Prove, by mathematical induction for all integers n ≥ 2.
(1 - 1/2) (1 - 1/3) (1 - 1/4)...(1 - 1/n) = 1/n

Answer:

Answer B is correct

Step-by-step explanation:

This is a trapezium.

The formula to find the area of a trapezium is,

1/2 ( Sum of the parallel sides ) × height

Let us find it now.

\(\sf \frac{1}{2}*(38+18)*16 \\\\\sf \frac{1}{2}*56*16 \\\\\sf \frac{1}{2}*896\\\\448cm^2\)

Answer:

a right angle

Step-by-step explanation:

Starting the formation of groups of four bits at the binary point instead of the left end of the number facilitates conversion between binary and decimal numbers, improves organization and readability, simplifies calculations, and aligns the binary number with its decimal equivalent.

When working with binary numbers, it is more common and practical to start forming groups of four bits at the binary point rather than the left end of the number.

The binary point is the equivalent of the decimal point in a binary number system. Starting at the binary point allows for easier conversion between binary and decimal numbers, as well as better organization and readability of large binary numbers.

Forming groups of four bits at the binary point allows us to convert each group into a decimal equivalent. These decimal values can then be added together to obtain the final decimal representation of the binary number.

By starting at the binary point, we can work with smaller groups of bits at a time, which simplifies calculations and reduces the chances of errors. This approach also enables us to track the place value of each group more efficiently.

Additionally, starting at the binary point helps in aligning the binary number with its decimal equivalent. This alignment is crucial when performing arithmetic operations such as addition, subtraction, multiplication, or division on binary numbers.

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Answer:

Si se invierten S/10 000 en acciones del tipo A, ¿cuánto de ganancia se obtendrá al cabo de seis meses?

$10,000 x 0.5% x 6 = $300

¿Cuánto se debe invertir en acciones del tipo B para que al cabo de seis meses se obtenga una ganancia de S/876,00?

interes compuesto = 0.9% trimestral

X · (1 + 0.009)² = X + $876

1.018081X = X + $876

0.018081X = $876

X = $876 / 0.018081 = $48,448.65

¿A qué tasa de interés compuesto anual la utilidad en un año es la misma para los dos tipos de acciones?

$1 x 106% = $1 x (1 + i)⁴

$1.06 = $1 x (1 + i)⁴

(1 + i)⁴ = $1.06 / $1 = 1.06

⁴√(1 + i)⁴ = ⁴√1.06

1 + i = 1.01467

i = 0.01467 = 1.467% trimestral

0.489% mensual capitablizable trimestralmente

Answer:

C

Step-by-step explanation:

Well it would be C/3Thrd because you are repeating 3(x-1) aren't you?

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

2m = 112

Step-by-step explanation:

monday = m

Tuesday = m - 112

therefore total = m + (m -112)

answer = 2m = 112

Answer:

C orB looks like it

Step-by-step explanation:

Answer:

3<40

since this is saying 3 is lower than 40

Answer:

it is 6.4

Step-by-step explanation:

hope this helps

plz tell me if I am right thank u

Answer:

C.

Step-by-step explanation:

None of these numbers have perfect square roots, but \(\sqrt{39}\) is the closest to the point on the number line. The square root of \(\sqrt{39}\) is 6. 244997998398398. Rounding that number we get approximately 6.3.

Answer:

x = 32.7

Step-by-step explanation:

High school geometry can throw you off really hard. One year, you're learning about transformations, then the next you have to write PROOFS. But it's alright because we can take this problem.

We can observe that we have a right triangle. Sadly, we can't use the Pythagorean Theorem to solve for x because we're not given the length of the hypothenuse. But, we could use one other thing: trigonometric functions.

Trigonometric functions are functions that relate sides of a triangle to an angle θ on that triangle. The three main trigonometric functions are sine, cosine, and tangent, and all three are defined as follows:

Sine θ  = Opposite / Hypothenuse

Cosine θ = Adjacent / Hypothenuse

Tangent θ = Opposite / Adjacent

You can memorize this by remembering the phrase: SOHCAHTOA. Note that an angle is opposite to a side if it's directly opposite from it and is adjacent to a side if the side is not the opposite side nor the hypothenuse, the longest side on a right triangle.

