Stock used to sell for $105.81 ten years ago.
[tex]CAGR = ((\frac{EV}{BV} )^{\frac{1}{n}}-1)*100[/tex]
Here, CAGR = Compounded Annual Growth Rate = -2.3%
EV = Ending Value = x
BV = Beginning Value = $83.80
n = No. of years = 10
Putting the values in the equation,
[tex]-2.3 = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)*100[/tex]
[tex]\frac{-2.3}{100} = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)[/tex]
[tex]\frac{-2.3}{100}+1 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex]\frac{100-2.3}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex]\frac{97.7}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex]0.977 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]
[tex](0.9777)^{10} = \frac{83.80}{x}[/tex]
[tex]\frac{83.80}{x}=0.792[/tex]
[tex]x = \frac{83.80}{0.792}[/tex]
x = 105.81
Hence, the beginning value is $105.81.
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Solve for x
20=.694(x+150)*2
Answer: x = -135.59
Step-by-step explanation:
20 = 0.694(x + 150)(2)
Step 1: Simplify both sides of the equation.
20 = 0.694 (x + 150)(2)
20 = 1.388x + 208.2 (use the distributive property)
20 = 1.388x + 208.2
Step 2: Flip the equation.
1.388x + 208.2 = 20
Step 3: Subtract 208.2 from both sides of the equation.
1.388x + 208.2 − 208.2 = 20 − 208.2
1.388x = −188.2
Step 4: Divide both sides by 1.388.
1.388x/1.388 = −188.2/1.388
x = −135.590778
Optional: Simplify
x = -135.59
A transversal intersects two lines. Which condition would always make the two lines parallel?
If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.
What do you mean by traversal line?
A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
What do you mean by angle?
An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.
From the figure,
x + 1 = 180°
y + 2 = 180°
Adding above equations,
x + y + 1 + 2 = 360°
Given ,
x + y = 1 +2
x + y + x + y = 360°
2(x + y) = 360°
x + y = 180°
Angles made on same side of transversal is supplementary . So the lines are parallel.
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"What are the coordinates of your reflected triangle A’B’C’?"
Please help! Thank you!
A' - (-1,4)
B' - (-1,8)
C' - (-5,4)
hope this helps
What is the coefficient of the 6th term of (2x - 7)9 ?
Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912
Step-by-step explanation:
[tex](2x-7)^9[/tex]
In this problem we use the following formula:
[tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]
a=2x b=-7 n=9
The 1th term of (2x-7)^9 is k=0
The 2th term of (2x-7)^9 is k=1
The 3th term of (2x-7)^9 is k=2
..........................................................
The 6th term of (2x-7)^9 is k=5
Hence,
[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]
- 33889212x⁴ is the coefficient of the 6th term in binomial theorem .
What is binomial theorem?
The formula for the binomial theorem is (a+b)n= nr=0nCr an-rbr, where r is a real number, a, and b are real numbers, and n is a positive integer. This equation aids in the expansion of binomial formulae like (x + a)10, (2x + 5)3, (x - (1/x)), and so forth.( 2x - 7 )⁹
compare with formula
a = 2x b = - 7 n = 9
The 1th term of (2x-7)^9 is k=0
The 2th term of (2x-7)^9 is k=1
The 3th term of (2x-7)^9 is k=2
...................................................
The 6th term of (2x-7)^9 is k=5
hence
⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵ = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵
= 9!/4! * 5! 2⁴x⁴( -7)⁵
= 126(16) ( - 16807 )(x)⁴
= - 33889212x⁴
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Edna needs to divide her savings of $35,286 equally among her 7 grandchildren. If she wants to do the calculation using the standard algorithm for division, how should she set up the division? Which number is the dividend, and which is the divisor? 50 POINTS HURRY
The dividend is 35286 and the divisor is 7. The value of the division is $540.8571
What is the value of the division?When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.
On the other hand, the number that is being divided by which is in this case 7 is the dividend.
The division will be:
= $35286 ÷ 7
= $540.8571
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Write and solve a proportion for each word problem.
(9)There are 9 strawberries in a quart package. How many
quart packages do you need if you want 62 strawberries?
We will need 7 quart package if we want 62 strawberries
What is division?
Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.
We are given that there are 9 strawberries in a quart package
Also we want 62 strawberries
Then how many quart will be required
Now we perform division to find the number of quart
62/9 = we get a value of 8.88
Which is very close to nine
Hence we will need 9 quart packages if we want 62 strawberries
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ms.folk at least 250 candies to reward her students she has 50 candies already and will buy more candy in bags with 20 candies in each write an inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies
50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies.
How to solve equations in word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:i) There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.(ii) Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Let x be the number of bags she bought:
50 + 20x ≥ 250
3x ≥ 200
x ≥ 200/3
x ≥ 66.67
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Walter bought cupcakes for his sister's birthday party. 39 out of the 52 cupcakes had sprinkles on top. What percentage of the cupcakes had sprinkles?
The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.
What is percentage?A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.
Given:
The total no cupcakes = 52,
The no of sprinkled cupcakes = 39,
Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100
Percentage of sprinkled cupcakes = 39 / 52 × 100
Percentage of sprinkled cupcakes = 75%
Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.
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Notebook paper is about 0.003 in. thick.
If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
The height of the stack of paper is 3145.73 in.
How to find how high the stack of paper be?Since the Notebook paper is about 0.003 in. thick, and you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times.
Since each piece of paper is halved, that means that the number of paper sheets doubles every time.
So, after halving n times, we would have 2 sheets of paper. Since the thickness of the Notebookpaper is 0.003 in, then the height after cuttin half n times is h = 2ⁿ × 0.003 in.
Since the paper is folded 20 times, n = 20.
So, the height h = 2ⁿ × 0.003 in.
h = 2²⁰ × 0.003 in.
h = 1048576 × 0.003 in.
h = 3145.728 in
h ≅ 3145.73 in
So, the height of the stack of paper is 3145.73 in.
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what is √3 + 1/3 and is the answer irrational or rational?
Answer:
Your answer would be 2.1.
Step-by-step explanation:
The square root of 3 is:
1.73205080757
Then since 1/3 is equal to 0.33, I added 0.33 to the square root of 3 to get:
2.06205080757
Then, I rounded it:
2.1
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
The number of square inches of the wrapping paper left over is 380 square inches
How to determine the amount of square inches left?From the question, we have the following parameters that can be used in our computation:
Box:
Dimension = 8 inches by 9 inches by 10 inches
Rectangular-shaped wrapping paper
Dimension = 2 feet by 3 feet.
The surface area of the box is
Box = 2(lw + lh + wh)
So, we have
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10)
Evaluate
Box = 484 square inches
The surface area of the wrapping paper is
Wrapper = lw
So, we have
Wrapper = 2 * 3
Evaluate
Wrapper = 6 square feet
Convert to square inches
Wrapper = 864 square inches
The amount of square inches left is
Amount left = Wrapper - Box
Amount left = 864 square inches - 484 square inches
This gives
Amount left = 380 square inches
Hence, the amount left is 380 square inches
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D/dx(e^x)=e^x prove please
The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,
Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]
So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]
The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,
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What are some points on a graph of the equation y=-1/3x-1
A few points (co-ordinates) for the given equations are :
(1,-1/2),(-1,1/4),(0,1),,(2,-1/4)
What are the points on the graph called?These points are called Coordinates, where the horizontal line denotes the x-axis and the verticle line is the y-axis.
Each point is identified by both x and y coordinates. A point's x-coordinate is a value that indicates how far the point is from the horizontal or x-axis origin.
According to the given information:y denotes the distance of the point on the vertical line from the origin
x denotes the distance of the point on the horizontal line from the origin
In the given equation y=-1/3x-1
We can substitute x with any integer (i.e any number among the positive or negative numbers)
Putting, x=1 in the given equation we get
y=-1/(3x1)-1
⇒ y=-1/3-1
⇒y=-1/2
Thus the coordinate when x=1 is (1,-1/2)
Similarly by putting x=0, 1, 2, -1 ;we get the following co-ordinates respectively
(0,1), (1,-1/2), (2,-1/4),(-1,1/4)
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In Gauss elimination the given system of simultaneous equations is transformed into
Answer:
row-echelon form
Step-by-step explanation:
Matrixes are commonly used to do Gaussian elimination. By reducing the need to manually specify the parameters at each step, this strategy decreases the work required to obtain the solutions. A system of equations equations is solved using the Gauss elimination method. Let's review the definitions of these equation systems. A set of linear equations with numerous unknown components is defined as a system of linear equations. Unknown factors can be found in various equations, as we all know.
