an investor has rs 30000 that he wants to invest in bank deposits, equity shares and unit trust. in view of the risk involved in buying equity shares he wants to invest an amount in equity share is equals to 20% of his total investment in bank deposits and unit trust. Because of certain tax exemptions available to him , he would like to maintain the ratio of 3:2 between investment in bank deposits and unit trust. determine the amount he would invest in each of the three forms of investment using inverse matrix method
Answers
The investor should invest Rs 12,000 in bank deposits, Rs 8,000 in a unit trust, and Rs 10,000 in equity shares.
The investor has a total of Rs 30,000 to invest in bank deposits, equity shares, and unit trusts. According to the given conditions, the investment in equity shares should be 20% of the total investment in bank deposits and unit trusts. Also, the ratio between investment in bank deposits and unit trust should be 3:2.
Let x be the investment in bank deposits, y be the investment in a unit trust, and z be the investment in equity shares. Based on the given conditions, we can create the following system of equations:
x + y + z = 30,000 (total investment)
z = 0.2(x + y) (equity shares condition)
x/y = 3/2 (ratio condition)
Using the inverse matrix method, we can rewrite these equations as a matrix equation:
|1 1 1| |x| |30,000|
|0.2 0.2 -1| |y| = |0 |
|3/2 -1 0 | |z| |0 |
To solve this matrix equation, we can compute the inverse of the coefficient matrix and multiply it with the constant matrix:
A = |1 1 1|
|0.2 0.2 -1|
|3/2 -1 0 |
A_inv = |2/5 -1/5 -1/5|
|-3/2 1/2 1/2|
|5/2 1/2 -3/2|
Multiplying A_inv with the constant matrix, we get:
|x| |12,000|
|y| = |8,000 |
|z| |10,000|
So, the investor should invest Rs 12,000 in bank deposits, Rs 8,000 in a unit trust, and Rs 10,000 in equity shares.
To learn more about Invest :
https://brainly.com/question/24558072
#SPJ11
Related Questions
Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
Answers
25% = 75/x
To solve for x, we can cross-multiply:
0.25x = 75
Then, we can divide both sides by 0.25:
x = 300
Therefore, there are 300 6th-grade students in total.
Use the parallelogram to find m
m
Answers
Using the parallelogram law to find m, the value of m is 50°.
What is the parallelogram law?The parallelogram law states that the sum of the squares for a parallelogram's four sides is equal to the sum of the squares for its two diagonals.
The parallelogram must have equal opposed sides in Euclidean geometry.
If ABCD is a parallelogram, then AB = DC and AD = BC, the parallelogram law is stated as:
2(AB)² + 2 (BC)² = (AC)² + (BD)²
If the parallelogram is a rectangle, the parallelogram law is stated as:
2(AB)² + 2 (BC)² = 2(AC)²
The value of the unknown angles in the parallelogram are as follows:
CED = 180 - (60 + 33 + 37)
CED = 50°
Learn more about parallelogram law at: https://brainly.com/question/23867486
#SPJ1
The quotient of a number and 2 increased by 8 is -15
Answers
n/6 + 2 = 4
n/6 + 2 - 2 = 4 - 2
n/6 = 2
(n/6)6 = 2(6)
n = 12
2X(5)=2X(-5)=20÷(-4)=-2X(5)=20÷(4)=4X(-5)=25÷(-5)=-20÷(4)=
Answers
4[1 2 -1 5]
Someone help me with this bs
Answers
Answer:
-12
Step-by-step explanation:
12 - 15 = -3
4 ( -3 )
= -12
Answer: -12
Step-by-step explanation:
We have 4[12 -15]
Next, we have subtract in the parentheses since it's part of PEDMAS
12-15
After that, we get -3. Whenever a you multiply a whole number with a negative number, the whole becomes negative.
12- 15= -3
And Lastly, we multiply.
4x -3= -12
Hope this helps!
a. y=-2x +10, y=-**
y,
5. y=-3x+10, y=-2x
c. y=
y=-*x+10,
-x+10, y=-2x
y=-2x+10, y=-*
c.
х
Answers
Answer:
C
Step-by-step explanation:
find the plot and interpret the point in the equation
Solve by completing the square.
j² + 14j + 5 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
Submit
or j =
=
Answers
Answer:
\(j = 7 \pm \sqrt{44}\)
Step-by-step explanation:
First, move the constant term to the other side of the equation.
\(j\² + 14j + 5 = 0\)
\(j\² + 14j = -5\)
Next, add the coefficient of the first degree j term divided by 2, then squared to both sides.
\(j^2 + 14j + (14/2)^2 = -5 + (14/2)^2\)
\(j^2 + 14j + (7)^2 = -5 + (7)^2\)
\(j^2 + 14j + 49 = -5 + 49\)
\(j^2 + 14j + 49 = 44\)
Now, we can factor the left side as a square.
