The Average return rate for the investment will be 3.2%.
The Return Rate can be defined as a profit that is made on investment .
In the Question
let the investment be "x" .
25% stocks in Company A have return rate of 6%.
Investment in Company A = (25% of x)
Return is 6% of investment = (25% of x) + 6% of (25% of x)
Return from company A= (25% of x)(1+0.06) ...as 25%=0.25 & 6%=0.06
= 0.25*x*(1.06) ...(i)
40% stocks in Company B have return rate of 2.5%.
Investment in Company B = (40% of x)
Return is 2.5% of investment = (40% of x) + 2.5% of (40% of x)
Return from company A = (40% of x)(1+0.025) ...
= 0.40*x*(1.025) ...(ii)
Stocks in Company C = 100 - 25 - 40 = 35%
35% stocks in Company C have return rate of 2%.
Investment in Company C = (35% of x)
Return is 2.5% of investment = (35% of x) + 2% of (35% of x)
Return from company C = (35% of x)(1+0.02) ...
= 0.35*x*(1.02) ...(iii)
Total Return = Return from Company A + Return from Company B + Return from Company C .
From equation (i) ,(ii) and (iii) we get
Total Return = 0.25*x*(1.06) + 0.40*x*(1.025) + 0.35*x*(1.02)
= 0.265x + 0.41x + 0.357x
= 1.032x
The Average rate of return = [tex]\frac{return- investment }{investment } \times100[/tex]
Substituting the value we get,
= (1.032x - x ) / x *100
= 0.032x /x * 100
= 0.032*100
= 3.2%
Therefore , the Average return rate for the investment will be 3.2%.
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How many GRAMS of aluminum are present in 1.40 grams of aluminum sulfate,
Al2(SO4)3?
54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.
What is meant by the term molecular mass/weight?A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.
It is applied to substances with molecules as constituent particles.The molecular mass expresses the mass of a molecule in relation to the mass of the 12C atom, that is assumed to be 12. Although molecular mass is indeed a dimensionless quantity, it is provided the unit Dalton or atomic mass unit to indicate that the mass is relative to 1/12th this same mass of a single carbon-12 atom.For the given question, the expression is;
aluminium sulphate Al₂(SO₄)₃
As three of aluminium is present in the aluminium sulphate.
And, molecular mass of one aluminium atom is 27 grams;
Thus, for 2 aluminium atoms = 2×27 = 54 grams.
Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.
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Watch help video
Find the distance between the two points in simplest radical form.
Answer:
(4, 3) and (-2, 0)
3√5
The distance between two points on an XY plane is calculated using the distance formula, which is employed in coordinate geometry or Euclidean geometry. The x-coordinate, often known as the abscissa, is a point's separation from the y-axis. The y-coordinate, often known as the ordinate, refers to a point's separation from the x-axis. A point on the x-axis has coordinates of the form (x, 0), and a point on the y-axis has coordinates of the form (0, y). We utilize the Pythagoras theorem in this case to determine the separation between any two points in a plane.
Distance formula = √ ( x₁ - x₂)² + ( y₁ - y₂)²
= √ 6² + 3²
=3√5
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addictive inverse of -7/8 and 7/8 8/7 -8/7
The additive inverse of the numbers given as -7/8 and 7/8 are 7/8 and -7/8
How to determine the additive inverse?The numbers are given as:
-7/8 and 7/8
As a general rule, the additive inverse of a number x is -x
This means that the additive inverse of the numbers given as -7/8 and 7/8 are 7/8 and -7/8
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The names of 20 students in the class will be put in a hat. The class consists of 12 freshmen, 6 sophomores, and 2 juniors. If a sophomore was chosen there, how likely is it that another sophomore will get to play today?
If a sophomore was chosen yesterday, the probability that a sophomore will be chosen again today is 3/10.
Given, number of students name put into the hat = 20
total number of freshmen in the class = 12
total number of sophomore in the class = 6
total number of juniors in the class = 2
we are asked to determine the probability that the sophomore will be selected the second day also = ?
Calculating a situation's probability allows us to determine its likelihood. Absolute certainty in forecasting is challenging in many situations. With its help, we are only able to anticipate the likelihood, or chance, that an event would occur.
from the given data,
n(s) = 20
n(A) = 6 ⇒ as the name selected in the first day is put back in the hat.
⇒ P(A) = n(A)/n(s)
P(A) = 6/20
P(A) = 3/10
hence the probability that the another day again a sophomore will be chosen is 3/10.
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6. Explain why (4, 1) is not a solution to the equation y=3x + 1.
