(5-4i)-(2-4i)
Complex numbers
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Answer:

y=0

Step-by-step explanation:

Answer:

y = [tex]\frac{9}{4}[/tex]

Step-by-step explanation:

The horizontal asymptote is the ratio of the coefficient of the highest degree term on the numerator and denominator, that is

9x² - 3x - 8 ← coefficient 9

4x² - 5x + 3 ← coefficient 4, thus

y = [tex]\frac{9}{4}[/tex] ← equation of horizontal asymptote

Answer:

0 handshakes

Step-by-step explanation:

There are 8 women of different heights.

Let the eight women be A, B, C, D, E, F, G and H

Assume A is taller than B and A decides to shake hands with B, B will refuse because A is taller. If this happens across the eight women then there will be 0 hand shakes.

If this assumption is taken out, we have 7+6+5+4+3+2+1 = 28

Answer:

0

Step-by-step explanation:

There are 0 handshakes because if A is taller than B, then A will want to shake hands with B, but B will not participate because she is shorter.

Answer:

Option 1 - [tex]\frac{At}{60}=g[/tex]

Step-by-step explanation:

Given : The goals against average (A) for a professional hockey goalie is determined using the formula [tex]A=60(\frac{g}{t} )[/tex]. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes.

To find : Which is an equivalent equation solved for g?

Solution :

Solve the formula in terms of g,

[tex]A=60(\frac{g}{t})[/tex]

Multiply both side by t,

[tex]At=60g[/tex]

Divide both side by 60,

[tex]\frac{At}{60}=\frac{60g}{60}[/tex]

[tex]\frac{At}{60}=g[/tex]

Therefore, option 1 is correct.

Answer:

a

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

since the camper gets old we will choose decay factor over the years and since t is in years in the explanation so t in the expression means years as well

The expression describes the initial value of the camper multiplied by its annual decay factor raised to the power of the number of years since purchase, corresponding to option C.

The expression 22,475(0.81)^t best describes the product of the initial value of the camper and its decay factor raised to the number of years since it was purchased. The correct choice that describes the expression is C. The initial value of the camper is given as $22,475. The factor 0.81 represents the annual depreciation rate, meaning that the camper loses 19% of its value each year (100% - 81% = 19% decay). The variable t stands for the number of years since the purchase. Therefore, each year, the value is multiplied by 0.81, repeatedly, to reflect the continuous decrease in value.

Answer:

$28,600

Step-by-step explanation:

Probably of 0.7 = 46000

Probability of 0.3 = 12000

The average profit = Sum of (x*Pr(x)

=0.7(46000) + 0.3(-12000)

= 32200 - 3600

= $28,600

The contractor should expect to earn $28,600 on the average

Answer:

384 lamps

Step-by-step explanation:

This is simply a multiplication problem. From the question, we know that each fixture needs 4 lamps with a single room needing 16 fixtures.

The number of lamps required by each room is thus 16 * 4 = 64 lamps

Now, the total number of lamps required by 6 rooms is thus 64 * 6 = 384 lamps

To find the total number of lamps required for 6 rooms, multiply the number of fixtures per room by the number of rooms, then multiply the result by the number of lamps per fixture.

To find the total number of lamps required for 6 rooms, we need to first determine the number of fixtures in 6 rooms. Since each room requires 16 fixtures, the total number of fixtures in 6 rooms would be 16 x 6 = 96 fixtures.

Each fixture requires 4 lamps, so to find the total number of lamps required for 96 fixtures, we multiply 96 x 4 = 384 lamps.

Therefore, 384 lamps will be required for 6 rooms.

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Answer:

The independent variable in the relationship is the Number of Months and should be placed on the x-axis .

The dependent variable in the relationship is the Number of Fish and should be placed on the y-axis .

Step-by-step explanation:

Independent variable is the variable that is being changed or controlled. It's the value that you would graph on the x-axis. Intuitively you would graph the months on the x-axis. I don't really know how to explain it other than that.

Dependent variable is the variable that is being measured. It's the value that is being graphed on the y-axis. You're measuring the amount of fish so that's your dependent variable.

