The exercise involves calculations with matrices A, B, and C. We need to determine if matrix products AB, BA, BC, and CB are defined. Additionally, we need to calculate the specific matrix products and determine if BC is equal to CB.
Let's perform the calculations step by step:
(a) To determine if AB is defined, we need to check if the number of columns in matrix A is equal to the number of rows in matrix B. If they are equal, the matrix product AB is defined. If not, the product is not defined.
Matrix A has 2 columns and matrix B has 2 rows, so the product AB is defined.
Calculating AB:
AB = [23 + 83 20 + 88]
[23 + 03 20 + 08]
= [30 64]
[6 0]
To calculate BA, we need to check if the number of columns in matrix B is equal to the number of rows in matrix A. In this case, matrix B has 2 columns and matrix A has 2 rows, so the product BA is also defined.
Calculating BA:
BA = [32 + 02 38 + 02]
[32 + 02 38 + 02]
= [6 24]
[6 24]
(b) To determine if BC is defined, we need to check if the number of columns in matrix B is equal to the number of rows in matrix C. In this case, both matrices have 2 columns and 2 rows, so the product BC is defined.
Calculating BC:
BC = [26 + 85 23 + 81]
[06 + 05 03 + 01]
= [52 22]
[0 0]
To calculate CB, we need to check if the number of columns in matrix C is equal to the number of rows in matrix B. In this case, matrix C has 2 columns and matrix B has 2 rows, so the product CB is also defined.
Calculating CB:
CB = [62 + 30 68 + 30]
[52 + 10 58 + 10]
= [12 48]
[10 40]
Is it true that BC = CB?
BC = [52 22]
[0 0]
CB = [12 48]
[10 40]
BC and CB are not equal. The matrix product is not commutative, so BC and CB may yield different results.
In summary:
(a) AB is defined and the result is:
AB = [30 64]
[6 0]
BA is also defined and the result is:
BA = [6 24]
[6 24]
(b) BC is defined and the result is:
BC = [52 22]
[0 0]
CB is also defined and the result is:
CB = [12 48]
[10 40]
BC and CB are not equal, indicating that matrix multiplication is not commutative.
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Which expression is equivalent to 3/x+2 + 5/x-4
A. -2x+22/(x+2)(x-4)
B. 2x-2/(x+2)(x-4)
C. 8/(x+2)(x-4)
D. 8x-2/(x+2)(x-4)
Answer:
A.−2x2+18x−88x+2
B.2x2+2x+8x+2
C.8x−32x+2
D.8x2+14x+8x+2
Step-by-step explanation:
A car rental agency charges $50 per week plus $0.50 per mile to rent a car.
a. Express the weekly cost to rent the car, f, as a function of the number of miles driven during the week, x.
b. How many miles did you drive during the week if the weekly cost to rent the car was $100?
John bought 5 notebooks for a total of $10. Which equation could be used to calculate the cost of the notebooks, y, based on the number
of notebooks purchased, x?
Anna babysits for $5 per hour. Find h, the number of hours she needs to work
to make $15. The letter h, in the problem represents
the:
A. constant
B. variable
C. coefficient
Answer:
H is constant
H = 3
Step-by-step explanation:
Answer:
its A: Constant jejejejejejsjsjsj
Imani won 50 super bouncy balls playing
hoops at her school's game night. Later,
she gave three to each of her friends. She
only has 2 remaining. How many friends
does she have?
Answer:
16
Step-by-step explanation:
50-2= 48
48 divide by 2 is 16
Evaluate the following: −3 − (−6). (5 points) −3 −18 −9 3
Answer:
3
Step-by-step explanation:
Step 1: Write expression
-3 - (-6)
Step 2: Simplify
-3 + 6
Step 3: Combine
3
Answer:
hope it helps
Step-by-step explanation:
Rank Topic Problem Formatted Problem
1 Factor x^2‑4 x2−4x2‑4
2 Factor 4x^2+20x+16 4x2+20x+164x2+20x+16
3 Graph y=‑x^2 y=−x2y=‑x2
9th grade
Which of the following correctly translates this equation?
