how many ft in miles?

The equation tan(30°) = 5/b can be used to solve for b. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle falls under the purview of the branch of mathematics known as trigonometry.

We are given a right angled triangle, with angle BCA = 90° and angle CAB = 30°. Also, the length of side BC is 5 centimeters, the length of BA is 10 centimeters, and the length of CA is b.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = 5/b

Here, θ = 30°

So,

⇒tan 30° = 5/b

Hence, the equation tan(30°) = 5/b can be used to solve for b.

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We know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

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 in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

So, the given expressions are:

7x - 4 and 6x - 4 - x

Now,

7x - 4 and 6x - x - 4

7x - 4 and 5x- 4

Then, we can easily say that the given expressions are not equivalent.

Therefore, we know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

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Complete questions:
Explain how you can tell if the expressions 7x – 4 and 6x – 4 – x are equivalent. Sample Response: 6x − x = 5x.

1. The new expression is now 5x − 4.

2. This is not equivalent to 7x − 4.

Answer:

x = -2

Step-by-step explanation:

-3x + 1 = 7

Subtract 1 from both sides:

-3x = 6

Divide -3 by both sides:

x = -2

The correct answer will be V =8×6×3 & V= 48×3. The volume of a rectangular prism = Length x Width x Height.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. Although capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is determined in cubic units.

Capacity. The total volume of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to contain, absorb, or absorb by an object (such as a solid substance, gas, or liquid).

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Answer:

Step-by-step explanation:

(90 +100) / 2 = 190/2 = 95

The values of x in the triangles are 9.23 and 7.5

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

The triangle

Using the above as a guide, we have the following:

cos(52) = x/15

Make x the subject of the formula

So, we have the following representation

x = 15 * cos(52)

Evaluate

x = 9.23

For the second triangle, we have

x = 17 * sin(26)

x = 7.5

Hence, the solution is 9.23 and 7.5

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The two column proof showing that ΔFHK ~ ΔGHJ is as detailed below.

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Statement 1: FG/FH = KJ/KH

Reason 1: Ratio of similar sides of a triangle

Statement 2: ∠H ≅ ∠H

Reason 2: Reflexive Property of Congruence

Statement 3: ΔFHK ~ ΔGHJ

Reason 3: SAS Similarity Theorem

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a. The subtοtal is $23.45, the tip is $4.22, and the tοtal cοst οf their meal is $27.67.

b. Each persοn wοuld pay $13.84.

The additiοn is a basic arithmetic οperatiοn that cοmbines twο οr mοre quantities intο a single sum. It is οne οf the fοur basic οperatiοns in arithmetic, alοng with subtractiοn, multiplicatiοn, and divisiοn.

In additiοn, the quantities being cοmbined are called addends, and the result οf the additiοn οperatiοn is called the sum. The additiοn is represented using the plus sign (+), which is placed between the addends. Fοr example, the additiοn expressiοn "3 + 5" means that we are adding 3 and 5 tοgether tο get a sum οf 8.

Fοr example, tο add the numbers 34 and 56, we start by adding the digits in the οne's place, which gives us 4 + 6 = 10. We write dοwn the 0 and carry the 1 οver tο the tens place. Then we add the digits in the tens place, which gives us 3 + 5 + 1 = 9. The final answer is 90.

a: Subtοtal = Hamburger + Guacamοle + Cheeseburger + Fries + Sοda + Milk

Subtοtal = $7.99 + $1.00 + $8.99 + $2.49 + $1.99 + $0.99

Subtοtal = $23.45

Tip = 18%×Subtοtal

Tip = 0.18 × $23.45

Tip = $4.22 (rοunded tο the nearest cent)

Tοtal = Subtοtal + Tip

Tοtal = $23.45 + $4.22

Tοtal = $27.67 (rοunded tο the nearest cent)

Therefοre, the subtοtal is $23.45, the tip is $4.22, and the tοtal cοst οf their meal is $27.67.

b: If Sue and her friend split the final cοst equally, each persοn wοuld pay half οf the tοtal cοst:

$27.67 / 2 = $13.84 (rοunded tο the nearest cent)

Therefοre, each persοn wοuld pay $13.84.

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For converting fractions to decimals, we need to divide numerator with denominator,

So, the value of 51/16 as a decimal is equal to 3.1875.

In mathematics, the ratio of two integers is how a fraction is defined in mathematics.

The fraction indicates that it is the numerator value to denominator value ratio.

A decimal number is one in which the decimal point separates the whole number component from the decimal component.

From the question,

As we need to convert the given fractional value to decimal.

So, for determining the equivalent decimal value, we will simply divide the value given in the numerator to the value given in the denominator.

So, dividing 51 by 16

We will get it as:

51/16: 51 16 = 3.1875

As a result, 51/16 is equivalent to 3.1875 in decimal form.

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The volume of each soup can is approximately 785.4 cubic centimeters.

The volume of a cylinder can be calculated using the formula:

Volume =[tex]\pi[/tex] ×[tex]radius^2[/tex]× height

where π (pi) is a mathematical constant approximately equal to 3.14159, the radius is the distance from the center of the circular base of the cylinder to its edge, and height is the vertical distance between the circular bases.

In other words, the volume of a cylinder is the amount of space occupied by the cylinder, and it depends on the size of the circular base and the height of the cylinder.

In this case, the radius of the can is given as centimeters and the height is also given as centimeters. So, we can substitute these values in the formula and calculate the volume:

Volume = π × [tex]radius^2[/tex] × height

Volume = π ×[tex]5^2[/tex] × 10

Substituting radius = 5 cm and height = 10 cm

Volume = 250π cubic centimeters

Volume ≈ 785.4 cubic centimeters (rounded to one decimal place)

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For someone earning $75,000 per year working 24 hours daily, their equivalent hourly wage would be approximately $8.56 per hour.

If someone worked 24 hours a day, every day of the year, they would work a total of 8,760 hours in a year. To calculate the hourly wage of someone earning $75,000 per year working 24 hours daily, you can divide the yearly salary by the total number of hours worked in a year.

Dividing $75,000 by 8,760 hours gives an hourly wage of approximately $8.56. This means that if someone earned $75,000 per year while working 24 hours a day, they would be earning an equivalent of approximately $8.56 per hour.

Additionally, laws and regulations related to working hours vary by country and industry, and many limit the maximum number of working hours per day or week.

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Answer:

Area is approximately 113.1

Answer: I’m pretty sure it’s c

Step-by-step explanation:

The expected temperature in Peoria Illionis on february 15 is 22.028≈22 degrees farenheit.

A measure of the temperature at high elevations in the Earth's atmosphere is called the atmospheric temperature. Many factors, such as incoming solar radiation, humidity, and altitude, affect it.

The average daily temperature in Peoria Illionis can be predicted by given formula ,

[tex]T=50-28cos[\frac{2\pi (x-31)}{365} ][/tex]

where , x is the number of day in year.

February 15 is (31+15)th day of the year

therefore, February 15 1s 46th day of the year.

now in the given formula,

[tex]T=50-28cos[\frac{2\pi (x-31)}{365} ]\\\\T=50-28cos[\frac{2\pi (46-31)}{365} ]\\\\T=50-28cos[\frac{2\pi (15)}{365} ]\\\\T=50-28cos[\frac{30\pi}{365} ]\\\\T=50-28cos[0.258]\\\\T=50-28(0.999)\\\\T=50-27.972\\\\T=22.028[/tex]

So , the expected temperature on february 15 is 22.028≈22 degrees farenheit.

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The height of the silo is approximately 81 meters to the nearest meter.

One of the most basic areas of mathematics, trigonometry has a wide range of applications. The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Let's draw a diagram to visualize the situation. We have a right triangle with the transit (T), the silo (S), and a point on the ground (G) where the surveyor is standing. The angle of elevation of the silo from the surveyor's position is 52º, and we know the distance TG = 65 m and the height of the transit HT = 1.7 m. We want to find the height of the silo, which is HS.

          S

          |\

          | \

    HS |  \  TG = 65 m

          |   \

          |    \

          |     \

          |      \

          |       \

          |        \

          T--------G

             HT = 1.7 m

Using trigonometry, we have the following equation:

tan(52º) = HS / TG + HT

Solving for HS, we get:

HS = (TG + HT) * tan(52º)

= (65 + 1.7) * tan(52º)

≈ 81.1 m

Therefore, the height of the silo is approximately 81 meters to the nearest meter.

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Answer:

1. the three sides to a right triangle is hypotenuse, opposite, and adjacent.

2. If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Step-by-step explanation:

hope this helped!!! <3

Answer:

Here is how to write and graph an inequality for the budget problem:

Let x be the number of large boxes and y be the number of small boxes. The total cost of the boxes must be less than or equal to the budget of $500. So, we can write the inequality as:

65x + 35y ≤ 500

To graph this inequality, we need to find the boundary line and the shaded region. The boundary line is the equation that we get when we replace the inequality sign with an equal sign, which is:

65x + 35y = 500

To graph this line, we need to find two points on it. We can do this by plugging in some values for x or y and solving for the other variable. For example, if x = 0, then y = 500/35 = 14.29. If y = 0, then x = 500/65 = 7.69. So, two points on the line are (0, 14.29) and (7.69, 0). We can plot these points on a coordinate plane and draw a solid line through them, since the inequality includes the equal sign.

To find the shaded region, we need to test a point that is not on the line and see if it satisfies the inequality. For example, we can test the point (0, 0), which is the origin. Plugging in x = 0 and y = 0 into the inequality, we get:

65(0) + 35(0) ≤ 500

0 ≤ 500

This is true, so the point (0, 0) is a solution to the inequality. This means that the shaded region is the area that includes the point (0, 0) and is below the line.