\((j+7)(j+7) = 44\)
\((j+7)^2 = 44\)
Finally, we can take the square root of both sides to solve for j.
\(\sqrt{(j+7)^2} = \sqrt{44\)
\(j+7=\pm\sqrt{44}\)
\(\boxed{j = 7 \pm \sqrt{44}}\)
Note that there are two solutions, as \(\sqrt{44\) could be positive OR negative because of the even root property:
if \(x^2 = a^2\),
then \(x = \pm a\)
because both \((+a)^2\) and \((-a)^2\) equal \(a^2\).
Bobby is reading a new book about dragons and wizards. He reads 1/5 of a chapter every night
before bed. There are 15 chapters in the book. How many days will it take Bobby to finish the
book?
Answers
Answer:
75 nights
Step-by-step explanation:
= 15 ÷ 1/5
= 15 × 5/1
=15×5/1 = 75
On a number line, P has coordinate-35 and Q has coordinate 21. Find PQ
Answers
Answer:
42
Step-by-step explanation:
because its 42
Part 1: 12% annual interest on 132000 for 8 days
Part 2: 12% annual interest on 106,750 for 20 days.
If it helps, it's a 5 year note. Assuming 365 days in a year.
Answers
The interest for Part 1 is approximately $385.10.
The interest for Part 2 is approximately $709.31.
To calculate the interest for Part 1 and Part 2The formula is as follows:
Interest is calculated as follows: Principal * Rate * Time
Where
Principal represents the starting sumThe interest rate is rateTime measures length in years.Part 1:
$132,000 is the principal.
(Decimal) Rate = 12% = 0.12
Time = 8 days/365 days.
How much interest is there in Part 1?
Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10
Therefore, the interest for Part 1 is approximately $385.10.
Part 2:
$106,750 as the principal
(Decimal) Rate = 12% = 0.12
Time = 20 days / 365 days.
How much interest will there be in Part 2
Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31
Therefore, the interest for Part 2 is approximately $709.31.
Learn more about annual interest here : brainly.com/question/15728540
#SPJ1
What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
domain is x is all real numbers where x does not equal 4 comma range is y is all real numbers where y does not equal 11
domain is x is all real numbers where x does not equal 7 comma range is y is all real numbers where y does not equal negative 4
domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11
domain is x is all real numbers where x does not equal negative 7 comma range is y is all real numbers where y does not equal 4
Answers
The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C
What is the domain of a function?The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.
Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.
Learn more about domain:https://brainly.com/question/13113489
#SPJ1
Answer:
The answer is C.
The sum of the first 12 terms of a geometric sequence with 10 as the first term and a common ratio of 0.3 is __________.
Answers
Answer: 14.2638366937
Step-by-step explanation:
A geometric sequence is a sequence in which each term is multiplied by a number, called the common ratio, to get the next term.
So, if the first term of the geometric sequence is 10 and the common ratio is 0.3, the sequence would be 10, 0.3(10), 0.3 x 0.3 x 10... and so forth. This becomes:
10, 3, 0.9, 0.27, 0.081, 0.00243, 0.00729, 0.002187, 0.0006561, 0.00019683, 0.000059049, 0.0000177147...
You add these first 12 terms to get 14.2638366937.
Find the Error, a student is simplifying the expression negative cube root 0.125 using rational numbers. The student claims that the expression cannot be simplified because it is not possible to take the square root of a negative number. Find the error made by the student and correct it. Need help ASAP. giving 50 points and brainliest if you solve
Answers
Answer:
Step-by-step explanation:
so the cube root of 0.125 is 0.5
make that a negative so -0.5
Find the 27th term of a sequence where the first term is – 7
and the common difference is 7.
Answers
175
Explanation:
1. an (any term) = 27
2. a1 (first term) = -7
3. d (common difference) = 7
• Use the explicit formula:
an = d(n - 1) + a1
a27 = 7(27 - 1) - 7
- Subtract inside the parenthesis ():
a27 = 7(26) - 7
- Distribute:
a27 = 182 - 7
- Subtract:
a27 = 175
A 10 kg ball moves at a speed of 15m/s. The ball collides with a wall causing it to rebound in the opposite direction at a speed of 23 m/s.
Calculate the impulse on the ball?
Answers
Answer:
The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.
The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.
So, the impulse on the ball is -80 kg m/s.
Getsteludydykoydkzkysdykykykd.
Find the slope of the line that contains the point (-8,3) and (4,1) show your work
Answers
Answer:
m=-1/6
Step-by-step explanation:
m=1-3/4+8=-2/12=-1/6
While driving your rental car on your vacation in Europe, you find that you are getting 13.3 km/of gasolineWhat does this value correspond to in miles per gallon?
