Given the points (2, 4) & (-1,-5), what is the equation of the line?

What is<br> 31 billion in scientific notation

IrinaVladis [17]

3.1 x 10 to the tenth power

8 0

3 years ago

The U.S. government has devoted considerable funding to missile defense research over the past 20 years. The latest development

Bad White [126]

Answer:

a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

b) $X \sim Bin(n =20, p=0.8)$

c) $P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

d) $P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

e) $E(X) = np = 20*0.8 = 16$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

Part b

$X \sim Bin(n =20, p=0.8)$

Part c

For this case we just need to replace into the mass function and we got:

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

Part d

For this case we want this probability: $P(X\geq 15)$

And we can solve this using the complement rule:

$P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

Part e

The expected value is given by:

$E(X) = np = 20*0.8 = 16$

5 0

3 years ago

Help me <br> 3.9x0.5+4 5/6 / 3 3/7

sergey [27]

3.9 · 0.5 + 4 5/6 ÷ 3 3/7
1.95 + 4 5/6 ÷ 3 3/7 multiplication left ot right
1.95 + 29/6 ÷ 24/7 convert to improper fraction
1.95 + 29/6 · 7/24 divide by fraction same as multiplication by reciprocal
1.95 + 203/144 multiply
1.95 + 1.40 (and a teensy bit more)
3.35

5 0

3 years ago

Jim filled 14 holes with 2/4 ton of sand in each. about how many tons of sand did he use?

choli [55]

Answer:

none of the above

Step-by-step explanation:

There are 14 holes * 2/4 per holes

14 * 2/4 = 7

7 tons

8 0

3 years ago

Read 2 more answers

If a cube with a 5-in side length is sliced in half. What is the surface area of the two pieces?

nydimaria [60]

Hello there!

1.) To start, first know that a cube has the same height, length, and width, meaning that all of the dimensions are 5-in. Then, when you slice it in half, this would mean that you have now reduced the width to half of its original. This would mean that the width is now 2.5 while the height and length remain 5.

Now that you have this information, you can now find the surface area by using this formula:

A= 2lw+2lh+2hw

Now plug in your values:

A=2(5)(2.5)+2(5)(5)+2(5)(2.5)

This would simplify to:

A=25+50+25

A=100 in squared

Therefore, the surface area of the two pieces are 100 inches squared.

2.) To start, first plug the measurements of the tank into the cylinder volume formula:

V= $\pi$ r^2h

V= $\pi$ (2.75)^2(10)

V= 237.58 cubic feet

Now, we must find how long it will take the tank to empty if the rate is 3.7 cubic feet per minute so divide the volume (in feet) by the rate:

237.58/3.7= 64.2108...

Rounded to the nearest hundredth, it would take approximately 64.21 minutes to empty the take when it is full.

:)

7 0

4 years ago