If z=3−5i, find |z|.

Answer: each salesperson sold 89 cars last year.

Step-by-step explanation:

The total number of sales people at the dealership shop is 13.

Last year they each sold the same number of cars. The total number of cars that they sold together last year was 1157. Therefore, the number of cars that each salesperson sold would be

Total number of cars sold/ number of salespersons

It becomes

1157/13 = 89

solving 1/3h+5 is greater then or equal to 1/6h+1 ([tex]\frac{1}{3}h+5\geq \frac{1}{6}h+1[/tex]) we get [tex]h\geq -24[/tex]

Step-by-step explanation:

We need to solve 1/3h+5 is greater then or equal to 1/6h+1

Writing in mathematical form:

[tex]\frac{1}{3}h+5\geq \frac{1}{6}h+1[/tex]

Solving and finding value of h

Adding -5 on both sides

[tex]\frac{1}{3}h+5-5\geq \frac{1}{6}h+1-5\\\frac{1}{3}h\geq \frac{1}{6}h-4[/tex]

Adding -1/6h on both sides

[tex]\frac{1}{3}h-\frac{1}{6}h\geq \frac{1}{6}h-4-\frac{1}{6}h\\\frac{1*2h-1*1h}{6}\geq -4\\\frac{2h-1h}{6}\geq -4\\\frac{1h}{6}\geq -4\\h\geq -4*6\\h\geq -24[/tex]

So, solving 1/3h+5 is greater then or equal to 1/6h+1 ([tex]\frac{1}{3}h+5\geq \frac{1}{6}h+1[/tex]) we get [tex]h\geq -24[/tex]

Keywords: Solving inequalities

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The inequality required is t < 55.

Given:

To qualify for the championship, a runner must complete the race in less than 55 minutes.

In this question, we are dealing with the time taken by runners to complete a race. Let's use 't' to represent the time in minutes of a runner who qualifies for the championship. The condition for qualification is that the runner must complete the race in less than 55 minutes.

So, the inequality that represents this situation is: t < 55.

Any runner who completes the race in less than 55 minutes will qualify for the championship.

Answer:

see explanation

Step-by-step explanation:

(1)

Given

[tex]\frac{n}{5}[/tex] = - 0.3

Since n is divided by 5 then use the inverse operation, multiplication.

Multiply both sides by 5 to clear the fraction

n = 5 × - 0.3 = - 1.5

(2)

Given

- 2n = 4 [tex]\frac{1}{3}[/tex] ← change to an improper fraction

- 2n = [tex]\frac{13}{3}[/tex]

Since n is multiplied by - 2 then use the inverse operation, division.

Divide both sides by - 2

n = [tex]\frac{13}{-6}[/tex] = - [tex]\frac{13}{6}[/tex]

Answer:

The exact value of cotФ  is  [tex]\frac{\sqrt{7}}{3}[/tex]  

Step-by-step explanation:

Given as:

The value of cosec Ф = [tex]\frac{-4}{3}[/tex]

Let the value of  cotФ = x

Now, According to question

∵  sinФ = [tex]\frac{1}{cosec\Theta }[/tex]                       .....1

Put the value of cosec Ф = [tex]\frac{-4}{3}[/tex] in eq 1

i.e  sinФ = [tex]\frac{1}{\frac{-4}{3} }[/tex]

Or,  sinФ = [tex]\frac{-3}{4}[/tex]

Again

∵ cosФ = [tex]\sqrt{1-sin^{2}\Theta }[/tex]

So,  cosФ = [tex]\sqrt{1-(\frac{-3}{4})^{2}}[/tex]

Or, cosФ = [tex]\sqrt{1-(\frac{9}{16})}[/tex]

Or,  cosФ = [tex]\sqrt{\frac{16 - 9}{16})}[/tex]

∴  cosФ = [tex]\frac{\sqrt{7}}{4}[/tex]

Again

we know that cotФ = [tex]\frac{cos\Theta }{sin\Theta }[/tex]

So,  cotФ  = [tex]\frac{\frac{\sqrt{7}}{4}}{\frac{-3}{4}}[/tex]

Or,  cotФ  = [tex]\frac{-\sqrt{7}}{3}[/tex]

As according to question sinФ lies in third quadrant

So,  cotФ  =  [tex]\frac{\sqrt{7}}{3}[/tex]

Hence, The exact value of cotФ  is  [tex]\frac{\sqrt{7}}{3}[/tex]   . Answer

Answer:

100

189

83

Step-by-step explanation:

Firstly, we can see that there are three aircrafts. Let the number of aircrafts in the second aircraft be x.

