Answers
9514 1404 393
Answer:
payment: $960.82; interest: $203,918balance: $317,306.36; interest: $227,306.36Step-by-step explanation:
The sum of payments made n times per year for t years and earning annual interest rate r is the value of a single payment multiplied by k, where ...
k = ((1 +r/n)^(nt) -1)/(r/n)
__
Problem 1
The multiplier k is ...
k = ((1 +0.08/4)^(4·25) -1)/(0.08/4) ≈ 312.232306
Then the quarterly deposit needs to be ...
$300,000/312.232306 ≈ $960.82
The sum of the 100 quarterly payments is ...
100 × $960.82 = $96,082
So, the amount of interest earned is ...
$300,000 -96,082 = $203,918
Quarterly payments are $960.82Interest earned is $203,918__
Problem 2
The multiplier k is ...
k = ((1 +0.072/12)^(12·30) -1)/(0.072/12) ≈ 1269.22544
Then the balance resulting from monthly deposits of $250 will be ...
$250 × 1269.22544 = $317,306.36
The total of the 360 payments is $90,000, so the interest earned is ...
$317,306.36 -90,000 = $227,306.36
Account in 30 years is $317,306.36Interest earned is $227,306.36_____
Additional comment
In the case of Problem 1, the deposit amount is rounded down to the nearest cent. This means that the account balance at the end of 25 years will be slightly less than $300,000. The difference is on the order of $0.96. This means both the account balance and the actual interest earned are $0.96 less than the amounts shown above.
In many of these school calculations, we ignore the effect of rounding the payment values. Similarly, we ignore the effect of rounding the account balance values for each monthly or quarterly statement. In real life, the final payment of a series is often adjusted to make up the difference caused by this rounding.
Also worthy of note is that the calculations here assume the payments are made at the end of the period, not the beginning. That makes a difference.
Related Questions
Can y’all help me on question 6?!
Answers
Answer:
B
Step-by-step explanation:
To find the area of a parallelogram you do A=(b)(h) so 20x8=160. It's 160ft^2 because area is measured in square units.
Since you are looking for area, you need the little 2 at the end to signify that it is squared feet, so that eliminated A and C
Now, the area for a parallelogram is base(height) so it would be 20(8) which is 160
Since we have previously eliminated A and C for not having the feet squared, it would be B
Please correct me if I am wrong, have a good day!
A shoreline observation post is located on a cliff such that the observer is 280 feet above sea level. The observer spots a ship approaching the shore and the ship is traveling at a constant speed.
Requried:
a. When the observer initially spots the ship, the angle of depression for the observer's vision is 6 degrees. At this point in time, how far is the ship from the shore?
b. After watching the ship for 43 seconds, the angle of depression for the observer's vision is 16 degrees. At this point in time, how far is the ship from the shore?
Answers
Using the slope concept, it is found that the distances from the shore at each moment are given by:
a) 2664 feet.
b) 976 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Item a:
The vertical distance is of 280 feet, with an angle of 6º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{6^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{6^\circ}}[/tex]
x = 2664.
Item b:
The vertical distance is of 280 feet, with an angle of 16º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{16^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{16^\circ}}[/tex]
x = 976.
More can be learned about the slope concept at https://brainly.com/question/18090623
calculate 3ab + b for a=2 and b=-3
Answers
To test this series for convergence
∝
∑ (4^n+7)/7^n
n=1
You could use the limit comparison test, comparing it to the series
∝
∑ r^n
n=1
Where r=???
Completing the test, it shows the series:
Answers
r should be 4/7. You're comparing the given series to a geometric series that converges. By the limit comparison test, you have
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{4^n+7}{7^n}}{\frac{4^n}{7^n}}=\lim_{n\to\infty}\frac{4^n+7}{4^n}=\lim_{n\to\infty}\left(1+\frac7{4^n}\right)=1[/tex]
and since this limit is positive and finite, and the series you're comparing to is convergent, then the first series must also be convergent.
HELPPP PLEASEEESSS
Which best describes the triangle?
acute and scalene
80
right and isosceles
6 in.