13.3km/L=__________mi/gal
Answers
The rental car is getting approximately 37.56 miles per gallon.
To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:
1 km/l ≈ 2.82475 mpg
Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:
13.3 km/l x 2.82475 mpg ≈ 37.56 mpg
So, your rental car is getting approximately 37.56 miles per gallon.
Learn more about conversion factor click;
https://brainly.com/question/30567263
#SPJ1
Need help asap pls and thx pic is attached
Answers
The value of x in the right triangle is 5.6 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side length x of the right triangle can be found using trigonometric ratios as follows:
tan 48 = opposite / adjacent
where
opposite side = x
adjacent side = 5
Hence,
tan 48 = x / 5
cross multiply
x = 5 tan 48
x = 5 × 1.11061251483
x = 5.55306257415
Therefore,
x = 5.6 units
learn more on right triangle here:https://brainly.com/question/12173004
#SPJ1
An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 99.5% confidence interval for the proportion who are not satisfied.
(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015. (You will need a critical value accurate to at least 4 decimal places.)(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?
Answers
Answer:
a) A sample size of 5615 is needed.
b) 0.012
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
The margin of error is:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
99.5% confidence level
So \(\alpha = 0.005\), z is the value of Z that has a pvalue of \(1 - \frac{0.005}{2} = 0.9975\), so \(Z = 2.81\).
(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.
This is n for which M = 0.015.
We have that \(\pi = 0.2\)
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}\)
\(0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}\)
\(\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}\)
\((\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}\)
\(n = 5615\)
A sample size of 5615 is needed.
(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?
Now \(\pi = 0.12, n = 5615\).
We have to find M.
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(M = 2.81\sqrt{\frac{0.12*0.88}{5615}}\)
\(M = 0.012\)
For each of the shapes below, state whether it is a regular polygon, an
irregular polygon or neither.
ASAAP NEED HELLPPP
Answers
Answer:
regular: Eirregular: A, B, Dneither: CStep-by-step explanation:
You want to identify the given shapes as a regular or irregular polygon, or neither.
Regular polygonA regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.
Polygon E is a regular polygon.
PolygonA polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.
Any simple polygon that is not a regular polygon is an irregular polygon.
Polygons A, B, D are irregular polygons.
CircleA circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.
<95141404393>
A sound engineer uses a cardioid microphone to record a musical performance. The microphone records sounds according to the equation r = 12 + 12sin(θ), where r is measured in meters.
What does the sum of the constant, 12, and the coefficient, 12, in the equation represent?
a) The maximum possible distance between the performer and microphone
b) The minimum possible distance between the performer and microphone
c) One half the maximum possible distance between the performer and microphone
d) One half the minimum possible distance between the performer and microphone
Answers
Answer:
A. The maximum possible distance between the performer and microphone
Step-by-step explanation:
Answer:
a - The maximum possible distance between the performer and microphone
Step-by-step explanation:
yes
Find the perimeter of a rectangular garden that has a width of 4x−6 and a length of 2x+4.
Answers
Answer:
perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4
If the median is 3.5, we can assume the mean is ____________than 3.5
Answers
We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
What is mean?The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.
According to question:We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.
For example, consider the following two data sets:
Set 1 data: 1, 2, 3, 4, and 5.
The median is 3.
The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.
Data set 2: 1, 2, 3, 4, 10
The median is 3.
The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.
In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.
Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
To know more about mean visit:
https://brainly.com/question/10853033
#SPJ1
What is 35% of 280?
Answers
Answer:
98
Step-by-step explanation:
Multiply.38*280
Answer:
98
Step-by-step explanation:
To find the answer I multiplied 280 by 0.35, that is how you can quickly find a percentage. For example if you would like to find what is 7% of 280 you can just multiply it by 0.07.
Their speed on the BOARDWALK is 5 feet per second.
Their speed on the SAND is 3 feet per second.
The dimensions are shown in the image.
Determine the amount of time it will take for Daniel and
for Brandon to get to the taco truck.
Use paper and/or a calculator as necessary,
Answers
Answer:
Daniel = 207 | Brandon = 196.2
Step-by-step explanation:
Brandon will reach the taco truck first.
• Daniel's time can be found by using the expression 327.6/3 + 489/5, which is 207 seconds.
• Brandon's time can be found by using the expression
327.6^+489^2/3 [Sqaured]
The time taken by Brandon will be 196.2 seconds while Daniel will be 207 seconds.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°.
⊕ Time is taken by Brandon ;
01) Time taken in sand
Time = 327.6/3 = 109.2 seconds.
02) Time is taken on the boardwalk
Time = 489/5 = 97.8 seconds.
Total time taken by Brandon = 109.2 + 97.8 = 207 seconds.
