Find the interest on an investment of $45,000
compound annually at 5.25% for 6 years
A = P(1 + r)t
Answers
Answer:
The interest on the investment is $16,170.93811
Step-by-step explanation:
The rule of the compound interest is \(A=P(1+\frac{r}{n})^{nt}\), where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periods in timet is the time∵ The investment is $45,000
∴ P = 45,000
∵ The interest on the investment is compounded annually at 5.25%
∴ r = 5.25% = 5.25 ÷ 100
∴ r = 0.0525
∴ n = 1 ⇒ compound annually
∵ It is for 6 years
∴ t = 6
→ Substitute them in the rule above
∵ \(A=45,000(1+\frac{0.0525}{1})^{1(6)}\)
∴ \(A=45,000(1.0525)^{6}\)
∴ A = 61,170.93811
∵ I = A - P, where I is the interest
∴ I = 61,170.93811 - 45,000
∴ I = 16,170.93811
∴ The interest on the investment is $16,170.93811
Related Questions
what is my height in a triangle
Answers
The height of the triangle is the distance that is found between the tip of the triangle at the top to the base of the triangle.
What is the height of a triangle?A triangle's height is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.
The length of a perpendicular segment from the base to the vertex directly across from it determines the height that corresponds to it. The vertex that is not an endpoint of the base is the one on the opposite side.
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What is 80% of 150? Please help
Answers
Answer:
the answer is x=120
Step-by-step explanation:
look at the photo for the mathematical explanation
Beatrice makes a jar of dry soup mix. The ingredients are:
1
3
4
4
3
=
7
4
4
7
cups uncooked rice
1
2
2
1
cup dry lentils
1
2
3
3
2
=
5
3
3
5
cups uncooked pasta
1
3
3
1
cup beef bouillon
1
4
4
1
cup dried onion flakes
1
2
2
1
cup dried peas
How much soup mix does this recipe make?
Answer the questions to find out.
The sum
7
4
4
7
+
1
2
2
1
+
5
3
3
5
+
1
3
3
1
+
1
4
4
1
+
1
2
2
1
gives the amount of mix.
1. Which property could you use to change the order of the addends? (2 points)
2. Which property could you use to change the grouping of the addends? (2 points)
3. Use these properties to rewrite
7
4
4
7
+
1
2
2
1
+
5
3
3
5
+
1
3
3
1
+
1
4
4
1
+
1
2
2
1
in a way that makes the addition easier. Explain how your changes simplify the addition. (3 points)
4. Simplify your sum to find the total amount of soup mix. Show your work. (3 points)
Answers
The total amount of soup mix is 50 cups. We arrived at this answer by simplifying the sum using the regrouping in step 3.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The commutative property of addition can be used to change the order of the addends.
The associative property of addition can be used to change the grouping of the addends.
We can regroup the addends in a way that makes the addition easier. For example, we can group the like terms together as follows:
(7 + 1) + (4 + 2 + 3 + 4 + 2 + 2) + (3 + 3 + 1 + 1) + (4 + 2 + 2 + 1) + (7 + 1)
This regrouping makes it easier to add the like terms together, since we can add the terms within each parentheses first, and then add the resulting sums together. For example, we have:
8 + 17 + 8 + 9 + 8
This simplifies to:
50
Therefore, The total amount of soup mix is 50 cups. We arrived at this answer by simplifying the sum using the regrouping in step 3.
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Also where would i go to get more answers for questions like this but not on this site
Answers
Find the equation of the tangent line to y 4^(x2–2x+5) at x = 4. y =
Answers
The given equation is y = 4^(x2–2x+5).To find the tangent line to the curve at x = 4, differentiate the given function with respect to x and find the slope of the tangent at x = 4.
Given function is y = 4^(x2–2x+5). In order to find the equation of the tangent line to the curve at x = 4, we need to differentiate the given function with respect to x and find the slope of the tangent at x = 4. Then we use the point-slope form of the equation to find the equation of the tangent line.The process of finding the equation of the tangent line to the curve is by first differentiating the given function.
