Ask question

Ask question

All categories

2 years ago

13

A goblet contains 222 red marbles, 666 green marbles, and 444 blue marbles. If we choose a marble, then another marble without p

utting the first one back in the goblet, what is the probability that the first marble will be green and the second will be green as well?

2 answers:

Firdavs [7]2 years ago

3 0

Answer : Probability( first will be green and second will be green as well) = 0.024989713

Explanation:

We have given that,

Number of red marbles = 222

Number of green marbles =666

Number of blue marbles =444

∴ Total number of marbles =1332

$P( \text{first marble will be green and the second will be green as well})= \frac{666}{1332}\times \frac{665}{1331}$

$=\frac{442890}{1772892}\\=0.024989713$

∴ Probability will be 0.024989713

Maksim231197 [3]2 years ago

3 0

Answer:

5/22

Step-by-step explanation:

1/2 x 5/11 = 5/22

You might be interested in

Colin has 18 pencils. How many kids (including Colin) can share these pencils evenly?

julsineya [31]

18 kids right? Or am I dumb? I feel like I’m wrong because this question seems so easy.

5 0

2 years ago

Read 2 more answers

The number of airline passengers in 1990 was 466 million. The number of passengers traveling by airplane each year has increased

taurus [48]

Answer:

2010.

Step-by-step explanation:

We have been given an exponential growth formula $P(t)=466\cdot 1.035^t$ , which represents number of passengers traveling by airplane since 1990.

To find the year in which 900 million passengers will travel by airline, we will equate the given formula by 900 and solve for t as:

$900=466\cdot 1.035^t$

$\frac{900}{466}=\frac{466\cdot 1.035^t}{466}$ $1.9313304721030043=1.035^t$

Take natural log of both sides:

$\text{ln}(1.9313304721030043)=\text{ln}(1.035^t)$

Using property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$\text{ln}(1.9313304721030043)=t\cdot \text{ln}(1.035)$

$0.658209129198=t\cdot 0.034401426717$

$\frac{0.658209129198}{0.034401426717}=\frac{t\cdot 0.034401426717}{0.034401426717}$

$19.1331927775=t\\\\t=19.1331927775$

This means that in the 20th year since 1990, 900 million passengers would travel by airline.

$1990+20=2010$

Therefore, 900 million passengers would travel by airline in 2010.

6 0

2 years ago

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

3 0

2 years ago

Read 2 more answers

Yan is climbing down a ladder. Each time he descends four rungs on the ladder, he stops to see how much farther he has to go. Wh

8090 [49]

Answer:

Descends

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

The water level of a river is 170 feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this

Vladimir [108]

Sample Answer: No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.

3 0

2 years ago

Read 2 more answers