The matrices A and B are given as:
A = [3/4 0]
[0 3/4]
B = [-4 0]
[0 -4]
2a) Compute AB:
AB = [3/4 0] * [-4 0]
[0 3/4] [0 -4]
= [3/4 * -4 + 0 * 0 3/4 * 0 + 0 * -4]
[0 * -4 + 3/4 * 0 0 * 0 + 3/4 * -4]
= [-3 0]
[0 -3]
2b) Compute BA:
BA = [-4 0] * [3/4 0]
[0 -4] [0 3/4]
= [-4 * 3/4 + 0 * 0 -4 * 0 + 0 * -4]
[0 * 3/4 + -4 * 0 0 * 0 + -4 * 3/4]
= [-3 0]
[0 -3]
2c) How did your answer in part (a) and (b) compare?
The answers in part (a) and (b) are the same. Both AB and BA resulted in the matrix [-3 0] [0 -3].
2d) Will this be true, in general, for any two matrices when you multiply them (assuming their dimensions line up so that they may be multiplied)? If so, explain your reasoning. If not, show an example of two matrices C and D such that CD≠DC.
No, this will not be true in general for any two matrices when you multiply them. The order in which matrices are multiplied matters, and in most cases, AB≠BA. Here is an example of two matrices C and D such that CD≠DC:
C = [1 2]
[3 4]
D = [5 6]
[7 8]
CD = [1 * 5 + 2 * 7 1 * 6 + 2 * 8]
[3 * 5 + 4 * 7 3 * 6 + 4 * 8]
= [19 22]
[43 50]
DC = [5 * 1 + 6 * 3 5 * 2 + 6 * 4]
[7 * 1 + 8 * 3 7 * 2 + 8 * 4]
= [23 34]
[31 50]
As you can see, CD≠DC.
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Suppose that a line passes through the points (5,1) and (-1.5).
Where will it pass through the x-axis?
The line passes through the x-axis at the point (13/2, 0).
To find where the line passes through the x-axis, we need to find the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis, so the y-coordinate of this point will be 0.
We can use the slope-intercept form of a line, y = mx + b, to find the x-intercept. First, we need to find the slope of the line, m. The slope is given by the formula:
m = (y2 - y1)/(x2 - x1)
Plugging in the given points, we get:
m = (5 - 1)/(-1 - 5)
m = -2/3
Now we can plug in one of the points and the slope into the equation to solve for the y-intercept, b:
1 = -2/3(5) + b
b = -13/3
So the equation of the line is:
y = -2/3x + 13/3
To find the x-intercept, we set y to 0 and solve for x:
0 = -2/3x + 13/3
x = 13/2
So the line passes through the x-axis at the point (13/2, 0).
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Compare the similarities and differences between Binomial and Normal distributions.
.What types of data does each use?
.What kinds of statistical formula and techniques are used with each?
.What similar characteristics do they share in their distributions?
Binomial and Normal distributions are two different types of probability distributions that are commonly used in statistics. Both distributions involve a set of possible outcomes, and the probability associated with each outcome.
The Binomial Distribution is used for discrete data such as coin flips, the number of defective items in a production run, and the number of wins and losses in a series of games. It is used with the formula P(x;n,p) and the techniques of probability, permutations, and combinations.
The Normal Distribution is used for continuous data such as height, weight, IQ scores, and test scores. It is used with the formula P(x;μ,σ) and the techniques of statistics, standardization, and z-scores.
Both distributions have the same basic shape and the same basic idea of a probability of a certain outcome. The main difference between them is that the Binomial Distribution is discrete and the Normal Distribution is continuous.
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Find the determinant of the triangular matrix.−37−605700−3
Determinant of the given triangular matrix is 105.
What is determinant of a matrix?The determinant of a matrix is a number that represents the volume or area of the matrix. It is calculated by using a formula that involves the entries of the matrix, and is used in solving linear equations and in proving theorems in linear algebra.
The determinant of a triangular matrix can be found by multiplying the elements on the main diagonal. In this case, the main diagonal elements are -3, 5, and -7.