⊕ Time is taken by Daniel;
By Pythagoras theorem
Distance by Daniel = √(327.6² + 489² ) = 588.60 feets.
Time = 588.60/3 = 196.2 seconds.
So the time taken by Brandon will be 207 seconds and Daniel will be 196.2 seconds.
For more information about triangle
https://brainly.com/question/2773823
#SPJ5
\(u'(s)=h^{-1} (u(s+h)-u(s-h))\)
Answers
The simplified form of the expression \(u'(s)=h^{-1} (u(s+h)-u(s-h))\) is \(u'(s) = \frac{du(s)}{ds}\)
Simplifying the expressionTo simplify the expression:
\(u'(s)=h^{-1} (u(s+h)-u(s-h))\)
We can first expand the terms inside the brackets:
\(u'(s) = h^{-1}u(s+h) - h^{-1}u(s-h)\)
Then, we can rewrite the expression with a common denominator:
\(u'(s) = \frac{u(s+h)}{h} - \frac{u(s-h)}{h}\)
Next, we can recognize that the expression inside the brackets is the definition of the forward difference quotient and the backward difference quotient, respectively.
Therefore, we can rewrite the expression as:
\(u'(s) = \lim_{h\to 0}\frac{u(s+h)-u(s)}{h} - \lim_{h\to 0}\frac{u(s)-u(s-h)}{h}\)
Finally, we can recognize that the first limit is the definition of the derivative of u at s, while the second limit is the negative of the derivative of u at s.
Therefore, we can simplify the expression as:
\(u'(s) = \frac{du(s)}{ds}\)
So the simplified form of the expression is \(u'(s) = \frac{du(s)}{ds}\)
Read more about derivative at
https://brainly.com/question/25324584
#SPJ1
Consumers Energy states that the average electric bill across the state is $67.16. You want to test the claim that the average bill amount is greater than $67.16. The hypotheses for this situation are Null Hypothesis: μ ≤ 67.16, Alternative Hypothesis: μ > 67.16. If the true statewide average bill is $51.28 and the null hypothesis is not rejected, did a type I, type II, or no error occur?
a. Type I Error has occured.
b. No error has occured.
c. We do not know the degrees of freedom, so we cannot determine if an error has occured.
d. Type II Error has occured
e. We do not know the p-value, so we cannot determine if an error has occured.
Answers
Answer:
B: No error has occured
Step-by-step explanation:
In statistical hypothesis testing, we have two types of errors namely Type I error and Type II error.
Type I error occurs when we reject the null hypothesis although it is true. Meanwhile, Type II error occurs when we fail to reject the null hypothesis null hypothesis even though it is false.
Now, we are given the null and alternative hypothesis as;
Null Hypothesis: μ ≤ 67.16
Alternative Hypothesis: μ > 67.16.
Where μ represents the statewide average bill.
We are also given the true statewide average bill is $51.28.
Now, the true statewide average bill falls within the range of the null hypothesis given.
Thus, we can't reject the null hypothesis since it is true.
Now, we are told the null hypothesis is not rejected and that is correct.
Thus, there is no error as it doesn't fall into the type I or the type II error.
please help (quickly) (you get 20 points(
Answers
The missing side of the right triangle has a length of 5 units.
Using the Pythagorean Theorem, we can find the length of the missing side of the right triangle. Recall that the Pythagorean Theorem states that for any right triangle, the sum of the squares of the lengths of the legs (the shorter sides) is equal to the square of the length of the hypotenuse (the longer side):
a² + b² = c²
where a and b are the lengths of the legs and c is the length of the hypotenuse.
In this triangle, we know that one leg has a length of 12 and the hypotenuse has a length of 13. Let's use a as the length of the other leg we're trying to find. Plugging these values into the Pythagorean Theorem, we get:
12² + a² = 13²
Simplifying and solving for a, we get:
a² = 13² - 12² a² = 169 - 144 a² = 25 a = 5
Therefore, the missing side of the right triangle has a length of 5 units.
To know more about Pythagorean Theorem, visit:
https://brainly.com/question/24252852
#SPJ1
Find the common difference of the sequence 4, 12, 20, ....
Answers
8
In this pattern, we have 4 12 then 20.
We can see that the difference 4 and 12 is 8.
Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.
What is the probability the he will choose a red marble
Answers
The probability that Tom will choose a red marble from the bag is 1/9.
Given that,
Tom is choosing at random from a bag of colored marbles.
Odds in favor = number of success : number of failures
Odds of getting a red marble = 1 : 8
This means that there ratio of red marbles to other marbles = 1 : 8
Number of red marbles = 1
Total number of marbles = 1 + 8 = 9
Probability of choosing a red marble = 1/9
Hence the required probability is 1/9.
Learn more about Probability here :
https://brainly.com/question/15936143
#SPJ1