Then the first has 89 more seats meaning it has a total seats of x + 89

The third has 17 fewer seats meaning x - 17

Now we are expected to find the number of seats on each of the aircraft officials.

We add all and then sum to the total 372.

This means

x + x + 89 + x - 17 = 372

3x + 72 = 372

3x = 300

x = 300/3 = 100

The aircrafts thus have 100 seats, 189 and 83 seats in no particular order

You can use any of the available methods for solving system of linear equations like method of elimination or method of substitution etc.

There are no solutions to the given system of equations.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

The given system of equations is

[tex]2x - 6y = 5\\x - 3y = -12[/tex]

Using second equation to get x in terms of y

[tex]x - 3y - 12\\x = 3y - 12[/tex]

Substituting this expression for x in place of x in first equation,

[tex]2x - 6y = 5\\2( 3y - 12) - 6y = 5\\6y - 24 - 6y = 5\\-24 = 5[/tex]

The last statement we got is incorrect.

That conclusion above shows that the given system of equation has no solution.

We could've detected it from the fact that

[tex]2x - 6y = 5\\\text{dividing both sides by 2}\\x - 3y = 2.5[/tex]

Converting both equations to slope intercept form, we get:

[tex]x - 3y = 0.5\\\\y = \dfrac{1}{3}x - \dfrac{1}{6}[/tex]

and

[tex]x - 3y = -12\\\\y = \dfrac{1}{3}x + 4[/tex]

We see that both lines have same slope but different y intercept, which tells that both lines are parallel but not coincident, thus, not intersecting and thus, no common point(common points are solutions).

The graph of this system of linear equation is given below where lines represented by both linear equations are plotted.

Thus,

There are no solutions to the given system of equations.

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Final answer:

To solve the system of equations using substitution, rearrange one of the equations to solve for a variable and substitute that expression into the other equation. In this case, the system of equations is inconsistent and has no solutions.

Explanation:

To solve the system of equations using substitution, we rearrange one of the equations to solve for a variable, then substitute that expression into the other equation. Let's solve the system of equations:

Equation 1: 2x - 6y = 5

Equation 2: x - 3y = -12

Therefore, the system of equations is inconsistent, and there are no solutions.

Answer:

  20 1/6 ft

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides:

  2×(5 1/3 ft) + 2×(4 3/4 ft) = 10 2/3 ft + 8 6/4 ft

  = 10 2/3 ft + 9 2/4 ft . . . . change 6/4 ft to 1 1/2 ft

  = 10 8/12 ft + 9 6/12 ft = 19 14/12 ft  . . . . . use common denominator of 1/12 ft

  = 20 2/12 ft . . . . . . change 14/12 ft to 1 2/12 ft; next reduce that fraction

  = 20 1/6 ft . . . . perimeter of Caleb's bathroom

Answer:

Step-by-step explanation:

The Standard Deviation Rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15.

Therefore, the range of IQ scores that many (68%) people have is between

100 - 15 and 100 + 15

It becomes

85 to 115

The range of  IQ scores for 68% of the people varies from 85  to 115

Given that the distribution of IQ (Intelligence Quotient) is approximately normal in shape

[tex]\rm Mean\; IQ =\mu = 100 \\Standard\; deviation = \sigma = 15[/tex]

According to the empirical relation for normal curve 68% of the data lies in the range

[tex]\rm \mu + \sigma\; to \; \mu - \sigma[/tex]

So the  lower limit of the range of  the normal distribution of IQ score  = 100 -15 = 85

The upper limit of the range of the normal distribution of IQ score  = 100 + 15 = 115

So we can conclude that the range of  IQ scores for 68% of the people varies from 85  to 115

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Answer:

  22 1/2 hours

Step-by-step explanation:

There are several ways you can get there. One way is to use table values to form a sum of 60:

  cars = 32×2 - 8×(1/2) = 64 -4 = 60

Then the corresponding hours are ...

  hours = 12×2 - 3×(1/2) = 24 -1.5 = 22.5

It will take 22.5 hours to wax 60 cars.

