sum of (3+3i)+(8+7i)

The two expressions are not equivalent.

The expression "fraction numerator log 25 over denominator log 3 end fraction" is equal to log 25 divided by log 3.

This is because the numerator represents the logarithm of 25 and the denominator represents the logarithm of 3, resulting in the ratio of the two logarithms.

On the other hand, the expression "fraction numerator ln 25 over denominator ln 3 end fraction" is not equal to log subscript 3 25. The numerator represents the natural logarithm (ln) of 25, and the denominator represents the natural logarithm of 3.

The natural logarithm uses the base e (2.71828), whereas the logarithm with subscript 3 uses the base 3.

Therefore, these two expressions are not equivalent.

log 25 divided by log 3 is equal to log subscript 3 25.

fraction numerator ln 25 over denominator ln 3 end fraction is not equal to log subscript 3 25.

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Answer: Order of operations

The amplitude of the function is 1/2, and the period of the function is π.

We know that,

The general form of a sine function is,

⇒ f(x) = A sin(Bx + C) + D,

where:

A is the amplitude

B is the angular frequency or 2π divided by the period

C is the horizontal shift

D is the vertical shift

Now, We have;

The function is,

⇒ f (x) = 1/2 sin 2x

Hence, By Comparing this to the function f(x) = 1/2 sin 2x, we can see that:

A = 1/2, which means that the amplitude of the function is 1/2.

B = 2, which means that the angular frequency is 2,

Or equivalently, the period of the function is 2π/2 = π.

Therefore, the amplitude of the function is 1/2, and the period of the function is π.

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The common ratios of the geometric series is 2 and the number of terms is 9.

The first term of the geometric series is 3, the last term is 768. The sum of the term is 1533.

Therefore, the common ratio and the number of terms can be found as follows:

aₙ = arⁿ⁻¹

where

Therefore,

768 = 3rⁿ⁻¹

rⁿ⁻¹ = 256

rⁿ / r = 256

rⁿ = 256r

Therefore, let's use the sum formula,

1533 = a(rⁿ - 1) / r - 1

1533 = 3(rⁿ - 1) / r - 1

511 = (rⁿ - 1) / r - 1

cross multiply

511r - 511 = rⁿ - 1

511r - 510 = rⁿ

511r - 510 = 256r

-510 = 256r  -511r

-510 = -255r

Therefore,

r = -510 / -255

r = 2

Hence,

common ratio = 2

Hence,

768 = 3(2)ⁿ⁻¹

256 = (2)ⁿ⁻¹

2ⁿ / 2 = 256

cross multiply

2ⁿ = 512

2ⁿ = 2⁹

n = 9

Therefore,

number of terms = 9

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The period and the amplitude of the given function is 4π and 2.

To find the amplitude and period of a function using its graph, you can follow these steps:

Identify the highest point and the lowest point on the graph. These points represent the maximum and minimum values of the function.

The amplitude is equal to half the difference between the maximum and minimum values of the function. In other words, it is the distance from the midline (average value) of the function to either the highest or lowest point on the graph.

Locate two consecutive peaks or troughs on the graph. A peak is a point where the graph reaches its highest point, and a trough is a point where the graph reaches its lowest point.

Measure the horizontal distance between these two consecutive peaks or troughs. This distance is called the period of the function.

If the distance between the two peaks or troughs is not explicitly marked on the graph, you can estimate it by counting the grid lines or using the scale of the x-axis.

Hence the period and the amplitude of the given function is 4π and 2.

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The probability of drawing a King and then another King is 1/221. Hence, the correct option is d. 1/221.

Number of favorable outcomes: There are 4 Kings in a deck of 52 playing cards. After drawing the first King, there will be 3 Kings remaining in the deck.

Number of possible outcomes: After drawing the first card, there will be 51 cards left in the deck. For the second card, any one of the remaining 51 cards can be drawn.

Thus, the probability can be calculated as follows:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

           = (4/52) * (3/51)

           = 12/2652

           = 1/221

Therefore, the probability of drawing a King and then another King is 1/221. Hence, the correct option is d. 1/221.

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Answer: 113.04

Step-by-step explanation:

btw, the question is

What's the surface area of a circle with a radius of 6.

Grammar XD

Anyways, the formula for an area of a circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is approx 3.14

6 square is 36

36*3.14 is 113.04

Please mark brainliest! :)

The transformation of f(x) to g(x) is (b) a horizontal transformation of function f 4 units left

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

The functions f(x) and g(x)

Where we have

f(x) = x³

g(x) = (x + 4)³

So, we have

Difference = 4 - 0

Evaluate

Difference = 4

This means that the transformation of f(x) to g(x) is f(x) is shifted left 1 unit to g(x).

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Answer:

D, E, and C would be regulars, and A and B would be irregulars.

Step-by-step explanation:

It asks to define whether a shape is a regular polygon, irregular polygon, or neither. An irregular polygon is a polygon with no similar sides while a regular polygon is a shape with the same length sides. D, E, and C would be regulars, and A and B would be irregulars. If the shape is open, then it is not a polygon.

