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3 years ago

48 liters is equivalent to 48,000 millimeters. What is this number of millimeters in scientific notation?

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

4 0

Step-by-step explanation:

The scientific notation:

$a\cdot10^k$ where 1 ≤ a < 10, and k ∈ Z (integer).

$48000=4.8000\cdot10^4=4.8\cdot10^4\\\\4\underbrace{8000}_{\leftarrow\bold{4}}=4.8\cdot10^{\bold{4}}$

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In the figure below, ∆ABC is similar to ∆DBE. Given that BE=10cm, AB=3cm and BD=4cm. Find the length of BC.

frez [133]

Check the picture below

solve for CB

3 0

3 years ago

Let Y1 and Y2 be independent exponentially distributed random variables, each with mean 7. Find P(Y1 > Y2 | Y1 < 2Y2). (En

ArbitrLikvidat [17]

Y₁ and Y₂ are independent, so their joint density is

$f_{Y_1,Y_2}(y_1,y_2)=f_{Y_1}(y_1)f_{Y_2}(y_2)=\begin{cases}\frac1{49}e^{-\frac{y_1+y_2}7}&\text{for }y_1\ge0,y_2\ge0\\0&\text{otherwise}\end{cases}$

By definition of conditional probability,

P(Y₁ > Y₂ | Y₁ < 2 Y₂) = P((Y₁ > Y₂) and (Y₁ < 2 Y₂)) / P(Y₁ < 2 Y₂)

Use the joint density to compute the component probabilities:

• numerator:

$P((Y_1>Y_2)\text{ and }(Y_1$

$=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1$

$=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty$

$=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16$

• denominator:

$P(Y_1$

(I leave the details of the second integral to you)

Then you should end up with

P(Y₁ > Y₂ | Y₁ < 2 Y₂) = (1/6) / (2/3) = 1/4

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2 years ago

Mr. Green is putting lights around 8 windows; each window is 3.5feet wide and 5 feet long. How many feet of light does he need?

zmey [24]

We must find the perimeter of all eight windows. To make it simpler for us, let's find the perimeter of one window and multiply it by 8.

2*3.5 + 2*5 = 7 + 10 = 17

17*8 = 136

Hope this helps!

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3 years ago

A shop owner offerad a 20% discount off the regular price of a mirror. The amount of the discount is 3$ what is the regular pric

Troyanec [42]

Answer:

$15

Step-by-step explanation:

$3 correspond is the 20% discount of the total price.

If the total price is x then you can express the discount as:

0.20x = 3

x = 3/0.20

x = 15

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3 years ago

A bag contains 5 red marbles, 6 blue marbles and 9 yellow marbles.

lilavasa [31]

Answer:

Step-by-step explanation:

The total number of marbles is 20

Question A

P(Red) = 4/20 = 1/5

P(yellow) = 9/20

P(Red then Yellow) = 1/5 * 9/20 = 9 / 100

Question B

P(B) = 6/20

P(B again) = 5/19 because you have 1 less total plus 1 less blue.

P(B and B) = 6/20 * 5/19

P(B and B) = 30/ 380 = 3/38

7 0

3 years ago