__

Another way to get there is to use proportions:

  hours/cars = 3/8 = ??/60

Multiply by 60 to find ??

  (60)(3/8) = ?? = 180/8 = 22.5 . . . . hours

_____

We can do these things because we have determined the relationship between hours and cars is proportional: 8/3 = 16/6 = 32/12. If it weren't proportional, some other strategy would be needed to answer the question.

Answer:

Here is a more clearer version of the same question ;

29 1.2. Constructing Direct Proofs 1. Let a, b, and c be real numbers with a 0. The solutions of the quadratic equation ax 2 + bx + c = 0 are given by the quadratic formula, which states that the solutions are xi and x2. where and x2 2a 2a (a) Prove that the sum of the two solutions of the quadratic equation ax2 + bx + c = 0 is equal to -b/a . (b) Prove that the product of the two solutions of the quadratic equation ax2 + bx + c = 0 is equal to c/a.

The proving of both a) and b) has been done

Step-by-step explanation:

The step by step explanation has been given in the attachment below.

Answer:

ff

Step-by-step explanation:

Answer: x = 5

Step-by-step explanation: This is an isosceles triangle, which means two sides are equal in length and two angles are equal in measurement.

Line BA = Line BC

Similarly, Angle A = Angle C

Angle A plus Angle C equals 146°

Also the sum of the interior angles of a triangle is 180°

Therefore, 146 + (6x + 4) = 180

Subtract 146 from both sides of the equation

6x + 4 = 34

Subtract 4 from both sides of the equation

6x = 30

Divide both sides of the equation by 6

x = 5

Answer:

b

Step-by-step explanation:

for sure

Answer:

Step-by-step explanation:

11)

√(343 x^4)=√(7×7×7×x^4)=7√7 x^2

Answer: 7√ 7x^2

7 √ 7= 18.52x^2

Step-by-step explanation:

√ 343x^4 = √ 7×49x^4

=7 √ 7x^4×1/2

=7 √ 7x^2

Answer:

Segments with positive slope, negative slope, zero slope and undefined slope are indicated in the attach.

Step-by-step explanation:

When you represent or consider a segment in a coordinate axis system, the slope of the segment is the variation in "x" axis in relation to variation in "y" axis, it means the quotient Δx/Δy. If we select two different pairs of points (x1, y1) (x2, y2) ⇒slope =  Δx/Δy ⇒ slope = (x2 - x1)/(y2 - y1).

There four main options:

- If  Δx/Δy > 0 ⇒ Positive slope (In this case: Δx >0 and Δy> 0 or Δx˂ 0 and Δy ˂  0).

- If Δx/Δy ˂  0 ⇒Negative slope (this happens when Δx > 0 and Δy˂0 or

Δx˂0 and Δy>0)

- If Δx/Δy = 0 ⇒ zero slope (This happens when Δx =0).

-If Δx/Δy =∅ ⇒ undefined slope (only when Δy = 0).

Given this explanation and considering the word MATH in a coordinated system, we clasiffied the segments as you can see in the attach. Segments denoted by: 1 have positive slopes, 2 negative slopes, 3 zero slope and 4 unddefined slope.

Final answer:

The side length of the largest cube that fits between two concentric spheres with radii of 15 and 33 is approximately 17.32.

Explanation:

To find the side length of the largest cube that fits between two concentric spheres (with the same center), we need to understand that the cube will fit within the smaller sphere and will be inscribed within it such that the diagonals of the cube's faces will be equal to the diameter of the smaller sphere.

The radius of the smaller sphere is given as 15.

Therefore, the diameter of this sphere, which is twice the radius, is 30.

Using the diagonal of a cube, which can be calculated with the formula √3 times the side length (s), it is found that

√3 × s = 30.

Solving for s gives us the maximum side length of the cube that would fit:

s = 30 / √3

s ≈ 17.32

Therefore, the side length of the largest cube is approximately 17.32.

Answer:

Each tank would have 27 gold fish in it.

Step-by-step explanation:

Given:

Number of fish tanks = 8

Number of gold fish = 216

We need to find the number of goldfish in each tank.

