The difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
To subtract the second polynomial from the first polynomial, we need to perform term-wise subtraction. Let's break down the process step by step:
The first polynomial is: 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n.
The second polynomial is: -6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n.
To subtract the second polynomial from the first, we need to change the signs of all terms in the second polynomial and then combine like terms.
First, let's change the signs of the terms in the second polynomial:
-(-6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n) = 6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n.
Now, we can combine like terms by adding or subtracting coefficients of similar monomials:
(11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n) - (6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n)
= 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n - 6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n
= (11m^(2)n^(5) - 6m^(2)n^(5)) + (-3m^(2)n^(3) + 3m^(2)n^(5)) + (5mn + m) + (-n + 2n)
= 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
Therefore, the difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
In summary, to find the difference, we changed the signs of all terms in the second polynomial and then combined like terms with the first polynomial. The resulting polynomial is the difference between the two original polynomials.
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QUESTION 1
A credit card has a balance of $1,400. The APR is 25% and the minimum payment is 3% of the balance. You will pay the minimum balance this month. If you do not use the card again then how much
should the balance be next month?
QUESTION 2
A credit card with an APR of 18% has a balance of $2500 on it. You make a $1400 payment that posts on the 11th day of a 31-day month. How much interest will you be charged for the month?
QUESTION 3
Suppose we have a card with an APR of 25%. The minimum payment is 7% of the balance Suppose we have a balance of $350 on the credit card. We decide to stop charging and to pay it off by making
the minimum payment each month.
Calculate the new balance after the first minimum payment is made.
Calculate the minimum payment that is due the next month.
QUESTION 4
Your credit card has a balance of $2500 and an interest rate of 21%. The credit card requires a minimum payment of 3%
Lennors
Answer:
Q1: $1,360, Q2: $30.83, Q3: $325.50, Q4: $75
Step-by-step explanation:
QUESTION 1:
If the minimum payment is made and no additional charges are made, the balance next month should be $1,400 minus 3% of $1,400, which is $1,360.
QUESTION 2:
To calculate the interest charged for the month, we need to determine the average daily balance. Assuming no other transactions, the average daily balance would be (($2,500 * 20) + ($1,100 * 10)) / 31 = $2,032.26. Multiply this by the APR of 18% and divide by 365 to get the daily interest rate. The interest charged for the month would be approximately ($2,032.26 * 0.18) / 365 * 31 = $30.83.
QUESTION 3:
After making the first minimum pyment, the new balance would be $350 minus 7% of $350, which is $325.50.
To calculate the minimum payment due the next month, we take 7% of the new balance, which is 7% of $325.50, equal to $22.79 (rounded to the nearest cent).
QUESTION 4:
The minimum payment required on a balance of $2,500 would be 3% of $2,500, which is $75.
The endpoints of segment XY are X(-2,3) and Y(7,4). The segment is translated along the vector <-3,1> and then rotated 90 degrees. What is the coordinate of X"?
The coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).
To find the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees, we need to follow these steps:
Translation: Add the components of the translation vector <-3, 1> to the coordinates of point X(-2, 3) to get the new coordinates of X'.
X' = (-2 + (-3), 3 + 1) = (-5, 4)
Now, we have the translated endpoint X'.
Rotation: To rotate the point X' by 90 degrees, we need to swap the x and y coordinates and negate the new x coordinate.
X" = (y-coordinate of X', -x-coordinate of X')
X" = (4, -(-5))
X" = (4, 5)
Therefore, the coordinate of point X" after translating segment XY along the vector <-3, 1> and then rotating it 90 degrees is X" (4, 5).
In summary, we first translate point X(-2, 3) along the vector <-3, 1> to get X' (-5, 4). Then, we rotate X' by 90 degrees to obtain X" (4, 5).
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MARKING AS BRAINLIST PLEASE HELP!!
The correct probability that either event will occur is 0.533.
What is probability?A measure of the likelihood of an event to occur.
P(A or B) = P(A) + P(B).
Probability = Number of favorable outcomes/Total number of outcomes
P(A) = 1/5 = 0.3
P(B) = 1/3 = 0.33
P(A) + P(B) = 1/5 +1/3
= 0.533
Probability = 0.533.
Therefore, the probability that either event will occur is 0.533.
