First you'll construct a three-dimensional solid out of some cardboard, following the instructions on the study sheet.



Then you'll compute the volume of your solid and answer a few questions about it. This isn't a thought experiment; you really do need to make this model. The point isn't just to learn a formula; it's to get a feeling for solids and volume. The word "feeling" here means real, physical, sense-of-touch, feeling. You're about to enter the three-dimensional world, and you'll need your senses to understand what you're doing.



Finally, you'll post answers to all the following questions:



Describe as best you can what your solid looks like. What cross sections did you use? What familiar solids does it remind you of?


Explain your method for calculating its volume. Would you have computed the same volume if you'd arranged your cross-sections differently? Is that what you'd expect to happen?


Explain your method for calculating its volume. Would you have computed the same volume if you'd arranged your cross-sections differently? Is that what you'd expect to happen?


What did you learn about volume from this experiment?

The operation you would use to solve [tex]6y=10[/tex] is division because we want to get the variable by itself. We use division because it' is the inverse of multiplication. So to solve [tex]6y=10[/tex], I would be dividing.

[tex]6y=10[/tex]

Divide both sides by 6(get the variable by itself):

[tex]\dfrac{6y}{6} =\dfrac{10}{6}[/tex]

[tex]=1.666667[/tex]

For the given values the probability less than 3 equals 0.38.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.

Given,

the probability of different scores

Probability of score less than 3 equals

= P(score 1) + P(score 2)

= 0.18 + 0.20

= 0.38

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7 with an exponent 4 is 2401. It can be expressed as,

          [tex]7^{4}[/tex] = 7. 7. 7. 7 = 2401

In the exponent form, two terms frequently in exponents are base and powers. Powers are mathematical expressions in the form [tex]x^{n}[/tex] , where x is the base and n is the exponent. Powers represent repeated multiplication, where the base is the number or variable that is multiplied repeatedly, and the exponent indicates how many times to multiply the base by itself.

We can write it in exponent form as [tex]7^{4}[/tex], where 7 is the base and 4 is the power. Power should always be written on top of the base.

It means 7 is multiplied 4 times. So, 7 × 7 × 7 × 7 = 2401

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5 , 7 , 8 represent the side of acute angled triangle.

The correct answer is set B.

Now, According to the question:

We use the following result:

When given 3 triangle sides then to determine if the triangle is acute angled , right angled or obtuse angled.

First find Square all 3 sides, then Sum the squares of the 2 shortest sides and then Compare the sum to the square of the last side.

if sum > Square of last side ⇒ it is Acute Triangle

if sum = Square of last side ⇒ it is Right Triangle

if sum < Square of last side ⇒ it is Obtuse Triangle  

a). 4  , 5 , 7

[tex]4^2 = 16 , 5^2 = 25 , 7^2 = 49[/tex]

16 + 25 = 41

∵ 41 < 49

⇒ It is an Obtuse Triangle.

b). 5 , 7 , 8

[tex]5^2 = 25 , 7^2 = 49 , 8^2 = 64[/tex]

25 + 49 = 74

∵ 74 > 64

⇒ It is an acute Triangle.

c). 6 , 7 , 10

[tex]6^2 = 36 , 7^2 = 49 , 10^2 = 100[/tex]

36 + 49 = 85

∵ 85 < 100

⇒ It is an Obtuse Triangle.

d). 7 , 9 , 12

[tex]7^2 = 49 , 9^2 = 81 , 12^2 = 144[/tex]

49 + 81 = 130

∵ 130 < 144

⇒ It is an Obtuse Triangle.

Therefore,5 , 7 , 8 represent the side of acute angled triangle.

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A pyramid with a square base has a volume of 1682.64 cubic meters.

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a shape is the distance around its edge. A shape's perimeter is always computed by summing the lengths of each of its sides. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length.

Here,

side=16.7 m

volume=1/3*16.7²*18.1

=1/3*5047.909

=1682.64 m³

The volume of a pyramid with a square base is 1682.64 m³.

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Answer:

The x value of a point where a vertical line intersects a function represents the input for that output y value. If we can draw any horizontal line that intersects a graph more than once, then the graph does not represent a function because that y value has more than one input.

Step-by-step explanation:

Answer:

Can't be answered, as written.

Step-by-step explanation:

Please check the equations.  As written, they are the same:

y=2x-4 and 6x-3y=12

The second, 6x-3y=12, can be rewritten:

-3y = -6x + 12

y = 2x - 4   is the same as the first equation.

========

I'll do an example based on a different first equation.  Let's try:

y = 4x-4 and 6x-3y=12

There are two equations and 2 unknowns.  We can solve this in either of two ways:  Mathematically and Graphically.  Let's try both.

Mathematically.

