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The total cost of the service in the light cell phone company is $24.05.

According to the statement,We have to find that the cost of the cellphone service.

So, For this purpose, we know that the

A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels.

From the given information:

Each bill includes a $19.95 service fee for 500 minutes plus a $3.95 communication tax and 15 cents for each minute over 500 minutes.

Then

Total cost become of 500 minutes = service fee + communication tax + Cost per minute

Then

Total cost become of 500 minutes = $19.95 + $3.95 + 15 cents

We know that the 0.15 dollars in 15 cents.

Then

Total cost become of 500 minutes = $19.95 + $3.95 + $0.15

Total cost become of 500 minutes =  24.05.

So, The total cost of the service in the light cell phone company is $24.05.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

Using the proportional side rule for similar triangles, all the values of x can be found as below.

Similar triangles are triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

1) Side lengths of bigger triangle are 32 + x and 24 + 9 = 33.

Corresponding proportional sides of smaller triangles are 32 and 24 respectively.

Using proportion,

\(\frac{32+x}{32}\) = \(\frac{33}{24}\)

Cross multiplying,

(32 + x) 24 = 32 × 33

768 + 24x = 1056

4x = 288

x = 12

2) Side lengths of bigger triangle are 33 + x and 20 + 14= 34.

Corresponding proportional sides of smaller triangles are x and 14 respectively.

\(\frac{33+x}{x}\) = \(\frac{34}{14}\)

462 + 14x = 34x

20x = 462

x = 23.1

3) Side lengths of bigger triangle are 30 + x + 5 = 35 + x and 36.

Corresponding proportional sides of smaller triangle are 30 and 20 respectively.

\(\frac{35+x}{30}\) = \(\frac{36}{20}\)

700 + 20x = 1080

20x = 380

x = 19

4) Side lengths of bigger triangle are x + 8 + 2x - 5 = 3x + 3 and 20 + 22.5 = 42.5.

Corresponding proportional sides of smaller triangles are 2x - 5 and 22.5 respectively.

\(\frac{3x+3}{2x-5}\) = \(\frac{42.5}{22.5}\)

67.5x + 67.5 = 85x - 212.5

17.5x = 280

x = 16

5) Side lengths of bigger triangle are 2x+4 +4 = 2x + 8 and x+7+3 = x + 10.

Corresponding proportional sides of smaller triangles are 2x + 4 and x + 7 respectively.

\(\frac{2x+8}{2x+4}\) = \(\frac{x+10}{x+7}\)

(2x + 8) (x + 7) = (x + 10) (2x + 4)

2x² + 8x + 14x + 56 = 2x² + 20x + 4x + 40

22x + 56 = 24x + 40

2x = 16

x = 8

6) Side lengths of bigger triangle are 2x + 8 + 5x - 4 = 7x + 4 and 82.

Corresponding proportional sides of smaller triangles are 2x + 8 and 28 respectively.

\(\frac{7x+4}{2x+8}\) = \(\frac{82}{28}\)

196x + 112 = 164x + 656

32x = 544

x = 17

Hence the values of x in each of the triangles are found.

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Answer: x-coordinate: 4

y-coordinate: -2

Step-by-step explanation:

The given system of linear equations:

y= x- 6   ..(i)

5x+3y = 14   ...(ii)

Substitute value of y in (ii), we get

\(5x +3(x-6)=14\\\\\Rightarrow\ 5x+3x-18=14\\\\\Rightarrow \ 8x=14+18\\\\\Rightarrow\ 8x=32\\\\\Rightarrow\ x=4\)

Put value of x in (i) , we get

\(y=4-6=-2\)

Hence, Required solution:  

x-coordinate: 4

y-coordinate: -2

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Therefore, there are 50 monkeys in total in the zoo when there are 20 monkeys that represent 2/5 of the total.

In mathematics, a fraction is a number that represents a part of a whole or a division of one quantity by another. Fractions are expressed as a ratio of two integers, separated by a horizontal or diagonal line, called the fraction bar. The number above the fraction bar is called the numerator, and the number below the fraction bar is called the denominator. Fractions can be written in different forms, such as mixed numbers, decimals, or percentages. They can be added, subtracted, multiplied, and divided using certain rules and operations. Fractions are used in many areas of mathematics, as well as in everyday life, such as in cooking, measurements, and financial calculations.