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Heeeeeelp pleaseeeeeeeeee!!!!!!!!!!!!L 3.11.3 Quiz: Comparing and Analyzing Function Types
Question 1 of 10
How would you describe the difference between the graphs of f(x)=2x² and
g(x)=-2x²?
A. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
OC. g(x) is a reflection of f(x) over the y-axis.
D. g(x) is a reflection of f(x) over the x-axis.
The correct statement regarding the reflection rules in this problem is given as follows:
D. g(x) is a reflection of f(x) over the x-axis.
How to define the reflection?The functions f(x) and g(x) in the context of this problem are defined as follows:
f(x) = 2x².g(x) = -2x².The entire function was multiplied by -1, meaning that the signal of the function was exchanged, hence the function was reflected over the x-axis.
As the function was reflected over the x-axis, the correct option in the context of the problem is given by option D.
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A boy walks 1260m on a bearing of 120°. How far south is he from his starting point
The boy is 630 meters south from his starting point.
To determine how far south the boy is from his starting pointWe must take into account the southward component of his shift.
We can imagine a right-angled triangle where the hypotenuse represents the boy's total displacement of 1260 meters, the angle between the hypotenuse and the south direction is 120°, and the side next to the angle represents the southward displacement given that the boy walks 1260 meters on a bearing of 120°.
We can use trigonometric functions to calculate the displacement to the south. Since the adjacent side and hypotenuse of a right triangle are connected in this instance, we will use the cosine function.
cos(120°) = adjacent / hypotenuse
cos(120°) = adjacent / 1260
Solving for the adjacent side (southward displacement):
adjacent = cos(120°) * 1260
adjacent = (-0.5) * 1260
adjacent = -630
The negative sign indicates that the southward displacement is in the opposite direction or "south" relative to the starting point.
Therefore, the boy is 630 meters south from his starting point.
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Enter the number that belongs in the green box
The angles of the triangle with sides 11, 12 and 20 are approximately 117.6 degrees.
We are given that;
The angles of triangle sides are 11, 12 and 20.
Now,
To find the angles of a triangle when its sides are given, we can use the law of cosines. The law of cosines states that c^2 = a^2 + b^2 - 2ab cos©, where a, b, and c are the sides of the triangle and C is the angle opposite to side c.
Using this formula, we can find the angle opposite to side 20 as follows: [tex]cos© = (a^2 + b^2 - c^2) / 2ab cos© = (11^2 + 12^2 - 20^2) / (2 * 11 * 12) cos© = -0.45 C = arccos(-0.45) C[/tex] = 117.6 degrees
Similarly, we can find the other two angles:[tex]cos(A) = (b^2 + c^2 - a^2) / 2bc cos(A) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) cos(A) = 0.25 A = arccos(0.25) A[/tex] = 75.5 degrees
[tex]cos(B) = (a^2 + c^2 - b^2) / 2ac cos(B) = (11^2 + 20^2 - 12^2) / (2 * 11 * 20) cos(B) = -0.55 B = arccos(-0.55) B[/tex]= 87 degrees
The triangle with sides 11, 12 and 20 are approximately 117.6 degrees, 75.5 degrees, and 87 degrees
Therefore, by the angle the answer will be 117.6 degrees.
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Out of a pool of 26 men and 29 women what is the probability that 6 men and 6 women will be selected?
Let's evaluate the probability based on the given information.
The number of ways to choose 6 men from 26 can be calculated as:
C(26, 6) = 26! / (6! * (26-6)!) = 26! / (6! * 20!) = 230,230.
The number of ways to choose 6 women from 29 can be calculated as:
C(29, 6) = 29! / (6! * (29-6)!) = 29! / (6! * 23!) = 177,100.
The total number of possible outcomes is the combination of selecting 6 men and 6 women from the given pool of 26 men and 29 women:
Total outcomes = C(26, 6) * C(29, 6) = 230,230 * 177,100 = 40,795,315,300.
Therefore, the probability of selecting exactly 6 men and 6 women from the given pool is:
Probability = 1 / Total outcomes = 1 / 40,795,315,300 ≈ 2.45 x 10^-11.
Hence, the probability is approximately 2.45 x 10^-11.
The cost of a season train ticket is reduced by $33.10 which corresponds to a 10%
reduction. Find the original cost of the season ticket.
Answer:
Let's denote the original cost of the season train ticket as "x".