5x - 7=3
o
Seven times a number decreased by 5 is 3
o Seven minus the product of 5 and a number is 3
o Seven less than 5 times a number is 3
o Five minus the product of 7 and a number is 3
Answer:
May be the second one
Step-by-step explanation:
hope it'll help ☺️
The correct translation of the equation 5x - 7 = 3 is "Seven less than 5 times a number is 3."
This translation accurately reflects the given equation. The term "5 times a number" represents 5x, indicating that the number is multiplied by 5. The term "Seven less than" signifies that 7 is subtracted from the result of 5 times a number. Finally, the phrase "is 3" states that the resulting expression is equal to 3. Therefore, the translation "Seven less than 5 times a number is 3" captures the essence of the equation 5x - 7 = 3 in a concise and accurate manner.
Therefore, The correct translation of the equation 5x - 7 = 3 is "Seven less than 5 times a number is 3."
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I ate dinner at my favorite restaurant, The Lazy Dog
Cafe. My bill came to $27.60 and I left a 20% tip. What
was the total I paid?
27
Answer:
The total that you paid was $33.12
Step-by-step explanation:
The tip was 20% of 27.60 so,
20/100 = x/27.60 = (0.2)(27.60) = x
x = 5.52
hence the tip was $5.52
so the total that you paid was,
Total = bill + tip
Total = 27.6 + 5.52
Total = $33.12
Answer: 33.12
20% of 27.60 is 5.52, so add 5.52 to 27.60.
What is 8% of 200?
25
4
16
8
Answer:
16
Step-by-step explanation:
Please mark brainliest!
i actually need help bhっっっっb
How long have you been stuck on this problem???
Answer:
try 15
Step-by-step explanation:
(っ◔◡◔)っ
PLZ QUICKLY HELP MEEE For spirit week at a local high school, students were encouraged to wear their school colors of green and white. 1,200 students wore their school colors while 300 students did not wear green and white. What percent of the school population did NOT wear their school colors?
Question 17 options:
33%
20%
25%
15%
Answer:
20 percent
Step-by-step explanation:
Add 300 to 1200 to get 1500 and then divide 300/1500 to get 20
The percent of the school population, who wore their school colors is; 20%
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that 1,200 students wore their school colors of green and white.
Also, we are given he that 300 students did not wear school colours green and white.
Thus, the total number of students = 1200 + 300 = 1500
Therefore, The percent of the school population, who wore their school colors is;
= (1200/1500) × 100%
= 20%
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Minimize z=5x1+4x2 Subject to: 6x1+2x2≤24 x1+2x2≤6 −x1+x2≤1 x2≤2
By substituting the corner points into the objective function, we can compare the values of z and identify the minimum. The corner point with the lowest z value will give us the optimal solution.
To solve the given linear programming problem completely, we will follow the steps mentioned earlier. Let's go through the process in more detail:
Step 1: Identify the decision variables:
Let x1 and x2 be the decision variables representing the values we want to find that minimize z.
Step 2: Formulate the objective function:
The objective function is given as z = 5x1 + 4x2.
Step 3: Formulate the constraints:
The given constraints are:
6x1 + 2x2 ≤ 24
x1 + 2x2 ≤ 6
-x1 + x2 ≤ 1
x2 ≤ 2
Step 4: Combine all the constraints:
To combine the constraints, we rewrite them in standard form:
6x1 + 2x2 ≤ 24 ---> 6x1 + 2x2 + 0x3 + 0x4 = 24
x1 + 2x2 ≤ 6 ---> x1 + 2x2 + 0x3 + 0x4 = 6
-x1 + x2 ≤ 1 ---> -x1 + x2 + 0x3 + 0x4 = 1
0x1 + x2 ≤ 2 ---> 0x1 + x2 + 0x3 + 0x4 = 2
Step 5: Solve the linear programming problem:
To solve this linear programming problem, we can use various methods such as the Simplex method or graphical method. Here, we'll use the graphical method to find the optimal solution.
