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3 years ago

Please help me out lolll

Mathematics

2 answers:

Amanda [17]3 years ago

6 0

The person above me is correct!! I just checked

Wewaii [24]3 years ago

5 0

Step-by-step explanation:

$\sin(30) = \frac{35}{x} \\ x \sin(30) = 35 \\ x = \frac{35}{ \sin(30) } \\ x = 70$

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Find the volume of the prism.<br> H-8cm L-12cm W-6cm

babymother [125]

Answer:

Step-by-step explanation:

Let’s break this apart.

Box= 12cm x 8cm x 6cm

Cube= 2cm x 2cm x 2cm

How many cubes fit in the box?

calculate the volume of the box. To do this, multiply the length by the width by the height (L x W x H)

12 x 8 x 6 = 576cm cubed

2. Calculate the volume of the cube. Once again we multiply L x W x H

2 x 2 x 2 = 8cm cubed

3. Next we divide the volume of the box by the volume of the cube

576 / 8 = 72 cubes

Therefore, it would take 72 cubes to fill a box.

3 0

3 years ago

Read 2 more answers

chegg Y=4X−2 XX has a PDF of f_X(x)=\begin{cases} 3e^{-3x} & 0 \leq x \\ 0 & \text{otherwise}\end{cases}f X (x)={ 3e −

Licemer1 [7]

$\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]$

so by definition of expectation,

$\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx$

Integrate by parts (twice).

$\displaystyle \int_a^b u\,dv = uv\bigg|_a^b - \int_a^b v\,du$

First, let

$u = (4x-2)^2 \implies du = 8(4x-2)\,dx \\\\ dv = 3e^{-3x} \, dx \implies v = -e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx$

Next,

$u = 4x-2 \implies du = 4\,dx \\\\ dv = e^{-3x} \, dx \implies v = -\dfrac13 e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}$

7 0

1 year ago

Which name gives the most information about the shape below?

Scrat [10]

Answer:

trapezoid

Step-by-step explanation:

There is only one group of shapes that could be a trapezoid

A square, a rectangle, a rhombus, a trapezoid, a kite, and other 4-sided shapes fall under the category of quadrilateral

A rhombus, a parallelogram, and a square are all rhombuses

5 0

3 years ago

How do i write 304,967,000 in word form

kakasveta [241]

Three hundred four million nine hundred sixty seven thousand

5 0

3 years ago

Read 2 more answers

Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.

amm1812

Answers:

(a) 73440
(b) 3060

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

18 choices for slot A
17 choices for slot B
16 choices for slot C
15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

$_nP_r = \frac{n!}{(n-r)!}$

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

-----------------------------------

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

$_nC_r = \frac{n!}{r!(n-r)!}$

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

$_nC_r = \frac{_nP_r}{r!}$

which can be rearranged into

$_nP_r = r!*\left( _nC_r \right)$

these formulas are handy to help us go back and forth between nCr or nPr.

8 0

3 years ago