The unit vector that makes an angle θ= 2π/ 3 with a positive X-axis is
A)(-√3/2, -1/2)
B)(-√3/2, 1/2)
c)(√3/2, -1/2)
D)(√3/2, 1/2)

Answer:

5

Step-by-step explanation:

5x3=15

15+6=21

Hope this helped pls give brainliest

In this scenario, each man shakes hands with all the other men (excluding himself) and with all the women (excluding his spouse). Therefore, each man shakes hands with \($25$\) people in total.

Since there are \($13$\) married couples, there are \($13$\) men and \($13$\) women. Hence, the total number of handshakes involving men is \($13 \times 25 = 325$\).

As for the women, they do not shake hands with each other, so we only need to consider the handshakes involving men. Therefore, the total number of handshakes among these \($26$\) people is \($325$\).

If you would like to represent this solution using LaTeX code, you can use the following snippet:

\(\text{Number of handshakes involving men} \\\\= \text{Number of men} \times \text{Number of handshakes per man} \\\\= 13 \times 25 = 325\)

Therefore, the total number of handshakes among the \($26$\) people is \($325$\).

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If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is \(\frac{dP}{dt}=200\)

The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.

dy/dx = f(x)

Here “x” is an independent variable and “y” is a dependent variable

According to the question,

Size of population at t time = P(t)

Also given ,The differential equations have a linear growth in the size of the population.

So, The degree of the variable must be one. And the equation of the population will be quadratic.

Therefore , dP/dt = 200 tells us the rate change of population with respect to time.

A derivative of linear function is constant .

Hence , option B is correct.

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Answer:

416 cm^2

Step-by-step explanation:

The formula for the area of a trapezoid is:

\(\frac{(b1+b2)*h}{2}\)

where b1 and b2 are the bases and h is the height. We can plug what we have into the formula:

\(\frac{(14 + 38)*16}{2}\)

\(\frac{(52)*16}{2}\)

\(52*8\)

416 cm^2

Answer:

The answer is probably 10.50

(sorry if im wrong)

Step-by-step explanation:

Answer: The answer would be A: 10.50

Step-by-step explanation: 6.25 x 4 since it’s 25% this will get you 25 you then take 42% of 25 and get 10.50

Answer:

Mp= Rs 650

Dis= 2.5

Sp=?

Now,

Dis=Mp-Sp

Sp=Mp-Dis

=650-2.5

=647.5

Answer:

answer is 633.75 Rs.

Step-by-step explanation:

650- 2.5/ 100× 650 650-16.25 = 633.75 RS. the selling price of the item is 633.75 Rs

a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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= 3600 / 54000

= 0,06666

x 100

≈ 6,7%

Answer:

x=-7

if you were to simplify and do all the correct steps then you would be able to get the correct answer and I hope this helps you

Answer:

He should have said that his small brother had 100 small building bricks, but lost 5 in total now.

Answer:

{-1, 2, 47}

Choice B

Step-by-step explanation:

Function is g(x) = x² - 2

Domain is the possible set of x values and range is the set of function values for that domain

Here Domain = {- 2, - 1, 7}. This means these are values for which the function value g(x) exists

(Note this is not the entire domain, only a subset of the domain)

At x = - 2, g(x) = (-2)² - 2 = 4 - 2 = 2

At x = - 1, g(x) = (-1)² -2 = 1 -2 = -1

At x = 7, g(x) = (7)² -2 = 49 - 2 = 47

These are the corresponding range values for the given domain

Both domain and range sets are expressed from lowest to highest so we get range of g(x) as

{-1, 2, 47}

Choice B

The circumference of the circle is 6.28 metres.

The area of the circle is 3.14 m².