According to the given information, a reduction of $33.10 corresponds to a 10% reduction in the original cost. We can set up the following equation to represent this:
10% of x = $33.10
To solve for x, we need to convert 10% to decimal form, which is 0.10. We can rewrite the equation as:
0.10 * x = $33.10
Simplifying the equation, we have:
0.10x = $33.10
To isolate x, we divide both sides of the equation by 0.10:
x = $33.10 / 0.10
x = $331.00
Therefore, the original cost of the season train ticket is $331.00.
Step-by-step explanation:
Janine built a raised garden bed that is 10 feet long, 5 feet wide, and 1.5 feet tall. She plans to fill the garden bed with premium soil that costs $16.31 per cubic yard. Recall that 1 yard = 3 feet. how much will it cost Janine to fill her garden bed with premium soil?
Answer: $45.31
Step-by-step explanation:
10*5*1.5=75
75/27 (formula)=2.77778
2.77778*16.31=45.31
What is the answer pls
By translation, the images of the vertices Q and S are Q'(x, y) = (- 1, 4) and S'(x, y) = (- 3, 2).
How to find the image of a point by translation
In this problem we find the representation of a parallelogram, which is formed by four vertices. The images of the vertices can be found by means of translation, whose formula is introduced below:
C'(x, y) = C(x, y) + T(x, y)
Where:
C(x, y) - Original pointT(x, y) - Translation vector.C'(x, y) - ImageIf we know that Q(x, y) = (4, 1), S(x, y) = (2, - 1) and T(x, y) = (- 5, 3), then the images of the points are:
Q'(x, y) = (4, 1) + (- 5, 3)
Q'(x, y) = (- 1, 4)
S'(x, y) = (2, - 1) + (- 5, 3)
S'(x, y) = (- 3, 2)
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In Boston, a popular restaurant recently added a delivery option. In reviewing the sales for this new delivery service, the restaurant found the mean delivery orders in a random sample of Friday nights was x¯=48 orders, with a margin of error of 12 orders.
The 95% confidence interval for the mean number of delivery orders on a Friday night is 36 to 60 orders.
What is the confidence interval?The confidence interval for the mean number of delivery orders on a Friday night is constructed assuming a 95% confidence level.
Given data:
Sample mean (x) = 48 orders
The margin of error (E) = 12 orders
To calculate the confidence interval, we'll use the formula:
Confidence Interval = x ± E
Substituting the values:
Confidence Interval = 48 ± 12
The lower limit of the confidence interval:
Lower Limit = 48 - 12 = 36
The upper limit of the confidence interval:
Upper Limit = 48 + 12 = 60
Therefore, the 95% confidence interval for the mean number of delivery orders on a Friday night is 36 to 60 orders.
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Complete question:
In Boston, A Popular Restaurant Recently Added A Delivery Option. In Reviewing The Sales For This New Delivery Service, The Restaurant Found The Mean Delivery Orders In A Random Sample Of Friday Nights Was X¯=48 Orders, With A Margin Of Error Of 12 Orders. Construct A Confidence Interval For The Mean Number Of Delivery Orders On A Friday Night.
7. De una caja que contiene 8 canicas verdes, 5 amarillas y 3 blancas se extrae una al azar. Determina la
probabilidad de que sea:
a) Verde
b) Amarilla c) Blanca
d) No amarilla e) Verde o blanca
answer:
a) 8
_ or 50%
16
b) 8 or 50%
_
16
c) 11 or 68.75%
_
16
5.2. The entrance fee for adults was R50 each and that for children was R20. If the school raised
R31 400 in total, write an equation in x to determine how many adults and how many children
attended the performance. Then solve the equation and write down the number of adults and
(4)
children attended the performance.
Answer:
Let's assume the number of adults attending the performance is represented by 'x', and the number of children attending is represented by 'y'.
According to the given information, the entrance fee for adults is R50 each, and for children is R20 each.
The total amount raised by the school is R31,400. We can write an equation based on the total amount raised:
50x + 20y = 31,400
This equation represents the total value of the entrance fees paid by adults and children.
To solve this equation, we need another equation to relate the variables 'x' and 'y'.
Since we don't have any other information about the number of adults or children, we cannot determine their relationship based on the given information. Therefore, we cannot find a unique solution for 'x' and 'y' unless there is additional information provided.
If there is additional information or if you have any specific values for 'x' or 'y', I can assist you in solving the equation and finding the number of adults and children attending the performance.
