Based on the given parameters, the amount of the investment after 4 years is $1030
How to determine the amount?The given parameters about the compound interest are
Principal Amount, P = $1000
Interest Rate, R = 0.85%
Time, t = 4
Number of times, n = 1 i.e. annually
Compound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R/n)^nt - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R/n)^nt - P
Evaluate the like terms
A = P(1 + R/n)^nt
Substitute the known values in the above equation
A = 1000 * (1 + 0.85%/1)^(1 * 4)
Express 0.85% as decimal
A = 1000 * (1 + 0.0085/1)^(1 * 4)
Evaluate the sum
A = 1000 * (1.0085/1)^(1 * 4)
Evaluate the exponent
A = 1000 * 1.03
Evaluate the product
A = 1030
Hence, the value of the investment is $1030
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when playing roulette at a casino, a gambler is trying to decide whether to bet $ on the number or to bet $ that the outcome is any one of the possibilities . the gambler knows that the expected value of the $ bet for a single number is . for the $ bet that the outcome is , there is a probability of of making a net profit of $ and a probability of losing $. a. find the expected value for the $ bet that the outcome is . b. which bet is better: a $ bet on the number or a $ bet that the outcome is any one of the numbers ? why?
The answers to both the subparts with the help of probability are:
(A) The $15 wager's expected value is a loss of $3.16.(B) Since the bet on a single number has a higher expected value, it is better.What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is equal to the variety of possible outcomes: the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2 (a head or tail).So, Item A:
The probability of earning $75 is 5/38.The likelihood of losing $15 is 33/38.The expected value is the total of each result times the associated probability, so:
[tex]E(X)=75 \frac{5}{38}-15 \frac{33}{38}=\frac{75(5)-15(33)}{38}=-3.16[/tex]The $15 wager should have a value of -3.16 dollars.
Item B:
The wager on a single number has an expected value of $-0.79 (or -$0.79).The best wager is a bet on a single number because it is higher than the expected value of the bet on multiple numbers.Therefore, the answers to both the subparts with the help of probability are:
(A) The $15 wager's expected value is a loss of $3.16.(B) Since the bet on a single number has a higher expected value, it is better.Know more about probability here:
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The complete question is given below:
When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 34 or to bet $15 that the outcome is any one of the five possibilities 00 comma 0 comma 1 comma 2 comma or 3. The gambler knows that the expected value of the $15 bet for a single number is negative 0.79 cents. For the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3, there is a probability of StartFraction 5 Over 38 EndFraction of making a net profit of $75 and a StartFraction 33 Over 38 EndFraction probability of losing $15. a. Find the expected value for the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3. b. Which bet is better: a $15 bet on the number 34 or a $15 bet that the outcome is any one of the numbers 00 comma 0 comma 1 comma 2 comma or 3? Why?
Can you please help me with 37
Solution:
The equation of the ellipse in the question is given as
[tex]\frac{(y-3)^2}{9}-\frac{(x-3)^2}{9}=1[/tex]Concept:
The general formula of a hyperbola is
[tex]\begin{gathered} \frac{(y-h)^2}{b^2}-\frac{(x-k)^2}{a^2}=1 \\ \text{Where } \\ h,k\text{ are the centres} \end{gathered}[/tex]From the above equation by comparing coeficient, we will have
[tex]\begin{gathered} a^2=9 \\ a=3 \\ b^2=9 \\ b=3 \\ (a,b)\Rightarrow(3,3) \\ h=3,k=3 \end{gathered}[/tex]The linear eccentricity c, will be
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{3^2+3^2} \\ c=\sqrt[]{9+9} \\ c=\sqrt[]{18} \\ c=3\sqrt[]{2} \end{gathered}[/tex]The vertices of the hyperbola will be calculate using the formula below
[tex]\begin{gathered} (h,k-b)\Rightarrow(3,3-3)\Rightarrow(3,0) \\ (h,h+b)\Rightarrow(3,3+3)\Rightarrow(3,6) \end{gathered}[/tex]The co-vertex are calculated using the formula below
[tex]\begin{gathered} (h-a,k)\Rightarrow(3-3,3)\Rightarrow(0,3) \\ (h+a,k)\Rightarrow(3+3,3)\Rightarrow(6,3) \end{gathered}[/tex]The foci of the hyperbola will be calculated using the formula below
[tex]\begin{gathered} \mleft(h,k-c\mright)\Rightarrow(3,3-3\sqrt[]{2)} \\ \mleft(h,k+c\mright)\Rightarrow\Rightarrow\Rightarrow\mleft(3,3+3\sqrt[]{2}\mright) \end{gathered}[/tex]The eccentricity, e is
[tex]e=\frac{c}{b}=\frac{3\sqrt[]{2}}{3}=\sqrt[]{2}[/tex]Hence,
The sketch of the graph is given below as
The foci is represented with the two red dots on the graph
The vertices are represented above by the two coordinates
Help please, geometry
factor the triminal
3x squared -15x+12
Given: 1 || m; 21 = 23
Prove: p | q
m
Р
3
9
2
Complete the missing parts of the paragraph proof.
