Ren will have to wait for approximately 31 years for the money compounded annually and a rate of 2.3% to double it's original investment.
Compound InterestCompound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
The formula of compound interest is given as
A = P(1 + r/n)^nt
A = compounded interest = $2000 (Since the investment doubled)r = rate = 2.3%n = number of times compounded = 12t = time = ?Substituting the values into the equation;
It will take approximately 31 years to double the investment.
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Can someone please help me? Thanks!!!
A triangle has a base length of 6ac² and a height 3 centimeters more than the base length. Find the area of the triangle if a = 2 and c = 3.
A. 3,078 cm²
B. 5,994 cm²
C. 2,025 cm²
D. 11,988 cm²
For each of the 4 stroke categories, consider a random variable representing the time of a randomly selected swimmer in that category. What is the standard deviation of the sum of the 4 random variables?.
The standard deviation of the sum of the 4 random variables is 10.23
The question is incomplete the complete question is
For each of the 4 stroke categories 2,4,6,8 consider a random variable representing the time of a randomly selected swimmer in that category is 0.6,0.8,0.2,0.7. What is the standard deviation of the sum of the 4 random variables?.
To calculate the Expected Value, we need to multiply each value by its probability and then sum the products up.
μ = E(x) = ∑xp(x)
That is, (0.6x2) + (0.8x4) + (0.2x6) + (0.7x8) = 1.2 + 3.2 + 1.2 + 5.6 = 11.2
Mean = 11.2
Now we take the first and second steps,
(2- 11.2)² x 0.6 = 84.64 x 0.6 = 50.78
(4 - 11.2)² x 0.8 = 51.84 x 0.8 = 41.47
(6 - 11.2)² x 0.2 = 27.04 x 0.2 = 5.4
(8 - 11.2)² x 0.7 = 10.24 x 0.7 = 7.16
Now we take the the third step and add our products together to get the variance V,
V = σ2 = ∑(x−μ)2P(x)
V = 50.78 + 41.47 + 5.4+ 7.16 = 104.81
Now we take the last step by taking the square root of the variance to get the standard deviation SD,
SD = σ = √σ2
Standard Deviation SD = √104.81 = 10.23
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Caho needed to get her computer fixed. She took it to the repair tore. The
technician at the tore worked on the computer for 5 hour and charged her
$102 for part. The total wa $627. Write and olve an equation which can be
ued to determine 2, the cot of the labor per hour.
Answer:
105
Step-by-step explanation:
627-102=525
525 divided by 5 is 105
Factorise this equation? Please helpp!!!!
Answer:
y = 2 ; y = -7
Step-by-step explanation:
sum of two numbers = 5
product of two numbers = -14
the two numbers are 7 and -2
(y-2)(y+7) = 0
y = 2
y = -7
What is the correct form of scientific notation for 306 x 10^7
a.30.6 x 10^8
b. .306 x 10^10
c.
It is in the correct form!
d.3 x 10^9
e.3.06 x 10^9
The decimal place should be after only 1 digit so the answer is e
find the annual salary of a person who is $835.50 per week and show working for the answer for this question
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5*52
= 43446
5. What is the range? Explain. (1 point)
The range of the given graph is [5, ∞).
Range.
Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.
Given,
Here we have the graph.
Through the given graph we have to find the range of the line.
As per the definition of range, we have identified that the range take the value of y axis.
While we lookin into the given graph, we have identified that the starting point of the line is
=> (0, 5)
In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.
And the end of the line is not pointed.
So, we can consider that this line goes infinitely.
So, the range of the graph is [5, ∞).
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=
Let A =
8
-7
equation.
3X=-3A + 4B
4
8].
0
-
and B=
X= (Simplify your answer.)
25
20
Find a matrix X satisfying the given
For the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].
As given in the question,
Given matrix are equal to :
A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]
Simplify the equation which satisfy the equation 3X = -3A + 4B is given by :
Substitute the value of matrix A and matrix B in the given equation we get:
3X = [tex]-3\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right] + 4\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]
⇒ 3X = [tex]\left[\begin{array}{ccc}-24&12\\21&0\\\end{array}\right] + \left[\begin{array}{ccc}8&20\\8&0\\\end{array}\right][/tex]
⇒ 3X = [tex]\left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]
To get the value of X divide both the side by 3 we have,
⇒ X = [tex]\frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]
Therefore, for the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].
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SOMEONE ANSWER QUICKK. Use the picture attached to solve #1!!!
1. What patterns do you notice in the table? Use complete sentences
2. Explain the relationship between the number of sides of the polygon, and the number of non-overlapping triangles in the polygon.
