Jeremy received a bill with a balance due of $35.60. After an error was corrected, the new balance was of the original balance due.
What was the new balance due?

The average rate of change of f(x) on the interval  30 ≤ x ≤ 60 is r = 1/5.

For a function f(x), we define the average rate of change over an interval:

a ≤x ≤b is given by:

( f(b) - f(a))/(b - a)

In this case we have the function defined by the table and the interval:

30 ≤ x ≤ 60

On the table we can see:

f(60) = 19

f(30) = 13

Then the average rate of change is:

r = (19 - 13)/(60 - 30) = 6/30 = 1/5

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The required length of the pieces is given as 20 ft, 16ft, and 14ft.

Given that,
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
according to the question,
Length of the first, second, and third  be x, y and z,
According to the question,
x + y + z = 50 - - - - - - - - (1)
x = y + 4
z = y - 2
put x and z in equation 1
y + 4 + y + y - 2 = 50
3y = 50-2
y = 48/3
y = 16 ft
Now,
x = 16 + 4 = 20 ft
z = 16 - 2 = 14 ft

Thus, the required length of the pieces is given as 20 ft, 16ft, and 14ft.

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Answer:

3(3+4) IS NOT EQUAL TO 3^3

Step-by-step explanation:

3(3+4)

Expand brackets to get 21 (3x3 = 9, 3x4 = 12, 9 + 12 = 21)

3^3 = 3 x 3 x 3

3x3 = 9

9 x 3 = 27

21 < 27

The operating income of Division B will increase by $640,000

Given that: Division B incurs variable costs of $10 per unit and  a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A

This cost of production by division B is:

cost = $10 × 80,000 = $800,000

Division B uses a transfer price of $18 per unit. That is:

Selling price = $18  × 80,000 = $1,440,000

Operating income increase = Selling price - cost

Operating income increase = $1,440,000 - $800,000 = $640,000

Therefore, Division B's operating income increase will be $640,000

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The liquid that Richard used in the punch is 1 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Richard made punch for a party. He used 1/2 cup of pineapple juice, 1/2 cup of ginger ale, and 1/4 cup of white grape juice.

The total fraction will be:

= 1/2 + 1/2 + 1/4

= 1 1/4 cups.

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Transcribed image text: (1 point) A tank contains 60 kg of salt and 2000 L of water. Water containing 0.8 min of salt enters the tank at the rate 6 min. The solution is mixed and drains from the tank at the rate 3 IA(t) is the amount of salt in the tank at time t measured in kilograms. min (a) A(0) = (kg) = 0.

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Answer: yes

Step-by-step explanation:

For the given triangle ABC,

The perimeter of ABC is 32.443 unit
The area of ABC is 30 unit^2

What is a vertex?
A triangle is created geometrically by the intersection of three line segments. Each side of a triangle has two ends, and the three sides' endpoints may intersect at three distinct places in a plane to form the triangle. The three locations where they cross each other are referred to as a triangle's vertices.

Solution explained:

The distances are found using the distance formula:

D=[tex]\sqrt{((y2-y1)^2+(x2-x1)^2)}[/tex]

Given A(2,8),B(16,2),C(6,2)

Now, calculate the distance

AB=[tex]\sqrt{((16-2)^2+(2-8)^2)}[/tex]=[tex]\sqrt{(14^2+6^2)}[/tex]=[tex]\sqrt{232}[/tex]

BC=[tex]\sqrt{((6-16)^2+(2-2)^2)}[/tex]=[tex]\sqrt{(10^2+0)}[/tex]=10

CA=[tex]\sqrt{((2-6)^2+(8-2)^2)}[/tex]=[tex]\sqrt{(4^2+6^2)}[/tex]=[tex]\sqrt{(16+36)}[/tex]=[tex]\sqrt{52}[/tex]

Perimeter=AB+BC+CA
               =32.443 unit

For the area (we note that BC is horizontal (parallel to the x-axis)), so

Area = (1/2)base * height

        =(1/2)10*(ya-yb)

        =(1/2)10*(8-2)

        =(1/2)10*6

        =30 unit^2

Hence, the perimeter is 32.443 units and the area is 30 unit^2

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The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

Given,

The population of a city can be modeled using the formula P=100,000e^(0.05t)

t is the number of years after 2012

P is the population of the city

We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.

