Answer:
One
Step-by-step explanation:
The equation 9x+7=8x+7 has only one solution. This can be seen by setting the two sides of the equation equal to each other and then solving for x.
First, we set the two sides equal to each other by canceling out the 7 on the right side of the equation:
9x+7 = 8x+7
Then, we move all of the terms that have an x on the same side of the equation, and all of the constant terms on the other side:
9x - 8x = 7 - 7
Next, we combine like terms on the left side of the equation:
x = 0
Finally, we solve for x to find the value of x that makes the equation true:
x = 0
Therefore, the only solution to the equation 9x+7=8x+7 is x=0.
The functions f and g are defined by the following tables:
Function
Find the following composition of two functions: (f o g)(0) and (g o f)(1).
Write the appropriate formula(s). What is the domain of the function g(x) ? What is the range of the function f(x) ?
The following composition of two functions ( f o g ) ( 0 ) = 1 and ( g o f ) ( 1 ) = 1 .
Given :
The functions f and g are defined by the following tables:
Tables :
x -2 -1 0 1
f ( x ) 1 2 1 0
x 1 -3 0 -4
g ( x ) -2 0 1 5
( f o g ) ( 0 ) = ( f ( g ( 0 ) )
from the table g ( 0 ) = 1
= ( f ( 0 ) )
= 1
( g o f ) ( 1 ) = ( g ( f ( 1 ) )
= ( g ( 0 ) )
= 1
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Ms.Jones bought a piece of cloth measuring 3 3/4 meters by 2 2/7. She bought the cloth at $14 per square meter. How much did Ms.Jones pay for the cloth?
Answer:
$120
Step-by-step explanation:
1) rewrite the mixed numbers into improper fractions. We do this by multiplying the denominator by the whole number, and then adding the numerator. The numerator stays the same:
[tex]3 \frac{3}{4} = \frac{(4 \times 3) + 3}{4} = \frac{15}{4} [/tex]
[tex]2 \ \frac{2}{7} = \frac{(7 \times 2) + 2}{7} = \frac{16}{7} [/tex]
So the length of the cloth = 15/4 meters
width of the cloth = 16/7 meters
2) Calculate the area of the cloth:
area = length × width
[tex]area \: = \: \frac{15}{4} \times \frac{16}{7} = \frac{240}{28} = \frac{60}{7} (simplest form)[/tex]
area = 60/7 m²
3) The cloth costs $14 per square meter, so the total cost of the cloth is:
the area of the cloth × cost of cloth per square meter
[tex]cost \: = \: \frac{60}{7} \times 14 = \frac{840}{7} = 120[/tex]
the cost is $120
Sarah budgeted $100 for new art supplies. When Sarah purchased the supplies, she
spend $75. What type of variance does this represent?
You are doing a Diffie-Hellman-Merkle key exchange with Aisha using generator 7 and prime 437. Your secret number is 227. Aisha sends you the value 308. Determine the shared secret key.
Answer:
382^2 mod
Step-by-step explanation:
To determine the shared secret key, we need to use the formula (g^a mod p)^b mod p = (g^b mod p)^a mod p, where g is the generator, p is the prime, a is our secret number, and b is the value sent by Aisha. Plugging in the values, we get (7^227 mod 437)^308 mod 437 = (7^308 mod 437)^227 mod 437.
To solve for the shared secret key, we first need to calculate (7^308 mod 437). This can be done by raising 7 to the 308th power and then taking the remainder when divided by 437. We can do this by repeatedly squaring 7 and taking the remainder each time. This results in the following sequence:
7^2 mod 437 = 49
7^4 mod 437 = 161
7^8 mod 437 = 267
7^16 mod 437 = 9
7^32 mod 437 = 49
7^64 mod 437 = 161
7^128 mod 437 = 267
7^256 mod 437 = 9
7^512 mod 437 = 49
Since 512 is greater than 308, we can stop here and use the value 49 as the result of 7^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: (49^227 mod 437)^308 mod 437 = (49^308 mod 437)^227 mod 437.
