A complex number is a number that can be written in the form a bi, where a and b are real numbers. in the complex number 4 2i, 4 is the part. in the complex number 4 2i, 2 is the part.

Option A is the correct answer because the missing step in the two column proof is;

Statement: XW/UT = XV/UV Reason: Corresponding sides of similar triangles are proportional

Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. Thus, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, we see from the two column proof that ΔTVU ∼ ΔWVX. This means that corresponding sides of both triangles are proportional or have corresponding proportions.

Thus, we can say that;

XW/UT = XV/UV

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If a circle graph was constructed from the results, the lake activity that has a central angle of 54° is A. Kayaking.

The central angle of each lake activity is computed as the proportion of the total number of campers in degrees.

A circle has 360°.  Proportionately, this total is divided among the lake activities according to the number of campers who participated.

Lake Activity             Number              Degrees

                              of Campers

Kayaking                     15                          54° (15/100 x 360°)

Wakeboarding            11                          40° (11/100 x 360°)

Windsurfing                 7                          25° (7/100 x 360°)

Waterskiing                13                          47° (13/100 x 360°)

Paddleboarding        54                        194° (54/100 x 360°)

Total number           100

Thus, Kayaking, proportionately, has a central degree of 54°.

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An algebraic expression which could equal n for some integer t include the following: C. 4t - 1.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1)

Since the remainder is equal to three (3) when a positive integer n is divided by 4, we would write an algebraic expression for the word problem and then evaluate it as follows;

n = 4t + 3

n = 4(t - 1) + 3

n = 4t - 4 + 3

n = 4t - 1.

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When a positive integer n is divided by 4, the remainder is 3. Which of the following could equal n for some integer t?

(A) 4t +2

(B) 4t

(C) 4t - 1

(D) 4t - 2

(E) 4t - 3

The sampling distribution of the sample mean c. is the probability distribution showing all possible values of the sample mean. The standard error of the proportion will become larger as d. p approaches .5

The sampling distribution of the sample mean is the probability distribution of the possible values of the sample mean, given a certain sample size and population distribution. It is a theoretical construct that describes how the sample mean is likely to vary across different samples of the same size, drawn from the same population. The sampling distribution of the sample mean is approximately normal, with the mean equal to the population mean and a standard deviation known as the standard error.

The standard error is a measure of the variability of a statistic, such as the sample mean.

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Answer:

256

Step-by-step explanation:

3 What is the sum of the geometric series 4 2,341 256 525 64 2,343 256 ... A: Geometric series are such finite or infinite series where every next term

Sam's height given the percentage and height of his mother is 120 cm

In order to find Sam's height, x, equate the Percentage of Sam's mother height to Sam's mother height

Percentage of Sam's mother height = Sam's mother height

125% of x = 150

1.25 × x = 150

1.25x = 150

x = 150/1.25

x = 120 cm

Therefore, Sam's height is 120 cm if the percentage of his mother's height is is 125% of Sam's height.

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Answer:

7

Step-by-step explanation:

In interval (1, ∞), function h is decreasing, option (C) is correct.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

h(x) = [tex]2^x[/tex] when x < 1,

And h(x) = √(x + 3) when x ≥ 1.

To find the interval when function h is decreasing,

Plot the graph of the function h(x) for the given intervals.

Since, in interval (-∞, 1) the graph is increasing.

And in the interval (1, ∞) the graph is decreasing.

Hence, correct option is option (C).

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Answer: 1000

Step-by-step explanation:

268 / n = 0.268

(268 / n) x n = 0.268 x n

268 = 0.268n

268 / 0.268 = 0.268n / 0.268

1000 = n

The equation (7x2-2xy +2)dx + (29-x2+7)dy = 0 is not exact, NS.

An equation is exact when the mixed partial derivatives of both sides of the equation are equal to each other. In this equation, we have derivatives of x and y, but the mixed partial derivatives are not equal, which means that the equation is not exact. Therefore, the solution is NS. An equation is exact if the sum of the differential terms on each side of the equation is equal to zero. This equation does not satisfy this condition, which is why it is not exact.

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The equation that represents two third times the difference of a number and four will be ten is  [tex]\frac{2}{3} x -4 =10[/tex] and number is 21.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Let the unknown number be represented as x.

The two thirds of a number is written as [tex]\frac{2}{3} x[/tex]

The difference of two-thirds of number and four is [tex]\frac{2}{3}x -4[/tex]

The equation is equal to 10, so the complete equation is written as:

[tex]\frac{2}{3}x -4=10[/tex]

Multiply both sides of the equation with 3.

[tex](\frac{2}{3}x -4) (3) = (10)(3)[/tex]

[tex]2x - 12 = 30[/tex]

Add 12 to both sides of the equation:

[tex]2x -12 + 12 = 30 +12[/tex]

[tex]2x = 42[/tex]

Divide both sides of the equation with 2.