So, how do we use trigonometry to solve the problem.

First, let's find our θ, the angle of our triangle. We can see that we have an angle of 61 degrees, so we can say that θ is 61 degrees. We can also say that θ is opposite to the side of 59 and adjacent to the side of x. We can put this into an equation and solve for x.

IMPORTANT: IF YOU ARE USING DEGREES, SET YOUR CALCULATOR TO DEGREES AND NOT RADIANS WHEN DOING CALCULATIONS.

tan θ = opposite / adjacent

tan(61) = 59 / x

x = 59 / tan(61)

x = 32.7

Therefore, we can say that x = 32.7.

Hey... The answer is A

Answer:

false

Step-by-step explanation

:

Answer:

x = cost of a chair = £22

y = cost of a table = £65

£765

Step-by-step explanation:

Let

x = cost of a chair

y = cost of a table

4x + 2y = 218 (1)

6x + 7y = 587 (2)

Multiply (1) by 6 and (2) by 4

24x + 12y = 1,308 (3)

24x + 28y = 2,348 (4)

Subtract (3) from (4) to eliminate x

28y - 12y = 2,348 - 1,308

16y = 1,040

y = 1,040/16

y = 65

Substitute y = 65 into (1)

4x + 2y = 218 (1)

4x + 2(65) = 218

4x + 130 = 218

4x = 218 - 130

4x = 88

x = 88/4

x = 22

x = cost of a chair = £22

y = cost of a table = £65

Find the total cost of buying twenty chairs and five tables

20x + 5y

Substitute the values of x and y

20x + 5y

= 20(22) + 5(65)

= 440 + 325

= £765

Answer:

y - (-9) = -10(x - 1)

Step-by-step explanation:

(1, -9) and (-10, 101)

Slope:

m=(y2-y1)/(x2-x1)

m=(101+9)/(-10-1)

m=110/(-11)

m = -10

Point-slope:

y - y1 = m(x - x1)

y - (-9) = -10(x - 1)

Answer: 16, 5 , 8.

Step-by-step explanation:

The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.

To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:

s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

where s is the arc length, t is the parameter, and (x, y, z) is the position vector.

We want the arc length to be 2, so we can set up the following equation:

2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

We can then choose a function for each component of the position vector, such as:

x = t

y = t²

z = sin(t)

We can now find the derivatives with respect to t:

dx/dt = 1

dy/dt = 2t

dz/dt = cos(t)

We can substitute these into the arc-length formula:

2 = ∫√(1)² + (2t)² + (cos(t))² dt

Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.

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The question is -

Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

The correct answer is:

(a) about 4% of the variation in y has been explained by the model.

The answer is (a) about 4% of the variation in y has been explained by the model.

The coefficient of determination (R-squared) is given as 0.03579295, which represents the proportion of the total variation in the dependent variable (calculus achievement scores) that is explained by the independent variable (algebra placement test scores) in the model.

Since R-squared is the square of the correlation coefficient (multiple R), we can also interpret the value of multiple R as the correlation between the two variables. In this case, multiple R is given as 0.18919025, indicating a weak positive correlation between the two variables.

The adjusted R-squared is negative (-0.2856094), which suggests that the model is not a good fit for the data. However, the question specifically asks for the proportion of variation in the dependent variable that is explained by the model, which is represented by R-squared. Therefore, the answer is (a) about 4% of the variation in y has been explained by the model.

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Answer:  f(x)= 2x -3

Step-by-step explanation:

Using the given information we can come up with two points that will be use to find the slope and y-intercept.  