Answer:

Step-by-step explanation:

An irregular polygon is a polygon that does not have equal sides or equal angles. In other words, its sides and angles are not the same throughout the shape. The irregularity can occur in terms of side lengths, angles, or both. Each side of an irregular polygon may have a different length, and the interior angles may vary as well.

A polygon is a closed two-dimensional shape with straight sides. It is formed by connecting line segments called edges or sides.

The following would be filled in the boxes using the distributive property:

(4 × 3 ) + (4 × 7 )

The distributive property is a mathematical concept that describes how multiplication distributes between addition and subtraction. It provides a rule for word expansion and expression condensing.

The distributive property allows us to factor polynomials, simplify expressions, and solve equations in algebra and arithmetic more quickly.

Having said that,

4 × (3 + 7) =(4 × 3 ) + (4 × 7 )

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The number of tickets abby older brother win 84 tickets

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

Abby = 52 tickets

Abby older brother = 32 tickets than her

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

Abby older brother = 32 tickets + Abby

substitute the known values in the above equation, so, we have the following representation

Abby older brother = 32 tickets + 52 tickets

Evaluate

Abby older brother = 84 tickets

Hence, abby older brother win 84 tickets

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The correct statement is: ii. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space. Option D

We have from the information given that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Then , we should know that;

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The position vector of point P, MP, is given by MP = 6i - j.

To find the position vector of point P, which is the midpoint of NO, we can use the midpoint formula.

The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

Midpoint (Mᵖ) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's find the position vector of point P using the given information:

Point N: N = 4i - 5j

Point O: O = 8i + 3j

Using the midpoint formula, we can find the coordinates of point P:

x-coordinate of P: (x₁ + x₂) / 2 = (4i + 8i) / 2 = 12i / 2 = 6i

y-coordinate of P: (y₁ + y₂) / 2 = (-5j + 3j) / 2 = -2j / 2 = -j

Therefore, the position vector of point P, MP, is given by:

MP = 6i - j

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The image of point (-1, 3) after the translation by vector (5, 2) is the point (4, 5).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They

The image of D(-1, 3) along the translation vector (5, 2) can be obtained by adding the vector (5, 2) to each point in D(-1, 3).

This results in the translated point

D(-1, 3) → (-1+5, 3+2) → D(4, 5).

Therefore, the image of point (-1, 3) after the translation by vector (5, 2) is the point (4, 5).

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The equation of graph is y= 1√(x-5) - 2 .

The equation of graph is y= 1√(x+3) + 4.

We have to write the equation in the form of y= a√(x-h) + k

From the graph 1, the value of h and k is

h = 5

k = -2

and, the value of a is

= rise/ run

= 1/1

= 1

So, the equation of graph is y= 1√(x-5) - 2

From the graph 1, the value of h and k is

h = -3

k = 4

and, the value of a is

= rise/ run

= 1/1

= 1

So, the equation of graph is y= 1√(x+3) + 4.

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The basic charge refers to a fixed fee or cost that is charged for a service or utility regardless of the actual usage or consumption.

In the given context, the term "basic charge" refers to a fixed fee or cost that is charged for a particular service or utility regardless of the actual usage or consumption.

It is a standard or minimum charge that is applied uniformly to all customers or users, typically to cover the basic infrastructure or administrative costs associated with providing the service.

The basic charge is often separate from any variable charges based on usage or additional services.

It is a recurring fee that customers are required to pay regardless of their specific usage level.

The purpose of the basic charge is to ensure a baseline revenue for the service provider and to contribute to the maintenance and operational costs of the service infrastructure.

It provides a consistent source of income and helps to distribute the costs among all customers fairly.

The basic charge is usually set at a fixed amount or a predetermined rate and may vary depending on the type of service or utility being provided, such as electricity, water, internet, or telecommunications.

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The complete question may be like: Define the basic unit of currency in the United States and explain its significance in the context

The equation of the axis of symmetry of the parabola is equal to x = 4.

In this problem we find the representation of a parabola whose axis of symmetry is parallel with y-axis. The axis of symmetry passes through the vertex of the parabola. The definitions of the vertex and the axis of symmetry are, respectively:

Vertex

(x, y) = (h, k)

Axis of symmetry

x = h

If we know that h = - 4, then the equation of axis of symmetry is x = 4.

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Answer: P(even) = 1/2

Step-by-step explanation:

in the data set, 1 2 3 4, only 2 are even out of the 4

2/4 = 1/2

P(even) = 1/2

The value of x is:

x = -32/3

Here, we have,

EF = ½(BC + AD) => Trapezoid Midsegment theorem

Substitute

21 = ½(24 + (-3x-14))

21 = ½(10 -3x)

Multiply both side by 2

42 = 10 -3x

Collect like terms

- 3x = 42 - 10

-x = 32/3

Divide both sides by -1

x = -32/3

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The value of h(8)-2.f(3) from the given functions is 16.

f(x)= -x²+8x-11, g(x)=14-2/3 x and h(x)=-x-7.

