Answer:
-$5,500
Step-by-step explanation:
The change in the one year from 2009 to 2010 was ...
18,500 -24,000 = -5,500
The annual rate of change in the boat's value was -$5,500.
Thus, the annual rate of change of the boat's value is $5,500 per year.
To find the annual rate of change of the boat's value, we need to determine how much the value decreased from 2009 to 2010 and then calculate the yearly decrease. The boat's value in 2009 was $24,000; in 2010, it was $18,500.
First, calculate the decrease in the boat's value from 2009 to 2010:
Decrease = Initial Value - Final Value
Decrease = $24,000 - $18,500 = $5,500
Since this decrease occurred over one year, the annual rate of change in the boat's value is $5,500 per year.
Therefore, the annual rate of change of the boat's value is $5,500 per year.
The probability that an American industry will locate in Shanghai, China, is 0.7, the probability that / / 60 Chapter 2 Probability it will locate in Beijing, China, is 0.4, and the probability that it will locate in either Shanghai or Beijing or both is 0.8. What is the probability that the industry will locate (a) in both cities? (b) in neither city?
Answer:
A) 0.3
B) 0.2
Step-by-step explanation:
We are given the following in the question:
P(Industry in Shanghai) = P(A) = 0.7
P(Industry in Beijing) = P(B) = 0.4
P(Industry in Shanghai or Beijing) = P(A∪B) = 0.8
a)We need to find the probability that the industry is located in both Shanghai and Beijing that is we need to find P(A∩B)
Formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
Putting the values we get,
0.8 = 0.7 + 0.4 - P(A∩B)
P(A∩B) = 0.3
Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.
b)Now, we need to find the probability that it is not in either cities
Probability = 1 - Probability(Industry in Shanghai or in Beijing)
= 1 - P(A∪B)
= 1 - 0.8
= 0.2
The probability that the industry will locate in both Shanghai and Beijing is 0.3, while the probability that it will locate in neither of the cities is 0.2.
Explanation:This problem is solved using the concept of probability in Mathematics. Let's denote A as the event that an industry with locate in Shanghai and B is the event that it will locate in Beijing.
The probability of A, P(A), is given as 0.7 and the probability of B, P(B), is given as 0.4. The probability it will locate in either of the cities, P(A U B), is given as 0.8.
We know, P(A U B) = P(A) + P(B) - P(A ∩ B), where P(A ∩ B) represents the probability the industry will locate in both cities. Using the given probabilities:
0.8 = 0.7 + 0.4 - P(A ∩ B), so P(A ∩ B), the probability the industry will locate in both cities, is equal to 0.3. (a)
The probability the industry will not locate in either of the cities, denoted as P'(A U B), is equal to 1 - P(A U B) = 1 - 0.8 = 0.2. (b).
This means there is a 30% chance the industry will locate in both Shanghai and Beijing, and a 20% chance it will locate in neither city.
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OMG HELP A GIRL OUT !!HELP ME PLEASE I NEED A 70%
1. Translate and solve: What number is 408% of 568? Round to the nearest hundredth.
2.In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the total percent decrease.
3.A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each bill does it contain?
4.Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound, and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?
Answer:
#1. 408% of 568
We get two equations from this
408% = x
568 = 100%
568/x=100%/408%
Solve and you'll get
408% of 568
=2317.44
2. New - Original = % change
712500 - 950000 = -237500
3. 10 at $1, 7 at $5
4. 2.2 lb. of raisins, 7.8 lb. of nuts
As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
What is equation?
" Equation is defined as the relation between the variables using sign of equality."
What is percentage?" Percentage is defined as the hundredth part of the given number."
According to the question,
1. 'x' represents the number
As per given condition,
x = 408% of 568
⇒ [tex]x= \frac{408}{100} (568)[/tex]
⇒ [tex]x = 2317.44[/tex]
Therefore, the number which is 408% of 568 is equals to 2317.44.
2. Total population of Detroit = 950,000
Population after 10 years = 712,500
Decrease in population = 950,000 - 712,500
= 237,500
Total percentage decrease in population = [tex]\frac{237500}{950,000}(100)[/tex]
= 25%
Therefore, total decrease in percentage of the population of Detroit is equals to 25%.
