Answer: =3x+6
Step-by-step explanation:
Find the determinant of the following matrix A by *only* using the 3 basic properties in Treil section 3 paragraph 3.1 (page 79), the determinant formula for triangular and diagonal matrices, and row or column operations. Explain your work. A= (1 0 2 0 3 0 1 2 3 4 1 0 3 0 5
0 0 0 2 4
1 0 3 0 8)
We must first transform matrix A into a triangular or diagonal matrix in order to determine its determinant.
Using the row operations to change the matrix, having three rows and five columns, in a triangular matrix, having three rows and three columns.
combining the first and second rows, then the first and third rows:
(1 0 2 0 3 0 1 2 3 4 1 0 3 0 5 (1 0 0 2 4 (1 0 3 0 8 (3 0 5 2 11
0 0 0 2 4 + 0 0 0 2 4) + 1 0 3 0 8) = 0 0 0 2 4
1 0 3 0 8) 2 0 6 0 16)
subtracting the second and third rows from the first row
We get a triangular matrix
(3 0 5 2 11 (0 0 0 2 4 (2 0 6 0 16 (1 0 5 0 3
0 0 0 2 4 - 0 0 0 2 4) - 2 0 6 0 16) = 0 0 0 2 4
2 0 6 0 16) 0 0 0 0 0)
Now that the matrix is triangular, we can use the determinant formula for triangular matrices, which states that the determinant of a triangular matrix is equal to the product of the diagonal elements. The diagonal elements of matrix A are 1, 0, and 0, so the determinant of matrix A is 0.
Therefore, the determinant of matrix A is 0, and we can find it by only using the three basic properties in Treil section the determinant formula for triangular and diagonal matrices, and row or column operations.
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Tim answered all the questions on the math test but got 10 wrong answers. He got 4 points for each correct answer, there were no penalty points for incorrect answers. His score was 76 points.
Write an equation to find the total number of questions (q) on Tim's math test
The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0
How to write and solve equation?Number of wrong questions = 10
Points received for right question = 4 points
Points received for wrong question = 0 points
Total of Tim's score = 76%
Let
the number of questions right answered by Tim be x.
Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer
= x × 4
= 4x
Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer
= 10 × 0
= 0
Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer
76 = 4x + 0
76 = 4x
divide both sides by 4
x = 76/4
x = 19
Hence, the number of question answered right by Tim are 19.
Total number of questions attempted by Tim
Total number of questions attempted by Tim
= number of questions answered right +number of questions answered Wrong
= 19 + 10
= 29
Hence, the total number of questions attempted by Tim is 29.
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PLEASE HELP
The variable y varies jointly with x and w when y = -42, x = 2, and w = -3.
1.) Find the constant of variation.
k =
2.) Find w when y = 3 and x = 1/14
w =
Answer:
1). The constant of variation is 7
2). w = 6 for the given values of x and y
Step-by-step explanation:
"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w. We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.
We are given one data point: y=-42 where x is 2 and w is -3. Let's put those values into our trrial expression:
y=Kxw
-42=K(2)(-3)
-42 = -6K
K = 7
The expression becames y = 7xwThe constant of variation is 7.
The value of w for y=3 and x=(1/14) would be:
y=7xw
3 = 7*(1/14)*w
3 = (1/2)*w
w = 6Answer:
1) k = 7
2) w = 6
Step-by-step explanation:
Joint variation equation
If y varies jointly with x and w:
[tex]\boxed{y \propto xw \implies y=kxw}[/tex]
for some constant k.