We know that angle 1 is congruent to angle 3 and that
line I is parallel to line m because
We see that
is congruent to
by the alternate
interior angles theorem. Therefore, angle 1 is
congruent to angle 2 by the transitive property. So, we
can conclude that lines p and q are parallel by the
Parallel lines l and m are intersected by p and q, which are also parallel. The parallelism of the lines p and q can be inferred.
What is meant by transitive property?According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."
Given: Line l is parallel to line m.
Angle 1 exists equal to angle 3.
Angles 1 and 3 are shown in the figure as equivalent angles that are equal.
Angle 1 created by line p and line l is equivalent to angle 3 created by lines q and m. Lines l and m are parallel as well. Since p and q form the same angle as two parallel lines, they too should be parallel.
In light of this, it can be said that lines p and q are parallel.
Therefore, it can be concluded that the lines p and q are parallel.
The complete question is:
Given: l || m; ∠1 ∠3 Prove: p || q Complete the missing parts of the paragraph proof. We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the
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r(x) = 8/9x - 17; r(x) = 15
Answer: 0.049382716
Step-by-step explanation: SOLVE FOR R, X
x=
4
1215
=303
4
3
=303.75
r=
81
4
≈0.049382716
Question
Which table represents a proportional relationship between x and y?
Responses
x 3 9 10 15
y 1 3 4 5
x 3 9 10 15 y 1 3 4 5
x 1 5 8 10
y 15 75 120 150
x 1 5 8 10 y 15 75 120 150
x 4 6 8 10
y 6 8 10 12
x 4 6 8 10 y 6 8 10 12
I don't know.
The table that represents a proportional relationship between x and y is table 2.
What is a proportional relationship?A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor.
A proportional relationship is one in which two quantities vary directly with each other.
For example,
y = kx
where,
k = constant of proportionality
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.
If those ratios are all the same, the table shows a proportional relationship.
Therefore, let's calculate the ratios of the table
1 / 155 / 75 = 1 / 158 / 120 = 1 / 1510 / 150 = 1 / 15Hence, the table 2 has a proportional relationship.
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Felipe is having a party. He'll have 4 tables for every 20 guests. Complete the table below showing the number of tables and the number of guests.
( Table: ?, 1 20,4 35,? ?,8 50,?)
Answer:
8
Step-by-step explanation:
Given mn, find the value of x.
(8x-7)°
(9x-28)°
Answer: top: x= -15 bottom: x= -37
Step-by-step explanation: First you need to get x by itself so for example on the top one you would do 8-8 to get x alone and then you would also do -7- 8 because whatever you do to one side you have to do to the other.
Hope this helped!!!
Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
The equation is y=2x+4.hope it's solved
If you multiply two polynomials, will you always get a polynomial? Try combining some polynomials to answer your question. Use the ones given by your teacher or make up your own polynomials. Keep a record of what polynomials you tried, and the results. When you think you have an answer to your question, explain your reasoning using equations, graphs, visuals, calculations, words, or in any way that will help others understand your reasons.
Polynomials are closed under the multiplication operation, meaning that the result of the multiplication between two polynomials will always be a polynomial.
How to multiply polynomials?To multiply polynomials, we first apply the distributive property, multiplying all terms, then we combine the like terms, that is, adding all the terms that have the same exponents.
