Answer: 4m-24n+3
Step-by-step explanation:
Expand and collect like terms!
[tex](17m-12n-1) + (4-13m-12n)\\= 17m - 12n - 1 + 4 - 13m - 12n\\=4m-24n+3[/tex]
Hope this helps <3
What is the mean and MAD for this data set\
Team A-(0,0,0,1,1,4,4,5,7,8)
Team B-(0,1,1,2,2,2,3,5,6,8)
if the distance between the line x+y-5 and 3x+3y-k=0 is √18, find the value of k.
Therefore, the value of k could be either 6 or 24 if the distance between the line x+y-5 and 3x+3y-k=0 is √18.
What is equation?An equation is a statement that two mathematical expressions are equal. It contains an equal sign and can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to solve problems, find unknown values, and model real-world situations.
Here,
To find the distance between the line x+y-5 and 3x+3y-k=0, we need to find the perpendicular distance between them.
The line x+y-5 can be written in slope-intercept form as y = -x + 5, and its slope is -1.
The line 3x+3y-k=0 can be rewritten as y = -x + k/3, and its slope is also -1.
Since the slopes of the two lines are the same, they are parallel. Therefore, the perpendicular distance between them is the distance between any point on one line and the other line.
Let's choose a point on the line x+y-5. We can choose (1,4) since it lies on the line. The distance between this point and the line 3x+3y-k=0 is:
|3(1) + 3(4) - k|/√(3²+3²)
Simplifying this, we get:
|15 - k|/3√2 = √18
Multiplying both sides by 3√2, we get:
|15 - k| = 3√2 * √18
= 9
This gives us two possible values for k:
15 - k = 9, which gives k = 6
or
k - 15 = 9, which gives k = 24
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Pizza sizes are based on the diameters of the pizza. Matthew, Raul, and Jerome ordered a 16-inch pizza that was cut into 12 equal slices. Each boy ate 4 slices of the pizza.
How many square inches of pizza did each boy eat? (Round your answer to the nearest whole square inch.)
A. 268 square inches
B. 50 square inches
C. 38 square inches
D. 67 square inches
Answer:
D. 67 square inches
Step-by-step explanation:
16 inches in diameter is an 8 inch radius. The area of a circle (the whole pizza) is
A = pi• r^2
= 3.14•8^2
= 64pi
= 200.96
The whole pizza is 200.96 square inches of pizza.
There are 12 pieces.
200.96 ÷ 12
= 16.746666...
Each slice is 16.75 sq inches.
The guys ate 4 pieces each.
16.75 × 4
= 67
Each guy ate 67 sq inches of pizza.
Maureen Webster, who is running for mayor in a city, claims that she is favored by 53% of all eligible voters of that city. Assume that this claim is true. What is the probability that in a random sample of 400 registered voters taken from this city, less than 49% will favor Maureen Webster?
The probability that a random sample of 400 registered voters from this town will have a Maureen Webster under the age of 49 is about 0.0951, or about 9.51%.
What does probability mean?Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes—how likely they are.
We can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1. First, we need to find the mean and standard deviation of the sample proportion, which is given by:
mean = p = 0.53
standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305
Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:
z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31
We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.
Therefore, we can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1.
First, we need to find the mean and standard deviation of the sample proportion, which is given by:
mean = p = 0.53
standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305
Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:
z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31
We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.
Therefore, the probability that a random sample of 400 registered voters from this town is under the age of 49 Maureen Webster is about 0.0951, or about 9.51%.
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PLEASE HELP ME ANSWER THIS I WILL GIVE BRAINLIEST OUT!
x+y=
−1
x−y=
−5
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The system has a single solution. The solution set is enter your response here.
(Type an ordered pair. Type integers or simplified fractions.)
B.
There are infinitely many solutions and the equations are dependent. The solution set is {(x,y) 2x+y=−1}.
C.
The system is inconsistent. The solution set is the empty set.
Answer:
A. The system has a single solution. The solution set is (x, y) = (-3, 2).
Step-by-step explanation:
You want the solution to the system of equations ...
x + y = -1x - y = -5Number of solutionsThese standard form equations are different, so they will have one solution.
SolutionThat solution can be found by adding the equations, eliminating the y-variable.
(x +y) +(x -y) = (-1) +(-5)
2x = -6
x = -3
y = x +5 = -3 +5 = 2 . . . . . . from the second equation
The solution is (x, y) = (-3, 2).
the relation between x^n and n! . Is x^n and n! are equal?you can use taylor series.