Given:
y = -42x = 2w = -3Substitute the given values into the joint variation equation and solve for k:
[tex]\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}[/tex]
Therefore, the equation is:
[tex]\boxed{y=7xw}[/tex]
To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:
[tex]\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}[/tex]
the homework consists of 36 independent problems. if the time taken to answer each question is a random variable with mean 6 minutes and a standard deviation 3 minutes. suppose we want to find the probability that all 36 problems in the homework will be completed in less than 180 minutes. which of the following is incorrect?
the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
given that
there are 36 independent problems
mean(μ) = 6minutes
standard deviation(σ) = 3 minutes
sample standard deviation = σ/[tex]\sqrt{n}[/tex]
= 3/[tex]\sqrt{36}[/tex]
=3/6
=0.5
the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes
now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
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students at a high school are asked to evaluate their experience in the class at the end of each school year. the courses are evaluated on a 1-4 scale – with 4 being the best experience possible. in the history department, the courses typically are evaluated at 10% 1's, 15% 2's, 34% 3's, and 41% 4's. mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
No , as we fail to reject the null hypothesis Mr. Goodman claim that his evaluations are significantly different than the history department's.
What is null hypothesis?
Statistics is the study of research and surveys on numerical data in mathematics. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.The null hypothesis is a broad assertion or default stance that there is zero happening or nothing happening in probability and statistics. For instance, there is no relationship between two measured occurrences or a connection between groups. Unless additional evidence has been presented to refute the theory, it is generally accepted that it is true in this context.Test statistic X2 =1.9196
p value =0.5893
No , as we fail to reject the null hypothesis Mr.Goodman claim that his evaluations are significantly different than the history department.
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in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees. find the length of w, to the nearest centimeter
The length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
Using cos law:
W = √(41² + 17² - 2×41×17 cos 134)
After solving:
W = 54.20 cm
Thus, the length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
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Madelyn is a high school basketball player. In a particular game, she made some free throws (worth one point each) and some two point shots. Madelyn made a total of 13 shots altogether and scored a total of 21 points. Determine the number of free throws Madelyn made and the number of two point shots she made.
The number of free throws = 5
The number of two point shots = 8
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of free throws be = x
Let the number of two point shots be = y
The total number of shots made by Madelyn is = 13
So , the equation is
x + y = 13 be equation (1)
The total number of points scored by Madelyn is = 21
So , the equation is
x + 2y = be equation (2)
On simplifying the equation , we get
Subtracting equation (1) from equation (2) , we get
2y - y = 8
y = 8
Therefore , the value of y is 8
And , The number of two points be = 8
Substituting the value for y in equation (1) , we get
x + y = 13
x + 8 = 13
Subtracting 8 on both sides of the equation , we get
x = 5
Therefore , the value of x is 5
And , the number of free throws is 5
Hence , The number of free throws = 5
The number of two point shots = 8
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how many different 12-bit strings begin with 0101, end with 1100 or have 0110 as the four middle bits?
There are 4 different 12-bit strings possible that begin with 0101, end with 1100 or have 0110 as the four middle bits.
We have to find the number of 12-bit strings that are starting with 0101, end with 1100 or have 0110 in the middle bits.
So, the first four position are reserved for 0101 and we have two options for the middle four bits and the end four positions.
So, we can write here,
Total possible different positions for 1100 and 0110 is,
= 2 x 2
= 4
Because, the two combination can appear simultaneously or they can appear one by one.
So, the total different 12-bit strings possible that have 0101 in the start, 1100 in the end or 0101 in the middle are 4.
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3x+12=-5x+28 necesito ayuda para mi examen please
Answer:
x = 2
Step-by-step explanation:
3x + 12 = -5x + 28
3x + 12+ 5x = -5x + 28 + 5x
8x + 12 = 28
8x + 12 - 12 = 28 - 12
8x = 16
8x/8 = 16/8
x = 2
Charlie went to purchase a new pair of
boots that were originally marked $89.
When he checked out they rang up $62.50.
What percent discount did Charlie
receive on the new boots?
30% was the discount recived
HELP PLEASE In MNO, M≈ O, NO = 10 and OM= 8. Find MN.
In the given triangle MNO, the length of MN is 10
Calculating the length of a side in a triangleFrom the question, we are to determine the length of the unknown side in the triangle
The side is MN
From the given information, we have that
In ΔMNO,
∠M ≅ ∠O
Thus,
ΔMNO is an isosceles triangle
Since angle M is congruent to angle O, the sides facing the two angles will also be congruent.
