There were 432 million mobile users in India last year and it went up to 540 million mobile users this year. Find the percent increase.

By using the definition of dilation with center at the origin, the scale factor of the dilation must be equal to 5.

Herein we find the coordinates of a point and its image on a Cartesian plane. The latter is the consequence of applying a dilation with center at the origin. Therefore, the following expression defines the transformation:

H'(x, y) = k · H(x, y)

Where:

If we know that H(x, y) = (6, 4) and H'(x, y) = (30, 20), then the scale factor is:

(30, 20) = k · (6, 4)

The expression is true for k = 5.

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Answer:

~18.28 ft. / 12 + 2π ft. (Read explanation please!)

Step-by-step explanation:

I) Find the square's perimeter:

Obviously, a square's perimeter is its side length x 4. However, there would be a semicircle on top of it. So, to find it we use:

4 x 3 = 16 ft. (Since 1 of the sides is covered by the semicircle)

II) Find the semicircle's perimeter:

Finding the semicircle's perimeter is a bit more complicated, but no worries! We can use this formula:

πr + 2r (pi x radius + radius x 2)

But WAIT: We need to make sure we remove that one side of the square we mentioned earlier. So we would use:

πr (pi x radius)

In terms of π, the perimeter would be:

2π = 2π ft.

Or, if you used a standard approximation of π, let's say 3.14, it would be:

2(3.14) = ~6.28 ft.

III) Add them up:

If we wanted to state the total perimeter using 3.14 as π, we would say the formula is:

2(3.14) + 4(3) = 18.28 ft.

Or in terms of π:

2π + 4(3) = 12 + 2π ft.

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280.

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Given data ,

Let the principal amount be = A

The value of A = $ 1400

Let the rate of interest be = r

The value of r = 10 %

Let the number of years = T

The value of T = 2 years

Now , the simple interest is calculated by the formula

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Substituting the values in the equation , we get

Simple Interest = ( 1400 x 10 x 2 ) / 100

Simple Interest = 14 x 20

Simple Interest = $ 280

Therefore , the simple interest in 2 years is $ 280

And , the total amount Patrick has to give back to the bank is given by the formula

Amount in 2 years = Principal + Interest

Amount in 2 years = 1400 + 280

Amount in 2 years = $ 1680

Therefore , the amount in 2 years is $ 1680

Hence , Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280

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Answer:Each step in this pattern increases by on block

Step-by-step explanation:

1-1 block

1-2 block

3-3

4-4

Answer:

≈100∘

Step-by-step explanation: I checked delta math

Answer:

3.5 in

Step-by-step explanation:

1in=6Miles

21=Miles

1in=6

1in=12

1in=18

.5in=3

____________

3.5IN = 21MILES

Answer:

∠ 6 = 55°

Step-by-step explanation:

∠ 2 and ∠ 6 are corresponding angles and are congruent , then

∠ 6 = ∠ 2 = 55°

The equation relating L to D is; L = 9 + D

Please find attached the graph of L = 9 + D, created with MS Excel

An equation is a statement of equivalence between two expressions, and a function maps a value in a set of input values to a value in the set of output values.

The initial length of the road = 9 miles

The length of road the construction crew is adding each day = 1 mile

The length in mile of the road after D days = L

The equation for the length is therefore;

The graph of the length of the road can therefore be obtained from the equation for the length by plotting the ordered pairs obtained from the equation.

Please find attached the graph of the equation created using MS Excel.

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I can help you with that problem i just did that on my own.

We need to roll the dice at least 260 times to have a probability greater than 20% of getting two or more double 4s.

To solve this problem, we can use the concept of the geometric distribution, which models the number of trials needed to get a success in a sequence of independent Bernoulli trials, where each trial has the same probability of success.

In this case, the success is rolling two or more double 4s, and the probability of success in each trial is:

P(success) = P(rolling double 4s) + P(rolling triple 4s) + P(rolling quadruple 4s)

= (1/6) × (1/6) + (1/6) × (1/6) × (1/6) + (1/6) × (1/6) × (1/6) × (1/6)

= 1/216 + 1/1296 + 1/7776

= 0.004630

Therefore, the probability of failure in each trial is:

P(failure) = 1 - P(success) = 0.995370

Let X be the number of trials needed to get two or more double 4s. Then X follows a geometric distribution with parameter p = 0.004630.

The probability of getting two or more double 4s in the first X trials is:

P(X ≥ 2) = 1 - P(X = 1) = 1 - p

The probability of getting two or more double 4s in the first 2X trials is:

P(X ≥ 2) + P(X ≥ 3) = (1 - p) + (1 - p) × p

The probability of getting two or more double 4s in the first 3X trials is:

P(X ≥ 2) + P(X ≥ 3) + P(X ≥ 4) = (1 - p) + (1 - p) × p + (1 - p) × p²

And so on...