So, the determinant of the triangular matrix is:
-3 * 5 * -7 = 105
Therefore, the determinant of the triangular matrix is 105.
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Does this equation have a solution?
10x + 12 = 20x - 2
Answer:
Answer and how to isolate the variablex=1.4
First, subtract 10x on both sides so you get
12=10x-2
Then add 2 odd both sides
14=10x
Then divide both sides by 10
14/10= 10X/10
So you get x=1.4
Find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0.
The values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.
To find k so that when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2, the remainder is 0, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x-a, the remainder is f(a).
So, if we let f(x) = x^(3)+kx^(2)+k^(2)x+14 and a = -2, we can find the value of k that makes the remainder 0.
f(-2) = (-2)^(3)+k(-2)^(2)+k^(2)(-2)+14 = 0
Simplifying the equation, we get:
-8 + 4k - 2k^(2) + 14 = 0
-2k^(2) + 4k + 6 = 0
Dividing by -2, we get:
k^(2) - 2k - 3 = 0
Factoring the equation, we get:
(k-3)(k+1) = 0
So, k = 3 or k = -1.
Therefore, the values of k that make the remainder 0 when x^(3)+kx^(2)+k^(2)x+14 is divided by x+2 are 3 and -1.
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What is the value of x
in the rational equation x5=618
The required, value of x in the rational equation x⁵=618 is approximately 4.951.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To solve for x in the rational equation x^5 = 618, we need to isolate x on one side of the equation.
Taking the fifth root of both sides, we get:
[tex]x = 618^{1/5}[/tex]
The approximate value of the fifth root of 618 is approximately 4.951.
Therefore, the value of x is approximately 4.951.
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A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.
Outcome Frequency
A, A 15
A, B 12
A, C 10
B, A 18
B, B 15
B, C 17
C, A 11
C, B 13
C, C 14
Based on the table, for what probability can you expect the spinner to not land on A?
0.66
0.47
0.33
0.10
The probability of the spinner not landing on A is 0.47.
How to find the probability you can expect the spinner to not land on A?To find the probability that the spinner does not land on A, we need to add up the frequencies of the outcomes where A does not appear, which are (B,B), (B,C), (C,B), and (C,C):
Frequency of not landing on A = Frequency(B,B) + Frequency(B,C) + Frequency(C,B) + Frequency(C,C)
Frequency of not landing on A = 15 + 17 + 13 + 14 = 59
The total number of outcomes is 125, so the probability of not landing on A is:
P(not A) = Frequency of not landing on A / Total number of outcomes
P(not A) = 59 / 125 = 0.47
Therefore, the probability of the spinner not landing on A is 0.47.
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Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below:
x 1 2
p(x) 0.04 0.05
(a) What is P(x = 4)? P(x = 4) = (b) What is P(x4)? P(x4) = (c) What is the probability that the selected student is taking at most five courses? P(at most 5 courses) = (d) What is the probability that the selected student is taking at least five courses? more than five courses? P(at least 5 courses) = P(more than 5 courses) = (e) Calculate P(3x6) and P(3 < x < 6). P(3x6) = P(3 < x < 6) =
a)0
b)0.09
c)0.09
d)0
e)P(3x6) = 0.09 P(3 < x < 6) = 0
A) P(x = 4) = 0
B) P(x4) = 0.09
C) P(at most 5 courses) = 0.09
D) P(at least 5 courses) = 0 P(more than 5 courses) = 0
E) P(3x6) = 0.09 P(3 < x < 6) = 0
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.Write an equation for the graph that passes through (0,4) and (5,19).
We can use the two-point form to find the equation of the line passing through the two given points:
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
where (x1, y1) = (0, 4) and (x2, y2) = (5, 19).
Substituting the values, we get:
y - 4 = ((19 - 4)/(5 - 0))(x - 0)
Simplifying the equation, we get:
y - 4 = (15/5)x
y - 4 = 3x
Adding 4 to both sides, we get:
y = 3x + 4
Therefore, the equation of the line passing through the points (0, 4) and (5, 19) is y = 3x + 4.