Answer:

"≥"

Step-by-step explanation:

1) Well, for the sake of clarity we'll use a circle on a number line to represent the point solution of each inequality.

2) Writing the system:

[tex]\left\{\begin{matrix}y\geqslant 3x&\\x\geqslant-2&\end{matrix}\right.[/tex]

3) We'll shade the circles and use "≥"

Final answer:

The correct inequality symbols that could be written in both circles for the system 'y 3x x –2' are '<=' and '>=', representing the relationships 'y <= 3x' and 'x >= -2' respectively.

Explanation:

To represent the given system of inequalities algebraically, one needs to identify the correct inequality symbols that could be used between the variables x and y. These symbols articulate the ordering and relationship between these variables.

Given the statement of the system 'y 3x x –2', the inequality symbols that could fit in the circles to complete the system algebraically could be '<=' for 'y <= 3x' and '>=' for 'x >= -2'. This means '<=' and '>=' are both inequality symbols that could be written in the circles to represent the relationship between the variables according to the rules of inequalities which define x is less than or equal to y (x <= y), and x is greater than or equal to y (x >= y).

Inequalities allow us to compare relative sizes or orders of numbers and to solve various algebraic problems dealing with quantity and relationships.

Answer:

  B) shifts the line 4 units down

Step-by-step explanation:

The point (x, f(x)) is moved to the point (x, f(x)-4), one with a y-coordinate 4 units lower. The line is shifted down 4 units.

Answer:

B) shifts the line 4 units down.

Step-by-step explanation:

The constant negative number makes a vertical translation of the parent function in the -y direction. Slope keeps intact. So, the right answer is B.

Answer:

Cannot give answer until Mile (x) is given

Step-by-step explanation:

The sum of the k for k=1 to k="n"=(n*(n+1))/2  , where "n" is the total integer.

In this problem n = 200

Sum = (200*201)/2  = 20,100

Answer: d. 112

Step-by-step explanation:

First Quartile is the median of the first half of ordered data (from  smallest to largest).

The given data : 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.

Arrange in Ascending order , we get

45,99, 108,116,118, 118, 118, 119,120, 121,124,130, 148

First half = 45,99, 108,116,118, 118

No. of elements = 6

First Quartile = Median of first half = Mean of middlemost terms

=[tex]\dfrac{108+116}{2}=\dfrac{224}{2}=112[/tex]

Hence, the First quartile = 112

Correct answer = d. 112

Answer:

Kobe attended barber school for 9 hours each day.

Step-by-step explanation:

Total number of hours completed by Kobe in barber school = 612 hours

Total number of days Kobe attended the school for = 68 days

We are given that Kobe attended school for same number of hours each day.

So, in order to find the number of hours Kobe attended each day we will use unitary method.

In 68 days Kobe completed = 612 hours of school

So, in 1 day he will complete = [tex]\frac{612}{68}=9[/tex] hours

Thus, Kobe attended barber school for 9 hours each day.

Answer:

Step-by-step explanation:

Let B divides AB in the ratio K:1

[tex]x=\frac{nx1+mx2}{m+n} \\y=\frac{ny1+my2}{m+n} \\\frac{-4}{5} =\frac{1*\frac{2}{3}+k*4}{k+1} \\-4k-4=\frac{10}{3} +20k\\-12 k-12=10+60k\\72k=-22\\36k=-11\\k=-\frac{11}{36} \\[/tex]

so B divides AB in the ratio 11:-36

[tex]x=\frac{-36*1+11 *\frac{-1}{2} }{11-36} \\x=\frac{83}{50}[/tex]

Answer:

[tex]\large \boxed{1.66}[/tex]

Step-by-step explanation:

1. Calculate the equation of the straight line joining A and C.

The equation for a straight line is

y = mx + b

where m is the slope of the line and b is the y-intercept.

