Answer:
A. $147.67
B. $26,581.49
C. Principal: 65.8352%
C. Interest: 34.1647%
The values:
a) PMT = $147.67.
b) $26580.6
c) Of the total amount paid, 65.84 percentage is paid toward the principal and 34.16 percentage is paid for the interest.
What is a loan calculation formula?The formula:
PV = PMT/i[1 - {1/(1+i)ⁿ]
PV denotes the loan sum.
PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)
Given:
Consider a student loan of $17,500 at a fixed APR of 6% for 15 years.
PV is the loan amount = 17500
PMT is the monthly payment .
i is the interest rate per month in decimal form (interest rate percentage divided by 12)
i = 0.06/12 = 0.005
n is the number of months (term of the loan in months)
n = 180 months.
The monthly payment,
PMT = PV i(1+i)ⁿ/{(1+i)ⁿ-1}
PMT = 17500(0.005)(1.005)⁴⁸/{(1.005)⁴⁸-1}
PMT = $147.67.
The total amount paid over the term of the loan,
= 147.67 x 180 = $26580.6
Of the total amount paid, 65.84 percentage is paid toward the principal and 34.16 percentage is paid for the interest.
Therefore, all the required values are given above.
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-5|4x - 4|- 9 = 31.
What’s the answer
What is the value of x
Answer: x = 60
Step-by-step explanation: Notice that these two angles are vertical angles.
Whenever two lines intersect, a pair of vertical angle is always formed.
Now, vertical angles are always congruent.
So we can setup the equation 2x + 24 = 144.
Solving from here, we first subtract 24 from both sides to get 2x = 120.
Now dividing both sides by 2, we find that x = 60.
So x = 60.
Answer:
c. 60°
Step-by-step explanation:
[tex](2x +24)\° = 144\°\\\\2x+24\°=144\°[/tex]
Collect like terms and simplify
[tex]2x\° =144\°-24\°\\\\2x\°=120\°[/tex]
Divide both sides of the equation by 2 and simplify
[tex]\frac{2x}{2} = \frac{120}{2} \\\\x =60\°[/tex]
Find the taylor series generated by f at x = a. f(x) = 1/9-x, a = 3.
Answer:
The generated Taylor series is;
f(x) = 1/6 + (x-3)/36 + (x-3)^2/216 + (x-3)^3/1296......
Kindly note that the series here is truncated at the third derivative, but if wanted, evaluation could be more than this
Step-by-step explanation:
Here, we are to find the Taylor series generated by f at x = a
Mathematically;
f(x)= 1/(9-x)
The f(a) at this point is calculated below;
f(a) = 1/(9-3) = 1/6
The first derivative is calculated below;
f'(x) = 1/(9-x)^2
f'(3) = 1/6^2 = 36
The second derivative is calculated below;
f''(x) = 2/(9-x)^3
f''(3) = 2/(9-3)^3 = 2/6^3 = 2/216 = 1/108
The third derivative is calculated as follows
f'''(x) = 6/(9-x)^4
f'''(3) = 6/(9-3)^4 = 6/6^4 = 1/216..
The Taylor series is thus given by;
f(x) = f(a) + f'(a) (x-a) + f''(a) (x-a)^2/2! + f'''(a) (x-a)^3/3! +...
Substituting the values of 3 for a at each of the points , we obtain the Taylor series as shown below;
f(x) = 1/6 + (x-3)/36 + (x-3)^2*1/108*1/2 + (x-3)^3*1/216*1/6 +...
f(x) = 1/6 + (x-3)/36 + (x-3)^2/216 + (x-3)^3/1296......
Write the complex number 4(cos 60 + i sin 60) in standard form 10. Use DeMoivre's Theorem to find (2+3i)6
Answer:
a) The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex], b) [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].
Step-by-step explanation:
a) The standard form of the complex number is [tex]z = a + i\cdot b[/tex], [tex]\forall \,a,b \in \mathbb{R}[/tex]. If we get that [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex], whose standard form is obtained by algebraic means:
1) [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] Given
2) [tex]z = (4\cdot \cos 60^{\circ})+i\cdot (4\cdot \sin 60^{\circ})[/tex] Distributive and Associative properties.
3) [tex]z = 2 + i\cdot 2\sqrt{3}[/tex] Multiplication/Result.
The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex].
b) The De Moivre's Theorem states that:
[tex]z = (a+i\cdot b)^{n}= r^{n}\cdot (\cos \theta + i\cdot \sin \theta)[/tex]
Where:
[tex]r =\sqrt{a^{2}+b^{2}}[/tex] and [tex]\theta = \tan^{-1} \left(\frac{b}{a}\right)[/tex].
