Magazine:

Teen world - $9.98 (12 issues in yearly subscription) $3.25 (cost of a single copy)

Soccer world - $19.97 (6 issues in a yearly subscription) $4.99 (cost of a single copy)

Book nation - $19.98 (12 issues in yearly subscription) $2.99 (cost of a single copy)

TV weekly - $46.28 (52 issues in a yearly subscription) $1.95 (cost of a single copy)




2. Which of the magazines saves you the
most money by purchasing a yearly
subscription instead of an equivalent
number of single copies? How much
will you save?

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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Answer:

The probability of getting a number greater than two or an odd number :

\(= \frac{5}{6}\)

Step-by-step explanation:

the sample space is {1 , 2 , 3 , 4  5 , 6}

• let A be the event “getting a number greater than two“

Then

A = {3 , 4 , 5 , 6}

Then

p(A) = 4/6 = 2/3

• let B be the event “getting an odd number“

Then

B = {1 , 3 , 5}

Then

p(B) = 3/6 = 1/2

We notice that The event “getting a number greater than two or an odd number” is the event A∪B.

Then

p(getting a number greater than two or an odd number)

= p(A∪B)

= p(A) + p(B) − p(A∩B)

Calculating p(A∩B) :

A = {3 , 4 , 5 , 6} and B = {1 , 3 , 5}

Then

A∩B = {3 , 5}

Then

p(A∩B) = 2/6 = 1/3

Conclusion :

p(A∪B)

= p(A) + p(B) − p(A∩B)

= 2÷3  + 1÷2  − 1÷3

= 1÷3 + 1÷2

= 5÷6

The probability of getting a number greater than two or an odd number is 0.8.

We have a roll die.

We have to find the probability of getting a number greater than two or an odd number.

The formula to calculate the probability of occurrence of an event 'A' can be written as -  

P(A)  =  \(\frac{No. \;of\;possible\;outcomes}{Total\;number\;of\;outcomes}\)

According to question -

For getting a number greater than two or an odd number, the total number of possible outcomes are - 5.

For rolling a die, the number of outcomes will be - 6

Hence, the probability of occurrence of Event A will be -

P(A) = \(\frac{5}{6}\) = 0.8

Hence, probability of getting a number greater than two or an odd number is 0.8.

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Answer:

0

Step-by-step explanation:

it says the answer is zero

Step-by-step explanation:

Set the equation

\((x - 4) {}^{2} \)

swap y and x

\((y - 4) {}^{2} = x\)

\(y - 4 = {x}^{2} \)

\(y = {x}^{2} + 4\)

So the inverse is

\( {x}^{2} + 4\)

The domain is [4, infinity)

The range is [0,infinity)

The domain of the inverse is [0, infinity)

The range is [4, infinity)

Answer: 108336

Step-by-step explanation:

given data:

cards on deck = 52

Since  2 queens are supposed to be in the  5 card hand. Therefore, 2 queens are choosen since we have a total of  4.

Since  2 Queens have been chosen already choosen. we are left with 3cards out of the hand of 5. This cards are to be choosen from the 48 remaining cards. Similarly same process would be used for other combination of playing cards.

(42∗483)+(43∗482)+(44∗481).

= (6 * 17296) + (4 * 1128 ) + (1 * 48)

= 103776 + 4512 + 48

=108336

Answer:36

Step-by-step explanation:

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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9514 1404 393

Answer:

  23.44

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation ...

  Tan = Opposite/Adjacent

  tan(38°) = x/30

  x = 30·tan(38°) ≈ 23.4386

  x ≈ 23.44

If you take the answer, 2786 and multiple by 21

You get 58,506

Which if you subtract from 58,511 you would get 5

Which is r

\((4x)^{2} (6x)^{5} \\4^{2} x^{2} (6x)^{5} \\16x^{2} (6x)^{5} \\16x^{2} *6^{5} x^{5} \\16x^{2} *7776x^{5} \\(16*7776)x^{2} x^{5} \\124416x^{2} x^{5} \\124416x^{2+5} \\124416x^{7}\)

Answer:

Step-by-step explanation:

Your choice is correct

Answer:

24

Step-by-step explanation:

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

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

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

D. 20 inches

Step-by-step explanation:

Area = length * width

20 * 20 = 400 square inches

20 inches

The vertex labels of Δ QRT are : ∠2 label is Q, ∠8 label is T and the remaining vertex label is R. The vertex labels for ΔSTR are: ∠5 label is S, ∠9 label is R and the remaining label is T.

The polygon having three sides and three vertices are known as triangle.

If we separate the two triangles as shown in the figure. We can find the vertex labels with the help of the angles marked in the figure.

For Δ QRT, the vertex labels are:

∠2 is Q, ∠1 is R and ∠8 is T

Similarly. for ΔSTR, the vertex labels are:

∠5 is S, ∠6 is T, and ∠9 is R

Hence,  For Δ QRT, we can label as ∠2 is Q, ∠1 is R and ∠8 is T and for ΔSTR we can label as  ∠5 is S, ∠6 is T, and ∠9 is R.

