MATHEMATICS HIGH SCHOOL

What is the next term in this geometric sequence
5/6,5/9,10/27,20/81

Answers

Answer 1
Answer: a_1=(5)/(6);\ a_2=(5)/(9);\ a_3=(10)/(27);\ a_4=(20)/(81)\n\n\nq=a_2:a_1\n\nq=(5)/(9):(5)/(6)=(5)/(9)\cdot(6)/(5)=(2)/(3)\n\n\na_5=a_4\cdot q\n\na_5=(20)/(81)\cdot(2)/(3)=(40)/(243)\to answer
Answer 2
Answer: (20/81) * (2/3) = 40/243;

the next term in this geometric sequence is 40/243.

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Katie wants to collect over 100 seashells. She already has 34 seashells in her collection. Each day, she finds 12 more seashells on beach. Katie can use fractions of days to find seashells. Write an inequality to determine the number of days, dd, it will take Katie to collect over 100 seashells

Answers

Answer:

12d+34>100  

Step-by-step explanation:

Let d be the number of days.

We have been that each day Katie finds 12 more seashells on beach, so after collecting shells for d days Katie will have 12d shells.  

We are also told that Katie already has 34 seashells in her collection, so total number of shells in Katie collection after d days will be: 12d+34

As Katie wants to collect over 100 seashells, so the total number of shells collected in d days will be greater than 100. We can represent this information in an inequality as:

12d+34>100

Therefore, the inequality 12d+34>100 can be used to find the number of days, d, it will take Katie to collect over 100 seashells.

Final answer:

In order to find out when Katie will have over 100 seashells, we use the equation 34 + 12d > 100. After simplifying, the inequality is d > 5.5. So, it will take Katie over 5.5 days to collect over 100 shells.

Explanation:

The question states that Katie already has 34 seashells and finds 12 more each day. This can be represented by the equation 34 + 12d, where d represents the number of days. In order to find out when Katie will have more than 100 seashells, we need to set this equation greater than 100 and solve for d.

So, 34 + 12d > 100. If we subtract 34 from both sides, we get 12d > 66. Then, divide both sides by 12 to solve for d. d > 66/12. The value of d in this case turns out to be approximately 5.5.

This means it will take Katie slightly over 5.5 days to collect over 100 seashells, given that she can use fractions of days to find seashells.

Learn more about Inequality here:

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Hello help me find out what is 42-22

Answers

20 :) hope that helped

14.88 to 12.32 find the ratio

Answers

14.88 to 12.32

14.88 : 12.32.         2 into 14.88 is 7.44,  2 into 12.32 is 6.16

7.44 : 6.16              2 into 7.44 is 3.72,  2 into 6.16 is 3.08

3.72 : 3.08              2 into 3.72 is 1.86,  2 into 3.08 is 1.54

1.86 : 1.54              2 into 1.86 is 0.93,  2 into 1.54 is 0.77

0.93 : 0.77

You can multiply both numbers by 100 to change it whole numbers.

0.93*100  : 0.77*100

93 : 77 

I need help with this please

Answers

The area of the first one would be the area of the rectangle minus the area of the circle, so 18*8 - (pi*3*3). That's equal to around 115.7257 inches squared.

The area of the second one would be the area of the triangle plus the area of the semicircle, so [(4*5)/2]*[(pi*2*2)/2]. That would be 20pi, or around 62.8319 ft squared

I'm not sure about the third one. Is it a trapezoid?

The voltage V required for a circuit is given by v=√(PR) , where P is the power in watts and R is the resistance in ohms.How many more volts are needed to light a 100-watt light bulb than a 75-watt light bulb if the resistance of both is 110 ohms? Round answer to the nearest tenth.

Answers

Answer:

✓11000-✓8250=~ 14 volts

Step-by-step explanation:

the answer is the difference by 100-watt light bulb to a 75 light bulb.

so, all you have to do is this:

v1-v2--------> ✓PR-✓P2R2

so you'll have ✓100.110-✓75.110= ✓11000-✓8250= 14

I hope it helps

Final answer:

By using the formula v=√PR, it is calculated that approximately 13.8 more volts are needed to light a 100-watt bulb than a 75-watt bulb, both having a resistance of 110 ohms.

Explanation:

To find out how many more volts are needed to light a 100-watt light bulb than a 75-watt light bulb, the amount of voltage required for each bulb is to be calculated using the given formula v= √PR, and then subtracted to find the difference.

For voltage required to light a 100-watt bulb:

v100= √(100W * 110 ohms) = 105.4 volts

For 75-watt bulb:

v75 = √(75W * 110 ohms) = 91.6 volts

The difference in voltage:

v100 - v75 = 105.4V - 91.6V = 13.8V

So, approximately 13.8 more volts are needed to light a 100-watt bulb than a 75-watt bulb, when rounded to the nearest tenth.

Learn more about Voltage calculation here:

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The mean distance from the surface of the earthto the surface of the moon is 376 000 km. What
is the distance in Scienu fic Notalion?

Answers

Answer: 4.76e5

Step-by-step explanation:
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