Answer:
x is 4 and y is 1
So we put 3 x 4 + 1
if it's equal 1 (since y is 1)
but in this case it equals 13 so it's wrong
Answer:
see explanation
Step-by-step explanation:
to determine if (4, 1 ) is a solution of the equation, substitute the x and y coordinates into the equation and if both sides are equal then it is a solution.
y = 3(4) + 1 = 12 + 1 = 13 ≠ 1
since y ≠ 13 then (4, 1 ) is not a solution to the equation
wHAT IS 1.42 - (-2.9)
[tex] \: \: \: \: \large\bf\implies \: 4.32[/tex]
Step-by-step explanation:[tex] \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32[/tex]
Additional information:First of all we know that to do this type of question that is ↓
(-)(-) = +(+)(+) = +(-)(+) = -(+)(-) = -Megan's text messaging plan costs $15 for the first 500 messages and 5¢ for each additional text message. If she owes $21.55 for text messaging in the month of May, how many text messages did she send that month?
Answer:
631
Step-by-step explanation:
This problem can be expressed as:
0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131
We also know that:
0.05x + 15 = x + 500
If x = 131:
x + 500
131 + 500
631
NO LINKS!! Please help me with these problems. Part 9a1
Answer:
Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)Range: [0, ∞)Continuity: Point discontinuity (hole) at x = 3.Step-by-step explanation:
Given function:
[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]
DomainThe domain is the set of all possible input values (x-values).
Factor the denominator of the function:
[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]
The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.
Therefore, the function is undefined when x = -1 and x = 3.
Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).
RangeThe range is the set of all possible output values (y-values).
As the domain is restricted, the range is also restricted.
Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.
Therefore, there is a point discontinuity at x = 3.
Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.
Therefore, there is an infinite discontinuity at x = -1.
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]
Therefore, there are no stationary points and no minimum/maximum points.
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]
[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]
[tex]\implies x+1 < 0 \implies x < -1[/tex]
[tex]\implies x+1 > 0 \implies x > -1[/tex]
Combine the intervals:
(-∞, -1) ∪ (-1, ∞)
Therefore:
The function is decreasing in the interval (-∞, -1) ∪ (-1, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
Range: [0, ∞)
Continuity: Point discontinuity (hole) at x = 3.
Infinite discontinuity (vertical asymptote) at x = -1.
None
Decreasing function: (-∞, -1) ∪ (-1, ∞)
Symmetry: Neither
Suppose you are throwing a lunch event for 100 people.
You decide to offer vegan options. You are not
sure how many vegans are attending, but a study shows that vegans occur at a rate of 5%. Assume the requirements for a binomial distribution are satisfied. What is the probability that you will have less than 10 vegans attending your event?
The probability of having less than 10 vegans attending the event, given that the binomial distribution requirements are satisfied, is 9%.
What are the requirements of a binomial distribution?The requirements of a binomial distribution include:
Independent observationsFixed number of observationsEqual probability of success for each observationEach observation falls into the success or failure categories.What is probability?Probability is the likelihood of an event occurring given the possibility of many outcomes.
Probability is computed as percentages, fractions, or decimals, and it cannot be more than 1.
Data and Calculations:Expected guests = 100
Expected vegans = 5%
Less than 10 vegans = 9
The chance that 9 vegans will attend the event = 9/100 = 9%.
Thus, the probability of having less than 10 vegans attending the event is 9%.
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Every day, Angeni's cupcake store sells 5,000 cupcakes in chocolate and vanilla
flavors. If the chocolate flavor is 3 times as popular as the vanilla flavor, how many of
each cupcake does the store sell per day?
The number of vanilla and chocolate flavoured cupcakes sold every day is 1250 and 3750, respectively.
Let the number of vanilla-flavoured cupcakes be "x".The number of chocolate-flavoured cupcakes is 3*x.A ratio in mathematics describes how many times one number contains another. A number is an arithmetic value used to represent a quantity and to do computations. Numericals are written symbols that represent numbers, such as "3." A number system is a logical writing system for representing numbers with digits or symbols.The total number of cupcakes that are sold is 5,000.According to the question, x + 3x = 50004x = 5000x = 5000/4x = 1250The number of vanilla-flavoured cupcakes sold every day is 1250.The number of chocolate-flavoured cupcakes sold every day is 3750.To learn more about numbers, visit :
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Suppose you are drawing a scaled copy of a triangle with one of the sides measuring 5 centimeters. If
you are using a scale factor of 2, how long will the corresponding side of the scaled copy be?
It will be 10
It will be
cm²
How long will the corresponding side of the scaled copy be if you use a scale factor
ctor of /?
It will be 12-1/2
long.
1³/?
How long will the corresponding side of the scaled copy be if you use a scale factor of
mm²
long.
vlong.