Step-by-step explanation:
Explain the difference:
4 times the sum of x and y and the sum of 4 x and y
Hello!
4 times the sum of x and y
4 * (x + y)
it's a mutliplication
the sum of 4x and y
= 4x + y
it's a sum
Answer:one is multiplying other is some.
Step-by-step explanation:
4xy and =4xy
these two are
Find all of square roots of 36i and write the answers in rectangular (standard) form
given f(x)=3x-5, solve for x when f(x)= (x-1)
Answer: Pretty sure it should be 2.
Step-by-step explanation:
maybe -2 but i dont think so
Apply the square root principle to solve (x – 2)^2 + 20 = 0.
Question 1 options:
A)
x = 2 + 2i , x = 2 – 2i
B)
x = –2 + 2i , x = –2 – 2i
C)
x = 2 + 2 , x = 2 – 2
D)
x = –2 + 2, x = –2 – 2
Answer:
швлалалаось.чллслслслсб вщлалс
Abiodun walks 5km due north,then12km due east.How far ia he from the starting point?
What is the volume of 15m tall, 3m wide and 4m long. What is the volume of the container?
Goodluck
The volume of the container is 180 cubic meters.
Given,
Length of the container = 4 meters
Width of the container = 3 meters
Height of the container = 15 meters
Let the container is a cuboid, as the shape of the container isn't mentioned.
Now, we know that,
The volume of a cuboid = Length of the cuboid × Width of the cuboid × Height of the cuboid
Therefore, the volume of the given container of cuboid shape = 4 × 3 × 15 cubic meters.
= 180 cubic meters.
Hence, the volume of the container is 180 cubic meters.
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TOURISM At a town with a large convention center, the cost of a hotel room has increased 5.1% annually.
If the average hotel room cost $48.00 in 1980 and this growth continues, what will an average hotel room
cost in 2012? Use y = a(1 + r)^t and round to the nearest cent.
a. $143.38
h
$235.79
$126 34
d
$87 19
Given statement solution is :- The average hotel room cost in 2012 would be $199.97, none of the provided options are correct.
To calculate the average hotel room cost in 2012, we can use the formula:
y = a(1 + r)^t
where:
y = future value (cost in 2012)
a = initial value (cost in 1980)
r = annual growth rate (5.1% or 0.051)
t = number of years (2012 - 1980 = 32)
Substituting the given values into the formula, we have:
y = $48.00(1 + 0.051)^32
Calculating the value:
y ≈ $48.00(1.051)^32
y ≈ $48.00(2.718282)^0.051(32)
y ≈ $48.00(2.718282)^1.632
y ≈ $48.00 * 4.171331
y ≈ $199.97
Rounding to the nearest cent, the average hotel room cost in 2012 would be $199.97.
Therefore, none of the provided options are correct.
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A bag contains 19 blue, 28 purple, 21 red, and 29 orange balls. You pick one ball at random. Find the probability that it is not orange. P(not orange) = Simplify your answer completely.
[tex]|\Omega|=19+28+21+29=97\\|A|=19+28+21=68\\\\P(A)=\dfrac{68}{97}[/tex]
David and Ken took part in a cycling race. Both of them did not change their speed throughout the race. David completed the race in 5 hours while Ken took 7 hours. Ken's average speed was 9.8 km/h less than David's average speed.
A) What was David average speed
B)What was the distance of the cycling race?
Let's assume David's average speed is S km/h.
A) To find David's average speed, we can use the formula: Speed = Distance / Time.
David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:
S = Distance / 5
B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.
Ken took 7 hours to complete the race, so we have:
S - 9.8 = Distance / 7
Now, we can solve the system of equations to find the values of S and Distance.
From equation (1): S = Distance / 5
Substitute this into equation (2):
Distance / 5 - 9.8 = Distance / 7
Multiply both sides of the equation by 35 to eliminate the denominators:
7 * Distance - 35 * 9.8 = 5 * Distance
7 * Distance - 343 = 5 * Distance
Subtract 5 * Distance from both sides:
2 * Distance - 343 = 0
Add 343 to both sides:
2 * Distance = 343
Divide both sides by 2:
Distance = 343 / 2 = 171.5 km
Therefore, the distance of the cycling race is 171.5 kilometers.
