If the expression AXB is defined, and A is a 3X5 matrix, then the dimension of B could be 5XN.
“N” could be the any number as in order to do any multiplication, the number of columns of first matrix and the number of rows of second matrix should be same in order to perform the multiplication between those matrices.
A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. If the matrix has m rows and n columns, it is referred to as a "m by n" matrix, abbreviated "mXn."
A matrix A multiplied by a matrix B yields a matrix C only when the number of columns in the first matrix A equals the number of rows in the second matrix B. To find the element cij, which is in the product's ith row and jth column, multiply the first element in the ith row of A by the first element in the jth column of B, the second element in the row by the second element in the column, and so on until the last element in the row is multiplied by the last element in the column; the sum of all these products yields the element cij.
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1 What is the greatest common factor (GCF) of 2-53 and 3²-7?
Determine the x and y intercept:
X -3 -2 -1 0 1
y 0 2 4 6 8
Learning curve: In psychological tests, it is found that students can memorize a list of words after t hours, according to the learning curve y = 50 - 50e^-0.3t, where y is the number of words a student can learn during the t^th hour of study. Find how many words a student would be expected to learn in the ninth hour of study.
A student is expected to learn approximately 46.535 words in the ninth hour of study.
What is the number of words a student would be expected to learn in the ninth hour of study.?Generally, To find the number of words a student is expected to learn in the ninth hour of study, we can substitute 9 for t in the learning curve equation:
y = 50 - 50e^-0.3(9)
Simplifying the exponent, we have:
y = 50 - 50e^-2.7
To calculate the value of e^-2.7, we can use a calculator or lookup the value in a table of common exponent values. The value of e^-2.7 is approximately 0.0693.
Substituting this value back into the equation, we have:
y = 50 - 50(0.0693)
Simplifying, we find:
y = 50 - 3.465
y = 46.535
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Find the equation of a line parallel to 4x + 4y = -28 that passes
through the point (−4, –4).
Oy-4=x-4
Oy+4= x +4
○y-4=− (x − 4)
Oy+4= (x+4)
Submit Answer
The equation of the line that passes through the point (-4,-4) is y=-x-8.
How to find equation of line?The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
What are three equations of line?The three equation of line are slope-intercept form, standard form and point-intercept form.
4x+4y=-28
Taking 4 common and dividing both sides by 4 gives
x+y= -7
y=-x-7
This means slope that is m=-1.
Now to find c in y=mx+c we need to use points (-4,-4).
-4=(-1)(-4)+c
c=-8
So the equation of line is y=-x-8.
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15 postcards and 10 envelopes = $1.7 envelope is 0.02 cents more expensive than postcard
Answer:
post cards cost .06 each and envelopes cost .08 each.
Step-by-step explanation:
Let p = the cost of the post cards
Let e = the cost of the envelopes
15p + 10e = 1.70
e = p + .02 Substitute p + .02 for e in the first equation
15p + 10(p + .02) = 1.70 Distribute the 10
15p + 10p + .2 = 1.70 Combine like terms
25p + .2 = 1.70 Subtract .2 from both sides
25p = 1.50 Divide both sides by 25
p = .06
Post cards cost .06 each.
Envelopes cost .08 each
ssdfmsfamong treatments1743 435.751.27error total5503.4615step 6 of 8: what is the variation of the individual measurements about their respective means? please round your answer to two decimal places.
The variation of the individual measurements about their respective means is 2295.04.
Given that,
The table of the treatments and total amount is
SS DF MS F
Among Treatments 4974.88 621.86 2.98
Error ?
Total 7269.92 19
We have to find how do the various measurements differ from their respective means.
We know that,
We know the formula
SSE= SSTotal -SST
= 7269.92-4974.88
=2295.04
The variation of the individual measurements about their respective means is SSE that is 2295.04
Therefore, The variation of the individual measurements about their respective means is 2295.04.
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if angle A=125 in the parallelogram below, what is the measure of angle B?
Answer:
angle B = 55°
.............
If you score in the 75th percentile, what does this mean? Your score is 75% Your score is in the third quartile Your score was in the bottom half of the class 25% of the scores were lower than yours
Third or upper quartile, or 75th percentile, is another name for this group. The figure at which 25% of the responses are higher and 75% of the answers are lower is known as the 75th percentile.
