Answer:
As x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].
Therefore, x = -5, x = 2 and y = 3 is the right option.
Step-by-step explanation:
As the given function is
[tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex]
Determining Vertical Asymptote:
The line x = L is a vertical asymptote of the function if if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
Such as
[tex]x^{2} +3x -10 = 0[/tex]
[tex](x-2)(x-5)=0[/tex]
[tex]x=2[/tex] [tex]or[/tex] [tex]x=-5[/tex]
x=−5 , check:
[tex]\lim_{x \to -5^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]
Since, the limit is infinite, then x = -5 is a vertical asymptote.
x = 2, check:
[tex]\lim_{x \to 2^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]
Since the limit is infinite, then x = 2 is a vertical asymptote.
Determining Horizontal Asymptote:
Line y=L is a horizontal asymptote of the function y = f(x), if either
[tex]\lim_{x \to \infty^{}}{f(x)=L}[/tex] or [tex]\lim_{x \to -\infty^{}}{f(x)=L},[/tex] and L is finite.
Calculating the limits:
[tex]\lim_{x \to \infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]
[tex]\lim_{x \to -\infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]
Thus, the horizontal asymptote is y=3.
So, x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].
Therefore, x = -5, x = 2 and y = 3 is the right option.
Keywords: asymptote, vertical asymptote, horizontal asymptote, equation
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I believe the answer is a.
Payment history is ____ of your credit score. 30% 35% 10% 15% Descrip
Answer:35%
Step-by-step explanation:
There are five nickels, five dimes and five quarters in your pocket. You randomly pick three coins and place them on the counter the first coin is a nickel, the second is a dime and the third is a quarter
Answer:
The question is incomplete, this is the complete question.;
There are five nickels, five dimes and five quarters in your pocket. You randomly pick three coins and place them on the counter the first coin is a nickel, the second is a dime and the third is a quarter.find the probability of this occurring.
The answer to the question is;
the probability of this occurring is 1/27
Step-by-step explanation:
Let n(N) =5 ( the number of nickels)
n(D) =5 ( the number of dimes) and
n(Q) = 5 ( the number of quarters)
P(N)= 5/15=1/3 (prob of picking a nickel)
P(D) =5/15=1/3 (prob of picking a dime)
P(Q) = 5/15= 1/3 (prob of picking a quatre)
The probability of picking the three= P(N)×P(D)×P(Q)
= 1/3×1/3×1/3
= 1/27
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone? (1) Jack is painting twice as fast as Tom. (2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours.
How did New World colonization, enabled by the vessel above, affect the economy of Europe?
Answer:
The New world colonization enabled by the vessel affect the European economy as it increased the amount of gold and silver brought into Europe, this lead to the development of the banking sector and also helped to promote the transition of Europe into a capitalist economy.
it brought a great deal of gold and silver into Europe, stimulating the banking industry and promoting Europe’s transition of capitalism
A department store purchases a dress for $80. To sell the dress to customers, the price is marked up by 19%. You hand the clerk $110. How much change will you get back?a. $30.00b. $15.20c. $95.20d. $14.80
Answer:
Amount returned will be $14.80
So option (D) will be correct answer
Step-by-step explanation:
We have given the purchase price of store = $80
To sell the dress price is marked up by 19 %
So marked up price [tex]=80+\frac{80\times 19}{100}=$95.2[/tex]
He give the $110 to clerk
We have to find the amount which is returned by clerk
So the amount will be equal to $110-$95.2 = $14.8
So option (d) will be correct answer
Ernie calculated the slope between two pairs of points. He found that the slope between ( ( -1, 4) 1 , 4 ) and (0, 0) ( 0 , 0 ) is -4 4 . He also found that the slope between (2, 7) ( 2 , 7 ) and (3, 3) ( 3 , 3 ) is -4 4 . Ernie concluded that all of these points are on the same line. Use the drop-down menus to complete the statements about Ernie's conclusion.
Answer:
His conclusion was incorrect.
