All categories

3 years ago

Help me asap please

Mathematics

1 answer:

Eva8 [605]3 years ago

6 0

Answer:

189

Step-by-step explanation:

Since the series is geometric with common ratio r, then

r = 6 ÷ 3 = 2

The terms in the series are twice the previous term, that is the series is

3 + 6 + 12 + 24 + 48 + 96 ← summing the terms gives

sum = 189

You might be interested in

Locate the point on the line segment between A(3, -5) and B(13, -15) given that the point is 4/5 of the way from A to B. Show yo

SVETLANKA909090 [29]

Answer:

C ( 11 , -11 )

Step-by-step explanation:

Solution:-

We are given two points in the cartesian coordinate system as:

A ( 3 , -5 ) B ( 13 , -15 )

The point C lies on the line segment from A to B. The ratio of segment given is:

AC / AB = 4 / 5

To solve such type of problems. We will use vector equation of line AC.

To form a vector equation of line representing AB. We will first determine the direction vector ( d ) that is parallel to the line AB as follows:

d = OB - OA

d = < 13 , -15 > - < 3 , -5 >

d = < 10 , -10 >

The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point B is expressed as:

< x , y > = OA + s*d

< x , y > = < 3, -5 > + s* < 10 , -10 >

The above equation satisfies all the points that lies on the line AB. To determine the coordinates of ( C ). We will plug in the appropriate value of parameter ( s ) and evaluate.

So point C is 4/5 th the magnitude of the distance AB from A. Hence, s = 4/5 as follows:

< x , y > = < 3 , -5 > + ( 4/5 ) * < 10 , -10 >

< x , y > = < 3 , -5 > + < 8 , -8 >

< x , y > = < 11 , -11 > ... Answer

8 0

3 years ago

Please help with 11c!?

Contact [7]

Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

11c)

This is compound growth problem. It goes by the formula:

$F=P(1+r)^t$

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

$F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t$

To solve exponentials, we can take Natural Log (Ln) of both sides:

$2=(1.08)^t\\Ln(2)=Ln((1.08)^t)$

Using the rule shown below we can simplify and solve:

$Ln(a^b)=bLn(a)$

We can write:

$Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064$

To the nearest year, that would be about 9 years

5 0

3 years ago

Carter Road his bike 9/10 of a mile from his house to his grandmothers house. On his way back home, he rode 3/8 of a mile before

jek_recluse [69]

Answer:

Step-by-step explanation:

Carter rode his bike 9/10 of a mile from his house to his grandmothers house. This means that the distance from Carter's house to his grandmother's house is 0.9 miles. On his way back home, he rode 3/8 of a mile before the tyre on his bike went flat. This means that he rode 0.375 miles before his tyre went flat. The distance he must walk before he gets home will be the total distance from home minus the distance that he rode. It becomes

0.9 - 0.375 = 0.575 miles

3 0

3 years ago

What is one fourth in decimal form

olga_2 [115]

.25 Is the answer If that helps you enough

3 0

3 years ago

Read 2 more answers

a slitter assembly contains 48 blades five blades are selected at random and evaluated each day for sharpness if any dull blade

son4ous [18]

Answer:

P(at least 1 dull blade)=0.7068

Step-by-step explanation:

I hope this helps.

This is what it's called dependent event probability, with the added condition that at least 1 out of 5 blades picked is dull, because from your selection of 5, you only need one defective to decide on replacing all.

So if you look at this from another perspective, you have only one event that makes it so you don't change the blades: that 5 out 5 blades picked are sharp. You also know that the probability of changing the blades plus the probability of not changing them is equal to 100%, because that involves all the events possible.

P(at least 1 dull blade out of 5)+Probability(no dull blades out of 5)=1

P(at least 1 dull blade)=1-P(no dull blades)

But the event of picking one blade is dependent of the previous picking, meaning there is no chance of picking the same blade twice.

So you have 38/48 on getting a sharp one on your first pick, then 37/47 (since you remove 1 sharp from the possibilities, and 1 from the whole lot), and so on.

Also since are consecutive events, you need to multiply the events.

The probability that the assembly is replaced the first day is:

P(at least 1 dull blade)=1-P(no dull blades)

$P(at least 1 dull blade)=1-(\frac{38}{48}* \frac{37}{47} *\frac{36}{46}*\frac{35}{45}*\frac{34}{44})$

$P(at least 1 dull blade)=1-0.2931$

P(at least 1 dull blade)=0.7068

5 0

3 years ago

Help me asap please​

Help me asap please