The McCandless method has four steps divide the stage, assign lights, use color and fill the empty spaces.
Setting up the McCandless method for a thrust stage involves several steps.
To light a thrust stage using the McCandless method, divide the space into separately illuminated sections as the first step. The size of the stage will determine how you do it, but there should be enough areas for uniform lighting throughout.
Assign lights to each part of your stage once you've divided it into lighting segments. Three lights per section is the traditional norm, although you should use as many or as few as necessary to provide a consistent effect.
Use color: After placing your lights in each region, you may use gels to balance out their hues. To balance out the shadows on the performers' faces, the McCandless technique recommends a mix of warm and cold hues.
Fill in the blanks: At this stage, your lighting setup should be clear enough for you to understand how it affects your actors and see any potential issues. Use smaller lights, such as Fresnels, to tone down any unnaturally lit areas and blend the performers' looks.
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The process of McCandless method is explained below.
According to the theory of "Into the Wild", the process of McCandless method calls for a combination of warm and cool colors to balance out the shadows on the actors' faces.
And here we know that for a double McCandless system, then you can achieve this by making two of the lights warm and the other two cool.
Here you can also have all your lights be similar, neutral colors.
Apart from this, we have the following steps to do it:
We have to choose the right type of visualization.
And then we have to declutter your visualization.
And then we have to focus your audience's attention.
And the final steps is to think Like a Designer.
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In school William learned that the average person produce 50 pounds I recyclables every month. But they usually throw away twice that much garbage. He wonders what that means for his family. William lives with his mother father and two sisters. About how many tons of garbage does Williams family throw away every year?
The amount of garbage thrown away each year by William's family, based on the details of the word problem, is 1.5 tons
What is a mathematical word problem?A word problem is a presentation of a mathematical question using complete sentences, rather than symbols and numbers, and for which the solution is obtained by using mathematical methods.
The amount (mass) of recyclable material a person produces each month = 50 pounds
The people in William's family are; His mother, father, two sisters
The number of people in Williams family = 5
The amount of recyclable material Williams family throw away each month = 50 × 5 pounds = 250 pounds
The number of months in a year = 12 months
The amount William's family throw away in a year = 12 × 250 pounds = 3000 pounds
1 pound = 0.0005 tons
Therefore;
3000 × 1 pound = 3,000 × 0.0005 tons = 1.5 tons
The Williams family throws away 1.5 tons of garbage each year.
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Jacqueline is buying grapes and apples from the Walmart produce section. Grapes are $3 per pound and apples are $4 per pound. Jacqueline's mother gave her $20 to spend. To determine the combinations of grapes and apples that she can afford to purchase,
Jacqueline wrote the inequality 3x+4y<20 .
Define the variables Jacqueline used based on the context.
Let x represent
Let y represent
Explain why the inequality sign s makes sense in this context.
Graph the inequality 3x+4y< 20.
The ordered pair (3,-4) is a solution to the inequality 3x + 4y s 20. Explain why this is not a viable solution in the context of buying grapes and apples.
The ordered pair (4,2) is a point on the boundary line. Explain what the ordered pair represents in the situation.
Answer:
Step-by-step explanation:
This should help
Please help me I have a learning disability and need help with this.
Define a variable and write the phrase as an algebraic expression.
four times as many apples
Let a =
Group of answer choices
the number of apples
as many
the number of trees
times
Answer:
The number of apples
Step-by-step explanation:
It would need apples to multiply into 4 so i believe thats the right answer
Determine the scale factor. Pre-Image: (-5, 3), (-2, 3), (-2, 1), (-5, 1) Image: (-10, 6), (-4, 6), (-4, 2), (-10, 2)
The scale factor, given the pre - image and the image, can be found to be 2.
How to find the scale factor ?The scale factor is the measure that either increases or decreases the size of a shape. When the scale factor is an integer then the size of the shape increases.
When the scale factor is a fraction with a larger denominator than numerator, the shape decreases.
