Mathematics College

Suppose that the world's current oil reserves is

R=1970 billion barrels. If, on average, the total reserves is decreasing by 24 billion barrels of oil each year, answer the following:

A.) Give a linear equation for the total remaining oil reserves, R, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.)

R=

B.) 12 years from now, the total oil reserves will bebillions of barrels.

C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately___years from now.

(Round your answer to two decimal places.)

Answers

Answer 1

From the given situation, we have that:

A) The linear equation is R(t) = 1970 - 24t.

B) 12 years from now, the total oil reserves will be 1682 billions of barrels.

C) Approximately 82.08 years from now.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, the parameters are given as follows:

b = 1970, m = -24.

Hence the linear function is:

R(t) = 1970 - 24t.

For item b, the amount is of R(12), hence:

R(12) = 1970 - 24(12) = 1682.

12 years from now, the total oil reserves will be 1682 billions of barrels.

For item c, we have to solve for t when R(t) = 0, hence:

1970 - 24t = 0

24t = 1970

t = 1970/24

t = 82.08.

Approximately 82.08 years from now.

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Related Questions

4.Add 13.24 + 35.67 +4.321

please explain in number form and as little as possible but still explaining

Answers

Answer:

Step-by-step explanation:

it should be 53.231 i think

Divide. 22 divided 8956 Enter your answer in the boxes as a mixed number in simplest form.

Answers

I'm going to assume you meant 89/56 and not 8965 due to the fact you are asking for a mixed number answer.

[tex]=\frac{22}{1}\div \frac{89}{56}[/tex]
[tex]=\frac{22}{1}\times \frac{56}{89}[/tex] <- Apply the fraction rule [tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]\frac{22\times \:56}{1\times \:89}[/tex] <- Apply the fraction rule [tex]\frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{1232}{1\times \:89}[/tex]
[tex]=\frac{1232}{89}[/tex]
[tex]13 \frac{75}{89}[/tex] <- Convert to mixed number and there is your final answer
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Solve the system of equations and choose the correct ordered pair. y=-2x+4 y=x-2

Answers

Answer:

(-6, -8)

Step-by-step explanation:

We have the following system of equations:
[tex]y = 2x+4[/tex] (1)

and

[tex]y=x-2[/tex] (2)

Set (1) = (2) since the LHS is y in both

We get

[tex]2x + 4 = x - 2[/tex]

Subtract x from both sides:

[tex]2x + 4 - x = x - 2 -x[/tex]

[tex]x + 4 = -2[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = -2 -4[/tex]

[tex]x = -6[/tex]

Substitute for x in Equation (2) to get
[tex]y = -6 - 2 = -8[/tex]

So the solution is (-6, -8)

Tyshawn took a taxi from his house to the airport. The taxi company charged a pick-up fee of $2.50 plus $3.50 per mile. The total fare was $79.50, not including the tip. Which equation could be used to determine m, the number of miles in the taxi ride?

Answers

79.50 - 2.50= 77.00 77.00 divided by 3.50 is 22. There was 22 total miles in the taxi ride

The required equation that would be used to determine m, the number of miles in the taxi ride is 2.50 + 3.50m = 79.50.

Given that,
Tyshawn took a taxi from his house to the airport. The taxi company charged a pick-up fee of $2.50 plus $3.50 per mile. The total fare was $79.50.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the number of miles be m,
Cost of the taxi of m miles = 3.50m
according to the question,
2.50 + 3.50m = 79.50

Thus, the required equation that would be used to determine m, the number of miles in the taxi ride is 2.50 + 3.50m = 79.50.

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It is 29.6°C at sea level. The environmental lapse rate between sea level and 1500 meters is 5.5 °C/1000m.
The environmental lapse rate between 1500 meters and 4000 meters is 12.1°C/1000m. The normal lapse rate
exists above 4000 meters. What will the temperature be at 6000 meters? Calculate your answer to one
decimal point.

Answers

The temperature at 6000 meters would be -21.9°C.

The lapse Rate refers to the rate of decline in air temperature with relation to increase in altitude.

Here, the lapse Rate is given as follows-

for 0-1500 meters: 5.5 °C/1000m

for 1500-4000 meters: 12.1°C/1000m.

and above 4000 meters: normal lapse rate

The Normal lapse Rate is 6.5°C per 1000 meters.

Now,

surface temperature at sea level = 29.6°C

the decline in temperature up to 1500m would be-

5.5°C/1000×1500 = 8.25°C

So the temperature at 1500 meter is 29.6 - 8.25 = 21.35°C

Further, the decline in temperature up to 4000m would be-

12.1°C/1000×2500= 30.25°C

So Temperature at 4000 meters is 21.35 - 30.25 = -8.9°C

Now, above 4000 meters, decline in temperature would be-

6.5°C/1000×2000= 13°C

So temperature at 6000 meters would be

-8.9°C - 13°C = -21.9°C

Thus, the temperature at 6000 meters would be -21.9°C

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Use inductive reasoning to find the next two terms in the sequence. What are the next two terms?

