I don't really understand how to do reference angles. I only need the last one, -60 degrees, does anyone know how to figure out it's reference angle?

I Don't Really Understand How To Do Reference Angles. I Only Need The Last One, -60 Degrees, Does Anyone

Answers

Answer 1

Answer: 60?

Step-by-step explanation:

The reference angle is the acute angle formed between the terminal side of an angle in standard position and the x-axis. To find the reference angle of an angle, you can follow these steps:

Determine the quadrant in which the angle terminates. For -60 degrees, this would be the fourth quadrant.

Determine the corresponding angle in the first quadrant by finding the angle formed between the terminal side and the x-axis. In the fourth quadrant, this angle is equal to 360 degrees minus the original angle. So for -60 degrees, the corresponding angle in the first quadrant is 360 - 60 = 300 degrees.

Subtract this angle from 360 degrees to find the reference angle. For -60 degrees, the reference angle is 360 - 300 = 60 degrees.

Therefore, the reference angle of -60 degrees is 60 degrees.


Related Questions

 HELP PLEASE!!!

calculate the distance between the points B= (0,6) and M= (8, -2) on the coordinate plane . round to the nearest 100th.

Answers

Answer:

Step-by-step explanation:

Using the distance formula:  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

    [tex]d=\sqrt{(8-0)^2+(-2-6)^2}[/tex]

        [tex]=\sqrt{64+64} \\[/tex]

        [tex]=\sqrt{128}[/tex]

        [tex]=11.3[/tex]

The lowest temperature ever recorded on earth was -89.2°C recorded in Antarctica in 1983.How many degrees Fahrenheit was that,to the nearest degree

Answers

The lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit.

To convert the temperature of -89.2°C to Fahrenheit, we can use the formula:

[tex]F = (C * 1.8) + 32[/tex]

Substituting:

°F = (-89.2 × 1.8) + 32

°F = -128.56 + 32

°F = -97

Therefore, the lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit. It's important to note that this is just an approximation as we rounded the result to the nearest degree. However, it gives us a good idea of how extremely cold the temperature was. It's worth mentioning that at such low temperatures, it's important to take appropriate precautions to avoid any adverse health effects.

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Match each integer with one that divides it.
18
matches
Choice
9
-14
matches
Choice
7
11
matches
Choice
11
65
matches
Choice
13

Answers

Integers are a type of number used in mathematics that represent whole numbers. They are typically denoted by the symbol Z, and can be positive, negative, or zero.

Integers do not include fractions or decimal points, so they are distinct from real numbers.

In Mathematics, integers are the collection of whole numbers and negative numbers.

18 matches 9

-14 matches 7

11 matches - 65

13 matches 65

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in the same distribution (mean is 70 and the standard deviation is 8. at least what fraction are between the following pairs

Answers

At least 68% of the data falls between 62 and 78, and at least 95% of the data falls between 54 and 86.

How to find the minimum fraction of the data?

To answer this question, we can use the empirical rule, also known as the 68-95-99.7 rule, which tells us that for a normal distribution:

About 68% of the data falls within one standard deviation of the meanAbout 95% of the data falls within two standard deviations of the meanAbout 99.7% of the data falls within three standard deviations of the mean

Using this rule, we can estimate the fraction of the data that falls between the following pairs:

Between 54 and 86:

To find the range of values that is within two standard deviations of the mean, we can subtract and add two standard deviations from the mean:

Lower bound: 70 - 2*8 = 54

Upper bound: 70 + 2*8 = 86

So, about 95% of the data falls between 54 and 86.

Between 62 and 78:

To find the range of values that is within one standard deviation of the mean, we can subtract and add one standard deviation from the mean:

Lower bound: 70 - 8 = 62

Upper bound: 70 + 8 = 78

So, about 68% of the data falls between 62 and 78.

Therefore, we can conclude that at least 68% of the data falls between 62 and 78, and at least 95% of the data falls between 54 and 86.

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A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the
function S=18.95 +0.60 M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I=4.90 +0.25 M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
C =

Answers

Hi. The terms of the standard charge and insurance charge equations are a little garbled, but it is possible to think that these are the right equations:

Standard charge, S = 18.95 + 0.60M, where 18.95 is the initial fee and 0.60 is the charge for each mile driven.

