The equation of the line perpendicular to -2y = 5x + 8 and passes through (10, -1) is y = 2 / 5 x - 5.
How to represent linear equation?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, the equation is perpendicular to -2y = 5x + 8 and passes through (10, -1).
Perpendicular lines have slopes that are negative reciprocals of one another.
Therefore,
-2y = 5x + 8
y = - 5 / 2 x - 4
Therefore,
slope = 2 / 5
Let's find the y-intercept using (10, -1)
-1 = 2 / 5(10) + b
-1 = 20 / 5 + b
b = -1 - 4
b = -5
Therefore, the equation of the line is y = 2 / 5 x - 5
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The student government snack shop sold 32 items this week.
For each snack type, what percentage of all snacks sold were of that type? Do not round your answers.
The percentages of each snack type that were sold are given as follows:
Fruit cup: 25%.Veggie sticks: 18.75%.Chips: 43.75%.Water: 12.5%.How to obtain the percentage?A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.
Hence the percentages for each type are obtained as follows:
Fruit cup: 8/32 x 100% = 25%.Veggie sticks: 6/32 = 18.75%.Chips: 14/32 = 43.75%.Water: 4/32 = 12.5%.More can be learned about proportions at https://brainly.com/question/24372153
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We want to know how a student’s level of education and their gender impacts both their annual income and amount of student loan debt. However, we want to account for the annual income of the student’s parents as well. So which Statistical Test are you going to use?
The statistical tests that van be used to analyze the relationship include multiple regression analysis and ANOVA.
How to explain the statistical test?There are several statistical tests that could be used to analyze the relationship between a student's level of education, gender, annual income, student loan debt, and the annual income of their parents.
One possibility is to use a multiple regression analysis, which would allow you to simultaneously examine the impact of all of these variables on annual income and student loan debt.
Another option could be to use a two-way ANOVA (Analysis of Variance) which would allow you to examine the interaction effects of the student's level of education and gender on annual income and student loan debt. And also, you can use chi-square test for categorical variables like gender. It ultimately depends on the specific research question and the type of data you have.
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Find the area of the figure.
Answer:
1) 143 square inches
2) 32 square inches
3)152 square yards
4) 150 square inches
Step-by-step explanation:
Finding the area:1) Parallelogram:base= 11 in ;height = 13 in
[tex]\sf \boxed{\text{Area of parallelogram = base * height}}[/tex]
= 11 * 13
= 143 square inches
2) Triangle:base = 8 cm ; height = 8 cm
[tex]\sf \boxed{\text {Area of triangle = } \dfrac{1}{2}*base * height}[/tex]
[tex]\sf =\dfrac{1}{2}*8 * 8\\\\= 4 * 8\\\\= 32 \ in^2[/tex]
3) Kite:diagonal = p = 7 + 12 = 19 yd
diagonal 2 = q = 8 + 8 = 16 yd
[tex]\sf \boxed{\text{Area of kite =} \dfrac{pq}{2}}[/tex]
[tex]\sf =\dfrac{19*16}{2}\\\\= 19*8\\\\= 152 \ yd^2[/tex]
4)Trapezium:a = 13 in ; b = 12 ; h = 12 in
a,b are the parallel sides of the trapezium.
[tex]\sf \boxed{\text{Area of trapezium = }\dfrac{(a + b)*h}{2}}[/tex]
[tex]\sf = \dfrac{(13+12)*12}{2}\\\\\\=\dfrac{25*12}{2}\\\\=25*6\\\\= 150 \ in^2[/tex]
you run an experiment in which you flip 3 coins, and each one lands heads or tails. your sample space can be written: {hhh, hht, hth, htt, thh, tht, tth, ttt}. assume all outcomes have equal probability.
The sample space consists of 8 possible outcomes, each with an equal probability of 1/8. The outcomes are the combinations of heads (h) and tails (t) when flipping 3 coins.
1. Determine how many possible outcomes there are in the sample space.
There are 8 possible outcomes in the sample space: hhh, hht, hth, htt, thh, tht, tth, and ttt.
2. Determine the likelihood of each result.
Since all outcomes have equal probability, the probability of each outcome is 1/8.