Here,

Let's call the total number of monkeys in the zoo "x".

We know that 20 monkeys represent 2/5 of the total number of monkeys in the zoo. We can set up an equation using this information:

2/5 x = 20

To solve for x, we can multiply both sides of the equation by the reciprocal of 2/5, which is 5/2:

(2/5 x) * (5/2) = 20 * (5/2)

Simplifying, we get:

x = 50

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Complete question:

In a zoo, there are 20 monkeys that represent 2/5 of the total. How many monkeys are there in total?

Answer:

x = 40°

Step-by-step explanation:

Two sides are the same length, so the angles opposite them are the same size.

The sum of the angles = 180°. One angle is 100°, so the sum of the remaining two angles is 80°.

Since the remaining two angles are congruent, each is 40°.

Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

6

Step-by-step explanation:

I Just answered the question on my test

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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The standard deviation of the examination grades in Maths SL for the class would be 1. 39.

First, list the grades based on their frequencies to be:

2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7

Then find the mean :

= ( 2 + 2 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 +7 + 7 + 7 + 7 + 7 ) / 32

= 5. 125

Then find the variance :

= ( ∑ ( x - mean ) ² / number of grades )

= ((2 - 4.85)² + (2 - 4.85)² + (3 - 4.85)² + (3 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (7 - 4.85)² + (7 - 4.85)² + (7 - 4.85)² + (7 - 4.85)² + (7 - 4.85)²) / 20

= 1. 921875

The standard deviation can be found by the formula :

 σ = √Variance

= √ 1. 921875

= 1. 39

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There is no point that is NOT included in the graph of the step function.

The coat check service charges $2 for the first hour and $1 for each additional hour or fraction of an hour.

To determine the point that is NOT included in the graph of the step function, we need to consider the charging scheme and analyze the pattern of charges.

The step function can be represented as follows:

For the first hour, the charge is a flat rate of $2.

For each additional hour or fraction of an hour, the charge is $1.

Let's analyze the points included in the graph:

(1, 2): This point represents the charge for the first hour, which is $2.

Now, let's consider the additional hours:

2. (2, 3): This point represents the charge for 2 hours, which is $2 for the first hour and $1 for the additional hour.

(3, 4): This point represents the charge for 3 hours, which is $2 for the first hour and $2 for the additional 2 hours.

(4, 5): This point represents the charge for 4 hours, which is $2 for the first hour and $3 for the additional 3 hours.

Based on the charging scheme, we can observe a pattern where the charge increases by $1 for each additional hour or fraction of an hour.

Since the charging scheme allows for any additional hour or fraction of an hour, there is no specific point that is excluded from the graph. Any positive value of x greater than or equal to 1 will have a corresponding point on the graph.

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Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

Answer: I believe

M = 80

Step-by-step explanation:

100 - 20 = 80

The width RQ of the river is approximately 61.98 ft.

To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.

Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.

From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.

Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.

From the given information, we know that TU = 68 ft.

Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.

The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

UQ² = TU² - US²

UQ² = 68² - 28²

UQ² = 4624 - 784

UQ² = 3840

Taking the square root of both sides, we have:

UQ = √3840

UQ ≈ 61.98 ft

Therefore, the width RQ of the river is approximately 61.98 ft.

Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.

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Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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Answer:

15-18

Step-by-step explanation:

The IQR is the middle 50% of a set of numbers

There are 8 numbers, so its the middle 4

The middle 4 consists of 15,15,16,18

The range is 15-18

Answer:

5ln3=ln(3^5)

Step-by-step explanation:

Given: 5ln(3)

Use rule: alog(b)=log(b^a), aln(b)=ln(b^a) (doesn't matter what the log base is)

Apply rule: ln(3^5)

The simplified expression when a polynomial is divided by a monomial is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.

Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S

For the given expression \((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\) factor the common term.