6 in.
1)) obtuse and isosceles
50°
50°
7.7 in.
acute and isosceles
Answers
Answer:
acute and isosceles
Step-by-step explanation:
Define:
Acute - All angles have a measure of less than 90 degrees
Obtuse - has an angle with a measure of more than 90 degrees
Right - has an angle with a measure of 90 degrees
Scalene - no congruent side lengths or angles
Isosceles - two congruent sides and two congruent angles
Equilateral - all congruent sides and all congruent angles
Identify:
The triangle shown has angles that measure less than 90 degrees which means that it's an acute triangle
The triangle also has two congruent sides and two congruent angles which means that it's an isosceles triangle.
So we can conclude that the triangle can be identified as an acute isosceles
please helppppppppp me
Answers
Tom and his four friends are going to a baseball game. If the total amount they spent on tickets was $50, how much did they spend on each ticket?
Answers
12.50 on each ticket
Step-by-step explanation:
12.50 x 4 = 50.00
A pizza has a radius of 7 inches. If it is cut into 6 equal slices, what is the area of each slice?
Answers
answer: each slide would be one sixth of the entire area; the entire area is (pi)(72).
Do not use pi = 22/7 because that's untrue. It's approximately 3.1416; round off later!
hope this helps
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
100, 20, 4, ...
Answers
Answer:
its a geometric progression. r=1/5 or 0.2
Heeeeeeeeeeelppppppppppppppppppp
Answers
A)
So please brainliest my answer I would really appreciate it and best of wishes!!
Using the diagram below, what is the measure of ZE?
Answers
Answer:
50
Step-by-step explanation:
Think of line AE as a transversal. with DE and AB cutting across it. If we draw it out, looking at the picture, we can see that angles A and E correspond, meaning that angle A = angle E = 50
0.135 written as a fraction is
Answers
Answer:
[tex] \frac{27}{200} [/tex]Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over 1000. Reduce the fraction.
Hope it is helpful...COMPARE METALS TO NONMETAL WHICH STATMEMENT IS TURE
A,BOTH METALS AND NONMETALS ARE SHINY
B,BOTH METALS AND NONMETALS CONDUCT HEAT AND ELECTRICITY
C,NONMETALS CONDUCT HEAT AND ELECTRICITY BUT METALS DO NOT
D,METALS HAVA A SHINY LUSTER BUT NONMETALS DO NOT
Answers
Answer:
OPTION D IS THE ONLY LEGIT OPTION.
Metals have a shiny Lustre but Non metals do Not!
Answer:
D
Step-by-step explanation:
A: false. Some of the non-metals are gasses. They can hardly be classified as shinny.
Some of the metals, though solid, are not exactly shinny either.
B: Most metals conduct heat and electricity to some degree. Non metals don't.
C: The exact opposite is true.
D: I think this is the expected answer.
Which conditional statement is represented by the Venn diagram below?
Quadrilateral
Square
A. If a shape is a square, then it is a quadrilateral.
B. If a shape is a square, then it is not a quadrilateral.
0
C. If a shape is a quadrilateral, then it is a square.
D. If a shape is a quadrilateral, then it is not a square.
Answers
B is incorrect because a square is a quadrilateral.
C is incorrect because not all quadrilaterals are squares.
D is incorrect because a shape can be square if it’s a quadrilateral.
I hope this helps!
