A customers monthly bill is $50 including taxes. You mom ’ll offer a 30% discount applicable towards the $50 on a monthly basis. The discount started being applied to his account on June 16. Therefore for the month of June the customer will receive a discount on a prorated basis on the monthly bill. The customers billing cycle begins on the first the month. What is the total billed amount for the month of June?

Step-by-step explanation:

sqrt(120) / sqrt(30) = sqrt(120/30) = sqrt(4) = 2

The quotient of √120 divided by √30 is 2.

Square root of a number is the value such that the value when multiplied to itself two times gives the original number.

It is denoted by the symbol √.

For example, square root of 16 is 4 since 4 × 4 = 16

The given numbers are √120 and √30.

We have to find the quotient when √120 is divided by √30.

Try to write each of the number as a product of perfect squares if possible.

√120 = √(4 × 30)

We know that √(ab) = √a √b

So, √120 = √4 × √30 = 2√30      (∵√4 =2)

√120 /√30 = 2√30 / √30 = 2    

Hence the required quotient is 2.

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Answer:

[tex](2,-1.5)[/tex]

Step-by-step explanation:

The midpoint formula goes as follows:

[tex](x,y)=(\frac{x1+x2}{2} , \frac{y1+y2}{2})[/tex]

Lets plug in our values, let x1 be -3, x2 be 7, y1 be 2, y2 be -5.

[tex](\frac{-3+7}{2} , \frac{2+-5}{2})[/tex]

Solve numerators

[tex](\frac{4}{2} , \frac{-3}{2})[/tex]

Solve

[tex](2 , -1.5)[/tex]

Therefore the midpoint must be at [tex](2,-1.5)[/tex]

The dividends per share on each class of stock for each of the four years for Seventy-Two Inc. are as follows:

                                            Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $32,000    $40,000    $36,000        $36,000

Outstanding shares          60,000      60,000      60,000           60,000

Dividend per share           $0.53       $0.67          $0.60             $0.60

                                          Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $0              $32,000     $44,000       $64,000

Outstanding shares        400,000    400,000     400,000       400,000

Dividend per share        $0              $0.08            $0.11              $0.16

                              3% Cumulative Preferred       Common Stock

Outstanding shares          60,000                        400,000

Par Value                            $20                              $25

Total value                       $1,200,000              $10,000,000

Annual dividend            $36,000 ($1,200,000 x 3%)

                                            Year 1       Year 2        Year 3           Year 4

Distributed Dividends    $32,000    $72,000    $80,000       $100,000

Cumulative Preferred      $32,000    $40,000    $36,000        $36,000

Common Stock                $0              $32,000    $44,000        $64,000

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The number of the students in the school that have had algebra is 203

The given parameters in the question are

The number of students that had algebra in the school is calculated as:

Algebra = Proportion of students taking algebra * Number of students in the school

The above equation can be represented as:

Algebra = np

Substitute values for n and p in the above equation

So, we have

Algebra = 290 * 70%

Express 70% as decimal i.e. 0.70

So, we have

Algebra = 290 * 0.70

Evaluate the product i.e. multiply 290 and 0.70

So, we have

Algebra = 203

Hence, the number of the students in the school that have had algebra is 203

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Answer:

(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

Step-by-step explanation:

by repeated use of the difference of squares factorising method, that is

a² - b² = (a - b)(a + b)

given

[tex]a^{8}[/tex] - [tex]b^{8}[/tex]

= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²

= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares

= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares

= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

It should be noted that organization was important in the thought process and calculation for an accurate solution.

It should be noted that problem-solving enables us to identify and exploit opportunities in the environment and exert control over the future.

In this case, problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations

Also, good problem solving activities provide an entry point that allows all students to be working on the same problem.

In this case, the open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding and problem solving develops mathematical power.

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In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.​< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.

Let's find the critical points of the inequality.

x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)

(x − 1)(x − 8) = 0 (Factor left side of equation)

x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)

x < 1 (Doesn't work in original inequality)

1 < x < 8 (Works in original inequality)

x > 8 (Doesn't work in original inequality)

The third option is the correct one.

Answer:

$270

Step-by-step explanation:

Find her gross income....then subtract taxes:

       30 hr/week * $10/hr        - $ 30     = $270

Answer:

  x = 0

Step-by-step explanation:

Substituting the given "point" into the equation gives the possibilities for x.

