S borrowed a loan of Rs 20000 from a person at 6% per annum simple interest and lent the same money as a loan to a businessman at the same rate of interest compounded annually. How much amount does he get the profit after 2 years? Find it.​

Answer:

y=5

Step-by-step explanation:

y equals 5 because x is 1 when you get it alone

Quadrilateral A: Parallelοgram, Rectangle, Rhοmbus, Square.

Quadrilateral B: Trapezοid, Isοsceles Trapezοid

Quadrilateral C: Kite, Trapezοid

Square and Rectangle:

Bοth have fοur right angles, but the square has fοur cοngruent sides, while the rectangle dοes nοt necessarily have cοngruent sides. Therefοre, a square is a rectangle, but nοt all rectangles are squares.

Rhοmbus and Square:

Bοth have all sides cοngruent, but the square alsο has fοur right angles, while the rhοmbus dοes nοt necessarily have right angles. Therefοre, a square is a rhοmbus, but nοt all rhοmbuses are squares.

Parallelοgram and Rhοmbus:

Bοth have οppοsite sides parallel, but the rhοmbus alsο has all sides cοngruent, while the parallelοgram dοes nοt necessarily have cοngruent sides. Therefοre, a rhοmbus is a parallelοgram, but nοt all parallelοgrams are rhοmbuses.

Trapezοid and Kite:

Bοth have twο pairs οf adjacent sides that are cοngruent, but the kite alsο has οne pair οf οppοsite cοngruent sides, while the trapezοid dοes nοt. Therefοre, a kite is a type οf trapezοid, but nοt all trapezοids are kites.

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A. In the alternate universe, the p subshell would have 5 orbitals.

B. In the alternate universe, the d subshell would have 10 orbitals.

In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.

A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).

B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).

Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.

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The solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.

What is a quadratic equation?

A quadratic equation is a type of polynomial equation that has the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants. The solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2-4ac)) / 2a

To solve for x in the equation 2x^2 -19x + 2 = -10x, we need to rearrange it in the standard form of a quadratic equation by isolating the x^2 term and moving the other terms to the other side:

2x^2 -10x -19x +2 = 0

2x^2 -29x +2 = 0

Now we can apply the quadratic formula:

x = (-b ± √(b^2-4ac)) / 2a

x = (-(-29) ± √((-29)^2-422)) / 2*2

x = (29 ± √(841-16)) / 4

x = (29 ± √(825)) / 4

Hence, the solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.

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m = 4/5 for the perpendicular line

m = -5/4 for the parallel line

y = -5/4x + 3

for the line above, m = -5/4

The line parallel to this line would have exactly the same slope m =  -5/4

The line perpendicular to this line would have a  slope equal the inverse with the opposite sign  

m = -5/4

So m = (1/(5/4)) is the slope of the m for the perpendicular line

m = 4/5

The most appropriate domain of the function is 0 ≤ x ≤ 22. This is because Alex can only walk from his home to the store within a maximum of 22 minutes, and the distance he walks can only be modeled within that time frame.

It is given that the function f(x) = 2.5x, which models the distance Alex walks in x minutes after leaving his house to go to the store. It takes him 22 minutes to walk from his home to the store. The most appropriate domain of the function is the range of x values that make sense in this context.

Step 1: Identify the minimum and maximum values for x.
In this case, the minimum value for x is when Alex starts walking, which is 0 minutes. The maximum value for x is when he reaches the store, which is 22 minutes.

Step 2: Express the domain as an interval.
The domain of the function can be written as an interval from the minimum to the maximum value, including both endpoints. Therefore, the domain is [0, 22].

Therefore, the most appropriate domain of the function f(x) = 2.5x, which models the distance Alex walks in x minutes after leaving his house to go to the store, is [0, 22].