If we know that [tex]z = (2+i\cdot 3)^{6}[/tex], then:
[tex]r = \sqrt{2^{2}+3^{2}}[/tex]
[tex]r =\sqrt{13}[/tex]
[tex]r \approx 3.606[/tex]
[tex]\theta = \tan^{-1}\left(\frac{3}{2} \right)[/tex]
[tex]\theta \approx 56.310^{\circ}[/tex]
The resulting expression is:
[tex]z = 3.606^{6}\cdot (\cos 56.310^{\circ}+i\cdot \sin 56.310^{\circ})[/tex]
[tex]z = 1219.585+i\cdot 1829.381[/tex]
Therefore, [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].
Students are paired in teams for a group science project. The number of hours each student spends working on the group project are recorded on the bar chart below. If Paloma and Abdul are a team, and Ben and Min are a team, how many more hours did Paloma and Abdul spend working on the project combined than Ben and Min?
Answer:
Paloma and Abdul combined spent 4 hours more working on the project than Ben and Min combined.
Step-by-step explanation:
Note: This question is not complete as the bar chart is not included. The bar chart is therefore included before answering the question. Please, see the attached jpeg file for the bar chart.
The explanation to the answer is now given as follows:
From the bar chart, we have the number of hours each student spends working on the group project as follows:
Numbers of hours spent by Paloma = 21 hours
Numbers of hours spent by Adbul = 18 hours
Numbers of hours spent by Ben = 13 hours
Numbers of hours spent by Min = 22 hours
The number of hours each group spent working on the group project is calculated as follows:
Numbers of hours spent by Paloma and Abdul = Numbers of hours spent by Paloma + Numbers of hours spent by Paloma = 21 hours + 18 hours = 39 hours
Numbers of hours spent by Ben and Min = Numbers of hours spent by Ben + Numbers of hours spent by Min = 13 hours + 22 hours = 35 hours
Th number of hours Paloma and Abdul spend working on the project combined more than Ben and Min combined = Numbers of hours spent by Paloma and Abdul - Numbers of hours spent by Ben and Min = 39 hours - 35 hours = 4 hours
Therefore, Paloma and Abdul combined spent 4 hours more working on the project than Ben and Min combined.
R= {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-2,
-1
о
1
2
Answer: -3,-1, and 1.
Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.
2605.40
Significant digits
What is the opposite of the opposite of -5?
Answer:
-5
Step-by-step explanation:
The opposite would be 5, but since we need the opposite of the opposite, the opposite of 5 is -5. Hope this helped and wasn't too confusing!
If vector AB = i+7j-2k and B is point (7,4,4). Find A.
Answer:
A is point ( 6, -3, 6)
Step-by-step explanation:
Here in this question, we are concerned with finding the coordinates of point A.
Since we do not know the coordinates of point A, let’s represent them as (x,y,z)
By vector properties; Mathematically ;
AB = (7,4,4) - (x , y, z)
Thus; AB = (7-x)i + (4-y)j + (4-z)k
From the question, we are told that AB is also i + 7j -2k
By comparison;
(7-x)i = i
7-x = 1
x = 7-1
x = 6
(4-y)j = 7j
4-y = 7
4-7 = y
y = -3
and lastly
(4-z)k = -2k
4-z = -2
4 + 2 = z
z = 6
So the coordinates of A are (6, -3, 6)
grades are due today and im stuck on this question . Any help ?
Answer: The answer is 17
Step-by-step explanation:
Because math is easy
evaluate z+z+z for x =2,y=-3,z=4
Answer:
12
Step-by-step explanation:
4+4+4=12
Point B lies between points A and C on Line segment A C . Let x represent the length of segment AB in inches. The length of line A C is 20 inches. The space between points A and B is labeled x. The space between points B and C is labeled 3 x. Use the segment to complete the statements. The value of x is . The length of Line segment A B in inches is . The length of Line segment B C in inches is .
AB = x
BC = 3x
AC = 20 inches = AB + BC
Let's plug our values into the equation above.
20 inches = x + 3x
Combine like terms
20 inches = 4x
Divide both sides by 4
5 = x
AB = x = 5 inches
BC = 3x = 3(5) = 15 inches
The value of x is
✔ 5
The length of Line segment A B in inches is
✔ 5
The length of Line segment B C in inches is
✔ 15
<3
A world class sprinter ran 200 m in 22.75s. What was her average speed?
m/s
Enter a number.
Answer:
8.8
Step-by-step explanation:
speed=distance/time
speed- ?
distance- 200m
time- 22.75s
?=200/22.75
?= 8.791...
round it so that it becomes 8.8
Consider these shapes.
Shape A
3x^2+ 2
7x2 + 4x + 8
Shape B
3x^2+ 2
If shape B is a square, which polynomial represents the difference of the areas of shape A and shape B?
A. 8x +8x + 12
B. 12x^4+ 12x^3 + 26x^2 + 8x + 12
C. 32x^2 + 8x + 28
D. 30x^4 + 12x^3 + 40x^2 + 8x + 20
Answer:
The correct answer is B :)
Step-by-step explanation:
The difference in the area of shape A and shape B is option B which is [tex]12x^{4}+12x^{3}+26x^{2} +8x+12[/tex].
What is area of rectangle and square?Area of rectangle and square is the extent of surface rectangle and square exhibits into them. The area of rectangle is length * breadth and the area of square is side*side.
How to find area?We have been given the length of shape A=[tex]7x^{2} +4x+8[/tex] and breadth be [tex]3x^{2} +2[/tex] and the side of shape B be [tex]3x^{2} +2[/tex].
Shape A looks like rectangle and shape B looks like square.
So the area becomes:
Area of shape A =[tex](3x^{2} +2) ( 7x^{2} +4x+8)[/tex]
we have to multiply both expressions
=[tex]21x^{4} +12x^{3} +24x^{2} +14x^{2} +8x+16[/tex]
=[tex]21x^{4} +12x^{3} +38x^{2}+8x+16[/tex]
Area of shape B=[tex](3x^{2} +2)(3x^{2} +2)[/tex]
=[tex]9x^{4} +6x^{2} +6x^{2} +4[/tex]
=[tex]9x^{4} +12x^{2} +4[/tex]
Difference=[tex]21x^{4}+12x^{3}+38x^{2} +8x+16-9x^{4} -12x^{2} -4[/tex]
=[tex]12x^{4} +12x^{3}+26x^{2} +8x+12[/tex]
Hence the difference between shape A and shape B is [tex]12x^{4} +12x^{3}+26x^{2} +8x+12[/tex].
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please help meee!! 20 points!!!!
SOMEONE HELP ME PLEASE ASAP!!!
Answer:
600
Step-by-step explanation:
0+.80x=60+.70x
-.70x=60-.70x
.10x=60
÷.10=÷.10
C=600
0+.80(600)=480
60+.70(600)=480
Directions: Write an integer for each situation,
1. an 8 degree rise in temperature
2. 47 feet below sea level
3. a 19-yard gain
4. overdrawing an account by $124
5. two strokes below par
6. a 20-foot extension
In integers , we represent quantity of terms such as rise, above , increment by positive integers whereas its opposite such as fall, below, decrement is denoted by negative integers.
1. an 8 degree rise in temperature
Required integer = 8
2. 47 feet below sea level
Required integer = = -47
3. a 19-yard gain
Required integer = 19
4. overdrawing(taken more money out of account than the account has) an account by $124
Required integer = - 124
5. two strokes below par
Required integer = -2
6. a 20-foot extension
Required integer = 20
Solve (−3) ⋅ 2. plz i need help
Answer: -6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
Rule: When multiplying or dividing two numbers with the same sign (both positive or both negative), the answer is positive. When multiplying or dividing two numbers with different signs (one positive and one negative), the answer is negative.
Here you have a negative number and a positive number. Since their signs are different, the product is negative.
(-3) * 2 = -6
Mrs. Berry’s class organized the lunch orders for their upcoming party in the table below.Lunch Orders for the Class Party
Lunch Choice
Number
Vegetarian Sandwich
3
Turkey Sandwich
7
Pepperoni Pizza
8
Cheese Pizza
10
Which ratio represents the number of orders for pepperoni pizza to cheese pizza?
A.4:5
B.5:4
C.StartFraction 10 Over 8 EndFraction
D.StartFraction 18 Over 10 EndFraction
Given:
Number of Vegetarian Sandwich = 3
Number of Turkey Sandwich = 7
Number of Pepperoni Pizza = 8
Number of Cheese Pizza = 10
To find:
The ratio which represents the number of orders for pepperoni pizza to cheese pizza.