To solve for the shared secret key, we need to find the value of 49^308 mod 437. This can be done using the same method as before, by repeatedly squaring 49 and taking the remainder each time. This results in the following sequence:
49^2 mod 437 = 67
49^4 mod 437 = 382
49^8 mod 437 = 221
49^16 mod 437 = 67
49^32 mod 437 = 382
49^64 mod 437 = 221
49^128 mod 437 = 67
49^256 mod 437 = 382
Since 256 is greater than 308, we can stop here and use the value 382 as the result of 49^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: 382^227 mod 437 = 382^227 mod 437.
To find the shared secret key, we need to calculate 382^227 mod 437. This can be done using the same method as before, by repeatedly squaring 382 and taking the remainder each time. This results in the following sequence:
what is the answer. a b c or d
all can be the answer I guess
To show 4 dimensional matching is NP complete, we want to reducte from 3 dimensional matching. The trick is to just pad each triple with an extra coordinate. We need to do this in a way that we don't really change the problem. One way to do this is to just repeat the last coordinate - so that the triple [a, b, c] is mapped to the quadruple [a, b, c, c].
NP finished. Only two jobs share resources with the reduction provided in section A.
what is coordinate?to put in the same order or rank. : to bring into a common action, movement, or condition : harmonize. coordinate schedules. She'll be coordinating the relief effort.
The overall issue is NP-complete. From Independent Set, this is a decrease. We substitute jobs for the graph's vertex points. If there is an edge connecting vertices v and w, we establish a resource called r v,w that v and w can share.
If k = 2, we are simply checking to see if there are any jobs that are resource-exclusive. By checking every pair of jobs, we can accomplish this using sheer force.
NP finished. Only two jobs share resources with the reduction provided in section A.
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Considered the father of sociology, a French philosopher who in 1822 used the term sociology or social physics, highlighting its scientific nature by comparing it to the queen of natural sciences.
The French character who is considered the father of sociology has been Auguste Comte.
¿Who was Auguste Comte?This character was a Frenchman, he himself was a philosopher and is recognized mainly by:
Start what is positivism and its associated elements.Start scientific sociology, that is, sociology with scientific elements and components.Due to the above, Auguste Comte is considered the initiator of the social sciences, which are currently very important sciences for the study of various events.
¡Hope this helped!
3x-12=2x+7 subtract 7 from both sides and subtract 3x from both sides
x=19
According to question,
3x-12=2x+7
Subtracting 7 from both sides
3x-12-7=2x+7-7
⇒3x-19=2x
Subtracting 3x from both sides
3x-19-3x=2x-3x
⇒-19=-x
⇒x=19
∴The value of x is 19.
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The complete question is Find the value of x in the equation 3x-12=2x+7 when 7 and 3x is subtracted from both sides.
hw11.3. projection onto a subspace consider the subspace of spanned by the orthogonal vectors let . compute the orthogonal projecti
The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
What is Projectile Motion ?An item or particle that is projected in a gravitational field, such as from the surface of the Earth, and moves along a curved route while solely being affected by gravity is said to be in projectile motion.
According to the given information
Given, [tex]$\quad b_1=\left[\begin{array}{c}2 \\ 2 \\ -2\end{array}\right], \quad b_2=\left[\begin{array}{l}2 \\ 0 \\ 2\end{array}\right], \quad w=\left[\begin{array}{c}-2 \\ 1 \\ -1\end{array}\right]$[/tex]
We know,
[tex]Proj_{v}(w)[/tex] = [tex]Proj_{b1}(w) + Proj_{b2}[/tex]
[tex]& =\left(\frac{w \cdot b_1}{b_1 \cdot b_1}\right) b_1+\left(\frac{w \cdot b_2}{b_2 \cdot b_2}\right) b_2[/tex]
[tex]w \cdot b_1 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{c}2 \\2 \\-2\end{array}\right][/tex][tex]=-4+2+2=0 \\[/tex]
[tex]w \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]-4+0-2=-6 \\[/tex]
[tex]b_2 \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}2 \\0 \\2\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]4+0+4=8[/tex]
Therefore
[tex]Proj_{v}(w)[/tex] = [tex]\left(\frac{0}{b_1 \cdot b_1}\right) b_1+\left(\frac{-6}{8}\right)\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]
[tex]& =0+\frac{-3}{4}\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]
[tex]& =\left[\begin{array}{c}\frac{-3}{2} \\0 \\-3 \\2\end{array}\right] \\[/tex]
[tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
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One man can paint a garage in 28 hours. After working for 12 hours, he was given a new job, and a second man finished the painting in 18 hours. How long would it take the second man to paint the whole garage alone? Show the setup/equation used to solve.
The number of hours taken by man to paint the whole garage alone is 31.5 hours.
Given that, one man can paint a garage in 28 hours.
What is time and work?The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.
Let x be number of hours taken by second man paint the whole garage.
Work done by first man be 1/28
So, work completed by first man =1/28 ×12
= 12/28
= 3/7
Remaining work is 1-3/7 =4/7
1/x ×18 =4/7
⇒ 18/x=4/7
⇒ 4x=126
⇒ x=126/4
⇒ x=31.5 hours
Therefore, the number of hours taken by man to paint the whole garage alone is 31.5 hours.
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20. Beatrice bought a new car for $28,000. She put down $5,000 and paid $550 for 60 months. What's the total finance charge to Beatrice?
A. $12,000
B. $10,000
C. $16,000
D. $23,000
Answer: B. $10,000
Step-by-step explanation:
$550x60+5,000=38,000
Subtract $38,000 by purchase price.: $28,000.
total is $10,000.
Company A has three times as many customers as company B while company C has 10 customers more than company B. Let x represent the number of customers held by company B, what is the expression so that it represents the total number of customers held by all three companies?
The expression that represents the total number of customers held by all three companies is 5x + 10.
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operands (multiplication, division, subtraction, and addition).
What differentiates a mathematical expression from an equation is the equal symbol because a mathematical expression does not have it.
In simple terms, a mathematical expression is like a phrase in the English language without the complete form of a sentence.
The number of customers held by Company B = x
The number of customers held by Company A = 3x
The number of customers held by Company C = x + 10
The total number of customer for all three companies = x + 3x + x + 10
= 5x + 10
Thus, mathematically, we can conclude that the three companies have 5x + 10 customers.
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The expression that represents the total number of customers held by all three companies is; 5X + 10
What is an Expression?An expression consists of one or more numbers or variables along with one more operation.
X + 1 is an example of an expression.
"X" is the variable, "+" is the operation and 1 is a number. Think of "X" as any number that is unknown.
Representing the variables;
X, Y and Z represents number of customers
Let Company A = Y
Let Company B = X
Let Company C = Z
But,
Company A = 3X
Company C = 10 + X
Therefore;
Total number of customers = Y + X +Z
Substituting;
Total number of customers = 3X + X + 10 + X
Total number of customers = 5X + 10
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I tried but i doubt that's the answer (NO USELESS ANSWERS I WILL REPORT YOU )
Answer:
Step-by-step explanation:
So, they want the equation of the 4 colored lines, not a coordinate.
a --> x=-4
b --> x=4
c --> y=4
d --> y=-2
bc they are horizontal and vertical lines so only one value is staying the same, depending on whether it's vertical or horizontal.
Hi i need help with this question.
The perimeter of the state of Wyoming, given the rectangle ABCD and the vertices, is 1, 282 miles
How to find the perimeter?The perimeter is the distance around the shape so to find the perimeter of the shape, you need to find the distance between the sides of the rectangle and then add them up.
The distance between vertices can be found by the formula :
= ((x2 – x1)² + (y2 – y1)²)
The distance between AB is therefore 3.65 miles.
The distance between BC is 2.76 miles
The distance between CD is 3.65 miles.
The distance between AD is 2.76 miles
The perimeter of Wyoming is therefore :
= ( 3.65 x 2) + ( 2.76 x 2 )
= 12.82 miles x 100
= 1, 282 miles
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Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
What is the probability that a randomly selected bike is green given that the bike has bike tires?
Simplify any fractions.
The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66
Given :
Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .
From the table given :
Total number of 6 road bikes = 4
Total road bikes = 2 + 4 = 6
Probability = 4 / 6
= 2 / 3
= 0.66
Hence the probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .
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kari is thinking about buying a laptop that cost $750 on sale if the sales tax is 7.5% how much money will she need in total to buy the computer
Answer: 806.25
Step-by-step explanation: First, we need to find how much the sales tax is worth in dollars. Recall the formula:
Worth = Wole number x part percent / 100
Now, plug in the numbers:
Worth = 750 x 7.5 / 100
So, 750 x 7.5 = 5625
So, 5625 / 10 = 56.25
But remember, $56.25 is the amount of the SALES TAX. To find the total, we need to add 56.25 to 750. So,
750 + 56.25 = 806.25
Therefore, $806.25 is the TOTAL AMOUNT she needs to pay.