In this experiment, we are flipping three coins, and each one lands either heads (h) or tails (t). Our sample space consists of all the possible combinations of heads and tails that can occur when flipping the coins. Therefore, our sample space is {hhh, hht, hth, htt, thh, tht, tth, ttt}. Since all outcomes have equal probability, the probability of each outcome is 1/8. This means that the probability of each combination of heads and tails is the same. For example, the probability of getting 3 heads is 1/8 and the probability of getting 2 heads and 1 tail is also 1/8.
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a clerk is wrapping two cube-shaped packages and wants to know the smallest amount of wrapping paper that can wrap each package. the edge length of the larger package is 3in. the greater than the length of the smaller package. the surface area of the larger package is 384 in^2. what is the surface area of the smaller package?
The surface of the smaller cubic package is 150 squared inches.
What is the surface area of the smaller package?Remember that for a cube of side length S, the surface area is given by:
A = 6*S^2
In this case,w we know that the surface area of the larger cube is 384 in^2, replacing that we will get:
384 in^2 = 6*S^2
S = √(384 in^2/6) = 8in
And the edge of the smaller package is 3 inches shorter, then its sidelength is:
s = 8in - 3in = 5in
Then its surface area is:
A = 6*(5in)^2 = 150 in^2
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140/297 write as simplest Fraction form
Answer:
is already in the simplest form. It can be written as 0.47138 in decimal form (rounded to 6 decimal places).
Find the GCD of numerator and denominator
GCD of 140 and 297 is 1
When you divide both the numerator and denominator by 1
The answer will remain the same
A monopolistic firm's marginal revenue function is
dr 100q+43
dq q² +4q+3
=
where output (=demand) is measured in 100s of units/week and revenue is measured in
$1000s/week. The firm's marginal cost function is constant, de/dq= 3, and cost is also
measured in $1000s/week.
If the demand (= output) for the firm's good increases from 2000 units/week to 2500
units/week, then their weekly revenue increases by [Select]
and their
weekly profit changes by [Select]
Comment: pay attention to the units.
The weekly profit changes by $1000s/week.
What is profit?
The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.
To find the increase in weekly revenue, we need to find the difference in revenue at the two output levels:
2500 units/week: Revenue = 100(2500) + 43 = 2543
2000 units/week: Revenue = 100(2000) + 43 = 2043
So the increase in weekly revenue is 2543 - 2043 = $500s/week.
To find the change in weekly profit, we need to subtract the change in cost from the change in revenue:
Change in cost: 2500 units/week - 2000 units/week = 500 units/week * 3 $1000s/week/unit = 1500 $1000s/week
Change in profit: $500s/week - $1500s/week = -1000
Hence, the weekly profit changes by $1000s/week.
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height and weight are two measurements used to track a childs development an organization measures child development by comparing the weights of children who are the same height and the same gender in a certain year weights for all 80 cm girls in the reference population had a mean
μ = 10.4 kg
and standard deviation
σ = 0.2 kg.
Weights are normally distributed.
X ~ N(10.4, 0.2). Calculate the z-scores that correspond to the following weights and interpret them. (Round your numerical answers to two decimal places.)
The z-score for a weight of 10.7 kg is 1.50, which means that the weight is 1.50 standard deviations above the mean of 10.4 kg.
Height and weight are two measurements used to track a childs development an organization measures child development by comparing the weights of children who are the same height and the same gender in a certain year weights for all 80 cm girls in the reference population had a mean
μ = 10.4 kg
and standard deviation
σ = 0.2 kg.
Weights are normally distributed.
X ~ N(10.4, 0.2). Calculate the z-scores that correspond to the following weights and interpret them. (Round your numerical answers to two decimal places.)
Weight = 10.7 kg
Z-score = 1.50
This means that the weight of 10.7 kg is 1.50 standard deviations above the mean of 10.4 kg.
First, calculate the difference between the weight (10.7 kg) and the mean (10.4 kg):
x - μ = 10.7 - 10.4 = 0.3
Then, divide the difference by the standard deviation:
(x - μ)/σ = 0.3/0.2 = 1.50
The z-score is 1.50, which means that the weight of 10.7 kg is 1.50 standard deviations above the mean of 10.4 kg.