Pick either equation and isolate one of the variables (x or y)

I'll chose the first, since the variable y is already isolated.  (the efficient approach)

y = 4x-4

Take the second equation and use the definition of y provided by the first equation in place of y is the second:

6x-3y = 12

6x-3(4x-4) = 12  [Substituted the value of y given in the first equation]

6x - 12x + 12 = 12

-6x=0

  x= 0

Use x = 0 in either equation to find y:

y = 4x-4

y=4*(0)-4

y = -4

The solution (where the lines intersect) is (0,-4)

We can also solve this graphically.  

Plot the two lines and look for their intersection.  The attached graph shows that to be (0,-4).

So on solving the provided question we can say that -  the length is 4.5 times the area Area of rectangle = A = x X 4.5x; x = 5

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

the length is 4.5 times the area

let length = x

breadth = 4.5 x

Aare of rectangle = A = x X 4.5x

100 = 4x^2

x = 5

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C) (0,3) is only solution set of the given system of inequality.

To solve the system of inequalities x + y ≥ 2 and 4x + y ≥ -1 , we can start by isolating the variables on one side of each inequality and then finding the intersection of the solutions.

given:

x+y ≥2     ----(i)

4x+y ≥-1    ----(ii)

subtracting (i) from (ii) we get

3x ≥ -3

=> x ≥ -1

now y ≥ 2- x

=> y ≥ 2 -(-1)

=> y ≥ 3

So, the solution set for the given system of inequalities is the set of all ordered pairs (x, y) such that x ≥ -1 and y ≥ 3.

and only option C(0,3) satisfies this equation.

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Answer:

Step-by-step explanation:

Assuming the correct question is "Can a triangle be formed with side lengths of 3, 4 and 7?"

3 + 4 = 7

so your answer is NO

Answer:

f(-4) = -20

f(1) = 5

f(2) = 10

f(3) = 15

f(6) = 30

Step-by-step explanation:

Since the equation is f(x) = 5x, you will have to substitute the x-values into the equation to find out what f(x) equals for each one.
For example, for x = -4, f(-4) would equal -20 since 5 * -4 = -20.
The rest would be:
f(1) = 5 * 1 = 5

f(2) = 5 * 2 = 10

f(3) = 5 * 3 = 15

f(6) = 5 * 6 = 30

Hope this helps!

A single mathematical phrase is referred to as a term. It might be a single number (positive or negative), a single variable (a letter), or a combination of variables multiplied but never added or subtracted. A factor is a number that divides another number by itself and leaves no residue.

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the words 4m and 5 are separated by the arithmetic sign + and m is the variable of the provided expression.

Here,

A term refers to a single mathematical phrase. It might be a single integer (positive or negative), a single variable (a letter), or a mixture of variables that have been multiplied but never added or subtracted. A factor is a number that divides another number by itself with no remainder.

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He will read 700 pages each day.He must be committed to reading this amount of pages each day in order to finish the book in two days.

1. There are 1400 pages in the book.

2. The book must be read in even days.

3. To find the number of pages read each day, divide 1400 by 2 (since it must be read in two days).

4. The answer is 700 pages read each day.

The book contains 1400 pages and must be read in two days. To find the answer, the number of pages must be divided by two. This means that each day, he must read 700 pages. This is the same amount each day, so he will read the same amount of pages for each day he reads it. He will have to read for two days in order to finish the book and will read 700 pages for each day. He must be committed to reading this amount of pages each day in order to finish the book in two days.

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Therefore , the solution to the given problem of equation comes out to be $12 for a geranium and $11 for a square foot of grass.

When connecting two statements, a mathematical equation uses its equal sign (=) to denote equivalence. An equation in algebra is a claim that establishes the comparability of two equations. For instance, the formula 5x + 5 = 14 establishes a link between the two integers. The spaces seen between phrases with either front of a letter are used to form a mathematical connection. The lone variable so the only outcome are frequently the symbol. For instance, 8x - 4 = 2.

Here,

To start, you should underline and group pertinent information. Sort the products according to the individual who purchased them. We can give each of the two purchased things a constant or letter as there are only two of them:

Kim

5 feet by 2 feet (X for short) of grass

10 geraniums, designated as "Y" geraniums; total cost: $175

Matt

9 ft 2 of grass (let's call it grass X).

Four geraniums, designated as Y.

$147 in total

Now that the data has been split, you may create two equations: one for Matt and one for Kim.

Kim

5x + 10y = $175

Matt 9x plus 4y = $147

Observe how the numbers remained constant, but I eliminated the units and substituted X or Y depends on just what we assigned. We can start solving now.

I'll take the x out of Kim's equation. the following steps:

1) 5x + 10y = $175 Rewriting the equation

2) If you'd want to perform y first, 5x = $175 - 10y (again, you can still do y first as we're trying to isolate x). That's exactly how I did it.)