Step-by-step explanation:
Since, slope of a line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the slope between (-1, 4) and (0, 0),
[tex]m_1=\frac{0-4}{0+1}=-4[/tex]
Also, the slope between (2, 7) and (3, 3),
[tex]m_2=\frac{3-7}{3-2}=\frac{-4}{1}=-4[/tex]
Now,
There are two cases possible,
Case 1 : line passes through (-1, 4) and (0, 0) is parallel to line passes through (2, 7) and (3, 3)
Case 2 : (-1, 4), (0, 0), (2, 7) and (3, 3) are on the same line
Hence, we can not say that they are on same line only after getting same slope.
i.e. his conclusion was incorrect.
Answer:
Okay so this picture is basically the answer for anyone who needs it...
Step-by-step explanation:
If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k ?
Answer:
any digit 0 to 9
Step-by-step explanation:
Nothing about your description of the number suggests that the 10s digit depends on the units digit. The tens digit can be any digit 0 to 9.
How do you do this problem?
Answer:
(2, 2)
Step-by-step explanation:
According to the distance formula, the distance between two points is:
d² = (x₂ − x₁)² + (y₂ − y₁)²
If one point is (x, y) and the other point is (1, 4), then:
d² = (x − 1)² + (y − 4)²
We know y² = 2x, so x = ½ y². Substituting:
d² = (½ y² − 1)² + (y − 4)²
The minimum distance is when dd/dy equals 0. We can either simplify first by distributing, or we can immediately take the derivative using chain rule.
If we distribute and then take the derivative:
d² = ¼ y⁴ − y² + 1 + y² − 8y + 16
d² = ¼ y⁴ − 8y + 17
2d dd/dy = y³ − 8
If we use chain rule instead without distributing:
2d dd/dy = 2(½ y² − 1) (y) + 2(y − 4)
2d dd/dy = y³ − 2y + 2y − 8
2d dd/dy = y³ − 8
Setting dd/dy equal to 0:
0 = y³ − 8
y = 2
x = ½ y²
x = 2
(2, 2) is the point on the parabola closest to (1, 4).
Graph: desmos.com/calculator/m4apqwsduk
Mrs.Cady constructs a cube with 1331 magnetic blocks. Then 256 students at her school and 388 students at another school each make an identical cube. How many magnetic blocks do the students use in all.
Answer:
857164 magnetic block.
Step-by-step explanation:
Given: Each cube constructed with 1331 magnetic block.
Mrs. cady has 256 student in her school and 388 student in another school make an identical cube.
First lets find out total number of students in both schools.
Total student= [tex]256+388= 644\ students[/tex]
∴ Total number of students is 644, who make identical cube.
Now, finding number of magnetic blocks do student use in all.
We will use unitary method.
Each cube require 1331 magnetic blocks.
As there are total 644 students making each cube
∴ 644 cubes require = [tex]644\ cubes\times 1331\ magnetic\ block= 857164[/tex]
∴ 857164 magnetic blocks, student use in all.
Which of the following triangles is closest to being right? Explain your reasoning.
Answer: Second triangle.
Step-by-step explanation:
For this exercise you need to use the Pythagorean Theorem. Based on it, you know that in a right triangle:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the right triangle and "b" and "c" are the legs.
In this case you can identify that the legs of the first triangle and the legs of the second triangle are equal. These are:
[tex]b=7\\c=3.3[/tex]
Knowing their values, you can substitute them into the Pythagorean Theorem and solve for "a":
[tex]a^2=(7)^2+(3.3)^2\\\\a=\sqrt{(7)^2+(3.3)^2}\\\\a=7.738[/tex]
Therefore, you can conclude that the triangle that is closest to being a right triangle is the second one.
On the track team, 35of the members are boys. Of these boys, 47 are sixth-graders. Of the sixth-grade boys on the team, 13 are runners. What fraction of the track team are sixth-grade boy runners?
Answer:
The number of runners is [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team .
Step-by-step explanation:
Given as :
The Total number of the member in team = x
The number of boys in team = [tex]\dfrac{3}{5}[/tex] of x
I.e number of boys in team = [tex]\dfrac{3 x}{5}[/tex]
Again
The number of sixth-grade boys = [tex]\dfrac{4}{7}[/tex] of total boys in team
I.e The number of sixth-grade boys = [tex]\dfrac{4}{7}[/tex] × [tex]\dfrac{3 x}{5}[/tex]
Or, The number of sixth-grade boys = [tex]\dfrac{12 x}{35}[/tex]
Again
The number of runners = [tex]\dfrac{1}{3}[/tex] of number of sixth-grade boys
i.e The number of runners = [tex]\dfrac{1}{3}[/tex] × [tex]\dfrac{12 x}{35}[/tex]
Or, The number of runners = [tex]\dfrac{4 x}{35}[/tex]
So, The number of runners = [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team
Hence,The number of runners is [tex]\dfrac{4 }{35}[/tex] of Total number of the member in team . Answer
Calculate the area of an isosceles right triangle who's hypotenuse is 42–√ inches.