Solution:
The ratio of number of orders for pepperoni pizza to cheese pizza is
[tex]\text{Ratio}=\dfrac{\text{Number of orders for pepperoni pizza}}{\text{number of orders for cheese pizza}}[/tex]
[tex]\text{Ratio}=\dfrac{8}{10}[/tex]
[tex]\text{Ratio}=\dfrac{4}{5}[/tex]
Therefore, the required ratio is 4:5 and option A is correct.
Answer:
4:5 and option A is correct.
Step-by-step explanation:
edge2020
Which homophone best completes the sentence? Though I prefer to eat fruit, I enjoy vegetables ________. your you’re too two
Though I prefer to eat fruit, I enjoy vegetables too.
A homophone is a word that is pronounced the same as another word but differs in meaning.
What are some examples of homophones?Homophones may consist of two or more words, although pairs are more common than three or more words that sound the same. Examples of homophones that have three words are to, too, and two, and their, there, and they're.
here, we have,
Though I prefer to eat fruit, I enjoy vegetables too.
A homophone is a word that is pronounced the same as another word but differs in meaning.
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The EPA standard for safe drinking water is a maximum of 1.3 milligrams of copper per liter of water. A water testing firm found 8.3 milligrams of copper in a 5-liter sample drawn from Jim and Sharon LeBlanc's
house. Is the water safe or not? By how much does the amount of copper exceed or fall short of the maximum allowed?
Is the water safe for drinking?
No
Yes
what do you mean by herbivores?
Answer:
An animal or insect that only eats vegetation, such as grasses, fruits, leaves, vegetables, roots and bulbs.
Step-by-step explanation:
Answer:
Plant eating dinosaurs
Step-by-step explanation:
Herbivores have the word herb in it which refers to it being a plant eating dinosaur so a carnivore has the word carn which also refers to it being a meat eating dinosaur.
help me out with this question
The population is the entire set of registered voters (11100) in the city. This is what the election officials care about, so they won't focus on any other city data.
Inside that population, the much smaller sample is generated to try to make an educated guess about what the population will do. In this case, the sample is the 400 people surveyed. If the sample was generated randomly enough, then it should be unbiased to give a good idea of what the population will do.
I add 45 to a certain number and then divide the sum by 2 the result is five the original number find the original number
Hey there! I'm happy to help!
Let's call this number n. We can create the following equation.
(n+45)/2=5
Let's solve. We multiply both sides by 2.
n+45=10
We subtract 45 from both sides.
n=-35.
Have a wonderful day! :D
Answer:
n=-35
Step-by-step explanation:
Solve forj.
-j - 9> -6 or -5j + 18 < 19
Answer:
j < 3
j > -1/5
Step-by-step explanation:
Question 1:
-j - 9 > -6
-j > 3
j < 3
Question 2:
-5j + 18 < 19
-5j < 1
j > -1/5
HELPPPP PLEASEEEEE I NEED THIS ASAP
Answer:
10:4
Step-by-step explanation:
5:2=10:4 because 5 times 2 is 10,
and 2 times 2 is 4.
So they make up to be 10:4
Based on the scatterplot of the transformed data and the residual plot, which type of model is appropriate for estimating print publication each year? A linear model is appropriate because the residual plot does not show a clear pattern. A power model is appropriate because the scatterplot of years and the log of circulation is roughly linear. An exponential model is appropriate because the scatterplot of years and the log of circulation is roughly linear and the residual plot shows no distinct pattern. Both an exponential and a power model would be appropriate because the log of circulation was used to develop the model.
Answer:
C
Step-by-step explanation:
Answer: c
Step-by-step explanation:
I just took the test and got it correct
HELP PLEASE I NEED THIS IN
Answer:
the degree is about 120
Step-by-step explanation:
b and a is about 60 something and so is b and c so add all that up and you get about 120 degrees.
The perimeter of a rectangle is 34 units. Its width is 6.56, point, 5 units.
Answer: equation for length 34- (6.5 times 2) that whole thing divided by 2
Step-by-step explanation:
You know the width and a rectangle has 2 PAIRS of equal sides so if you know the width you just have to multiply that by 2 [ to account 4 the other side with the same length] and subtract that from the perimeter! Then you divide that answer by 2 to get what one side's length is!
hope that helped if it was not helpful sorry because i am a first grader :/
please answer or i move down grade again
Answer:
x is a 33° angle
Step-by-step explanation:
The two angles are supplementary meaning the measure of both angles adds up to 180°. You can tell they are supplementary because the angle is a straight line. so all you need to do is subtact 147 from. 180 to get the measure of x .
Answer:
x+147=180 ( sum of supplementary angle)
or, x = 180-147
or, x = 33
so the value of x is 33°