3) (5x)÷5 = ($175 - 10y)÷5 (divide both aspects of the equation by 5) 

4) 5x + 10y = $175

=>5x + 10($12) = $175 

5x + 10($12) = $175  

Add the value of y = $12 to Kim's equation to get 5x + $120 = $175.

5) 5x = $175 - $120

=> 5x = $55

=>  x = $11

x = $11

Therefore , the solution to the given problem of equation comes out to be $12 for a geranium and $11 for a square foot of grass.

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Answer: 11 x - 11 y

Step-by-step explanation: 11 (x - y) 11 x - 11 y

The area of the triangle is 12 in². Option C is the correct option.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

The base of the triangle is 6 inches.

The height of the triangle is 4 inches.

The area of a triangle is half of the product of the base and height.

The area of the given triangle is

1/2 × 6×4

= 3×4

=12 in²

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Answer:

Part A: 2

Part B: 10° F

Step-by-step explanation:

Part A

The rate of change is calculated by dividing the difference in temperature by the time.

rate of change = (7°F)/(3 1/2 hours)

rate of change = 7/3.5

rate of change = 2

Answer: 2

Part B

The rate of change tells us that each hour that passes, the temperature decreases by 2° F.

In 5 hours, 5 × 2 = 10, so the change in temperature will be 10° F.

Answer: 10° F

A: you're finding the area where he needs carpet so you do 30x20 and 10x10 and then add those together B: you're seeing how much it would cost to carpet the bedroom so you take the answer from problem A and multiply it by 3

Answer: b = 2 19/30  c = 3 13/30

Step-by-step explanation:

1 4/5 + 5/6

= 1 49/30

= 2 19/30

2 1/10 + 1 2/3

= 3 13/30

Answer:

b)

[tex]2 \times \frac{19}{30} [/tex]

c)

[tex]3 \times \frac{23}{30} [/tex]

Step-by-step explanation:

b)

x - 5/6 = 1 × 4/5

x - 5/6 = 9/5

x = 5/6 + 9/5

x = (25+54)/30

x = 79/30 (or 2×19/30)

c)

x - 2 × 1/10 = 1 × 2/3

x - 21/10 = 5/3

x = 21/10 + 5/3

x = (63+50)/30

x = 113/30 (or 3×23/30)

After solving tan² (0) = 1 on the interval [0, π), The answers are A and B where 0 < A, A = 22 and B = 4.

A set of intervals on the real line are used to create an interval graph, which is an undirected graph in graph theory. Each interval has its own vertex, and there is an edge between vertices where its intervals intersect. It is the graph created by intersecting the intervals.

Chordal and perfect graphs both exist as interval graphs. In these graphs, an optimal graph colouring or maximum clique can be found in linear time, and they are recognisable. The interval graphs comprise all proper interval graphs, which are defined from a set of unit intervals in the same manner.

[tex]$\tan x-1=0 \rightarrow \tan x=\pm 1$[/tex]

Trig table give [tex]$\tan x=1=\tan \left(\frac{\pi}{4}\right)$[/tex]

Trig unit circle gives another arc that has same tan value:

[tex]$x=\left(\frac{\pi}{4}+\pi\right)=\left(\frac{5 \pi}{4}\right)$[/tex]

and

[tex]$ tan \ x=-1=\tan \left(\frac{3 \pi}{4}\right)$[/tex]

Trig circle gives another angle: [tex]$x=\frac{3 p}{4}+\pi=\frac{7 \pi}{4}$[/tex]

In the interval [tex]$(0, \pi)[/tex]   there are 4 answers: [tex]$\frac{\pi}{4} ; \frac{3 \pi}{4} ; \frac{5 \pi}{4} ; \text{and} \frac{7 \pi}{4}$[/tex]

7(22/7)/4

= 22/4

A = 22

B = 4

Thus, After solving tan² (0) = 1 on the interval [0, π), The answers are A and B where 0 < A, A = 22 and B = 4.

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Finding the mirror image of a curve with respect to a line is a relatively straightforward task.

Mirror image is an exact reflection of an object or an image as seen in a mirror. It is an image that is flipped from left to right, with the left side of the image becoming the right side and vice versa. This type of reflection is also known as a lateral inversion. In art and photography, mirror images are often used for aesthetic purposes and to create symmetry.

Firstly, you need to determine the line of reflection. This can be identified by using the angle bisector of the two lines that form the curve. Once you have identified the line of reflection, draw a line perpendicular to it. This is the axis of symmetry.

Next, draw a line parallel to the axis of symmetry. This line will serve as the mirror line. Now, you can start plotting the points of the curve with respect to the mirror line. To do this, take the midpoint of the curve and reflect it across the mirror line. Then, take the points on either side of the midpoint, and reflect them across the mirror line as well. Repeat this process for all the points on the curve.