3. 'x' represents the bill of $1
'y' represents the bill of $5
As per the condition given equation we have,
$1x + $5y = $45 ______(1)
x = y + 3 ______(2)
Substitute the value of equation (2) in (1) we get,
[tex]1(y + 3) + 5y = 45\\\\\implies 6y = 45-3\\\\\implies y \frac{42}{6} \\\\\implies y = 7[/tex]
Substitute the value y in (2) we get,
[tex]x= 7 + 3\\\\\implies x =10[/tex]
Therefore , cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. 'x' represents the pounds of raisins
'10- x ' represents the pounds of nuts
Cost of trail mix from raisins and nuts per pound = $6.96
Therefore,
Cost of 10 pounds of trail mix of raisins and nuts = $(6.96 ×10)
= $69.6
Cost per pound of raisins = $3.45
Cost per pound of nuts = $7.95
Equation formed as per given condition we get,
[tex]3.45x + 7.95(10-x) = 69.6\\\\\implies 3.45x + 79.5 -7.95x = 69.6\\\\\implies -4.5x = 69.6 - 79.5\\\\\implies-4.5x= -9.9\\\\\implies x =\frac{9.9}{4.5}\\ \\\implies x = 2.2 pounds[/tex]
Pounds of raisins = 2.2pounds
Pounds of nuts = 10 - 2.2
= 7.8 pounds
Therefore, pounds of raisins is equals to 2.2 and pounds of nuts is equals to 7.8 for the trail mix.
Hence, As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
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Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes?
Answer:
30 parts
Step-by-step explanation:
We are given that machine produces 100 parts twice as fast as machine B does.
Machine produces 100 parts in 40 minutes.
We have to find number of parts produces by machine A in 6 minutes.
According to question
Machine A takes time to produce 100 parts =[tex]\frac{40}{2}=20 minutes[/tex]
Machine A and machine B produces parts at constant rate.
Machine A produces parts at the rate=[tex]\frac{100}{20}=5 parts /minute[/tex]
In one minute,Machine A produces =5 parts
In 6 minutes , machine B produces =[tex]5\times 6=30[/tex] parts
Hence, machine A produce parts in 6 minutes=30
A vase contains 7 red flowers, 3 white flowers, and 5 yellow flowers. If George selects a flower from the vase for his wife, what is the probability that he will select a red one.
Answer:
The answer to your question is: P(A) = 0.47
Step-by-step explanation:
Data
7 red flowers
3 white flowers
5 yellow flowers
Probability that he select a red one
Formula
P(A) = Number of favorable cases of A / total number of outcomes
Number of favorable cases = 7
Total number of outcomes = 7 + 3 + 5 = 15
Substitution
P(A) = 7 / 15
P(A) = 0.47
What is the slope for 3x + 2y = 8
Answer:
[tex] -1 \frac{1}{2} = m[/tex]
Step-by-step explanation:
3x + 2y = 8
-3x - 3x
___________
2y = -3x + 8
___ _______
2 2
y = -1½x + 4
↑
rate of change [slope]
I am joyous to assist you anytime.
You have purchased a new warehouse. To finance the purchase, you’ve arranged for a 25-year mortgage for 75 percent of the $4,200,000 purchase price. The monthly payment on this loan will be $18,300.
What is the APR on this loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Final answer:
Explanation on how to calculate the APR for a mortgage loan based on provided information.
Explanation:
To calculate the APR on the loan, we first need to determine the total amount paid over the life of the loan. The total payment per month is $18,300, and the loan term is 25 years. So, the total payment over 25 years would be $18,300 x 12 months x 25 years = $5,220,000.
Next, calculate the total interest paid by subtracting the loan amount from the total payments: $5,220,000 - 75% of $4,200,000 = $5,220,000 - $3,150,000 = $2,070,000.
Finally, use the formula for APR: APR = (Total Interest Paid / Loan Amount) x 100%. Therefore, APR = ($2,070,000 / $3,150,000) x 100% ≈ 65.71%. So, the APR on this loan is approximately 65.71%.
I move east a distance of 4km, south a distance of 2 km, and then west a dostance of 1km. What is the cartesian cordinates relative to my starting point ?
Answer:
In x: 4-1=3
In y: -2
Cartesian coordinates: (3,-2)
Step-by-step explanation:
If we move horizontally we must consider only the x axis, if we move to east it is positive, and if we move to west it is negative.
f we move vertically we must consider only the y axis, if we move to north it is positive, and if we move to south it is negative.
Sarah begins at a negative position along the x-axis. Sarah moves in the positive x-direction, turns around and then moves in the negative x-direction. Her final position is more negative that her initial position. Is the magnitude of Sarah's displacement greater than, less than, or equal to the distance she travels?