3/4, 2/3, 5/8, 3/5 …

Answers

by using inductive reasoning, we get the next 2 terms as 7 / 12 and 4 / 7.

We are given a sequence:

3 / 4, 2 / 3, 5 / 8, 3 / 5

We need to find the next two terms by using the inductive reasoning.

Now, we can also write this sequence as:

3 / 4, 4 / 6, 5 / 8, 6 / 10

Now, we can see that, in each term, the numerator is increasing by 1 and the denominator is increasing by 2 units.

So, the 5th term will be:

Numerator = 6+ 1 = 7

Denominator = 10 + 2 = 12

5th term = 7 / 12

And the 6th term will be:

Numerator = 7 + 1 = 8

Denominator = 12 + 2 = 14

6th term = 8 / 14 = 4 / 7

Therefore, by using inductive reasoning, we get the next 2 terms as 7 / 12 and 4 / 7.

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Why do you think it is important to follow the order of operations? What will happen if you ignore it?

Answers

Answer: It is important to follow the order of operations because you want to make sure you get an accurate result and it ensures that you can understand and approach a mathematical problem easily. It's also important too because it sets a standard of how to solve equation so without it, equations could have multiple answers and that won't be right.

Laine reads 200 pages in 240 minutes.
If Laine reads 25 pages at the same rate, how long will it take her?

Answers

Laine will take 30 minutes to read 25 pages.

Given Laine reads 200 pages in 240 minutes.

We need to find the time taken to read 25 pages, if Laine reads at the same rate.

First, let us find out the time taken to read one page.

240 minutes are taken to read 200 pages

This implies that the time taken to read 1 page = 240/200 minutes

This implies that the time taken to read 1 page = 6/5 minutes

Therefore, the time taken for 25 pages = 25 ×(6/5) minutes

⇒ The time taken for 25 pages = 30 minutes

Hence, Laine will read 25 pages in 30 minutes, if she reads 200 pages in 240 minutes.

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8
LO
5
15
4
1
In the figure shown above, all the corners form right angles. What is the area of the figure in squ
O 33 square units
O 66 square units
O 70 square units
O 120 square units

Answers

The area of the given figure is 70 square units, that is, option 3.

The area of a rectangle = length × breadth

Here, we need to find the area of the shaded region.

To do this, we will subtract the area of the smaller rectangle from the larger one.

The area of the larger rectangle = 8 × 15

= 120 square units

Now, the we have one side of the smaller rectangle which is 5, the other side will be (15 - 4 - 1) = 10 units.

The area of the smaller rectangle = 10 × 5

= 50 square units

Thus, the area of the shaded region = 120 - 50

= 70 square units

Hence, the area of the figure is 70 square units.

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Your question was incomplete. Please find the missing figure below.

The lines below are perpendicular. If the slope of the green line is 2/3, what is the slope of the red line? m = A. 2/3B. – 2/3C. –3/2 D. 3/2

Answers

Answer: c

Step-by-step explanation:

C is correct

Consider the following polygon. Determine the measure of both angles A and B. A= (16x+7) B= (13x+2)

please help me T - T

Answers

The measure of both angles A and B

Angle A= 16(7.8)+5= 129.8

Angle B =13(7.8)+4= 105.4

What is Hexagon?

A hexagon can be defined as a closed two-dimensional polygon with six sides.

Hexagon has 6 vertices and 6 angles also.

Hexa means six and gonia means angles.

According to the given statement;

Hexagons have six sides, and so does this figure.

You can calculate the degrees in a shape by doing (n-2)180. With n being the number of sides(6)

There are 720 degrees in a hexagon.

1) Now write the following equation:

(16x+7)+(13x+2)+95+170+155+88=720

2) Combine alike terms:

26x+517=720

3) Subtract 538 from both sides:

26x=203

4) Divide both sides by 26

x=7.8

5) Plug in 7.8 as X in the original two equations for A and B

A- 16(7.8)+5= 129.8

B- 13(7.8)+4= 105.4

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Look at the imagine. Help asap.

Answers

2x-1 < x+3

5x-1 > 6-2x

x-5 < 0

solve the inequality for x.

x < 4

x > 1

X < 5

find the intersection

X ∑ {1,4}

Alternative form: {x I 1 < x < 4}

∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern. For example, the sum of the first 4 squared integers, 12+22+32+42, follows a simple pattern: each term is of the form i2, and we add up values from i=1 to i=4.

