C=22°, a = 14 m, b = 8 m find area of ABC to the nearest tenth

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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The area of the triangle is 59.6\(m^2\)

Now, According to the question:

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

In the question, Area unit is not mentioned.

But i take the unit in meter.

Now, We have the given data is:

In triangle HPK:

K = 8 m

P = 14.9 m

To find the area of triangle.

We know that :

Area of Triangle is  = 1/2 × b × h.

A  = 1/2 × 8 × 14.9

A = 59.6 \(m^2\)

Hence, The area of the triangle is 59.6

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Answer:

\(y = 2 \sqrt{6} \)

Step-by-step explanation:

\( \frac{y}{ \sin(60) } = \frac{4 \sqrt{2} }{ \sin(90) } \\ \frac{y}{ \frac{1}{2} \sqrt{3} } = \frac{4 \sqrt{2} }{1} \\ y = 4 \sqrt{2} \times \frac{1}{2} \sqrt{3} \\ y = 2 \sqrt{6}\)

Answer: linear combo of terms involving x & y, with respective numbers determining their contribution to the expression

Answer:

answer is 2

Step-by-step explanation:

as you know the speed is calculated by dividing the distance travelled by time spent (s=d/t)

so we can write this as d/t=100

when u make d as the subject u get d=100t

Answer:

D: The maximum value is 0

Step-by-step explanation:

Choice A is true because the x-intercepts are shown on the graph and are both -2 and 2.

Choice B is true because the parabola intercepts the y axis at 2.

Choice C is true because the AoS runs down the vertex which happens to be on the point (0,2).

Choice D is false because this parabola has no maximum value (parabolas continue forever unless stated otherwise).

36/60

=0.6

60% is your answer

Answer:

1

Step-by-step explanation:

Any number raised to the power of 0 equals to 1

Step-by-step explanation:

Hey there!

Given;

\( {7}^{0} \)

The answer would be one (1).

Reason: Anything to the power "0" is 1.

So, 7^0 is 1.

Hope it helps...

The surface area and volume of cement block is  1336 in² and 880 in³

To find the total surface area of a cuboid, add the areas of all six faces. Suppose l, b and h be the length, breadth and height of a cuboid, then the total surface area will be 2(lb + bh + hl). The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

Surface area of given cement block is = 10×8×2+20×10×2+(20×8 - 6×4×3)×2 + 4×10×2×3 +6×10×2×3

= 160 + 400 + 176 + 240 + 360

= 1336 in²

Volume of cement block is 20 × 8× 10 - 3×6×4×10

= 1600 - 720

= 880 in³

Hence, the surface area and volume of cement block is  1336 in² and 880 in³

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Answer:

ll only

Step-by-step explanation:

The probability of getting a score of 80% or higher on a 5-question true/false quiz when guessing (with a 50-50 chance of being correct) on every question is 1/16, while the probability of getting a score of 80% or higher on a 20-question true/false quiz is 1/1048576.

        What is the probability of getting a score of 80% or higher on a 5-question true/false quiz when guessing (with a 50-50 chance of being correct) on every question

                  A quiz consists of 5 questions. A student guesses each of the questions. The probability of guessing a question correctly is 0.5.

        Therefore, the Probability of getting a score of 80% or higher is = Probability of getting 4 or 5 questions right. To get 4 out of 5, we have to consider all possibilities of choosing 4 out of 5 questions correctly. A number of ways of choosing 4 out of 5 questions correctly is 5.

       A number of ways of guessing the 5 questions is 2^5.

       Therefore, the probability of getting 4 out of 5 correct is 5/32. To get 5 out of 5, we have to consider only one possibility.

       A number of ways of guessing 5 questions is 2^5.

       Therefore, the probability of getting 5 out of 5 correct is 1/32.

        So, the probability of getting a score of 80% or higher = Probability of getting 4 or 5

questions right = 5/32 + 1/32 = 6/32 = 3/16.

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What if instead, the quiz has 20 questions,

           If the quiz has 20 questions, the probability of getting a score of 80% or higher is 1/2^20 = 1/1048576.