Here,

Substitute 300000 in for P and solve for t

300000=100000e^0.05t

Divide both sides by 100000:

We get,

3 = e^0.05t

Multiply both sides by the natural log (ln)

Then,

ln(3) = 0.05t

Now, divide 0.05 on both sides to get t by its self

t = ln(3) / 0.05

Therefore,

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

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They should charge for its premium in order to have an expectation of $0 for the policy is $85.

Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, probability of alive 100-0.00142

= 0.99858

P(A)=0.99858A+0.00142(A+60000)

Put A=0, in the obtained function, we get

P(0)=0.99858(0)+0.00142(0+60000)

=0.00142×(60000)

=$85.2

= $85

Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.

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The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.

Quadratic equation :

To solve the quadratic equation:

h(t) = 0 = -5t² +33t+ 4

[tex]t = \frac{-b \pm\sqrt{(b)^2 - 4ac}}{2a}[/tex]

[tex]t = \frac{-33 \pm\sqrt{(33)^2 - 4(-5)(4)}}{2(-5)}[/tex]

t = {(-33) ±√(1169)}/(-10)

t = -0.1190

t = 6.719

neglecting the negative term we get :

t = 6.719 seconds

This represents that the ball hits the ground after 6.719 seconds.

The ball thrown vertically upward, the ball hits the ground after 6.719 seconds.

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By performing some simple mathematical operations, the answers to all the subparts are:

So, the answers after multiplication are:

Therefore, by performing some simple mathematical operations, the answers to all the subparts are:

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Equation which is equivalent to the formula solved for r in term of A is   [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].

What is circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

A circle is also termed as the locus of the points drawn at an equidistant from the centre.

What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.

What is circumference?

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.

Given that;

[tex]A = \pi{({r+2})^{2}}[/tex]

[tex](r+2)^{2} =\frac{A}{\pi}[/tex]  (equivalent transformation)

[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]

[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]

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Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Step-by-step explanation:

I assume our task is to find that point of time, when it reaches the highest point.

and the function is

h(t) = -16t² + 96t + 112

well, a maximum or minimum of a curve (function) is found as a zero solution of the first derivative of the function.

given the nature of the function, the extreme point has to be a maximum (the firecracker goes up and then down again).

h'(t) = -32t + 96

we are looking for the zero :

0 = -32t + 96

32t = 96

t = 3 seconds

so, after 3 seconds, the firecracker reaches its highest point, which is at

-16×3² + 96×3 + 112 = -16×9 + 96×3 + 112 =

= -144 + 288 + 112 = 256 ft

FYI - we know for x = 0 (the starting point) the height of the starting window was 112 ft.

Answer:

Step-by-step explanation:

3/5 pool/hr * 10hr = 6 pool

The exact value of Cosθ is -1/√10 .

In the question ,

it is given that ,

the value of tanθ = 3/1 ,

that means the perpendicular = 3x

and the base of the triangle is = 1x,

So ,By Pythagoras Theorem

hypotnuse² = perpendicular² + base²

hypotnuse² = (3x)² + (1x)²

hypotnuse² = 9x² + 1x²

hypotnuse² = 10x²

hypotnuse = (√10)x

So , Cosθ = base / hypotnuse

Cosθ = 1x/(√10)x

Cosθ = 1/√10

Since , [tex]\theta[/tex] lies in the second quadrant ,

and in second quadrant Cos is negative ,

So , Cosθ = -1/√10

Therefore , The exact value of Cosθ is  -1/√10  .

The given question is incomplete , the complete question is

If Tanθ = 3 , θ lies in the second quadrant. Use a Pythagorean identity to find the exact value of Cosθ ?

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Answer: 1 hour and 30 minutes or 1.5 hours

Answer:

1 hour and 30 minutes

Step-by-step explanation:

The expected change in the dividend of a 6% preferred stock is $75.

Given that, the required rate of return drops instantly from 8% to 6%.

A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.

The value of preferred stock = $100

Annual dividend = 100 × 6% = $6

Price of preferred stock when required return is 8% = Annual dividend / Required rate of return

= 6/8%

= 6 ×100/8

= $75

Therefore, the expected change in the dividend of a 6% preferred stock is $75.

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Using mathematical operations, the amount that would be saved by buying 3 dresses instead of buying per piece is $3.40.

The mathematical operations include the following basic operations: addition, subtraction, division, and multiplication.

Mathematical operations determine the results of mathematical expressions and problems.

