If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.
Calculating the Sum of Money in 35 yearsGiven information is as follows,
Principal, P = $400
Rate = 8%
Time, T = 35 years
n = 12 (Compounded monthly)
The amount for compound interest is given as,
A = [tex]P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}[/tex]
A = [tex]400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}[/tex]
A = 6,517.02
A = $6,517 (to the nearest cents)
Calculating the Amount Put in AccountSince, $400 is deposited every month for 35 years,
Amount Put in 35 years for this compound interest =$400 × 12 × 35
= $168,000
Calculating the Compound InterestA = P + CI
Thus, the compound interest is given by,
CI = A - P
CI = 6517 - 400
CI = $6,117
I will earn a total interest of $6,117
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You deposit $4000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $162,272.32.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of years$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32
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Complete the following table given this information: (Do not round intermediate calculations.) Cost of machine $ 94,000 Residual value $ 4,000 Useful life 5 years Estimated units machine will produce 100,000 Actual production: Year 1 60,000
Year 2 15,000 Use MACRS table.
Straight line method?
Units of production?
Declining balance?
MACRS (5-year class)
The completion of the following table under different depreciation methods is as follows:
Depreciation Expense:Method Year 1 Year 2
Straight line $18,000 $18,000
Units of production $54,000 $13,500
Declining balance $37,600 $22,560
MACRS (5-year class) $18,800 $30,080
Data and Calculations:Cost of machine = $94,000
Residual value = $4,000
Depreciable value = $90,000 ($94,000 - $4,000)
Estimated useful life = 5 years
Depreciation expense:
Straight-line method = $18,000 ($90,000/5)
Estimated units of produciton = 100,000
Unit depreciation rate = $0.90
Actual production Depreciation
Year 1 = 60,000 $54,000 ($0.90 x 60,000)
Year 2 = 15,000 $13,500 ($0.90 x 15,000)
Declining Balance:
Year 1 = $37,600 ($94,000 x 40%)
Year 2 = $22,560 ($94,000 - $37,600) x 40%
MACRS:
Year 1 = $18,800 ($94,000 x 20%)
Year 2 = $30,080 ($94,000 x 32%)
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The perimeter of a right angled triangle, with hypotenuse c=101cm and one side b=20cm, is:
Answer:
220
Step-by-step explanation:
We need to find the 3rd side length
We already know the hypotenuse and one side, so we can use the Pythagorean formula.
101^2 = a^2 + 20^2. A is the third side, and solving for it, we find that it equals 99.
Side 1 = 101
Side 2 = 99
Side 3 = 20
101 + 99 + 20 = 220
The total age of Sana, Rabia and Saleem is 47 years. What was the total of their ages three years ago?
Answer:
38
Step-by-step explanation:
I'll say that Sana's age is A, Rabia's age is B, and Saleem's age is C.
A + B + C = 47
Three years ago, everyone was three years younger, so we can write the expression as:
(A-3) + (B-3) + (C-3) = x
x is the total age three years ago.
The above equation is the same thing as:
A + B + C - 9 = x
Since we know that A + B + C is 47, we use that number instead.
47 - 9 = x
38 = x
So three years ago, their total age was 38 years old.
You make a scale drawing of a tree using the scale 5 inches. = 27 feet. If the tree is 67.5 feet tall, how tall is the scale drawing?
Answer:
12.5 inches
Step-by-step explanation:
We use proportion to calculate the scale drawing
27 feet = 5 inches, so
67.5 feet = more inches (we know that it would be bigger than 5 inches)
We then put the bigger number on top and crossmultiply by saying:
67.5 over 27 × 5
Your answer should come out as 12.5 inches.
A role-playing game uses an 11-sided die that displays the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 What is the probability that someone throws the 11-sided die one time and rolls a number 9 or higher? Express your answer as a percentage rounded to one decimal place
Using it's concept, it is found that there is a 27.3% probability that someone throws the 11-sided die one time and rolls a number 9 or higher.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 11 numbers, 3 of which are 9 or higher, hence the probability is:
p = 3/11 = 0.273 = 27.3%.
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A random sample of n D 225 and xN D 21 was drawn from a normal population with a known
standard deviation of 26:8: Calculate the 95% confidence interval of the population mean.
Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the other parameters are:
[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]
The interval is: (17.5, 24.5).
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Using the data in the table, which statement is true?
The true statement is mean > median
How to determine the true statement?The mean is the average value.