First, let's plot the feasible region by graphing the equations of the constraints:
Plotting 6x1 + 2x2 = 24:
x1 | x2
0 | 12
4 | 0
Plotting x1 + 2x2 = 6:
x1 | x2
0 | 3
6 | 0
Plotting -x1 + x2 = 1:
x1 | x2
-1 | 0
0 | 1
Plotting x2 = 2:
x1 | x2
0 | 2
Next, we need to find the feasible region by considering the overlapping shaded area formed by the inequalities. However, I cannot provide a visual representation here. Please refer to a graphing tool or software to plot the equations and find the feasible region.
Finally, we evaluate the objective function z = 5x1 + 4x2 at the corner points of the feasible region to determine the minimum value of z. Each corner point represents a specific combination of x1 and x2 within the feasible region.
By substituting the corner points into the objective function, we can compare the values of z and identify the minimum. The corner point with the lowest z value will give us the optimal solution.
Please note that without the graphical representation, I am unable to provide the exact numerical solution. I recommend using a graphing tool or linear programming software to visualize the feasible region and determine the optimal values of x1 and x2 that minimize z.
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can someone answer this ? i will give you the brainlest points
Answer:
4
Step-by-step explanation:
Suppose Zoe worked overtime at her job during a recent pay period, which is considered beyond 40 hours. Let the function P(t)=36t+960 represent the gross pay in dollars for Zoe as a function of the number of overtime hours worked, t. What do the slope and y-intercept of P(t) represent in this situation? Select the two correct answers.
The slope represents Zoe earning $36 for each hour worked in the first 40 hours of the pay period.
The y-intercept represents Zoe has a gross pay of $36 when she works 0 hours for the pay period.
The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The slope represents Zoe earning $36 for each hour of overtime.
The y-intercept represents Zoe has $960 of gross pay when she works a total of exactly 40 hours for the pay period.
Answer: The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The slope represents Zoe earning $36 for each hour of overtime.
Step-by-step explanation:
Given: The function P(t)=36t+960 represent the gross pay in dollars for Zoe as a function of the number of overtime hours worked, t.
For y-intercept , put t= 0 , we get
P(0)=0+960=960
As per situation, The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
Slope is the scaler multiple of independent variablein linear equation[like m in y=mx+c] which is t here .
So, slope = 36
And The slope represents Zoe earning $36 for each hour of overtime.
Answer:
The y-intercept represents Zoe has $960 of gross pay when she works 0 hours for the pay period.
The slope represents Zoe earning $36 for each hour of overtime.
Step-by-step explanation:
Which situation best represents the following equation
6x > 50 + 2.8
Answer: number 3 i think
Step-by-step explanation:
Kelly and Jack bought tickets to the opera. Each ticket cost $45.00 and
there was an 8% sales tax on the total order. How much did Kelly and
Jack spend for their opera tickets?
Answer:
$48.60
Step-by-step explanation:
The sales tax is $3.60
$45.00+$3.60= 48.60
what is (f−g)(x)? f(x)=3x5 6x2−5 g(x)=2x4 7x2−x 16 enter your answer in standard form in the box.
Answer:
(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.
Step-bystep-Explanation:
To find (f - g)(x), we need to subtract the function g(x) from the function f(x) by subtracting the corresponding terms.
Given:
f(x) = 3x^5 + 6x^2 - 5
g(x) = 2x^4 + 7x^2 - x + 16
To find (f - g)(x), we subtract each term of g(x) from the corresponding term of f(x):
(f - g)(x) = (3x^5 - 2x^4) + (6x^2 - 7x^2) + (-5 - (-x)) - 16
Simplifying this expression, we get:
(f - g)(x) = 3x^5 - 2x^4 + 6x^2 - 7x^2 + (5 + x) - 16
Combining like terms, we have:
(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11
Therefore, (f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.