A suitable compromise between representing the great majority of measures and being unaffected by outliers is the 75th percentile. The 75th percentile is a suitable choice for identifying medium- to long-term trends even if it is less steady than the median. Additionally, we believe that when establishing performance budgets, the 75th percentile is the ideal figure to employ. Although the term "percentile" is frequently used, it lacks a common definition. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall. You may already be aware of your test score of 67 out of 90. But without you know the percentile you fall into, that number has no actual relevance. If you know that you scored in the 90th percentile, it signifies that you outperformed 90% of test-takers.
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Mitch sells thingamabobs. His revenue is modeled by the function
R(h) = 5h+8 for every h hours he spends working. His overhead cost is
modeled by the function C'′(h) = h² + 7h − 16. After how many hours does
he break even?
The number of hours to breakeven will be 5 hiurs
How to calculate the breakeven?The breakeven is the point at which the cost and the revenue are equal.
Since Mitch sells thingamabobs. His revenue is modeled by the function R(h) = 5h+ + 8 for every h hours he spends working and his overhead cost is modeled by the function C'′(h) = h² + 7h − 16.
This wll be:
Revenue = Cost
5h + 8 = h² + 7h - 16
Collect like terms
h² + 7h - 5h - 16 = 0
h² - 2h - 16 = 0
Solving the equation will give h as 5.
The number of hours will be 5 hours.
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Does the picture represent a function?
Yes or No
Answer: Yes
Step-by-step explanation: To determine if this graph represents a function, we use what is called the vertical line test.
In other words, if we can draw a vertical or straight up and down line that passes through more than one point on the graph, the relation is not classified as a function.
In this case, it's impossible to draw such a line that hits more than one point on the graph so the relation is a function.
The cost of 7 sandwiches and 5 milkshakes is $79. The cost of 2 sandwiches and 5 milkshakes is $44. How much does one sandwich cost and one milkshake cost?
Cost of one sandwich is $7 and cost of milkshake $5.
What is an equation?
In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
According to question:
let cost of one sandwich be x and cost of milkshake be y .
7x + 5y = $79 -------(1)
2x + 5y = $44 -------(2)
subtracting equation 2 from 1 , we get
5x = 35
x = $7
so cost of one sandwich is $7.
now substituting value of x in equation 1 , we get
7(7) + 5y = 79
49 +5y = 79
5 y = 20
y = 4
so cost of one milkshake is $5.
Hence cost of one sandwich is $7 and cost of milkshake $5.
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Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V=P(1-r)^t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 1/2 years
According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.
What is the equation?The equation is a mathematical statement or model that shows that two mathematical expressions are equal.
In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.
Cost of the new car = $25,000
Depreciation rate per annum = 20%
Value of the car = V
The price paid initially = P = $25,000
The annual rate of depreciation = r
Depreciation period = 4¹/₂ years
Equation model: V=P(1-r)^t
Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂
= $9,158.93
= $9,200
Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.
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3 times 1 1/2 times 2 1/2 
Answer:
6
Step-by-step explanation:
Trust the process
Five times a number is 375. What is the number?
Answer:
75.
Step-by-step explanation:
We need to divide 375 by 5 since we are looking for 5 times a number. This will give us the answer, 75.
Answer:
75.
Step-by-step explanation:
We need to divide 375 by 5 since we are looking for 5 times a number. so the answer is 75
Which of the following equations has the sum of its roots as 3?
A. 2x2-3x+6=0
B. -x2+3x-3=0
C. 3x2-3x+3=0
D. x2+5x+6=0
-x2+3x-3=0 is the equation that has the sum of its roots as 3.
What is meant by sum of roots?A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.
Write general formula for the sum of roots.Sum of roots= -b/a
Sum of root is defined as:
Sum of root = -b/a
Consider option B -x^2+3x-3
a=-1 , b=3
Sum of root= - 3/(-1)=3
So B is the correct option of the following question.
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(2x^2 - 4x + 3) + (5x - 6x^2 - 1)
Answer:
The answer is (-4x² + x + 2)
Step-by-step explanation:
(2x² - 4x + 3) + (5x - 6x² - 1)
open the brackets
2x² - 4x + 3 + 5x - 6x² - 1
rearrange the priority order
2x² - 6x² - 4x + 5x + 3 - 1
combine like terms
-4x² + x + 2
Thus, The answer is (-4x² + x + 2)
Find x, given
AD = BC = 6m.
The value of x in the trapezium is 60 degrees.
How to find the angle of a trapezium?A trapezium is a quadrilateral . The sum of angles in the trapezium is 360 degrees. The legs of the trapezium ABCD are congruent.
The length AB and CD are parallel to each other.