We want to find the smallest value of X such that P(X ≥ 2) + P(X ≥ 3) + P(X ≥ 4) + ... exceeds 0.2.

That is:

(1 - p) + (1 - p) × p + (1 - p) × p² + ... > 0.2

Using the formula for the sum of an infinite geometric series, we can simplify this expression to:

1 / (1 - (1 - p)) - 1 > 0.2

1 / p - 1 > 0.2

1 / p > 1.2

X > 1 / p × 1.2

Plugging in the value of p, we get:

X > 1 / 0.004630 × 1.2

X > 259.7

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Answer:

length = 62.41 inches

Step-by-step explanation:

Using pythagoras theorem -

Let

a = hypotenuse

b = height

c = length

a^2 = b^2 +c^2

75^2 = 41.6^2 + c^2

Therefore,

75^2 - 41.6^2 = c^2

5625 - 1730.56 = c^2

389.44 = c^2

square root (389.44) = c

62.40544848 = c

Answer:

62 inches.

Step-by-step explanation:

and finally, take the square root of the number we are left with after subtracting \(B^{2}\) , or 1730.56, from 5625, or \(C^{2}\)

5625 - 1730.56 =3894.44

\(\sqrt{3894.44}\) = 62.405

Answer:

-5|0|-7

-6|-4|-2

-1|-8|-3

I'm guessing it is addition

Hope this helps

Step-by-step explanation:

Step-by-step explanation:

\( = 15.6 \times 100 \div 43\)

\( = 36 \: million\)

The no. of people whole likes only roller coasters is 19.

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Let N(U) be the no. who likes at least one of the rides which is

N(U) = (60 - 8) = 52 as 8 people do not like either kind of ride.

Given, The number of people who like roller coasters is 42 and the number who do not like water rides is 23.

∴ The no. of people who only likes roller coasters is (42 - 23) = 19.

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The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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If a differentiable function f: ℝ³ ⟶ ℝ has an absolute maximum value K ≠ 0 and an absolute minimum m, then the function f must have a critical point where the derivative of the function is zero (or undefined).

Given that, suppose f : ℝ³ ⟶ ℝ is a differentiable function which has an absolute maximum value K ≠ 0 and an absolute minimum m.

Since f is continuous on a compact set, it follows that f has a global maximum and a global minimum. We are given that f has an absolute maximum value K ≠ 0 and an absolute minimum m. Then there exists a point a ∈ ℝ³ such that f(a) = K and a point b ∈ ℝ³ such that f(b) = m.Then f(x) ≤ K and f(x) ≥ m for all x ∈ ℝ³.

Since f(x) ≤ K, it follows that there exists a sequence {x_n} ⊆ ℝ³ such that f(x_n) → K as n → ∞. Similarly, since f(x) ≥ m, it follows that there exists a sequence {y_n} ⊆ ℝ³ such that f(y_n) → m as n → ∞.Since ℝ³ is a compact set, there exists a subsequence {x_nk} and a subsequence {y_nk} that converge to points a' and b' respectively. Since f is continuous, it follows that f(a') = K and f(b') = m.

Since a' is a limit point of {x_nk}, it follows that a' is a critical point of f, i.e., ∇f(a') = 0 (or undefined). Similarly, b' is a critical point of f. Therefore, f has at least two critical points where the derivative of the function is zero (or undefined). Hence, the statement is true.

Therefore, the above explanation is verified that if a differentiable function f: ℝ³ ⟶ ℝ has an absolute maximum value K ≠ 0 and an absolute minimum m, then the function f must have a critical point where the derivative of the function is zero (or undefined).

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The equation of the Amount paid for a trip is given by:

where x is the number of miles of the trip, while y is the total amount paid for the trip.

If we are to use a graph to solve the problem, we need a table of values first.

We shall choose 5 values for x which range from (0 to 10) in steps of 2.

The corresponding y values must be gotten by substituting these x values into the equation of the trip given above.

From the calculations done above, we have the coordinates of our graph to be:

(0, 3)

(2, 4)

(4, 5)

(6, 6)

(8, 7)

(10, 8)

Thus, we can create our table of values:

Thus, with this table of values, we can plot the graph. The plotted graph is shown below:

Therefore, the total number of miles you can travel with $20 is 34 miles

Answer:

171 \(in^2\)

19.5 \(in^2\)

Step-by-step explanation:

To find the area of a parallelogram, one uses the following formula,

\(A=(base)(hieght)\)

Substitute in the given values, and find the area of the parallelogram.

1.

Base = 16

Hieght = 11

 \(Area=(base)(height)\\= (11)(16)\\=176\)

2.