To find the scale factor, look at the relationship between a point on the pre - image and the corresponding point on the image. For the points, ( -5, 3 ) and ( -10, 6 ) the scale factor would be :
= -10 / -5 or, = 6 / 3
= 2 = 2
The scale factor is therefore 2.
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for which of the following values of m is m to power (91) + 2m to power (90) the square of an integer?
a) 20
b) 24
c) 27
d) 30
e) 34
explain
We can rewrite m^91 + 2m^90 as (m+2m^90)^2 - m^90.
We are looking for values of m such that m+2m^90 is an integer.
For m = 30, m+2m^90 = 30 + 230^90 = 30 + 2(30^90) = 60, which is an integer.
For m = 24, m+2m^90 = 24 + 224^90 = 24 + 2(24^90) = 48, which is also an integer.
For the other values of m, m+2m^90 is not an integer. Therefore, the only values of m for which m^91 + 2m^90 is the square of an integer are m = 24 and m = 30.
Explain briefly the difference between spot heights and trigonometrical stations or points.
Answer:
Step-by-step explanation:
A spot height shows exact heights by a black dot with a number next to it. The number is the height above sea level in metres. Trig points or Triangulation Pillars are another way of spotting the top of a mountain on a map
the _______ _______ is a statement of no change comma no effect comma or no difference.
The null hypothesis is a statement of no change, no effect, or no difference.
The null hypothesis is a statement or assumption that there is no relationship between two variables or no difference between two groups, and any observed differences are likely due to chance. It is often denoted as H0. In scientific research, the null hypothesis is usually tested against an alternative hypothesis, which proposes that there is a relationship or difference.
For example, in a medical study, the null hypothesis might be that a new treatment has no effect on a certain disease, while the alternative hypothesis is that the treatment does have an effect. The researcher would then collect data and use statistical methods to test the null hypothesis against the alternative hypothesis.
It's important to notice that a failure to reject the null hypothesis doesn't mean the null hypothesis is true, it only means that there isn't enough evidence to reject it.
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HELP PLEASE
HELP ME PLEASE
HELPPPPPPPPPP
10 POINTS
We can simplify the given expression -6x - 12 + 8y + 16x to get:
10x - 12 + 8y
How to simplify the following expression?Here we want to simplify the expression below:
-6x - 12 + 8y + 16x
To simplify this we need to try to find common factors, the only common factor that we can see on the equation is "x", then we can rewrite the expression:
-6x - 12 + 8y + 16x
-6x + 16x - 12 + 8y
Now we can rewrite the first two terms as:
(-6 + 16)*x - 12 + 8y
10x - 12 + 8y
That is the simplified expression.
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edurado has $24 saved. if he saves $8 each week how much money will he have in 5 weeks
Answer:
Step-by-step explanation: 40$
Find the slope of the line that passes through the points \left(10,8\right)(10,8) and \left(4,12\right)(4,12).
Write your answer as a simplified fraction.
3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).
What is the Equation of line?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
Given, two coordinates of a line [tex]\left(10,8\right) and \left(4,12\right)[/tex]
The slope of the line formula is:
[tex]m = \frac{y₂ - y₁}{ x₂ - x₁}[/tex]
Let's substitute our numbers.
[tex]m = -\frac{8 -12}{4-10}[/tex] = -4/6
The GCF of these two numbers is 2
So, our slope = -2/3
The general equation of a line is y = mx +c
Therefore the equation of the line is y = -2/3x + c
Since, this line passes through ( 10, 8 )
Hence, it must satisfy these coordinates
8 = -2/3 * 10 + c
44/3 = c
Thus the equation of the line is y = -2/3x +44/3
the equation of the line is 3y + 2x = 44.
Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.