For which values of [tex]n[/tex] is Dehidral group [tex]D_{n}[/tex] commutative?
n = 2, in which case D2 is just the cyclic group of order 2, which is commutative.
n is a multiple of 4, in which case Dn is a product of two cyclic groups of order n/2, which are commutative.
What is a cyclic group?A cyclic group is a mathematical group that is generated by a single element, which is called a generator. In other words, a cyclic group is a group in which all elements can be obtained by repeatedly applying the group operation to a single element.
Formally, a cyclic group is defined as a group G that has an element g such that every element of G can be written as a power of g. That is, for every element x in G, there exists an integer n such that x = gⁿ, where gⁿ denotes the product of g with itself n times.
According to the given informationThe Dihedral group, denoted by Dn, is a group of symmetries of a regular n-gon. It has 2n elements and is not commutative in general, except for some special cases.
Group Dn has a presentation:
Dn = ⟨r, s | rⁿ = s² = (sr)² = e⟩
where r represents a clockwise rotation of 2π/n radians and s represents a reflection about a line through the center of the n-gon.
If n is odd, then the group Dn is not commutative, because rs is not equal to sr. This can be seen by considering the effect of the two operations on the vertices of the n-gon.
However, if n is even, then the group Dn is commutative in certain cases. Specifically, Dn is commutative if and only if the two generators r and s commute, i.e., if rs = sr. This happens when either:
n = 2, in which case D2 is just the cyclic group of order 2, which is commutative.
n is a multiple of 4, in which case Dn is a product of two cyclic groups of order n/2, which are commutative.
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A printer prints 17 prints per minute. How many minutes will it take to print 200 pages? Express your answer to the nearest whole number.
Answer:
12 minutes
Step-by-step explanation:
200/17
= 11.7
round up
12 minutes
Find the exact value of x.
Applying the Pythagorean theorem, the exact values of x are:
1. x = 13 2. x = 4 3. x = 6 4. x = 8 5. x = 15 6. x = √7
How to Find the Exact Value of x Using the Pythagorean Theorem?If a and b are smaller sides (legs) of a right triangle, and c is the longest side (hypotenuse), the Pythagorean theorem states that:
c = √(a² + b²).
Apply the Pythagorean theorem to find the exact value of x:
1. x = √(12² + 5²)
x = 13
2. x = √(5² - 3²)
x = 4
3. x = √(10² - 8²)
x = 6
4. x = √(17² - 15²)
x = 8
5. x = √(12² + 9²)
x = 15
6. x = √(4² - 3²)
x = √7
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A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 7 centimeters by 3 and three-fifths centimeters by 2 and two-fifths centimeters.
What is the surface area of the prism?
four hundred five and three twenty-fifths cm2
two hundred two and fourteen twenty-fifths cm2
one hundred one and seven twenty-fifths cm2
fifty and sixteen twenty-fifths cm2
The surface area of a rectangular prism is the sum of the areas of all its faces. The answer is B) two hundred two and fourteen twenty-fifths cm²
What is Surface Area?Surface area refers to the total area occupied by the surface of an object. It is found by adding up the areas of all the faces or surfaces of the object. For example, the surface area of a cube is found by multiplying the length of one edge by itself, and then multiplying the result by six, since a cube has six faces of equal area.
What is rectangular prism?A rectangular prism is a three-dimensional solid shape that has six faces, where each face is a rectangle. It is also known as a rectangular parallelepiped.
According to given information :
To find the surface area of the rectangular prism, we need to find the area of each face and then add them together. Using the given dimensions, we can see that the six faces have areas of:
Front and back faces: 7 cm x 2 and 2/5 cm = 29 and 3/5 square cm each
Top and bottom faces: 3 and 3/5 cm x 2 and 2/5 cm = 9 and 9/25 square cm each
Side faces: 7 cm x 3 and 3/5 cm = 25 and 1/5 square cm each
Adding these areas together, we get a total surface area of:
2(29 and 3/5) + 2(9 and 9/25) + 2(25 and 1/5)
= 59 and 1/5 + 18 and 18/25 + 50 and 2/5
= 127 and 11/25 square cm
Therefore, the closest answer to the surface area of the prism is B) two hundred two and fourteen twenty-fifths cm²
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what is 60 items ordered 14 items per case ?