Insurance charge, I = 4.90 + 0.25M, where 4.90 also represents an initial fee and 0.25 a charge for each mile driven.

Then, the total cos, C = S + I =>

C = (18.95 + 0.60M) + (4.90 + 0.25M) which you can rearrange to show the like terms one next to each other =>

C = (18.95 + 4.90) + (0.60M + 0.25M), now add up the like terms=>

C = 23.85 + 0.85M which is the equation is the most simplified form

Answer: C = 23.85 + 0.85M

Which function models the area of a rectangle with side lengths of 2x – 4 units and x + 1 units? What is the area when x = 3?
A. f(x) = 2x2 – 4x + 4; A = 10 B. f(x) = 2x2 + 8x – 4; A = 38 C. f(x) = 2x2 – 8x + 4; A = 2 D. f(x) = 2x2 − 2x − 4; A = 8

Answers

Answer:

Area of rectangle, [tex]f(x) = 2x^2 - 2x - 4[/tex].

Step-by-step explanation:

We are given with side lengths of a rectangle are (2x-4) units and (x+1) units. It is required to find the area of rectangle.

The area of a rectangle is equal to the product of its length and breadth. It is given by :

[tex]A=L\times B[/tex]

Let us consider, L = (2x-4) units and B = (x+1) units

Plugging the side lengths in above formula:

[tex]A=(2x-4)\times(x+1)[/tex]

[tex]A = 2x^2 + 2x-4x - 4[/tex]

[tex]A=2x^2-2x-4[/tex]

So, the function that models the area of a rectangle is [tex]f(x) = 2x^2 - 2x - 4[/tex].

1. Create a cubic function that is not the parent function.
2. Explain how to graph your cubic function using transformations from the parent function. Be specific in your response and use correct mathematical language.
Number your responses 1 and 2 so your instructor can tell which question you're responding to.
This is the graph of the parent function. For example is I wanted to shift it down the function becomes: f(x)=x^3-7 (vertical transformation; shifted 7 down).
y=x²
When a function is shifted, stretched (or compressed), or flipped in any way from its "parent function, it is said to be transformed, and is a
transformation of a function

Answers

The given cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] is obtained by translating the parent cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] 2 units to the left and 5 units down.

What are cubic function?

A cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to complex numbers.

Cubic function:

[tex]$f(x) = (x+2)^3 - 5$[/tex]

Graphing the cubic function using transformations:

To graph the given cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] using transformations from the parent function [tex]$f(x) = (x+2)^3 - 5$[/tex] we can follow the following steps:

a) Start with the parent function [tex]$y=x^3$[/tex] and mark the points on the graph.

b) Translate the graph horizontally by 2 units to the left to obtain [tex]$y=(x+2)^3$[/tex].

c) Shift the graph vertically down by 5 units to get the final graph [tex]$y=(x+2)^3-5$[/tex]

d) Check the intercepts and end behavior of the function to ensure the graph is correct.

Therefore, the given cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] is obtained by translating the parent cubic function [tex]$f(x) = (x+2)^3 - 5$[/tex] 2 units to the left and 5 units down.

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in a school of hundred students, 40 are in the hockey team and 70 are in the football team.
Each student is in at least one team. Find the number of students who are in both teams.​

Answers

Answer: There are 10 students who are in both the hockey and football teams.

Step-by-step explanation: We can use the principle of inclusion-exclusion to find the number of students who are in both the hockey and football teams.

The total number of students in both teams is the sum of the number of students in the hockey team and the number of students in the football team, minus the number of students who are in both teams (to avoid double-counting):

Total = Hockey + Football - Both

Substituting the given values, we get:

100 = 40 + 70 - Both

Simplifying, we get:

Both = 40 + 70 - 100

Both = 10

Therefore, there are 10 students who are in both the hockey and football teams.

b) There are x number of books that worth Rs. 35 each and 5 books worth Rs. 30 each in a parcel prepared as a gift. The value of two such parcels is Rs. 580. i. Build up an equation using the above information. ii. Find the value of x by solving the equation.​

Answers

Answer:

Equation: 2(357+30×5) = 580

x=4

Step-by-step explanation:

In one package, there is such a relationship:

357+30X5 = y

(Y is the price of a package)

The price of two parcels is 580:

then. 24=580

y= 290

x=4, so: equation: 2(35x+150) =580

Step-by-step explanation:

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?

