the monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). the monthly cost for 45 minutes of calls is $14.40 and the monthly cost for 102 minutes is $19.53. what is the monthly cost for 66 minutes of calls?

Answer:

-5/4

Step-by-step explanation:

To find the slope, we have to use this formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

in this case -2 is your first x

5 would be your first y

2 would be your second x

and 0 is your second y

so:

0 - 5

-------    = -5/4

2 - (-2)

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

so the longest leg of the larger triangle will be "z" and the shorter leg of it will be "y", so let's find those fellows using proportions

[tex]\cfrac{x}{16}=\cfrac{9}{x}\implies x^2=144\implies x=\sqrt{144}\implies \boxed{x=12} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{x}=\cfrac{25}{16}\implies \cfrac{y}{12}=\cfrac{25}{16}\implies y=\cfrac{(12)(25)}{16}\implies \boxed{y=\cfrac{75}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{z}=\cfrac{9}{x}\implies \cfrac{~~ \frac{75 }{4 } ~~}{z}=\cfrac{9}{12}\implies \cfrac{75}{4z}=\cfrac{3}{4}\implies 300=12z \\\\\\ \cfrac{300}{12}=z\implies \boxed{25=z}[/tex]

Answer:

A.  The graph that Larry created is a correct representation of his company's charges.

Step-by-step explanation:

The equation for the services charges, y, is made up of the $10 initial service call fee plus $5 times the number of hours, x.

y = 5x + 10

Try any 2 values for x to see if they fits the graph.

x(hr)   y($)

0        10

1         15

4        30

This is the line already drawn on the graph.  Larry did everything correctly, so options B, C, and D are all false/incorrect.

The exponential growth of three sections is given below.

Exponential growth means whose growth more rapid in proportion.

An exponential function is of the form , where b is a positive number not equal to 1.

The value of b determines whether tha function is an exponential growth or an exponential decay.

An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.

Given the function= y 4(5/6)^x

B= 5/6 < 1

Therefore, the function  is an exponential decay.

Given the function

Therefore, the function  is an exponential growth.

Therefore, the function  is an exponential growth is y= 129(1.63)^x is an exponential growth.

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The solution to the inequality 4x + 10 < 6 is x < -1.

Given the inequality;

4x + 10 < 6

Solve for x.

Move all terms not containing x to the right side of the inequality by subtracting 10 from both sides of the inequality.

4x + 10 < 6

4x + 10 - 10 < 6 - 10

4x < 6 - 10

Subtract 10 from 6

4x < -4

Divide each term by 4 and simplify

4x < -4

4x/4 < -4/4

Simplify the left-hand side

x < -4/4

Simplify the right-hand side

x < -1

The result in inequality form is x < -1.

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The temperature at 6 pm is given as follows:

-40.2 ºF.

To obtain the temperature at 6 pm, we keep looking at the temperature for each interval given in the problem.

At 9 am, the temperature is given as follows:

-10.2ºF.

Between 9am and noon, the temperature rose 1.9°F, hence the temperature at noon is given as follows:

-10.2 + 1.9 = -8.3ºF.

Between noon and 3pm, the temperature dropped 16.4°F, hence the temperature at 3 pm is given as follows:

-8.3 - 16.4 = -24.7ºF.

Between 3pm and 6pm, the temperature dropped 15.5°F, hence the temperature at 6 pm is given as follows:

-24.7 - 15.5 = -40.2 ºF.

(subtracting the decline from the previous temperature, as we did for previous intervals).

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The time that it will take for the shadow to travel 1150 miles is; 30 minutes

Let y represent the distance in miles    

Let x represent the time in minutes

The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles

Thus, the coordinates are;

(60, 2300) and (20,  2300/3)

The slope is;

m = (2300 - 2300/3)/(60 - 20)

m = 115/3 mi/min

Thus, the linear equation in point slope form is;

y - 2300 = (115/3)(x - 60)

This gives;

y = (115/3)x

When y = 1150 miles, we have;

1150 = (115/3)x

x = 30 minutes

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If a caterer made a sandwich 6feet 6inches long for a party and 3 feet 8 inches added to the sandwich The total length of the sandwich is 122 inches

The height of the sandwich = 6 feet 6 inches

Convert to the inches

We know 1 feet = 12 inches

6 feet 6 inches = 6 × 12 + 6

= 72 + 6

= 78 inches

The height added to sandwich = 3 feet 8 inches

Convert to inches

3 feet 8 inches = 3 × 12 + 8

= 36 + 8

= 44 inches

The new height of the sandwich = 78 + 44

= 122

Therefore, the final height of the sandwich is 122 inches

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504 ways are there to line up all of the tas such that each tas with recitation partner(s) is standing next to them

Given :

cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation.

Number of ways = 9P6 * 9C3 * 1 / 5!

= 9! / ( 9 - 6 ) ! * 9! / ( 9 - 3 ) ! * 1 / 5!