Answer:
spam
Step-by-step explanation:
spam spam spam
At a sale, dresses were sold for $17 each. This price was 85% of a dress's original price. How much did a dress originally cost?
The original cost of the dress is $14.45
How to calculate the original cost of the dress ?The dresses were sold for $17 each
This price was 85% of the original price
Therefore the original cost of the dress can be calculated as follows
85/100= 0.85
The first step is to calculate the original pre sale price
17= 0.85x
x= 17/0.85
= 20
The original cost of the cloth is
= 0.85 × 17
= 14.45
Hence the original cost of the cloth is $14.45
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There were 256 farmers in the county 30 years ago 5/8 of those farmers have changed occupations how many of the 256 farmers changed occupations
The answer is 27 for your math
Step-by-step explanation:
Anna and Julia are at point P. Point Q is due North of point P. They disagree about the shortest route from P to Q. Anna walks on a bearing of 330°, and then changes to a bearing of 040°, which takes her straight to Q. Julia walks 3 km on a bearing of 0200, after which she walks on a bearing of 300°, which then takes her straight to Q. Who took the shorter route?
The Shorter route as per the bearing calculations is taken up by Julia.
What is a bearing?
The angle from the north line, expressed in degrees, is the correct bearing to a given point. The real bearing will simply be referred to as the bearing.A point's bearing is the number of degrees inside the angle measured counterclockwise from the north line towards the line connecting the point and the compass's center.When describing the direction from one point in relation to another, a bearing is utilized.Bearing calculations are illustrated below:
Route Taken up by Anna
360-330= 30°
First angle =90-30= 60°
Second angle= 60+(90-40) =110°
Third angle= 180-(110+30)= 40°
Route taken up by Julia:
First angle =20°
Second angle= 300-(180+20)=100°
Third angle=180-(20+100)=60°
Hence, the Shorter route as per the bearing calculations is taken up by Julia and bearing diagram is attached with the solution as an image.
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You have a Chick-fil-A gift card worth $50. After you buy lunch on Monday, its value is $46.50. After you
buy lunch on Tuesday, its value is $43. Write an explicit formula to represent the amount of money left on
the card as an arithmetic sequence.
What is the value of the gift card after you buy 12 lunches?
List the interval(s) on which f is increasing.
The interval(s) in which f is increasing is/are: _____________.
(Type your answer in interval notation. Use a comma to separate answers as needed.)
The intervals on which the function f of x is increasing is:
(6, 0) U (2, 4) U (7, 9)
In which intervals is the function increasing?When we have the graph of a function, we can identify if it is increasing if, reading from left to right, we can see that the graph of the function goes upwards.
For the graphed function, we can see that it increases for the values:
-6 < x < 0
2 < x < 4
7 < x < 9
Writing this in interval notation, we have:
(6, 0) U (2, 4) U (7, 9)
This is the list of intervals on which the function f(x) is increasing.
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Convert the following metric units of length.
100 kilometers to meters
a 100,000 m
b 10,000 m
c 108,076 m
d 109,076 m
The conversion of 100 kilometers to meters would be,
100 kilometers = 100,000 meters
The correct answer is an option (a)
In this question we need to convert the metric units of length.
We need to convert 100 kilometers to meters.
We know that, 1 kilometer = 1000 meters
Let 100 kilometers = p meters
So, we get an expression,
p × 1 = 100 × 1000
From this expression we get,
p = 100,000 meters
This means, 100 kilometers = 100,000 meters
Therefore, the conversion of 100 kilometers to meters would be,
100 kilometers = 100,000 meters
The correct answer is an option (a)
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a normal window has the shape of a rectangle surmounted by a semicircle. if the perimeter of the window is 34 ft, express the area A of the window as a function of the width x of the window
The 34 feet perimeter and width, x, of the window which is in the shape of a rectangle surmounted by a semicircle is, A = 17•x - x²•(1/2 - π/8)
How can the area of the window be expressed as a function of x?The shape of the window = A rectangle surmounted by a semicircle
Perimeter of the window, P = 34 feet
Width of the window = x
Required; The area, A, of the window as a function of x
Solution:
Diameter of the semicircle = x
Length of the semicircular arc = π•x/2
Let y represent the height of the window, we have;
P = 2•y + x + π•x/2 = 34
Therefore;
y = (34 - (x + π•x/2))/2 = 17 - x•(1 + π/2)/2
Area of the window, A = x × y + π•x²/8
Which gives;
A = x × (17 - x•(1 + π/2)/2) + π•x²/8 = 17•x - x²/2 - x²•π/8
A = 17•x - x²/2 - x²•π/8 = 17•x - x²•(1/2 - π/8)
Therefore;
Window area, A = 17•x - x²•(1/2 - π/8)
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Proportion Word Problems Maze Worksheet
One US dollar equals 0.84 euros. Margo wants to exchange $400 for euro. How many euros will she receive in exchange?
