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Juliette [100K]
3 years ago
9

An exam was given to a group of freshman and sophomore students. The results are below:

Mathematics
1 answer:
leonid [27]3 years ago
8 0
B(the student was a freshman or received a C)
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Three side lengths of a right triangle are given which side length should you substitute for the hypotenuse in Pythagorean theor
ankoles [38]

Answer:

The longest length which you are given.

Step-by-step explanation:

The hypotenuse is the longest side in a right angled triangle. The largest side in a right angled triangle is known as the hypotenuse.

8 0
3 years ago
Miguel wants to build a container out of sheet metal that has a volume of about 320 cubic inches . He
ZanzabumX [31]

Answer:

  cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

__

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

<h3>Rectangular Prism</h3>

The relevant formulas are ...

  V = LWH

  A = 2(LW +H(L +W))

for length L, width W, and height H.

<u>a)</u><u> prism 1</u>

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

  V = (8 in)(8 in)(5 in) = 320 in³

  A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

<u>b)</u><u> prism 2</u>

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

  V = (10 in)(8 in)(4 in) = 320 in³

  A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

__

<h3>Cylinder</h3>

The relevant formulas are ...

  V = πr²h

  A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

  V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

  A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

__

<h3>Square Pyramid</h3>

The relevant formulas are ...

  V = 1/3s²h

  A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

  V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

  A = (10 in)(10 in + 2×14 in) = 380 in²

__

<h3>Summary</h3>

The proposed figures have volume and area (rounded to the nearest unit) as follows:

  \begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}

The proposed <em>cylinder</em> requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

<em>Additional comment</em>

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

3 0
1 year ago
(1.3x + 2.4) + (-6.1x – 3.2)
melisa1 [442]

Step-by-step explanation:

In simplify form: 1.3x+2.4-6.1-3.2 = -4.8x-0.8

or factor the expression: =-4/5×(6x+1) Alternate form: -0.8(6x+1). I hope this helps.

8 0
3 years ago
if a bag contains 16 red ,4yellow,20blue,8white balloons, what is the part-to-whole ratio of red balloons to all balloons
TEA [102]
Its 16/48 i hope this helps
5 0
3 years ago
Figure b is a scale image of Figure A, as shown. Figure a is an Rectangle with 9 on left side and 12 on bottom of rectangle. and
Ronch [10]

The scale factor that was applied to figure A to produce figure B is: 11/3 = 3.67.

<h3>How to Find the Scale Factor of a Dilation?</h3>

The ratio of the corresponding dimensions of the image to the preimage gives the scale factor of any dilation.

That is:

Scale factor = dimension of image (new figure) / corresponding dimension of pre-image (original figure).

The scale factor that was applied to figure A to produce figure B = dimension of figure B / corresponding dimension of figure A.

A dimension of figure B = 33

Corresponding dimension of figure A = 9

Therefore, we would find the scale factor as shown below:

The scale factor that was applied to figure A to produce figure B = 33/9

= 11/3 = 3.67

Therefore, the scale factor that was applied to figure A to produce figure B is: 11/3 = 3.67.

Learn more about the scale factor on:

brainly.com/question/2826496

#SPJ1

6 0
1 year ago
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