Answer:
A = 441 in²
Step-by-step explanation:
An isosceles right triangle is a triangle with two equals sides (the legs ). In this particular case the base of the triangle will be the length of one side and at the same time the height of the triangle will be the other leg. Hypotenuse as always is the opposite side to the right angle.
The area of a triangle is
A = (1/2) * b* h
If we are going to compute the area of such triangle we have to find the length of one side That will be the base of the triangle and at the same time that will be the height of the triangle.
In any right triangle hypotenuse is:
H² = L₁² + L₂² (1)
As was explain before in this particular case L₁ = L₂
Then
H² = L₁² + L₁² ⇒ H² = 2 L₁² H = √2 * L₁ ⇒ L₁ = 42/√2
Then area of the
A = (1/2)* ( 42/√2) * ( 42/√2 ) ⇒ A = 1/4 * (42)²
A = 441 in²
Multiplying by number is the same as?
Multiplying is simply the same as repeated addition. For example:
[tex]5 \times 3 = 5 + 5 + 5[/tex]
Or:
[tex]4 \times 7= 4 + 4 + 4 + 4 + 4 + 4 + 4[/tex]
Answer:
Below.
Step-by-step explanation:
Adding the number the same number of times as the multiplier.
For example
2 * 3 = 2 + 2 + 2.
Mary is consuming at a point on her budget line. Her income is $40 a week, and she purchases hamburgers and grilled cheese sandwiches. If both goods cost $2 each, and she purchases five hamburgers, how many grilled cheese sandwiches does Mary buy?
Answer:
Mary buy $30 / $ 2 = 15 grilled cheese sandwiches
Step-by-step explanation:
five hamburgers cost 42 x 5 = $10
money left for grilled cheese sandwiches = $40 - $ 10 = $ 30
each grilled cheese sandwiches cost $2
Mary buy $30 / $ 2 = 15 grilled cheese sandwiches
Many people believe that the daily change of price of a company's stock on the stock market is a random variable with mean 0 and variance 2. That is, if Yn represents the price of the stock on the n-th day, then Yn = Yn-1 + Xn, n > 1 where X1, X2, . . . are independent and identically distributed random variables with mean 0 and variance 2. Suppose that the stock's price today is 100. If 2 = 1, use CLT to approximate the probability that the stock's price will exceed 105 on the 10-th day?
Final answer:
Using the Central Limit Theorem, the probability that the stock's price will exceed $105 on the 10th day is calculated to be approximately 13.14%, assuming that the daily change of the stock price is a random variable with a mean of 0 and a variance of 2 and starting from a stock price of $100.
Explanation:
The question is asking to calculate the probability that a company's stock price will exceed $105 on the 10th day, given that the stock price today is $100 and that the daily change of price is a random variable with a mean of 0 and a variance of 2. To answer this, we can use the Central Limit Theorem (CLT) since we have a sum of independent and identically distributed random variables. According to the CLT, the sum of these random variables (or the stock price on the 10th day) will approximate a normal distribution as the number of days increases. For the 10th day, the expected price is the initial price (which is $100) plus 10 times the expected daily change (10*0 = 0), so the expected price is still $100. The variance of the sum of the daily changes is 10 times the variance of a single day (10*2), which equals 20, and the standard deviation is the square root of the variance, which is approximately 4.47.
We are trying to find the probability that the stock price is greater than $105. To do this, we convert the stock price into a z-score using the formula:
z = (X - μ) / σ
where X is the stock price we are interested in ($105), μ is the mean of the stock price on the 10th day ($100), and σ is the standard deviation (approximately 4.47). So we have:
z = (105 - 100) / 4.47 = 1.12
Using standard normal distribution tables or a calculator, we find that the probability of a z-score being greater than 1.12 is approximately 0.1314 (or 13.14%). Therefore, the probability that the stock's price will exceed $105 on the 10th day is about 13.14%.