The line passes through the points (-½, 4) and (1, ⅔)

(a) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{\frac{2}{3} - 4}{1 - (-\frac{1}{2})}\\\\& = & \dfrac{-\frac{10}{3}}{\frac{3}{2}}\\\\& = & \dfrac{-10}{3}\times{\dfrac{2}{3}}\\\\& = & \dfrac{-20}{9}\\\\\end{array}[/tex]

(b) Find the y-intercept

Insert the coordinates of one of the points into the equation

[tex]\begin{array}{rcl}y & = & mx + b\\4 & = & \dfrac{-20}{9}\left(-\dfrac{1}{2}\right) + b \\\\4 & = & \dfrac{10}{9} + b\\\\b & = & \dfrac{36}{9} - \dfrac{10}{9}\\\\b & = & \dfrac{26}{9}\\\\\end{array}[/tex]

(c) Write the equation for the line

[tex]y = -\dfrac{20}{9}x + \dfrac{26}{9}[/tex]

2. Calculate the value of x when y = -⅘

[tex]\begin{array}{rcl}y & = & -\dfrac{20}{9}x + \dfrac{26}{9}\\\\-\dfrac{4}{5} & = & -\dfrac{20}{9}x+ \dfrac{26}{9}\\\\36 & = & 100x -130\\100x & = & 166\\x & = & 1.66\\\end{array}\\\text{The value of x is $\large \boxed{\mathbf{1.66}}$}[/tex]

The graph below shows your three collinear points.

Answer:

Minimum number of weeks = 4

Step-by-step explanation:

Charles earns $5 each week .Also he makes $15 each week by mowing his neighbours lawn.

Thus , in total , he earns a total of $20 each week.

We have to find the minimum number of weeks needed to make $75 .

Number of weeks required = [tex]\frac{money required}{money made per week}[/tex]

                                   = [tex]\frac{75}{20}[/tex]

                                    =3.75

Since the number of weeks, W, is an integer, choose the next highest integer.

Hence the minimum number of weeks required = 4

Answer: Expected value is -4.48.

Step-by-step explanation:

Since we have given that

Cost of ticket for a raffle = $7

Number of tickets sold = 640

Amount winner wins = $1600

So, we need to find the expected value.

So, it becomes,

[tex]E[x]=\sum xp(x)\\E[x]=-7\times \dfrac{639}{640}+(1600+7)\times \dfrac{1}{640}\\\\E[x]=\dfrac{-4473+1607}{640}\\\\E[x]=\dfrac{-2866}{640}\\\\E[x]=-4.48[/tex]

Hence, Expected value is -4.48.

Answer:

The answer is: [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

The sample space when tossing a coin three times is [HHH, HHT, HTH, HTT, THH, THT, TTH, TTT]  and the total number of occurrence is 8.

Getting Head on first toss, tail on second and third is: HTT and it occurs just once in our sample space.

Therefore, the probability of getting Head on first toss, tails on second and third tosses is: [tex]\frac{1}{8}[/tex]

Note probability = [tex]\frac{number of possible occurrence}{number of total occurrence}[/tex]

Given:

$ 1.50 / gallon

1 gallon = 28 miles;

Solution:

$ 24.00 / $ 1.50 = 16 gallons

16 gallons x 28 miles = 448 miles

have a nice day:)

Answer:they would drive 448 miles if they spend $24 on gasoline

Step-by-step explanation:

The Morrison’s car uses one gallon of gasoline for every 28 miles. If gasoline costs $1.50 per gallon, then the cost of driving 28 miles would be $1.5.

Therefore, the number of miles can they drive if they spend $24 on gasoline would be

(28 × 24)/1.5 = 448 miles

Answer:

To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.

Multiply to convert larger units to smaller units.

Divide to convert smaller units to larger units.

When the units are smaller, you need more of them to express the same measure.

When the units are larger, you need fewer of them to express the same measure.

Answer:

To convert between units, you're usually given one measure and asked to convert to another measure.

Step-by-step explanation:

Going to smaller units means going to bigger numbers so you multiply and going to bigger units means going to small. or in other words if you need to convert from a larger unit to a smaller unit Multiply. and if you need to convert from a smaller unit into a larger unit Divide. When converting customary units of measure from a larger unit to a smaller unit, multiply the the larger unit by its smaller equivalent unit.