Since all the factors of the multiplications will be of polynomial terms, the results of the multiplication will be polynomial, and so will the like terms combined, hence polynomials are closed under the multiplication operation.
One example of multiplication of polynomials is given as follows:
(x² - 1)(x² + 1) = x²x² + x² - x² - 1 = x^4 - 1.
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does anyone know what 4/5 x 2/5 in simplest form is?
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Algebra Not in Algebra Total
Physics 5 14
Not in Physics
Total 29 40
33
38
2
5
Answer:38
Step-by-step explanation:
sense it subteact between
Answer: 38
Step-by-step explanation: subtract between
What is the slope of (15,-51) and (-29,-45)
Answer:
slope = (-3/22)
Step-by-step explanation:
(15, -51), (-29, -45)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -45 - (-51) -45 + 51 6 ÷ 2 -3
m = ------------ = ----------------- = -------------- = ------------ = --------
x₂ - x₁ -29 - 15 -44 -44 ÷ 2 22
I hope this helps!
Answer:
Gradient/slope: y2-y1/x2-x1
y1= -51
y2= -45
x1= 15
x2= -29
Slope:
-45-(-51)/-29-15
= -45+51/-44
= -6/44
divide both by 2
= -3/22
PLEASE HELP
Name the reciprocal you will use to multiply
-6/5k=12
Answer:
-5/6
Step-by-step explanation:
The reason why the reciprocal is -5/6 is because to isolate the variable with a fraction attached is to multiply it by swapping the numerator and denominator. Also making sure that if the number is a negative, to multiply the number by another negative to cancel it out.
11. Write a function rule for the area of a rectangle with a length 7 m more than three
times its width. What is the area of the rectangle when its width is 3 m?
The area of the rectangle when its width is 3 m is 39m².
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
A function rule for the area of a rectangle with a length 7 m more than three times its width.
Area of rectangle = Length(Width)
Area of function = (w) (3w+7)
Area of function = 3w² + 7w
If w = 3m
Area of function = 3(3)² +7(3)
Area of function = 3(9) + 21
Area of function = 18 + 21
Area of function = 39
the area of the rectangle when its width is 3 m is 39m².
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I need help with this fraction problem! It can be either adding, subtracting, dividing, or multiplying fractions.
[tex]compare 2.01 x 10 and 2.8 x 10 which number is larger[/tex]
When you compare 2.01 x 10 and 2.8 x 10, the larger number is 2.8 × 10.
What is multiplication?It should be noted that multiplication simply means the product of a number. This is usually illustrated by the symbol ×.
In this case, it should be noted that 2.01 × 10 = 20.1
It should also be noted that 2.8 × 10 = 28
Therefore, the larger number is 2.8 × 10.
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2. we want to estimate the mean of a population. a random sample of subjects is selected and the sample mean is computed. what is the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8?
Given,
Sample mean = ±3 of true mean
Standard error = 1.8
Therefore,
Required probability of sample mean being within 3 units of the true mean is,
P ( sample mean - 3 < mean < sample mean + 3 )
= P [( sample mean - 3 ) - mean / 1.8 ] < mean - sample mean / 1.8 < [ ( sample mean + 3 ) - mean / 1.8 ]
= P ( - 1.67 < ∉ < 1.67)
= P (∉ < 1.67) - P( ∉ < 1.67)
= 0.952 - 0.047
= 0.905
Hence, the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8 is 0.905.
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All of the following represent three multiplied by six except:
03x6
03-6
O3(6)
3:6
Help please
Answer:
Except the last one 3:6 because its not multiplied by six but divided. Therefore the correct answer is the last one
Step-by-step explanation:
hope it helps
two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability of choosing a diamond and then, without replacement, a black card? express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
13/102
Step-by-step explanation:
We start with 52 playing cards. Of these 52 cards, 13 are diamonds, So the probability of a diamond is 13/52, or 1/4. There are now 51 cards left. Since the diamond is a red card, there are 26 black cards. So the probability of a black card is 26/51. Multiplying 1/4 and 26/51, and then simplifying, we have 13/102.