So, we have
Mean = Sum/Count
This gives
Mean = (8 * 1 + 10 * 3 + 14 * 2)/(1 + 3 + 2)
Evaluate
Mean = 11
The mode is the measure with the highest frequency.
So, we have
Mode = 10
The median is the middle element
So, we have
Median = 10
The mean (11) is greater than the mode and the median
Hence, the true statement is mean > median
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How to solve for X in the triangle
Answer:
22.6
Step-by-step explanation:
a^2+b^2=c^2
8^2+b^2=24^2
b^2=512
b=22.6
Answer:
[tex]x = 16\sqrt{2}[/tex]
Step-by-step explanation:
we are given a right triangle.
then
In order to determine x we need to use
the Pythagorean theorem:
[tex]x^{2}+8^{2}=24^{2}[/tex]
⇔ x² + 64 = 576
⇔ x² = 576 - 64
⇔ x² = 512
⇔ x² = 2⁹
⇔ x² = 2 × 2⁸
[tex]\Longleftrightarrow x=\sqrt{2\times 2^{8}} =\sqrt{2\times \left( 2^{4}\right)^{2} }[/tex]
[tex]\Longleftrightarrow x= \sqrt{\left( 16\right)^{2} } \times \sqrt{2[/tex]
[tex]\Longleftrightarrow x = 16\sqrt{2}[/tex]
a display at an aquarium has sea stars to wolf eels in a ratio 4 : 5. It also has 5/8 as many rockfish as sea stars. there are 40 more wolf eels than rock fish. How many sea stars are there?
The number of sea stars is 64.
What is a ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.
In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."
This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.
According to the question,
Ratio of sea stars to wolf eels = 4:5
Number of rock fish= 5/8 (Number of sea stars)
Number of wolf eels - Number of rock fish = 40
Using the given information, we get,
Number of sea stars = 8/5 (Number of rock fish)
On simplification,
Number of wolf eels = 80
So, number of sea stars = (4/5)*80
= 64
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how to be smart
please help
I
23
12
N
L
12
23
O
K
M
18
18
Answer: [tex]\sqrt{407}[/tex]
Step-by-step explanation:
In this triangle, we know that [tex]IJ=46, IK=24, JK=36[/tex].
So, using the Law of Cosines in triangle IJK,
[tex]36^2 = 46^2 + 24^2 - 2(46)(24) \cos (\angle JIK)\\\\-1396=-2(46)(24) \cos(\angle JIK)\\\\\cos (\angle JIK)=\frac{349}{552}[/tex]
Using the Law of Cosines in the triangle LIK,
[tex](KL)^2 = 23^2 + 24^2 - 2(23)(24) \cos (\angle JIK)\\\\(KL)^2 = 23^2 + 24^2 - 2(23)(24)\left(\frac{349}{552} \right)\\\\(KL)^2 = 407\\\\KL=\sqrt{407}[/tex]
From atop a 15 m lighthouse, a man spots a dolphin 50 m out to sea. Find the angle of depression from the man to the dolphin, to nearest degree.
Answer:
16.7 degrees
Step-by-step explanation:
Fill in the blank
Timothy runs a public transportation service in his town. He has learned from his accountant that his organization is a liable to a special kind of tax. Which tax would Timothy have to pay from his organization?
Timothy would have to pay the _______ tax for his transportation service.
Answer:
road
Step-by-step explanation:
Find the interest rate for a principal of $6514 and charged $45415 in interest for 15 years.
Answer:
the answer is 46.47937775048613
Miranda works 25 hours a week at a wage rate of $10. Thus, her total weekly income is $250. On this income, she pays total taxes of $12.50. However, she calculates that on the last hour that she works, she pays $2.50. Miranda average take rate is ___% Miranda marginal tax rate is ___%
Step-by-step explanation:
Ig by dividing 12.50 and 250
What is the frequency of the function f (x). f (x) = -2sin x/4 +3
Answer: [tex]8\pi[/tex]
Step-by-step explanation:
The period is [tex]\frac{2\pi}{1/4}=8\pi[/tex].
Draw the graph of changing length of shadow of a stick from 12pm to 5pm.
The graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.
When an object (like the stick in the cartoon) blocks some of the Sun's light, it casts a shadow. The shadow always points away from the Sun. How long the shadow is depends on how low or high the Sun is in the sky. If the Sun is low, we see a longer shadow. Is the Sun is high, we see a shorter shadow.