A

8

B

16

Correct Answer

C

24

D

28

Medium

Open in App

Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is B)

Let the shopkeeper buy x number of books. 

According to the given condition cost of x books =Rs80

Therefore cost of each book =x80

Again when he had brought 4 more books

Then total books in this case =x+4

So cost of each book in this case =x+480

According to Question, 

x80−x+480=1

x(x+4)80(x+4)−80x=1

x2+20x−16x−320=0

(x−16)(x+20)=0

x=16orx=−20

Hence the shopkeeper brought 16 books

Match the description with its mathematical expression. Residual from an estimated regression equation Choose the correct answer below. obo Oba o O y o bo +61 oy

Answers

We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".

What is the correct expression?

Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".

Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".

Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.

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A rectangular solid (with a square base) has a surface area of 433.5 square centimeters. Find the dimensions that will result in a solid with maximum volume. 1. ____ cm (smallest value). 2. _____ cm 3. ______ cm (largest value)

Answers

Hence, 1) 6 cm (smallest value), 2) 6 cm, and 3)15.167 cm are the approximate dimensions which will result in a material with the biggest volume (largest value).

Describe surface area using an example.

A 3D object's surface area is indeed the entire area that all of its faces cover. For instance, the surface area of a cube has been its surface area if we need to determine how much paint is needed to paint it. It's always calculated in square units.

Let the height be y as well as the side length of a square base be x. The rectangular solid's surface area is then determined by:

When we simplify this equation, we obtain:

The rectangular solid's volume is determined by:

V = x² × y = x² × (433.5 - 4x²) / (2x)

When we simplify this equation, we obtain:

V = 216.75x - 2x³

We must determine the value of x that maximizes V in order to determine the dimensions that lead to a solid with the maximum volume. Using V's derivative with x as the base, we can calculate:

dV/dx = 216.75 - 6x²

By setting this to 0 and figuring out x, we obtain:

216.75 - 6x² = 0

x² = 36.125

x ≈ 6.005

When we rewrite the equation for y using this value of x, we obtain:

y ≈ 15.167

Thus, the following dimensions will produce a solid with the largest volume:

1. 6 cm (smallest value)

2. 6 cm

3.15.167 cm (largest value)

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PLS HELP ME ASAP I WILL MARK THE BRAINLIEST

Answers

Answer:

The formula for the nth term of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

In this case, a1 = -8 and r = -2. Therefore, we have:

a2 = a1 * r = (-8) * (-2) = 16

a3 = a2 * r = 16 * (-2) = -32

a4 = a3 * r = (-32) * (-2) = 64

So, the next three terms of the sequence are 16, -32, and 64.

Answer:

a₂ = 16

a₃ = -32

a₄ = 64

Step-by-step explanation:

The general formula for a geometric sequence is:

[tex]a_n=a_1 \cdot r^{n-1}[/tex]

where:

a₁ is the initial term.r is the common ratio.

Substitute the given values of a₁ and r into the formula to create an equation for the nth term:

[tex]\implies a_n=(-8) \cdot (-2)^{n-1}[/tex]

To find the values of a₂, a₃ and a₄, substitute n = 2, n = 3 and n = 4 into the equation.

[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{2-1}\\&=(-8) \cdot (-2)^{1}\\&=(-8) \cdot (-2)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_3&=(-8) \cdot (-2)^{3-1}\\&=(-8) \cdot (-2)^{2}\\&=(-8) \cdot (4)\\&=-32\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{4-1}\\&=(-8) \cdot (-2)^{3}\\&=(-8) \cdot (-8)\\&=64\end{aligned}[/tex]

Can someone help me out?

Answers

The probability of a. rolling an even or 3 is 2/3. b. Rolling an even or a number greater than 2 is 5/6. c. Rolling an odd or a number less than 6 is 5/6. d. Rolling a 2 and a 4 is 0.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. A sample space is made up of all potential results of an experiment. Tossing a coin, for instance, has two possible outcomes: head or tail. An experiment is a trial or procedure carried out to generate a result.

