9) Write 4-4√3i in Trigonometric Form (Polar Form). Use radians for the angles.

The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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As number is rounded off to 30,000, the correct option is A i.e, it is closer to 30,000 than 29,000.

We look at the last three digits and round to the closest thousand. If these digits total 500 or more, the thousands digit is rounded up; if they total less than 500, the thousands digit is rounded down while remaining the same.

For example, to solve this question we have to check whether 16796 is closer to 16000 or 17000 in the counting. In this case, 16796 is closer to 16000, hence 17000 is the round figure of 16796.

In this problem, as the number is said to be rounded off to the nearest thousand is 30,000, this means that, the number is closer to 30,000 than 29,000.

The question is incomplete. The picture of number line is missing. It is placed in the attachment below.

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The probability that atleast one ball is red is 14/15.

Given that:-

Number of red balls = 4

Number of black balls = 2

One ball is randomly selected, without replacement, the second ball is selected.

We have to find the probability that atleast one ball is red.

There are four ways in which this can happen:-

RR, BR, RB, BB

Where R stands for Red ball and,

B stands for Black ball.

We know that,

Probability that no ball is red + Probability that atleast one ball is red = 1

Hence, we can write,

Probability that atleast one ball is red = 1 - Probability that no ball is red

P(BB) = (2/6)*(1/5) = 1/15

Hence,

Probability that atleast one ball is red = 1 - (1/15) = 14/15

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Thus, the output of the loop is non-deterministic.

Let us consider the loop and the conditions given:

While the condition `x ≠ 0` holds, the loop will continue.

Within the loop, there are two possible paths: `y:=y1` or `y:=y2`.

Since the path to take is non-deterministic, there are two possible outputs:

Either y will be assigned a value of y1 or y2.

Here, it is impossible to determine which assignment will be executed; there is no way to know if x will be decremented once or twice.

This demonstrates that the behavior is non-deterministic, and the possible outputs are `[y1,y2]`.

Thus, the output of the loop is non-deterministic.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:87.5%

Step-by-step explanation:

Given

Henry received \(\frac{7}{8}\) of the votes in the election

i.e. 7 parts of votes are in favor of Henry out of 8

In terms of percentage, it is  given by

\(\Rightarrow \dfrac{7}{8}\times 100=87.5\%\)

Answer:

355.83 yd²

Step-by-step explanation:

A = (B + b)h/2

A = (21.6 yd + 19.3 yd)(17.4 yd)/2

A = 355.83 yd²

Answer:

6

+

9

3

+

5

Step-by-step explanation:

Answer:

35.60

Step-by-step explanation:

Multiply the original price $89 times the mark down percentage 60%

You get 53.40, then subtract it from 89.

Answer:

She paid $35.60 for the jacket.

Step-by-step explanation:

Answer:

m = -12

Step-by-step explanation:

everything is ok til the 3rd equation line

-15m - 30 = -12m + 6

-30 - 6 = -12m + 15m

-36 = +3m

-36/3 = m--------> 3 x -12 = - 36

-12 = m

Answer:

hope this helps you

14 packages will be needed for 28 children if each child gets 4 pencils and has 8 pencils in a package.

Given:

There are 8 pencils in a package.

Total number of children = 28

Each child gets 4 pencils

Total number of pencils needed for 28 children = 28 × 4

                                                                              = 112 no.

Now find out the number of packages for 28 children.

The number of packages needed for 28 children = Total number of pencils needed/ Pencils in a package ........ (1)

As

Total number of pencils needed = 112

Pencils in a package = 8

Put in the above equation (1).

Number of packages needed for 28 children = 112/8

The number of packages needed for 28 children is 14.

Therefore the 14 packages will be needed for 28 children if each child gets 4 pencils.

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Answer:C

Step-by-step explanation: I believe it is C according to my calculations

Answer:C

Step-by-step explanation:

The side lengths of triangle ABC that are missing such as BC and AB would be = 4 and 5.7 respectively.

To calculate the missing lengths of the triangle ABC, the sine rule must be obeyed. That is;

a/sinA = b / sinB

Where a = line BC = ?

A = 45°

b = line AC = 4

B = 180-(90+45) = 45°

That is;

a/sin45° = 4/sin45°

Make a the subject of formula;

a = 4.

Using Pythagorean formula;

c² = a²+b²

= 4²+4²

= 16+16 = 32

c = √32

= 5.7

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Of course, if you don't know the admission fee per person, you'll have to get that information before you can crunch the numbers. But armed with the equation c = sP, you'll be well on your way to figuring out the cost of admission for any group size.

As per the question given,  

Picture this: You're planning a group outing to an amusement park, and you want to know the total cost of admission for your crew. Let's call the admission fee for each person "s" and the number of people in your group "P." The equation to determine the total cost of admission, "c," is simply c = sP.

So if you have 13 people in your group and you know the admission fee per person, you can easily calculate the cost of admission for your crew. Just substitute P = 13 into the equation and multiply by s. It's that simple!