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Using the arrangements formula, it is found that there is a 0.0286 = 2.86% probability that all the girls are ahead of all the boys.

The number of possible arrangements of n elements is the factorial of n, that is:

\(A_n = n!\).

The total number of outcomes is the arrangement of 7 elements, hence:

T = 7! = 5040.

The desired number of outcomes is all girls(3!), then all boys(4!), hence:

D = 3! x 4! = 6 x 24 = 144.

Hence, the probability is:

p = D/T = 144/5040 = 0.0286.

There is a 0.0286 = 2.86% probability that all the girls are ahead of all the boys.

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The solution to the equation 2(t - 5) = 48 is t = 29.

To solve the equation 2(t - 5) = 48, we can use the following steps:

Distribute the 2 to the terms inside the parentheses:

2t - 10 = 48

Add 10 to both sides of the equation to isolate the variable term:

2t = 58

Divide both sides of the equation by 2 to solve for t:

t = 29

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To find the midpoint, we must take the sum of both values and then divide by two.

In this case, our values are -6 and 14

-6 + 14 = 8

8 / 2 = 4

B is located at 4 on the number line.

Answer:

\(y - 8 = \frac{5}{3}(x - 1)\)

Step-by-step explanation:

1) Use the slope formula, \(\frac{y_2 - y_1}{x_2 - x_1}\), and the given points to find the slope. \(x_1\) and \(y_1\) represent the x and y values of one point the line must intersect, and \(x_2\) and \(y_2\) represent the x and y values of another point the line must also intersect:

\(\frac{(3)-(8)}{(-2)-(1)}\)

= \(\frac{-5}{-3}\)

= \(\frac{5}{3}\)

2) Using the point-slope formula, \(y-y_1 = m (x - x_1)\), use the slope you just calculated and substitute it for m. Choose any of the two points given (I chose (1,8)) and substitute its x and y values for \(x_1\) and \(y_1\). Don't worry, the equation of the line is the same no matter which point you choose (unless the question specifies which one you need to choose):

\(y - 8 = \frac{5}{3}(x - 1)\)

Answer:

Let me explain to you. So this is basically like Long Division just your are multiplying the dividen by 10.

Step-by-step explanation:

Answer:

To be honest I think it is D

Step-by-step explanation:

Stochastic processes in finance are modeled using a formula such as the Geometric Brownian Motion equation, which is used to predict the random variations in asset prices and inform investor decisions.

Stochastic processes in finance are processes that are randomly determined, with the outcomes being uncertain. These processes are used to model financial markets, and are useful for forecasting future price movements. These processes are usually modeled using a formula, such as the Geometric Brownian Motion (GBM) equation:

dS = μSdt + σSdz

Where dS is the change in the price of an asset over a short time period, μ is the drift term (expected rate of return), S is the current price of the asset, dt is the time period, σ is the volatility, and dz is a random variable.

This equation is used to model the random variations of an asset’s price, and can be used to predict future price movements. By understanding the GBM equation and its parameters, investors can make more informed decisions when trading financial instruments.

Stochastic processes in finance are modeled using a formula such as the Geometric Brownian Motion equation, which is used to predict the random variations in asset prices and inform investor decisions.

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Complete question

What is the Geometric Brownian Motion equation and how is it used in stochastic processes in finance?

An equivalent expression for x to -3 power is x³. The power of a number is an expression representing the number of times it has to be multiplied by itself. Therefore, an equivalent expression for x^(-3) is 1 / x^3.

known as an exponent, or a power.The negative exponent means that the number is in the denominator, not in the numerator. A negative exponent is the opposite of a positive exponent, which represents multiplication. A negative exponent represents division.A negative exponent can be changed to a positive exponent by taking the reciprocal of the number and changing the exponent's sign.Example: If x is a number raised to -3 power then an equivalent expression would be `1/x³`. Also, if `x³` is given, the equivalent expression is `1/x³`.In summary, an equivalent expression for x to -3 power is x³.

An equivalent expression for x to the power of -3 can be obtained by using the concept of negative exponents. To rewrite x^(-3) in a different form, we can apply the rule that states x^(-n) is equal to 1 / x^n.