Let's find the angle x as follows:
Therefore, using trigonometric ratios,
cos x = adjacent / hypotenuse
Where
adjacent side = 3 m
hypotenuse side = 6 m
Hence,
cos x = 3 / 6
cos x = 1 / 2
x = cos ⁻¹ 0.5
x = 60 degrees
Therefore,
x = 60 degrees.
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four feet of wire is used to form a square and a circle. how much wire should be used for the square and how much should be used for the circle to enclose the maximum total area
The total maximum area enclosed by both the shapes square and a circle using given wire is equal to 2.27 square feet.
As given in the question,
Let 'x' be the side length of the square
And 'r' be the radius of the circle.
Length of the wire = 4 feet
Maximum side length of the square is:
4x = 4
⇒ x = 1feet
Maximum area of the square = x²
= 1²
= 1
Maximum radius of the circle is:
2πr = 4
⇒ r = 2 / π
Maximum area of the circle = πr²
= π × (2/π)²
= 4 / π
Total maximum area enclosed by square and a circle
= 1 + (4/π)
= 1 + 1.27
= 2.27 square feet.
Therefore, the total maximum area enclosed by square and a circle from the given wire is equal to 2.27 square feet.
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In the United States, the common paper size is called letter size and measures 8. 5 by 11 inches. Let
V(x)= (8. 5-2x)(11-2x) (x) be the volume in cubic inches of a box made from a letter size paper
by cutting out squares of side length x in inches from each corner and then folding up the sides.
What is a reasonable domain for V in this context? Explain or show your reasoning.
PLs help
Answer:
0 < x < 4.5
Step-by-step explanation:
You want the reasonable domain of V(x) = (8.5 -2x)(11 -2x).
Reasonable domainThe equation describes volume (V) and cut length (x), so both need to be positive. Volume will be positive when ...
8.5 -2x > 0
4.25 > x
The reasonable domain is 0 < x < 4.5.
Write the equation of the circle with a radius of 10 and a center at (3,-1)
Answer:
[tex]\textsf{b)} \quad (x-3)^2+(y+1)^2=100[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
center = (3, -1)radius = 10Substitute the given center and radius into the formula to create the equation of a circle with the given parameters:
[tex]\implies (x-3)^2+(y-(-1))^2=10^2[/tex]
[tex]\implies (x-3)^2+(y+1)^2=100[/tex]
The ratio of cats to dogs in a room is 4:5, If there are 20 cats in the room, how many dogs are there
Answer: 25 dogs
Step-by-step explanation:
We know that every 4 cats will be with 5 dogs
So
First, take 20 divided by 4 = 5
Then take 5 times 5 = 25 dogs
Andrea is 165 cm tall, correct to the nearest cm. Joel is 170 cm tall, correct to the nearest 10 cm. Calculate the upper and lower bound for each person.
Andrea lower bound =
Andrea upper bound =
Joel lower bound =
Joel upper bound=
Answer:
Step-by-step explanation:
andrea lb: 164.5cm
andrea ub: 165.5 cm
joel lb: 165
joel ub: 175
an automobile assembly line runs for 9 3/4 hours each day. employees work 3/4-hour shifts. how many shifts are there in each day
A. 9 shifts
B. 10 shifts
C. 12 shifts
D. 13 shifts
Answer:
D 13 shirt
Step-by-step explanation:
9 [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{3}{4}[/tex]
[tex]\frac{39}{4}[/tex] x [tex]\frac{4}{3}[/tex] = 13
what is the quadratic equation in standard form with rational coefficents that has a root of 5+4i?
Answer:
x^2 -10x + 41 = 0
Step-by-step explanation:
They gave you a root. A root is a solution, is a zero, is an x-intercept(if real).
This is a working backwards problem. They gave you an answer and want the equation back again.
x = 5 + 4i
working backwards:
x - (5 + 4i) = 0
x - 5 - 4i = 0
This left side is a factor of your equation.
If 5+4i is a root then 5-4i is also a root. So do the same thing:
x = 5 - 4i
x - (5 - 4i) = 0
x - 5 + 4i = 0
x - 5 + 4i and
x - 5 - 4i are the factors. Multiply them together to find the quadratic equation. Use distributive property or difference of squares or an area model to model. See image.