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Answer: 17160 feet

Step-by-step explanation:

We know that 5280 feet = 1 mile

So all we have to do is multiply 3 1/4 by 5280

Let's split the 3 and 1/4 up to make the multiplication easier

3×5280=15840

\(\frac{1}{4}\)×5280=\(\frac{5280}{4} =1320\)

Now add them together

15840+1320=17160

Answer:

When adding or subtracting a constant outside the radical sign, it only affects the overall value of the expression, but not the square root itself. The square root symbol only applies to the value inside it, so any constant added or subtracted outside will not change the result of the square root. For example:

√(9 + 4) = √9 + √4 = 3 + 2 = 5

√(9) + 4 = 3 + 4 = 7

As you can see, adding or subtracting a constant outside the radical sign only changes the final result of the expression, but not the value inside the square root.

Answer:

the effect is when graphing the constant determines how far up or down to move it, compared to the original parent function.

Step-by-step explanation:

It is possible that blood pressure levels could change after listening to soothing music, but it is unclear from the data given whether this is the case or not.

A sample of 15 people is a relatively small sample size, so it may not be representative of the population as a whole. In addition, it is not clear what method was used to select the sample, so there may be issues with sampling bias.

Furthermore, the presence of an outlier in the data could indicate that there are other factors influencing the change in blood pressure, such as an underlying medical condition or a reaction to a specific type of music. This outlier could also significantly affect the overall results of the study, making it difficult to draw reliable conclusions.

Therefore, it is not possible to determine from the information given whether or not blood pressure levels change after listening to soothing music. A larger and more carefully selected sample would be needed to provide more reliable results.

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Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the zeros of f(x) = x³ -5x² -22x -16, given that a factor is x+2.

Using synthetic division (see attachment), we find the quadratic factor to be (x² -7x -8), so we have ...

  f(x) = (x +2)(x² -7x -8)

The quadratic can be factored using our knowledge of the divisors of -8 to give ...

  f(x) = (x +2)(x +1)(x -8)

The zeros of f(x) are the values of x that make these factors zero:

  x = -2, -1, 8 . . . . . zeros of f(x)

__

Additional comment

We know the product of binomial factors is ...

  (x -a)(x +b) = x² -(a-b)x -ab

This means we can factor the quadratic by looking for factors of 8 that have a difference of 7. We know that 8 = 8·1 and that 8-1=7, so the values of 'a' and 'b' we're looking for are a=8, b=1.

The "zero product rule" tells you a product is zero only if one of the factors is zero. That is how we know to look for the zeros of the binomial factors of f(x). For example, x+2=0 ⇒ x=-2 is a zero of f(x). (The remainder of 0 in the synthetic division also tells us f(-2)=0.)

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Answer:

Diagram is not so perfect

OR = distance travelled by the jet plane.

Step-by-step explanation:

Let point J be the jet plane and OJ be the constant height at jet plane is flying and OR be the distance jet plane is travelling.

h =

\(1700 \sqrt{3} \)

Now,

From the figure i drew (1st)

taking 60 as reference angle,

tan60° = p/b

or,

\(tan60 = 1700 \sqrt{3} \div b\)

\(b \: = 1700 \sqrt{3} \div tan60\)

so, b = 1700m

inital distance = 1.7km(OR)

now,

tan 30 = p/b

\(tan30 = 1700 \sqrt{3} \div b \\ or \: b = 1700 \sqrt{3} \div tan30\)

so, b = 5100 m

so, final distance = 5.1 km(OR)

Now,

distance travelled = final distance - initial distance

distance travelled = 5.1 km - 1.7km

distance travlled = 3.4 km

Now,

time = 17 seconds

= 0.00472 hour.

Now,

speed = d/t

or, speed = 3.4/0.00472

so, speed = 720.3389km/hr

so, speed = 720 km/hr approximately

Answer:

Step-by-step explanation:

V of a cone V=3.14* r^2*h/3

942=3.14*r^2*9/3

r^2=942/(3.14*3)=100

r=sqrt100=10

The radius of the cone when the volume of 942 cubic inches and a height of 9 inches should be 10.