= 9! / 3! * 9! / 6! * 1/5!

= 9 * 8 * 7 * 6 / 3 * 2 * 9 * 8 * 7

= 9 * 8 * 7

= 504 ways

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17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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The flux = 0

According to the divergence theorem, the volume integral of the divergence of a vector point function "F" taken over the volume "V" encompassed by the surface "S" is equal to the surface integral of the normal component of F taken over the closed surface "S." As a result, the divergence theorem is symbolically represented as:∬ v ∫ ▽ F → .

The sphere is presumably closed, so we can use the divergence theorem.

▽ F  =d(xy)/dx + d(yz)/dy + d(zx)/dz

▽ F =x + y + z

Now convert to spherical coordinates:

x=ρsinφcosθ,

y=ρsinφsinθ,

z=ρcosφ

The flux is then given by the volume integral for the radius 6

[tex]\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} = 36 }[/tex]   f.ds = [tex]\int\limits\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} < =36 }[/tex] (x+y+z) dv

Thus the flux = 0

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The median number of telephone line in thousands is 0

The number of telephone lines in each country = 250000

From the given dot plot

The data set will be

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250, 250, 250, 250, 250, 500, 750, 750, 1000, 1000, 1250, 1750

The median of the data set is the middle term of the ordered data set. The order of the data set maybe ascending or descending order

There are 28 terms in the data set the middle terms will be 14th and 15th

Both 4th and 15 terms are 0

Therefore, the median is 0

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Answer:

Below

Step-by-step explanation:

There are three ATOMS in each MOLECULE H2 O    

                                   (two hydrogen one Oxygen)

Each mole of MOLECULES = 6.022 x 10^23

     6.022 X 10^23     X 3  = 1.81 x 10^24 atoms

The Insurance policy's anticipated value in this case is -20.

What is Insurance?

Insurance is a tool for risk management. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.

Given,

Man pays -118 for one year

coverage = 140000

probability = 0.9993

The method used to calculate the insurance policy's expected value is:

= Chance that he won't live to see the end of the year * Coverage value - The cost of the insurance

= (1 - 0.9993)*140,000 - 118

= -20.

In this situation, the man's insurance coverage is expected to be worth -20.

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Answer:  x=12,-4

Step-by-step explanation:

As it is given, 1% of left tree is decaying every year.

Number of tree left after 8 years.

A = P{1-R/100}^[tex]^{T}[/tex] = 10M{1-1%/100}^  [tex]^{8}[/tex]

= 10M *(0.99)[tex]^[/tex]^[tex]^{8}[/tex]

= 9227446

If round at hundredth, then,

Number of tree = 9227400.

Identify the asset's cost. Get the asset's total depreciable value by deducting the projected salvage value from the asset's purchase price. Determine the asset's useful life. The annual depreciation amount is obtained by dividing the sum of steps (2) and (3) by the figure determined in steps (3).

Depreciation is the practice of deducting the cost of a company asset over a number of years as opposed to just one. There are four primary ways to depreciate assets: linear, twofold declining, sum of the years' digits, and manufacturing units.

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Answer: 1134 m^2

Step-by-step explanation:

First, you would plug in "9" to replace the variable. It would be 7(9) and 4(9). Parenthesis means multiplication.

Then, you would multiply. 7 x 9 = 63, 4 x 9 = 36

The area of a triangle is bh/2. So, 63x36=2268, 2268/2=1134.

I believe the answer is 1134 m^2.

The firm's profit margin is 4.17%.

To calculate the firm's profit margin, also known as the return on sales, you need to divide the firm's net income by its total sales. In this case, you are given the firm's return on assets (ROA), which is equal to the firm's net income divided by its total assets.

You can use this information to set up the following equation:

ROA = [tex]\frac{net \ income}{total \ assets}[/tex]

Plugging in the given values, you get:

8%= [tex]\frac{net \ income} {5,960,000}[/tex]

Solving for net income, you find that the firm's net income is

8% × 5,960,000 = 476,800.

Now that you know the firm's net income, you can calculate its profit margin by dividing its net income by its total sales. To do this, you need to know the firm's total sales.

You can use the firm's asset turnover ratio, which is equal to its total sales divided by its total assets, to calculate its total sales. In this case, the asset turnover ratio is 1.9, so you can set up the following equation:

asset turnover ratio = [tex]\frac{total \ sales}{total \ assets}[/tex]

Plugging in the given values, you get:

[tex]1.9 =\frac {total \ sales }{5,960,000}[/tex]

Solving for total sales, you find that the firm's total sales are

1.9 × 5,960,000 = 11,444,000.

Now that you know the firm's total sales, you can calculate its profit margin by dividing its net income by its total sales:

[tex]profit \ margin = \frac{net \ income}{total \ sales}[/tex]

[tex]= \frac{476,800}{11,444,000}= 4.17%[/tex]

Therefore, the firm's profit margin is 4.17%.

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If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

A quadrilateral is a closed shape that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The sum of quadrilateral interior angles is always 360 degrees. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.