Set A and the universal set U are defined as follows.
U={f, g, h, p, q, r}
A= {g, p, r}
Find the following sets.
Write your answer in roster form or as 0.
(picture attached)
The value of the sets are A ∩ ∅ = ∅ and A' ∪ U = {f, g, h, p, q, r}.
How to determine the sets?Given: U = {f, g, h, p, q, r} and A = {g, p, r}
We are to find: (a)A ∩ ∅ and (b) A' ∪ U
(a) A ∩ ∅
The symbol ∩ means intersection. This tells us what sets have in common. Also, the symbol ∅ means an empty set or null. That is a set that does not have any element
The intersection of a set with the empty set is the null set. Thus:
A ∩ ∅ = ∅
(b) A' ∪ U
The set U is called the universal set
A' means elements not in set A but in set U
The symbol ∪ means union, A' ∪ U will give a list of elements in A' and U combined without repetition. Thus:
A' ∪ U = {f, h, q} ∪ {f, g, h, p, q, r} = {f, g, h, p, q, r}
Therefore, A ∩ ∅ = ∅ and A' ∪ U = {f, g, h, p, q, r}. They should be entered into the boxes accordingly
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1) If A = {piano, guitar, violin) and B = (guitar, piano, violin) then B_______A
For the given two sets A and B, the set B is equal to A.
Set:
A set is the collection of well-defined objects or elements. It is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
Given.
Here we have the two sets
A = {piano, guitar, violin) and
B = (guitar, piano, violin)
Now, we need to find the relation between B and A.
While we looking into the given sets,
Set A has 3 elements in it and
Set B has 3 elements in it.
So, the size of both sets are equal.
And now we have to looking at the elements in it.
While we checking the elements, instead of the order both have the same elements.
Therefore, the set B is equal to set A.
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How do I solve this question
The partial fraction is proved.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
=3x²+8x+4/(x²-4)(3x-2)
=3x2+8x+4/(x2-4)(3x-2)
= 3x2+6x+2x+4/(x2-4)(3x-2)
=3x(x+2)+2(x+2)/(x2-4)(3x-2)
Hence proved, l.h.s = r.h.s
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Write an equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5)
An equation of the parabola is y =
Equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.
Given points:
(-4, 7), (-3, 9), and (4,-5).
Let parabola equation be y = a[tex]x^{2} +bx+c[/tex].
substitute (-4,7)
7 = a(16)+b(-4)+c
16a-4b+c-7 = 0.
substitute (-3,9)
9 = a(9)+b(-3)+c
9a-3b+c-9 = 0
substitute (4,-5)
-5 = 16a+4b+c
16a+4b+c+5=0.
solving three equations we get,
a = -1/2 , b = -3/2 and c = 9
substitute a,b and c values we get,
y = (-1/2)[tex]x^{2}[/tex] + (-3/2)x + 9
y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.
Therefore the equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.
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A speed of 60 mph is equal to 88 ft/sec. Find the speed to the nearest mile per hour of an aircraft that travels 1000 ft/sec.
The speed of the aircraft is 682 mph
How to determine the speed of the aircraft to the nearest mile per hour?Given that: A speed of 60 mph is equal to 88 ft/sec
If an aircraft travels at a speed of 1000 ft/sec, the speed to the nearest mile per hour can be calculated by using the unit ratio of
of mph to ft/s, that is:
60/88 = m/1000
m = 6x1000/ 88 = 60000/88 = 682 mph
Therefore, the speed of the aircraft to the nearest mile per hour is 682 mph
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268 + 88 in the form of a(b+c)
Answer:
4(67 + 22)
Step-by-step explanation:
1. Find the greatest common factor(in this case it is 4)
2. Divide both 268 and 88 by 4 and you get 67 and 22
3. Put it in the requested format and you are left with 4(67 +22)
What is the answer for 6:3(3+3)
Answer:
the answer according to my solution is 06
Which algebraic expression represents the amsplit the cost of a $20.00 gift?