Solution:

Now we know that;

Number of gold fish must be equal in each tank.

To find the number of gold fish in each tank we will divide Number of gold fish by Number of fish tanks.

framing in equation form we get;

number of gold fish in each fish tank = [tex]\frac{216}{8} = 27 \ fish[/tex]

Hence Each tank would have 27 gold fish in it.

Answer: Using Pythagoras Rule the ladder touches 13.75ft ~ 14ft up the wall.

Step-by-step explanation: Using the Pythagoras Rule the Hypothenus is the leaning hieght of the ladder 15ft

And the base is 6ft. Now let's find the height of the wall h¹

h¹ = √{15² - 6²}

h¹ =√{225 - 36}

h¹ = √189

= 13.74ft

Answer:

.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The square sheet has an area of 100 square meters.

Hence, the width of the sheet is [tex]\sqrt{100} = 10[/tex] meters.

The scale factor is needs to be in such a way, so that the film's wide will be match perfectly with the square sheet. Hence, 35x millimeters = 10 meters = 10000 millimeters .

[tex]x = \frac{10000}{35} = 285.7143[/tex].

Answer:

Step-by-step explanation:

Answer:

The answer to your question is 40.60°

Step-by-step explanation:

Data

Right triangle

Opposite side = 6

Adjacent side = 7

Process

1.- To find angle A, use trigonometric functions.

The trigonometric function that relates the opposite side and the adjacent side is tangent

           tanA = [tex]\frac{Opposite side}{Adjacent side}[/tex]

2.- Substitution

           tan A = [tex]\frac{6}{7}[/tex]

3.- Find tan⁻¹A

        tan⁻¹ A = A = 40.60°

Answer:

A

Step-by-step explanation:

(3n²+2n+4)(2n-1)

to solve this multiply through by using each term in one bracket to multiply all terms in the second bracket to open the bracket.

3n²(2n-1) + 2n(2n-1) +4(2n-1)

6n³-3n² +4n²-2n+8n-4

6n³+n²+6n-4

Hence the correct option is A

Answer:

a

Step-by-step explanation:

Answer:

The signal will not be picked up if he drives from the first city to the second city as far as he drives along a straight line.

Step-by-step explanation:

The attachment to the answer clearly explains why no signal will be picked up

Answer:

The answer is 38.5 miles

Step-by-step explanation:

From the attached diagram

AC represents the distance needed to be traveled before picking the signal.

Using Pythagoras'rule to solve for AC from triangle ACO

(AO)^2 = (AC)^2 + (CO)^2

(60)^2 = (AC)^ + (46)^2

(AC) = ✓[(60)^2 - (46)^2]

AC = 38.5 miles

Answer:

number  ,proportion

Step-by-step explanation:

Data is a collection of facts, such as numbers, words, measurements, observations. Data is organised in graphs or charts for analysis and conclusions.

A frequency distribution lists the number of occurrences of each category of data.

A relative frequency distribution lists  the proportion of occurrences of each category of data.

A frequency distribution lists the number of occurrences, and a relative frequency distribution lists the proportion of occurrences of each category of data. Frequency tables compile occurrences, while relative frequencies are calculated as a ratio of the frequency to the total number of observations. Histograms and bar graphs visually represent these distributions.

A frequency distribution lists the number of occurrences of each category of​ data, while a relative frequency distribution lists the proportion of occurrences of each category of data. When we compile a frequency table, the data are organized so that we know how many times a particular value or category occurs. For example, a frequency distribution can inform us that 15 students spend five hours or more studying for an exam.

Conversely, a relative frequency distribution provides us with a ratio or fraction that represents how often a value appears relative to the entire set of data. To calculate relative frequency, one would divide each frequency by the total number of observations. If 20 students were surveyed, and 5 studied for more than five hours, the relative frequency would be 5/20 or 0.25 (which can also be expressed as 25%).

Graphical representations such as histograms and bar graphs are valuable for visualizing both frequency and relative frequency. A histogram is suitable for displaying the distribution of interval or ratio variables, particularly with a large number of cases. Bar graphs are more commonly used for nominal or ordinal data, which usually involves fewer categories.