Cost of a dress = $6.20

Cost of 3 dresses = $15.20

Cost per dress if 3 dresses were bought = $5.067

Amount saved for buying 3 dresses instead of one = $3.40 ($6.20 x 3 - $15.20)

Thus, mathematically, the customer would save $3.40 by buying 3 dresses for $15.20 instead of buying at $6.20 per unit.

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Hope this helps!! :]

Histogram for the following intervals will be,

5-9 (4)

10-14 (3)

15-19 (5)

20-24 (3)

Acc to our question-

hence, histogram will show the values.

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Answer:

cubic root 10 power 1

Step-by-step explanation:

Apply the rule

x

m

n

=

n

√

x

m

to rewrite the exponentiation as a radical.

3

√

10

1

Anything raised to

1

is the base itself.

3

√

10

The result can be shown in multiple forms.

Exact Form:

3

√

10

Decimal Form:

2.15443469

…

Answer: y > -3/4x + 2

Step-by-step explanation:

Answer:

x = 22

Step-by-step explanation:

Solve for x:

x/11 = 2

multiply both sides by 11:

11(x/11) = 11(2)

x = 22

Answer:

x = 22

Step-by-step explanation:

[tex] \sf \frac{x}{11} = 2[/tex]

Use cross multiplication.

[tex] \frac{x}{11} = \frac{2}{1} \\ \\ \sf x = 2 \times 11 \\ \\ \sf \: x = 22[/tex]

Answer:

32 students were on each bus.

Step-by-step explanation:

First deduct 9 students from the total number: 265 - 9 = 256

Then divide the students among the total number of buses, which is 8: 256/8 = 32

So there are 32 students on each bus.

Hope this helps

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The straight line y = x -1 is shown figure  

To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.

Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.

After calculating the coordinates, use the resultant points to plot the line as a graph.  

Here we have a line

y = x -1  

To sketch the graph we need to make a value table as given below

First take x values as, -1,  0, 1 from that find the values of y  

At  x = -1 => y = -1 - 1 = -2

At  x = 0 => y = 0 - 1 = -1

At  x = 1 =>  y = 1 - 1 = 0  

From the above calculations, the value table is

        x   -1   0   1

        y   -2  -1  0      

Use the above value and Sketch the graph

[ the resultant graph is shown below ]

The straight line y = x -1 is shown figure    

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The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:

                                          FIFO          LIFO

Ending inventory          $10,250     $12,800

Cost of goods sold       $17,000     $14,450

FIFO, which means First-in, First-out, computes the cost of goods sold based on the assumption that the physical flow of goods sold depends on the earlier inventory in stock.

FIFO can be applied under both the perpetual and periodic inventory systems, unlike LIFO.

LIFO means Last-in, First-out, and as a cost flow assumption assigns the cost of goods sold based on the latest inventory purchases.

LIFO cannot be used under the perpetual inventory system.

Date        Activities                       Units     Unit Rate      Total Cost

April 1     Beginning inventory       220          $50             $11,000

April 5    Purchases                        100          $60                6,000

April 10   Purchases                         50          $45                2,250

April 16   Sales                              -300          $80

April 25  Sales                                -20          $95

April 30  Purchases                      200          $40                8,000

Total                                              570                             $27,250

Units sold                                      320

Ending inventory                         250

FIFO:

Ending Inventory = $10,250 (200 x $40 + 50 x $45)

Cost of goods sold = $17,000 ($27,250 - $10,250)

LIFO:

Ending Inventory = $12,800 (220 x $50 + 30 x $60)

Cost of goods sold = $14,450 ($27,250 - $12,800)

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In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

Graphing the polygon and reflection in a graph:

A polygon is a 2 - dimensional shape, that is formed by three or more straight edges. To graph, a polygon, plot the given points on the plane and connect the vertices using straight lines, without crossing any lines.

To reflect the image in the line y = x, switch the values of x to y and y to x. After switching the points, join the formed points and draw the reflected image.

Here we have

A(2, -1),  B(-1, 2),  C(2, 3),  D(4,2)

After switching the values of x to y and y to x the resultant points are

A'(-1, 2),  B'(2, -1),  C'(3, 2),  D'(2,4)

In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

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A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

example :

y=4+2x+x

y = 3x + 4

y = 3x + 4 is a polynomial that has exponent equal to 1.

Therefore A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

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The solution to the system graphed is (2, 0).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that changes over time is represented by a line graph.

Given:

From the graph we have two line red and purple.

The intersecting point for both line is (2, 0).

Hence, the solution to the system graphed is (2, 0).

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