Answer:
5 cases
10 additional units
Step-by-step explanation:
Given that:
Total number of units needed = 60 units
Total number of units per case = 14
Hence, the total number of cases required will
be: Number of units needed / number of units per
case
Number of cases required = 60/14 = 4.285 (this be up to 60 units)
means that 5 cases are required as 4 cases won't
With 5 cases, we have exceeded the required units needed:
Additional units will be: (145)-60
Additional units = 70 - 60 = 10 units
Step-by-step explanation:
if it helped u please mark a brainliest :))
brainliest and 20 points to whoever shows work the best
The value of the variable x for the arc angle CD and DE is -1and the arc angle FCE = 230°. Also x = 5 for the arc angles RS, ST, TU, and UR, and the arc angle RS = 70°.
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
Thus:
17). 2[(x + 131) + (x + 51)]° = 360°
2x + 182° = 180°
2x = 180° - 182°
2x = -2
x = -1
arc angle CD = -1 + 51 = 50°
arc angle DE = -1 + 131 = 130°
arc angle FCE = 2CD + DE
arc angle FCE = 2(50) + 130 = 230°
18). 92 + 27x + (11x + 8) + 15x - 5 = 360°
53x + 95° = 360°
53x = 360° - 95°
53x = 265
x = 5
arc angle RS = 15(5) - 5 = 70°
Therefore, the value of the variable x for the arc angle CD and DE is -1and the arc angle FCE = 230°. Also x = 5 for the arc angles RS, ST, TU, and UR, and the arc angle RS = 70°.
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6.) If it's midnight in North America and the Earth has rotated 180, then how many hours have passed?
Answer: 12 hours (noon)
Step-by-step explanation:
**For simplicity's sake, we'll use military time (Zulu time).**
- It is 00:00 in North America.
- If one full rotation means a day has passed, or more specifically, that 24 hours have passed, then that means the Earth has rotated 360°.
- So if 360° = 24 hrs, then 180°, being 360/2, or half a rotation, will be 24/2 hrs, or 12 hours.
- So the time is now 12:00, or noon.
A bank loaned out $19,500, part of it at the rate of 4% annual interest, and the rest at 14% annual interest. The total interest earned for both loans was $1,180.00. How much was loaned at each rate?
The amount that was loaned are $15,500 at 4% annual interest and $4000 at 14% annual interest.
Given that,
A bank loaned out $19,500.
Amount loaned at 4% annual interest = x
Amount loaned at 14% annual interest = 19,500 - x
Total interest earned for both loans = $1,180
0.04x + 0.14 (19,500 - x) = 1180
0.04x + 2730 - 0.14x = 1180
-0.1x = -1550
x = 15,500
Amount loaned at 4% annual interest = x = $15,500
Amount loaned at 14% annual interest = 19,500 - x = $4000
Hence the loaned amount are $15,500 and $4000.
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how to get complete exponential functions y=1/6
The missing values of y in the exponential function are 6 and 1/36.
What is the missing parts of the table?The missing part of the table is calculated as follows;
The exponential function is given as;
y = (1/6)×
when x = -2, the value of y is calculated as;
y = (1/6)⁻² = 36
when x = -1, the value of y is calculated as;
y = (1/6)⁻¹ = 6
when x = 2, the value of y is calculated as;
y = (1/6)² = 1/36
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Where does a pattern begin?
Answer:
In Mathematics, a pattern is a repeated arrangement of numbers, shapes, colours and so on. The Pattern can be related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern. Sometimes, patterns are also known as a sequence.
pleasee helppp don’t js guess or put something random pls i beg
Answer:
C. -3x + 2y = 20
Step-by-step explanation:
Since the slope of line P is -2/3, and line Q is perpendicular to line P, the slopes of lines P and Q will be negative reciprocals. So the slope of line Q is 3/2. Since (-6, 1) is on line Q, we have:
1 = (3/2)(-6) + b
1 = -9 + b
b = 10
y = (3/2)x + 10
2y = 3x + 20
-3x + 2y = 20, so the correct answer is C.
You are driving 70 miles per hour going to the beach. You started driving 10 miles closer to the beach then you normally would. How far away are you from home after 2 hours of driving?
If you started driving 10 miles closer to the beach then you normally would, after 2 hours of driving, you are 130 miles away from home.
Assuming that the distance to the beach from your home is "d" miles, you normally drive "d - 10" miles before reaching the beach.