We differentiate the given function as follows:d/dx(y) = d/dx[4^(x2–2x+5)] => d/dx(y) = 4^(x2–2x+5) * d/dx[x2–2x+5]
=> d/dx(y) = 4^(x2–2x+5) * [2x - 2]When x = 4,d/dx(y) = 4^(42–2*4+5) * [2*4 - 2]
=> d/dx(y) = 4^(5) * [6]
=> d/dx(y) = 6 * 1024
The slope of the tangent at x = 4 is: m = 6 * 1024
The point is: (4, y)We substitute the values in the point-slope form of the equation of the line:y - y1 = m(x - x1)
=> y - y1 = m(x - 4)
=> y - y1 = 6 * 1024 (x - 4)
Where x1 = 4, y1 = 4^(42–2*4+5)
=> y1 = 4^(5)
=> y1 = 1024
Therefore, the equation of the tangent line to y = 4^(x2–2x+5) at x = 4 is y - 1024 = 6 * 1024 (x - 4).
Therefore, we can conclude that the equation of the tangent line to y = 4^(x2–2x+5) at x = 4 is y - 1024 = 6 * 1024 (x - 4).
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A set of weights includes a 4 lb barbell and 6 pairs fo weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pouds can be represented by
Answers
Weight (in lbs) = 4 + 20x
Where:
• 4 lbs is the weight of the barbell
• There are 6 pairs of weight plates available, with each pair weighing 20 lbs.
• x is the number of pairs of plates added to the barbell.
• So adding x pairs of plates results in 20x lbs of additional weight.
• 4 + 20x represents the total weight of the barbell and plates.
For example:
If you add 3 pairs of plates (x = 3), the total weight would be:
4 + 20(3) = 4 + 60 = 64 lbs
If you add 1 pair of plates (x = 1), the total weight would be:
4 + 20(1) = 4 + 20 = 24 lbs
If you add all 6 pairs of plates (x = 6), the total weight would be:
4 + 20(6) = 4 + 120 = 124 lbs
Some key points:
1) The initial weight of the barbell alone is 4 lbs.
2) Each pair of weight plates adds 20 lbs. So x pairs adds 20x lbs.
3) The total weight depends on the number of plate pairs (x) added, according to the equation:
Weight = 4 + 20x
4) x can be any number from 0 to 6, depending on how many plate pairs are added.
The total weight will be 4 lbs + (20 lbs x number of plate pairs).
5) The weight can range from a minimum of 4 lbs up to a maximum of 124 lbs depending on how many of the 6 available plate pairs are added.
Does this help explain the problem and solution? Let me know if any part of the explanation is unclear or if you have additional questions! I can also provide another example if needed.
The core concept is representing the total weight as the initial weight of the barbell plus the additional weight of plates, where each plate pair adds 20 lbs. Let me know if this helps summarize the key idea.
Please ask any follow up questions you may have! I'm happy to help explain further.
What is the range of the function below?
h(x) = {(2, 3), (5, 7), (6, -3), (4, 2)}
O {-3, 2, 3, 7)
O {5, 12, 3, 6)
O {2, 4, 5, 6)
O (2, 3, 5, 7, 6, – 3, 4, 2)
Answers
Answer:uyuy uy
the rang is 5 times 6 is 9 the rang is 5 times 6 is 9 the rang is 5 times 6 is 9
Step-by-step explanation:
Please and thank you
Answers
Selecting a US State Choose one of the 50 states at random. a. What is the sample space? [Type your answer here] b. What is the probability that it begins with M? [Type your answer here] c. What is the probability that it doesn't begin with a vowel?