Sleepy is eight years younger than scoopy. Doc is 5 times as old as scoopy. The sum of their age is 55. How old are each of them? This is the exact problem from worksheet.
Answer:
The age of Sleepy is 1 .
Then the age of Scoopy is 9.
The age of Doc would be 45.
Step-by-step explanation:
We have to find the ages of all the three people based on the given equations.
Let the age of Sleepy be x. Since Scoopy is 8 years older than Sleepy, the age of Scoopy would be (x+8).
Also Doc is 5 times as old as Scoopy so his age is 5(x+8).
Now the sum of the ages of all three is 55.
Writing equation for this,
x + x + 8 + 5(x+8) = 55
7x + 48 = 55
7x = 7
x = 1
So the age of Sleepy is 1 .Then the age of Scoopy is 9.
The age of Doc would be 45.
By solving the linear equations given by the problem, it is found that Scoopy is 10 years old, Sleepy is 2 years old, and Doc is 50 years old.
Explanation:This problem is a system of linear equations, a topic in the field of mathematics. The task is to find out the age of Sleepy, Scoopy, and Doc. Let's denote Scoopy's age as 'S', Sleepy's age as 'S - 8' (since Sleepy is eight years younger than Scoopy), and Doc's age as '5S' (since Doc is 5 times as old as Scoopy). The equations can be written as below:
Scoopy's age = SSleepy's age = S - 8Doc's age = 5SIt is known that the sum of their ages is 55, which gives us our second equation:
S + (S - 8) + 5S = 55
By solving this equation, we find that S = 10. So Scoopy is 10 years old. Accordingly, Sleepy is 10 - 8 = 2 years old and Doc is 5 * 10 = 50 years old.
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Estimate the quotient 430 divided by 9
Answer:
47.77778 but really it's just 47
The taylor family brought 6 suitcases with them on their trip to italy. They paid $72 to check their luggage in with the airport. What was the cost for each piece of luggage
Answer:
$12
Step-by-step explanation:
72/6=12
Each of the suitcases cost 12 dollars and in total, all 6 suitcases equated to 72 dollars.
Answer: the cost for each piece of luggage is $12
Step-by-step explanation:
The total number of suitcases that the Taylor family brought on their trip to Italy is 6. They paid $72 to check their luggage in with the airport. Therefore, the cost for each piece of luggage would be
Total amount paid for 6 pieces of luggage divided by the total number of pieces of luggage. It becomes
72/6 = 12
Prove that if f : A → B, g : B → C, and g ◦ f is injective , then f : A injective
Answer:
Check it down.
Step-by-step explanation:
Injective functions or One to one functions are functions in each one element of A set is is mapped to another element of B set
1) Let's start by listing supposition and their respective Reasons
Suppose:
[tex]g\circ f[/tex] is injective then [tex]f:A\rightarrow B[/tex] is also injective.
Reason: Given
2) Since we are dealing with injective (one to one) functions, we can rightly proceed:
[tex]f(x)=f(y) \:such \:as\: x,y \in A[/tex]
[tex]g(f(x))=g(f(y))[/tex]
Given the fact that [tex]g\circ f[/tex]
[tex]x=y[/tex]
Then we can say that since [tex]g\circ f[/tex] f: A is an injective too ("one to one" ) function.
What is the slope of the line that passes through (-3, 2) and (1, 2)?
Answer:
0
Step-by-step explanation:
Slope of a line which passes through two points (x1,y1) and (x2,y2) is given by:
\frac{y2-y1}{x2-x1}
(x1,y1) = (-3,2)
(x2,y2) = (1,2)
Substituting the values in the equation to determine the slope of the line:
= \frac{2-2}{1-(-3)}
= \frac{0}{4}
=0
So the slope of the given line is 0.
This is intuitively evident as well as the y coordinates of the two given points are the same.
Lizzie solve you equation 2+3x+3=3(x+3)+2x rand got an answer of x=2. Without solving the equation, determine whether or not Lizzy's answer is correct. Show all work and provide reasoning for your answer.
Lizzie's answer is not right as two sides are not equal.