Since there is  a volume of 942 cubic inches and a height of 9 inches

We know that

Volume of a cone V=\(3.14* r^2*h/3\)

So,

\(942=3.14*r^2*9/3\\\\r^2=942/(3.14*3)=100\)

r =\(\sqrt 100\)

=10

hence, The radius of the cone when the volume of 942 cubic inches and a height of 9 inches should be 10.

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For the equation x^3 + 27y^4 = In  y' at (-3, 1) is -27/107 by using implicit differentiation y' = 3x^2 / (y - 108y^3).

To find y' using implicit differentiation and then evaluate y' at (-3,1) for the given equation x^3 + 27y^4 = ln(y), follow these steps:

1. Differentiate both sides of the equation with respect to x, remembering to apply the chain rule when differentiating with respect to y.

d/dx(x^3) + d/dx(27y^4) = d/dx(ln(y))

2. Apply the chain rule on the right-hand side:

3x^2 + 27(4y^3)(dy/dx) = (1/y)(dy/dx)

3. Solve for dy/dx (which is y'):

dy/dx(y - 108y^3) = 3x^2

y' = dy/dx = 3x^2 / (y - 108y^3)

4. Evaluate y' at (-3, 1):

y'(-3, 1) = 3(-3)^2 / (1 - 108(1)^3)

y'(-3, 1) = 27 / (-107)

So, y' = 3x^2 / (y - 108y^3), and y'(-3, 1) = -27/107.

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Answer:

Step-by-step explanation:

To find the possible length and breadth of the rectangle, we need to factor the given expression:

x^2 - 6x + 8 = (x - 4)(x - 2)

Therefore, the length and breadth of the rectangle can be any combination of (x-4) and (x-2).

For example, if we choose (x-4) as the length and (x-2) as the breadth, we have:

Length = x - 4

Breadth = x - 2

Conversely, if we choose (x-2) as the length and (x-4) as the breadth, we have:

Length = x - 2

Breadth = x - 4

So, the possible length and breadth of the rectangle are (x-4) and (x-2), and vice versa.

Answer:(x-4) and (x-2)

Step-by-step explanation:

The approximate probability that fewer than 325 drivers in the sample regularly wear a seat belt is approximately 0.0087.

To solve this problem, we can calculate the probability both exactly using the binomial distribution and approximately using the normal distribution.

Exact Calculation using Binomial Distribution:

The probability of success (drivers wearing a seat belt) is given as p = 0.70, and the sample size is n = 500. We want to find the probability of having fewer than 325 successes.

Using the binomial distribution, we can calculate this probability:

P(X < 325) = P(X = 0) + P(X = 1) + ... + P(X = 324)

Let's calculate it using the binomial probability formula:

P(X < 325) = Σ(k=0 to 324) [C(n, k) * \(p^k * (1-p)^{n-k}\)]

where C(n, k) is the binomial coefficient (n choose k), given by C(n, k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the exact probability.

Approximate Calculation using Normal Distribution:

According to the properties of the binomial distribution, if n is large and p is sufficiently far from 0 or 1, the binomial distribution can be approximated by a normal distribution with mean μ = np and standard deviation σ = √(np(1-p)).

In this case, np = 500 * 0.70 = 350 and np(1-p) = 500 * 0.70 * 0.30 = 105.

Therefore, we can approximate the probability as:

P(X < 325) ≈ P(Z < (325 - 350) / √(105))

where Z is a standard normal random variable.

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the Z-score. Let's calculate it:

P(Z < (325 - 350) / √(105)) ≈ P(Z < -2.38)

Using the standard normal distribution table, we can find that the cumulative probability for Z = -2.38 is approximately 0.0087.

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The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).

Given that:

Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store.

The store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars ($0.05) from selling accessories.

The following steps can be used in order to determine the equation that represents the predicted amount y:

Step 1 - According to the given data, the store makes x dollars selling computer products.

Step 2 - It is also given that, in January and February of this year, the store made $2,500 from sales of accessories and services.

Step 3 - So, the linear equation that represents the given situation is:

y = 0.05x + 2500

Hence the answer is The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).

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Answer: Option 4

Step-by-step explanation:

The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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Answer:

Step-by-step explanation:

-9pi/8

23pi/8

-25pi/8

I think its.