Answers
Sample space of randomly selecting a US state is 50, the probability that the US state begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.
a. What is the sample space?The sample space for randomly selecting one of the 50 US states is 50, i.e., the list of the 50 states.
b. What is the probability that it begins with M?The number of states that begin with M is 8. Therefore, the probability that the randomly selected US state begins with M is 8/50 or 4/25.
c. What is the probability that it doesn't begin with a vowel?There are 20 US states that don't begin with a vowel. Therefore, the probability that a randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.
Randomly selecting a US state requires knowing the sample space, which in this case is 50. A sample space represents all possible outcomes of a random experiment. Therefore, the sample space for this problem represents the list of all 50 US states that can be randomly selected. The probability that a randomly selected US state begins with M can be calculated by dividing the number of states that begin with M by the total number of states. There are 8 US states that begin with M, hence, the probability of selecting a state that begins with M is 8/50 or 4/25. Finally, the probability that the randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.
In conclusion, the sample space of selecting a US state randomly is 50, the probability that it begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.
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hey guy i need help wit this ASAP
Answers
Answer:
15x^2+5x^3+9
Step-by-step explanation:
(7x^2+8x^2)+5x^3+9
15x^2+5x^3+9
for the antimony trichloride system, we assume only dilution when calculating concentrations. by making this assumption, are we adding random or systematic error to our data? explain the error in this assumption.
Answers
In the antimony trichloride system, when we assume only dilution when calculating concentrations, we are introducing a systematic error to our data.
The error in this assumption is that dilution is not the only process that occurs when calculating the concentration of the antimony trichloride system.
What is the antimony trichloride system?Antimony trichloride system refers to the equilibrium that is formed when antimony trichloride (SbCl₃) is dissolved in water. The reaction of antimony trichloride with water results in the formation of antimony ions (Sb⁺³) and chloride ions (Cl⁻). This reaction is represented by the following equation:
SbCl₃ + H₂O ↔ Sb⁺³ + 3Cl⁻
The equilibrium constant of the reaction is known as the antimony trichloride ionization constant (Kc).
Why is the assumption of dilution only introducing a systematic error to our data?The assumption of dilution only when calculating the concentration of the antimony trichloride system is introducing a systematic error in our data. This is because the reaction of antimony trichloride with water is not the only process that occurs when we are calculating the concentration of the system.
There are other factors that may affect the concentration of the system, such as temperature and pressure. Therefore, by assuming that dilution is the only process that affects the concentration of the antimony trichloride system, we are introducing a systematic error to our data. This error may result in inaccurate results when we are conducting experiments related to the antimony trichloride system.
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Solving Triangles Homework
For each angle measure, round to the 10th place, if necessary.
1. Using triangle RQP,
a. Find mzR using an inverse trig ratio.
b. Find m/P
hQp
3.1
R
89
Answers
The measure of ∠R using an inverse trigonometric ratio is 70.8° and the measure of angle P is 19.2°.
What are Trigonometric Functions?Trigonometric functions are the real functions which are the functions of an angle of a triangle.
They are the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given is a triangle RQP where RQ = 3.1 and PQ = 8.9.
∠Q is the right angle.
(a) We know that, tangent of an angle in a right triangle is the ratio of opposite side to adjacent side.
tan R = QP / QR
tan R = 8.9 / 3.1
tan R = 2.87
R = tan⁻¹ (2.87)
R = 70.796° ≈ 70.8°
(b) Sum of the interior angles of a triangle is 180°.
∠P + ∠R + ∠Q = 180°
∠P + 70.796° + 90° = 180°
∠P + 160.796 = 180°
∠P = 19.204 ≈ 19.2°
Hence the measure of angles P and R are 19.2° and 70.8° respectively.