Answer:

2 hours working on problems, 2 hours reading

Step-by-step explanation:

The question is incomplete. Here is the complete question:

Ben is a hard-working college senior. One Thursday, he decides to work nonstop until he has answered 150 practice problems for his math course. He starts work at 8:00 AM and uses a table to keep track of his progress throughout the day. He notices that as he gets tired, it takes him longer to solve each problem.

Time          |   Total Problems Answered

8:00 AM   |   0

9:00 AM   |   60

10:00 AM |   105

11:00 AM  |   135

Noon   |   150

The marginal, or additional, gain from Ben's first hour of work, from 8:00 AM to 9:00 AM, is 60 problems.

The marginal gain from Ben's third hour of work, from 10:00 AM to 11:00 AM, is 30 problems.

Later, the teaching assistant in Ben's math course gives him some advice. Based on past experience, the teaching assistant says, "working on 40 problems raises a student's exam score by about the same amount as reading the textbook for 1 hour". For simplicity, assume students always cover the same number of pages during each hour they spend reading.

Given this information, in order to use his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems, and how many should he have spent reading?

The marginal or additional gain in the above question is calculated by obtaining the difference in problems solved between two selected time frames . For example, the marginal or additional gain from Ben's 11 AM to Noon work is :

Additional gain from 11 AM to Noon = 150 - 135 = 15 problems

Ben should therefore make his decision at the margin. Each hour, he should select the option that will improve his exam grade by the largest amount. If he can do more than 40 problems in an hour, working on problems will help raise his grade more for that hour than reading would.The marginal gain from the first hour is 60 problems. The marginal gain from the second hour is 45 problems. He will stop there, because he will get only 30 problems done if he spends the third hour working on problems. Therefore, he should stop working on problems and spend his remaining 2 hours reading instead.

Answer:

Assuming he works at a constant rate, the daily rate Mark rakes lawns in the fall is 40% of the daily rate he mows lawns in the summer.

Step-by-step explanation:

Fall:

5 neighbours' lawns / 2.5 hours = 2 lawns per hour

Summer:

6 neighbours' lawns / 1.2 hours = 5 lawns per hour

2 x 100% / 5 = 40%

2 is 40% of 5

The percent of the daily rate should be 40%.

One day in the fall, Mark raked the leaves on 5 neighbors’ lawns in 2.5 hr. One day in the summer, he mowed 6 neighbors’ lawns in 1.2 hr.

For fall

= 5 neighbours' lawns ÷  2.5 hours = 2 lawns per hour

For Summer:

= 6 neighbours' lawns ÷ 1.2 hours = 5 lawns per hour

Now

[tex]= 2 \times 100\% \div 5[/tex]= 40%

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Answer:

D. 21

Step-by-step explanation:

Given:

m arc AC = 69

Segment AB is tangent to circle O at point A.

We need to find the ∠ ABC

Solution:

Now we can say that;

By inscribed angle theorem which states that;

"Central angle is equal to arc subtended by it."

m∠O = 69 (Central angle)

Also Given:

Segment AB is tangent to circle O at point A.

Now by radius tangent property which states that;

"Radius which touches to closet point on the tangent is always perpendicular."

so we can say that;

m∠OAB = 90

Now in Δ OAB.

m∠O = 69

m∠OAB = 90

Now we know that;

"Sum of all angles of triangle is 180."

m∠O + m∠OAB + m∠ABO = 180

Substituting the values we get;

[tex]69+90+m\angle ABO=180\\\\159+m\angle ABO=180[/tex]

Subtracting both side by 159 we get;

[tex]159+m\angle ABO-159=180-159\\\\m\angle ABO=21[/tex]

Now we can say that;

m∠ABO = m∠ ABC = 21 (same angles)

Hence  m∠ ABC is 21.

Answer:

  4

Step-by-step explanation:

Put the numbers in the expression in place of the corresponding variables and do the arithmetic.

  [tex]\dfrac{8^2}{2^4}=\dfrac{64}{16}=4[/tex]

Answer:

4

Step-by-step explanation:

Answer:

Option 3) area space occupied by any sample of matter              

Step-by-step explanation:

We define volume of an object as:

Option 3) area space occupied by any sample of matter

It is not a unit for measuring distance.

It cannot be defined as amount of matter in an object force per unit