If Renaldo buys 6 small gift boxes, then y = 6. To find how many large gift boxes he can afford, we need to plug in y = 6 into the inequality and solve for x. We get:

65x + 35(6) ≤ 500

65x + 210 ≤ 500

65x ≤ 290

x ≤ 290/65

x ≤ 4.46

This means that Renaldo can buy at most 4 large gift boxes if he buys 6 small gift boxes. However, since x has to be a whole number, the largest possible value for x is 4. So, Renaldo can buy 4 large gift boxes and 6 small gift boxes and still stay within his budget.

I hope this helps!

Step-by-step explanation:

In an experimental study, the variable of interest is a changing quantity that would be measured. A number of these different factors, known as the original study factors, are monitored so that information on how the factors impact some other interesting as the predictor variables, or merely the response, can be obtained.

Is the variable under consideration an independent variable?

Interesting outcome variable

This is also referred to as a regression model or an interest component. It is a "input" variable that serves as a factor that what a researcher is able within a contained way to test this same impact of changing the amounts of the predictor variables on the overall result measured. An observation falls under the category of data collection case.

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1. Option B. A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable

2. Option C. Amount of smoking and lung cancer, height and weight of people, price of a good and demand of the good

Examples of pairs of variables that are correlated:

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The conventional conversion rates state that 1.72 is equivalent to 5.504 feet.

We use the unit of the meter to measure the distance between any two objects, but we may also use the unit of the foot for short distances because these two units are interchangeable.

One meter is equivalent to 3.2 feet using common conversion factors used in the US.

The measurement of 1.72 metres into feet may be determined using the same conversion factor.

We shall thus write 1 m = 3.2 ft.

1.72m is 1.78 x 3.2 feet, or 5.504 feet.

The result is that 1.78 meters is equivalent to 5.696 feet.

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An equation describing r as a function of A and π is r = √(A/π).

Mathematically, the area of a circle can be calculated by using this formula:

A = πr²

Where:

In this exercise, you are required to make "r" the subject of the formula in the given mathematical expression by using the following steps.

By dividing both sides of the mathematical expression by π, we have the following:

r² = A/π

By taking the square root, we have:

r = √(A/π)

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Complete Question:

Make r the subject: A = πr²

The relationship between quart to ml is that 1 quart is equal to 946.6 mililitres.

Quart and ml both are the unit of volume. ml is abbreviated form of mililitres and the two units are related together. Here is how they are related -

1 quart is equal to 946.6 mililitres.

Thus, in this method we can simply relate and calculate the quart amount of liquid in mililitres. Let us interpret the above mentioned statement through example. For instance, we need to know the mililitres in 0.25 quart. Here is how we will solve this.

Quantity in mililitres = quantity in quart × amount of mililitres in one quart

Quantity of mentioned liquid in mililitres = 0.25 × 946.4

Performing multiplication on Right Hand Side of the equation

Quantity of mentioned liquid in mililitres = 236.6 mililitres

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The conversied value of 152 centimetres in feet is equals to the 4.98 feet.

Unit conversion, by definition, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for time minutes to hours, or other units.

How to convert centimeters to feet : 1 meter is a measure of length and equals approximately 3.28 feet.

152 meters = 152×3.28 feet = 498.56 feet --(1)

But we need to convert 152 centimeters to feet. So change meters to centimeters. As you know, 1 meter is 100 centimeters, so 152 meters = 15200 centimeters --(2). Now from equations (1) and (2),

15200 centimeters = 498.56 feet,

Divide both parts by 100,

=> 152 centimetres = 498.56/100 feet

= 4.98 feet

Hence required value is 4.98 feet.

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The area of the teacher workroom is 64 feet squared

The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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Answer:

The correct answer is B. 60 and 64. When y is directly proportional to x, it means that the ratio of y to x remains constant. In this case, when x=6, y=36, which means that the ratio of y to x is 36/6. Since the ratio is constant, we can use that ratio to find the values of y when x=8 and x=10. When x=8, y = (36/6)x8 = 60 and when x=10, y = (36/6)x10 = 64.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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The value of the residual for Shawna's weight and height is 12.4 and option 2 is the correct answer.

A linear equation is one that has the form Ax+By=C. This definition comes from mathematics. It consists of two variables combined with a constant value that exists in each of them.

The collection of all values that, when substituted for unknowns, cause an equation to hold true is known as the solution. Two fundamental algebraic rules using the additive property and the multiplicative property are utilised to determine the solutions for equations needing a single unknown raised to a power of one.

The equation given to predict the weight from height is:

ŷ = -260 + 6.6x

Given that, Shawna’s height was 64 inches.

Substituting the value in x we have:

ŷ = -260 + 6.6x

ŷ = -260 + 6.6(64)

ŷ = 162.4

The actual weight is given as 150 pounds.

The residual value of the weight from the predicted formula is:

r = 162.4 - 150

r = 12.4

Hence, the value of the residual for Shawna's weight and height is 12.4 and option 2 is the correct answer.

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Answer:

-12.4

Step-by-step explanation:

The number of hours you have to wait is 300 minutes.

What is the unit rate?

A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Given that,

You are told to you will have to wait 5 hours in a line with a group of other people.

Based on the above information, the calculation is as follows:

We know that

1 hour = 60 minutes

  5*60

= 300  minutes

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