Ling painted a picture of a local historic landmark for her history project. First, she painted a statue using a mix of black and white paint. Then, she painted a stone building using double the amount of black paint and double the amount of white paint. Which structure was a darker shade of gray?
Answer: Neither They were the same shade of Grey.
Step-by-step explanation:
it’s the right answer trust me
Color would be the same for both statue and stone buildings.
Let's, consider paint black as = x
and paint white as = y
If both the paints are mixed then paint z which is grey is formed.
Represented as,
x(black) + y(white) = z(grey)
Whereas, for the stone building double the amount of black and white colors are being used,
2x + 2y = 2z, coating of grey color would be also double.
Canceling 2 from both sides,
x + y = z
x(black) + y(white) = z(grey)
Therefore color would be the same for both statue and stone buildings.
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can you simplify 27/7
When we divide 27 by 7, we have 3; 3 * 7 = 21
27 - 21 = 6; we have a remainder of 6
Divide the remainder by 7, we have 6/7
Therefore, we have:
[tex]3\frac{6}{7}[/tex]What is the range? 0 2 0 3 3 1 5 3 1 6 Submit
Solution
0 2 0 3 3 1 5 3 1 6
For this case the range is defined like this:
Range = Max -Min
The maximum = 6
Minimum =0
Then the solution would be:
Range = 6-0 =6
Make x the subject of m= n + x/p
Answer:
[tex]x[/tex] = m - n x p
Step-by-step explanation:
m - n = [tex]x[/tex]/p
[tex]x[/tex] = m - n x p
Answer:
x = pm - pn
Step-by-step explanation:
Make x the subject:To make 'x' as the subject, isolate 'x'.
[tex]\sf n + \dfrac{x}{p}=m\\\\\text{Subtract 'n' from both sides,}\\\\\dfrac{x}{p}=m-n\\\\\text{Multiply both sides by p,}\\\\p*\dfrac{x}{p}=p*(m-n)\\\\[/tex]
x = pm - pn
Which expression is equivalent to [tex]5^{4} x (5-^{2} )^{3}[/tex]
The simplified expression of 5^4 * 5^-6 is 5^-2
How to evaluate the expression?The expression is given as
5^4 * (5^-2)^3
Evaluate the product of exponents
So, we have
5^4 * 5^-6
The base of the above expression are the same
i.e. Base = 5
This means that we can apply the law of indices
So, we have
5^4 * 5^-6 = 5^(4 -6)
Evaluate the sum in the above equation
So, we have
5^4 * 5^-6 = 5^(4 -6)
Evaluate the difference in the above equation
So, we have
5^4 * 5^-6 = 5^-2
Hence, the simplified expression of the expression given as 5^4 * 5^-6 is 5^-2
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Rick sells sherriff badges to all of his friends. He earns a 25% commission on his sales per week. This past week she sold $ 100.00 worth of badges. How much did he make in commission total?
A pole 9 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Ella measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Give crown and 10 points please please i need for now
1.
1- I, 2- II, 3- III, 4-IV, 5- V, 6- VI, 7- VII, 8- VIII, 9- IX, 10- X.
2.
26 = 10+10+5+1 = XXVI
17 = 10 + 5+2 = XVII
29 = 10+ 10+ 9 = XXIX
30 = 10+10+10 = XXX
3.
15 = XV
21 = XXI
26= XXVI
33 = XXXIII
35= XXXV
44 = XLIV
49 = XLIX
50 = L
4.
70 = LXX
80= LXXX
83 = LXXXIII
89 = LXXXIX
90= XC
100= C
5.
date today X / X/ XXXXII = 10/10/2022
the year 2022 = XXXXII
A carpenter has 2 pipes which are 60 dm and 72 dm long respectively. he cuts them into equal lengths. what is the greatest possible length of each pipe?
Using greatest common factor (GCF), the greatest possible length of each pipe is 12 dm.
The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.
If a carpenter has 2 pipes which are 60 dm and 72 dm long, respectively and he cuts them into equal lengths, then the greatest possible length of each pipe is the GCF of 60 and 72.
60 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
72 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 72
common factors : 1, 2, 3, 4, 6, 12
GCF = 12
Hence, he should cut the two pipes into 12 dm long.
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