That is,
NO ≅ MN
From the given information,
NO = 10
Therefore,
MN = 10
Hence, the length of MN is 10
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decrease £16855.21 by 3.5% rounded to 2 dp
The lowered value will thus be £16265.28.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
Therefore, the decreased sum is: 16265.2777 = 16855.21 - (16855.21 3.5/100) = (16855.21 - 589.93235).
Next, we'll round the number to two decimal places: 16265.2777, 16265.278, and 16265.28
Hence, The lowered value will thus be £16265.28.
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three factories produce light bulbs to supply the market. factory a produces 20%, 50% of the tools are produced in factory b and 30% in factory c. 2% of the bulbs produced in factory a, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory c are defective. a bulb is selected at random in the market and found to be defective. what is the probability that this bulb was produced by factory b?
0.27 = 0.0027% probability that this bulb was produced by factory B.
Given,
In the question:
Three factories produce light bulbs to supply the market. Factory a produces 20%, 50% of the tools are produced in factory B and 30% in factory C. 2% of the bulbs produced in factory A, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory C are defective.
We use the conditional probability formula to solve this question. It is
P(A|B) = P(A∩B) / P(A)
In which,
P(B|A) is the probability of event B happening, given that A happened.
P(A∩B) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Bulb is defective.
Event B: Produced by factory A.
Probability of a bulb being defective.
2% of 20%(factory A)
1% of 50%(factory B)
3% of 30%(factory C). So
P(A) = 0.02 x 0.2 + 0.01 x 0.5 + 0.03 x 0.3
P(A) = 0.018
Defective and from factory B:
1% of 50%. So
P(A∩B) = 0.01 x 0.5 = 0.005
What is the probability that this bulb was produced by factory B?
P(A|B) = P(A∩B) / P(A)
P(A|B) = 0.005/ 0.018
P(A|B) = 0.27
Hence, 0.27 = 0.0027% probability that this bulb was produced by factory B.
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Plot the points (6, 4) and (3, 2) and find the slope.
Answer:
Slope is 2/3.
Step-by-step explanation:
I can't help you plot the points, but the slope formula is y2-y1/x2-x1.
2-4/3-6. -2/-3. This simplifies to 2/3.
type 1500 words in 30 minutes __ words per minute
Answer:
50
Step-by-step explanation:
1500/30=50
Answer:
50 words per minute
brainliest plss
Professor Very Busy needs to allocate time next week to include time for office hours. He needs to forecast the number of students who will seek appointments. He has gathered the following data:
Week #Students
6 Weeks ago 83
5 Weeks ago 110
4 Weeks ago 95
3 Weeks ago 80
2 Weeks ago 65
Last Year 50
What is this week's forecast using the naive approach? Assume that a decreasing trend in student appointments exists.
Other than the original data point 6 weeks ago, there is a clear trend over the last 5 weeks with continuously decreasing demand, so this week's forecast is last week's demand plus the difference between last week's demand and the demand two weeks ago. 50 + (50 - 65) = 35
Professor Very Busy needs to allocate time next week to include time for office hours then TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0
Smooth the pattern as well as the arrangement to get the outlook this year.
S(Week 5) = TAF(Week 5) + alpha*(Actual(Week 5) - TAF(Week 5))
= 75 + 0.5(65 - 75) = 70
S(Week 6) = TAF(Week 6) + alpha*(Actual(Week 6) - TAF(Week 6))
= 65 + 0.5(50 - 65) = 57.5
T(Week 6) = T(Week 5) + beta*(TAF(Week 6) - TAF(Week 5) - T(Week5))
= -5 + 0.1(65 - 75 - (-5)) = -5 + (-0.5) = -5.5
Therefore, TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0
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y=-7x-1
Can you help me please, I need to graph it
thank you in advance
Answer:
The dots shown in the graph are the answers.