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Show how the recursive rule f(0) = a and f(n)=f(n-1)+d for n ≥ 1 generates the explicit rule
f(n)= a + dn for n ≥ 0.
f(0) =
f(1) = f(0)+d=
f(2)=f(1)+d= (a + d) +d=
f(3) =f(2)+d= (a + 2d)+d=
f(4)=f(3)+d= (a +3d)+d=
Generalizing these results gives f(n)=
On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
Here,
[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)
g(x) = -3(x-5)(x+1)
[tex]g(x) = -3(x-5)(x+1)[/tex]
g(x) = -3 + 12x + 15
y-intercept of g(x) is (0,15)
Therefore , the solution to the given problem of the equation comes out be y-intercept of g(x) is (0,15).
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What are 4 examples of data types?
The 4 examples of data types are Integer - a whole number that can be positive, negative, or zero. Float - a number with decimal points. String - text or characters. Boolean - a true or false value.
Data types are the different kinds of data that can be stored in a computer system. They are used to define the type of data a variable can hold.
The four most commonly used data types are Integer, Float, String, and Boolean.
An Integer is a whole number that can be either positive, negative, or zero. Integers are used for counting and manipulating whole numbers.
A Float is a number with decimal points. It is used for storing numerical values that require a more precise representation.
A String is a set of characters and text. It is used for storing textual information such as names and addresses.
A Boolean is a true or false value. It is used for evaluating logical expressions and making decisions based on certain conditions.
Overall, data types are used to specify the kind of information that a variable can store and to ensure that data is stored in a consistent and organized manner.
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A ____________ is a table in which frequencies correspond to two variables.
A
▼
relative frequency table
Pearson correlation coefficient table
standard normal distribution table
contingency table
is a table in which frequencies correspond to two variables
Answer:relative frequency table
Step-by-step explanation:
Which graph represents the function f of x equals 4 x?
The graph would be a straight line with a slope of 4, passing through the origin.
The equation f(x) = 4x can be expressed in slope-intercept form as y = 4x + 0, where the slope is 4 and the y-intercept is 0. This means that the graph of f(x) = 4x is a straight line with a slope of 4 that passes through the origin (0, 0).
The graph of f(x) = 4x is a line with a positive slope that passes through the origin and extends infinitely in both the positive and negative directions. The y-intercept is 0 and the x-intercept can be found by setting y = 0 and solving for x, which gives x = 0. For any given x-value, the corresponding y-value can be found by substituting the x-value into the equation f(x) = 4x and solving for y. As x increases, y increases proportionally, so the graph represents a linear, increasing relationship.
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Ruby is designing a new board game, and is trying to figure out all the
possible outcomes. How many different possible outcomes are there if
she flips a coin, rolls a fair die in the shape of a cube that has six sides
labeled 1 to 6, and spins a spinner with three equal-sized sections
labeled Walk, Run, Stop?
Answer:
Submit Answer
attempt 1 out of 2
The maximum possible outcome for the given situation is 36.
What is Probability?The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
Given, Ruby is designing a new board game and is trying to figure out all the possible outcomes. she flips a coin, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.
Since there are three things happening simultaneously and favorable moments will be chosen by all three.
Thus Maximum possible outcome = 2 * 6 * 3 = 36
Therefore, For the given situation, 36 outcomes are available in total.
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The owner of a men’s store bought 150 suits for a total of $32,500. If he wishes to sell them for at least $66,000, how much per suit should he charge?
Answer:
x > or equal to $440
Step-by-step explanation:
66,000/150=440
what is 10c and 12d gcf using distributive property
The GCF of 10c and 12d using the distributive property is 2.
Greatest Common Factor:The largest of all the common factors between any two or more numbers is known as the GCF (Greatest Common Factor).
A single term can be multiplied by the sum or difference of two or more other words according to the distributive property.
According to Distributive property,
=> ab + ac = a(b + c)
Where 'a' will be the GCF of ab and ac.
Here we have
10c and 12d
By using the Distributive property,
=> 10c + 12d = 2 (5c + 6d)
Therefore,
The GCF of 10c and 12d using the distributive property is 2.
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Equation reveals its extreme value without needing to be altered. the extreme value of this equation has a at the point ( , ).
The extreme value of this equation has a minimum at the point (2,5).
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
All of given options contain quadratic functions. One way to determine the extreme value is squaring the expression with variable x.