There are 4 numbers possible 156, 257, 358 and 459.

The value a digit in a number represents based on where it is in the number is known as place value.

Let 25 is a number, then the place value of 2 is 20.

Let the three-digit number is x5y,

Then the number whose digits are switched is y5x,

The number x5y can be written according to its place value = 100x + 50 + y

Similarly, y5x can be written according to its place value = 100 y + 50 + x

The number y5x is 495 more than the number x5y

Implies that,

100 y + 50 + x - (100x + 50 + y) = 495

99y-99x - 495

99(y-x) = 495

y-x = 5

The numbers can be 156, 257, 358 and 459.

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Final answer:

To find the three-digit number with the tens digit being 5 and the number increasing by 495 when the hundreds and ones digits are switched, set up an equation using placeholders for the hundreds and ones digits, solve the equation to find these digits, and deduce the original number, which is 459.

Explanation:

The question involves finding a three-digit number based on given conditions about digits and their positions. We know that the tens digit is 5. If we switch the hundreds and the ones digits, the number increases by 495. This implies that the ones digit must be less than the hundreds digit, as switching them results in a larger number. Let's denote the hundreds digit by 'a' and the ones digit by 'c'.

The original number can be represented as 100a + 50 + c, and after switching, the number becomes 100c + 50 + a. The problem states that the latter is 495 units larger than the original number. So, we can set up the following equation:

100c + 50 + a = (100a + 50 + c) + 495

Simplifying the equation gives us:

99c - 99a = 495

This simplifies to:

c - a = 5

Since 'a' and 'c' are digits, the only possibility is that a = 4 and c = 9. Therefore, the original number is 459.

The right answer is Option B.

Step-by-step explanation:

Given,

Purchase price of car with sales tax = $17300

DMV fees = 1.25%

Amount of DMV fees = 1.25% of purchase price

Amount of DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]

Amount of DMV fees = $216.25

Total price = Purchase price + DMV fees

Total price = 17300 + 216.25

Total price = $17516.25

The total price of car with DMV fees is $17,516.25

The right answer is Option B.

Keywords: percentage, addition

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Final answer:

The total price of the car including DMV fees of 1.25% is (B) $17,516.25, which is found by adding the DMV fees of $216.25 to the purchase price of $17,300.

Explanation:

The question asks for the total price of a car including DMV fees, which are 1.25% of the purchase price of the car after sales tax.

To find the DMV fees, first convert the percentage to a decimal by dividing 1.25 by 100, which gives us 0.0125. Then multiply the purchase price after sales tax, $17,300, by 0.0125 to get the DMV fees.

The calculation is: $17,300 x 0.0125 = $216.25.

Finally, add the DMV fees to the purchase price to get the total price: $17,300 + $216.25 = $17,516.25. Therefore, the correct answer is B. $17,516.25.

Answer:

66 cups of fruit juice will be required .

Step-by-step explanation:

According to the question ,

90 Cups of fruit juice is required for making of 210 cups of punch .

So,

For making of one cup of punch ,

[tex]\frac{90}{210}[/tex] =  [tex]\frac{3}{7}[/tex] cups of fruit juice will be required ,

Thus,

For making of 154 cups of punch ,

Total number of cups of fruit juice required will be [tex]\frac{3}{7}[/tex]×154.

= 66 cups.

Thus a total of 66 cups of fruit juice will be required.

Answer:  a. 0.04

Step-by-step explanation:

Given : Number of multiple choice questions  = 2

Choices given in each question = 5

Since only one choice is correct out of 5.

So, the probability of selecting the correct answer = [tex]\dfrac{1}{5}[/tex]

Also, both questions are independent of each other.