A. f + 20
B. 20f
C. 20 ÷ f
D. f ÷ 20
Answer:
The answer is C: 20 ÷ f
Step-by-step explanation:
What is the solution to (x + 2)(x - 3)² > 0?
The solution is x > -2 and x > 3
x is greater than -2 and x is greater than 3.
This can be represented by the number line Option D.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
(x + 2) (x - 3)² > 0
This can be written as,
x + 2 > 0 and (x - 3)² > 0
x + 2 > 0
x > -2 _____(1)
(x - 3)² > 0
Squaring both sides.
x - 3 > 0
x > 3 _____(2)
From (1) and (2) we get,
x > -2 and x > 3
Thus,
The solution is x > -2 and x > 3
x is greater than -2 and x is greater than 3.
This can be represented by the number line Option D.
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Exercise 4.3
1. Given f=x^2 y; the change in for the total differential of fis given by df = Pdx+Qdy.
Find P, Q at x=1 and y=-1
(Ans: P= -2; Q=1)
Question one
By using the concept of differentiation, it can be calculated that
value of P is -2 and value of Q is 1
What is differentiation?
Differentiation is the process where the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus
Here differentiation is used
f(x) = [tex]x^2y[/tex]
[tex]df = 2xydx+x^2dy[/tex]
Here P = 2xy, Q = [tex]x^2[/tex]
At x = 1, y = -1
P = 2(1)(-1) = -2
Q = [tex](-1)^2[/tex] = 1
So value of P is -2 and value of Q is 1
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A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write
its equation. Let the x-axis represent the number of pints and the y-axis represent the number of
servings. Use only fractional form, if necessary.
10 Servings
9
8
7
6
S
3
2
1
0
0 1 2
The equation is y =
5
6
7
8
Pints
9 10
2.
69
Prin
Tur
Sav
The equation of the line representing the given situation is y = (3/4)x , the graph of the equation is shown below .
In the question ,
it is given that ,
a refreshment stand makes 3 large serving of frozen yogurt from 4 pints .
also given that number of pints is represented by x - axis .
the number of servings is represented by y - axis .
the equation of the line is represented by y = mx + c .
we get c = 0, because at 0 pint there is no servings
hence , the equation becomes y [tex]=[/tex] mx .
According to the question ,
3 = m*4
m = 3/4 .
Substituting the value of m in the equation , we get
y = (3/4)x
the graph of the equation is shown below .
Therefore , The equation of the line representing the given situation is y = (3/4)x .
The given question is incomplete , the complete question is
A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write its equation. Let the x-axis represent the number of pints and the y-axis represent the number of servings. Use only fractional form, if necessary.
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I have no equal sides what am i
Answer:
Scalene
Step-by-step explanation:
a scalene triangle has three sides different angles none of its sides are equal in length
Answer:
A scalene triangle or quadrilateral has no equal sides.
The money used in Switzerland is called
the Franc. The exchange rate is $5 for 6
Francs. Find how many dollars you would
receive if you exchanged 18 Francs.
Solve for x.
please help asap!
Define Variable
Solve the Problem
Write the inequality
Do you think mark will be able to accomplish his goal
The inequality will be represented by p ≥ 33 for at least 15 points.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Mark must score at least 11 points to have an average of 10 points per game.
The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...
(8+14+10+20+5++p)/6 ≥ 15
57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify
p ≥ 33
Mark must score at least 33 points in the next game to average at least 15 points per game.
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Anthony wants to start making periodic investments in a retirement account. He will make a yearly contribution of $3,000 at the beginning of each year. The account will pay 7.2% interest, compounded monthly. How much will his account be worth after 35 years?
After 35 years, Anthony's account is going to be worth $34193.12
How to solve for the compound interestThe formula for the compound interest is given as
[tex]A = P(1 + r)^t[/tex]
Where we have the principal = 3000
the rate of interest = 7.2%
The period of time = 35 years
We have to input these values in the formula above so that we would have
A = 3000 ( 1 + 0.072)³⁵
A = 3000 x 11.398
= $34193.12
Hence we would have that after the period of 35 years, the account would be worth $34193.12
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