Finally, connect the reflected points to form the mirror image of the curve. This will give you the same curve, just flipped across the mirror line. It is important to note that the mirror image of the curve will be a mirror reflection of its original shape, but its orientation may be different.

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The null hypothesis is H0: u = 447, the alternative hypothesis is given as: H1: u ≠ 447

A null hypothesis is a statement that there is no significant difference between two groups or no relationship between two variables. The alternative hypothesis, on the other hand, is the statement that there is a significant difference or relationship between the groups or variables.

In statistical hypothesis testing, we test the null hypothesis against an alternative hypothesis. If the data provides enough evidence against the null hypothesis, we can reject it in favor of the alternative hypothesis.

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0.6×1.5=0.9 I know this answer come my home

The polygon given, based on the vertices of the points on the polygon, is not a parallelogram.

Parallelograms are such that there are two vertical parallel lines and two horizontal parallel lines. What this means is that two points on the parallelogram will share the same position on the x axis, and the other two points will share the position on the y - axis.

For instance, the vertices of a parallelogram would be P(−4,0), Q(0,4), R(4,0), and S(0,−4) where you see that two points share the same x coordinates and two share the same y coordinates.

This is not the same with W(-7,-4), X(1,-6), Y(5,-13), Z(1,-12) so this is not a parallelogram.

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Note that the correct Two-way relative frequency table for the data is: (Option A) which is given as follows.

Movie Preference

Action                   Drama    Comedy    Row       Totals

High School        23.0%      13.2%         6.9%      43.1%

College                11.5%       29.3%         16.1%      56.9%

Column totals      34.5%     42.5%          23%      100%

See the tabularized format attached.

Tables of two-way relative frequency indicate percentages rather than counts. They are useful for determining whether or not two variables are related.

Thus, the first choice is the accurate depiction of a two-way frequency table since it shows the percentage of students in each group (high school and college) who picked each movie genre (action, drama, comedy), as well as row and column totals that sum up to 100%. The other three selections are incorrect because they lack percentages or column and row totals.

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Answer:

33!

Step-by-step explanation:

We can use the opposite of division (multiplication) to find what this number could be.

These are the multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, etc.

There are the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, etc.

As you can see, the lowest number that is both a multiple of 3 and 11 is 33.

The standard form of the equation is 8x+5y = -20.

What is standard form of the equation?

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.

Here the given equation is

=> [tex]\frac{1}{2}y=\frac{-4}{5}x-2[/tex]

=> [tex]\frac{1}{2}y=\frac{-4x-10}{5}[/tex]

=> 5y = 2(-4x-10)

=> 5y = -8x-20

=> 8x+5y = -20.

Hence the standard form of the equation is 8x+5y = -20.

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1. The graph that has a slope of -2/3 and a y-intercept of 2 is given as follows:

Graph of a line passing through the points (0,2) and (3,0).

2. The graph that represents the equation y = 0.5x - 1 is given as follows:

Graph of a line passing through the points (-2,-2) and (0,-1).

3. The graph that represents the relation is given as follows:

Graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point (0,58) and (1, 56).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the graph that has a slope of -2/3 and a y-intercept of 2, we have that:

The y-intercept and the slope of the equation y = 0.5x - 1 is given as follows:

-1, meaning that the function passes through the point (0,-1).

When x = -2, the value of the function is given as follows:

y = 0.5(-2) - 1

y = -1 - 1

y = -2.

Hence the other point is (-2,-2).

For the relation in item 3, we have that when x increases by 3, y decays by 6, hence the slope m is given as follows:

m = -6/3

m = -2.

Hence:

y = -2x + b.

When x = 2, y = 54, hence the intercept b is given as follows:

54 = -2(2) + b

b = 58.

Hence the function is:

y = -2x + 58.

The points are:

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It represents the average amount of change in the function per unit throughout that time period.

Divide the change in y-values by the change in x-values to calculate the average rate of change. When analyzing changes in measurable parameters like average speed or average velocity, finding the average rate of change is quite helpful.

The formula R = D/T, or rate of change equals the distance traveled divided by the time required to do so, can be used to approach rate-of-change problems in general.

It represents the average amount of change in the function per unit throughout that time period. It is generated from the slope of the straight line joining the interval's ends on the graph of the function.

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The graph of linear equation y = 3x - 2 have a slope of 3 and y intercept of -2

An equation is an expression that shows the relationship between variables and numbers.

The linear equation is in the form:

y = mx + b

where m is the rate of change and b is the y intercept.

Given that the graph of y = 3x - 2 is shown. It passes through the point (0, -2) and (1, 1)

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