If you drive for 2 hours at 70 miles per hour, you will have traveled a total distance of:
distance = speed x time = 70 x 2 = 140 miles
However, this distance includes the 10 miles that you started closer to the beach than normal. Therefore, the distance you have traveled from your home is:
distance from home = 140 - 10 = 130 miles
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There are four rational numbers which are listed smallest to largest, A, B, C, and D.
If the numbers are 5/3, 7/15, 6/10, and 25/5 identify which is A, which is B, which is C, and which is D.
Okay, let's list the 4 rational numbers from smallest to largest:
5/3
7/15
6/10
25/5
So:
5/3 is A
7/15 is B
6/10 is C
25/5 is D
Recently, Tom found he was a distant relative of General James Wolfe who died at the battle on the Plains of Abraham in 1759. When he died in 1759 he left $100 in his will which now belongs to Tom. The money has been in a savings account where it has been earning interest at 3.5% per year, compounded annually. How much will Tom have in the year 2022? Round to the nearest cent, do not put $ sign or commas in answer.
In 2022, Tom will have approximately 157783.78 in his account.
How to solve for the future valueFuture Value (FV)
= Principal (P) * (1 + Interest Rate (R))^Number of Years (N)
In this case:
Principal (P) = $100
Interest Rate (R) = 3.5% = 0.035
Number of Years (N)
= 2022 - 1759
= 263 years
Now we can plug in the values into the formula:
FV = $100 * (1 + 0.035)^263
FV ≈ $100 * 1577.837835196 (rounded to 9 decimal places)
FV ≈ $157,783.78 (rounded to 2 decimal places)
So, in 2022, Tom will have approximately 157783.78 in his account.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
People who made more money generally completed more years of college than those who made less money . So correct option is D.
Describe Graph?A graph is a visual representation of data or information that uses a set of points or nodes, connected by lines or curves, to convey relationships or patterns. Graphs can be used to illustrate data in a way that is easy to understand and analyze.
There are several types of graphs, each with its own strengths and weaknesses depending on the type of data being presented. Some common types of graphs include:
Line graph: A line graph displays data as a series of points connected by a line, and is commonly used to show trends or changes over time.
Bar graph: A bar graph displays data using rectangular bars, with the length or height of each bar representing the quantity of data being measured. Bar graphs are useful for comparing different values or categories.
Pie chart: A pie chart shows data as a circular graph, with each slice representing a portion of the whole. Pie charts are commonly used to show proportions or percentages.
Scatter plot: A scatter plot displays data as a set of points on a two-dimensional plane, with each point representing the values of two variables. Scatter plots are useful for identifying patterns or trends in the relationship between two variables.
Histogram: A histogram displays data as a set of bars, with the height of each bar representing the frequency or number of occurrences of data within a certain range or interval.
Graphs can be an effective way to communicate complex information in a simple and easy-to-understand way. They are commonly used in fields such as science, economics, and social sciences, as well as in everyday life to display data and make comparisons.
People who made more money generally completed more years of college than those who made less money .
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Tom jogs 4 1/6 miles from his house. He then jogs 5 4/5 miles farther. How many miles has Tom jogged in all? Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
To solve the problem, we need to add the two distances Tom jogged:
4 1/6 + 5 4/5
To add the two mixed numbers, we need to convert them into improper fractions:
4 1/6 = (6 x 4 + 1) / 6 = 25 / 6
5 4/5 = (5 x 5 + 4) / 5 = 29 / 5
Now we can add the two fractions:
25/6 + 29/5
To add the fractions, we need to find a common denominator:
LCM of 6 and 5 = 30
25/6 x 5/5 = 125/30
29/5 x 6/6 = 174/30
Now we can add the fractions:
125/30 + 174/30 = 299/30
The sum of the distances in improper fraction form is 299/30 miles. To write the answer as a mixed number in simplest form, we need to divide the numerator by the denominator:
299 / 30 = 9 29/30
Therefore, Tom has jogged 9 29/30 miles in all.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #3
If the graph of f(x) is changed to [tex]f(x) = 4(\frac{5}{7} )^{x}-2[/tex], the graph of f(x) would be translated down by 2 units.
An equation of the new horizontal asymptote is y = -2.
What is a translation?In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this scenario, we can logically deduce that the graph of the parent function f(x) was translated or shifted downward (vertically) by 2 units.
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A ladder leans against the side of a house. The angle of elevation of the ladder is 64 degrees when the bottom of the ladder is 9ft from the side of the house. How high is the top of the ladder from the ground? Round your answer to the nearest tenth.