Length of shadow due to the Sun's light is smallest when the Sun is vertically above. This happens at 12 noon.
Thus the graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.
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Given that y varies directly with x in the table, find the
value of y if the value of x is 5.
We know that this ratio is directly because the two magnitudes go up.
In this case we will get the proportionality constant by dividing any term of the second magnitude by the first.
For example:[tex]9 \: \div \: 3 \: = \: \boxed{3}[/tex]
Now that we know that k = 3, we can know how much "y" will be if x = 5.
We just multiply:
[tex]3 \: \times \: 5 \: = \: \boxed{ \bold{ 15}}[/tex]
Answer: y = 15what two equal numbers add to the number 40
Answer:
3+37
11+29
17+23
20+20
Step-by-step explanation:
It's 20
(20+20 = 40)
Hope this helps!
What is the equation of the directrix?
The equation of the directrix is y = -5
How to determine the directrix equation?The equation is given as:
(x -1)^2 = 12(y + 2)
Express 12 as a product of 4 and 3
(x -1)^2 = 4 * 3(y + 2)
The parabola is represented as:
(x -h)^2 = 4p(y - k)
Where the directrix is
y = k - p
By comparison, we have:
k = -2 and p = 3
So, we have:
y = -2 - 3
Evaluate
y = -5
Hence, the equation of the directrix is y = -5
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a. If you wanted to draw a circle around this triangle that passed through points A, B, and C as shown by circle P, what steps would you take to do that? b. What steps would you take to draw a circle within the triangle such that each side of the triangle became a tangent line to the circle as shown by circle R? c. If a line drawn from point B to point P measures 2 inches, what is the diameter, circumference, and area of circle P in terms of I? d. Describe how you would find the area of the region bounded by segment BC and arc BDC in terms of a if the arc measure of arc BDC is 60°
The circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
Steps involved in inscribing a triangleThe steps involved in inscribing a triangle;
Construct two chords on the circle.Then , draw a perpendicular bisector to the chords with the compass which must meet at the center of the circle. Make a line from the center to one of the farthest points of the chords.Draw two lines to form a 30 degree with the radius on the opposite side.Stretch out these two lines to make two chords on the circle. The two chords should make angle of 60 degrees to each other.Then connect the other extreme of the two chords this makes an equilateral triangle.If the line drawn from point B to point P measures 2 inches, then the diameter is
= 2 × 2
= 4 inches.
The formula for calculating the circumference of a circle is given as;
Circumference = 2 π r
Radius = diameter/ 2
Radius = 4/2 = 2 Inches
Substitute the values
Circumference = 2 × 3. 142 × 2
Circumference = 12. 57 inches
Area = π r²
Area = 3. 142 × 2²
Area = 3. 142 × 4
Area = 12. 57 square inches
Thus, the circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
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Example 2.11: Solve the following
a) 4x² +10x = 6
Answer:
[tex]\huge\boxed{\sf \{-3, 1/2\}}[/tex]
Step-by-step explanation:
Given equation:4x² + 10x = 6
Take 2 common
2(2x² + 5x) = 6
Divide 2 to both sides
2x² + 5x = 3
Subtract 3 to both sides
2x² + 5x - 3 = 0
Using mid-term break
2x² + 6x - x - 3 = 0
Take common
2x(x + 3) - 1(x + 3) = 0
Take (x + 3) common
(x + 3)(2x - 1) = 0
Either,
x + 3 = 0 OR 2x - 1 = 0
x = -3 OR 2x = 1
x = -3 OR x = 1/2
Solution Set = {-3, 1/2}[tex]\rule[225]{225}{2}[/tex]
Answer: x = 3 or (-1/2)
Step-by-step explanation:
Given equation
4x² + 10x = 6
Subtract 6 on both sides
4x² + 10x - 6 = 6 - 6
4x² + 10x - 6 = 0
Use cross-multiplication to factorize the quadratic
Starting with:
2x -6
2x 1
This gives us:
(2x - 6) (2x + 1) = 0
Assume each value in the parenthesis to be 0
PART I:
2x - 6 = 0 ⇒ Given equation
2x - 6 + 6 = 0 + 6 ⇒ Add 6 on both sides
2x / 2 = 6 / 2 ⇒ Divide 2 on both sides
[tex]\boxed{x=3}[/tex]
PART II:
2x + 1 = 0 ⇒ Given equation
2x + 1 - 1 = 0 - 1 ⇒ Subtract 1 on both sides
2x / 2 = -1 / 2 ⇒ Divide 2 on both sides
[tex]\boxed{x=-\frac{1}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What is the value of x when (f o g)(x) =-8
Answer:
I think the answer is 3.