Given that, you roll a single fair 6 sided die.

a. Rolling an even or 3:

P(even or 3) = P(even) + P(3) - P(even and 3)

P(even or 3) = 1/2 + 1/6 - 0

P(even or 3) = 2/3

b. Rolling an even or a number greater than 2:

P(even or >2) = P(even) + P(>2) - P(even and >2)

P(even or >2) = 1/2 + 4/6 - 1/3

P(even or >2) = 5/6

c. Rolling an odd or a number less than 6:

P(odd or <6) = P(odd) + P(<6) - P(odd and <6)

P(odd or <6) = 3/6 + 5/6 - 1/3

P(odd or <6) = 5/6

d. Rolling a 2 and a 4:

P(Rolling a 2 and a 4) = 0.

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why is the probability that a continuous random variable is equal to a single number zero? (i.e. why is P(X=a)=0 for any number a)

Answers

The probability that a continuous random variable takes on a single specific value is zero because the continuous random variable can take on any value within a range or interval, and there are an infinite number of values that it can take on within that interval.

The probability that a continuous random variable is equal to a single number is zero. The explanation is that a continuous random variable has an infinite number of possible values. As a result, the probability of any single value, including the one you're interested in, is always 0.

To put it another way, it's almost impossible for a continuous random variable to equal a specific value. Consider the following example:

Suppose you're attempting to hit a target on a wall. If the target is the size of a pinpoint, the probability of striking it is virtually zero. In the same way, with continuous random variables, the probability of landing on a single point is practically zero because there are an infinite number of possible outcomes. As a result, the probability of any one of them occurring is tiny.

A continuous random variable may be defined over any interval of real numbers, which is one of its distinguishing features. The amount of time it takes to finish a marathon, the height of a randomly chosen person in a group, and the length of a telephone conversation are all examples of continuous random variables.

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Una pelota es lanzada horizontalmente desde la azotea de un edificio de 54 m de altura y Llega al suelo a 32 m de la base. Cuál fue la rapidez inicial de la pelota?

Answers

The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.

A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.

Height of building = 54 m

Height of ground from base = 32 m Calculates the initial speed of the ball.

Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,

d = 1/2×g×t²

where g --> acceleration due to gravity

t --> time

d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².

So, 54 m = (1/2) × 9,81 m/s² × t²

=> t² = 54/4.90

=> t² = 540/49

=> t² = 11.02 sec²

=> t = 3.31963 ~ 3.32 sec

So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,

=> 32 m = 0 + v₀ₓ × 3.32 sec

=> v₀ₓ = 32/3.32

=> v₀ₓ = 9.6385 ≈ 9.64 m/sec

Hence, required value is 9.64 m/sec.

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Complete question:

A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?

find the inverse of the function

F(x) = x² + 2x₁ [-1, 00]

Answers

To find the inverse of the function F(x) = x² + 2x over the interval [-1, 0], we need to follow these steps:

1. Replace F(x) with y to get y = x² + 2x.
2. Rearrange the equation to isolate x: y = x² + 2x becomes x² + 2x - y = 0.
3. Use the quadratic formula to solve for x in terms of y:

x = (-2 ± sqrt(4 + 4y)) / 2
x = -1 ± sqrt(1 + y)

4. Since the domain of F(x) is [-1, 0], we only consider the negative square root in the expression for x:

x = -1 - sqrt(1 + y)

5. Replace x with its inverse function notation, denoted by F^(-1)(y):

F^(-1)(y) = -1 - sqrt(1 + y)

Therefore, the inverse of the function F(x) = x² + 2x over the interval [-1, 0] is given by F^(-1)(y) = -1 - sqrt(1 + y).

Difference between 6z and z to the power of 6

Answers

Answer:

[tex]6z \: = 6 + z \: \\ z {}^{6} = z \times z \times z \times z \times z \times z \\ [/tex]

The mathematical statement in the form of expression can be written as 15625z⁶.

What is algebraic expression?