- tan = opposite/ adjacent
- tan 64 = x(the height of the ladder)/ 9ft
- 2.050= x/9ft
-x= 9ft * 2.050
- x= 18.45ft = 18.5 ft= 19 ft
so x or the unkown height is 19 ft
rex industries has two products. They manufactured 12,539 units of products A and 8,254 units of product B. What is the activity rate for each cost pull?
The activity rate for Cost Pool A is $7.97 per unit of Product A, and the activity rate for Cost Pool B is $6.06 per unit of Product B.
What is the activity rate?The activity rate is a cost accounting term that refers to the cost that a company incurs for each unit of a particular activity or process. It is calculated by dividing the total cost of an activity or process by the total number of units produced or processed.
The purpose of calculating activity rates is to allocate the cost of a particular activity or process to the products or services that use that activity or process. This helps to determine the true cost of producing a product or service and to make informed decisions about pricing, profitability, and resource allocation.
According to the given informationIn order to calculate the activity rate for each cost pool, we need to know the total cost for each cost pool.
Let's assume that there are two cost pools: Cost Pool A and Cost Pool B.
If we know the total cost for each cost pool, we can calculate the activity rate for each cost pool by dividing the total cost by the total number of units produced.
For example, if the total cost for Cost Pool A is $100,000 and 12,539 units of Product A were produced, then the activity rate for Cost Pool A would be:
Activity Rate for Cost Pool A = Total Cost for Cost Pool A / Total Units of Product A
Activity Rate for Cost Pool A = $100,000 / 12,539 units
Activity Rate for Cost Pool A = $7.97 per unit of Product A
Similarly, if the total cost for Cost Pool B is $50,000 and 8,254 units of Product B were produced, then the activity rate for Cost Pool B would be:
Activity Rate for Cost Pool B = Total Cost for Cost Pool B / Total Units of Product B
Activity Rate for Cost Pool B = $50,000 / 8,254 units
Activity Rate for Cost Pool B = $6.06 per unit of Product B
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On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate.
Do not round your intermediate computations, and round your answer to three decimal places.
Step-by-step explanation:
so, overall, 63% will grow.
that means, every seed has a 63% chance to grow. in other words, the probabilty to grow is 0.63 (as 63% means 63 out of 100 = 0.63).
and a chance of
1 - 0.63 = 0.37
to not grow.
fewer than 8 out of 9 seeds means not 8 and not 9.
it is
1 - P(8) - P(9)
with P(x) means the probability that exactly x seeds out of the 9 grow/germinate.
the chance for a group of exactly 8 out of 9 seeds to grow is then the probabilty for 8 to grow and 1 not to grow :
0.63⁸ × 0.37 = 0.009181764...
but these are 8 seeds out of 9.
and we calculated the probability for only one possible grouping.
how many groups of 8 can we build out of 9 ?
as the sequence does not matter, and we cannot have repetitions (every seed can only count as 1), we have combinations
C(9, 8) = 9! / (8! × (9-8)!) = 9!/8! = 9
so, the total probability P(8) for exactly 8 seeds out of 9 to grow/germinate is
9 × 0.63⁸ × 0.37 = 9 × 0.009181764... = 0.082635875... ≈
≈ 0.083
now, the chance for a group of exactly 9 out of 9 seeds to grow is then the probabilty P(9) for all 9 to grow :
0.63⁹ = 0.015633814... ≈ 0.016
the probabilty that fewer than 8 out of the 9 will grow/germinate is
1 - 0.082635875... - 0.015633814... = 0.901730311... ≈
≈ 0.902
Liliana's monthly budget is represented by the pie chart below. All amounts
are in dollars.
What percentage of her monthly budget does Liliana spend on car expenses?
A. 11%
B. 13%
C. 16%
D. 6%
Answer:
Step-by-step explanation
The first step is to add up all of the numbers to get the total budget.
Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300
Then to find the percentage for a certain category it is:
[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]
So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense
Answer:
Step-by-step explanation
The first step is to add up all of the numbers to get the total budget.
Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300
Then to find the percentage for a certain category it is:
[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]
So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense
A company applies for a €170,000 mortgage loan to be repaid with fixed monthly installments at a 2,25% annual nominal interest rate compounded over 25 years. Please, find the amounts that would correspond to the following items:
a) The amount of the monthly installments, the total amount paid, and the interest to be paid over those 30 years.
b) The principal pending at the end of year 10 and the amount of interest paid in those 10 years.
c) The amounts corresponding to the first 4 years of the loan amortization schedule.
