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prisoha [69]
3 years ago
11

Julia needs to make a box in the shape of a rectangular prism with a height of 3 inches and a volume of 243 cubic inches. The di

mensions, in inches, must be whole numbers greater than 1. Julia claims that the length and the width must be equal. Part A: What dimensions would support Julia's claim about the length and with of the box? Part B: What dimensions would not support Julia's claim about the length and width of the box. Part A length =______________ Part A width=_____________________. Part B length_________________Part B Width=_____________________.
Mathematics
2 answers:
umka2103 [35]3 years ago
7 0
The volume of a rectangular prism is equal to length*width*height. In this case, we have V = 243 and H = 3.
243 = LW(3), so LW = 81, where L & W are whole numbers greater than 1. There are only 3 possible pairs of values for this: 27*3, 9*9, and 3*27 (we cannot use 1*81 or 81*1, since we need dimensions > 1).
Part A. This could be true if Length = 9 in and Width = 9 in, as 9*9 = 81.
Part B. The claim could be false if Length = 27 in and Width = 3 in, as 27*3 = 81, but 27 is not equal to 3.
*Note that the width cannot be longer than the length.
natulia [17]3 years ago
6 0
Part A.
 sqrt 81 = 9; L = 9 ; W = 9 inches

Part B.
if length =27 , width =3, though 27*3 = 81 but then 27 is not equal 3. So false
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DJ Titus is making a playlist for a radio show; he is trying to decide what 10 songs to play and in what order they should be pl
Dominik [7]

Answer:

Different playlists possible = 18287141644800

Step-by-step explanation:

Given - DJ Titus is making a playlist for a radio show; he is trying to

            decide what 10 songs to play and in what order they should be

            played.

            Step 1 of 2 : If he has his choices narrowed down to 7 blues,

                                 7 disco, 5 pop, and 7 reggae songs.

To find - He wants to play no more than 4 reggae songs.

              How many different playlists are possible ?

Proof -

Given that he wants to play no more that 4 reggae songs.

So the possibility of choice of reggae song is 0, 1, 2, 3, 4

Now,

Case I -

If 0 reggae song is selected

⇒All 10 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₁₀ ₓ ⁷C₀ = 92,378

Case II -

If 1 reggae song is selected

⇒All 9 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₉ ₓ ⁷C₁ = 646,646

Case III -

If 2 reggae song is selected

⇒All 8 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₈ ₓ ⁷C₂ = 1,587,222

Case IV -

If 3 reggae song is selected

⇒All 7 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₇ ₓ ⁷C₃ = 1,763,580

Case V -

If 4 reggae song is selected

⇒All 6 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₆ ₓ ⁷C₄ = 949,620

So,

Total possible ways = 92,378+ 646,646+ 1,587,222+ 1,763,580+ 949,620

                               = 5,039,446

⇒Total possible ways = 5,039,446

Now,

Also the 10 songs selected can arranged themselves in 10! ways. ( because order of song played does not matter )

∴ we get

Different playlists possible = 10! × 5,039,446

                                          = 18287141644800

⇒Different playlists possible = 18287141644800

6 0
2 years ago
Con las cuatro cartas que se muestran en la figura se pueden formar diferentes números. Por ejemplo: 8232 o 3822. ¿Cuántos númer
densk [106]

Answer:

Se pueden formar 9 números pares.

Step-by-step explanation:

Dado que con cuatro cartas se pueden formar diferentes números, como por ejemplo 8232 o 3822, para determinar cuántos números pares de cuatro dígitos y diferentes puedes formar con estas cuatro cartas se debe realizar la siguiente tabla:

8232 - 8322 - 8223 = 2 pares 1 impar

2832 - 2823 - 2382 - 2328 - 2283 - 2238 = 4 pares 2 impares

3822 - 3282 - 3228 = 3 pares

Por lo tanto, se pueden formar 9 números pares.

5 0
2 years ago
12. The weight of 7 chocolate bars in grams are 131, 127,125,127,133,129 and 127
Amanda [17]

Answer:

The range is from 125 to 133.

Step-by-step explanation:

That's the lowest and highest the weights go, therefore the range is from 125 and anything in between up to 133.

7 0
3 years ago
Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .
anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

We need to begin with the definition of tangent:

tan (x) =\frac{sin(x)}{cos(x)}

So we can replace into our formula and we got:

tan(x-y) = \frac{sin(x-y)}{cos(x-y)}   (1)

We have the following identities useful for this case:

sin(a-b) = sin(a) cos(b) - sin(b) cos(a)

cos(a-b) = cos(a) cos(b) + sin (a) sin(b)

If we apply the identities into our equation (1) we got:

tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}   (2)

Now we can divide the numerator and denominato from expression (2) by \frac{1}{cos(x) cos(y)} and we got this:

tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}

And simplifying we got:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

And this identity is satisfied for all:

(x-y) \neq \frac{\pi}{2} +n\pi

8 0
2 years ago
A wheelchair access ramp has an angle of elevation of 41 degrees. If the ramp reaches to the top of a 26 inch high porch, how lo
Gemiola [76]

Answer:

HAHA THAT DISABLED F-WORD

Step-by-step explanation:

7 0
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