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is to find the mathematical statement -

"Difference between 6z and z to the power of 6"

We can write the given mathematical statement in the form of expression as -

(6z - z)⁶

(5z)⁶

5⁶ x z⁶

125 x 125 x z⁶

15625z⁶

Therefore, the mathematical statement in the form of expression can be written as 15625z⁶.

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use the y-and -x intercept to write the equation of the line y intercept (0,6), x intercept (-2,0)

Answers

Answer:

  3x -y = -6

Step-by-step explanation:

You want the equation of the line with intercepts (0, 6) and (-2, 0).

Intercept form

The equation of the line with x-intercept 'a' and y-intercept 'b' is ...

  x/a +y/b = 1

For the given intercepts, the equation is ...

  x/(-2) +y/6 = 1

Standard form

In standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:

  3x -y = -6

__

Additional comment

You can get slope-intercept form by solving for y, or you can recognize that ...

  slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3

Since you already know the y-intercept, you can write the slope-intercept equation as ...

  y = 3x +6

There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.

James has 27 metres of red wire and 12 metres
of black wire. He needs to cut both wires into
smaller pieces so that all of the smaller pieces are
the same length and there is no wire left over. The
length of each piece must be a whole number of
metres.
What is the longest he can make each smaller
piece of wire? Give your answer in metres (m).

Answers

Answer:

3m

Step-by-step explanation:

red wire = 27

black wire= 12

so, we take HCF (highest common factor)

which would be 3 so all the wires would be cut into 3m long.

I hope it helps.

Answer:2m

Step-by-step explanation:

as the factors of 12 are:1, 2, 3, 4, 6 and 12

and the factors of 26 are:1, 2, 13 and 26

so if you are talking meters 2 would be the longest

i hope you get this right x

GEOMETRY
determine whether each pair of triangles is similar. give details about each set of sides or angles. give the theory used. write a similarity statement.

Answers

The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

What is the Angle Side Angle Congruence Theorem?

The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:

m < W = m < Z.m < V = m < Y.

The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

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the weyland corporation, owns five offices that it leases to other businesses. the lease per square foot differs by building due to its location and amenities. currently, all buildings are fully leased, and detailed data is given below. calculate the weighted average price per square foot of the five offices owned by weyland corp. round your answer to 2 decimal places (include zero if necessary). price per sq. ft. ($) number of sq. ft. building 1 75 125,000 building 2 85 37,000 building 3 90 77,500 building 4 45 35,000 building 5 50 40,000

Answers

The weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.

Building Price per square ft ($) Number of sq. ft Building 1 75 and 125,000, Building 2 85 and 37,000, Building 3 90 and 77,500, Building 4 45 and 35,000, Building 5 50 and 40,000. Now, the formula to calculate weighted average price per square foot is,

Weighted Average Price per square foot = [ (Price per sq. ft of Building 1 * Number of sq. ft of Building 1) + (Price per sq. ft of Building 2 * Number of sq. ft of Building 2) + (Price per sq. ft of Building 3 * Number of sq. ft of Building 3) + (Price per sq. ft of Building 4 * Number of sq. ft of Building 4) + (Price per sq. ft of Building 5 * Number of sq. ft of Building 5) ] / Total sq. ft of all buildings.

Applying the values in the formula,

Weighted Average Price per square foot = [(75 * 125000) + (85 * 37000) + (90 * 77500) + (45 * 35000) + (50 * 40000)] / (125000 + 37000 + 77500 + 35000 + 40000)= [9375000 + 3145000 + 6975000 + 1575000 + 2000000] / 297500= 23092500 / 297500= 77.72

Therefore, the weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.

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Suppose that S is a set. Then the power set of S, P(S) is the set containing all subsets of S.P(∅) = {∅}P({a,b})= {∅, {a}, {b}, {a,b}}Remember that the cardinality of a set is the number of elements in it, i.e. |S|.If S is any finite set, even the empty set, it is the case that |P(S)| = 2". Suppose we want to prove this using induction. Also suppose thatthis is our base case:Base: n=0. Then S must be the empty set, and IP(∅)| = 1 which is equal to 20.Which of the following is the best choice for our inductive hypothesis?Select one:a. Suppose that |P(S) = 2" for all sets S with cardinality for any natural number nb. Suppose that IP(Sn)| = 2" for n=1,2,...,kc. Suppose that IP(S₁)| = 2" for n=0,1,...,kd. Suppose that IP(Sn)| = 2" for any natural number ne. Suppose that IP(S)| = 2" for all sets S with cardinality n, n=0,1,...,kf. Suppose that IP(S)| = 2" for all sets S with cardinality n, n=1,2,...,k

Answers

The best choice for our inductive hypothesis is option e. Suppose that IP(S)| = 2" for all sets S with cardinality n, n=0,1,...,k. This states that for all sets S with a cardinality of n, where n is any natural number (from 0 to infinity), the power set of S, P(S), has a cardinality of 2".