Answer:
1 us dollar =0.84 euros so,400 us dollar =084x400 so, she will receive 336 euros in exchange.
The length of a rectangular garden is 5 m greater than the width. The area of the garden is 66 m² Find the dimensions of the garden.
L = 10 and w= 5 are the dimensions of the rectangular garden.
What is a rectangle, exactly?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.Let the width of the garden be a
Length of the garden = a + 5
Area = l * w
66 = ( a+ 5 ) * a
66 = a² + 5a
a² + 5a -66 = 0
a² + 11a - 5a - 66 = 0
a( a + 11 ) -5 ( a + 11) = 0
( a + 11 ) ( a - 5) = 0
so a + 11 = 0 ⇒ a = -11
a - 5 = 0 ⇒ a = 5
Width cannot be negative.
l = a + 5 = 10
w = 5
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Find f(a + 7).
f(x) = x² + 5
hi
f(a+7)
f(x) =x²+5
by remplacing X by (a+7) :
then f(a+7) = (a+7)²+5
= a² +2*a*7 +49 +5
= a² +14a +54
3x + 2 = 5x-8 how do I solve this
Answer:
x = 5
Step-by-step explanation:
Anna solves the expression 6(5+3) and gets the result 48. Jojo solves the same expression and gets the result 33. Who is correct?
Answer:
Anna is correct.
Step-by-step explanation:
Using PEMDAS, you need to add the terms in the parentheses first.
After adding, you get 8×6 = 48
Jojo made the mistake of multiplying 6 and 5 first, and then adding 3.
Need help with this paper please
Answer:
Step-by-step explanation:
A divided by b is 4, then what’s is b divided by a?
Answer:
the answer is
Step-by-step explanation:
A is more likely to be 12 and B could be 3
so 12/3=4
and
3/12= 0.25
In a bag there are 72 candy bars. 40 of them are snickers, 24 of them are milky ways, the rest are Kit Kats.
Answer: 8 kitkats
Step-by-step explanation:
40+24= 64
72-64=8
Answer:
Total candy bars to snickers = 72:40 or simplified 9:5
Ratio of kit kats to milky ways = 8:24 or simplified 1:3
Ratio for kit kats to total candy bars = 8:72 or simplified 1:9
Step-by-step explanation:
72 = 40 + 24 + x
x = 8
Multiply (-1 13/14) x (1 5/9) what is the product? enter your answer in the box
Answer: -3
Step-by-step explanation:
turn mixed numbers into improper fractions, simplify, and solve- see attached
Answer:
-3
Step-by-step explanation:
to find the answer first turn both numbers into improper fractions
-1 13/14 becomes -27/14
1 5/9 becomes 14/9
now multiply them
[tex]\frac{-27}{14} * \frac{14}{9}[/tex]
you can cancel out the 14s
[tex]\frac{-27}{1} * \frac{1}{9}[/tex]
now divide 9 to the top of the first fraction and to the bottom of the second one
[tex]\frac{-3}{1} * \frac{1}{1}[/tex]
now multiply
-3/1 is your answer
that is basically -3
A square window has an area of x2 + 12x + 36 square feet. Find the length of one side of the square. Question 25 options: (x – 6) feet (x + 6) feet (x + 4) feet (x – 9) feet
The length of one side of the square is x+6
Area of a squareThe formula for calculating the area of a square is expressed as:
A = L^2
where
L is the side length of the square
Given the following parameters
A = x^2 + 12x + 36 square feet
A = (x+6)^2
(x+6)^2 = L^2
L = x + 6
Hence the length of one side of the square is x+6
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The perimeter of the triangle shown is 89 meters. Find the length of each side.
Greetings from Brasil...
The perimeter is the sum of all sides of the triangle. In this case
P = (2X) + (X) + (4X - 9)
as P = 89
89 = (2X) + (X) + (4X - 9)
89 = 7X - 9
7X = 98
X = 98/7
X = 14X:
X meters = X = 14
---------------------------------------------
2X:
2X meters = 2 · X = 2 · 14 = 28
---------------------------------------------
(4X - 9):
(4X - 9) meters = (4 · X - 9) = (4 · 14 - 9) = (56 - 9) = 47
shonda went for a drive in her new car. She drove for 147.5 miles at a speed of 59 miles per hour. For how many hours did she drive?
Answer:
2.5
Step-by-step explanation:
By Using s = d/ t
So t = d / s
t = 147.5 / 59= 2.5