Using (x, y) = (x, 8), the inequality becomes ...

  3x -4 < 8

Solving for x gives ...

  3x < 12 . . . . . . . add 4

  x < 4 . . . . . . . divide by 3

Any value of x less than 4 will make (x, 8) a solution to the inequality. For example, ...

  x = 0 . . . . . . (0, 8) is a solution to the inequality

The  techniques that can be used to best explain for each equation that I have created are:

A)  For  graphing -  This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended

(b) For factoring:  x^2 -3x +4 '

Where: (x-4)(x+1)=0

Then x=-1, 4

(c) For  square root method:   x^2 = 64

Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8

(d) For  completing the square:  x^2 + 4x = 11 and x^2 +4x + 4

Note that:  x^2 +4x + 4

= x^2 + 4x = -4

= x^2 +4x + 4 = -4 + 4

= (x+2)^2 = 0

So, x = -2

(e) For quadratic formula: 6x² + 7x -19 =0  

x= [-b + or - sqr(b² - 4ac)]/2a

Note that b=7

a=6

c=-19

Therefore

x= [-7+ or - sqr(49+4(6)(9)]/2

2.  if the discriminant is said to be negative,   then the equation is one that is made up of two imaginary or complex solutions.

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See full question below

You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.

a. graphing

b. factoring

c. square root method

d. completing the square

e. quadratic formula

2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?

Answer: 8.7 the mean is 20

Step-by-step explanation:

Answer:

  263.08 m²

Step-by-step explanation:

The fraction of circle area that a sector represents is proportional to the central angle.

  circle area/circle angle = sector area/sector angle

  circle area / 360° = 85.5 m² / 117°

Multiplying by 360°, we have ...

  circle area = (360/117)(85.5 m²) = 263.08 m²

The area of the circle is about 263.08 m².

Answer: The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter . The incircle touches each side of the triangle

g(x) is a translation of 6 units downwards.

Here we have the function:

y = f(x) = 3x + 1

Notice that the y-intercept of f(x) is:

f(0) = 3*0 + 1 = 1

The y-intercept of f(x) is y = 1.

Now, we know that the y-intercept of g(x) is -5. then:

g(x) = 3x - 5 = f(x) - 6

Meaning that g(x) is a translation of 6 units downwards.

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Answer:

translated 2

units up

g(x)= f(x-2)

Step-by-step explanation:

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:

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Answer:

302.5

Step-by-step explanation:

5 1/2 = 5.5

55 miles per hour * 5.5 hours

55*5.5

302.5

Answer:

  3.9¢ per cup per week

Step-by-step explanation:

Revenue is the product of price and quantity sold. The rate of change in any of these quantities can be found by solving the derivative equation at using the given values.

Revenue (r) is the product of price (p) and quantity sold (q):

  r = pq

Differentiating with respect to time, we have ...

  r' = p'q +pq'

The values given for the problem are ...

Using the above derivative relation, we have ...

  0 = p'(50) +39(-5) . . . . . . fill in given values

  p' = 195/50 = 3.9 . . . . . . add 195, divide by 50

The price must be raised at the rate of 3.9 cents per week to maintain unchanging revenue.

The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;

[tex] \: (q \: \circ \: r) (1)= - 15[/tex]

[tex] \: (r \: \circ \: q) (1)= -18[/tex]

The given functions are;

q(x) = 2•x + 1

r(x) = -5•x - 3

The evaluation of the composite functions can be presented as follows;

[tex](q \: \circ \: r) (x)= q(r(x))[/tex]

Therefore;

[tex](q \: \circ \: r) (1)= q(r(1))[/tex]

Which gives;

[tex](q \: \circ \: r) (1)= q( - 8)[/tex]

q(-8) = 2×(-8) + 1 = -15

Therefore;

[tex](q \: \circ \: r) (1)= - 15[/tex]

Similarly, we have;

[tex](r \: \circ \: q) (1)= r(q(1))[/tex]

q(1) = 2×1 + 1 = 3

r(3) = -5×3 - 3 = -18

Which gives;

[tex](r \: \circ \: q) (1)= -18[/tex]

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Answer:

Step-by-step explanation:

Simply plug in a 3 where you see an x in the function:

[tex]f(3)=3(3)^2-7[/tex] so

f(3) = 3(9) - 7 and

f(3) = 27 - 7 so

f(3) = 20

Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.

a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.

b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.

c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.