3.Explain the relationship between the number of sides of the polygon and the sum of the interior angles. Use complete sentences.
1. The patterns regarding the polygons are given as follows:
The number of non-overlapping triangles on a polygon of n sides is of n - 2.The sum of the interior angles of a polygon of n sides is: (n - 2) x 180º.For regular polygons, the measures of each interior angle is: [(n - 2) x 180º]/n.The sum of the exterior angles of any polygon is: 360º.The measure of each exterior angles for each regular polygon is: 360º/n.2. The relationship between the number of sides of the polygon, and the number of non-overlapping triangles in the polygon is:
The number of non-overlapping triangles in the polygon is two less than the number of sides.
3. The relationship between the number of sides of the polygon and the sum of the interior angles is:
The sum of the interval angles of a triangle is given by the multiplication of 180º and the number of non-overlapping triangles in the polygon.
How to obtain the patterns?The patterns in the context of this problem are all obtained from the last row of the table, and they are all axioms for polynomial relations.
For item 2, the relationship is given by the third column of the last row, and for item 3, by the fourth column.
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If AL = 27, find AP and PL.
Answer:
AP = 18, PL = 9
Step-by-step explanation:
assuming AL, is a median of the triangle
then AP = [tex]\frac{2}{3}[/tex] AL = [tex]\frac{2}{3}[/tex] × 27 = 18
PL = [tex]\frac{1}{3}[/tex] AL = [tex]\frac{1}{3}[/tex] × 27 = 9
The midpoint of
AB
is M(-3, 2). If the coordinates of A are (−1,−3), what are the coordinates of B?
Answer:
AM=M-A
-3 -1. -2
2 -. -3. = 5
-3. -2. -5
2. +. 5. =. 7
Can somone solve this with a reason why they chose the answer
Check the picture below.
An isosceles triangle has perimeter 50cm and each of the equal
sides is 15 cm. find the area of triangle
Answer:
hope this will help you..
Gabrielle picked 5 5/6 pounds of berries. She divided them evenly among 7 containers. How many pounds of berries did Gabrielle put in each container?
The pounds of berries that Gabrielle put in each container, given the pounds of berries she picked, are 5/6 pounds
How to find the pounds of berries?Gabrielle was able to pick 5 ⁵/₆ pounds of berries. First convert this to an improper fraction for easier calculations:
= 5 ⁵/₆
= ((6 x 5) + 5) / 6
= 35 / 6
The pounds of berries that went into each container is:
= Pounds of berries / Number of containers
= 35 / 6 ÷ 7
= 35 /6 x 1/7
= 35/42
= 5/6 pounds
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In the figure below, m<1 = (x+81)° and m<2=2x°.
1=
Find the angle measures.
1
2
The angle measures are ∠1 = 66°, ∠2 = 114°.
Given that m<1 = (x+81)° and m<2=2x°.
Here ∠ 1 and ∠ 2 are adjacent angles and are supplementary ( sum to 180°), then
2x + x + 81 = 180 , that is
3x + 81 = 180 ( now subtract the number 81 from both the sides )
3x = 99 ( now divide both the sides by the number 3 )
So that, x = 33
Thus, putting the value of x in the below equations:
∠ 1 = 2x = 2 × 33 = 66°
∠ 2 = x + 81 = 33 + 81 = 114°
Hence the answer is the angle measures = ∠1 = 66°, ∠2 = 114°.
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a random sample of college basketball players had an average height of 66.35 inches. based on this sample, (65.6, 67.1) found to be a 94% confidence interval for the population mean height of college basketball players. select the correct answer to interpret this interval
Based on the data the correct interpretation of the interval is that we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. (Option B)
In statistics, a confidence interval indicates the probability that a population parameter will lie between a set of values around the population mean. It measures the degree of certainty or uncertainty in a sampling method. It is a range of values which are bounded above and below the statistic's mean that likely would contain an unknown population parameter. Confidence level is the percentage of certainty or probability of the confidence interval would include the true population parameter when a random sample is repeatedly drawn. Hence, in the given case based on the information we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches.
Note: The question is missing options which are A. We are 94% confident that the population mean height of college basketball players is 66.35 inches. B. We are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. C. A 94% of college basketball players have heights between 65.6 and 67.1 inches. D. There is a 94% chance that the population mean height of college basketball players is between 65.6 and 67.1 inches.
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Spinner has 10 equally sized sections, one of which is blue and nine of which are yellow. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on yellow and the coin toss is tails?
The probability that the spinner lands on yellow and the coin toss is tails is 9/10.