If you input 0 you get -3  so the point will be (0,-3)

If you input 7  you get 11  so the point will be (7,11)

Now use the points to find the difference in their y coordinates and divide it by the difference in their x coordinates to find the slope.

y coordinates:  -3 - 11 = -14

x coordinates:  0 - 7 = -7

  -14/-7 = 2

Since the slope is two, we will use the slope intercept formula (y = mx +b) to find the b which is the y intercept.

Use one of the points and input its x and y coordinates into the formula including the slope to solve for b.

-3= 2(0) +b

-3 = 0 + b

b = -3  

f(x) is the same as y in the formula, meaning that the equation will be  

 f(x) = 2x -3

In other words, in 100 tyre rotations, the vehicle will have travelled 7,854 inches, or roughly 196.06 feet or 59.79 metres.

The amount of rotations around a central point or axis that a shape or object undergoes is referred to in mathematics as the order of rotation. For illustration, a shape with a 180-degree revolution about its centre has an order of rotation of 2. Similar to this, a shape rotated by 120 degrees has an order of revolution of 3. The idea of rotational symmetry, which describes a property of some shapes and objects that enables them to appear the same after a certain amount of rotation, and the order of rotation are closely related concepts.

given

The circumference of the tyre, which is determined by the following calculation, equals the distance covered by the vehicle in one rotation of its tyres.

C = πd

where the tire's width is d and its circumference is C. Using the tire's circumference of 25 inches as a plug-in, we obtain:

C is 25 times 78.54 inches.

As a result, one tyre rotation on the vehicle will cover a distance of 78.54 inches.

We can easily multiply the distance covered by one tyre rotation by 100 to determine how far the car will drive in 100 rotations:

78.54 inches per revolution times 100 rotations equals 7,854 inches of distance travelled.

In other words, in 100 tyre rotations, the vehicle will have travelled 7,854 inches, or roughly 196.06 feet or 59.79 metres.

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An isosceles triangle is a triangle which has two sides of equal length.

Since it has two sides of equal length, the isosceles triangle has two equal base angles.

If one base angle is 67.5º then the other base angle has to be 67.5º too.

For any triangle, the sum of all internal angles equals 180º. Let's say the unknown angle is x, then:

x + 67.5º + 67.5º = 180º

Let's solve for x:

x = 180º - 67.5º - 67.5º

x = 180º - 135º

x = 45º

Answer: the measure of the vertex angle is 45º.

To determine who has run the shortest distance, we need to compare the distances each person has run.

Let's assume that the total distance of the race is "x" units.

Zac has run 1/2 of the race, which is equal to (1/2)x units.

Amy has run 3/4 of the race, which is equal to (3/4)x units.

Harry has run 1/4 of the race, which is equal to (1/4)x units.

To compare the distances, we can convert the fractions to decimals:

Therefore, Harry has run the shortest distance, as he has only run 0.25x units, which is less than the distances run by both Zac and Amy.

Alternatively, we can also compare the fractions directly by finding a common denominator. The common denominator of 2, 4, and 8 (the denominators of 1/2, 3/4, and 1/4) is 8.

Again, we can see that Harry has run the shortest distance, as he has only run 2/8 or 1/4 of the race, which is less than the distances run by both Zac and Amy.

Answer: Rolling a die and obtaining a number follows a binomial distribution.

Expected value of binomial distribution is

E[X]=np

where n is number of toss and p is probability of obtaining the number.

Therefore here the expected value of obtaining a number 4 is:

E[X]=900∗16=150

Step-by-step explanation:

It is expected that a number greater than 4 will be rolled 300 times

The sample space of a die is:

S = {1,2,3,4,5,6}

The probability of obtaining a number greater than 4 is:

\(p = 2/6\)

\(p = 1/3\)

In 900 rolls, the expected number of number greater than 4 is:

\(E(x) = p *n\)

This gives

\(E(x) = 1/3 *900\)

\(E(x) =300\)

Hence, it is expected that a number greater than 4 will be rolled 300 times

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(a) The statement is true.

Proof: By definition, a rational number is any number that can be expressed as the quotient of two integers. Let's consider two rational numbers, a and b, where a = p/q and b = r/s, where p, q, r, and s are integers and q ≠ 0 and s ≠ 0.