The circumference and the area of a circle can be found as follows:

area of the circle = πr²

where

Therefore, the diameter of the circle is 2 metres.

r = 2 / 2 = 1 metres

Hence,

area of the circle = 3.14 × 1²

area of the circle = 3.14 m²

Therefore,

circumference of the circle = 2πr

where

r = radius

circumference of the circle = 2 × 3.14 × 1

circumference of the circle = 6.28 metres

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Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)

The given parameters are:

Slope, m = 3/4

Point, (x,y) = (3,-2)

The equation of the line is calculated using:

y - y1 = m(x - x1)

Substitute the known parameters

y + 2= 3/4(x - 3)

From the question;

Andy's equation is y + 2 = 3/4(x - 9/4)

The above equation is different from the actual equation y + 2= 3/4(x - 3)

Hence, Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)

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I hope this helps you

Using relations in a right triangle, it is found that the distance between Q and T is given by:

\(h = 32\sqrt{2}\)

The relations in a right triangle are given as follows:

Researching the problem on the internet, it is found that:

Hence:

\(\sin{45^\circ} = \frac{32}{h}\)

\(\frac{\sqrt{2}}{2} = \frac{32}{h}\)

\(h = \frac{64}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\)

\(h = 32\sqrt{2}\)

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The calculated value of the expected number of spin is 216

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

Yellow or purple outcomes = 12

P(Yellow or purple) = 1/18

using the above as a guide, we have the following:

Yellow or purple outcomes = P(Yellow or purple) * Expected number of spin

So, we have

1/18 * Expected number of spin = 12

Rewrite as

Expected number of spin = 12 * 18

Evaluate

Expected number of spin = 216

Hence, the expected number of spin is 216

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The demand equation is given to be:

where p is the price and x is the number of units sold.

If the price per unit is $14.75, the number of units will be calculated as follows:

Subtracting 32 from both sides, we have:

Multiply both sides by -1:

Square both sides:

Subtract 1 from both sides:

Divide both sides by 0.0001:

The number of units sold will be 2,965,625 units.

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

The point-slope form of the line is y - (3/4) = 5(x - (3/4)).

The point-slope form of a line is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. To find the point-slope form of a line that has a slope of 5 and passes through the point (3/4, 3/4), we can plug in the values for the slope and the point into the point-slope formula. This gives us y - (3/4) = 5(x - (3/4)). This is the point-slope form of the line.

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You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

So the answer is that you are 18 years old this year.

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You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

"s1" = 1 + 8 = 9

"s2" = 1 + 9 = 10

9 = 3 * 10

So the answer is that you are 18 years old this year.

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The given sequence is 6, 4.8, 3.6, 2.4, 1.2, ...

To find the nth term of this sequence, we can observe that each term is obtained by multiplying the previous term by 0.8. Therefore, the common ratio between the terms is 0.8.

To find the nth term, we can use the formula: an = \(a1 * r^{n-1)},\) where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

For this sequence, a1 = 6 and r = 0.8.

For the 1st term (n = 1): a1 = 6

For the 2nd term (n = 2): a2 =\(6 * 0.8^{(2-1)}\) = 4.8

For the 3rd term (n = 3): a3 =\(6 * 0.8^{(3-1)}\) = 3.84

For the 4th term (n = 4): a4 = \(6 * 0.8^{(4-1)}\)= 3.072

For the 5th term (n = 5): a5 =\(6 * 0.8^{(5-1)}\) = 2.4576

Therefore, the nth term for this sequence is an = 6 * 0.8^(n-1), and the 1525th term would be a1525 = \(6 * 0.8^{(1525-1)}.\)

The given sequence is 13, 11, 9, 7, 5, ...

To find the nth term of this sequence, we can observe that each term is obtained by subtracting 2 from the previous term. Therefore, the common difference between the terms is -2.

To find the nth term, we can use the formula: an = a1 + d * (n-1), where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.

For this sequence, a1 = 13 and d = -2.

For the 1st term (n = 1): \(a1 = 13\)

For the 2nd term (n = 2): \(a2 = 13 + (-2) * (2-1) = 11\)

For the 3rd term (n = 3): \(a3 = 13 + (-2) * (3-1) = 9\)

For the 4th term (n = 4): \(a4 = 13 + (-2) * (4-1) = 7\)

For the 5th term (n = 5): \(a5 = 13 + (-2) * (5-1) = 5\)

Therefore, the nth term for this sequence is an = \(13 + (-2) * (n-1\)), and the 1525th term would be \(a1525 = 13 + (-2) * (1525-1).\)

The given explicit formula for the arithmetic sequence is nth = 65 - 100n.