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The most likely outcomes for a particular project are estimated as follows;
Unit price:
§ 80
Variable cost:
§ 60
Fixed costi
§ 440,800 Expected
sales:
40,600 units per year However, you recognize that some of these estimates are subject to error. Suppose each variable turns out to be either 5% higher or 5% lower than the initial estimate. The project will last for 10 years and requies an initial investment of $14 milion, which wil be depreciated straight line over the projeci life to a final value of
zero. The firm's tax rate is 21%, and the required rate of retum is 14%. a. What is project's NPV in the best-case scenario, that is, assuming all variables take on the best possible
value?
b. What is project's NPV in the worst-case scenario? Note: For all the requirements, a negative amount should be indicated by a minus sign. Enter your answers in dollars, not in millions. Do not round intermediate calculations. Round your answers to the
nearest dollar amount.
Answers
To calculate the project's NPV in the best-case scenario, we need to consider the best possible values for each variable.
Here are the steps-
Step 1: Calculate the annual cash inflow.
Annual revenue = Unit price * Expected sales
= $80 * 40,600
= $3,248,000
Step 2: Calculate the annual cash outflow.
Annual variable cost = Variable cost * Expected sales
= $60 * 40,600
= $2,436,000
Annual fixed cost = Fixed cost
= $440,800
Annual depreciation = Initial investment / Project life
= $14,000,000 / 10
= $1,400,000
Annual tax = (Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation) * Tax rate
= ($3,248,000 - $2,436,000 - $440,800 - $1,400,000) * 0.21
= $208,720
Step 3: Calculate the annual net cash flow.
Annual net cash flow = Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation - Annual tax
= $3,248,000 - $2,436,000 - $440,800 - $1,400,000 - $208,720
= $162,480
Step 4: Calculate the NPV using the best-case scenario cash flows.-
\(NPV = Initial investment + (Annual net cash flow / (1 + Required rate of return)^n)\)
\(= -$14,000,000 + ($162,480 / (1 + 0.14)^1) + ($162,480 / (1 + 0.14)^2) + ... + ($162,480 / (1 + 0.14)^10)\)
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a contractor removed 357 cubic yards of earth from a building site. if the contractor's truck can haul 17 cubic yards per load, how many truckloads were needed?
Answers
If the contractor's truck can haul 17 cubic yards per load, then 21 truckloads are needed.
Earth removed from a building site is 357 cubic yards.
A contractor's truck can haul 17 cubic yards per load.
To find how many truckloads were needed, we needed to divide the earth removed from the building site by the contractor's truck capable of hauling.
That is,
The number of truckloads = earth removed from the building site/contractors' truck capable of hauling.
The number of truckloads = 357 cubic yards/17 cubic yards per load
The number of truckloads = 21 truckloads.
Therefore, the required truckloads are 21.
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Simplify the expression: 7y + 6 - 1 + 12y
Can you also explain pls
I dont get this thing at all and im still not halfway thru my hwwww
Answers
Write the equation
7y + 12y + 6 - 1Arrange the equation so that it will be easy to calculate
19y + 5Add variables with variables (7y with 12y) and constants with constant ( +6 with (-1))
Required Answer:- 19y + 5
Answer:
19y + 5
Step-by-step explanation:
7y + 6 - 1 + 12y
Combine like terms
7y + 12y = 19y
6 - 1 = 5
Finally, combine the two answers into an expression
19y + 5
27% of adults would pay more for environmentally friendly products. You randomly select 10 adults. Find the probability that the number of adults who would pay more for environmentally friendly
products is (a) exactly two. (b) more than two, and (c) between two and five, inclusive.
(a) P(2) - (Round to the nearest thousandth as needed.)
Answers
The Poisson probability law states that the probability of at least two changes every day is 0.0263. Thus, 0.0263% of changes happen twice or more each day.
Who defines probability?The mathematical method it explains for calculating probability calculates all the probabilities of something occurring in the setting of specific random events. A probability's proximity to the value or, alternatively, its distance from zero can make one less confidence in the outcome. The confidence level is based on how close the probability value is, which is calculated using a number range from 0 and 1.
Here,
calculation
The probability distribution function for X is the average number of times the event happens over a specific period of time.
In this experiment, the frequency, or x, at which an event occurs is counted.