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The speed of the raft if the speed of the patrol-boat was 12 km/hour, and it caught the raft in 5 hours 20 min later is 2.857 km/hours.

What is the speed of a body?

The speed of a body is the rate at which it covers the total distance is in the time taken. The speed of the body is given as,

\(S=\frac{D}{T}\)

Here, (d) is the distance travelled by the body, and (t) is time taken by the body to cover that distance.

A raft was sent away from point A downstream. A patrol-boat left A 5 hour and 20 min later and caught up with the raft 20 km away from point A.

Total time the patrol boat took in hours is,

\(T = 5 + \frac{20}{60}\)

T=5+0.3333

T=5.3333 hours

The speed of the patrol boat is 12 km/hour, and it caught up with the raft 20 km away from point A. Thus, the time taken with this speed to cover 20 km distance is,

\(T=\frac{20}{12}\)

T=1.6667 Hours

Thus, the total time is,

T=5.3333+1.6667

T=7 Hours

Now as the raft travel 20 km in 7 hours. Therefore, find the speed of raft by putting the values in above formula as,

\(S=\frac{20}{7}\)

S=2.857 kmph

A) 500

B) 54 minutes

C) 68cents and 60 cents

D)

E) $40.95

A proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.

Proportions can be written as equivalent fractions or as equal ratios.

A) 42% = 210

100% = (210 x 100)/42

= 500 people

B) 135 berries = 15 minutes

    486 berries = ??minutes

= (486 x 15)/135

= 54 minutes

C) unit price = $6.75/10 = 0.675cents or 68cents

    ii) unit price = $7.25/12 = 0.604cents or 60cents

D) Inconclusive question.

E) 40% of 65 = $26

65 - 26 = $39

Tax = 5% = $1.95

Total = $39 + 1.95

Final Price of jacket = $40.95

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The proportionate reduction in error for knowing the value of the independent variable is 0.54.

The variable which does not depend on any variable and hence independent are known as independent variable.

Given that,

sum of squares for a regression equation was 153.7 = SST

error sum of squares was 82.6 = SSE

SS (reg) = SST - SSE

                153.7 - 82.6

                 SS(reg) = 71.1

The proportionate reduction in error for knowing the value of the independent.

             = 1 - \(\frac{(SS)reg}{SST}\)

             = 1 - \(\frac{71.1}{153.7}\)

             = 1 - 0.46

             = 0.54

The proportionate reduction in error for knowing the value of the independent variable is 0.54.

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The slope of a line parallel to f(x) = 3-12x is -12.

The slope of a line that is parallel to the function f(x) = 3-12x is -12. When two lines are parallel, they have the same slope. In this case, the given function is in the form y = mx + b, where m represents the slope. Therefore, we can directly determine that any line parallel to f(x) = 3-12x will have a slope of -12.

This means that for every one unit increase in the x-direction, the corresponding y-value will decrease by 12 units. Parallel lines have the same steepness or rate of change, and in this scenario, the rate of change is a decrease of 12 units in the y-direction for every one unit increase in the x-direction.

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The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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Answer:

1.8

Step-by-step explanation:

1.2p - 2q

Let p = 3.5 and q = 1.2

1.2 ( 3.5) - 2(1.2)

Multiply

4.2 - 2.4

Subtract

1.8

Answer:

d, they are both parameters because they mean allllll the juniors and seniors, not just pulling out a few and taking a sample

Step-by-step explanation:

Answer:

The answer is "D".

Step-by-step explanation:

3.45 is a parameter and 3.62 is a parameter.

Answer:

x=15

Step-by-step explanation:

1. Solve

4x-6=54

4x-6+6=54+6 <=== Add 6 to both sides

4x=60

4x÷4=60÷4 <=== divide by 4 on both sides

x=15

2. Check

4x15-6=54 <=== Replace x with 15 to check

60-6=54 <=== 4x15 equals 60

54=54 <=== 60-6 equals 54 and 54=54

so it is correct!!

Answer:

(5,21)

Step-by-step explanation:

multiply the second equation by 4

=4x-20y=-400

now subtract the second from first

4x-4x = 0

-y-(-20y) = 19y

-1-(-400) = 399

19y = 399

divide equation by 19

399/19 = 21

y = 21

input 21 into any of the equations

4x-21=-1

4x=20

divide equation by 4

x=5

answer is (5,21)

Answer:

4(-m - y)

Explanation:

Variables can be negative.

Answer:

We can calculate the slope of the secant line for the given function from n=1 to n=5.

g(1) = 10(1.02)¹ = 10.2

g(5) = 10(1.02)⁵ = 12.7

The secant line can be calculated using the formula:

Slope of secant line = (g(5)-g(1))/(5-1)

= (12.7-10.2)/(5-1)

= 2.5/4

= 0.625

Therefore, the average rate of change of the function g(n) from n=1 to n=5 is 0.625.

Step-by-step explanation: