Find the inverse of the function f(x)=√x+3.

Answer:

Step-by-step explanation:

To find the hiker's elevation above sea level upon reaching High Point Vista, we need to add up the elevation gain from the start of the trail to High Point Vista. We can use the table to do this:

Elevation gain from start to Old Cabin: -32.78 ft (negative because the hiker loses elevation)

Elevation gain from Old Cabin to Ruby Falls: 8634 ft

Elevation gain from Ruby Falls to Thunder Gorge: -14725 ft (negative because the hiker loses elevation)

Elevation gain from Thunder Gorge to High Point Vista: 346.47 ft

To find the hiker's elevation above sea level at High Point Vista, we add up these elevation gains:

179 ft (start) - 32.78 ft + 8634 ft - 14725 ft + 346.47 ft = -5668.31 ft

The negative value means that the hiker is below sea level at High Point Vista, which is not possible. Therefore, there must be an error in the elevation gain listed for one of the points of interest. It's possible that the elevation gain for Ruby Falls is incorrect, as it seems unlikely that the hiker would gain more than 8000 ft in elevation between Old Cabin and Ruby Falls. Without more information, it's difficult to say for sure where the error lies.

Answer:

cos^2 θ/2 = (cos θ + 1)/2.

Step-by-step explanation:

We can use the identity cos 2θ = 2cos^2 θ - 1 to derive an identity for cos^2 θ/2:

cos 2(θ/2) = cos θ

Replacing θ/2 with x:

cos 2x = cos 2(x/2)

Using the double angle formula for cosine:

cos 2x = 2cos^2 x - 1

Substituting θ/2 for x:

cos θ = 2cos^2 (θ/2) - 1

Rearranging this formula, we can solve for cos^2 θ/2:

2cos^2 (θ/2) = cos θ + 1

cos^2 (θ/2) = (cos θ + 1)/2

Therefore, cos^2 θ/2 = (cos θ + 1)/2.

A. The equations representing plant height after a given number of days are:

B. To graphically represent the system of equations, we can plot the points that correspond to the height of each plant after a given number of days. For example, after 5 days, the first plant is 15 cm tall (2(5) + 5 = 15) and the second plant is 18 cm tall (3(5) + 3 = 18).

You can draw this graph as a coordinate plane with the horizontal axis representing the number of days since the initial measurement and the vertical axis representing the height of the plants in centimeters.

C. To find the height of each plant after 15 days, we can plug t = 15 into the equations we encountered in letter A:

It is a set of two or more equations that share common variables and are solved jointly.

Therefore, a system of equations is used when one wants to find the values of variables capable of satisfying all the equations of the system, whose solutions represent the points where the graphs of the equations in the Cartesian plane.

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Answer:

Answer:

Step-by-step explanation:

a. 4x + 8

b. 14x

c. 8x + 12

d. 6x + 6y + 6z

Answer:

Step-by-step explanation:

1]4(x+2)

using distributive property ,

Multiply 4 to x and 2

4x + 8

2]4(2x+3)

using distributive property ,

Multiply 4 to 2x and 3

= 4 x 2x + 4 x 3

= 8x +12

3](6 + 8).x

= (14).x

14x

4] 6(x + y + z)

using distributive property ,

multiply 6 to x and y and z

6.x + 6.y + 6.z

6x + 6y +6z

Answer: We will start by using the identity cos² A + sin² A = 1 to replace sin² A with cos² A - 1 in the expression 1 - 2sin A sin B sin C:

1 - 2sin A sin B sin C = 1 - 2sin A (cos B cos C - sin B sin C) [Using the product-to-sum formula for sin (B + C)]

= 1 - 2sin A cos B cos C + 2sin A sin B sin C

Now, we will use the identity cos (180° - x) = -cos x to replace cos C with -cos (A + B):

cos² A + cos² B - cos² C = cos² A + cos² B - cos² (A + B)

= cos² A + cos² B - (cos² A cos² B - 2cos A cos B sin A sin B)

= cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B

= (cos² A)(1 - cos² B) + (cos² B)(1 - cos² A) + 2cos A cos B sin A sin B

= cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B

Now, we will use the identity sin (A + B) = sin A cos B + cos A sin B to rewrite the last term:

cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B

= cos² A + cos² B - cos² A cos² B + 2sin A sin B cos A cos B

= (cos² A)(1 - cos² B) + (cos² B)(1 - cos² A) + 2sin A sin B cos A cos B

= (cos² A + cos² B - 1) + (1 - cos² A)(1 - cos² B) + 2sin A sin B cos A cos B

= 2sin² A sin² B + 2sin A sin B cos A cos B

= 2sin A sin B (sin A cos B + cos A sin B)

= 2sin A sin B sin (A + B)

= 2sin A sin B sin (180° - C) [Using A + B + C = 180°]

= -2sin A sin B sin C

Substituting this expression back into the original equation, we get:

cos² A + cos² B - cos² C = 1 - 2sin A sin B sin C

Therefore, the expression is proved.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Square pyramid (since the base is a square)

Area base [tex]= 8^2=64mm^2[/tex]              (area of square)

Area each side [tex]= \frac{1}{2} base[/tex]×[tex]height[/tex]    (area triangle formula)

                          = [tex]\frac{1}{2}[/tex]×[tex]8[/tex]×[tex]10[/tex]

                          = [tex]40 mm^2[/tex]

Total area [tex]= 4triangles + square base[/tex]

                 [tex]=4[/tex]×[tex]40+64[/tex]

                 [tex]=224 mm^2[/tex]

Most nations adopt the international standard ISO 216, which specifies the dimensions of an A4 sheet.

ISO (International organization fr Standardization) is an independent, non-governmental body that develops standards to ensure the effectiveness, safety, and quality of goods, services, and systems.

Obtaining an ISO quality management certification can greatly benefit your company by increasing productivity, efficiency, and customer satisfaction.

The international standard ISO 216, which is widely used worldwide, specifies the dimensions of an A4 sheet. A4 paper measures 210 x 297 mm r 21 x 29.7 cm.

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The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.

A function in mathematics is a relationship between a domain—a set of possible inputs—and a range—a set of potential outputs—with the property that each input is linked to precisely one output. Frequently, a mathematical expression, equation, or formula will be used to describe a function. They are a fundamental idea in calculus, algebra, and other branches of mathematics, used to explain how one quantity relies on another.

given

Let Q(x) = 7.25x 36.25 be a model for his daily earnings, where x is the quantity of bracelets he sells.

Q(5) = 23.5, which indicates that Quincy will make $23.50 if he sells 5 wristbands today.

The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.

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The retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.

Two or more expressions with an Equal sign is called as Equation.

The wall needs to be at least 60 inches tall, and we already have a 12-inch piece of stone, so we need to stack enough rows of bricks to reach a height of:

60 inches - 12 inches = 48 inches

Each row of bricks adds 1.5 inches to the height

we can divide the remaining height of 48 inches by the height of each row:

48/1.5 = 32 rows

Therefore, the retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.

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Answer:

The decoded message is: "Steve Jobs".

Step-by-step explanation:

The given code is a sequence of binary digits, which represents the ASCII code of a message in binary form. To decode the message, we need to convert each 8-bit binary sequence into its corresponding ASCII character.

1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011

To decode this message, we split it into 8-bit sequences:

01010011 --> 'S'

01110100 --> 't'

01100101 --> 'e'

01110110 --> 'v'

01100101 --> 'e'

00100000 --> ' '

01001010 --> 'J'

01101111 --> 'o'

01100010 --> 'b'

01110011 --> 's'

Therefore, the decoded message is: "Steve Jobs".

Answer:

The decoded message is: "Steve Jobs"

Step-by-step explanation:

Converting the binary code to ASCII, we get:

01010011 = S

1110100 = t

1100101 = e

1110110 = v

1100101 = e

0100000 = (space)

1001010 = J

1101111 = o

1100010 = b

1110011 = s

So the decoded message is: "Steve Jobs"

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

Here are the steps to decode the given binary code:

Break the binary code into groups of 8 digits, as each group represents a single ASCII character.

Convert each group of 8 digits into its corresponding ASCII character using a binary-to-text converter or an ASCII code chart.

Write down the decoded ASCII characters in the order in which they appear in the original binary code.

Let's follow these steps to decode the given binary code:

The given binary code is: 1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011

We break this binary code into groups of 8 digits:

1010011 = 53

1110100 = 74

1100101 = 65

1110110 = 76

1100101 = 65

0100000 = 32

1001010 = 74

1101111 = 111

1100010 = 98

1110011 = 115

We convert each group of 8 digits into its corresponding ASCII character using an ASCII code chart:

53 = S

74 = t

65 = e

76 = v

65 = e

32 = (space)

74 = J

111 = o

98 = b

115 = s

We write down the decoded ASCII characters in the order in which they appear in the original binary code:

Decoded message: "Steve Jobs"

ASCII mean?

ASCII stands for American Standard Code for Information Interchange. It is a character encoding standard that assigns unique numeric codes to represent text characters. The ASCII standard includes codes for uppercase and lowercase letters, digits, punctuation marks, and various other symbols. Each ASCII character is represented by a unique 7-bit binary code, allowing computers and other devices to communicate and display text in a consistent manner. The ASCII standard was first published in 1963 and has since been expanded and updated to include additional characters and support for different languages.

Answer:

24.6063 ft

Step-by-step explanation:

The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

This problem can be solved using the probability , where we have a fixed number of trials (10 children) and a fixed probability of success (one-in-two chance of getting the disease).

The probability of getting exactly k successes in n trials, each with probability p of success, is given by the binomial probability formula:

P(k) = (n choose k) * [tex]p^k * (1-p)^{(n-k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of a set of n.

For this problem, we have n = 10, p = 1/2 (since the children have a one-in-two chance of getting the disease), and we want to find P(5) and P(7).

P(5) = (10 choose 5) * ([tex]1/2)^5 * (1/2)^{(10-5)} = 0.2461[/tex] (rounded to four decimal places)

P(7) = (10 choose 7) * [tex](1/2)^7 * (1/2)^{(10-7)} = 0.1172[/tex] (rounded to four decimal places)

Hence, The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.

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The system of inequalities is y < x + 2 and 5y ≤ -2x + 10

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

The blue and the red lines

For the blue line, we have the following points

(0, 2) and (-2, 0)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 2

Using the points, we have

-2m + 2 = 0

m = 1

So, we have

y = x + 2

The lower part is shaded and the line is a dotted line

So, we have

y < x + 2

For the red line, we have the following points

(0, 2) and (5, 0)

The equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 2

Using the points, we have

5m + 2 = 0

m = -2/5

So, we have

y = -2/5x + 2

The lower part is shaded and the line is a shaded line

So, we have

y ≤ -2/5x + 2

Multiply through by 5

5y ≤ -2x + 10

Hence, the system is y < x + 2 and 5y ≤ -2x + 10

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Using the equation, we found the following:

1) Expected Population in the year 2014 = 41100

2) Predicted year when the population will reach 54000 = 2020

3) The rate of population changes = 2150

4) The number of years for the population doubled since 2008 =9.12

What is a linear equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

Given,

the population in 2008 = 28,200

the population in 2012 = 36,800

The population is growing linearly.

Assume a linear equation,

p(x) = 36800 + kx

where,

   p(x) = population

  x = years since 2012.

k = increase in population

p(0) = 36800

p(-4) = 36800 - 4k

28200= 36800 -4k

4k = 36800 - 28200

k = 2150

Then the linear equation becomes,

p(x) = 36800 + 2150x

1) Population in 2014

x = 2014 - 2012 = 2

From the equation,

p(2) = 36800 + 2150 * 2 = 41100

2) x when p(x) = 54000

From the equation,

54000  = 36800 + 2150x

2150x = 17200

x = 8

Year = 2012 + 8 = 2020

3) Rate of population change = (population in 2012 - population in 2008) / number of years = 36800-28200 / 4 = 2150

4) Population doubled since 2008

p(x) = 2 * 28200 = 56400

We have to find x , when p(x) = 56400

Using the linear equation,

56400 = 36800 + 2150x

x = 9.12

Therefore using the equation, we found the following:

1) Expected Population in the year 2014 = 41100

2) Predicted year when the population will reach 54000 = 2020

3) The rate of population changes = 2150

4) The number of years for the population doubled since 2008 =9.12

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The required container can hold approximately 1570.8 cubic inches of soil.

By enclosing units in containers—that is, by circling, boxing, or otherwise enclosing units—container numbers indicate magnitude. The worth of each container's contents is multiplied by the number system's fundamental unit. Typically, the basis is either 2 or 10 (the decimal system) (the binary system).

To find the volume of the container, we can use the formula for the volume of a cylinder:

[tex]$$ V = \pi r^2 h $$[/tex]

where r is the radius of the base (half the diameter) and $h$ is the height of the cylinder.

In this case, the diameter of the container is 10 inches, so the radius is half that, or 5 inches. The height is given as 20 inches. Substituting these values into the formula, we get:

[tex]$$ V = \pi (5\text{ in})^2 (20\text{ in}) = \pi (25\text{ in}^2)(20\text{ in}) \approx 1570.8 \text{ in}^3 $$[/tex]

Therefore, the container can hold approximately 1570.8 cubic inches of soil.

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Complete question:

Thomas loves tomatoes he plans to fill the container with soil to grow his own tomato plant the diameter of the container is 10 inch and height 20 inch how much soil will the container hold.

Answer:

Step-by-step explanation:

1 jacket and 2 notebooks

(just my guess but you might get it right)

(also use desmos scientific calculator its a lot better)

Answer:

he sold 35 notebooks

Step-by-step explanation:

first you subtract 40.00 from 92.50 equaling 52.50 then you divide 52.50 by 1.50.

2k + 5 = 2(8) + 5 = 16 + 5 = 21

k is substituted into the expression

The gas has a capacity of 22 litres at 0 degrees Celsius and increases by 225 litres for each degree above that.

Volume is the amount of space a thing takes up, whereas capacity is the amount of substance it can hold, such as a solid, liquid, or gas. Volume is typically measured in cubic units, whereas capability can be measured in virtually any other unit, such as litres, gallons, pounds, and so on.

According to the problem statement, the volume of the gas and the temperature T in degrees Celsius have a direct relationship. Furthermore, we know that the gas expands by 225 litres for every degree of temperature rise. With this knowledge, we can create the equation shown below:

V = 22 + 225T

where T is indeed the temperature is degrees Celsius and V is the gas's volume in liters.

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Answer:

A. 62 units

Step-by-step explanation:

To find the perimeter of the rectangle, you have to use the Pythagorean theorem.

a^2 + b^2 = c^2 - Formula

24^2 + b^2 = 25^2 - Plug in values

576 + b^2 = 625 - Simplify

b^2 = 49 - Isolate the variable

b = 7 - Solve

After finding the height, find the perimeter.

P = 2b + 2h

P = 2(24) + 2(7)

P = 48 + 14

P = 62 units

Based on the information in the graph, we can infer that the length of Main St between 5th Ave. and 6th Ave. is 0.24km.