The function rule C = 40n + 210 relates the number of months n to cost in dollars C of a phone plan and budget phone. Make a table of the input/output pairs to show the cost of the phone and phone plan after 2, 12 and 24months
(Please help. I need this)
Answers
Answer:
Input - Output
2 - $290
12 - $690
24 - $1170
Step-by-step explanation:
Cost after n months:
The cost after n months is given by the following function:
[tex]C(n) = 40n + 210[/tex]
After 2 months:
This is C(2). So
[tex]C(2) = 40(2) + 210 = 80 + 210 = 290[/tex]
After 12 months:
This is C(12). So
[tex]C(12) = 40(12) + 210 = 480 + 210 = 690[/tex]
After 24 months:
This is C(24). So
[tex]C(24) = 40(24) + 210 = 960 + 210 = 1170[/tex]
Table:
Input - Output
2 - $290
12 - $690
24 - $1170
the two solids below are similar and the ratio between the lengths of their edges is 4:7 what is the ratio of their surface areas? A 7:4 B 16:49 C 16:29 B 64:343
Answers
9514 1404 393
Answer:
B. 16:49
Step-by-step explanation:
The area ratio is the square of the edge length ratio:
area ratio = (4:7)² = 4²:7² = 16:49
_____
It might help you to recall that area is the product of two linear dimensions if each is multiplied by 4/7, the resulting product will be multiplied by (4/7)².
A = LW
A' = (4/7L)(4/7W) = (4/7)²(LW) = (16/49)·A
Ezra had 46 green marbles. Then he bought 6 bags of blue marbles. There were 8 marbles in
each bag. How many marbles does Ezra have now?
marbles
Answers
Answer:
94 marbles
Step-by-step explanation:
46 green marbles + (6 bags x 8 pieces of marbles) = 94 marbles
A dictionary has 88,728 words. Out of that Mohan read 35,427 words. How many words are left for him to read?
Answers
[tex]\sf \bf {\boxed {\mathbb {Given:}}}[/tex]
Total number of words in the dictionary = 88,728 words
No. of words that Mohan read = 35,427 words
[tex]\sf \bf {\boxed {\mathbb {To\:find:}}}[/tex]
No. of words left for Mohan to read.
[tex]\sf \bf {\boxed {\mathbb {Solution:}}}[/tex]
[tex]\sf\purple{53,301 \:words. }[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
No. of words left for Mohan to read = Total no. of words in the dictionary - No. of words that Mohan read
= ( 88, 728 - 35, 427 ) words
= 53,301 words
[tex]\large\mathfrak{{\pmb{\underline{\red{Mystique35 }}{\red{❦}}}}}[/tex]
Amy has a bag with 2 pink marbles and 3 purple marbles. She picks two marbles. How much greater is the probability of Amy picking two consecutive pink marbles if she replaces her first marble as opposed to her leaving the first marble she picks out of the bag?
Answers
Answer:
2/5 is the answer bc there are 5 total marbles and you have more purple marbles then pink ones so the answer is 2/5 or 40%
For a rock concert a rectangular field of size 100 m by 50 m was reserved for the
audience.
The concert was completely sold out and the field was full with all the fans standing.
Which one of the following is likely to be the best estimate of the total number of people
attending the concert?
2000
5000
20000
50000
100000
Answers
Answer:
5000
Step-by-step explanation:
but this depends upon how much room each person needs
A store only sells 20-pound bags of ice. Over the weekend, the store sells 800 bags of ice, making $3,400. On Monday, the store sells 80 bags of ice. How much money does the store make selling ice on Monday?
Answers
= £4.25 per bag
80 X £4.25 = £340
The amount of money the store makes selling ice by the same ratio will be $340.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
The store sells 800 bags of ice, making $3,400.
Ratio = 3400/800
With the same ratio,
The store sells x amount of bags of ice,
x/80 = 3400/800
x = $340
Hence "The store will make $340 from selling ice using the same ratio".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ2
Find the area of the figure round to the nearest tenth
Answers
Answer:
Area of given figure = 60.8 mm² (Approx.)
Step-by-step explanation:
Given:
Length of figure = 9.3 mm
Width of figure = 7.8 mm
Height of triangular cut = 3 mm
Find:
Area of given figure
Computation:
Area of given figure = [(Length)(Width)] - Area of triangle
Area of given figure = [(9.3)(7.8)] - [(1/2)(b)(h)]
Area of given figure = [(9.3)(7.8)] - [(1/2)(7.8)(3)]
Area of given figure = [(9.3)(7.8)] - [(1/2)(7.8)(3)]
Area of given figure = [72.54] - [(1/2)(7.8)(3)]
Area of given figure = [72.54] - [11.7]
Area of given figure = 60.8 mm² (Approx.)