What is probability?
Probability shows the likelihood of an event happening. it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No of blue=1
No of yellow=9
No. of total possible outcome=10
Therefore the probability that the spinner lands on yellow and the coin toss is tails P= 9/10.
P= 9/10
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Find the y-intercept of the line. If needed use "/" for a fraction. b=
y=10+4x
Y-intercept(b)= 10
equation wasnt written in the correct order so b is 10
jada sells b books and m magazine subscriptions to raise money for a choir trip. She earns $4 for each book and $3 for each magazine subscription she sells, and she earns a total of $96 toward the cost of her choir trip. The equation that models the situation is 4b + 3m = 96.
[tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex] for the equation that models.
Jada sells b books and m magazine subscriptions to raise money for a choir trip. She earns $4 for each book and $3 for each magazine subscription she sells, and she earns a total of $96 toward the cost of her choir trip.
Given that
1. Jada sells b books and m magazines
2. She earns $4 for each book and $3 for each magazine
3. Total amount she earned is $96
Given equation is
4b + 3m = 96
Solve 4b + 3m = 96 for b
Subtract 3m from both sides
4b + 3m - 3m = 96 - 3m
4b = 96 - 3m
Now divide both sides by 4
= [tex]b = \frac{96-3m}{4}[/tex]
So, the answer for b is [tex]\frac{96-3m}{4}[/tex]
Now, solve 4b + 3m = 96 for m
Subtract 4b from both sides
4b + 3m - 4b = 96 - 4b
= 3m = 96 - 4b
Now divide both sides by 3
= [tex]m = \frac{96-4b}{3}[/tex]
So, the answer for m is [tex]\frac{96-4b}{3}[/tex]
Hence the answer is [tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex] for the equation that models.
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1.5 devided by 2.5 rounded to the nearest tenth
Answer:
1
Step-by-step explanation:
1.5/2.5= 0.6
0.6 nearest tenth is 1
0.0-0.5 --0
0.6-0.9 --1
Christine knits 22 centimeters of scarf each night. Write an equation that shows the relationship between the nights xx and the length knitted y.
The equation that shows the relationship between the nights and the length knitted is y = 22x.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the nights = x
Let the length knitted = y
The appropriate equation will be:
y = (22 × x)
y = 22x
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3 9 8 hours. the tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. find the time in which each tap can separately fill the tank
The smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.
How to calculate time taken to fill the tank for each tap?
Given,
Time taken for two tap together to fill the tank = [tex]9\frac{3}{8}[/tex] hours = [tex]\frac{75}{8}[/tex] hours
Time taken for smaller tap to fill the tank = x hours
Time taken for larger tap to fill the tank = x - 10 hours
So,
Tank filled by two tap together in 1 hour = [tex]\frac{8}{75}[/tex]
Tank filled by smaller tap in 1 hour = [tex]\frac{1}{x}[/tex]
Tank filled by larger tap in 1 hour = [tex]\frac{1}{x-10}[/tex]
Then, tank filled by two tap together is equal to tank filled by smaller tap and larger tap. So,
[tex]\frac{8}{75} = \frac{1}{x} + \frac{1}{x-10}[/tex]
[tex]\frac{8}{75} = \frac{x-10+x}{x(x-10)}[/tex]
[tex]\frac{8}{75} = \frac{2x-10}{x^{2}-10x}[/tex]
[tex]8x^{2}-80x = 150x - 750[/tex]
= [tex]8x^{2} - 230x + 750[/tex]
= [tex]2(4x^2 - 115x + 375)[/tex]
= [tex]4x^2 - 100x - 15x + 375[/tex]
= [tex](4x - 15) (x - 25)[/tex]
If, x = [tex]\frac{15}{4}[/tex] then x - 10 for larger tap equal to [tex]\frac{15}{4}[/tex] - 10 = [tex]- \frac{25}{4}[/tex] < 0 hours, so it is impossible.
Then, x must be 25. So, for larger thank is 25 - 10 = 15.
Smaller tap take 25 hours to fill the tank
Larger tap take 15 hours to fill the tank.
Thus, the smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.
Your question is not complete, but most probably your full questions is (image attached)
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Solve tan 9°
=x/2.6
Give your answer to 2 d.p.
Answer:
x= 0.41
Step-by-step explanation:
tan 9° =[tex]\frac{x}{2.6}[/tex]
x= 2.6 tan9° (cross multiply)
x= 0.41 (solve trignomatic function)
PLEASE HELP!!!
find the missing length indicated for each
Using the triangle proportionality theorem, the missing lengths that are indicated are:
1. 35
2. 14
3. 28
4. 18
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when a line is drawn to be parallel to any side of a triangle that it intersects two of the side of the triangle at two different points, then the two sides are divided proportionally or in the same ratio.