Answer:
he magnitude of Sarah's displacement is less than the distance she travels
Step-by-step explanation:
Hi!
The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.
So:
[tex]displacement = |x_{final} -x_{initial}| \\distanceTraveled = 2|x_{return}-x_{initial}| + displacement\\[/tex]
Since all the terms are positive:
[tex]x_{displacement}<x_{traveled}[/tex]
Does the function x^2 + xy = 1 have any symmetry?
Answer:
No.
Step-by-step explanation:
The equation does not match the form of any conic section.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
Answer:
Step-by-step explanation:
Let's get this in a form we can better recognize. we'll rearrange it until we have y by itself.
x^2 + xy = 1
xy = 1 - x^2
y = 1/x - x
There, much better. Now, just looking at the graph you can tell there's no symmetry along the x or y axis. If you do not know how to check for symmetry along x=y or origin symmetry let me know. But checking for those does show that there is no symmetry along y = x but there is origin symmetry.
To determine that you just make all x and ys negative, and then see if you can get back to the original. Again, let me know if you don't get determining symmetry through algebra and I'd be happy to explain each of the variations; x ais, y axis, y=x and origin.
Problem Carroll bikes 111 kilometer east, 444 kilometers north, and then 555 kilometers east again. How far is Carroll from her starting position, to the nearest tenth of a kilometer?
Answer:
The answer to your question is: 800.4 km
Step-by-step explanation:
Data:
111 km to east
444 km to north
555 km to east
How far is from her starting position?
See the picture please
To do this problem, we must to find the hypotenuse of a right triangle where one cathetus is 444 km and the other one is the sum of 111 and 555km.
them the pythagorean theorem says c² = a² + b²
c² = 444² + (111+555)²
c² = 444² + 666²
c² = 197136 + 443556
c² = 640692
c = 800.4 km
Answer: 7.211
Step-by-step explanation:
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Mr. Spindero periodically visits a hospital clinic where he takes various paper and pencil tests that document the progression of his dementia. A(n) ____ is most likely to be administering the tests.
Answer:
A neuropsychologist is most likely to be administering the tests.
Step-by-step explanation:
Mr. Spindero periodically visits a hospital clinic where he takes various paper and pencil tests that document the progression of his dementia.
A neuropsychologist is most likely to be administering the tests.
Certain disorders within the brain and nervous system can alter the normal behavior and cognitive function of a person.
So, a neuropsychologist deals with such patients. He specializes in understanding the relationship between the physical brain and behavior.
Tom and Jerry have two tasks to do all day: makedishes and build fences. If Tom spends all day makingdishes, he will have make 16 dishes. If he instead devotes his day to building fences, Tom will build 4 fences. If Jerry spends his day makingdishes, he will make 14 dishes; if he spends the day building fences, he will build 7 fences. After looking at the production possibilities for both Tom and Jerry, we can conclude that:
Answer:
If production is to be maximized, Jerry should build fences and Tom should make dishes.
Step-by-step explanation:
Tom can build more fences per day than Jerry, and Jerry can make more dishes per day than Tom. Each has his special skill, and production will be maximized when that special skill is utilized.
HELP!!! PLEASE!!!!
.
Answer:
A: 6.624×10⁸ m/dayB: 1.9872×10¹⁰ mC: 19.872 Gm or 1.9872×10¹ GmStep-by-step explanation:
For the first two parts, you need to know the number of hours in a day, and the number of days in 30 days (!?). No doubt, these numbers are familiar to you.
Part A.
The distance traveled in 24 hours (1 day) is 24 times the distance traveled in one hour.
distance per day = (27,600,000 m/h)×(24 h/day) = 662,400,000 m/day
Since you are familiar with place value and powers of 10, you know you can write this as ...
662,400,000 m/day = 6.624×100,000,000 m/day = 6.624×10⁸ m/day
__
Part B.
Using the result from Part A, we know that 30 days' travel will be 30 times one day's travel:
distance in 30 days = (30 days)×6.624×10⁸ m/day = 198.72×10⁸ m
= 1.9872×10¹⁰ m
__
Part C.
Your judgment is required to determine a "suitable unit." I might choose gigameters, abbreviated Gm. "giga-" is a prefix meaning 10⁹, so the distance traveled in 30 days could be written as ...