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a) find slope
19-4/5-0 = 15/5 = 3
plug into equation
y = 3x + b
plug in coordinate pair to solve for b
4 = 3(0) + b
4 = 0 + b
b = 4
y = 3x + b
For f(x)=6x+8 and g(x)= 5x, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = _____ (Simplify your answer.)
The composite functions and their domains are:
(a) (fog)(x) = 30x + 8, domain: all real numbers
(b) (gof)(x) = 30x + 40, domain: all real numbers
(c) (fof)(x) = 36x + 56, domain: all real numbers
(d) (gog)(x) = 25x, domain: all real numbers
The composite functions are formed by substituting one function into another. We can find the composite functions for f(x)=6x+8 and g(x)=5x by following these steps:
(a) (fog)(x) = f(g(x)) = f(5x) = 6(5x) + 8 = 30x + 8
The domain of (fog)(x) is the set of all real numbers, since there are no restrictions on the values of x.
(b) (gof)(x) = g(f(x)) = g(6x+8) = 5(6x+8) = 30x + 40
The domain of (gof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
(c) (fof)(x) = f(f(x)) = f(6x+8) = 6(6x+8) + 8 = 36x + 56
The domain of (fof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
(d) (gog)(x) = g(g(x)) = g(5x) = 5(5x) = 25x
The domain of (gog)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
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It takes 4 minutes for the wheel to make one complete rotation. Put a star at Bo’s location after riding the wheel for 21 minutes
After 21 minutes the location of BO in the wheel is EO
How to find BO after 21 minutesThe location of BO after 21 minutes is solved using the data:
It takes 4 minutes for the wheel to make one complete rotation
hence in 21 minutes the rotation covered is
= 21 / 4
= 5.25
This is 5 complete rotations and 0.25 (a quarter rotation).
0.25 rotation is
=0.25 * 360
= 90
Each gap in the wheel is
360 / 12 = 30 degrees
hence three steps from B which is EO
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Find the y intercept and slope of the linear equation x+y=-6 1/2
The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
To find the y-intercept and slope of the linear equation x +y=-6 1/2, we
need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y by subtracting x from both sides of the equation:
x + y = -6 1/2
y = -x - 6 1/2
Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.
Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
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A line passes through the points (2, −2) and (3, −9). Write its equation in slope-intercept
form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
An equation in slope-intercept form is y = -7x + 12.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (2, -2), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-2) = (-9 - (-2))/(3 - 2)(x - 2)
y + 2 = (-9 + 2)/(3 - 2)(x - 2)
y = -7x + 14 - 2
y = -7x + 12
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Jimmy is paying for a meal with group of friends. They received great service, so he is giving a 20% tip. The meal came to 166.60 before sales tax. How much will he leave as a tip?
Tip=$
Jimmy will leave a $33.32 tip for the great service.
What is the total of the cost?
Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.
To calculate the tip, we need to first find 20% of the total cost of the meal (before sales tax):
20% of 166.60 = 0.20 x 166.60 = 33.32
Therefore, Jimmy will leave a $33.32 tip for the great service.
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A movie sells only adult tickets and child tickets for one movie the theater sells 126 tickets in all the tape diagram shows the ratio of adult tickets to child tickets the theater sells what does each square of the diagram represent?
Answer:
So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.
Step-by-step explanation:
Assuming that the tape diagram shows the ratio of adult tickets to child tickets as 3:2, we can represent this as follows:
AAA
AAA
AAA
CCC
CCC
In this diagram, each square represents a certain number of tickets. To determine how many tickets each square represents, we need to know the total number of squares in the diagram.
There are a total of 3 + 3 + 3 + 2 + 2 = 13 squares in the diagram. Since the theater sold 126 tickets in total, we can divide 126 by 13 to find out how many tickets each square represents:
126 ÷ 13 ≈ 9.69
So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.
Which of the following proves these triangles as congruent?
Answer:
AAS
Step-by-step explanation:
Answered this question before on Acellus.
Numeric For the following exercises, use the given information to find the unknown value. 24.yvaries directly asx. Whenx=3, theny=12. Findywnehx=20. 25.yvaries directly as the square ofx. Whenx=2, theny=16. Findywhenx=8. 26.yvaries directly as the cube ofx. Whenx=3, theny=5. Findywhenx=4
When x = 4, y = 320/27.