The monthly installments are €761.94, the total amount paid is €809.68 , and the interest paid is €72,904.00 over 25 years. The principal pending at the end of year 10 is €136,148.95, and the interest paid in 10 years is €33,851.05. The amounts corresponding to the first 4 years are Year 1 - €166,105.68, Year 2 - €162,059.00, Year 3 - €157,857.39, and Year 4 -€153,498.11
To find the amount of the monthly installments, we can use the formula
M = P * (r / (1 - (1 + r)⁻ⁿ))
where M is the monthly installment, P is the principal amount borrowed, r is the monthly interest rate, and n is the total number of monthly payments.
First, we need to convert the annual nominal interest rate to a monthly rate
r = 2.25% / 12 = 0.1875%
Next, we need to find the total number of monthly payments
n = 25 years * 12 months/year = 300 months
Using the formula, we get
M = 170,000 * (0.001875 / (1 - (1 + 0.001875)⁻³⁰⁰)) = €809.68 (rounded to the nearest cent)
The total amount paid over the 25 years would be:
Total amount paid = M * n = €809.68 * 300 = €242,904.00
The interest paid over those 25 years would be
Interest paid = Total amount paid - Principal amount borrowed = €242,904.00 - €170,000 = €72,904.00
To find the principal pending at the end of year 10, we can use the formula for the remaining balance on a loan
B = P * ((1 + r)ⁿ - [tex](1 + r)^t[/tex] / ((1 + r)ⁿ - 1)
where B is the remaining balance, P is the principal amount borrowed, r is the monthly interest rate, n is the total number of monthly payments, and t is the number of monthly payments made.
After 10 years, the number of monthly payments made would be
t = 10 years * 12 months/year = 120 months
The remaining number of monthly payments would be
n - t = 300 - 120 = 180 months
Using the formula, we get
B = 170,000 * ((1 + 0.001875)³⁰⁰ - (1 + 0.001875)^¹²⁰) / ((1 + 0.001875)³⁰⁰ - 1) = €136,148.95
To find the amount of interest paid in those 10 years, we can subtract the remaining balance from the original principal amount:
Interest paid = Principal amount borrowed - Remaining balance = €170,000 - €136,148.95 = €33,851.05
To find the amounts corresponding to the first 4 years of the loan amortization schedule, we can use an amortization schedule calculator or a loan amortization formula. Here are the amounts for the first 4 years
Year 1
Beginning balance: €170,000.00
Monthly payment: €809.68
Principal paid: €3,894.32
Interest paid: €6,594.51
Ending balance: €166,105.68
Year 2
Beginning balance: €166,105.68
Monthly payment: €809.68
Principal paid: €4,046.67
Interest paid: €6,442.16
Ending balance: €162,059.00
Year 3
Beginning balance: €162,059.00
Monthly payment: €809.68
Principal paid: €4,201.61
Interest paid: €6,287.22
Ending balance: €157,857.39
Year 4
Beginning balance: €157,857.39
Monthly payment: €809.68
Principal paid: €4,359.28
Interest paid: €6,129.55
Ending balance: €153,498.11
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76. Write an equation of
the line that passes
through (3,-2) and
is (a) parallel and
(b) perpendicular to
the line shown.
-2
y
1,3 | 5x
(2,-1)
(1,-4)
The equation of the line that passes through (3,-2) and is (a) parallel to the line is y = 3x - 11 and (b) perpendicular to the line is y = - 1 / 3 x - 2.
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form.
The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptHence, let's find the equation of a line passing through (3, -2) and is parallel to the line shown.
Parallel line have the same slope.
Hence,
m = -4 + 1 / 1 - 2
m = -3 / -1
m = 3
Therefore,
y = 3x + b
-2 = 3(3) + b
b = -2 - 9
b = -11
The equation is y = 3x - 11
Hence, let's find the equation of a line passing through (3, -2) and is perpendicular to the line shown.
The slopes of perpendicular lines are negative reciprocals of one another.
hence,
m = - 1 / 3
Therefore,
y = - 1 / 3 x + b
-2 = - 1 / 3(3) + b
b = -2 + 1
b = -2
Therefore, the equation is y = - 1 / 3 x - 2.
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