Step-by-step explanation:
Answer: (-0.25, .75)
Solve using substitution.
y = 6x + 2
y = 6x 10
Answer:
Step-by-step explanation:
1/27,20/9
consider the following binomial experiment: a study in a certain community showed that 5% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia? a) 520.00 b) 22.23 c) 50.99 d) 9880.00 e) 49400.00 f) none of the above.
The number of those who have insomnia has a standard deviation of 22.23.
Given,
People suffer from insomnia = 5%
Total number of people in the community = 10,400
We have to find the standard deviation of the number of people who suffer from insomnia;
Here,
p = 0.05
q = 0.95
n = 10,400
Then,
np = 10400 x 0.05 = 202
Now,
npq = 202 x 0.95 = 494
Standard deviation = √npq = √494 = 22.23
That is,
The standard deviation of the number of people who suffer from insomnia is 22.23
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The dimensions of a room with one window and one door are shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square feet.
PLEASE HELP ASAPPP!!! THX (multi-answer)
A reasonable estimation of the total area of the room to be painted is:
A. 2[(30+40) x 8] = 2(70 x 8) = 2 x 560 = 1,120 ft²E. [2(40) x 8] + [2(30) x 8] = 640 + 480 = 1,120 ft².What is an estimation?Estimation involves the approximation of values with number rounding.
Estimates make it easier to do some mathematical operations involving fractions or decimals.
What is the area?The area is the space occupied by a two-dimensional object.
The area is always the product of the length and width (height or depth).
Given the dimensions of the room:
Length of one side = 29¹/₂ ft
Height of the four sides = 8 ft
Length of the second side = 38³/₈ ft
Based on estimation, the dimensional values are approximated to:
Length of one side of the rectangular room = 30 ft
Height of the four sides = 8 ft
Length of the second side of the rectangular room = 40 ft
There are four walls for the room, and we can deduct the areas of the door and window, but these are not given, so we ignore them.
The area of the four walls can be computed as follows:
Area of two sides with same dimensions = 480 ft² [2(30 x 8)]
Area of two sides with same dimensions = 640ft² [2(40 x 8)]
Total area = 1,120 ft² (480 ft² + 640 ft²)
Thus, the options that satisfy the estimated area of the four walls of the room are Options A and E.
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Morgan has an investment worth $13000 after 20 years if his original investment was for $15000 what must the interest rate have been
Answer:
8%
Step-by-step explanation:
pls mark brainliest
Answer : The interest rate have been 8 %
Step-by-step explanation :
First we have to calculate the simple interest.
As we know that:
Simple interest = Total amount - Principle
Simple interest = $130,000 - $50,000
Simple interest = $80,000
Now we have to calculate the interest rate.
Using simple interest formula:
where,
S.I = simple interest = $80,000
P = principle = $50,000
R = interest rate = ?
T = time = 20 years
Now put all the given values in the above formula, we get:
Therefore, the interest rate have been 8 %
Found answer from Alleei!
If f(x) = -x^2 + 3, Find f(-3)
x^2 means x to the power of 2
Answer:
-6
Step-by-step explanation:
-(-3)²+3
-9 + 3
-6
the height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm.use excel to find which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? round your answer to the nearest hundredth.
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
A normal distribution has symmetrically distributed data that is skew-free. As one proceeds away from the center, values tend to decrease and tend to cluster more frequently in that area. The mean, mode, and median of a normal distribution are all equal measures of central tendency.
Given data:
X: height of seaweed.
X~N (μ;σ²)
μ= 10 cm
σ= 2 cm
We will calculate the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X ≤ x) = 0.30
P(X ≥ x) = 0.70
Now by using the standard normal distribution,
we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
translates the Z value to the corresponding X value.
P(Z ≤ z) = 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
X= (Z * σ) + μ
X = (-0.52 * 2)
= 8.96
hence, the value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3
The smallest square achieving this length : 38² = 1444.