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Answer:

The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.

An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.

Answer:

2.5

Step-by-step explanation:

multiply -5 by -1/2

Answer:

the marked price of a mobile is 25% above its cost price when it is sold at a gain of 10%, the profit amount to RS 725 find the marked price of the mobile

Step-by-step explanation:

Hope this helps.......

Answer:

sin∅ = 12/13

Step-by-step explanation:

use pythagorean theorem to find the missing side

a² + 5² = 13²

a² = 13² - 5²

a² = 169 - 25

a² = 144

a = 12

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

Sin∅ = opp/hyp

sin∅ = 12/13

Answer:

Yes

Step-by-step explanation:

The value of x from the given rectangle is 55 inches and the expression to represent the perimeter is 2(x+5).

Given that, length of a rectangle is x units and width is 5 units.

We know that, the perimeter of a rectangle is 2(Length+Breadth)

Perimeter = 2(x+5)

Here, the perimeter of a rectangle is 120 inches.

Now, 120 = 2(x+5)

x+5=60

x=55 inches

Therefore, the value of x from the given rectangle is 55 inches and the expression to represent the perimeter is 2(x+5).

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The answer of the given question based on the circle and rectangle is , the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

Perimeter is a measurement of the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is often measured in units of length, such as centimeters, meters, or feet.

To find the perimeter and area of the composite shape formed by a rectangle and two semicircles, we can break it down into its individual components and then add them up.

First, let's find the perimeter. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The perimeter can be calculated as:

Perimeter = 2 × (semicircle circumference) + rectangle perimeter

The circumference of circle is by the formula 2πr, where r is the radius. Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the circumference of each semicircle is:

C = 2πr = 2π(7.5) = 15π feet

The perimeter of the rectangle is simply the sum of its four sides, which is:

P = 2(length + width) = 2(15 + 4) = 38 feet

Putting it all together, we have:

Perimeter = 2 × 15π + 38 ≈ 83.8 feet

Now let's find the area. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The area can be calculated as:

Area = (semicircle area) + rectangle area

The area of a circle is given by the formula πr². Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the area of each semicircle is:

A = (1/2)πr² = (1/2)π(7.5)² = 44.18 feet²

The area of the rectangle is simply its length multiplied by its width, which is:

A = length × width = 15 × 4 = 60 feet²

Putting it all together, we have:

Area = 2 × 44.18 + 60 = 148.4feet²

Therefore, the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

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Answer: 44 Minutes

Step-by-step explanation: 20/5 = 4  ||  4x11 = 44

The force on the longer side of the aquarium is 515200 N.

Given,Aquarium's width = 2 ft, length = 4 ft, and height = 2 ft.To find:The force on the longer side of the aquarium.Solution:The longer side of the aquarium is 4 ft long.

The force on the longer side of the aquarium can be calculated using the formula:

F = ρghA

Where,F = force on the surface ρ = density of the fluid h = depth of the fluidA = area of the Surface We know that the density of water is ρ = 1000 kg/m³.

The area of the surface is A = l × h = 4 × 2 = 8 sq ft (as the aquarium is rectangular)

The depth of the fluid (water) on the longer side is h = 2 ft.

The force on the longer side can be calculated as follows:

F = ρghA= 1000 × 32.2 × 2 × 8= 515200 N

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Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Explanation:

The TI-84 calculator is fairly powerful and can handle things like this, but it's not needed to be honest. Any calculator will do.

"csc" is shorthand for "cosecant". It's the reciprocal of sine.

csc = 1/sin

Recall that

sin = opposite/hypotenuse

which means

csc = 1/sin = hypotenuse/opposite

What we'll need are the hypotenuse and opposite sides. Plot the points (0,0) and (-20,21). Draw a segment between them. This forms the hypotenuse of the right triangle shown below. This triangle is in the quadrant Q2 in the upper left corner. The hypotenuse 29 is found using the pythagorean theorem a^2+b^2 = c^2.

Use a = 20 and b = 21 to find c = 29.

According to that diagram, we can then say:

csc = hypotenuse/opposite = 29/21

Answer:

forgot to add a pic

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello friend!!!

here's ur answer

1) <y = 180 - 74 = 106° ( linear pair )

<x = <y ( alternate angles )

therefore, <x = <y = 106°

2) <x = 68° ( corresponding angles )

<y = 180 - 68 = 112° ( linear pair )

<z = 112° ( vertically opposite angles )

Hope this helps

plz mark as brainliest!!!!!

The missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

The equation of the function is given as:

y = 5^x

And the x value is given as

x = 2

To determine the missing value, we start by substituting 2 for x in the function y = 5^x

So, we have:

y = 5^2

Evaluate the exponent

y = 25

So, the complete coordinate is (2, 25)

Hence, the missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

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