The z-score for a weight of 10.7 kg is 1.50, which means that the weight is 1.50 standard deviations above the mean of 10.4 kg.
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video rental company offers a plan that includes a membership fee of $10 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $42 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?
The number of DVDs will be 19 for the first plan.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the video rental company offers a plan that includes a membership fee of $10 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $42 per month for unlimited DVD rentals.
The number of the DVDs will be calculated as:-
C₁ = 2D + 10
The cost for the second plan is,
48 = 2D + 10
2D = 38
D = 38 / 2
D = 19
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facotrs of an expression based on your result from part (a) what are the factors of the polynomial x^3-5x^2-12x 36
The factors of the polynomial x³ - 5x² - 12x + 36 are (x-5) and -12(x+3).
What is the Factorisation of Polynomial?
The factors are the polynomials that are multiplied to produce the original polynomial.
The polynomial x³ - 5x² - 12x + 36 can be factored by grouping. We can factor a common factor of x out of the first two terms and the last two terms.
x³ - 5x² - 12x + 36= x(x² - 5x) -12x(1) +36(1)
= x(x-5)(x+1) -12(x+3)
So, the factors of the polynomial x³ - 5x² - 12x + 36 are (x-5)(x+1) and -12(x+3).
We can also factorize this polynomial by using polynomial division.
we can divide x² - 5x by x, remainder will be -5x and we can divide -12x+36 by x+3, remainder will be 0
x³ - 5x² - 12x + 36 = (x(x-5) -12(x+3))
Hence, the factors of the polynomial x³ - 5x² - 12x + 36 are (x-5) and -12(x+3).
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A (-3,4),(-4,3),(-4,1),(-2,-4)
B
C
D
Answer: Second one (B)
Step-by-step explanation:
We can count every point as 1. As we look at choice A, the point (-4, 3) doesn't exist on the graph, so we can move to the next choice. Choice B contains all points listed on the graph. We know this because coordinates/points are read as (x,y), where x moves either right (positive) or left (negative), and y moves up (positive) or down (negative) depending on what the given point is.
Answer:
The second one:
(-3,4) (3,4) (1,-4) (-2,-4)
Explanation :
The easiest way to find the right answer is to determine the points given on the graph (x, y)
From the first quarter (x, y) : (3,4)
The sec quarter (-x, y) : (-3,4)
The third quarter (-x, -y) :(-2,-4)
And the fourth quarter (x, - y): (1,-4)
Now, all you have to do is find the right answer from the choices
Maria clothing store sold $5230 worth of items last week. She invested half of her income
from the week in new items to sell. Then she paid herself $300 salary for the week. A
manufacturer gave her a rebate of $500 for items that were reduced at the factory. What was
her ending balance?
Write the expression and find the balance.
(5230-300+500)/2; $2715
(5230/2)-300 + 500; $2815.
(5230/2) +500 - 300; $2815
Answer:
Step-by-step explanation:
Maria clothing store sold $5230 worth of items last week. She invested half of her income from the week in new items to sell.Then she paid herself $300 salary for the week. A manufacturer gave her a rebate of $500 for items that were reduced at the factory. What was her ending balance? Write the expression and find the balance.
The area of a circle is 27 square meters. Determine the radius. Use 3 for pi
The radius of a circle with area of 27 square meters is 3 meters.
What is area of a circle?
The area of a circle is the space encircled or encompassed by its circumference. It is represented in the form of square units.
Area of circle(A)= πr^2
where 'r' represents the radius of the circle
We are given that area of a circle is 27 square meters i.e.
⇒πr^2 = 27
The value of π is 3
So, we get
⇒3r^2 = 27
⇒r^2 = 9
⇒r = 3
Hence, the radius of a circle with area of 27 square meters is 3 meters.
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if"(x) changes from to-atX-2 , what is happening at x = 2 ? (Check all that apply. There may or may not be multiple correct answers.) A. an inflection point a relative min a change in direction (increasing to decreasing)B. a relative max a critical point a change in concavity
At x = 2, there is an inflection point and a change in trend (from increasing to decreasing).