1.9872×10¹⁰ m = 19.872×10⁹ m = 19.872 Gm = 1.9872×10¹ Gm
_____
Comment on "suitable unit"
In my engineering career, I would often choose units from the list of SI prefixes, so that exponents were a multiple of 3. That means any given measurement or calculation result ranged from 1 to 999, multiplied by some suitable choice of units. Here, the distance traveled in 30 days would be left as (about) 19.9 Gm. The choice of units is intended to avoid the need for scientific notation.
The meaning of "a more suitable unit in scientific notation" is unclear in this context. I would say a "more suitable unit" is Gm, whose value in scientific notation is 10^9 m or 10^6 km.
Miriam is picking out some movies to rent, and she is primarily interested in comedies and foreign films. She has narrowed down her selections to 10 comedies and 15 foreign films. How many different combinations of 3 movies can she rent if she wants at least two comedies?
Answer:
There are 795 combinations.
Step-by-step explanation:
The number of ways or combinations in which we can select k element from a group of n elements is given by:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.
Then, the number of combinations for every case are:
1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:
[tex]10C2*15C1=\frac{10!}{2!(10-8)!}*\frac{15}{1!(15-14)!}[/tex]
[tex]10C2*15C1=675[/tex]
2. Choose 3 Comedies from the 10. This is calculated as:
[tex]10C3=\frac{10!}{3!(10-3)!}=120[/tex]
Therefore, there are 795 combinations and it is calculated as:
675 + 120 = 795
A study revealed a strong, linear, negative association between a decrease in salary and amount spent on clothes. Another study revealed a strong, linear, negative association between decrease in salary and amount spent on food. When the data were combined, the association became positive. What is this an example of?
A. simpson's paradoxB.observational studyC.experimental studyD.cause-and effect realtionshipE.error by the statistician
Answer:
A. simpson's paradox
Step-by-step explanation:
The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.
Before running any regressions make sure to check for multicollinearity. How did you check for multicollinearity? If there is multicollinearity, how do you plan to resolve it? Are there any other issues with the dataset we have to consider before running the regressions?
Answer:
Multicollinearity
Step-by-step explanation:
In a linear regression model, we predict the dependent variable(y) with the help of independent variable[tex](x_i)[/tex].Our aim is to minimize the residuals and make the best prediction.Multicollinearity refers to the situation when there is correlation between the independent variables.This could lead to wrong predictions and increase residualsMulticollinearity can be checked with the help of VIF, variance inflation factor.The industry accepted value of VIF is 5. A VIF greater than 5 means collinearity.In order to treat multicollinearityy, we could plot scatter plot between different independent variables and remove one of the variable that is correlated.Before running the linear regression model, we should make sure that there is no correlation between independent and dependent variable, residuals to be normally distributed, no auto correlation.. Online Medical Info USA Today posted this question on its web "How often do you seek medical information online?" Of 1072 Internet users who chose to respond, 38% of them responded with "frequently." What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? What is wrong with this type of sampling method?
Answer:
The term used to describe this type of survey is - voluntary response sample or self elected sample.
The thing that is wrong with this type of sampling is that only those people will respond who have a strong interest in the particular topic.
Also, it is quite possible that only 38% responses do not reflect the opinions of the whole general population.
PLEASE HELP!!!
The area of a triangle is given by the
formula A = 1/2bh Solve this for h.
Answer:
h = [tex]\frac{2A}{b}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] bh
Multiply both sides by 2 to clear the fraction
2A = bh ( isolate h by dividing both sides by b )
h = [tex]\frac{2A}{b}[/tex]
Answer: h = 2a/b
Step-by-step explanation:
help :( .
solve step by step
Answer:
x=-y/g
Step-by-step explanation:
m-y=m+gx
m-m-y=gx
-y=gx
x=-y/g
What is the place value of 2 in 24,398,407,268
Answer:
20,000,000,000 or 200
Step-by-step explanation:
depending on which 2 you are asking for
The place value of 2 in the number 24,398,407,268 is 20 billion, as it is in the ten billion place.
The place value of 2 in the number 24,398,407,268 refers to the position of 2 in the number and its corresponding value. In this case, the 2 is in the ten billion place. To find the value of 2 in that position, we multiply it by 10 billion (109). Therefore, the place value of 2 in this number is 20 billion (2 x 10^9).