ANSWER PLEASE! DEADLINE 11:00 45+ POINTS
1.
The list represents the number of students who left school early in a 12-day period.
48, 62, 75, 43, 32, 52, 70, 63, 81, 40, 38, 67
Find the mean and interpret its meaning as it relates to the number of students who left school early.
2. The ages of a group of teachers are listed.
25, 32, 33, 35, 41, 43, 45, 48, 52, 55, 60, 62
If another teacher with an age of 45 is added to the data, how would the mean be impacted?
THANKS! ANSWER FAST!
Answer: To find the mean of the number of students who left school early, we must add all of the numbers together and then divide the sum by the number of days.
48 + 62 + 75 + 43 + 32 + 52 + 70 + 63 + 81 + 40 + 38 + 67 = 671
The mean of the number of students who left school early is 56.75 (671 / 12).
This mean represents the average number of students who left school early each day over the 12-day period. It tells us that on average, about 56.75 students left school early each day.
Step-by-step explanation: 2. The mean of the group of teachers' ages is currently (25+32+33+35+41+43+45+48+52+55+60+62)/12=45.5. If another teacher with an age of 45 is added to the data, the mean will be (25+32+33+35+41+43+45+45+48+52+55+60+62)/13=44.5. The mean will be slightly lower, as the additional value of 45 is being added to the sum, but the number of values being averaged is also increasing by 1.
Under an anticockwise rotation about the point O, AOAB is mapped onto AOA'B'. Determine the angle of rotation.
Check the picture below.
let's notice that the triangle is an equilateral triangle, meaning all its sides are congruent and likewise, all its angles are also congruent.
Which of the following designs involves repeated measurement of a variable before and after some event?
Group of answer choices
nonequivalent control group design
interrupted time-series design
matched group factorial design
multiple regression design
The design that involves repeated measurement of a variable before and after some event will be matched group factorial design. Hence, option C is correct.
What is Matched group factorial design?In this kind of experimental design, the research's participants are divided into groups, and key factors are matched to each group. The variables that are used to match the respondents must have an impact on the original study conclusion (the dependent variable).
The benefit of using matched group factorial design is,
Fewer people are needed for this kind of investigation, which could also produce more accurate results and results that are based on more information.
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(XA) 26. In a certain community, 65% people speak Newar language and 45% people speak Gurung language. Find percentage of people who can speak (i) both the languages. (ii) Newari only (iii) Gurung language only.
Answer: (i) 10% (ii) 60% (iii) 40%
Step-by-step explanation:
(i) Newar language = 65%
Gurung language = 45%
Total covers = 110 but to sum it up to base that is 100% then 110-100 is 10.
so, 10% of people speak both the language.
(ii) people who speak only Newari only would be 60% as 5% among them speak Gurung language.
(iii) people who speak only Gurung only would be 40% as 5% among them speak Newari language.
In the diagram below, AB || CD, AD || BC, m/ABC = 110°,
m/CDE = 37° and m/ECB = 43°. Find m/DEC.
A
B
110°
E
D
37°
43°
C
Use photo to understand better PLEASE HELP
PLEASE HELP WILL MARK BARINLIEST
Answer:
Your answer is A.
Step-by-step explanation:
Find all the roots for this polynomial using the steps below.
P(X)=x^3+3x^2+3x+2
List the 4 possible rational roots.
Plug each possible rational root into P(x) to determine which is a root of the polynomial.
Divide P(x) by the root you found in part 2 using synthetic division.
Write the fully factored form of P(x).
Use the quadratic formula to find the solutions of the quadratic factor.
List the 3 solutions of the P(x).
Answer:
[tex]p(x)=(x+2)(x^2+x+1)[/tex]
[tex]x=-2[/tex]
[tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex]
[tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]p(x)=x^3+3x^2+3x+2[/tex]
Rational Root Theorem
If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).