Option B contain the expression where you can see perfect square. Thus, equation y =-3(x-2)^2+5 (choice B) reveals its extreme value without needing to be altered.
To determine the extreme value of this equation, you should substitute x=2 (then x value that makes expression in brackets becomes equal to zero) into the function notation:
y =-3(x-2)^2+5
substitute x = 2,
y =-3(2-2)^2+5
y =0+5
y =5
Therefore, The extreme value of this equation has a minimum at the point (2,5).
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The extreme value of this equation has a minimum at the point (2,5).
Now, According to the question:
All of given options contain quadratic functions. One way to determine the extreme value is squaring the expression with variable x.
Option B contain the expression where you can see perfect square. Thus, equation :
y = [tex]-(x - 2)^2 + 5[/tex]
(choice B) reveals its extreme value without needing to be altered.
To determine the extreme value of this equation, you should substitute x=2 (x-value that makes expression in brackets equal to zero) into the function notation:
y = [tex]-(2 - 2)^2 + 5[/tex]
Hence, The extreme value of this equation has a minimum at the point (2,5).
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The complete question is this:
Select the correct answer from each drop-down menu.
Consider the equations below.
Use the equations to complete the following statements.
Equation __ reveals its extreme value without needing to be altered. The extreme value of this equation has a ____ at the point (__,__ ).
length of Mahi-Mahi: 3 ft 8 in.
length Great White Shark: 18 ft
The difference in length between Mahi-Mahi and White Shark will be 14 feet 4 inches.
How to illustrate the expression?The expression has to do with the relationship between the variables that are provided or the data given regarding an information.
Since the length of Mahi-Mahi: 3 ft 8 in and the length Great White Shark: 18 ft. The difference in length will be:
= 18 - 3 feet 8 inches
= 14 feet 4 inches.
The difference in length is 14 feet 4 inches.
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Complete question
length of Mahi-Mahi: 3 ft 8 in.
length Great White Shark: 18 ft
What is the difference in length
When you listen to the sound of a bouncing ping-pong ball that has been dropped onto a cement floor, what mathematical pattern do you hear? Explain,
A drop of water is denser than a ping-pong ball.
Usually, water is made of particles that are firmly pressed together. In differentiation, plastic (the material ping pong balls are made of) may be a lightweight fabric and the particles are not as firmly stuffed together.
The thickness of a ping pong ball is 0.0840 g/cm³, though water’s thickness is 997 kg/m³. Subsequently, ping pong balls aren’t about as thick as water and will continuously coast and surface greatly quickly.
The ping pong ball appears to oppose gravity and coast within the air.
Ping-pong balls drift within the water since they are amazingly lightweight, empty, and filled with air. Too, the water’s surface pressure makes it simple for the ping pong ball to drift.
In expansion, water is denser than ping pong balls, making them look for the most noteworthy point of water.
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The sound which we hear when the pig pong ball is bounced on the floor
is 19.48 DB
The repeating of sounds, especially in rhyme, is the form of repetition that most people connect with poetry. Alliteration, assonance, and onomatopoeia are other sound patterns in poetry that give additional meaning in addition to rhyme. Every one of these audio elements has a certain purpose in a poem.
a) [tex]\sum \ log(n)[/tex]
by expanding the series for each value of n is
log (1) + log (2) + log(3) + log (4) + ......... + log ( 96)
simplify the expanded form we get
0 + 0.3010 + 0.4771+0.6020 ......................... + 1.982
=> 149.9963
b) [tex]\sum_{n=0}[/tex] to infinity [tex]\sqrt{0.9^n}[/tex]
formula for the sum of number in geometric progression
is a/1-r
to find the ratio of the successive terms
plugging into the formula
r = [tex]\frac{a_{n+1}}{a_n}[/tex]
r = [tex]\frac{\sqrt{0.9^{n+1}} }{\sqrt{0.9^n} }[/tex]
=> r = [tex]\frac{\sqrt{0.9^n \times 0.9} }{\sqrt{0.9^n} .1}[/tex]
=> r = [tex]\frac{\sqrt{0.9} }{1}[/tex]
=> r = [tex]\sqrt{0.9}[/tex]
=> a = [tex]\sqrt{0.9^0}[/tex]
=> a = [tex]\sqrt{1}[/tex]
=> a= 1
by applying the formula having the value a =1 is
[tex]\frac{1}{1-\sqrt{0.9} }[/tex]
rationalize the denominator by multiplying with [tex]1+\sqrt{0.9}[/tex]
=> [tex]\frac{1+\sqrt{0.9} }{(1-\sqrt{0.9} ) (1+\sqrt{0.9}) }[/tex]
=> 19.4868
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Which quadrant or axis contains the point (−5, 3)?