[tex]\frac{2x}{2} = \frac{42}{2}[/tex]

[tex]x=21[/tex]

Hence the equation that represents two third times the difference of a number and four will be ten is  [tex]\frac{2}{3} x -4 =10[/tex] and number is 21.

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The complete sentence is  - The rate of change of the bus is less than the rate of change of the motorcycle. The bus is moving slower than the motorcycle.

As a set of inputs with one output for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one output. In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). One input results in one output when using a function, which is a type of rule. by Alex Federspiel, the photo's author. Here, y=x2 serves as an illustration. A single output for y results from any input for x. Since x is the input value, we would state that y is a function of x.

given

as the graph shows that the bus and motorcycle travels a distance

The bus's rate of change is lower than the motorcycle's rate of change, to give the whole sentence. The motorcycle is traveling more slowly than the bus.

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Therefore , the solution to given problem of fraction comes out to be 5.2 metric tons per hour.

To represent a whole, divide it into any number of equally parts, or fractions. How many units of a particular size there are is expressed using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of such numerator to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or population of a sophisticated fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces. For instance, 12 is used to denote half of the a total number or item.

Here,

Given : Six and a half metric tons of soil are removed from a construction site by a construction company in one and a half hours.

Thus,

5/3 hours and 13/2 metric ton

So,

=> 13/2 / 5/4

=> 13/2 * 4/5

=> 52/10

=>5.2

Therefore , the solution to given problem of fraction comes out to be 5.2 metric tons per hour.

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Therefore , the solution of the given problem of integral comes out to be 8ln2 is solution for the integral expression.

The region beneath a curve among two set limits is referred to as a definite integral. The representation of the definite integral for such a function of two variables), defined to reference to the x-axis, is ∫ baf(x)dx a b f (x) d x, where an is the lower bound and b is the upper bound.

Here,

Given :

[tex]\int\limits \int\limitsa_R[/tex] 3xy²/x²+ 1 dA

=> R = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} ·

So,

=>  [tex]\int\limits^1_{x=0} \int\limits^2_{y=-2}[/tex] 3xy²/x²+ 1  dxdy

=> [tex]\int\limits^1_{x=0}[/tex] 3x / x²+ 1  [tex]\int\limits^2_{y=-2}[/tex] y²

=>[tex]\int\limits^1_{x=0}[/tex] 3x / x²+ 1 ( y³/2)²dx

=>   [tex]\int\limits^1_{x=0}[/tex] 3x / x²+ 1 (8 + 8 /3) dx

=> [tex]\int\limits^1_{x=0}[/tex] 16x/x²+ 1

=> 8 [ln(x²+ 1) ]

=>  8 [ln2 -ln1 ]

=>8ln2

Therefore , the solution of the given problem of integral comes out to be

8ln2 is solution for the integral expression.

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The probability of all five people are still living is 0.1317.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability (Event) = Favorable Outcomes/Total Outcomes = x/n

Let us check simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

As per the given data,

Probability of a person living in these conditions for 30 years or more[tex]$=p=2 / 3$[/tex]

Total number of samples[tex]$=n=5$[/tex]

Let [tex]$X$[/tex] be the number of people living.

[tex]$X \sim \[/tex] Binomial [tex](n=5, p=2 / 3)$[/tex]

Probability mass function of [tex]$X$[/tex]  :

[tex]$$P(X=x)=\left(\begin{array}{l}n \\x\end{array}\right) p^x(1-p)^{n-x}$$[/tex]

a) Probability that all five people are still living:

[tex]$$P(X=5)=\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5}=0.1317$$[/tex]

b) Probability that at least three people are still living:

[tex]$$P(X=5)=\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5}=0.1317$$[/tex][tex]$$\begin{aligned}& P(X \geq 3)=P(X=3)+P(X=4)+P(X=5)=\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{2}{3}\right)^3\left(1-\frac{2}{3}\right)^{5-3}+ \\& \left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{2}{3}\right)^4\left(1-\frac{2}{3}\right)^{5-4}+\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5} \\& =0.7902 \\&\end{aligned}$$[/tex] c) Probability that exactly two people are still living:

[tex]$$P(X=2)=\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{2}{3}\right)^2\left(1-\frac{2}{3}\right)^{5-2}=0.1646$$[/tex]

Therefore, the probability of all five people are still living is 0.1317.

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Answer:

О  B. Standard deviation.

Step-by-step explanation:

Standard deviation measures the dispersion of a data distribution (variability in scores).

...

The constant rate of change can be represented by the cost of milk. The correct option is (A).

When two quantities have some dependence in their values they can be said proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.

The options can be analysed as follows,

(A) Suppose the cost of milk per gallon be C.

And, the number of gallons be n.

Then, the total cost is given as nC.

