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tamaranim1 [39]

2 years ago

14

A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from

the bag. What expression would give the probability that one marble is yellow and the other marble is red? P(Y and R) = P(Y and R) = P(Y and R) = P(Y and R) = -----We Have Reached 50 Thanks!!! The 50pts Question Will Be Up Tomorrow Around 8:00am - 10:00am Stay Toon!!!!!!!!!!

2 answers:

Kryger [21]2 years ago

8 0

Answer:

The expression would give the probability that one marble is yellow and the other marble is red is,

$P(Y\cdot R\ And\ R\cdot Y)=P(Y)P(R)+P(R)P(Y)$

Step-by-step explanation:

A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. So in total there are 25 marbles.

Hence,

Probability of getting yellow ball = $P(Y)=\dfrac{8}{25}$

Probability of getting red ball = $P(R)=\dfrac{5}{25}$

Probability that one marble is yellow and the other marble is red is,

$P(Y\cdot R\ And\ R\cdot Y)=P(Y)P(R)+P(R)P(Y)=\dfrac{8}{25}\cdot \dfrac{5}{25}+\dfrac{5}{25}\cdot \dfrac{8}{25}=0.128$

elena-14-01-66 [18.8K]2 years ago

7 0

Y and r: 0.04 or 4% ---------------------

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In a normally distributed data set a mean of 55 where 95% of the data fall between 47.4 and 62.6, what would be the standard dev

tresset_1 [31]

Answer:

The standard deviation of that data set is 3.8

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 55

95% of the data fall between 47.4 and 62.6. This means that 47.4 is 2 standard deviations below the mean and 62.6 is two standard deviations above the mean.

Using one of these points.

55 + 2sd = 62.6

2sd = 7.6

sd = 7.6/2

sd = 3.8

The standard deviation of that data set is 3.8

6 0

2 years ago

A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour what is the

vlabodo [156]

<span>A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour. What is the train’s original speed?
***
let x=original speed
x+5=increased speed
travel time=distance/speed
..
lcd:x(x+5)
150(x+5)-150x=x(x+5)
150x+750-150x=x^2+5x
x^2+5x-750=0
(x-25)(x+30)=0
x=25
What is the train’s original speed? 25 mph</span>

7 0

2 years ago

The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in

Marina86 [1]

Answer:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

Step-by-step explanation:

Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"

We have the following formula in order to find the sum of cubes:

$\lim_{n\to\infty} \sum_{n=1}^{\infty} i^3$

We can express this formula like this:

$\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2

$\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

If we operate and we take out the 1/4 as a factor we got this:

$\lim_{n\to\infty} \frac{n^2(n+1)^2}{n^4}$

We can cancel $n^2$ and we got

$\lim_{n\to\infty} \frac{(n+1)^2}{n^2}$

We can reorder the terms like this:

$\lim_{n\to\infty} (\frac{n+1}{n})^2$

We can do some algebra and we got:

$\lim_{n\to\infty} (1+\frac{1}{n})^2$

We can solve the square and we got:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

3 0

2 years ago

Which is the graph of f(x) = (x + 3)(x – 2)? On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a

amm1812

Answer:

On a coordinate plane, a parabola opens up

It goes through (negative 3, 0), has a vertex at (negative 0.5, negative 6.25), and goes through (2, 0).

Step-by-step explanation:

f(x) = (x + 3)(x – 2)

We know that parabola opens up since the x^2 term is be positive

it has zeros at x=-3 and x=2

x+3 =0 and x-2 =0 from the zero product property

The vertex is halfway between the zeros

(-3+2)/2 = -1/2

x=-1/2

f(-1/2) = (-1/2+3) (-1/2-2) = 2.5 * -2.5 =-6.25

The vertex is (-1/2, -6.25)

8 0

2 years ago

a man who weighs approximately 140 pounds has two,12 ounce beers and one 1 1/2 oz. shots of liquor in one hour. what is his esti

Alinara [238K]

The <u>correct answer</u> is:

0.08.

Explanation:

To calculate the BAC, we first find the amount of alcohol (in grams) of the drinks. In the US, a standard drink has 14 g of alcohol. The man has 2 beers and 1 shot; this is 3 standard drinks:
3*14 = 42

This has 42 g of alcohol.

Next we convert the weight in pounds to grams. We do this by multiplying by 454:
140*454 = 63560

Next we multiply by the gender constant. For men, this is 0.68:
63560(0.68) = 43220.8

We divide the grams of alcohol by this number:
42/43220.8 = 0.000972

Multiply this by 100:
0.000972(100) = 0.0972

This is the BAC right after drinking. To account for the time that has passed, we multiply the number of hours by 0.015:
1(0.015) = 0.015

We subtract this from our immediate BAC:
0.0972-0.015 = 0.0822 ≈ 0.08

5 0

2 years ago

Read 2 more answers