Here,

f(-4)-f(1)= -(-4)²+8(-4)-11

= -16-32-11

= -59

g(9)+h(-14)

= 14- 2/3 (9) + [-(-14)-7]

= 14-6+7

= 15

h(8)-2.f(3)

= -8-7-2×-(3)²+8×3-11

= -15-2×(-9)+24-11

= -15+18+24-11

= -26+42

= 16

1/2 g(-6)+f(-2)

= 1/2 [14-2/3 (-6)]+[-(-2)²+8(-2)-11

= 1/2 [14+4]+[-4-16-11]

= 9-31

= -22

Therefore, the value of h(8)-2.f(3) from the given functions is 16.

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The equation of the axis of symmetry of the quadratic function in this problem is given as follows:

x = -4.

The equation of the axis of symmetry of the quadratic function is a vertical line given as follows:

x = xv.

In which xv is the x-coordinate of the vertex of the quadratic function.

The vertex of a quadratic function is the turning point of the quadratic function, hence it has a x-coordinate of 4 and the equation of the axis of symmetry of the quadratic function in this problem is given as follows:

x = -4.

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The point (x, y) = (- 1, 2) (Point A) is the solution to the system of linear equations.

In this problem we find the representation of two linear equations set on Cartesian plane, the system consists in two equations with two variables. We are asked to find the solution to the system of linear equations. Graphically speaking, the solution to the system of linear equations is represented by a point of intersection.

Then, by direct inspection, we find that the solution to the system of linear equations is (x, y) = (- 1, 2). (Point A)

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Answer:

2/5

Step-by-step explanation:

4 raspberry / 10 total

4/10

2/5

The missing length x = 18. 4

To determine the value of the missing side, we need to take note of the following;

The different trigonometric identities are expressed as;

The sine identity is represented with the fraction;

sin θ = opposite/hypotenuse

From the information given, we have;

θ = 61 degrees

x is the opposite side

21 is the hypotenuse

Substitute the values, we have;

sin 61 = x/21

cross multiply the values, we have;

x = 0.8746(21)

Multiply the values, we have;

x = 18. 4

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The complete question:

Find the missing length x. Round your answer to the nearest tent

theta = 61°

Hypotenuse = 21

Opposite = X

The domain and the range of the graph are

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

(-2, -1), (0, 1), (2, 3)

The above are a list of ordered pairs

The rule of a function is that

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

Domain = (-2, 0, 2)

Range = (-1, 1, 3)

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The interquartile range for the data-set in this problem is given as follows:

IQR = 22.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

The data-set in this problem has 10 elements, divided into two halves as follows:

The first quartile is the middle element of the first half, hence it is given as follows:

45.

The third quartile is the middle element of the second half, hence it is given as follows:

67.

Then the IQR is given as follows:

IQR = 67 - 45

IQR = 22.

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Answer:

Rounded to the nearest hundredths, the volume of the cylinder is approximately 58.91 cm^3.

Step-by-step explanation:

To find the volume of a cylinder, you need to know its radius (r) and height (h). In this case, the radius is given as 5 cm and the height is 0.75 cm.

The formula for the volume of a cylinder is:

V = π * r^2 * h

where π is a mathematical constant approximately equal to 3.14159.

Let's substitute the given values into the formula:

V = π * (5 cm)^2 * 0.75 cm

V ≈ 3.14159 * (25 cm^2) * 0.75 cm

V ≈ 58.909 cm^3

Answer: 0.6156 or in fraction form, 62%

Step-by-step explanation: To find the probability that at least one of the two people does not go on vacation, we subtract the probability that both of them go on vacation from 1. The probability that both go on vacation is 0.62 * 0.62 = 0.3844.

Therefore, the probability that one or both of them does not go on vacation is 0.6156, or about 62%.

Answer: 0.2356 and 0.1444

Step-by-step explanation:

62% of Americans go on Vacation

So out of 100 Americans, 62 go on vacation

The chance of one of them NOT going on vacation is 100-62 or 38%, however, the other person has to go on vacation, so it's 38%*62% or 0.2356, approx 40%*60% or 0.24

The chance of both of them do not go on vacation is 38%*38%, or 0.1444 or approx 40%*40% or 0.16 (very rough calculating)

Answer:

23.90 years

Step-by-step explanation:

To find the half-life of a radioactive substance, we can use the formula:

[tex]\boxed{\begin{minipage}{10 cm}\underline{Half-life formula}\\\\$ t_{1/2} =\dfrac{\ln 2}{k}$\\\\where:\\\\ \phantom{ww}$\bullet$ $t_{1/2}$ is the half-life. \\ \phantom{ww}$\bullet$ $k$ is the decay constant (percentage decay rate per year)\\ \end{minipage}}[/tex]

In this case, the decay constant is 2.9% or 0.029 (expressed as a decimal). Therefore, substitute k = 0.029 into the formula:

[tex]t_{1/2} =\dfrac{\ln 2}{0.029}[/tex]

[tex]t_{1/2} =23.9016269...[/tex]

[tex]t_{1/2} =23.90\; \sf years\; (2\;d.p.)[/tex]

Therefore, the half-life of the radioactive substance, rounded to 2 decimal places, is approximately 23.90 years.

Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!