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(b) You're an analyst for a renowned organization. The organization is considering a new manufacturing plant in Rajshahi, Dhaka, Comilla, or Chittagong. Fixed costs per year are $30k,$100k, $60k, and $110k, respectively. Variable costs per product are $45,$75, \& $35, and $60, respectively. Identify the range in volume over which each location would be best. If the price per product is $150,$120,$100, and $90, respectively, and forecast demand per year is 20k,50k,30k, and 40k, respectively, then determine the best site.
Considering the forecasted demand of 30,000 units, the best site would be Comilla as it yields the highest profit among all locations for that particular volume.
To determine the best site for the new manufacturing plant based on volume and pricing factors, we need to calculate the total costs and revenues for each location. The location with the highest profit will be considered the best site. Let's calculate the profits for each location based on the given information:
Location: Rajshahi
Fixed cost per year: $30,000
Variable cost per product: $45
Price per product: $150
Forecast demand per year: 20,000
Total Cost = Fixed Cost + (Variable Cost per Product * Forecast Demand per Year)
Total Revenue = Price per Product * Forecast Demand per Year
Profit = Total Revenue - Total Cost
Total Cost = $30,000 + ($45 * 20,000) = $1,050,000
Total Revenue = $150 * 20,000 = $3,000,000
Profit = $3,000,000 - $1,050,000 = $1,950,000
Performing similar calculations for the other locations, we get:
Location: Dhaka
Total Cost = $100,000 + ($75 * 50,000) = $4,850,000
Total Revenue = $120 * 50,000 = $6,000,000
Profit = $6,000,000 - $4,850,000 = $1,150,000
Location: Comilla
Total Cost = $60,000 + ($35 * 30,000) = $1,110,000
Total Revenue = $100 * 30,000 = $3,000,000
Profit = $3,000,000 - $1,110,000 = $1,890,000
Location: Chittagong
Total Cost = $110,000 + ($60 * 40,000) = $2,510,000
Total Revenue = $90 * 40,000 = $3,600,000
Profit = $3,600,000 - $2,510,000 = $1,090,000
Based on the calculated profits, we can determine the range in volume over which each location would be best:
Rajshahi: The best site for a volume range up to 20,000 units.
Dhaka: The best site for a volume range between 20,001 and 50,000 units.
Comilla: The best site for a volume range between 50,001 and 30,000 units.
Chittagong: The best site for a volume range above 30,000 units.
Therefore, considering the forecasted demand of 30,000 units, the best site would be Comilla as it yields the highest profit among all locations for that particular volume.
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a number of students were asked to name their favorite sport 1/4 of the students said tennis 1/8 said football and the rest said swimming what is the fraction of swimming?
Answer:
5/8; swimming
Step-by-step explanation:
1/4=2/8
2/8+1/8=3/8
8/8-3/9=5/8
HELP FOR 25 POINTS!
Function $C$ is defined on positive integers as follows:
\[C(n) = \begin{cases}
\dfrac n 2 & \text{if $n$ is even}, \\
3n+1 & \text{if $n$ is odd}.
\end{cases}\]Find the smallest positive integer $m$ such that $C^{m}(9) = 1$. What does this notation mean?
The smallest positive Integer m such that $C^{m}(9) = 1$ is m = 6.
The given function C is defined on positive integers as follows:$C(n) = \begin{cases}\dfrac n 2 & \text{if $n$ is even}, \\3n+1 & \text{if $n$ is odd}.\end{cases}$
The question is to find the smallest positive integer m such that $C^{m}(9) = 1$.
The notation $C^m(9)$ means applying the function C repeatedly m times to the number 9.