What is inflection point?The function can change from being "concave up" to "concave down" or vice versa at points known as inflection points. Where the second derivative changes signs can be used to locate them. A point of inflection is defined as the location where the second derivative of a function, f′′, equals zero. To make the geometric significance of this clearer, we must wait a moment. If the curve "bends" upward, a portion of the graph of f has a concave upward slope. For instance, the entire popular parabola y=x2 is concave upward.
Here,
At x = 2, there is an inflection point, a relative minimum, and a direction change (from increasing to decreasing).
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Approximately how much principal would need to be placed into an account earning 3.575% interest compounded
quarterly so that it has an accumulated value of $68,000 at the end of 30 years?
a. $23,706
b. $23,377
c. $52,069.
d. $58,944
Please select the best answer from the choices provided
The compound interest the answer is b)$23377.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
We know that for compound interest, A = [tex]P(1+\frac{r}{n})^n[/tex]
Where,
A = Future amount = $68,000
P = ??
r = 3.575% annual = 0.03575
n = 4 as interest is compounded quarterly
t = time in year = 30 years
Putting the values,
=> 68000 = P [tex](1+\frac{0.03575}{4})^{4*30}[/tex]
=> 68000 = P[tex](1+\frac{0.03575}{4})^{120}[/tex]
=> 68000 = P (1.0089375)[tex]^{120}[/tex]
=> P = $23377.5
Hence the correct option is b)$23377.
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Write an equation (any form) for the quadratic graphed below:
I added the photo of the graph
Check the picture below.
so we are really looking for the equation of a parabola whose vertex is at (2 , 3) and it passes through (4 , 1)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=2\\ k=3\\ \end{cases}\implies y=a(~~x-2~~)^2 + 3\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=1 \end{cases}[/tex]
[tex]1=a(4-2)^2+3\implies -2=a(2)^2\implies -2=4a \\\\\\ \cfrac{-2}{4}=a\implies -\cfrac{1}{2}=a~\hfill \boxed{y=-\cfrac{1}{2}(x-2)^2 + 3}[/tex]
If Bob is driving along a toll road and passes the first toll reader at 12:00 and is traveling 50 miles an hour, he then passes the second reader 12 miles later at 12:10.
Using the Mean Value Theorem, can you prove that Bob was driving faster than 55 miles per hour at some point?
Responses
Bob’s average speed was 60 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 60 miles/hr and the , Mean Value Theorem, can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the , Mean Value Theorem, cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 60 miles/hr and the Mean Value Theorem cannot be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
How to determine the true statementWe have the following parameters
Rate = 50 miles per hour
Time = 12:00 to 12:10 where he passed the second reader after 12 miles
This means that he drove 12 miles in 10 minutes or 1/6 hour
The speed within this interval is calculated as
Speed = 12/(1/6)
Evaluate
Speed = 72 miles
So, at a point t, Bob was driving at an instantaneous speed of 72 miles per hour, which is faster than 55 miles per hour.
Therefore, Bob was traveling faster than 55 miles per hour at some point between the two toll readers.
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Eliminiation Please!
0.5x + 0.5y = -2
x - 0.25y = 6
Answer:
x = 4; y = -8
Step-by-step explanation:
0.5x + 0.5y = -2
x - 0.25y = 6
Rewrite the first equation. Multiply both sides of the second equation by 2 and write below the first equation. then add the equations.
0.5x + 0.5y = -2
+ 2x - 0.5y = 12
---------------------------
2.5x = 10
x = 4
x - 0.25y = 6
4 - 0.25y = 6
-0.25y = 2
y = -2/0.25
y = -8
x = 4; y = -8
Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission. What percent commission does she get?
Answer =
I got 2 i did math wrong... please help
The percentage of commissions is obtained as follows:
2%.
How to obtain the percentage of commission?The percentage of commission is obtained applying the proportions in the context of this problem.
A proportion is applied as the sales commission percentage is given by the sales commission divided by the total number of sales, and then multiplied by 100%.
The parameters for this problem are given as follows:
$60,000 in sales.Commission of $1,200.Hence the percentage can be then obtained as follows:
1200/60000 x 100% = 2%.
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Write an algebraic expression as indicated.
Two numbers total 123. Let x represent one of the numbers. Write an algebraic expression for the other number.
The other number can be represented as 123-x.
