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3 years ago

How many 3 3/4 inch wires can be cut from a spool if wire that is 100 inches how much will be left over

Mathematics

1 answer:

Akimi4 [234]3 years ago

6 0

How many 3 $\frac{3}{4}$ wires can be cut from a spool of wire that is 100 inches long?

How many inches will be left over?

Number of pieces of wires = length of spool of wire ÷ length of each piece of wire.

Number of pieces = 100 ÷ 3 $\frac{3}{4}$ = 100 ÷ $\frac{15}{4}$

That gives $\frac{100 * 4}{15}$

Simplifying gives $\frac{400}{15}$ = $\frac{80}{3}$

This is equivalent to 26 $\frac{2}{3}$ pieces

So 26 pieces of wires can be cut from a spool and $\frac{2}{3}$ of a piece will be left over.

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A closed can, in a shape of a circular, is to contain 500cm^3 of liquid when full. The cylinder, radius r cm and height h cm, is

Gemiola [76]

To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder: $V= \pi r^2h$
where
$V$ is the volume
$r$ is the radius
$h$ is the height

We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words: $V=500cm^3$ . We also know that the radius is r cm and height is h cm, so $r=rcm$ and $h=hcm$ . Lets replace the values in our formula:
$V= \pi r^2h$
$500cm^3= \pi (rcm^2)(hcm)$
$500cm^3=h \pi r^2cm^3$
$h= \frac{500cm^3}{ \pi r^2cm^3}$
$h= \frac{500}{ \pi r^2}$

Next, we are going to use the formula for the area of a cylinder: $A=2 \pi rh+2 \pi r^2$
where
$A$ is the area
$r$ is the radius
$h$ is the height

We know from our previous calculation that $h= \frac{500}{ \pi r^2}$ , so lets replace that value in our area formula:
$A=2 \pi rh+2 \pi r^2$
$A=2 \pi r(\frac{500}{ \pi r^2})+2 \pi r^2$
$A= \frac{1000}{r} +2 \pi r^2$
By the commutative property of addition, we can conclude that:
$A=2 \pi r^2+\frac{1000}{r}$

7 0

3 years ago

Which of the following are identities? Check all that apply

Natasha2012 [34]

Answer:

A, C

Step-by-step explanation:

Actually, those questions require us to develop those equations to derive into trigonometrical equations so that we can unveil them or not. Doing it only two alternatives, the other ones will not result in Trigonometrical Identities.

Examining

A) True

$\frac{1-tan^{2}x}{2tanx} =\frac{1}{tan2x} \\ \frac{1-tan^{2}x}{2tanx} =\frac{1}{\frac{2tanx}{1-tan^{2}x}}\\ tan2x=\frac{1-tan^{2}x}{2tanx}$

Double angle $tan2\alpha =\frac{1 -tan^{2}\alpha }{2tan\alpha}$

B) False,

No further development towards a Trig Identity

C) True

Double Angle Sine Formula $sin2\alpha =2sin\alpha *cos\alpha$

$sin(8x)=2sin(4x)cos(4x)\\2sin(4x)cos(4x)=2sin(4x)cos(4x)$

D) False No further development towards a Trig Identity

$[sin(x)-cos(x)]^{2} =1+sin(2x)\\ sin^{2} (x)-2sin(x)cos(x)+cos^{2}x=1+2sinxcosx\\ \\sin^{2} (x)+cos^{2}x=1+4sin(x)cos(x)$

7 0

3 years ago

Read 2 more answers

Express tan J as a fraction in simplest terms

Goryan [66]

Answer is TanJ=8/15 if that’s what your asking

6 0

2 years ago

Read 2 more answers

At last week's track meet, Stacy ran 9/12 of a km, Jules ran 4/5 of a km, and Raul ran 3/4 of a mile. Which two students ran the

koban [17]

Answer: No two students ran same distance

Step-by-step explanation:

Given

Stacy ran $\frac{9}{12}$ of a km i.e.

$\Rightarrow 1\times \dfrac{9}{12}=\dfrac{3}{4}=0.75\ km$

Jules ran $\frac{4}{5}$ of a km i.e.

$\Rightarrow 1\times \dfrac{4}{5}=0.8\ km$

Raul ran $\frac{3}{4}$ of mile i.e.

$\Rightarrow 1\times \dfrac{3}{4}=0.75\ miles\\\\\text{1 mile=1.6 km}\\\\\Rightarrow 0.75\ miles=1.2\ km$

So, no two students ran the same distance.

6 0

2 years ago

Melissa collected data from a group of people regarding whether or not they prefer turkey or ham and whether or not they prefer

dedylja [7]

Answer:

I’m pretty sure it’s B)- Z

Step-by-step explanation:

18. The correct table must display the following information.

38% prefer turkey with mayonnaise 20% prefer turkey with mustard 24% prefer ham with mayonnaise 18% prefer ham with mustard

In tables Z and W, each table totals 50 people.

To find the relative frequencies of the data in these tables, divide each number in the table by 50.

In tables X and Y, each table totals 100 people.

To find the relative frequencies of the data in these tables, divide each number in the table by 100.

The only table which is a possible representation of the data collected is table Z.

Likes Baseball

Does Not Like Baseball

Total

Likes Football Does Not Total Like Football

0.50 0.64 0.54

0.50 0.36 0.46 1.00 1.00 1.00

Mayonnaise Mustard

Total

Turkey

19 ÷ 50 = 0.38

10 ÷ 50 = 0.20

29 ÷ 50 = 0.58

Ham

12 ÷ 50 = 0.24

9 ÷ 50 = 0.18

21 ÷ 50 = 0.42

Total

31 ÷ 50 = 0.62

19 ÷ 50 = 0.38

50 ÷ 50 =1.00

3 0

3 years ago