Using this rule, we can express x^(-3) as:1 / x^3

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The equivalent expression for `x` to the power of `-3` is `1/x³`.

A power in mathematics is a shorthand method of indicating that a number is multiplied by itself many times.In an exponential expression, the base indicates the number that is being multiplied repeatedly.

The exponent indicates how many times the base number should be multiplied.

If an exponent is negative, the number will be taken as its reciprocal, meaning that it will be inverted.

For example, `2⁻³` can be calculated as follows: `1 / 2³ = 1 / 8`.

Thus, for `x⁻³`, we can write its equivalent expression as follows:`x⁻³ = 1 / x³`

Therefore, the equivalent expression for `x` to the power of `-3` is `1/x³`.

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a) The partial derivative of tan(x + y) + cos z = 2 is ∂z/∂y = -sec²(x + y) / (1 - sin z).

b) The partial derivative of xlny + y²z + z² = 8 is  ∂z/∂y = -x / (2yz + y²)

To find the first partial derivatives of z implicitly, we differentiate both sides of the given equations with respect to the variables involved.

(a) For the equation tan(x + y) + cos z = 2:

Differentiating with respect to x:

sec²(x + y) * (1 + ∂z/∂x) - sin z * ∂z/∂x = 0

∂z/∂x = -sec²(x + y) / (1 - sin z)

Differentiating with respect to y:

sec²(x + y) * (1 + ∂z/∂y) - sin z * ∂z/∂y = 0

∂z/∂y = -sec²(x + y) / (1 - sin z)

(b) For the equation xlny + y²z + z² = 8:

Differentiating with respect to x:

ln y + x/y * ∂y/∂x + 2yz * ∂z/∂x = 0

∂z/∂x = -ln y / (2yz + x/y)

Differentiating with respect to y:

x/y + 2yz * ∂z/∂y + y² * ∂z/∂y = 0

∂z/∂y = -x / (2yz + y²)

These are the first partial derivatives of z obtained by differentiating implicitly with respect to the respective variables involved in each equation.

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Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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For k ≠ 1, the system has a unique solution, and for k = 1, the system has no solution. There is no value of k for which the system has infinitely many solutions.

To determine the value(s) of k for which the system has no solution, a unique solution, or infinitely many solutions, we will analyze the given system of linear equations:
1) kx + 2y = 4
2) 2x - 4y = -8
Step 1: Simplify the second equation:
Divide both sides of equation 2 by 2:
x - 2y = -4
Step 2: Compare the equations:
Now the system looks like this:
1) kx + 2y = 4
2) x - 2y = -4
Step 3: Determine the relationship between the equations:
a) If k ≠ 1, the equations represent two different lines, which will have a unique solution (intersection point).
b) If k = 1, the equations are multiples of each other:
1x + 2y = 4
1x - 2y = -4
In this case, the lines are parallel and never intersect, which means the system has no solution.
c) There is no value of k for which the system has infinitely many solutions since the given equations cannot represent the same line.
So, the answer is: For k ≠ 1, the system has a unique solution, and for k = 1, the system has no solution. There is no value of k for which the system has infinitely many solutions.

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Solution

- The area of a rectangle is

- The rectangular garden's area can thus be found by finding the product of its length 51/2 feet and its width 1 1/5 feet.

- This is done below:

Final Answer

The Area of the rectangular garden is 6.6 square feet

The correct statement regarding whether the graph is a one-to-one function is:

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

An one-to-one function is a function in which each output is related to only one input, that is, there are no horizontally aligned points.

These horizontally aligned points happen when an horizontal line is traced on the graph of the function, and crosses the function more than once.

From the graph of the function given by the image at the end of the answer, it can be seen that this line would cross the function twice for values of y between 0 and 2, hence the correct option is:

The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

The problem asks for the correct statement regarding the function given on the image at the end of the answer.

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Answer

A $15

Step-by-step explanation: Babyton my name

Answer:

49 degrees

Step-by-step explanation:

Complementary angles are 2 angles that add up to 90 degrees. Subtract 41 from 90 to get 49 to find the other angle.

Hope this helped!