Graph f(x) = x2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry
The given function : [tex]f(x)=x^2+2x-3[/tex]
Using completing the squares, we have
[tex]f(x)=x^2+2x+1-1-3[/tex] [∵ [tex](x+1)^2=x^2+2x+1[/tex]]
[tex]f(x)=(x+1)^2-4[/tex] (1)
Comparing (1) to the standard vertex form [tex]f(x)=(x-h)^2+k[/tex] , the vertex of function is at (h,k)=(-1,-4)
For x-intercept, put f(x)=0 in (1), we get
[tex]0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4[/tex]
Square root on both sides, we get
[tex]x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1[/tex]
∴ x intercepts : x= (-3,0) and (1,0)
For y-intercept put x=0 in (1), we get
[tex]f(1)=(1)^2-4=1-4=-3[/tex]
∴ y intercept : (0,-3)
Axis of symmetry : [tex]\dfrac{-b}{2a}[/tex]
In [tex]f(x)=x^2+2x-3[/tex] , a=1 and b=2
Axis of symmetry=[tex]\dfrac{-2}{2(1)}=-1[/tex]
A graph of the quadratic equation [tex]f(x) = x^2 + 2x - 3[/tex] with its key features is shown on the coordinate plane in the image below.
What is the graph of a quadratic function?In Mathematics and Euclidean Geometry, the standard form of a quadratic function is represented by the following equation;
[tex]y = ax^2 + bx + c[/tex]
Where:
x and y represents the data points on the graph.a represents the leading coefficient.Since the leading coefficient (value of a) in the given quadratic function [tex]f(x) = x^2 + 2x - 3[/tex] is positive one (1), we can logically deduce that the parabola would open upward and the solutions are the x-intercepts. Furthermore, the key features of this quadratic function include the following;
The vertex is (-1, -4).The mininum value is equal to -4.The axis of symmetry is x = -1.x-intercepts: (-3, 0) and (1, 0)The parabola opens upward.The y-intercept is (0, -3).Read more on quadratic functions here: brainly.com/question/29499209
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Complete Question;
Graph [tex]f(x) = x^2 + 2x - 3[/tex], label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry
You are driving home from school steadily at 95 km/h for 180 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 4.5 h. (a) How far is your hometown from school? (b) What was your average speed?
Answer:
(a) 349.34
(b) 77.63 km/h
Step-by-step explanation:
Distance you covered before it rain S = 180 km
Speed v = 95/km
Time taken to cover 180 km = [tex]\frac{S}{v}[/tex]
= [tex]\frac{180}{95}[/tex]
= 1.89473 hrs.
Total time to cover the distance between school to home T = 4.5 hrs.
Remaining time t = T - t
= 4.5 - 1.89473
= 2.60527 h.
Velocity after travel 180 km. v' = 65 km/h
Distance traveled in this velocity S' = v'(t)
= 2.60527 × 65
= 169.34 km
(a) distance of hometown from school = 169.34 + 180 = 349.34 km.
(b) Your average speed V = [tex]\frac{S}{T}[/tex]
= [tex]\frac{349.34}{4.5}[/tex]
= 77.63 km/h
Which word best completes this definition? Two lines are _____ if and only if they lie in the same plane and do not intersect. A parallel B perpendicular C bisectors D transversals
Answer:
Parallel
Step-by-step explanation:
All of the other answers give examples of lines that intersect at some point.
Answer:
transversal
Step-by-step explanation:
The line is called transversal. A transversal is a line which intersects two or more parallel lines
A gym charges a $25 sign-up fee plus $25 per month. You have a $200 gift card for the gym. When does the total spent on your gym membership exceed the amount of your gift card?
Answer:
After 7 months
Step-by-step explanation:
DATA:
⇒ Sign-up fee = $25
⇒ Monthly fee = $25
⇒ Number of months = y
⇒ Gift card = $200
Form an equation to calculate when the total spent on gym would exceed the amount of the gift card
Sign-up fee + (monthly fee x number of months) = Gift card amount
25 + 25y = 200
25y = 200-25
25y = 175
y = 7
Therefore, the total spent on your gym membership exceeds the amount of your gift card after 7 months.
Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill?
Answer: 2 hours
Step-by-step explanation:
Given : Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively.
Let t be the time taken by both of them working together.
Then, according to the question, we have
[tex]\dfrac{1}{t}=\dfrac{1}{3}+\dfrac{1}{6}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{2+1}{6}\ \ [\because\ L.C.M. (3,6)=6]\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{6}=\dfrac{1}{2}\\\\\Rightarrow t=2[/tex]
Hence, it will take 2 hours by the two machines .
