describe un movimiento a velocidad lineal constante (v), en metros por segundo, debido a una aceleración radial que está en la forma de tensión (T), en newtons, a través de la cuerda. En consecuencia, la velocidad máxima permitida es determinada a partir de las leyes de Newton:
T = m · (v² / R)
Donde:
m - Masa, en kilogramos.v - Velocidad lineal, en metros por segundo.R - Longitud de la cuerda, en metros.Si sabemos que m = 2 kg, R = 5 m y T = 40 N, entonces la maxima velocidad lineal permitida es:
40 N = (2 kg) · v² / (5 m)
v = 10 m / s
La maxima velocidad lineal permitida es igual a 10 metros por segundo.
ObservaciónBrainly no dispone de suficientes problemas en español sobre el movimiento circular uniforme.
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HELPPPPP
How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Answers
Answer:
Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.
What are perfect square expressions?
Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².
Square of the subtraction: (a - b)² = a² - 2ab + b².
The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.
For the expressions in this problem, we have that:
The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.
The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.
Hope this helps :)
Step-by-step explanation:
9. Find an infinite set A such that a. A is finite and b. A is infinite. Use the real numbers R as the universal set.
Please show work.
Answers
An infinite set is infinite from start to end, but both sides can have continuity, unlike a finite set, which has both start and end elements. The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values. It returns a Boolean value for each vector element.
What exactly is a finite number?A countable number less than infinity that is the cardinality of a finite set - that is, some natural number, possibly zero. A genuine number, such as the result of a measurement (of time, length, area, etc.)In other words, it is a set that can be finished counting. 1,3,5,7, for example, is a finite set with four elements. The finite set element is a natural number, i.e. a non-negative integer. A set is infinite if it has an infinite number of elements; finite if the elements can be counted.In R, there are two kinds of infinity. Inf and -Inf represent positive and negative infinity, respectively, whereas NaN stands for 'Not a Number.'Hence, The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values.
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A) What is the probability that a 13-card bridge hand contains i) All 13 hearts? ii) 13 cards of the same suit? iii) Seven spades and six clubs?
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Using the hypergeometric distribution, the probabilities are given as follows:
a) All 13 hearts: [tex]1.57 \times 10^{-12}[/tex]
b) 13 cards of the same suit: [tex]6.30 \times 10^{-12}[/tex]
c) Seven spades and six clubs: [tex]5.4 \times 10^{-9}[/tex]
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
Parameter x is the number of successes.Parameter N is the size of the population.Parameter n is the size of the sample.Parameter k is the total number of desired outcomes.The general parameters in this problem are given as follows:
N = 52, as a standard deck has 52 cards.n = 13, as 13 cards will be chosen.In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}[/tex]
For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:
[tex]p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}[/tex]
For item iii, we want:
Seven spades from a set of 13.Six clubs from a set of 13.Hence the probability is given as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}[/tex]
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6 plus 8 divided by 2
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Using the PEMDAS ( In order to know the order of the operations)
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Accordint to this, we need to divide first, and then we need to add the resultant number, so:
[tex]\begin{gathered} 6+8\div2=6+4=10 \\ \\ \end{gathered}[/tex]Answer:
10
use the ruler to determine the quotients of 1 divided 1/10 and 4 divided 1/10
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First:
1 divided 1/10:
1 divided 1/10= 10.
2. 4 divided 1/10:
Using the same procedure:
4 divided 1/10= 40.
Using the ruler:
this implies counting each millimeter contained in 1 centimeter, when it is 1 centimeter, there are ten centimeters, and when it is 4 cm there are 40 mm.
Answer:
1 divided 1/10= 10
4 divided 1/10= 40