To find the first five terms, we substitute n = 1, 2, 3, 4, and 5 into the formula:

For the 1st term (n = 1): \(a1 = 65 - 100 * 1 = -35\)

For the 2nd term (n = 2): \(a3 = 65 - 100 * 3 = -235\)

For the 3rd term(n = 3): \(a3 = 65 - 100 * 3 = -235\)

For the 4th term (n = 4): \(a4 = 65 - 100 * 4 = -335\)

For the 5th term (n = 5): \(a5 = 65 - 100 * 5 = -435\)

Therefore, the first five terms of this arithmetic sequence are: -35, -135, -235, -335, -435.

To find the 39th term, we substitute n = 39 into the formula:

\(a39 = 65 - 100 * 39 = 65 - 3900 = -3835\)

Therefore, the 39th term of this arithmetic sequence is -3835.

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Answer:

sec(π/6 - x) = R.H.S = 2/(√3cosx + sinx)  = L.H.S.

Step-by-step explanation:

sec(π/6 - x) = 1/cos(π/6 - x)

Using compound angle formula,

cos(A - B) = cosAcosB + sinAsinB where A = π/6 and B = x.

So, cos(π/6 - x) = cos(π/6)cosx + sin(π/6)sinx , cosπ/6 = √3/2 and sinπ/6 = 1/2

cos(π/6 - x) = cosπ/6cosx + sinπ/6sinx = (√3/2)cosx + (1/2)sinx

sec(π/6 - x) = 1/cos(π/6 - x)

= 1/(√3/2)cosx + (1/2)sinx = 2/(√3cosx + sinx)

= L.H.S

So, sec(π/6 - x) = R.H.S = 2/(√3cosx + sinx)  = L.H.S

Answer:

22= 2(pi)(r)(45/360)

28.01

C=176

Step-by-step explanation:

Each statement about integer is:

Statement A: If positive is subtracted from a negative integer, the difference is negative integer.

This statement is sometimes true.

If a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer. For example, if -5 is subtracted from -3, the difference is -8, which is a negative integer. However, if -3 is subtracted from -5, the difference is 2, which is a positive integer. The difference sign depends on which value is the bigger one.

Statement B: If a positive integer is subtracted from a positive integer, the difference is a positive integer.

This statement is sometimes true.

If a positive integer is subtracted from a positive integer, the difference can be a positive integer or a negative integer. For example, if 3 is subtracted from 5, the difference is 2, which is a positive integer. However, if 5 is subtracted from 3, the difference is -2, which is a negative integer.

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Answer:

YUH

Step-by-step explanation:

Answer:

you'll see...

Step-by-step explanation:

Given that the transformed graph is of function f(x) = (x + 2)^4 + 6 and the parent function g(x) = x^4

The transformed graph function g(x) was shifted two (2) units to the left and was translated six (6) units upward.

When the function is shifted to the right, the factor of x will be negative and when it's shifted to the left, the factor of x will be positive.

Therefore, function g(x) = x^4 is shifted 2 units to the left and translated 6 units upward to form f(x) = ( x + 2 )^4 + 6.

The constant of proportionality of y and x in the graph is given as follows:

k = 3/4.

In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:

k = y/x.

A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.

The marked point on the graph has the coordinates given as follows:

(4,3).

Meaning that the constant of proportionality of y and x in the graph is calculated as follows:

k = y/x = 3/4.

(division of the value of the y-coordinate by the value of the x-coordinate).

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Answer:

x =5

Step-by-step explanation:

Tangents from same external point have equal length.

KJ = LJ

4x - 1 = 2x + 9

Add 1 to both sides

4x = 2x + 9 + 1

4x  = 2x + 10

Subtract '2x' from both side

4x - 2x = 10

2x= 10

Divide both sides by 2

x = 10/2

x = 5

Answer:

82 inches squared

Step-by-step explanation:

7*3*2 = 42

7*2*2 = 28

3*2*2 = 12

42 + 28 + 12 = 82

Answer:

x = 4

Step-by-step explanation:

sin 30 = x/8

0.5 = x/8

x = 4