Simplify: (7a − 9c) − (−12a − 33c) − (−21a + 10c)
Answer:
The answer is 40a+14c
Step-by-step explanation:
Step 1: Open the brackets
7a-9c+12a+33c+21a-10c
Step 2: Group all the like terms
Like terms are terms with similar variables, for example;
(7a, 12a, 21a) are all like terms since they have a common variable (a)
(-9c, 33c,-10c) are also like terms since they have a common variable (c)
Step 2: Solve
(7a+12a+21a)+(33c-10c-9c)=40a+14c
The answer is 40a+14c
Is it possible for a linear system to have a unique solution if it has more equations than variables? If yes, give an example. If no, justify why it is impossible.
Answer:
Yes
Step-by-step explanation:
Yes it is possible, if the equations are equivalent. For example in one variable, we have x=2 and if we add the equation 2x=4 both considered on the Real numbers, then the system has two equations and one variable, more equations than variables and yet the solution is unique x=2.
Answer:
Yes, it's possible.
Step-by-step explanation:
We know that a linear system has a unique solution if it has the same number of equations than variables (but remember that you musn't have a linear combination of equations).
So it is possible to create a system with more equations than variables, with a unique solution.
Example:
1) X + Y + Z = 3
2) 2X + 2Y + 2Z = 6
3) X + Y = 2
4) X + Z = 2
This is a 4 equation and 3 variable system. Pay attention to equation number 1) and 2). They are a linear combination (number 2 is the number 1 multiplied by 2). So, for this system you can basically ignore one of them.
If you do that, you will have 3 equations and 3 variables, with a unique solution. In this case solution is X = 1, Y = 1, Z = 1.
Now, let's see if equation number 2 satisfies:
2x1 + 2x1 + 2x1 = 6
6 = 6
With this simple example we proved that you can have a linear system with a unique solution if it has more equations than variables.
I don’t understand :( can someone help me please and asap !!!!!
Answer:
A. $16,079
Step-by-step explanation:
You are given the income of a married couple and the tax table applicable to married couples. To find the amount of tax owed, you first find the applicable line in the table, then do the computation it tells you.
The applicable line for an income of $110,000 is the one that says ...
"77,401 to 165,000"
The left (Tax Rate) column of that line has "22%", and the right (Tax Owed) column tells you the computation you need to make.
You find "the excess over $77,400" by subtracting that amount from the $110,000 income:
the excess over $77,400 = $110,000 -77,400 = $32,600
__
Then the tax owed is 22% of this amount plus $8907:
tax owed = $8,907 + 0.22 × 32,600
= $8,907 + 7,172
tax owed = $16,079
A 3-gallon container of laundry detergent costs $20.76. What is the price per quart?
The price per quart of a 3-gallon container of laundry detergent is $1.73.
Explanation:To find the price per quart, we need to convert the 3-gallon container into quarts. Since there are 4 quarts in a gallon, there are 4 x 3 = 12 quarts in a 3-gallon container
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Final answer:
The answer calculates the price per quart of laundry detergent from a 3-gallon container and provides estimated costs for 40 oz. and 90 oz. sizes. All calculations are based on the given information and formula.
Explanation:
Price of 3-gallon container: $20.76
Price per quart: $20.76 / 12 quarts = $1.73 per quart
If the detergent were sold in a 40 oz. size: Estimated cost = $1.73 x 3.33 = $5.76
If the detergent were sold in a 90 oz. size: Estimated cost = $1.73 x 7.5 = $12.98
Now consider just the second sentence of the multistep word problem. Sentence 2: If four times the brother's age is subtracted from three times the sister's age, the difference is 40. Give an equation that represents this statement using b as the age of the brother and s as the age of the sister. Express your answer in terms of s and b.
Answer:
4b - 3s = 40
4b = 40 + 3s
b = 40 - 3s/4
4b - 3s = 40
4b - 40 =3s
4b - 40 /3 = s
The age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the age of the brother be b and the age of the sister be s
If four times the brother's age is subtracted from three times the sister's age, the difference is 40.
So the equation that represents this statement is:
⇒ 4b - 3s = 40
⇒ 4b = 40 + 3s
Divided by 3 into both sides and solve for b,
⇒ b = 40 - 3s/4
Now solve for b,
⇒ 4b - 3s = 40
⇒ 4b - 40 =3s
Divided by 3 into both sides
⇒ s = 4b - 40/3
Hence, the age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3
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