Which implies that the total cost is proportional to the number of gallons.

It can be considered as a case of constant rate of change.

The remaining option do not show this type of relation.

Hence, the constant rate of change is shown by the cost of milk for number of gallons.

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Answer:

35 Feet

hope you like it : )

Two rays that extend in opposing directions from the same endpoint but have different lengths are said to be a pair of opposite rays. Rays having same endpoint E but not in the opposite directions are ED and EC.

A pair of opposite rays is defined as two rays that have the same terminus and extend in opposite directions, but have different lengths.

Consequently, a straight line is always created when two rays that are facing one another unite.

Two rays that make up an angle are referred to as its two sides.

Each of these rays originates and finishes at the vertex.

A ray is always named by beginning with the letter of the endpoint (where the ray starts), followed by the name of another point along the ray in the direction the ray advances.

Rays ED and EC share the same terminal E but do not go in the opposite directions.

These two rays have different trajectories and collide at point E. The other pair of rays, EA and EB, also have the same end point (at E), but they do not travel in the other way.

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Expression  8[cos(pi/2) + i sin (pi/2)]  is equal to ([tex]\sqrt{3\\}[/tex] + i )³.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression  ([tex]\sqrt{3\\}[/tex] + i )³ lets simplify it

Apply the binomial formula [tex](a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}[/tex]

You can find the coefficient multipliers in row 3 of Pascal's triangle.

=> 3[tex]\sqrt{3}[/tex] + 3*     ([tex]\sqrt{3}[/tex])²* i + 3* √3* (i)² + (i)³

=> 3√3 + 9i  - 3√3 -i

=> 8i

Now simplify the given equations in the options

For 6[cos(pi/2) + i sin (pi/2)]

=> 6[ 0  + 1*i ]

=> 6i

For 8[cos(pi/2) + i sin (pi/2)]

=> 8[ 0  + 1*i ]

=> 8i

For 6 [cos(pi/6) + i sin (pi/6)]

=> 6[ √3 / 2 + i/2]

For 8 [cos(pi/6) + i sin (pi/6)]

=> 8 [ √3 / 2 + i/2]

Therefore, ([tex]\sqrt{3\\}[/tex] + i )³ is equals to the value of equation  8 [cos(pi/2) +  i*sin(pi/2)].

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Answer:14

Step-by-step explanation:

Number of miles to travel for result in both taxi services costing the same amount for that trip will be 60 miles.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Taxi service A costs $5 plus $0.25 for every mile traveled.

And, Taxi service B costs $8 plus $0.20 for every mile traveled.

Now,

Let the number of miles for both taxi reach at same time = x

So, We can formulate;

For Taxi A;

The total cost for x mile = $5 + $0.25x

For Taxi B;

The total cost for x mile = $8 + $0.20x

So, For same number of miles,

⇒ $5 + $0.25x = $8 + $0.20x

⇒ 0.25x - 0.20x = 8 - 5

⇒ 0.05x = 3

⇒ x =3/0.05

⇒ x = 300/5

⇒ x = 60 miles

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Answer:

77.77

Step-by-step explanation:

100% × 77 = 77.

Adding an extra 1%,

101% × 77 = 77.77

Where 100% = 1 and

101% = 1.01

The equivalent exponential functions for this problem are defined as follows:

A. A(n) = 1,000(1.10)^t

B. A(n) = 1,000(1 + 0.008)^12t.

An increasing exponential function is defined as follows:

A(t) = A(0)(1 + r)^t.

In which the parameters are given as follows:

For this problem, the function is defined as follows:

A(n) = 1000(1 + 0.10)^t.

Hence:

A(n) = 1100(1.10)^t.

Meaning that option A is correct.

Using monthly compounding, then the function would be defined as follows:

A(n) = 1000(1 + 0.10/12)^12t.

A(n) = 1000(1 + 0.008)^12t.

Meaning that option B is also correct.

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The percentage for regular soda will be 20%.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

Since William's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 45 sodas in all, 9 of which were regular.

The percentage for regular will be:

= 9 /45 × 100

= 20%

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The equation for the tangent to the graph of y = arcsin(x/2) at the origin is y = x. This means that for any given x-value, the corresponding y-value is equal to that x-value, creating a line with a slope of 1. This line is tangent to the graph of y = arcsin(x/2) at the origin, which is (0, 0).

To find the equation for the tangent to the graph of y = arcsin(x/2) at the origin, we must first find the slope at the origin. We can do this by taking the derivative of the function y = arcsin(x/2) with respect to x.

The derivative of

y = arcsin(x/2) with respect to x is y' = (1/2)cos(x/2).

At the origin, x = 0, so the slope of the tangent at the origin is

y' = (1/2)cos(0) = 1.

Therefore, the equation for the tangent to the graph of

y = arcsin(x/2) at the origin is y = x, which has a slope of 1.

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