A parallelogram is formed when both pairs of opposite sides of a quadrilateral are congruent. A parallelogram is formed when one pair of opposite sides of a quadrilateral are parallel and congruent.

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P(tail) = Probability of getting a tail on the coin

P(tail)=1/2

P(4)=Probability of getting the number '4' on the dice.

P(4)=1/6

P(tail and 4)=Probability of getting tail on the coin and number '4' on the dice.

P(tail and 4)=p(tail multiply with 4)

P(tail and 4)= 1/2×1/6

P(trail and 4)=1/12

Hope this helps!

Answer:

16

Step-by-step explanation:

4 / 2

2 / 2

1

4 = 2²

16/2

8/2

4/2

2/2

1

16 = 2^4

lowest common denominator = 2^4 = 16

Answer: 40

Step-by-step explanation:

Answer: 20

Step-by-step explanation:
5x^2

5 ( 2 )^2 (substituting the value of x)

5 ( 2 x 2) (working out the exponents of x)

5 (4) (solving the brackets)

20

Answer: C: 4.9

The original answer is 4.8989, so I rounded 8 to the nearest hundredth and got the answer of 4.9. Having a Mathematics calculator also helps with math like this.

The percentage change of the first quantity with reference to the second quantity: 480 units, 560 units is: -14.29%.

First step is to find the difference between the two numbers

Difference = New Number - Original Number

Difference =  480 -560

Decrease  = -80

Now let find the percentage change

Percentage change = Decrease  / Original Number × 100

Percentage change = -80 /560 × 100

Percentage change = -14.29%

Therefore we can conclude that the percentage change is -14.29%.

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Answer:  -27≥x  OR  x>7

Step-by-step explanation:

[tex]\displaystyle\\a)\ -7\geq \frac{x}{3}+2 \\\\\-7-2\geq \frac{x}{3}+2-2\\\\ -9\geq \frac{x}{3} \\\\[/tex]

Multiply both parts of the equation by 3:

[tex]\displaystyle\\-9(3)\geq \frac{x}{3}(3)\\\\\boxed {-27\geq x}[/tex]

[tex]\displaystyle\\b)\ \frac{3x+1}{2} > 11[/tex]

Multiply both parts of the equation by 2:

[tex]\displaystyle\\\frac{3x+1}{2}(2) > 11(2)\\\\3x+1 > 22\\\\3x+1-1 > 22-1\\\\3x > 21[/tex]

Divide both parts of the equation by 3:

[tex]\boxed{x > 7}[/tex]

The expression evaluates because the variable truck weight's true value is present. The correct answer is (C).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given,

In the following expression, the variable truck weight has the value 70000 and the variable weight limit has the value 80000.truck weight < weight limit.

Expression,

Truck weight < Truck limit

The value of expression evaluate,

It is true.

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The perimeter of the isosceles  triangle with side lengths 3·x, (4·x - 7), and (1/2·x + 9) is 51[tex]\frac{1}{14}[/tex]

An isosceles triangle is a triangle that has a pair of congruent sides and according to the triangle inequality theorem, a pair of congruent angles.

The lengths of the sides of the isosceles triangle are;

3·x, 4·x - 7, and 1/2·x + 9

Let the sides, 3·x and 4·x - 7 represent the congruent sides of the triangle, we get;

3·x = 4·x - 7

4·x - 3·x = x = 7

x = 7

The length of the sides of the triangle, found by plugging in x = 7 in the specified expressions for the lengths of the sides of the triangle are therefore;

Length of the first side; 3·x = 3 × 7 = 21

The length of the second specified side; 4·x - 7 = 4 × 7 - 7 = 21

Length of the third specified side; (1/2×x) + 9 = (1/(2 × 7)) + 9 = 1/14 + 9

The perimeter of the triangle is the sum of the lengths of the sides of the triangle, therefore;

The perimeter of the triangle is; 21 + 21 + 1/14 + 9 = 51 [tex]\frac{1}{14}[/tex]

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Answer:   (4b, -3a)

Reason:

When reflecting over the line y = x, we swap the positions of the x and y coordinates.

The reflection rule is [tex](\text{x},\text{y}) \to (\text{y},\text{x})[/tex]

As an example: [tex](2,3) \to (3,2)[/tex]

Option D (No, as there are two heights associated with the wrist circumference of 16 cm.

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph.

The wrist circumferences and heights of six kids in Alyssa's class are represented by a collection of points in the graph that is shown.

The height is represented by the y axis, and the wrist circumference by the x axis.

Any relation is referred to as a function if there is only one value of y for any given value of x. The graph is referred to as a function if it passes the vertical line test, which requires that a vertical line be drawn and only touch the graph once.

There are two y values (162 and 165) on the above graph for the x value of x=16.

The graph is not a function as a result.

Among the possibilities The correct response is option D, "No," since the wrist circumference of 16 cm pairs with two heights.

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