Mark is hosting a "Who Dunnit?" party at his house. He plans on taping off a triangular section of his backyard to represent the crime scene. If the sides measure 23 feet, 15 feet, and 32 feet, how much tape will be needed? DO NOT ANSWER JUST TO STEAL MY POINTS!!
Answers
Answer:
70 feet
Step-by-step explanation:
Given
[tex]Sides: 23ft, 15ft, 32ft[/tex]
Required
The tape needed
This implies that we calculate the perimeter (P)
This is calculated as:
[tex]P = \sum sides[/tex]
So:
[tex]P = 23ft +15ft + 32ft[/tex]
[tex]P = 70ft[/tex]
Answer:
dude why does it say your in college?!?
Step-by-step explanation:
Also I DON'T KNOW just kidding um before some fork tard deletes my answer Hi how are you????
HELP ME PLS I SUCK AT MATH I NEED ANSWER ASAP
Answers
B) 5-3= 2
C) 15-7=8
D) 8-3=5
E) +12-5=7
7056 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows and the number of plants in each row
Answers
Answer:
84 rows
84 plants on each row
Step-by-step explanation:
Given
[tex]Plants = 7056[/tex]
Required
The number of rows
Since the number of rows (r) and the plants on each row (p) are the same, then the area to be planted on is:
[tex]Plants = r * p[/tex]
Where
[tex]r =p[/tex]
So, we have:
[tex]Plants = r * r[/tex]
[tex]Plants = r^2[/tex]
This gives:
[tex]7056 = r^2[/tex]
Take square roots
[tex]84 = r[/tex]
Rewrite
[tex]r = 84[/tex]
What is the area of a regular hexagon (6 sides) whose
ℎ ℎ 6 ℎ ℎ ℎ ℎ 3√3 ? Show work
A) 54√3 2
B) 36√3 2
C) 108√3 2
D) 18√3 2
Answers
Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
A researcher uses an independent-measures t test to evaluate the mean difference between two treatments and obtains t(12) = 4.00. If the researcher had used an ANOVA to evaluate the data, what F-ratio would be obtained?
a. F(1, 11) = 2.00
b. F(1, 12) = 16.00
c. F(1, 12) = 2.00
d. F(1, 11) = 16.00
Answers
Answer:
B). F(1, 12) = 16.00
Step-by-step explanation:
'ANOVA' is a measure employed for 'analysis of a variance' in a given set of data of treatments or populations. While t-test helps in comparing their means.
As per the question, the F-ratio using ANOVA would be 'F(1, 12) = 16.00.' In order to calculate the variances, the distinction among the samples. The б^2 denotes the difference of representative means which is augmented by n(in case of samples being same). So, the ratio of F(1, 12) would be б^2 i.e. 4^2 = 16 since the sample sizes are distinct. Thus, option B is the correct answer.
It is reported in USA Today that the average flight cost nationwide is $445.99. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually greater than $445.99. What are the appropriate hypotheses for this test
Answers
Answer:
[tex]H_0[/tex] : [tex]\mu \leq 445.99[/tex]
[tex]H_a[/tex] : [tex]\mu > 445.99[/tex]
Step-by-step explanation:
It is given the average cost of the flight nationwide is $ 445.99
I wanted to [tex]\text{perform the hypothesis test}[/tex] to determine that the true average is greater than $ 445.99
Let the hypothesis that the true average is actually greater than $445.99
Therefore,
the [tex]\text{null hypothesis}[/tex] for the test is :
[tex]H_0[/tex] : [tex]\mu \leq 445.99[/tex]
And the alternate hypothesis is :
[tex]H_a[/tex] : [tex]\mu > 445.99[/tex]
I have a linear equation word problem pic to follow
Answers
In parallelogram JKLM if m
Answers
Answer:
155 degree
Step-by-step explanation:
x + 25 = 180 degree (sum of adjacent angles of a parallelogram are equal)
x = 180 - 25
x = 155 degree
