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4 years ago

Annual rate of interest = 6.5

Mathematics

1 answer:

liq [111]4 years ago

6 0

Answer:

The principal value is Rs.4266.75.

Step-by-step explanation:

Using compound interest formula,

Compound interest = Amount - Principal

Amount is given by, $A=P(1+r)^t$

So, $I+P=P(1+r)^t$

Where, P is the principal

I is the interest I=Rs.1222

r is the interest rate r=6.5%=0.065

t is the time t=4 years

Substitute the value in the formula,

$1222+P=P(1+0.065)^4$

$1222+P=P(1.065)^4$

$1222+P=1.2864P$

$1.2864P-P=1222$

$0.2864P=1222$

$P=\frac{1222}{0.2864}$

$P=4266.75$

The principal value is Rs.4266.75.

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An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false

asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let $p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1)$ be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that $p(\lambda)=\det(B-\lambda I)$ . 0 is a root of p, so we have that $p(0)=\det(B-0 I)=\det B=0$ .

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.

8 0

3 years ago

g: Consider the following game. A coin is flipped. If it lands tails we stop playing and winnothing. If it lands heads we spin a

galben [10]

Answer:

E[W] = $25 (assuming the currency is in dollars)

Var(W) = 1041.67

Step-by-step explanation:

Probability of winning first starts with the coin toss.

For a win, the coin needs to land on heads.

Probability of that = 1/2 = 0.5

Then probability of winning any amount = 1/100 = 0.01

Total probability of winning any amount = 0.5 × 0.01 = 0.005

But expected value is given by

E(X) = Σ xᵢpᵢ

where xᵢ is each amount that could be won

pᵢ is the probability of each amount to be won and it is the same for all the possible winnings = 0.005

So,

E(W) = Σ 0.005 xᵢ

Summing from 0 to 100 (0 indicating getting a tail from the coin toss). This could be done with dome faster with an integral sign

E(W) = ∫ 0.005 x dx

Integrating from 0 to 100

E(W) = [0.005 x²/2]¹⁰⁰₀

E(W) = [0.0025 x²]¹⁰⁰₀ = 0.0025(100² - 0²) = 0.0025 × 10000 = $25

Variance is given by

Variance = Var(X) = Σxᵢ²pᵢ − μ²

μ = expected value

We calculate the expression, Σxᵢ²pᵢ which is another sum from 0 to 100

Σxᵢ²pᵢ = Σ 0.005xᵢ²

Σ 0.005 xᵢ² = ∫ 0.005 x² dx

Integrating from 0 to 100

∫ 0.005 x² dx = [0.005 x³/3]¹⁰⁰₀ = [0.1667x³]¹⁰⁰₀ = 0.1667(100³ - 0³) = 1666.67

Var(W) = 1666.67 - 25² = 1666.67 - 625 = 1041.67.

5 0

3 years ago

Find the equilibrium point for the pair of supply and demand functions. Demand: q=18/x Supply: q=x/2

storchak [24]

Answer:

The equilibrium point is at x = 6

Step-by-step explanation:

Given

$Demand (q) = \frac{18}{x}$

$Supply (q) = \frac{x}{2}$

Required

Determine the equilibrium point

The equilibrium point is determined by

$Demand = Supply$

Substitute values for Demand and Supply

$\frac{18}{x} = \frac{x}{2}$

Cross Multiply

$x * x = 18 * 2$

$x^2 = 36$

Take positive square root of both sides

$x = 6$

Hence;

The equilibrium point is at x = 6

5 0

4 years ago

X+ y + z = -3 3y - Z = 4 2x- y - 2z = -5

snow_lady [41]

Answer:

(-3, 1, -1)

Step-by-step explanation:

x + y + z = -3 --> (1)
3y - z = 4 --> (2)
2x - y - 2z = -5 --> (3)

Add up (1) and (2)

x + 3y + y + z - z = -3 + 4 ⇒ x + 4y = 1 --> (4)

Double (2) and subtract from (3)

2x - y - 2z - 2(3y - z) = -5 - 2(4) ⇒ 2x - y - 2z - 6y + 2z = -5 - 8
2x - 7y = -13 --> (5)

Double (4) and subtract (5)

2(x + 4y) - 2x + 7y = 2 + 13 ⇒ 2x + 8y - 2x + 7y = 15 ⇒ 15y = 15 ⇒ y = 1

Finding x

x + 4(1) = 1 ⇒ x = 1 - 4 ⇒ x = -3

Finding z

-3 + 1 + z = -3 ⇒ z = -1

So the answer is:

(-3, 1, -1)

4 0

3 years ago

The cost of a canoe rental is $15 deposit plus $6 per hour.The total rental cost is

Scrat [10]

Answer:

its 90

Step-by-step explanation:

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3 years ago