Apply the triangle proportionality theorem to find all the missing length that are indicated. Let the missing side be represented as x.
Problem 1:
x/28 = 15/12
x = (28)(15)/12
x = 35
Problem 2:
x/28 = 6/(18 - 6)
x/28 = 6/12
x/28 = 1/2
x = 28/2
x = 14
Problem 3:
x/35 = 12/(12 + 3)
x/35 = 12/15
x/35 = 4/5
x = (35)(4)/5
x = 28
Problem 4:
x/54 = 8/24
x/54 = 1/3
x = 54/3
x = 18
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Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play. Each pair of wings is made with 3/4 yard of fabric. The fabric costs $8 per yard.
You'll apply properties of multiplication in the following steps to find the total cost of the fabric.
1. Use multiplication to write an expression for the amount of fabric needed to make 13 pairs of wings.
2. Multiply the amount of fabric by the price per yard to find an expression for the total cost.
3. Use the associative and commutative properties to rearrange the terms in the expression to make it easier to calculate. Explain why the rearranged expression is easier to work with.
4. Simplify your expression to find the total cost. Show your work.
Given that Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play. Each pair of wings is made with 3/4 yards of fabric. The fabric costs $8 per yard. The total cost of the fabric is $78.
What is the total cost?The total cost formula is used to get a total by combining the variable and fixed expenses of delivering commodities.
The step-by-step is given as follows:
1) Total cost (TC) = 3/4 (P) x 13
2) 1 pair of wings = 3/4 yard fabric
Recall that the price of 1 yard of fabric = $8
3) 1 pair of wings = $8 x 3/4 = $6
4) Therefore total cost = $6 x 13 = $78
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3a×(a-b)-2a×(a+b)
Me ajudem por favor.
Answer:
a^2 - 5ab
Step-by-step explanation:
[3a * (a-b)] - [2a * (a+b)]
[3a(a) - 3a(b)] - [2a(a) + 2a(b)]
3a^2 - 3ab - (2a^2) - (2ab)
3a^2 - 2a^2 - 3ab - 2ab
a^2 - 5ab
Does the quadratic function
f(x) = 9x² + 6x + 1 have one,
two, or no real zeros? Utilize the
quadratic formula to determine
the answer.
[?] real zero(s)
Answer:
it is c
Step-by-step explanation:
you do 9x2 6+1 = 7 + 18 =25
The population of white-tailed deer i growing rapidly in the united tate. In 1905 the population wa approximately 5x10^5 and in 2000 the population wa approximately 2x10^7 how many time larger wa the population of white tailed deer in 2000 than it wa in 1905
The population of white tailed deer was increased by 40 times .
What are white tailed deer?
The medium-sized white-tailed deer is a native of North America, Central America, and South America as far south as Peru and Bolivia. It is often referred to as the white tail or Virginia deer.
Main body:
population of white tailed deer in 1905 = 5*10^5
population of white tailed deer in 2000 = 2*10^7
Population increase can be calculated by using simple division ,
calculating :
⇒ 2*10⁷/5*10⁵
⇒ 2*10⁽⁷⁻⁵⁾/ 5
⇒ 2*10²/ 5
⇒ 200/5
⇒ 40
Hence population increased by 40 times from 1905 to 2000 for white tailed deer.
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An actual distance of 50km corresponds to 4 cm on the map
Answer:
Incomplete question.
Step-by-step explanation:
4 cm = 50 km
1 cm = 50/4 = 12.5 km
Use above ratio or
50 km = 4 cm
1 km = 4/50 = 0.08 cm
A bicycle rider is riding at a rate of 15 km/h for 4/9 of his ride, 10 km/h for 2/9 of his ride, and 8 km/h for the remainder of the ride. How much of his ride is he riding at a rate greater than 8 km/ h?
A bicycle rider rides 24 km riding at a rate greater than 8 km/ h.
Given that, a bicycle rider is riding at a rate of 15 km/h for 4/9 of his ride.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Let total number of km be x.
Distance1 =4/9 x
Distance2 =2/9 x
Remaining distance = x-(4x/9 + 2x/9)
= x-6x/9
=(9x-6x)/9
= 3x/9
Now, time =1 hour
8 = 3x/9 ÷ 1
⇒ 8×9=3x
⇒ x=24 km
Hence, a bicycle rider rides 24 km riding at a rate greater than 8 km/ h.
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