It means , The probability of answering the two multiple choice questions correctly if random guesses are made

=( Probability of selecting the correct answer in question 1 ) x ( Probability of selecting the correct answer in question 2 )

= [tex]\dfrac{1}{5}\times\dfrac{1}{5}= 0.04[/tex]

Hence, the required probability =0.04

Answer:

As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]

Step-by-step explanation:

Given:

From the graph, we can conclude that:

The function has vertical asymptotes at [tex]x=-3\ and\ x=2[/tex]

The function has horizontal asymptote at [tex]f(x)=0[/tex]

Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.

Now, as [tex]x \to -3^{+}[/tex] means the right hand limit of the function at [tex] x=-3[/tex]

From the graph, the right hand limit is the right side of the asymptote of the function at [tex] x = -3[/tex]. The right side shows that the function is tending towards negative infinity.

Therefore, As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]

Answer:

  2

Step-by-step explanation:

A is on the line QA', which is 1.25+1.25 = 2.50 units long*. Thus the scale factor is ...

  QA'/QA = 2.50/1.25 = 2

The scale factor is 2.

_____

* There are two points on the line QA that are 1.25 units from A. One of them is point Q. If A' is coincident with Q, then the scale factor is 0, and line segment A'B' is the single point Q. We don't believe that is intended to be the case, so we assume that point A' is farther along AQ, hence 2.5 units from Q.

Answer:

A.True

Step-by-step explanation:

Multiple of 3 is given by

3,6,9,12,15,18,,,,

Let one number a=6

6 is a multiple of 3.

Another number =5

5 is not a multiple of 3.

Sum of 6 and 5=6+5=11

We know that

11 is not a multiple of 3.

Therefore, if one number is a multiple of 3 and the other is not , then the sum of these number is not a multiple of 3 is true.

Option A is true

The function that represents the number of math problems solved in a class is given by ????(x, y) = (15/7)* x / y, where x represents time and y represents the number of student questions. The constant of variation 'k' is 15/7.

Given that the number of math problems solved (????) in class is influenced by time duration (x) and the number of student questions (y), we can infer a relationship. We can define a constant of variation (k), which stands for the number of problems solved per time unit and per question. Based on the provided situation where 5 problems were solved in 6 minutes with 14 questions, we calculate k as k = ????(x/y) = 5(6/14) = 30/14 = 15/7.

Therefore, the function that represents this scenario is ????(x, y) = (15/7)* x / y, where x is the length of time and y is the number of student questions.

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Answer:

The coordinates of  A'(8,-5)

Step-by-step explanation:

we know that

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places

so

The rule of the reflection across the line y=x is

(x,y) -----> (y,x)

we have the point A(-5,8)

Applying the rule of the reflection across the line y=x

A(-5,8) ----> A'(8,-5)

see the attached figure to better understand the problem

Answer:

[tex]k=-\frac{2}{7}[/tex]

Step-by-step explanation:

The two equations given represent two straight lines in 2-D graph.

The two lines will not intersect if they are parallel.

Hence the two equations will not have solution if the lines are parallel and not coincident.

The condition for 2 lines given by the equations :

ax+by+c=0

dx+ey+f=0 to be parallel but not coincident is:

[tex]\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}[/tex]

here a=2  b=-3k  c=-1  d=4  e=k+2  f=-5

[tex]\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}[/tex]

But also:

[tex]\frac{-3k}{k+2}\neq\frac{1}{5}[/tex]

Hence the value of k is -2/7.

Answer:

10

Step-by-step explanation:

The individual scores in the data are represented by frequency denoted by f column. f column depicts that how many times the individual scores are occurring in the data set. Hence to calculate the amount of individual score in the data set we simply add all frequencies. n=sum of f=2+4+1+3=10. Hence there are 10 individual scores present in the entire data set.

The number of individual scores in the given frequency distribution set is 10, obtained by adding the frequencies together.

In the given question, it's the frequency distribution that is given with scores X: 5, 4, 3, and 2 with their respective frequencies f: 2, 4, 1, and 3. To find the total number of individual scores in the entire set, you simply sum up all the frequencies. So, 2+4+1+3 equals 10. So, the number of individual scores in the entire set is 10. Hence, the correct answer is c. N = 10.

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