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2 years ago

Find the 5th (not fourth) of given geometric sequence. 2000, 1000, 500,...

Mathematics

1 answer:

Greeley [361]2 years ago

8 0

Answer:

125

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

1000/2000 = 1/2

We multiply each term by 1/2

2000, 1000, 500

To find the next term 500*1/2 = 500/2 = 250

To find the 5th term

250*1/2 = 125

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Before the distribution of certain statistical software, every fourth compact disk (CD) is tested for accuracy. The testing proc

lilavasa [31]

Answer:

a) For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:

$P(R) =\frac{1}{4} =0.25$

The failure probability for each program are given by:

$P(F_1) = 0.01 , P(F_2) = 0.03 , P(F_3) = 0.02 , P(F_4) = 0.01$

For this case we assume that each test is independet form the others.

We can calculate the probability that all 4 programs works properly like this:

$P(4 work) = (1-0.01)*(1-0.03)*(1-0.02)*(1-0.01)= 0.932$

So then the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

And if we use the fact that we have 4 possible test the true probability of interest would be:

$P(R \cap F) = P(R)*P(F) = 0.25*0.068=0.017$

b) $p= P(F'_1) P(F'_4) *(1- P(F'_2)*P(F'_3))$

And replacing we got:

$p =(1-0.01)*(1-0.01) *[1- (1-0.03)(1-0.02)]= 0.99*0.99*[1- 0.97*0.98]= 0.0484$

c) From part a we now that the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

So then if we have 100 CDs the expected number of rejected Cd's are:

$100*0.068= 6.8 \approx 7$

Step-by-step explanation:

Part a

For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:

$P(R) =\frac{1}{4} =0.25$

The failure probability for each program are given by:

$P(F_1) = 0.01 , P(F_2) = 0.03 , P(F_3) = 0.02 , P(F_4) = 0.01$

For this case we assume that each test is independet form the others.

We can calculate the probability that all 4 programs works properly like this:

$P(4 work) = (1-0.01)*(1-0.03)*(1-0.02)*(1-0.01)= 0.932$

So then the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

And if we use the fact that we have 4 possible test the true probability of interest would be:

$P(R \cap F) = P(R)*P(F) = 0.25*0.068=0.017$

Part b

For this case we want the probability that it failed program 2 or 3

So then we can find this probability like this:

$p= P(F'_1) P(F'_4) *(1- P(F'_2)*P(F'_3))$

And replacing we got:

$p =(1-0.01)*(1-0.01) *[1- (1-0.03)(1-0.02)]= 0.99*0.99*[1- 0.97*0.98]= 0.0484$

Part c

From part a we now that the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

So then if we have 100 CDs the expected number of rejected Cd's are:

$100*0.068= 6.8 \approx 7$

3 0

2 years ago

Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 39° and side c = 13.

hram777 [196]

Answer:

Part 1) $b=8.2\ units$

Part 2) $a=10.1\ units$

Part 3) $A=51\°$ and $C=90\°$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

$sin(B)=AC/AB$

we have

$AB=c=13\ units$

$AC=b$

$B=39\°$

substitute

$sin(39\°)=b/13$

solve for b

$b=(13)sin(39\°)$

$b=8.2\ units$

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

$cos(B)=BC/AB$

we have

$AB=c=13\ units$

$BC=a$

$B=39\°$

substitute

$cos(39\°)=a/13$

solve for a

$a=(13)cos(39\°)$

$a=10.1\ units$

step 3

Find the measure of angle A

we know that

In the right triangle ABC

$C=90\°$ ----> is a right angle

$B=39\°$

∠A+∠B=90° ------> by complementary angles

substitute the given value

$A+39\°=90\°$

$A=90\°-39\°$

$A=51\°$

5 0

2 years ago

there are 32 forwards and 80 guards in leos basketball league. eo must include all players on a team and wants each team to have

Marrrta [24]

Close. The greatest common factor between 32 and 80 is 16 not 8.

32 (forwards) / 16 (teams) = 2 forwards on each team.

80 (guards) / 16 (teams) = 5 guards on each team.

3 0

2 years ago

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sesenic [268]

Anytime you find an equality that is always true, it means that there are infinitely many solutions.

If you arrive at 12=12, it means that the equations are always equal.

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2 years ago

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harina [27]

Answer:

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