If y varies directly as x, it means that y = kx, where k is a constant. To find k, we can use the given information:
When x = 3, y = 12
12 = k * 3
k = 4
Now that we know k, we can find y when x = 20:
y = k * x
y = 4 * 20
y = 80
Therefore, when x = 20, y = 80.
25. If y varies directly as the square of x, it means that y = k * x^2, where k is a constant. To find k, we can use the given information:
When x = 2, y = 16
16 = k * 2^2
k = 4
Now that we know k, we can find y when x = 8:
y = k * x^2
y = 4 * 8^2
y = 4 * 64
y = 256
Therefore, when x = 8, y = 256.
26. If y varies directly as the cube of x, it means that y = k * x^3, where k is a constant. To find k, we can use the given information:
When x = 3, y = 5
5 = k * 3^3
k = 5/27
Now that we know k, we can find y when x = 4:
y = k * x^3
y = 5/27 * 4^3
y = 5/27 * 64
y = 320/27
Therefore, when x = 4, y = 320/27.
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Find an angle in each quadrant with a common reference angle with 12°, from 0°≤θ<360°
Answer: the first quadrant : 12° i the second quadrant : 168° i
the third quadrant : -168° i the forth quadrant : 348°.
Step-by-step explanation:
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What is the volume of the composite solid?
The volume of the composite solid is 5104 cubic ft.
What is triangular prism?A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.
The area of a triangular prism is given as:
V = 1/2(bhl)
Here, h = 22 - 12 = 10 ft.
Substituting the values we have:
V = 1/2(13)(10)(32)
V = 2080 cubic ft.
The volume of the rectangular prism is given as:
V = lwh
V = (28)(9)(12)
V = 3024 cubic ft.
The volume of the composite solid is:
V = V1 + V2
V = 2080 + 3024
V = 5104 cubic ft.
Hence, the volume of the composite solid is 5104 cubic ft.
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Carys calculates the total amount E, in dollars, theat she earns for working h hours using the equation E=10h. How many dollars does she earn per hour?
Answer:
She earns 10 dollars per hour.
Step-by-step explanation:
They substituted h for the amount of hours, since it is unknown. And you can see 10 is multiplied with h. So that is how much she earns an hour.
HELP PLS PLS PLS PLS
DUE TOMORROW AND WORTH 50 POINTS AND I GIVE THE BRAINLESS!!
PLS STRESSING TIMES
Answer: 1,068 and wil
Step-by-step explanation:
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Steve gets 4 points for every correct answer and looses 1 point for every wrong answer. If he answered 30 questions and scored 20 points, write a system of equations.
Answer:
Option B.
Step-by-step explanation:
Let r represent right questions and w represent wrong questions
Total number of questions can be written as:
r + w = 30
We can multiply the question type by the number of points and set it to equal to the total points:
4r - 1w = 20
Thus, our two equations match with Option B best.
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Adding rational expressions with different Subtract. (5)/(2)-(1)/(2d) Simplify your answer as much as possible.
The simplified rational expression of (5)/(2)-(1)/(2d) is (5d-2)/(2d).
To add rational expressions with different denominators, we first need to find a common denominator. In this case, the common denominator is 2d.
Once we have the common denominator, we can multiply each fraction by a factor that will give us the common denominator. For the first fraction, we need to multiply by d in the numerator and denominator. For the second fraction, we need to multiply by 2 in the numerator and denominator.
After multiplying, we can combine the numerators and keep the common denominator.
So, the steps to simplify (5)/(2)-(1)/(2d) are as follows:
1. Find the common denominator: 2d
2. Multiply the first fraction by d/d: (5d)/(2d)
3. Multiply the second fraction by 2/2: (2)/(2d)
4. Combine the numerators and keep the common denominator: (5d-2)/(2d)
5. Simplify the numerator: (5d-2)/(2d)
Therefore, the simplified rational expression is (5d-2)/(2d).
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Watch help video Ise synthetic division to find the result when 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2. If there is a remainder, express the result in the form
Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).