In a survey of 653 randomly chosen workers from a manufacturing plant, 68 said that they prefer to work the night shift. The manufacturing plant employees a total of 2,700 workers. Based on this in formations,about how many plant workers refer the night shift?
Answer:
Approximately 281 workers prefer working the night shift
Step-by-step explanation:
68/653 = 0.104134
2700 * 0.104134
281.16
ou run an experiment in which you flip 3 coins, and each one lands heads or tails. your sample space can be written: {hhh, hht, hth, htt, thh, tht, tth, ttt}. assume all outcomes have equal probability.
The sample space can be written as {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Each outcome has a probability of 1/8, since there are 8 equally likely outcomes in total.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event A, denoted as P(A), is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this experiment, the sample space is the set of all possible outcomes of flipping 3 coins. Each coin can land either heads (H) or tails (T), so there are 2^3 = 8 possible outcomes of flipping all three coins.
The sample space can be written as {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Each outcome has a probability of 1/8, since there are 8 equally likely outcomes in total.
Hence, The sample space can be written as {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Each outcome has a probability of 1/8, since there are 8 equally likely outcomes in total.
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Differentiate the given function.
y=x² √4x-3
Answer: I hope this helps you
Step-by-step explanation:
[tex]y=x^2\sqrt{4x-3}\implies \cfrac{dy}{dx}=\stackrel{\textit{\LARGE product rule}}{2x\sqrt{4x-3}~~ + ~~x^2\cdot \stackrel{\textit{chain rule}}{\cfrac{1}{2}(4x-3)^{-\frac{1}{2}}(4)}} \\\\\\ \cfrac{dy}{dx}=2x\sqrt{4x-3}~~ + ~~\cfrac{2x^2}{\sqrt{4x-3}}\implies \cfrac{dy}{dx}=\cfrac{8x^2-6x+2x^2}{\sqrt{4x-3}} \\\\\\ \cfrac{dy}{dx}=\cfrac{6x^2-6x}{\sqrt{4x-3}}\implies \cfrac{dy}{dx}=\cfrac{6x(x-6)}{\sqrt{4x-3}}[/tex]
Please HELP
Tyshawn is ordering a taxi from an online taxi service. The taxi charges four dollars for just a pick up then an additional $1.50 per mile driven. write a linear function in the form of (y= mx+b) to represent the situation.
A linear function in the form of (y = mx + b) to represent the situation is y = 1.5x + 4.
What is the two factors?The equation y = 4 + 1.5x is a mathematical representation of the relationship between the two factors that determine the cost of the taxi ride. It is a linear equation, where y is the total cost of the taxi ride, x is the number of miles driven, and the numbers 4 and 1.5 are the coefficients.
In this equation, y is the dependent variable, and x is the independent variable.
The cost of the taxi ride is determined by two factors: the flat fee for the pickup and the additional cost per mile driven.
Let y be the total cost of the taxi ride, measured in dollars.
Let x be the number of miles driven, measured in miles.
The flat fee for the pickup is $4, and the additional cost per mile driven is $1.50.
So, the total cost of the taxi ride, y, is equal to the flat fee plus the additional cost per mile driven multiplied by the number of miles driven.
y = 4 + 1.5x
This can also be written in the form of (y= mx+b) where y is the total cost of the taxi ride, x is the number of miles driven, m is the cost per mile and b is the flat fee or initial cost.
So, the function in the form of (y= mx+b) is y = 1.5x + 4
This is a linear function because the variable x is raised to the power of 1, and the relationship between x and y is a straight line.
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Rousey Incorporated, had a cash flow to creditors of $16,830 and a cash flow to shareholders of $7,370 over the past year. The company also had net fixed assets of $49,630 at the beginning of the year and $57,040 at the end of the year. Additionally, the company had a depreciation expense of $12,180 and an operating cash flow of $50,935. What was the change in net working capital during the year?
the change in net working capital during the year will be $6,935.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Rousey Incorporated, had a cash flow to creditors of $16,830 and a cash flow to shareholders of $7,370 over the past year.