Step-by-step explanation:
Given equation is;
2+3x+3=3(x+3)+2x
Lizzy got;
x=2
We will put this value of x in Equation to determine if the sides are equal or not.
[tex]2+3(2)+3=3(2+3)+2(2)\\2+6+3=3(5)+4\\11=15+4\\11\neq 15[/tex]
Lizzie's answer is not right as two sides are not equal.
Keywords: linear equation, addition
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If the mix ratio for certain chemical is 1:6 when it is mixed with water (chemical:water), how much water would be mixed with 1/2 gallon of the chemical?
Answer:3 gallons of water would be mixed with 1/2 gallon of the chemical
Step-by-step explanation:
If the mix ratio for certain chemical is 1:6 when it is mixed with water. This means that for every 1 gallon of the chemical, 6 gallons of water is required.
Therefore, the number of gallons of water that would be mixed with 1/2 gallon of the chemical becomes
1/2 × 6 = 3 gallons of water.
Answer: 3 gallons of water would be mixed with 1/2 gallon of the chemical
Step-by-step explanation:
If the mix ratio for certain chemical is 1:6 when it is mixed with water. This means that for every 1 gallon of the chemical, 6 gallons of water is required.
Therefore, the number of gallons of water that would be mixed with 1/2 gallon of the chemical becomes
1/2 × 6 = 3 gallons of water.
Help plz... I forgot how to find the angles...can someone tell me how to do it por favor...y
gracias
Answer: a=70°
b=45°
c=65°
d=45°
e=70°
f=110°
Step-by-step explanation:
a=70°
b=180°-135°=45°
c=180-(70+45)=180-115=65°
c=65°
e=70°
d=180-(c+e)=180-(65+70)=180-135=45°
d=45°
f=180-e=180-70=110°
Quick movers charges $50 a day and $0.50 per mile . ABC movers charges $45 a day and $0.75 a mile at how many miles Is the cause the same for both companies?
Answer:
At 20 miles both companies cost will be same.
Step-by-step explanation:
Let Number of miles be 'x'.
Given:
Quick movers charges $50 a day and $0.50 per mile .
So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.
framing in equation form we get;
Quick movers charges = [tex]50+0.5x[/tex]
Also Given:
ABC movers charges $45 a day and $0.75 per mile .
So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.
framing in equation form we get;
ABC movers charges = [tex]45+0.75x[/tex]
We need to find the number of miles at which both companies cost are are same.
Solving to find the same we get;
[tex]50+0.5x=45+0.75x[/tex]
Combining like terms we get;
[tex]0.75x-0.5x=50-45\\\\0.25x=5[/tex]
By Division property of equality we will divide both side by 0.25 we get;
[tex]\frac{0.25x}{0.25} =\frac{5}{0.25} \\\\x= 20 \ miles[/tex]
Hence at 20 miles both companies cost will be same.
Final answer:
By setting up an equation to equate the charges of Quick Movers and ABC Movers, it is determined that at 20 miles, the costs for both companies will be the same.
Explanation:
To find at how many miles the cost for both Quick Movers and ABC Movers is the same, we set up an equation where the cost of each company is equal. Quick Movers charges $50 a day plus $0.50 per mile, and ABC Movers charges $45 a day plus $0.75 per mile. Let's use m to represent the miles.
The equation based on the costs given will be:
50 + 0.50m = 45 + 0.75m
To solve the equation, we first bring all the m terms to one side and the constants to the other:
0.50m - 0.75m = 45 - 50
This simplifies to:
-0.25m = -5
Dividing both sides by -0.25, we find:
m = 20
Therefore, the cost for both companies is the same at 20 miles.
A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size n
a. has the same probability of being selected
b. has a probability of 1/n of being selected
c. has a probability of n/(N-1) of being selected
d. has a probability of 1/N of being selected g
Answer:
a) has the same probability of being selected
Step-by-step explanation:
A simple random sampling means that each possible sample of size n has the same probability of being selected.
Then your answer is:
a) has the same probability of being selected
The definition of a simple random sampling method implies that each possible sample of a given size has an equally likely chance of being selected. Hence, option a. 'has the same chance of being selected' is the correct answer.