To find David's average speed, substitute the distance into equation (1):
S = Distance / 5 = 171.5 / 5 = 34.3 km/h
So, David's average speed was 34.3 km/h.[tex][/tex]
Answer:
A) 34.3 km/h
B) 171.5 km
Step-by-step explanation:
Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:
[tex]\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}[/tex]
This distance for the cycling race can now be used to determine David's average speed:
[tex]\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}[/tex]
Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.
Determine: minimum, maximum, median, 1st quartile, and 3rd quartile
10,12,7,9,4,15,20,21
Minimum: _____
Maximum:_____
Median:_______
1st Quartile:____
3rd quartile:____
The minimum is the smallest value in the data set:
Minimum: 4
The maximum is the largest value in the data set:
Maximum: 21
The median is the middle value in the data set. Since there are an even number of values in this data set, we take the average of the two middle values:
Median: (10 + 12)/2 = 11
To find the quartiles, we first need to find the median of the lower half and upper half of the data set:
Lower half: 4, 7, 9, 10
Upper half: 12, 15, 20, 21
Median of lower half: (7 + 9)/2 = 8
Median of upper half: (15 + 20)/2 = 17.5
The first quartile (Q1) is the median of the lower half of the data set:
1st Quartile: 8
The third quartile (Q3) is the median of the upper half of the data set:
3rd Quartile: 17.5
Therefore: Minimum: 4 Maximum: 21 Median: 11 1st Quartile: 8 3rd Quartile: 17.5
I hope this helps! Let me know if you have any other questions.
If I have $25. How many cheeseburgers can I get if they are 2.50 each?
Answer:
We can get 10 cheeseburgers.
Step-by-step explanation:
To find out how many cheeseburgers we can buy if:
we have $25 andeach cheeseburger costs $2.50,we can divide the money we have by the cost of each cheeseburger.
To make the division simpler, we can multiply both numbers by 10.
$25 / $2.50 = $250 / $25
From this form of the division, we can clearly see that the amount of money we have is 10 times the cost of one burger because it is 25 with a 0 on the end, which is the result of multiplying by 10.
Therefore, we can get 10 cheeseburgers.
find the area of the triangle whoose side are 12,16 and 21 units
Answer:
[tex]A =[/tex] 95.45
Step-by-step explanation:
[tex]A=s(s﹣a)(s﹣b)(s﹣c)[/tex]
[tex]s=a+b+c[/tex]
Solving for A
A=1
4﹣[tex]a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1[/tex]
4-[tex]124+2·(12·16)2+2·(12·21)2﹣164+2·(16·21)2﹣214≈95.45123[/tex]
≈ 95.45123
Help! The white shark can grow to a length of 21 feet. This is 35% of the maximum length of the sperm whale. Find the maximum length of the sperm whale. If necessary, round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Use mid segment formula to find
a) x=
b) EF=
c) BC=
A
E
B
لی
3
D
4x+6
9x+4
F
Answer:
x = 5EF = 26BC = 49Step-by-step explanation:
Given midsegment EF = (4x+6) and base segment BC = (9x+4) of a trapezoid with base AD = 3, you want the value of x and the lengths of the two segments EF and BC.
MidsegmentThe midsegment parallel to the base segment is the average of the lengths of the parallel bases.
4x +6 = 1/2((9x +4) +3))
8x +12 = 9x +7 . . . . . . . . . multiply by 2 and simplify
5 = x . . . . . . . . . . . . subtract 8x+7
SegmentsUsing this value of x, we find the lengths of the segments to be ...
EF = 4·5 +6 = 26
BC = 9·5 +4 = 49
Check(BC +AD)/2 = EF
(49 +3)/2 = 52/2 = 26 . . . . as required
<95141404393>
Section 1 Mathematics Multiple-C 6 Isla can run 800 metres in 10 minutes. At this rate, how many kilometres can she run in 50 minutes?
The quilt is made of squares with diagonals.
The length of BD is 4.
a. Find the length of AE. Round answer to the hundredths.
b. Find the area of square ABCD.
A camera has a listed price $859.95 of before tax. If the sales tax rate is 9.5% , find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$941.65
Step-by-step explanation:
Salex tax:We have to find the sales tax of the camera.
tax rate = 9.5%
listed price = $859.95
[tex]\sf Sales \ tax = tax \ rate * listed \ price[/tex]
= 9.5 % * 859.95
= 0.095 * 859.95
= $81.70
To find the total cost, add the sales tax to the listed price.
Total cost = 859.95 + 81.70
= $941.65