To use synthetic division to find the result of the given polynomial division, we need to follow these steps:
1. Write the coefficients of the dividend polynomial in a row: 2 10 8 1 24
2. Write the constant term of the divisor with the opposite sign in front of the row: -2 | 2 10 8 1 24
3. Bring down the first coefficient: -2 | 2 10 8 1 24
-----------
2
4. Multiply the first coefficient by the divisor's constant term and write the result under the second coefficient: -2 | 2 10 8 1 24
-----------
2 -4
5. Add the second coefficient and the result from step 4: -2 | 2 10 8 1 24
-----------
2 6
6. Repeat steps 4 and 5 for the remaining coefficients: -2 | 2 10 8 1 24
-----------
2 6 4 -6
7. The last number in the row is the remainder. If it is 0, the division is exact. If not, we need to express the result in the form: quotient + (remainder)/(divisor)
In this case, the quotient is 2x^(3)+6x^(2)+4x-6 and the remainder is 36. So the result of the division is:
2x^(3)+6x^(2)+4x-6+(36)/(x+2)
Therefore, the result of the division 2x^(4)+10x^(3)+8x^(2)+x+24 divided by x+2 using synthetic division is 2x^(3)+6x^(2)+4x-6+(36)/(x+2).
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Precalculus Project 2 1) In multiplying two real numbers, we are familiar with the "Zero-Product Property from both Intermediate and College Algebra. Recall that this says that if you have two numbers and y such that the product xy = 0, then either x = 0 or y=0 or they are both zero. This is not true for matrices. In other words, given matrices A and B. A could be a nonzero matrix and B could be a nonzero matrix and you would still obtain AB=0. Let A = [-12 4]
[ 15 -5]
Construct a 2 x 2 matrix B such that AB is the zero matrix.
"Use two different nonzero columns for B. *Clearly show your multiplication that gets your zero matrix.
AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.
When multiplying two matrices, we use the dot product of the rows of the first matrix and the columns of the second matrix to obtain the entries of the resulting matrix. In order for the product of two matrices to be the zero matrix, the dot product of each row of the first matrix with each column of the second matrix must be zero.
Let's construct a 2 x 2 matrix B such that AB is the zero matrix. We can use two different nonzero columns for B to obtain the zero matrix. Let's start with the first column of B:
B = [b1 b3]
[b2 b4]
We need to find values for b1, b2, b3, and b4 such that the dot product of each row of A with each column of B is zero. Let's start with the first row of A and the first column of B:
-12b1 + 4b2 = 0
We can rearrange this equation to solve for b2 in terms of b1:
b2 = 3b1
Now let's look at the second row of A and the first column of B:
15b1 - 5b2 = 0
Substituting the value of b2 from the first equation gives us:
15b1 - 5(3b1) = 0
Simplifying gives us:
0 = 0
This equation is always true, so we can choose any value for b1 and find the corresponding value for b2. Let's choose b1 = 1:
b2 = 3(1) = 3
Now let's look at the first row of A and the second column of B:
-12b3 + 4b4 = 0
We can rearrange this equation to solve for b4 in terms of b3:
b4 = 3b3
Now let's look at the second row of A and the second column of B:
15b3 - 5b4 = 0
Substituting the value of b4 from the first equation gives us:
15b3 - 5(3b3) = 0
Simplifying gives us:
0 = 0
This equation is always true, so we can choose any value for b3 and find the corresponding value for b4. Let's choose b3 = 2:
b4 = 3(2) = 6
Now we have the values for all of the entries of B:
B = [1 2]
[3 6]
Let's check our work by multiplying A and B:
AB = [-12 4] [1 2]
[ 15 -5] [3 6]
= [(-12)(1) + (4)(3) (-12)(2) + (4)(6)]
[(15)(1) + (-5)(3) (15)(2) + (-5)(6)]
= [0 0]
[0 0]
So AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.
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The lengths of the bases are 62 inches and 6 feet. The perpendicular distance between the bases of a trapezoid is 5 feet. What is the area of a trapezoid in square inches?
The area of the trapezoid is 335 square inches.
What is Trapezoid ?