Square:
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. The complete length of a square's boundary is its perimeter. As a result, the length of each side can be added to determine the square's perimeter. Since a square has four sides, its perimeter may be calculated by adding all four of its sides. The space a square takes up is its area.
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sampling on campus. you see a woman student standing in front of the student center, now and then stopping other students to ask them questions. she says that she is collecting student opinions for a class assignment. explain why this sampling method is almost certainly biased.
Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.
What do you mean by sampling?
Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.
According to the question,
A true sampling would be a mixed demographic group. A sampling from several like areas:
e.g. infront of the student store, infront of the regular store, infront if a food pantry, infront of ... or even better do a blind survey.
Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.
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Which of the following graphs could represent a quartic function?
On the assumption that each curve has only real roots, the quartic function is the graph C.
What graph does represent a quartic equation?
In this question we have four choices of graphs of polynomials, that is algebraic expressions of the form:
p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m - 1, m}
Where m is the grade of the polynomial.
The factor form of the polynomial is described below:
p(x) = a · Π (x - rₙ), for n = {0, 1, 2, 3, ..., m - 1, m}
If we consider that each choice has real roots, then the grade of the polynomial coincides with the number of times that the curve pass through the x-axis. Then, the graph C represent a quartic function, that is, a polynomial with grade 4 with the special feature that is a function of the form f(x) = a · x² · (x - r₁) · (x - r₂).
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If f(x)=x/3 and g(x)=6x+9 which is equal to f(g(x))
Answer:
f(g(x)) = 2x + 3
Step-by-step explanation:
f(g(x)) is called a composite function
To compute f(g(x)) simply substitute whatever g(x) definition is wherever there is an x in f(x)
We have [tex]g(x) = 6x + 9[/tex]
[tex]f(x) = \dfrac{x}{ 3}[/tex]
So instead of x just use 6x + 9 to get
[tex]f(g(x)) = \dfrac{6x+9}{3} = 2x + 3[/tex]
-7/8 is greater than or equal to m - 13/8
Answer:
Step-by-step explanation:
greater than
Answer: Greater than
a ship is off course. if the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours?
Ship travels 33miles in 3 hours.
What is distance?
Distance is the actual distance that a body travels. Additionally known as path length. For instance, the path length for an item going from point O to point P will be distance OP = 360 m. It is a scalar quantity, the distance. It lacks direction and just possesses magnitude.
Ship travels in one hour = 11miles
Therefore, Ship travels in 3 hours = 11×3
= 33miles
Hence, Ship travels 33 miles in 3 hours.
*SHIP OFF COURSE IS NOT GIVEN IN THE QUESTION.
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Complete the following (use the straight-line method): Auto: $40,000 Residual: $4,000 Estimated life: 5 years Year Cost Depreciation Accumulated Book Expense Depreciation Value
After 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
Given,
Cost of auto =$40,000
Residual value =$4000
Estimated lifetime =5 years
Straight-line Method:-
Depreciation cost can be calculated by formula,
[tex]Depreciation=\frac{cost\ of\ assest-residual}{estimated\ lifetime}[/tex]
It is constant for every year.
Accumulated depreciation can be calculated by formula,
[tex]Accumulation\ Depreciation=\frac{cost\ of\ assets-residual}{estimated\ lifetime}*Number\ of\ years[/tex]
Book value at start of year is nothing the cost of asset at that year and Book value at end of year is difference between cost of asset at that year and depreciation cost.
Using the above formulas all the values for each year is caculated and formed into a table.
Year BookValue DepreciationCost Accumulation Book Value
Start End
1 $40,000 $7,200.00 $7,200 $32,800
2 $32,800 $7,200.00 $14,400 $25,600
3 $25,600 $7,200.00 $21,600 $18,400
4 $18,400 $7,200.00 $28,800 $11,200
5 $11,200 $7,200.00 $36,000 $4,000
Thus, after 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
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