To find the value of Main St. between 5th Ave. and 6th Ave we must perform the following mathematical procedure:

In accordance with the above, what we did was a relationship between the fractions that represent the length of each street. In this case we had to clear the x that represented Main St. between 5th Ave. and 6th Ave.

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Answer:

0.96

Step-by-step explanation:

Bella owns a small business selling ice-cream. She knows that in the last week 50 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card.

Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.

50 cash, 2 debit card, and 4 credit card.

50+2+4= 56

There were a total of 56 customers. 50+4=54 customers paid with cash or a credit card.

Probability the next customer will pay with cash or a credit card:

54

56

​

= 0.964285...

≈ 0.96

Round to the nearest hundredth

The probability as a decimal to the nearest hundredth is

0.96

The values in the table using the expression (time=2 × no. of pages) will be 0.5, 5 and 8.5.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to produce a value.

Expressions can be simple or complex, and can involve arithmetic, algebraic, or logical operations. Some examples of expressions include:

In each of these examples, the expression consists of one or more terms that are combined using operations such as addition, subtraction, multiplication, division, or exponentiation.

Now,

As given pages = 8 and time= 16 minutes

this can be deduced by expression Time=2 × no. of pages

Then for time= 1,10 and 17 minutes

no. of pages will be 1/2,10/2 and 17/2.

Hence, the table will be:

Pages           8       0.5         5        8.5

Minutes      16        1           10       17

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Answer:

( x − a ) 2 + ( y − b ) 2 = r 2

SA = 2π(1.3)² + 1.3π(3.8) is the equation that calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown.

The correct equation to calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder is:

SA = 2πr(h + r)

where r is the radius of the cylinder (which is half of the diameter), and h is the height of the cylinder.

In this case, the radius is 1.3 centimeters (half of the diameter of 2.6 centimeters), and the height is 3.8 centimeters. Therefore, the correct equation to calculate the surface area (amount of wrapping paper needed) is:

SA = 2π(1.3)(3.8 + 1.3)

SA = 2π(1.3)(5.1)

SA ≈ 41.82 square centimeters

So, the amount of wrapping paper needed to completely cover the cylinder is approximately 41.82 square centimeters.

Identify the relevant measurements of the cylinder: In this case, the problem states that the cylinder has a diameter of 2.6 centimeters and a height of 3.8 centimeters.

Calculate the radius of the cylinder: The radius of the cylinder is half of its diameter. So, divide the diameter by 2: 2.6/2 = 1.3 centimeters. Therefore, the radius of the cylinder is 1.3 centimeters.

Use the formula for the surface area of a cylinder: The formula for the surface area of a cylinder is SA = 2πr(h + r), where r is the radius of the cylinder and h is its height. Plug in the values for r and h: SA = 2π(1.3)² + 1.3π(3.8).

Thus, SA = 2π(1.3)² + 1.3π(3.8) is the equation that alculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown.

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The value of x using trigonometric ratios, we get = 36.87°

Trigonometry uses the following six trigonometric ratios: sine, cosine, tangent, secant, and cotangent. Sin, cos, tan, sec, cosec, and cot are acronyms for these ratios.

Trigonometric ratios can be used to compare the relative angles of any two sides of a right-angled triangle, which has three sides altogether.

Here.

tan x° = 9/12

⇒ (tan x°) = (9/12)

⇒ x° = 36.86989765

⇒ x = 36.87°

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Answer: PP(Percentage) + PP or PP(1.%)

Step-by-step explanation:

Answer:

t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

Step-by-step explanation:

Solve for t:

16 t^2 - 23 t + 18 = 0

Divide both sides by 16:

t^2 - (23 t)/16 + 9/8 = 0

Subtract 9/8 from both sides:

t^2 - (23 t)/16 = -9/8

Add 529/1024 to both sides:

t^2 - (23 t)/16 + 529/1024 = -623/1024

Write the left hand side as a square:

(t - 23/32)^2 = -623/1024

Take the square root of both sides:

t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32