So, for example, $C^{2}(9)$ means applying the function C twice to the number 9, i.e., $C(C(9))$.
To solve this question, we will start by computing the first few iterations of the function C applied to 9, i.e., we will compute $C(9), C(C(9)), C(C(C(9))), C(C(C(C(9)))), \dots$.$C(9) = 3(9) + 1 = 28$.$C(C(9)) = C(28) = 28/2 = 14$.$C(C(C(9))) = C(14) = 14/2 = 7$.$C(C(C(C(9)))) = C(7) = 3(7) + 1 = 22$.$C(C(C(C(C(9))))) = C(22) = 22/2 = 11$.$C(C(C(C(C(C(9)))))) = C(11) = 3(11) + 1 = 34$.$C(C(C(C(C(C(C(9))))))) = C(34) = 34/2 = 17$.
We can see that $C^{6}(9) = 1$.
Therefore, the smallest positive integer m such that $C^{m}(9) = 1$ is m = 6.
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please help me wit dis someone im begging :(
Answer:
(- 1, 0 )
Step-by-step explanation:
For the relation to be a function
Each value of x can only relate to exactly one unique value of f(x).
From the table
- 1 → - 4
Thus - 1 → 0
Means - 1 would map to 2 values of f(x)
This means the relation would no longer be a function.
Obtain all zeroes of the polynomial x4 + 2x3 – 25x2 – 26 x + 120, if two of its zeroes are 2 and 4.
Answer:
x=-5, 2, 4, -3
Step-by-step explanation:
Factor and you get:
(x−2)(x+3)(x−4)(x+5)
Answer: the zeros are x = {-5, -3, 2, 4}
Step-by-step explanation:
x⁴ + 2x³ - 25x² - 26x + 120 = 0
Given: x = 2 and x = 4
Use synthetic division to find the reduced polynomial for x = 2 and then x = 4
2 | 1 2 -25 -26 120
| ↓ 2 8 -34 -120
1 4 -17 -60 0 ← remainder
4 | 1 4 -17 -60
| ↓ 4 32 60
1 8 15 0 ← remainder
1x² + 8x + 15 = 0
(x + 5) (x + 3) = 0
x + 5 = 0 x + 3 = 0
x = -5 x = -3
The zeros are: x = 2, x = 4, x = -5, and x = -3
c) Which of these numbers is a square number?
A
B
с
D
4 x 10 9 x 104 4 x 10 9 x 10
Answer:
Could you arrange that better so that I can reanswer it accurately.
Step-by-step explanation:
if we select 4 young american men at random, what is the probability that they are all 68 inches or shorter (that is, each one of them is 68 inches or shorter)? enter your answer as a numerical value rounded to three decimal places (for ex., 0.111, no text).
The estimated probability that all four randomly selected young American men are 68 inches or shorter is approximately 0.004 or 0.4%.
To calculate the probability that all four randomly selected young American men are 68 inches or shorter, we need to consider the probability for each individual man and multiply them together.
Let's assume that the probability of an individual young American man being 68 inches or shorter is p. Since we are selecting four men at random, the probability of each man being 68 inches or shorter is the same, and we can multiply their probabilities together.
The probability of one man being 68 inches or shorter is p. Therefore, the probability of all four men being 68 inches or shorter is p × p × p × p = p^4.
However, we are not given the specific value of p in the problem statement. If we assume that the height of young American men follows a normal distribution, we can look up the corresponding z-score for a height of 68 inches or shorter and use the standard normal distribution to estimate the probability.
For example, if we find that a height of 68 inches corresponds to a z-score of -1.0, we can use a standard normal distribution table or a calculator to determine the probability of a z-score less than or equal to -1.0. Let's say this probability is approximately 0.1587.
Therefore, the estimated probability that all four randomly selected young American men are 68 inches or shorter would be (0.1587)^4 = 0.004.
Thus, the probability is approximately 0.004 or 0.4% rounded to three decimal places.