Answer:
not sure
Step-by-step explanation:
not sure sqauredxfree bagdes
=answer
Jade buys a blouse and a skirt for of their original price. She pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt?
Part A
Which equation represents the situation?
O 0.75= 31.50
(18)= 31.50
O 0.75(s 31.50)=18
O
Part B
(18+5)= 31.50
Use the Distributive Property to solve the equation.
The equation that represents the situation could be 3/4(18 + s) = 31.50 and the solution is s = 24 thus option (D) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
Part (A)
Given that;
Cost of skirt = s
cost of blouse = $18
She bought it at 3/4 of that cost,
The Total pay = 3/4 of the total cost
3/4(18 + s) = 31.50
Part (B)
By the distributive property of multiplication then we get;
3/4(18) + 3/4(s) = 31.50
3/4(s) = 31.50 - 13.5
3/4(s) = 18
s = 18 x 4/3 = 24
Hence "The answer is s = 24"
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-a? - 2bc - Icl
if a = -2, b = 3,
and c = -3
problem in the photo
algebra
Therefore , the solution of the given problem of algebra comes out to be the value of expression is 17.
Algebra: What Is It?Algebra is one of the numerous variables of mathematics. Algebra is, broadly defined, the study of numeric and the rules for employing them in formulae. It is a common theme that goes through practically all of mathematics. Algebra is the branch of mathematics that provides the most assistance in describing circumstances or issues through the use of formulas. In algebra, we use integers, such like 2, 7, 0.068, etc., which have a defined or definite value. Algebra slight changes like x, y, & z in addition to utilizing integers.
Here,
Given :
a= -2
b= 3
c = -3
so,
=> -a- 2bc - |c|
=> 2 -2*3*-3 - |-3|
=> 2 + 18 -3
=> 17
Therefore , the solution of the given problem of algebra comes out to be
the value of expression is 17.
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Find the area of the figure, round to the nearest hundredth.
The area of the given figure is 51.63 m².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
In the given combination figure, there are three geometrical shapes rectangle, triangle and semicircle.
Now, in triangle base =3 m and height =5 m
So, area of a triangle = 1/2 ×Base×Height
= 1/2 ×3×5
= 7.5 m²
In rectangle length= 6 m and width =5 m
Area of rectangle = Length×Width
= 6×5
= 30 m²
In semicircle, radius =6/2 =3 m
Area of a semicircle = πr²/2
= 3.14×3×3/2
= 14.13 m²
Total area = 7.5+30+14.13
= 51.63 m²
Therefore, the area is 51.63 m².
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What is the coefficient of 5x² in 5x² 5x?
Answer:
Step-by-step explanation:
i think 1
The shopkeeper gave a bill to him. The bill was in two digits but was mistakenly interchanged, thereby undercharging him by $45. 0. He remembered the sum of the digits to be 9, find the actual value of the bill?.
The actual value of the bill can either be $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bill.
A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.
The bill of customer was mistakenly interchanged by $45.
The sum of the two digits of the bill is 9.
Now,
9 = 9 + 0 or,
9 = 8 + 1 or,
9 = 1 + 8 or,
9 = 5 + 4 or,
9 = 2 + 7 or,
9 = 7 + 2 or,
9 = 3 + 6 or,
9 = 6 + 3
Therefore, $45 bill can be mistakenly interchanged by $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bills.