Cash flow from assets:
= Cash flow to creditors + Cash flow to shareholders
= $16,965 + $7,559
= $24,524
Since
Net capital spending = Net fixed assets at the end - Net fixed assets at the beginning + Depreciation expense
Cash flow from financial assets = Operating cash flow - Net capital spending - Change in working capital
$24,524 = $51,136 - ($57,130 - $49,705 + $12,252) - Change in working capital
$24,524 = $51,136 - $19,677 - Change in working capital
$24,524 = $31,459 - Change in working capital
Change in working capital = $31,459 - $24,524
= $6,935
Therefore, the change in net working capital during the year will be $6,935.
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Trapezoid ABCD has parallel sides AB and CD, of lengths 12 and 18, respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with DA and BC, respectively. Find PQ.
PQ is the length of the line segment that is parallel to AB and CD, which intersects DA at P and BC at Q. The length of PQ can be found using the Pythagorean Theorem.
Let PQ = x.
Since the line is parallel to AB and CD, the triangles APE, PQC, and BQD are all right triangles.
Using the Pythagorean Theorem,
12^2 + x^2 = 18^2
x^2 = 18^2 - 12^2
x^2 = 324 - 144
x^2 = 180
x = √180
Therefore, PQ = √180
Since the line through E is parallel to AB and CD, the triangles APE, PQC, and BQD are all right triangles. Using the Pythagorean Theorem, we can calculate the length of PQ. We let PQ = x and set up the equation 12^2 + x^2 = 18^2. After solving for x^2, we get x^2 = 180, and x = √180. Therefore, PQ = √180. This is the length of the line segment that is parallel to AB and CD which intersects DA at P and BC at Q.
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List all possible rational zeros of the function f(x) = 3x^3 + 2x^2 – 3x + 2
Answer:
j
Step-by-step explanation:
l
Dinesh is a mason and he takes Rs 3,250 for 5 days working everyday. If he received only Rs 7,800 in two weeks, how many days was he absent in his work?
Given Dinesh earns Rs 3,250 for 5 days working everyday, we can divide the total by 5 to find that he earns Rs 650 daily. Because there are 14 days in two weeks, we can set up an equation:
650 • 14 = Rs 9,100
This means if Dinesh worked every day for two weeks, he would earn Rs 9,100; however, we are told he earns 7,800 in the two weeks. Upon subtraction of 9,100 and 7,800, we will find that Dinesh earned Rs 1,300 less than he would have for a full two weeks.
We know Dinesh earns Rs 650 daily, so we can divide 1,300 by 650 to find that he was absent for 2 days out of the two weeks.
Prove that V is infinite dimensional if and only if there is a sequence of vectors v1,v2,... in V such that the list (v1,v2,...,vn) is linearly independent for
Let (v₁, v₂ . . . vₙ) be a list of vectors in V. This list is linearly independent if and only if the list (v₁ - v₂, v₂ - v₃ . . . . , vₙ₋₁ - vₙ, vₙ) is linearly independent.
Observe that,
0 = a₁(v₁ - v₂) + . . . .+ aₙ₋₁(vₙ₋₁ - vₙ) + aₙ vₙ
= a₁ v₁ + (a₂ - a₁)v₂ + . . . . + (aₙ - aₙ₋₁)vₙ
So,
(v₁ - v₂, v₂ - v₃. . . . vₙ₋₁ - vₙ, vₙ)
These are linearly independent if and only if a₁ = a₂ = . . . .= aₙ = 0, if and only if a₁ = a₂ - a₁ = . . . . . aₙ - aₙ₋₁ = 0, if and only if
(v₁, v₂, . . . ., vₙ)
are linearly independent.
--The given question is incomplete, the complete question is
"Prove that V is infinite dimensional if and only if there is a sequence of vectors v₁, v₂ . . . vₙ in v such that the list (v₁ - v₂, v₂ - v₃ . . . . , vₙ₋₁ - vₙ, vₙ) is linearly independent."--
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In 2010, the population of a city was 144,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 7%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
Answer:
144600
Step-by-step explanation:
In 2010, pop'n 144,000.
From 2010 to 2015, the population grew by 8%.
so by 2015 = 144000*1.08 = 155520
From 2015 to 2020, it fell by 7%.
so 155520 * (1-7%) = 155520 * 0.93 = 144634
round to the nearest 100 = 144600