Explanation:The simple random sampling method is a statistical method used to select individual samples from a large population where each sample is given an equal chance of being selected. In a simple random sampling of size n from a finite population of size N, each possible sample of size n would have the same probability of being selected. Therefore, the correct answer is a. has the same probability of being selected.
It is crucial to note that the probability of a sample being selected is not dependent on its size (n) nor the total size of the population (N), as options b, c, and d suggest. Instead, it is determined solely by the sampling method, i.e., simple random sampling.
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If a lift takes 40 seconds to go to the fourth floor from the ground floor then how much time will it take to go to sixteenth floor from the fourth floor
Answer:
120 seconds
Step-by-step explanation:
if the elevator is moving at a constant rate, then it takes 10 seconds to move up one floor, to travel from the 4th to the 16th floor, it will take 120 seconds total to travel 10 floors
Over the course of four weeks Mia spent 35 1 2 hours training for a race. Michael spent 1 1 2 times that amount training for the same race. How many hours did Michael spend training? A) 49 1 2 hours B) 53 1 4 hours C) 71 hours D) 73 1 4 hours
Answer:Michael spent 53 1/4 hours
training.
Step-by-step explanation:
Over the course of four weeks Mia spent 35 1 2 hours training for a race. This can be written in decimal point as 35.5 hours.
Michael spent 1 1 2 times that amount training for the same race. Converting 1 1 2 to decimal, it becomes 1.5 hours.
This means that the number of hours that Michael spent training will be 35.5 × 1.5 = 53.25 hour.
Converting 53.25 hours to mixed fraction, it becomes
53 1/4 hours
Answer:
The answer is B
Step-by-step explanation:
Some coconuts fall out of a tree. Mercy is greedy and takes half, Joe grabs what he can, and gets five more than Frank. Frank gets one coconut. How many fell off the tree
Answer:
Total Number of Coconuts which fell from tree are 14.
Step-by-step explanation:
Given:
Some coconuts fall out of a tree.
Mercy is greedy and takes half,
Joe grabs what he can, and gets five more than Frank.
Frank gets one coconut.
We need to find Total number of coconuts fell from tree.
Number of Coconuts franks has = 1
Now Given that Joe grabs what he can, and gets five more than Frank.
Number of Coconuts Joe has = Number of Coconuts franks has + 5 = 1 + 5 = 6
Also Given Mercy is greedy and takes half.
It means mercy took half of coconuts and rest half were took by Frank and Joe
Hence Number of Coconuts Mercy has = Number of Coconuts franks has + Number of Coconuts Joe has = 6 + 1 = 7
Now Total Number of Coconuts is equal to sum of Number of Coconuts Mercy has and Number of Coconuts Joe has and Number of Coconuts frank has.
Total Number of Coconuts = 7 + 1 + 6 = 14
Hence Total Number of Coconuts which fell from tree are 14.
Derek and Donnie mow 15 lawns over two 2 days. If Derek mows 3 lawns per hour and Donnie mows 2 lawns per hour, write an equation in standard form that models this.
Answer:the two equations that model the situation are
x + y = 48
3x + 2y = 15
Step-by-step explanation:
Let x represent the total number of hours that Derek worked.
Let y represent the total number of hours that Donnie worked.
Derek and Donnie mow 15 lawns over two 2 days. There are 24 hours in a day. Therefore, the number of hours in 2 days would be 2 × 24 = 48 hours. Therefore
x + y = 48 - - - - - - - - - -1
If Derek mows 3 lawns per hour and Donnie mows 2 lawns per hour, it means that
3x + 2y = 15 - - - - - - - - - 2
Mailing on a weekly salary of $385 plus a 70% commission on a sale at a gift shop how much would she make in a work week if she had sold for 4300 worth of merchandise
Answer:
Total Amount made by Mailing in a week is $3395.
Step-by-step explanation:
Given:
Fixed Salary = $385
Percentage of Commission on Sale = 70%
Total Sale = 4300
we need to find Total amount made by Mailing in a week.
We will first find the amount made on commission.
Amount made on commission = [tex]\frac{70}{100} \times 4300 = \$3010[/tex]
Now Total Amount made by Mailing in a week is equal to sum of Fixed Salary and Amount made on commission.
Framing in equation form we get;
Total Amount made by Mailing = $385 + $3010 = $3395.
Hence Total Amount made by Mailing in a week is $3395.