Suppose that S is a set. Then the power set of S, P(S) is the set containing all subsets of S.P(∅) = {∅}P({a,b})= {∅, {a}, {b}, {a,b}} Remember that the cardinality of a set is the number of elements in it, i.e. |S|. If S is any finite set, even the empty set, it is the case that |P(S)| = 2". Suppose we want to prove this using induction. Also suppose that this is our base case: Base: n=0. Then S must be the empty set, and IP(∅)| = 1 which is equal to 20. therefore with all these conditions, the answer is option e. IP(S)| = 2" for all sets S with cardinality n, n=0,1,...,kf.

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A cube has a surface area of 24 ft². What is the length of one edge of the cube?​

Answers

The length of one edge of the cube is 2 feet long whose surface area is 24 ft sq.

What is surface area?

Surface area is a measure of the total area that the surface of an object occupies. In geometry, it is the sum of the areas of all the faces or surfaces of a three-dimensional object

According to question:

The surface area of a cube is given by the formula 6s², where s is the length of one edge of the cube.

We are given that the surface area of the cube is 24 ft², so we can set up the equation:

6s² = 24

Dividing both sides by 6 gives:

s² = 4

When you square the two sides, you get:

s = ±2

Since the length of a side cannot be negative, the only valid solution is:

s = 2

The cube's one edge is therefore 2 feet long.

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The performance of a cyclist in a race is affected by whether it rains or not that day.
The probability the cyclist crashes is
4/5 when it's raining and
1/10 when it's dry.
On any given day, the probability of rain is
1/4
What is the probability it was raining given the cyclist crashes?

Answers

In light of the cyclist crashes, the likelihood of it being raining is 16/33, or roughly 0.485.

What are examples and probability?

It is predicated on the likelihood that something will occur. The fundamental underpinning of theoretical probability is the justification for probability. For instance, the theoretical chance of receiving a head while tossing a coin is ½. If it rains, let R stand for that, and if the cyclist crashes, let C stand for that. We're looking for P(R|C), or the likelihood that it will rain given the crashes involving cyclists. The Bayes theorem can be used to resolve this issue:

P(R|C) = P(C|R) × P(R) / P(C)

Where P(R) is the likelihood of rain, P(C) is the likelihood that the cyclist will crash regardless of the weather, and P(C|R) is the likelihood that the cyclist will crash given that it is raining.

According to the problem statement, we know that:

P(C|R) = 4/5 (the probability of crashing given that it's raining)

P(C|not R) = 1/10 (the probability of crashing given that it's not raining)

P(R) = 1/4 (the probability of rain)

We may use the rule of total probability to determine P(C):

P(C) = P(C|R) × P(R) + P(C|not R) × P(not R)

where P(not R) = 1 - P(R) = 3/4.

When we change the values, we obtain:

P(C) = (4/5) × (1/4) + (1/10) × (3/4) = 11/40

We can now enter each value into Bayes' theorem as follows:

P(R|C) = (4/5) × (1/4) / (11/40) = 16/33

As a result, there is a 16/33, or roughly 0.485, chance that it had been raining when the cyclists crashed.

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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP

Answers

Answer:

3c + 19

Step-by-step explanation:

Perimeter: P = a + b + c

P = (c + 10) + (c + 6) + (c + 3) = 3c + 19

4. Alice is creating a pyramid with toy rectangular-prism-shaped blocks
that measure 1 inch by 2 inches by 2 inches. She places 8 blocks in
the first row. Then she places 6 blocks on top of the first row and 4
blocks on top of the second row. If she continues the pattern until
the top row has 2 blocks, what is the volume of the final pyramid?