Now, let's examine the sum of a and b: a + b = (p/q) + (r/s).

We can find a common denominator by multiplying the denominators: a + b = (ps)/(qs) + (rq)/(sq).

Combining the fractions with the common denominator, we have: a + b = (ps + rq)/(qs).

Since p, q, r, and s are all integers, their products and sums are also integers. Therefore, the numerator (ps + rq) and the denominator (qs) are both integers. This means that a + b is expressed as the quotient of two integers, making it a rational number.

Hence, the statement is true.

(b) The statement is true.

Proof: Let's consider an integer, n, and a rational number, a = p/q, where p and q are integers and q ≠ 0.

The sum of n and a can be expressed as: n + a = n + (p/q).

We can rewrite n as the fraction n/1: n + a = (n/1) + (p/q).

To find the common denominator, we multiply the denominators: n + a = (nq)/(1q) + (p1)/(q1).

Combining the fractions, we have: n + a = (nq + p)/(q1).

(c) The statement is false.

Counterexample: Consider the irrational numbers √2 and -√2.

Both √2 and -√2 are irrational because they cannot be expressed as the quotient of two integers, and they are distinct from each other.

However, the product of √2 and -√2 is (-√2) * (√2) = -2, which is a rational number since it can be expressed as the quotient of two integers (-2/1).

Therefore, the product of two distinct irrational numbers can be rational, which contradicts the statement. Hence, the statement is false.

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Answer: 1/3

Step-by-step explanation:

Number of red marbles = 5

Number of blue marbles = 9

Number of yellow marbles = 8

Number of and black marbles = 6

Total number of marbles = 28

If Taylor pulled out a yellow one and didn't replce it, there'll be 27 marbles left since one has been removed, then the probability of picking blue marbles will be:

= Number of blue marbles / Total marbles

= 9 / 27

= 1/3

The probability of picking a blue marble is 1/3.

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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The equation is in terms of cosine, we can use the inverse cosine function to find the value of x. Therefore, x = arccos(-9/16), where arccos is the inverse cosine function. The solution to the equation is x = arccos(-9/16), and this value can be expressed in radians.

In the first problem, we are asked to verify the identity sin(x/2 - x) = cos(x). By simplifying the expression step by step, we can confirm whether the identity holds.

Starting with sin(x/2 - x), we can use the angle subtraction formula for sine to rewrite it as sin(x/2)cos(x) - cos(x/2)sin(x). Simplifying further, we have cos(x)sin(x/2) - cos(x/2)sin(x).

Using the double-angle formula for sine, sin(2θ) = 2sin(θ)cos(θ), we can rewrite sin(x/2) as 2sin(x/4)cos(x/4). Substituting this into our expression, we get cos(x) * 2sin(x/4)cos(x/4) - cos(x/2)sin(x).

Now, using the double-angle formula for cosine, cos(2θ) = cos²(θ) - sin²(θ), we can rewrite cos(x/2) as cos²(x/4) - sin²(x/4). Substituting this into our expression, we have cos(x) * 2sin(x/4)cos(x/4) - (cos²(x/4) - sin²(x/4))sin(x).

Expanding and simplifying this expression, we get 2sin(x)cos²(x/4) - sin(x)sin²(x/4) - cos²(x/4)sin(x) + sin³(x/4).

Finally, using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we can simplify the expression to cos(x), which matches the right-hand side of the identity. Therefore, we have verified the identity sin(x/2 - x) = cos(x).

In the second problem, we are asked to solve the equation 17cos(x) + 9 - cos(x) = 0. By combining like terms, we have 16cos(x) + 9 = 0.

Next, we can isolate cos(x) by subtracting 9 from both sides, resulting in 16cos(x) = -9.

Finally, we solve for cos(x) by dividing both sides of the equation by 16, giving us cos(x) = -9/16.

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Answer:

60

Step-by-step explanation:

what am i supposed to answer frl