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezoid.
First, we need to convert the lengths of the bases and the perpendicular distance to the same units. Let's convert 6 feet to inches:
6 feet = 6 x 12 inches = 72 inches
Now we can calculate the area of the trapezoid using the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the bases and h is the perpendicular distance between them.
Substituting the given values, we get:
Area = (62 + 72) * 5 / 2
Area = 134 * 5 / 2
Area = 670 / 2
Area = 335 square inches
Therefore, the area of the trapezoid is 335 square inches.
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Given the graph of the quadratic function, determine the features.
For the given quadratic function the features are:
Domain: (-∞, ∞): Range :[-1, ∞)Vertex: (-3, -1)Explain about the quadratic function?A parabola, a U-shaped curve, is the shape of a quadratic function's graph.
The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of a quadratic function, is where the parabola will open up.There are three characteristics that all quadratic functions share:
A quadratic function's graph is always a parabola with an end behaviour that is either upward or downward; its domain will be all real numbers; and its vertex is really the lowest point once the parabola opens upwards.Thus, for the given quadratic function the features are:
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A store manager adjusts the price of an item each week that the item goes unsold. The price of the unsold item, in dollars, after x weeks can be modeled by the exponential function f(x)=320(0.90)^x
: The initial price of the store item before the store manager made any price adjustments were: _________
Can someone help me solve this?
Thanks!
Answer:
The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.
Plugging x=0 into the given function, we get:
f(0) = 320(0.90)^0 = 320(1) = 320
Therefore, the initial price of the store item was $320.
Employees frequently need to work in team projects. We examine the difference in the team efficiency, when employees work in teams through distance working (e.g. with online meetings) in relation to teamwork with physical presence. Data are collected from a sample of 87 employees that have worked in a team project through online meetings and 74 employees that have worked in a team with physical presence. The employees filled a questionnaire, where one question was "The teamwork was efficient", on a scale from 1-5, where 1=strongly disagree and 5=strongly agree. The mean score in this question for the team that had used online meetings was 2.63, with a standard deviation of 0.92, while for the team that had worked with physical presence the mean was 2.35, with a standard deviation of 0.81. Test if teamwork with distance meetings appears to be generally more efficient for employees, in relation to teamwork with physical presence. Use a 1% level of significance.
This hypothesis test indicates that the team efficiency when working through distance working (e.g. with online meetings) is not generally more efficient than when working with physical presence.
The research question being examined is whether teams that work through distance working (e.g. with online meetings) are generally more efficient than those that work with physical presence. To answer this question, a hypothesis test can be used with a 1% level of significance.
The null hypothesis (H0) is that there is no difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence. The alternative hypothesis (H1) is that there is a difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.
To test this hypothesis, a two-tailed independent t-test was used. The mean score for the team that had used online meetings was 2.63 with a standard deviation of 0.92 and for the team that had worked with physical presence the mean was 2.35 with a standard deviation of 0.81. The t-statistic obtained was 1.71 and the corresponding p-value was 0.093.
Since the p-value (0.093) is not less than the level of significance (0.01), the null hypothesis cannot be rejected. Therefore, the data suggests that there is not a significant difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.
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Mandla, a farmer, wants to buy a new tractor. The tractor costs R160 000 excluding VAT He can pay a deposit of R20 000. He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 % a. What will his instalment be? b. How much interest will he pay? c. How much will he pay in total for the tractor over 60 months?
a) Amount financed is, R164,000
b) Total interest over 60 months is, R98,400
c) The farmer would pay a total of R262,400 after 60 months.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The tractor costs R160 000 excluding VAT
And, He can pay a deposit of R20 000.
Here, He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 %
Hence, We get;
Total price with VAT = R160,000 + 15% of R160,000
= R184,000
Hence, We get;
Amount financed = Total price - Deposit
= R184,000 - R20,000
= R164,000
Thus, Total interest over 60 months = R164,000 x 10% x 5
= R98,400
Here, Total payment = Amount financed + Total interest
= R164,000 + R98,400
= R262,400
Therefore, The farmer would pay a total of R262,400 after 60 months.
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