Answers

The final pyramid has a volume of 16 cubic inches. To find this, first multiply the number of blocks in each row together. 8 blocks in row 1 = 8 x 2 x 2 = 32; 6 blocks in row 2 = 6 x 2 x 2 = 24; 4 blocks in row 3 = 4 x 2 x 2 = 16; and 2 blocks in row 4 = 2 x 2 x 2 = 8. Then add all these numbers together to get 32 + 24 + 16 + 8 = 80. Finally, divide this number by 3 to get the volume, 80/3 = 16.

An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e.g. 98.765) (b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e.g. 98.76), (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?

Answers

The probability that all 10 sprinklers will operate correctly in a fire is approximately 0.028,  probability that at least 7 of the sprinklers will operate correctly in a fire is approximately 0.95 and the probability of at least one sprinkler operating correctly in a fire is at least 0.98, we need to have at least 7 sprinklers in the ballroom.

The sprinklers activate correctly or not independently can be found by:

(A) If the probability if all the sprinklers will operate correctly in fire is:

P(all 10 sprinklers operate correctly) = (0.7)¹⁰= 0.028247 (rounded to 3 decimal places)

Therefore, the probability that all 10 sprinklers will operate correctly in a fire is approximately 0.028.

(b) The probability that at least 7 of the sprinklers will operate correctly can be calculated using the binomial distribution with n = 10 and p = 0.7:

P(at least 7 sprinklers operate correctly) = P(X >= 7) = 1 - P(X < 7)

where X is the number of sprinklers that operate correctly.

Using a binomial calculator or table, we can find that:

P(X < 7) = 0.0518 (rounded to 4 decimal places)

Therefore:

P(at least 7 sprinklers operate correctly) = 1 - P(X < 7) = 1 - 0.0518 = 0.9482 (rounded to 2 decimal places)

So, the probability that at least 7 of the sprinklers will operate correctly in a fire is approximately 0.95.

(c) We need to find the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98. This is equivalent to finding the smallest value of n such that:

P(at least one sprinkler operates correctly) >= 0.98

Using the complement rule, we can rewrite this as:

P(no sprinkler operates correctly) <= 1 - 0.98 = 0.02

The probability that no sprinkler operates correctly in a fire is:

P(no sprinkler operates correctly) = (0.3)¹⁰

So we need to solve for n in the inequality:

(0.3)ⁿ <= 0.02

Taking the natural logarithm of both sides and using the logarithmic rule for inequalities, we get:

n >=ln(0.02) / ln(0.3) ≈ 6.52

Therefore, we need at least 7 sprinklers to ensure that the probability that at least one operates correctly is at least 0.98.

Therefore, The probability that all 10 sprinklers will operate correctly in a fire is approximately 0.028,  probability that at least 7 of the sprinklers will operate correctly in a fire is approximately 0.95 and the probability of at least one sprinkler operating correctly in a fire is at least 0.98, we need to have at least 7 sprinklers in the ballroom.

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Subtract the given equation

3x-(4x-11)

Answers

Answer:

3x - (4x - 11) = 3x - 4x + 11 = -x + 11

Step-by-step explanation:

The Jones family has two dogs whose ages add up to 15 and multiply to 44. How old is each dog?

Answers

As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

What is factoring?

Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.

What is an equation?

An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.

In the given question,

Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:

x + y = 15

We also know that their ages multiply to 44, so we can write:

x * y = 44

Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.

One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:

y = 15 - x

We can substitute this expression for y into the second equation:

x × (15 - x) = 44

Expanding the left side, we get:

15x - x^2 = 44

Rearranging and simplifying, we get a quadratic equation:

x^2 - 15x + 44 = 0

We can factor this equation as:

(x - 11)(x - 4) = 0

Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.

Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.

If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.

Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

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Transversals of Parallel lines: corresponding angles

Answers

The required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.

What are corresponding angles?

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.

Either both are acute or both are obtuse.

By creating an F shape, we can typically identify comparable angles.

So, now after reading the description we know exactly what are corresponding angles.

Now, we can easily tell that the pair of corresponding is:

∠HIK and ∠EFI


Therefore, the required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.

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