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Vladimir79 [104]
3 years ago
13

What is the value of the fourth term in a geometric sequence for which a1=30 and r=1/2

Mathematics
1 answer:
lisov135 [29]3 years ago
8 0

Answer:

a(4) = 15/4

Step-by-step explanation:

The general formula for a geometric series with common ratio r and first term a(1) is

a(n) = a(1)*r^(n - 1)

and so, if a(1) = 30 and r = 1/2, we have

a(n) = 30*(1/2)^(n - 1)

and the fourth term is then:

a(4) = 30*(1/2)^(4 - 1) = 30/8 = 15/4

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Oxford currently generates 45,000 tons of garbage per year. but the city is launching some recycling initiatives to bring that n
barxatty [35]

Answer:

-Exponential Decay

-Decay factor is (1-0.05)

Step-by-step explanation:

-Given that the number decreases by a defined rate each year from the initial size by 5%,

-This is an exponential decay function of the form:

y=Ae^{-rt}

Where:

y is the quantity/size after time t

A is the initial size

r is the rate of decay

-Our function can the be written as

y=45000e^{-0.05t}

Hence, the decay rate/factor is 0.05

#Alternatively

The exponential decay can be of the form:

y=ab^x

Where:

y is the size at time x, a is the initial size, x is time and b is the decay factor.

b is of the form b=(1-r),\ \  r=decay\  rate

y=ab^x\\\\y=45000(1-0.05)^x

Hence, the decay factor is (1-0.05)

8 0
3 years ago
Using only whole numbers, how can you draw three rectangles with perimeter of 12 units
Assoli18 [71]
Perimeter means the sides add up to 12. 
Rectangles have two pairs of equal sides. 

2(one side) + 2(another side) = 12
2 (one side + another side) = 12 
(one side + another side) = 6 

To draw a rectangle with a perimeter of 12 units, the two adjacent sides must add up to 6. 
1 + 5
2 + 4 
3 + 3

3 0
3 years ago
Find the area of the shaded region.
Anvisha [2.4K]

Answer:

73.4 cm^2

Step-by-step explanation:

The equation is :

πr^2

Substitute the radius in:

π(5)^2

Solve:

Area of full circle = 25π

(Note : leave this answer in terms of 'pi' so it is easier to handle

Next, find the area of the sector

The equation for this is:

(angle/360) x πr^2

Substitute the values in:

(80/360) x π(5)^2

Solve :

Area of sector = (50/9)π

Now, find the area of the triangle:

1/2 absinC

Substitute the values in:

1/2(5)(5) x sin(80) = 12.31009691

Subtract this answer from the area of the sector

Answer = 5.14319607

Subtract this from the area of the whole circle

Answer = 73.39662073

To the nearest tenth, that would be 73.4 cm^2

Mark brainliest pls

3 0
3 years ago
What does x equal in the equation 2x + y - 3z equals -12
lidiya [134]
2x+y-3z=12

2x=4z-y

x=2z-y/2
8 0
3 years ago
How many minutes are in 25% of one day?
Elden [556K]

Hello!

To understand this question we first need to find some common measurements to make this math easier.

One day is equal to 24 hours.

One hour is equal 60 minutes.

One day in hours would be equal to 24 · 60, or 1440 minutes.

1440 is equal to 100% of our day.

To find 50% we can then divide that value in half to get 720 minutes.

Half of that value, or 25%, is equal to 360 minutes.


4 0
3 years ago
Read 2 more answers
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