The likelihood of the event happening throughout each period is equal.
The number of occurrences in one period is independent of the number in other intervals.
the first step is to set the discrete random variable X to the number of website content updates.
Let's say that there are on average x content changes every day.
The Poisson probability law states that the probability of at least two changes every day is 0.0263.
Consequently, 0.0263% of changes that occur twice or more
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A 36-oz bottle of water costs $2.88.
What is the cost per ounce?
Answers
The cost of the water bottle per ounce is $0.077.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a 36-oz bottle of water costs $2.88. The cost of 1 ounce of the bottle is calculated as,
1 OZ = 1.04 ounces
36 OZ = 36 x 1.04 ounces
36 OZ = 37.44 ounces
37.44 ounces = $2.44
1 ounce = $2.44 / 37.44
1 ounces = $0.077
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Find the magnitude of WX for W(3, -3, 1) and X(8, -3, -6)
Answers
Answer:
Step-by-step explanation:
\(WX=\sqrt{(8-3)^2+(-3+3)^2+(-6-1)^2 } \\=\sqrt{25+0+49} \\=\sqrt{74}\)
Answer:
sqrt 74
Step-by-step explanation:
edge 2020, just did the practice
Julianne is using a biking app that compares his position to a simulated bike or traveling Julianne’s target speed. When Julianne is behind the simulated biker he has a negative position. I took a screenshot of the problem I am having difficulty with.
Answers
Given
\(\begin{gathered} Speed=20\frac{km}{h} \\ Time\text{ }taken=15\text{ }minutes \\ Initial\text{ }distance=2\frac{1}{4}km \end{gathered}\)To find:
The average speed of Julian.
Explanation:
It is given that,
\(\begin{gathered} Speed=20\frac{km}{h} \\ Time\text{ }taken=15\text{ }minutes \\ Initial\text{ }distance=2\frac{1}{4}km \end{gathered}\)That implies,
\(\begin{gathered} Distance\text{ }traveled=Speed\times Time \\ =20\frac{km}{h}\times15minutes \\ =20\frac{km}{h}\times15(\frac{1}{60})h \\ =20\frac{km}{h}\times\frac{1}{4}h \\ =5km \end{gathered}\)Therefore,
\(\begin{gathered} Average\text{ }speed=\frac{Final\text{ }distance-Initial\text{ }distance}{Time\text{ }taken} \\ =\frac{(5-2\frac{1}{4})km}{\frac{1}{4}h} \\ =\frac{5-\frac{9}{4}}{\frac{1}{4}}\frac{km}{h} \\ =\frac{\frac{20-9}{4}}{\frac{1}{4}}\frac{km}{h} \\ =11\frac{km}{h} \end{gathered}\)Hence, the average speed of Jean is 11 km/h.
Determine if it’s a function or not
Answers
Answer:
C is not a function but D is
Step-by-step explanation:
For one input, you can only have one output for this to be a function. For table C, the input of 4 has 4 different outputs, so it cannot be a function.
D is a function however, because each input has only one output, even if the output is the same number.
Find the square root of 8281 using long division technique
Answers
How many types of traders are there in a derivative security
market and who are they?
Answers
In a derivative security market, there are typically four types of traders:
Hedgers: Hedgers are market participants who use derivatives to manage or offset risks associated with their underlying assets. They enter into derivative contracts to protect themselves from potential adverse price movements.
Speculators: Speculators are traders who take on risk in the hopes of making a profit from price movements in derivative securities. They do not have an underlying exposure to the asset but engage in derivative trading solely for speculative purposes.
Arbitrageurs: Arbitrageurs seek to exploit price discrepancies between related assets in different markets. They simultaneously buy and sell similar assets or derivatives in different markets to take advantage of price differentials.
These categories are not mutually exclusive, and individuals or entities may engage in multiple roles simultaneously or switch between them depending on market conditions and their investment objectives.