Step-by-step explanation:
First make arrow diagram of function f and g.
Then show it as composite function of fog(x) in arrow diagram.
Then in range you find -8 whose domain as x is 3.
Which of the following is not a characteristic of both observational studies and experiments
Data collected about a population is not a characteristic of both observational studies and experiments.
What is an experiment?Through experiments, two variables' cause and effect relationships are examined. This is where they differ from observations and interviews, which can only assume the existence of contexts and cannot provide evidence for them. The environment of the test subjects is managed in an experiment depending on the issue.
Three things characterize statistical experiments in general:
There are various outcomes that the experiment could produce.
In an experiment, the cause, the independent variable, is changed while the effect, the dependent variable, is measured and any unrelated factors are controlled.
It is possible to anticipate every outcome.
Chance determines how the experiment turns out.
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Point One = (0, -2)
Point Two = (-3,-5)
Slope-Intercept Form
Answer:
y = x - 2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this formula, "m" represents the slope and "b" represents the y-intercept. Before writing our equation in this form, we first need to find the slope. The slope can be found using the point-slope formula:
y₁ - y₂ = m(x₁ - x₂)
In this formula, "m" represents the slope, "x₁" and "y₁" represent the values from Point One, and "x₂" and "y₂" represent the values from Point Two. You can find the slope by plugging the values from the points into the equation and then simplifying.
x₁ = 0 x₂ = -3
y₁ = -2 y₂ = -5
y₁ - y₂ = m(x₁ - x₂)
(-5 - (-2)) = m(-3 - 0)
-3 = m(-3)
1 = m
Now that we have a value for the slope, we can use the values from either one of the points to solve for the y-intercept (from the slope-intercept form equation).
m = 1
x = 0
y = -2
y = mx + b
-2 = (1)(0) + b
-2 = 0 + b
-2 = b
Therefore, the equation of the line in slope-intercept form is:
y = x - 2
a using the strategy to determine the area of the large rectangle
b explain how this strategy relates to the binomial multiplication
c focused on multiplying two binomials, explain a strategy that can be used to multiply any two polynomials
The area of the large rectangle by using the strategy is; 168cm².
What is the area of tge large rectangle?The area of the rectangle can be determined by multiplying the length and width of the rectangle as follows;
Area = Length × width
Area = (10cm + 4cm) × (10cm × 2cm)
Area = (100+20+40+8)cm²
Area = 168 cm².
The strategy used above entails that the two binomials used to represent the length and width of the rectangle are multiplied according to binomial multiplication.
The strategy is that each term of the first binomials is used to multiply the terms in the second polynomial and the aggregate result of the multiplications is determined.
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30 POINTS!,!!!!!!!!!!!!
A packaging factory is open from Monday to Saturday. In a particular week, 15,000 packets were packed on Monday and the factory was also closed on Tuesday. If no less than 100,000 packets should be packed in that week, what is the minimum equal number of packets that must be packed per day for the remaining days?
Answer:
A minimum of 21250 packets per day.
Step-by-step explanation:
If Monday produced 15,000 packets, and Tuesday was closed they produced 15,000 packets in 2 days.
The factory is open 6 days a week.
They need 100,000 packets.
They have 15,000 packets.
6 subtract 2 is 4.
100,000 subtract 15,000 is 85,000.
They need 85,000 packets in 4 days.
That is a minimum of 21250 packets per day.
Place value in thousands for the 0 in 10000
The place value in thousands for the 0 in 10000 is 0 thousands
Place valueFrom the question, we are to the determine the place value in thousands for the 0 in the given number
The given number is
10000
The place value in thousands for the 0 in 10000 is 0 thousands
Hence, the place value in thousands for the 0 in 10000 is 0 thousands
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Find two positive numbers whose difference is 5 and the
sum whose squares is 557.
Answer: 19 and 14
Step-by-step explanation:
19^2+14^2= 557
What I did to start it is I tried 20 and 15 because I know the square roots of those and once I added them I saw that their sum was too big, so then I tried 19 and 14 because 19-14 is 5. It was really just guess and check :)