Base = 1.5

Hieght = 13

\(Area=(base)(hieght)\\=(1.5)(13)\\=19.5\)

The correct statements regarding the sum of \(1 + \sqrt{25}\) are given by:

Rational numbers are numbers that can be represented by fractions, such as integers and terminating or repeating decimals.

In this problem, we have the sum of two terms, one and the square root of 25, both of which are rational, as:

Hence the correct options are:

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Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Step-by-step explanation:

Step 1: Define

3(14 + x) = 57

Step 2: Solve for x

Answer:

x=5

Step-by-step explanation:

First multiply 3(14+x) = 42 + 3x

Now you have the equation 42 + 3x =57

Then subtract 42 from both sides

The equation would be 3x = 15

Divide 3 from each side to get the x value

15/3=5

So therefore your answer would be x = 5

Hope this helps!

Answer: 4(7-u)

Step-by-step explanation:

In order to factor, you have to find the GCF (Greatest Common Factor)

28:1, 28, 2, 14, 4, 7

4:1, 4, 2

The greatest common factor here is 4.

You can factor out 4 from this equation, therefore making it 4(7-u)

Answer:

The sentance you but then would be than which would be Hay más mesas en la cocina que en mi habitación but the word then would be entonces and example sentance is entonces iré allí which is then i will go over there

and than is que, an example sentace en lugar de que yo vaya allí which is rather than me going over there

Step-by-step explanation:

Answer:

Hi Alycia! The answer to your question is Hay más mesas en la cocina que en mi habitación

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

xD

The correct statement is: 11 - 6 = 5. To find the interquartile range (IQR) for set of data represented by box plot, we need to understand the components of the box-and-whisker plot and their relationship to IQR.

Given information:

The number line ranges from 1 to 15.

The whiskers range from 1 to 14.

The box ranges from 6 to 11.

A line divides the box at 9.5.

The IQR is the range of values within the box, representing the middle 50% of the data.

To calculate the IQR, find the difference between the upper quartile (Q3) and the lower quartile (Q1).

In this case, the upper quartile (Q3) is 11, and the lower quartile (Q1) is 6.

Calculate the IQR: Q3 - Q1 = 11 - 6 = 5.

Therefore, the correct statement is: 11 - 6 = 5. This finds the interquartile range for the set of data represented by the box plot.

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Answer:

\( D= 375 - (-150) m = 375m +150 m= 525 m\)

So then the distance between the submarine and the airplace is 525 m

Step-by-step explanation:

For this case we know that the submarine is 150 m below the sea level and the airplane is 375 m above the sea level and we want to find the difference between the heights and we got:

\( D= 375 - (-150) m = 375m +150 m= 525 m\)

So then the distance between the submarine and the airplace is 525 m

Answer:

\(2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}\)

Step-by-step explanation:

The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be \(y\). The magnitude of \(40\text{ m/s}\) will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is \(60^{\circ}\), we have:

\(\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}\)(Recall that \(\sin 60^{\circ}=\frac{\sqrt{3}}{2}\))

Now that we've found the vertical component of the velocity and launch, we can use kinematics equation \(v_f^2=v_i^2+2a\Delta y\) to solve this problem, where \(v_f/v_i\) is final and initial velocity, respectively, \(a\) is acceleration, and \(\Delta y\) is distance travelled. The only acceleration is acceleration due to gravity, which is approximately \(9.8\:\mathrm{m/s^2}\). However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.

What we know:

Solving for \(v_f\):

\(v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}\)

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

The longer rope is 31.9882ft long or 975cm.

The shorter rope is 31.0039ft long or 945cm.

Step-by-step explanation:

Convert 63ft to cm, which is 1920cm.

Divide 1920cm by 2. Which give 960cm. So if both sides were cut equally this would be the length but one is 15cm longer.

So we add 15cm to 960 cm, which is 975cm, thus thats the length for the longer rope.

To find the shorter one we just subtract 15cm from 960cm and we get 945cm.

Convert both final measurements back to ft if required.

To calculate the value of the reward function V(s), you can use the following equation:

V(s)=max a,b R(s,a,b) where,max a,b represents taking the maximum value over all possible actions a and b for state s.

The value of the reward function V(s) represents the maximum possible reward that can be obtained in state s. It is calculated by considering all possible actions a and b in state s and selecting the action pair that results in the maximum reward.

The player is placed in a random room with a randomly selected quest at the beginning of each game episode. The reward function R(s,a,b) provides the rewards for different combinations of actions a and b in state s. The goal is to find the action pair that yields the highest reward for each state.

By calculating the maximum reward over all possible action pairs for each state, we obtain the value of the reward function V(s). This value can be used to evaluate the overall potential reward or value of being in a particular state and guide decision-making in the game.

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