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a can of soup has a volume of 20 pi cubic inches. the diameter of the can is 4 inches. What is the height of the can
Answers
Answer:
5 inchesStep-by-step explanation:
A can is cylindrical in nature and volume of a cylinder is expressed as;
V = πr²h where;
r is the radius of the cylindrical can
h is the height of the can.
Given parameters
Volume of the can of soup = 20πin³
diameter of the can = 4inches
Since diameter = 2r
radius = d/2 = 4/2 = 2inches
Required parameter.
Height of the can
Substituting the given parameters into the formula to get the height h will give;
20π = πr²h
20 = r²h
20 = 2²h
20 = 4h
Divide both sides by 4:
4h/4 = 20/4
h = 5inches
Hence the heighr of the can is 5 inches
(PLUS 2) Instead suppose the contest always starts with $100 and adds $20 to the pot when people give wrong answers. How many people would have to guess incorrectly for the winner to get $1360? Show your work. (You'll need to know the 'starting value' and 'rate of change' Once you create the equation, substitute the 1360 into the correct position) pelt i
Answers
Answer:
63
Step-by-step explanation:
trial and error aint that hard
Which graph has a slope of 4/5?
Answers
Answer:
\(\boxed{ Graph. B}\)
Step-by-step explanation:
Hey there!
Well slope is aka rise/run,
so starting at the red dot and rising 4 units an ruing to the right 5 units,
graph b is the correct answer.
Hope this helps :)
Graph B has a slope of 4/5.
How is a slope calculated?Slope is calculated with the aid of finding the ratio of the "vertical change" to the "horizontal alternate" among (any) distinct factors on a line.
What is a slope in a straight line?Typically, the slope of a line offers the measure of its steepness and path. The slope of an instant line among two factors says (x1,y1) and (x2,y2) may be without problems decided by finding the difference between the coordinates of the points. The slope is commonly represented by using the letter 'm'.
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a canister of cheese ball measures 12 inches high and its base has a diameter of 6 inches. what is the volume of a canister (rounded to the nearest 10
Answers
The volume of the canister is 339.1 cubic inches.
The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.
The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.
Using the formula, we can calculate the volume of the canister as follows:
V = π×3²×12
V = 108×3.14
V = 339.1 cubic inches
Therefore, the volume of the canister is 339.1 cubic inches.
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Which of the following statements regarding sample size, bias, and variability is NOT true? a) A larger sample size reduces variability b) A larger sample size reduces bias c) The best statistic has low to no bias and little variability d) As sample size increases, the distribution approaches a normal distribution
Answers
The statement "A larger sample size reduces bias" is NOT true. Increasing the sample size does not directly reduce bias. Bias is related to systematic errors in sampling or measurement, and it is not necessarily affected by sample size. Increasing the sample size can, however, improve precision and reduce variability by providing more information about the population.
Increasing the sample size does not inherently reduce bias. Bias refers to systematic errors that are unrelated to the sample size itself. Bias can occur due to factors like flawed study design, measurement errors, or selection bias. Simply increasing the sample size does not address these underlying issues.
However, a larger sample size can improve the precision of estimates and reduce variability. With a larger sample, there is more information available, which leads to narrower confidence intervals and more reliable statistical estimates. Additionally, as the sample size increases, the distribution of the sample tends to approximate a normal distribution due to the Central Limit Theorem. This approximation to a normal distribution allows for the application of certain statistical methods that assume normality.
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what is 30 -12 · 2 in order of operations
Answers
Answer:
6
Step-by-step explanation:
Malea sells engraved necklaces
over the Internet. She purchases 50 necklaces
for $400, and it costs her an additional $3 for
each personalized engraving. If she charges
$20 each, how many necklaces will she need to
sell in order to make a profit of at least 5225?
Answers
Answer:
581
Step-by-step explanation:
Answer in the picture
What is the area of the figure?
Answers
Multiply 16 by 14
then subtract 14 from 38 which gives you 24
Multiply 24 by 20