The coterminal angles of ( 7π/8 ) are ( 9π/8 ) , ( -9π/8 ) and ( 23π/8 )

Angles with the same starting side and terminal side are said to be coterminal angles. Depending on whether the given angle is in degrees or radians, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. Coterminal angles can be found in an unlimited number of ways.

To find the coterminal angles of angle θ

The measure of coterminal angle is θ ± 360n,  if θ is measured in degrees.

And , measure of coterminal angle isθ ± 2πn,  if θ is measured in radians.

Given data ,

Let the angle be represented as θ

Now , the value of θ = ( 7π/8 )

On simplifying the equation , we get

To find the coterminal angles of angle θ

θ ± 2πn,  if θ is measured in radians.

Substituting the values in the equation , we get

x₁ = ( 7π/8 ) + 2π

x₁ = ( 23π/8 )

And ,

x₂ = 2π - ( 7π/8 )

x₂ = ( 9π/8 )

And ,

x₃ = ( 7π/8 ) - 2π

x₃ = ( -9π/8 )

Hence , the coterminal angles are ( 9π/8 ) , ( -9π/8 ) and ( 23π/8 )

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The calculated volume of the prism is 897 cubic ft

From the question, we have the following parameters that can be used in our computation:

The trapezoidal prism

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (13 + 10) * 6

Evaluate

Base area = 69

Also, we have

Height = 13

So, the volume is

volume = 13 * 69

Evaluate

volume = 897

Hence, the volume of the prism is 897 cubic ft

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Answer:

Step-by-step explanation:

Yes they are equivalent

Hope it helps!

*Gotta go fast*

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

The equation can be used to determine t, the weight of the textbooks is t = 0.7w

Given:

let

Total weight = w

Weight of notebook = n

Weight of backpack = b

Weight of textbook = t

w = n + b + t

where

n = 4 pounds

b = 2 pounds

t = 0.7w

So

w = 4 + 2 + 0.7w

w - 0.7w = 4 + 2

0.3w = 6

w = 6/0.3

w = 20

Recall,

t = 0.7w

= 0.7(20)

= 14 pounds

Therefore, the weight of the textbook is 14 pounds

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Answer:

12

Step-by-step explanation:

1 inch = 20 miles

240 miles ÷ 20 miles =

12 inches

Answer:

12 inches

Step-by-step explanation:

Hey there!

Well to solve the given question we need to use fractions,

if 1 inch is 20 milles, we can set up the following.

\(\frac{1}{20} = \frac{x}{240}\)

Cross multiply

240 = 20x

Divide both sides by 20

x = 12

So it is 12 inches in the map.

Hope this helps :)

Answer:

4

Step-by-step explanation:hrllo sdkksfdjg jdskl fg

The answer is c. an antibiotic. An antibiotic does not possess psychoactive properties and does not produce changes in consciousness or brain activity.

Psychoactive drugs are substances that have the ability to alter consciousness, mood, perception, cognition, or behavior. They can produce changes in the brain's chemistry, leading to various effects on the central nervous system.

a. A stimulant is a psychoactive drug that increases alertness, energy, and activity. Examples include drugs like caffeine, amphetamines, and cocaine.

b. A hallucinogenic is a psychoactive drug that induces hallucinations and alters perception, often leading to sensory distortions and changes in thought processes. Examples include substances like LSD, psilocybin mushrooms, and peyote.

d. A depressant is a psychoactive drug that slows down brain activity, producing a sedative effect. Depressants include substances like alcohol, benzodiazepines, and opioids.

c. An antibiotic, on the other hand, is not a psychoactive drug. Antibiotics are medications used to treat bacterial infections by inhibiting the growth of bacteria or killing them. They do not have direct effects on consciousness or alter brain activity.

In summary, while a stimulant, hallucinogenic, and depressant are all examples of psychoactive drugs that can alter consciousness, an antibiotic does not possess psychoactive properties and does not produce changes in consciousness or brain activity.

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