Which of the following numbers are rational?

Evaluate the expression 10b/a if b = 6 and a = 2

zimovet [89]

Answer:

30

Step-by-step explanation:

10b/a

b = 6

a =2

10(6)/2

10x6 / 2 = 60/2

= 30

8 0

2 years ago

Read 2 more answers

Which equation is not equal to 6^3/6^6 ?: 1/6^2 6^-3 1/216 1/6^3

SCORPION-xisa [38]

The answer would be 60 because its multiplication all those numbers

4 0

2 years ago

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

EleoNora [17]

Answer:

a) $P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)$

And we can use the probability mass function and we got:

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

And adding we got:

$P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061$

b) $P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182$

c) $P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

$P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054$

And replacing we got:

$P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886$

d) $E(X) = 20*0.2= 4$

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".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=20, p=0.2)$

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

We want this probability:

$P(X \leq 2)= P(X=0)+P(X=1)+P(X=2)$

And we can use the probability mass function and we got:

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

And adding we got:

$P(X \leq 2)=0.0115+0.0576+0.1369 = 0.2061$

Part b

We want this probability:

$P(X=4)$

And using the probability mass function we got:

$P(X=4)=(20C4)(0.2)^4 (1-0.2)^{20-4}=0.2182$

Part c

We want this probability:

$P(X>3)$

We can use the complement rule and we got:

$P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$P(X=0)=(20C0)(0.2)^0 (1-0.2)^{20-0}=0.0115$

$P(X=1)=(20C1)(0.2)^1 (1-0.2)^{20-1}=0.0576$

$P(X=2)=(20C2)(0.2)^2 (1-0.2)^{20-2}=0.1369$

$P(X=3)=(20C3)(0.2)^3 (1-0.2)^{20-3}=0.2054$

And replacing we got:

$P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886$

Part d

The expected value is given by:

$E(X) = np$

And replacing we got:

$E(X) = 20*0.2= 4$

3 0

2 years ago

a. How wide must a wall footing be if the load is 9,500 pounds per foot of wall length, and the footing rests on a sandy gravel?

Phantasy [73]

Answer:

a) 38"

b) L = 5.7'

Step-by-step explanation:

a) Given

P = 9,500 lb/ft

Thick = 18"

We assume an allowable bearing pressure of σ = 3000 lb/sf

If Stress = Force / Area

σ = P/A

Solving for area

A = P/σ ⇒ A = 9,500 lb/ft/3000 lb/sf

⇒ A = 3.167 sf, or 3.167 ft wide, per foot of length.

⇒ A = 38" wide

We can see the pic 1 in order to understand the answer.

b) Given

P = 65,000 pounds = 65,000 lb

Thick = 18" = 1.5'

We assume an allowable bearing pressure of σ = 2000 lb/sf

If Stress = Force / Area

σ = P/A

Solving for area

A = P/σ ⇒ A = 65,000 lb/2000 lb/sf

⇒ A = 32.5 sf

then A = L² ⇒ L = √A = √(32.5 sf) = 5.7 ft

Finally L = 5.7'

We can see the pic 2 in order to understand the answer.

3 0

2 years ago

Find the volume of the cylinder using 3.14 for pi. Please help Asap

Luda [366]

$\huge\pink{Answer}$

Volume = πr2h

= π×82×8

= 512π

= 1608.495438638 meters3

= 1608.5 approx

5 0

2 years ago

Read 2 more answers