Answer:
x² - 10x + 41 = 0
Step-by-step explanation:
complex roots occur as a conjugate pair.
given x = 5 + 4i , then x = 5 - 4i is also a root
the corresponding factors are
(x - (5 + 4i) ) , (x - (5 - 4i) ) , that is
(x - 5 - 4i) and (x -5 + 4i)
the quadratic equation is then the product of the factors, that is
(x - 5 - 4i)(x - 5 + 4i) = 0
multiply each term in the second factor by each term in the first factor.
x² - 5x + 4ix - 5x + 25 - 20i - 4ix + 20i - 16i² = 0 ← collect like terms
x² - 10x + 25 - 16i² = 0 [ note i² = - 1 ]
x² - 10x + 25 + 16 = 0
x² - 10x + 41 = 0 ← in standard form
one apple and six bananas cost £2.70
one apple and eight bananas cost £3.50
Work out the cost of an apple and a banana
PLSSS HELP TYSM
Answer:
An apple costs 0.30 pounds and a banana costs 0.40 pounds.
Step-by-step explanation:
Let's think of apples as x and bananas as y.
Using the given information, you can write two equations.
[tex]x+6y=2.70[/tex]
[tex]x+8y=3.50[/tex]
x can also be written as
[tex]x=2.70-6y[/tex]
We can plug this equation into the second one to solve for y, or the cost of a banana.
[tex](2.70-6y)+8y=3.50[/tex]
[tex]2y=0.8[/tex]
[tex]y=0.4[/tex]
Now that we know the cost of a banana, we can go back to the first equation and solve for x, or the cost of an apple.
[tex]x+6(0.4)=2.70[/tex]
[tex]x=0.30[/tex]
Therefore, an apple costs 0.30 pounds and a banana costs 0.40 pounds.
Graph the line that passes through the coordinates below and determine which statement is true.
A.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
D.
The line that passes through the given coordinates represents a proportional relationship because the line passes
Answer:
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
the cdc estimated that 12% of women who have recently given birth suffer from ppd. however, this research only reflected self-reported cases. therefore, one group dedicated to helping women and their families with ppd believes that the true percentage of women who suffer from ppd is much higher. the group conducts a simple random sample of 139 women who had given birth in the last year and discovers that 25 of them report having ppd. based on this evidence, can the group claim that the true percentage of women who have ppd is greater than 12%? use a 0.05 level of significance. step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
The actual percentage of female people with ppd is more than 12%.
What is ppd ?Many women experience postpartum depression (commonly known as PPD), which is a medical disorder. After giving delivery, there are intense emotions of sadness, anxiety (concern), and exhaustion that persist for a long time. You may find it challenging to care for both you and your infant as a result of these feelings. PPD can occur at any point following childbirth. Within 1 to 3 weeks of giving birth, it frequently begins. To get better, it need treatment.
What does true percentage mean in statistics?And that's basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score. The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it's the same result on a different scale
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What is 8/15 simplyfied??
Answer:
8/15
Step-by-step explanation:
There is no GCF (greatest common factor) in this. These numbers are relatively prime.
Wendy spent 1/4of her paycheck on Monday and
3/7of it on Tuesday. She spent the rest of her
paycheck over the next 3 days. If Wendy spent $18 on each of the 3 days, what was the amount of
her paycheck
Answer:
$56.00
Step-by-step explanation:
Check:
1/4(56) + 3/7(56) + 18 =
14 + 24 + 18 = 56
See the picture below. I wanted to figure out what fraction of the paycheck was the 18.
I took 1 which is the whole pay check and subtracted out the fractions that I knew were spent 1/4 and 3/7. That left me with 9/28. So I knew 9/28 of the paycheck was 18 dollars. I drew out 28 squares. 9 of those squares was worth $18. That meant that each square was worth $2. 2 x 28 = 56
Which of the following pairs of linear equations are consistent or inconsistent XY 8 3x -- 3y 16?
The equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.
What are linear equations?Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
The definition of linear equations, the standard form for linear equations involving one variable, two variables, or three variables, and examples of each will all be covered in detail in this article.
Find the value of the variable that causes the equation to be true in order to solve linear equations.
Utilize the inverse of the variable's multiplier and divide or multiply both sides by it.
To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.
So, we have the pair of linear equations:
x – y = 8 and 3x – 3y = 16
(a1/a2) = 1/3
(b1/b2) = -1/-3 = 1/3
(c1/c2) = 8/16 = 1/2
Since, we know that (a1/a2) = (b1/b2) ≠ (c1/c2).
The equations have no solutions and run parallel to one another. The pair of linear equations is hence incoherent.
Therefore, the equations have no solutions and run parallel to one another. The pair of linear equations is hence inconsistent.
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Complete question:
Find out whether the following pairs of linear equations x – y = 8 and 3x – 3y = 16 are consistent/inconsistent.