Possible p-values
Factors of the constant term: ±1, ±2
Possible q-values
Factors of the leading coefficient: ±1
Therefore, all the possible values of p/q:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 2}{\pm 1}=\pm1,\pm2[/tex]
Substitute each possible rational root into the function:
[tex]x=-1 \implies p(-1) =(-1)^3+3(-1)^2+3(-1)+2=1[/tex]
[tex]x=1 \implies p(1) =(1)^3+3(1)^2+3(1)+2=9[/tex]
[tex]x=-2 \implies p(-2) =(-2)^3+3(-2)^2+3(-2)+2=0[/tex]
[tex]x=2 \implies p(2) =(2)^3+3(2)^2+3(2)+2=28[/tex]
Therefore, x = -2 is a root of the polynomial since f(-2) = 0.
Divide the polynomial by the root using synthetic division:
[tex]\begin{array}{c|crrr}-2 & 1 & 3 & 3 & 2\\\cline{1-1} & \downarrow &-2&-2&-2\\ \cline{2-5} & 1&1&1&0\end{array}[/tex]
The bottom row (except the last number) gives the coefficients of the quotient. Therefore, the quotient is:
[tex]x^2+x+1[/tex]
So the fully factored form of p(x) is:
[tex]p(x)= (x+2)(x^2+x+1)[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore, the solutions to the quadratic factor are:
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3\cdot -1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3} \sqrt{-1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\:i}{2}[/tex]
The 3 solutions of p(x) are:
[tex]x=-2[/tex][tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex][tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]Question 12
The plans for a zipline are shown. Use two points to determine the slope of the zipline. Then verify that the slope is the same by choosing a
different set of points.
y
B
A
C
The slope of the zipline is Enter your answer as a fraction or decimal.
The slope of the zipline in the given diagram is; -1/3
How to find the slope of the line?The slope of a line is defined as the change in y values divided by change in corresponding x-values.
The formula to find slope here will be;
Slope = (y₂ - y₁)/(x₂ - x₁)
Let us pick two points along line BD namely points C and D.
Coordinate of point C is (7, 2)
Coordinate of point D is; (10, 1)
Thus;
Slope = (1 - 2)/(10 - 7)
slope = -1/3
Let us pick point B and point D now.
Coordinate of point B is; (1, 4)
Thus slope of BD = (4 - 1)/(1 - 10)
= -3/9 = -1/3
The slopes are equal and as such that is the slope of the zip line
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Customers depart from a bookstore according to a Poisson process with rate A per hour Each customer buys a book with probability p, independent of everything else. Find the distribution of the time until the first sale of a book. Find the probability that no books are sold during a particular hour. Find the expected number of customers who buy a book during a particular hour.
The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].
The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]
As per the details share in the above question are as follow,
Poisson process with a rate λ per hour
While customer buys a book with probability p
First we have to find the distribution of the time until the first sale of a book.
Second to find the probability that no books are sold during a particular hour.
Third to find the expected number of customers who buy a book during a particular hour.
Giving the duration till a book sells its first copy
Consider,
Following are some instances of waiting times,
[tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
Now, to calculate the likelihood that no books will be sold at a specific time.
[tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex]
The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].
Consider the Poisson distribution to determine the anticipated number of book purchases during a specific hour.
[tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]
The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex].
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If the distance between points P(3.a) and Q(3, 1) is 4 units then find the value of a.)
Answer:
a = -3
Step-by-step explanation:
The explanation is in the image
g if the determinant of a matrix is , and the matrix is obtained from by adding times the second row to the first, then
Therefore the solution to the given matrix problem is
a)det(B) = det(A) = 3 ,det(B) = 3*det(A) = 9 and c)det(B) = -det(A) = -3
What is matrix ?A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity.
Here,
The following will be demonstrated using determinant properties:
A)Det(B) = 3
B) Det(B) = 9
C) det(B) = -3
Assuming A is a 4x4 matrix, we can see that:
det(A) = 3.
a) In this case, we are adding one row to another row by performing a transformation to the data in A. These operations don't alter the matrix's determinant, therefore in this instance:
det(B) = 3 = det(A)
b) If K is used to multiply a row of A to produce B, then:
B = det(K*det) (A).
In this situation, we have:
det(A) = 3*det(B) = 9
c) If we switch two rows around once (this is an odd permutation), the determinant's sign changes:
det(B) = -det(A) = -3
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The complete question is "If the determinant of a 4 by 4 matrix A is det(A) = 6, and the matrix D is obtained from A by adding 9 times the third row to the first, then det(D) is equal to?"
