Write a formula for the general term or nth term for the sequence. Then find the indicated term. three fourths comma three sixteenths comma StartFraction 3 Over 64 EndFraction comma StartFraction 3 Over 256 EndFraction ...; a 8

Answers

Answer 1

Answer: Sequence: 3/4, 3/16, 3/64, 3/256
a8=?
a1=3/4
a2=3/16
a3=3/64
a4=3/256

a2/a1=(3/16)/(3/4)=(3/16)*(4/3)=4/16=1/4
a3/a2=(3/64)/(3/16)=(3/64)*(16/3)=16/64=1/4
a4/a3=(3/256)/(3/64)=(3/256)*(64/3)=64/256=1/4
a2/a1=a3/a2=a4/a3=r=1/4

an=a1*r^(n-1)
an=(3/4)*(1/4)^(n-1)
an=(3/4)*(1)^(n-1)/(4)^(n-1)
an=(3/4)*(1/4^(n-1))
an=(3*1)/[4*4^(n-1)]
an=3/4^(1+n-1)
an=3/4^n

n=8→a8=3/4^8
a8=3/65,536

Answers:
The general term or nth term for the sequence is: an=3/4^n
a8=3/65,536

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!!HELP!!A stage designer paid $4 per square foot for flooring to be used
in a square room. If the designer spent $600 on the flooring, about how long is a
side of the room? Round to the nearest foot.

• How is the area of a square related to its side length?

• How can you estimate the length of a side of a square?

Answers

The area of a square relates to its side length as Area = Side Length × Side Length. To estimate a side length, knowing $4/sq ft cost and $600 spent, Side Length ≈ 12 feet.

The area of a square is related to its side length by the formula:

Area = Side Length × Side Length

or Area = Side Length²

To estimate the length of a side of a square,

use the given information that the designer paid $4 per square foot for flooring and spent $600 on the flooring.

The cost of the flooring is directly proportional to its area, which is determined by the square of the side length.

Let's set up an equation using the cost and area:

Cost of flooring = Cost per square foot × Area

$600 = $4/sq ft × Side Length²

Solving for Side Length²

Side Length² = $600 / $4/sq ft

Side Length² = 150 sq ft

Taking the square root of both sides to find the side length:

Side Length ≈ √150

Side Length ≈ 12.25 feet

Rounded to the nearest foot, the side length of the room is approximately 12 feet.

Therefore, the estimated length of a side of the room is about 12 feet.

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Answer:

$150

Step-by-step explanation:

600 divided by 4

The marks on a combination lock are numbered 0 to 39. If the lock is at mark 19, and the dial is turned one mark clockwise, it will be at mark 18. If the lock is at mark 19 and turned 137 marks clockwise, at what mark will it be

Answers

Answer:

Mark 2

Step-by-step explanation:

There are 40 marks on the lock.

Every full turn of 40 marks, the lock will come back to mark 19.

137/40 = 3R17

You can make three full turns (which is equivalent to doing nothing), and then you must move 17 more marks.

19 - 17 = 2

The lock will be at mark 2.

If the lock is at mark 19 and turned 137 marks clockwise, it will be at mark 2.

What is combination lock?

Combination lock is opened by rotating a set of number dials or marks graduated in a sequence.

The marks on a combination lock are numbered 0 to 39. If the lock is at mark 19, and the dial is turned one mark clockwise, it will be at mark 18. If the lock is at mark 19 and turned 137 marks clockwise,

137 = 40a +b where b<40

Divide 137 by 40, so we get the quotient 3 i.e., a =3.

Substitute a = 3 , the value of b is

b = 17

If the lock is at mark 19 and turned 137 marks clockwise, it will be at mark,

19-17 = 2

Thus, If the lock is at mark 19 and turned 137 marks clockwise, it will be at mark 2.

Learn more about combination lock.

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Kenny worked 6.5 hours on Monday, and 5 hours on Tuesday. If he received a check for $143.75 for working those 2 days, how much does Kenny make per hour?

Answers

Answer:

Kevin makes $12.50 per hour.

Step-by-step explanation:

If Kevin works 6.5 hours on Monday and 5 hours on Tuesday, he works a total of 11.5 hours. Over 11.5 hours he makes $143.75. To find your answer, you have to divide your total earned, 143.765, by the total time worked, 11.5 hours. Your answer should then be 12.5, which is the amount per hour kevin earns.

In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. In another city known for biotech firms, 334 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. Perform a two-proportion hypothesis test to determine whether there is a difference in the proportions of college graduates with outstanding student loans who currently owe more than $50,000 in these two cities. Use α=0.05. Assume that the samples are random and independent. Let the first city correspond to sample 1 and the second city correspond to sample 2. For this test: H0:p1=p2; Ha:p1≠p2, which is a two-tailed test. The test results are: z≈−1.17 , p-value is approximately 0.242

Answers

Answer:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

$p_v =2*P(Z<-1.182)=0.2372$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_(1)=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_(2)=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_(1)=800$ sample 1

$n_(2)=800$ sample 2

$p_(1)=(311)/(800)=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_(2)=(334)/(800)=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)