Part 2: Taylor will invest (b) $1,733.00 per month.

a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.

b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.

c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.

3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.

a. None had more money at their retirement.

b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).

Gross monthly income = $4,500

APR = 5.25% compounded monthly

N (# of periods) = 480 months (12 x 40 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

PMT (Periodic Payment) = $450 ($4,500 x 10%)

Results:

FV = $733,253.26 ($517,253.26 + $216,000)

Sum of all periodic payments = $216,000 ($450 x 480)

Total Interest = $517,253.26

Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)

N (# of periods) = 240 months (12 x 20 years)

I/Y (Interest per year) = 5.25%

PV (Present Value) = $0

FV (Future Value) = $733,253.26

Results:

PMT = $1,733.00

Sum of all periodic payments = $415,920 ($1,733 x 240

Total Interest = $317,333.26

Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)

Thus, based on the time value of money of investments, it is more profitable to start investing early.

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Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.

The first thing to do is to find out the number of students who are studying either Spanish or Chinese:

= Total number of students - Students studying both Spanish and Chinese

= 374 - 100

= 274 students

Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:

274 = 2x + x

Solving gives:

2x + x = 274

3x = 274

x = 274 / 3

x = 91 students

The number studying Spanish is twice this number so will be:

= 91 x 2

= 182 students

In conclusion, there are 182 student studying Spanish.

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The current value of his Roth IRA is $215,658.00

What is Roth IRA retirement account?

Roth IRA retirement account is a retirement account where the contributions to the account are invested after taxes after have been deducted.

In other words, when the individual make contributions, taxes are first of all, deducted so as to invest the after-tax contribution into the Roth IRA account

The account lost 1/3 of its original value of $215,658

balance after the loss=$215,658-(1/3*$215,658)

balance after the loss=$ 143,772.00

Now the account regained 1/2 of its new balance of $ 143,772.00

balance now=$143,772.00+(1/2*$143,772.00)

balance now=$215,658.00

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Complete with the missing fractions:

michael wittry has been investing in his roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origiInal value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?

First find volume of both the cylinders:

Cylinder Volume Formula: πr²h

(r => radius, h => height)

*Container A:

r = 8

h = 15

πr²h = π(8)²(15) = 960π³

*Container B:

r = 11

h = 13

πr²h = π(11)²(13) = 1573π³

What % of container B is empty after the pumping is complete?

The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:

[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)

Hope it helps!

Answer:

13. Answer: 0

17. Answer: 3

19. Answer: 2

Step-by-step explanation:

13. f(g(3))

First find g(3) on the right graph.

We see that at x = 3, g(x) = 4

So g(3) = 4

Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer

17.f(f(5))

f(5) = 1

f(f(5)) = f(1) = 3 answer

19. g(g(2))

g(2) = 0

g(g(2)) = g(0) = 2 answer

Answer:

129792

Step-by-step explanation:

         156

     ×  832

    ----------

         312

      468

+  1248

---------------

  129792

The equation of this given condition  in the intercept form would be

y = 5x + 24.99

The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.

The linear equation written in the form

y = mx + b

is in slope-intercept form where: m is the slope, and b is the y-intercept.

In the given question the slope of the equation is 5 as $5 is charged for every GB used while $24.99 would be the intercept.

Thus the equation of this given condition  in the intercept form would be

y = 5x + 24.99

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There is no answer because there cannot be one to one function inverse.

Answer:

OB:.242.T gives it's area in square inches

Answer:

Second number line

Step-by-step explanation:

This second line is the only line on which

[tex]-7\frac{1}{2} \text{ appears to the left of } 0 \text{ on the line (Point R)}\\+1 \text{ appears to the right of } 0 \text{ on this number line (Point T) }\\[/tex]

Answer:

○B (second option)

Step-by-step explanation:

In the second option, we can see that the point T is at +1. The point R is between -7 and -8, therefore we understand that it is at a value of [tex]\bf -7\frac{1}{2}[/tex].

All the other options have the points R and T at values not asked for in the question.