\((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)\)

Cancelling the -4:

\(= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)\)

Hence, the simplified expression is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

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Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

Answer:

$2.03

Step-by-step explanation:

2.25-(2.25*.1)=2.025

Discount:-

\(\\ \tt\longmapsto 0.1(2.25)\)

\(\\ \tt\longmapsto 0.22\)

Price after deducting discount

\(\\ \tt\longmapsto 2.25-0.22\)

\(\\ \tt\longmapsto \$2.03\)

Done

The final parametric equations describing the plane's motion are:

x(t) = 0 + (425 km - 0) * t = 425t

y(t) = 0 + (736.6 km - 0) * t = 736.6t

z(t) = 1650 meters

where t varies from 0 to 1.36 hours.

Let's set up a coordinate system with the origin at sea level beneath Denver.

We'll use the x-axis to point east, the y-axis to point north, and the z-axis to point upward.

The plane starts directly above Denver at an altitude of 1650 meters.

We can represent this as the initial point P₀(0, 0, 1650).

The plane then flies to Bismark, which is about 850 km in the direction 60° north of east from Denver.

Let's represent the position of Bismark as the point P₁(x, y, z), where x and y are the horizontal displacements (east and north, respectively), and z is the altitude above sea level.

Since the plane flies at a constant height of 7500 meters above the line joining Denver and Bismark, the altitude z remains constant at 7500 meters.

Let's calculate the horizontal displacements x and y:

The eastward displacement x can be found using the cosine of the angle (60°) and the distance to Bismark (850 km):

x = 850 km * cos(60°) ≈ 425 km

The northward displacement y can be found using the sine of the angle (60°) and the distance to Bismark (850 km):

y = 850 km * sin(60°) ≈ 736.6 km

Now, we can write the parametric equations for the plane's motion:

x(t) = x₀ + (x₁ - x₀) * t

y(t) = y₀ + (y₁ - y₀) * t

z(t) = z

where:

x₀ = 0 (initial x-coordinate at Denver)

y₀ = 0 (initial y-coordinate at Denver)

z = 1650 meters (altitude above sea level at Denver)

x₁ = 425 km (x-coordinate at Bismark)

y₁ = 736.6 km (y-coordinate at Bismark)

The parameter t represents the time in hours.

The plane's motion is constant, so t will vary from 0 to the time it takes to travel from Denver to Bismark at a speed of 625 km/hour.

To find the time it takes, we can use the distance formula:

Distance = Speed * Time

850 km = 625 km/hour * Time

Time = 850 km / 625 km/hour ≈ 1.36 hours

A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters).

It travels at 625 km/hour at a constant height of 7500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60∘ north of east from Denver.

Assume the origin is at sea level beneath Denver, that the x-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours.

So, the time it takes for the plane to travel from Denver to Bismark is approximately 1.36 hours.

The final parametric equations describing the plane's motion are:

x(t) = 0 + (425 km - 0) * t = 425t

y(t) = 0 + (736.6 km - 0) * t = 736.6t

z(t) = 1650 meters

where t varies from 0 to 1.36 hours.

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Answer:

91.85 hope this helps :))))))

Answer:

since ellen wants to buy all these items we add the prices together

19.95+41.25+30.65

this equals 91.85

so ellen needs $91.85 to buy all of the items she wants

Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

Answer:

0.722 is the answer when converting inches to miles

If 4/10 of Lake Okeechobee is covered in a harmful algal bloom in the first month, then 6/10 of the lake is not covered in the bloom.

In the second month, if 90% of the lake is covered in the bloom, then 10% of the lake is not covered in the bloom.

Since the amount of the lake that is covered by the bloom increased from 4/10 to 9/10, this is an increase of:

(9/10) / (4/10) = (9/10) x (10/4) = 2.25 times

Therefore, the algal bloom increased by 2.25 times.

Answer:

Step-by-step explanation:

First of all we need to convert 14.0 acres to m²

1.00 acre = 4046.86 m²

14.0 acres = 14 × 4046.86 = 56656.04 m²

Area of a circle = πr²

where

r is the radius

To find the radius substitute the value for the area into the above formula and solve for the radius

That's

\(56656.04 = \pi {r}^{2} \)

Divide both sides by π

We have

\( {r}^{2} = \frac{56656.04}{\pi} \)

Find the square root of both sides

\(r = \sqrt{ \frac{56656.04}{\pi} } \)

r = 134.29139

r = 134.29 m to 2 decimal places

Hope this helps you

Answer:

we have no way of knowing

Step-by-step explanation:

it could be a jedi mind trick.