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If a shopkeeper undercharges a customer by interchanging the digits of the bill by $45 and the sum of the digits is 9, then the actual value of the bill is 72 dollars.
Therefore the answer is $72.
Let the tenth and once place value digits of the actual value of bill be x and y. Then actual value of bill in dollars is expressed by
10x + y
The value of bill obtained by interchanging the two digits in dollars is
10y + x
It is said that by interchanging digits the shopkeeper undercharged him by $45.0, that is
(10x + y) - (10y + x) = 45
9x - 9y = 45
Dividing by 9
[tex]\frac{9x + 9y}{9} = \frac{45}{9}[/tex]
x - y = 5
He remembers that the sum of the digits is 9, that is
x + y = 9
Solving the system of equations
x + y = 9
x - y = 5
Adding the equations
(x + y) + (x - y) = 9 + 5
2x = 14
Dividing by 2
x = 7
Substituting x = 7 in first equation
7 + y = 9
y = 2
The actual value of the bill is
10x + y = 10×7 + 2 = 72
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The value of 5 × (7 + 3)2 ÷ 4 this expression is
PLEASE HELP
Answer: 25
Step-by-step explanation:
Seth uses 20 nails to make a birdhouse. He wants to make 60 birdhouses to sell at the county fair. There are 30 nails in a box. How many boxes will he need?…..Could someone tell me what type of operation I have to use?
To build 60 birdhouses, Seth will need 40 boxes of nails
What is proportion?A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)
Seth uses 20 nails for a birdhouse. This means that to build 60 birdhouses, Seth will need 60×20 = 1200 nails
In each box there are 30 nails;
This means that 1200 nails will contain 1200/30 boxes = 40 boxes.
Therefore the number of boxes of nails Seth will need to build 60 birdhouses is 40.
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Which is the slope of the line that passes through the points (- 3/5 and 1 3?
The slope(m) of the line that passes through the points (1, −3) and (3, −5) is m = -1.
The slope of a line determines the inclination of the line with the positive x-axis.
The slope of the line passing through (x1, y1) and (x2, y2) is given by m =(y2 - y1) / (x2 - x1)
Given that,
Here, (x1, y1) = (1, −3) and (x2, y2) = (3, −5)
m = (y2 - y1) / (x2 - x1)
m = [-5 - (-3)] / [3 - 1]
m = [-5 + 3] / [2]
m = [-2] / 2
m = -1
Slope = m = -1
Thus, The slope(m) of the line that passes through the points (1, −3) and (3, −5) is m = -1.
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in how many ways can people be seated in a row of chairs if three of the people, john, wilma, and paul, refuse to sit in three consecutive seats?
The total number of ways to seat the people in a row such that John, Wilma, and Paul refuse to sit in three consecutive seats is 4320.
There are a few different ways to approach this problem, but one possible method is to use the principle of inclusion-exclusion.
We start by counting the total number of ways to seat the people in a row of chairs without any restrictions. Since there are n chairs, there are n! ways to seat the people in a row.
Next, we count the number of ways to seat the people in a row such that John, Wilma, and Paul are seated in three consecutive seats. Since there are n-2 chairs between the three chairs that John, Wilma, and Paul are not allowed to sit in, there are (n-2)! ways to seat the people in a row such that John, Wilma, and Paul are seated in three consecutive seats.
Finally, we use the principle of inclusion-exclusion to find the total number of ways to seat the people in a row such that John, Wilma, and Paul are not seated in three consecutive seats.
The total number of ways to seat the people in a row such that John, Wilma, and Paul are not seated in three consecutive seats is n! - (n-2)!
For example, if there are 7 chairs, the total number of ways to seat the people in a row such that John, Wilma, and Paul are not seated in three consecutive seats is 7! - (7-2)! = 5040 - 720 = 4320
So, the total number of ways to seat the people in a row such that John, Wilma, and Paul refuse to sit in three consecutive seats is 4320.
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