A 6 percent, semiannual coupon bond has a yield to maturity of 7.4 percent and a Macaulay duration of 5.7. The bond has a modified duration of _____ and will have a _____ percentage increase in price in response to a 25 basis point decrease in the yield to maturity5.4966; 1.37
25 bps decrease in interest rate, bond price increases by 1.425% when A bond with a 6 percent semiannual coupon has a 5.7.
Given that,
A bond with a 6 percent semiannual coupon has a 5.7 Macaulay duration and a 7.4 percent yield to maturity. A 25 basis point drop in yield to maturity will result in a ____ percentage price rise for the bond, which has an adjusted duration of .
We have to fill the blank.
We know that,
% increase in bond price = Duration of bond × % change in interest rate
= 5.70×0.25%
= 1.4250%
Therefore, 25 bps decrease in interest rate, bond price increases by 1.425% when A bond with a 6 percent semiannual coupon has a 5.7.
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Find a parametric representation for the part of the sphere (a surface, not a solid) of radius 4 centered at the origin that lies (a) inside the cone z= 3(x2 +y 2) (b) inside the cone x= 31(y 2 +z 2 )
c) inside the cone y= x +z 2
Hint: you may want to use spherical-like coordinates, where the roles of x,y and z are permuted.
Answer:
Read carefully below
Step-by-step explanation:
We can use spherical coordinates to represent the points on the sphere. These coordinates are typically denoted as (r, θ, φ), where r is the radius of the sphere, θ is the polar angle, and φ is the azimuthal angle.
In order to find a parametric representation of the part of the sphere that lies inside the given cones, we can use the following approach:
First, we need to find the intersection of the sphere and the cone. This is the set of points that satisfy the equations of both the sphere and the cone.
Then, we can use spherical coordinates to represent these points on the sphere.
Finally, we can use these spherical coordinates as parameters in a parametric equation of the form x = x(r, θ, φ), y = y(r, θ, φ), z = z(r, θ, φ) to represent the points on the part of the sphere that lies inside the cone.
Let's use this approach to find a parametric representation of the part of the sphere that lies inside the cone z = 3(x^2 + y^2) in the first case.
To find the intersection of the sphere and the cone, we need to solve the following system of equations:
x^2 + y^2 + z^2 = 16 (equation of the sphere)
z = 3(x^2 + y^2) (equation of the cone)
Substituting the second equation into the first equation, we get:
x^2 + y^2 + 9(x^4 + y^4) = 16
This equation represents an ellipse in the xy-plane. We can use the parametric equations of an ellipse to represent the points on this ellipse:
x = a * cos(t)
y = b * sin(t)
where a and b are the semi-major and semi-minor axes of the ellipse, respectively, and t is a parameter that varies from 0 to 2π.
We can now use spherical coordinates to represent the points on the part of the sphere that lies inside the cone. We can let r be the radius of the sphere (r = 4), θ be the polar angle (0 ≤ θ ≤ π), and φ be the azimuthal angle (0 ≤ φ ≤ 2π).
The parametric equations of the sphere in spherical coordinates are:
x = r * sin(θ) * cos(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(θ)
Substituting the equations for x and y from the ellipse into the equations for x and y from the sphere, we get:
x = 4 * sin(θ) * cos(φ) = a * cos(t)
y = 4 * sin(θ) * sin(φ) = b * sin(t)
z = 4 * cos(θ) = 3(x^2 + y^2) = 3(a^2 * cos^2(t) + b^2 * sin^2(t))
We can solve for a and b in terms of r and θ:
a = 4 * sin(θ)
b = 4 * sin(θ)
Therefore, the parametric equations for the part of the sphere that lies inside the cone z
Solve the problem by finding x. I don’t know how to? Do you.
The solution of the logarithmic equation:
ln(x - 7) = 3
Is x = 27.09
How to solve the logarithmic function?Here we have the following logarithmic function:
ln(x - 7) = 3
And we want to solve this for x.
Remember that the logarithmic function is the inverse of the exponential function, so now we can use the exponential function in both sides so we get:
exp( ln(x - 7) ) = exp(3)
x - 7 = exp(3)
Now we can add 7 in both sides so we isolate x, we will get:
x = exp(3) + 7
x = 27.09
That is the solution of the logarithmic equation.
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