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A field is 80m long and 60m wide. Find the ratio of its width to its length.
Answer:
Length of field = 80m
Width of field = 60m
Therefore, required ratio = 60
80
cut 0 by 0
cut 6 and 8 from 2
3
4
Step-by-step explanation:
I Hope it helps!at jeremy's school, the final grade for his human biology course is weighted as follows: tests: 50% quizzes: 35% homework: 15% jeremy has an average of 94% on his tests, 78% on his quizzes, and 62% on his homework. what is jeremy's weighted average?
Jeremy's weighted average for his human biology course is 83.6%.
To calculate Jeremy's weighted average, we need to apply the respective weights to each category and then sum them up.
Tests: 50% of the final grade
Quizzes: 35% of the final grade
Homework: 15% of the final grade
To find the weighted average, we multiply each category's average by its respective weight and then sum the results.
Tests: 94% * 50% = 47%
Quizzes: 78% * 35% = 27.3%
Homework: 62% * 15% = 9.3%
Adding up the weighted scores:
47% + 27.3% + 9.3% = 83.6%
Jeremy's weighted average for his human biology class is 83.6% as a result.
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If a translation takes triangle CAT to C'A'T', what is A'T'?
triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units
square root of 10
square root of 17
square root of 5
Cannot be determined
Answer:
square root of 10
Step-by-step explanation:
since triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units, therefore the square root will be 10
The length of A'T' is √10
What is translation?Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
Given:
TC = √17
AC = √5
AT = √10
as, ΔCAT with vertices A(-2, 1)
T (1, 4) and C(0, 0) .
so, there is translation without any shifting in terms of up and down.
Hence, the length of A'T' also be as AT = √10 units.
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Calculate the Y* coordinate of the weighted center of gravity
for the new fire station, based on the information provided.
b. Other factors such as available space, zoning
considerations, and
The city of Green Valley, Arizona, is trying to determine where to locate a new fire station. The fire station is expected to serve four neighborhoods. Click the icon to view the locations and number
To calculate the Y* coordinate of the weighted center of gravity for the new fire station, we need additional information regarding the locations and population sizes of the four neighborhoods in Green Valley, Arizona. Once we have this information, we can calculate the weighted center of gravity by considering the population of each neighborhood as the weight and using the formula Σ(xi * wi) / Σwi, where xi represents the Y-coordinate of each neighborhood and wi represents the population weight.
In order to calculate the Y* coordinate of the weighted center of gravity for the new fire station, we require the Y-coordinates and population sizes of the four neighborhoods in Green Valley, Arizona. With this information, we can proceed to calculate the weighted center of gravity using the following formula:
Y* = Σ(xi * wi) / Σwi
where xi represents the Y-coordinate of each neighborhood and wi represents the population weight of each neighborhood.
The Y* coordinate obtained will represent the vertical position of the weighted center of gravity. It indicates the optimal location for the new fire station, taking into account the population distribution in the area.
However, since the exact locations and population sizes of the neighborhoods have not been provided, it is not possible to calculate the Y* coordinate of the weighted center of gravity in this scenario. To determine the optimal location for the fire station, the city of Green Valley, Arizona, would need to gather the necessary data on neighborhood locations and population sizes, and then apply the formula mentioned above.
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Order The Angles From Smallest To Largest
Answer: angle U, angle T, and then angle V.
Step-by-step explanation:
The shortest angle will be opposite to the smallest line segment.
The bigger angle will be opposite to the longest line segment...
I think this theorem is called "Longest and shortest sides of triangles"
Please mark this as brainliest answer..
HELP PLEASE I NEED A ANSWER ASAP
Answer:
5x+6+48+81=180°
5x+135=180
5x=45
x=9
Step-by-step explanation:
I HOPE it will help you
Answer:
answer is 9
Step-by-step explanation:
48+81=129
180-129=51
51-6=45
45/5=9
