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3 years ago

B is 30 more than a. b is 6 times as many as a. Find the values of a and b.

Mathematics

2 answers:

kicyunya [14]3 years ago

6 0

Answer:

a = 6 and b = 36

Step-by-step explanation:

Set up equations:

b = 30 + a

b = 6a

Subtract the two equations:

b = 6a

- (b = 30 + a)

5a - 30 = 0

5a = 30

divide both sides by 5

a = 6

Plug a = 6 into the original equation:

b = 30 + 6

b = 36

you could also do:

b = 6 * 6

b = 36

yanalaym [24]3 years ago

5 0

Answer:

Step-by-step explanation:

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In a class of 19 students, 3 are math majors. A group of four students is chosen at random. (Round your answers to four decimal

KatRina [158]

Answer:

(a) The probability is 0.4696

(b) The probability is 0.5304

Step-by-step explanation:

The total number of ways in which we can select k elements from a group n elements is calculate as:

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

So, the number of ways in which we can select four students from a group of 19 students is:

$19C4=\frac{19!}{4!(19-4)!}=3,876$

On the other hand, the number of ways in which we can select four students with no math majors is:

$(16C4)*(3C0)=(\frac{16!}{4!(16-4)!})*(\frac{3!}{0!(3-0)!})=1820$

Because, we are going to select 4 students form the 16 students that aren't math majors and select 0 students from the 3 students that are majors.

At the same way, the number of ways in which we can select four students with one, two and three math majors are 1680, 360 and 16 respectively, and they are calculated as:

$(16C3)*(3C1)=(\frac{16!}{3!(16-3)!})*(\frac{3!}{1!(3-1)!})=1680$

$(16C2)*(3C2)=(\frac{16!}{2!(16-2)!})*(\frac{3!}{2!(3-1)!})=360$

$(16C1)*(3C3)=(\frac{16!}{1!(16-1)!})*(\frac{3!}{3!(3-3)!})=16$

Then, the probability that the group has no math majors is:

$P=\frac{1820}{3876} =0.4696$

The probability that the group has at least one math major is:

$P=\frac{1680+360+16}{3876} =0.5304$

The probability that the group has exactly two math majors is:

$P=\frac{360}{3876} =0.0929$

6 0

3 years ago

The lifetime of a certain transistor in a certain application has mean 900 hours and standard deviation 30 hours. Find the mean

tamaranim1 [39]

Answer:

$E(T)=E(X1 + X2 + X3 + X4 =E(x1) + E(x2) + E(x3) + E(x4)$

$E(T) =900+900+900+900 =3600$

And the mean would be:

$\bar X = \frac{T}{4} = \frac{3600}{4}= 900$

And the standard deviation of total time would be:

$SD(T)=\sqrt(Var(T)) = sqrt(Var(X1) + Var(x2) + Var(x3) + Var(x4))$

$\sigma=sqrt(30^2+30^2+30^2+30^2) =\sqrt(3600) =60$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let total life time of t four transistors T = X1 + X2 + X3 + X4 (where X1,X2,X3 and X4 are life time of individual transistors

For this case the mean length of time that four transistors will last

$E(T)=E(X1 + X2 + X3 + X4 =E(x1) + E(x2) + E(x3) + E(x4)$

$E(T) =900+900+900+900 =3600$

And the mean would be:

$\bar X = \frac{T}{4} = \frac{3600}{4}= 900$

And the standard deviation of total time would be:

$SD(T)=\sqrt(Var(T)) = sqrt(Var(X1) + Var(x2) + Var(x3) + Var(x4))$

$\sigma=sqrt(30^2+30^2+30^2+30^2) =\sqrt(3600) =60$

6 0

3 years ago

Susan borrowed $700 from a bank that charges simple interest at a rate of 12% .She borrowed this money for 2 years

andrew11 [14]

Answer:

The interest on the loan is $168

The principal plus interest is $868

Step-by-step explanation:

The interest on the amount is given by the formula below:

I=PRT

I is the interest on the loan,which is the unknown

P is the actual amount borrowed known as the principal which is $700

T is the duration of the loan in years which is years

R is the rate of interest on the loan which is 12% annually

I=$700*12%*2

I=700*0.12*2=$168

In other words,by borrowing $700 ,Susan would pay back the $700 plus $168 interest,which totals $868 in two years time

7 0

4 years ago

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Is X-1 a factor of x^5-1?

Musya8 [376]

Answer: No

Explanation:

According to factor theorem, if f(x)=0 then x is a factor of the given function or equation.

As x-1 is a factor

We equate x-1=0

x=1

Substituting in x^5-1, we have 1^5-1 =1-1=0.

Hence, it's a factor.

When coming to x^5+1, it would become 1^5+1=1+1=2

So x-1 isn't a factor of x^5+1.

4 0

2 years ago

Write a function that represents the situation. Your $840 annual bonus increases by 5% each year

Mazyrski [523]

Answer:

$f(x) = (840)\times (1.05)^{x}$ where f(x) is the bonus every year and x is in number of years

Step-by-step explanation:

The function that represents the situation where $840 annual bonus increases by 5% each year is given by

$f(x) = (840)\times (1.05)^{x}$ where f(x) is the bonus every year and x is in number of years

5 0

3 years ago

B is 30 more than a. b is 6 times as many as a. Find the values of a and b.​

B is 30 more than a. b is 6 times as many as a. Find the values of a and b.