05601
4. Some chemistry students estimated that a small block of copper would weigh 500 grams. The
actual mass of the copper was 428 grams. What is the percent of error to the nearest hundredth
percent?
The percent of error to the nearest hundredth percent is
%.

Answers

The percent of error to the nearest hundredth percent is 16.82 % when the estimated mass is 500 g and the actual mass is 428 g.

We are given that:

Some students estimated that a small block of Copper will have the mass = 500 g

Estimated mass = 500 g

But now, the actual mass was found out and it came = 428 g

Actual mass = 428 g

The error in estimation was:

Error = 500 g - 428 g

Error = 72 g

Percentage of error = 72 g / 428 g × 100

Percentage of error = 7200 g / 428 g %

Percentage of error = 16.82 %

Therefore, we get that the percent of error to the nearest hundredth percent is 16.82 %.

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For the rational function f(x)=2−x4x+6, find the point on the graph at the function value f(x)=1.

Answers

The point on the graph at the function value f(x)=1 is x = -4/5

How to find the point on the graph at the function value f(x)=1?

The equation of the function is given as:

f(x) = 2 - x4x + 6

Rewrite the rational function, properly as follows:

f(x) = 2 - x/4x + 6

When f(x) = 1, we have:

2 - x/4x + 6 = 1

Cross multiply

2 - x = 4x + 6

Collect the like terms

4x + x = 2 - 6

Evaluate the like terms

5x = -4

Divide by 5

x = -4/5

Hence, the point on the graph at the function value f(x)=1 is x = -4/5

Answers

Answer:

-5/40

Step-by-step explanation:

(1/40)(4) + (10/40)(2) - (29/40)(1)

Name the property shown 0+8=8

Answers

Answer:

Step-by-step explanation:

commutative

5. identify

45 is added to the data set 9, 1, 9,7, 2

Answers

The new data set is the {54,46,54,52,47}.

According to the statement

We have to find that the value of the data set.

So, For this purpose, we know that the

A data set is a collection of related, discrete items of related data that may be accessed individually or in combination or managed as a whole entity.

From the given information:

45 is added to the data set 9, 1, 9,7, 2

It means the data set is the

{ 9, 1, 9,7, 2}

Then the number 45 is added into the each elements of the data.

Then

9+45 = 54

1+45 = 46

9+45 = 54

7+45 = 52

2+45 = 47.

The new data set is the {54,46,54,52,47}

So, The new data set is the {54,46,54,52,47}.

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how to solve tangent

Answers

Step-by-step explanation:

tan x = 1 / (cot x)

Tangent Formula Using Sin and Cos

We know that sin x = (opposite) / (hypotenuse), cos x = (adjacent) / (hypotenuse), and tan x = (opposite) / (adjacent). Now we will divide sin x by cos x.

(sin x) / (cos x) = [ (opposite) / (hypotenuse) ] / [ (adjacent) / (hypotenuse) ] = (opposite) / (adjacent) = tan x

Thus, the tangent formula in terms of sine and cosine is,

tan x = (sin x) / (cos x)

The trapezoids are similar. What is the value of x? 50 75 35 7 10

Answers

Answer:

The correct value of x is 15.

Step-by-step explanation:

Each side of the larger trapezoid is 5 times each corresponding side of the smaller trapezoid.

A recipe calls for 4 boxes of rice to serve 13 people.

If you want to serve 39 people, what should you do?

CLEAR CHECK

Answers

Answer:

Use 12 boxes of rice

Step-by-step explanation:

4/13 becomes x/39

to get from 13 to 39 you multiply 13 by 3 so you do the same to 4

3*4 is 12

Solve for x:
A) 27
C) 39
E) 30
79⁰
(2x+1)
B) 23
D) 35

Answers

Answer:

C 39

Step-by-step explanation:

took the test

which one does not belong 4/6, 8/14, 12/18, 6/9

ratios and rates

Answers

Answer:

8/14

Step-by-step explanation:

All of the other ratios can be simplified to 2/3

James wants to have earned $7,592 amount of interest in 16 years. Currently he finds that his
annual interest rate is 9.04%. Calculate how much money James needs to invest as his principal in
order to achieve this goal..
I=p.r.t
Solve for p
r = 8.63% or .0863
t = 24 years
I = $8613
Round answers to the nearest hundredth (two decimal places). The answer will not have a dollar
sign, and be rounded to the nearest cent.
I

Answers

a) James have to invest 5,248 dollar and 89 cent to earn $7,592 amount of interest in 16 years .

b) Principal amount of money , which is to be invested is 4158 dollar and 46 cent .

This is a problem from simple interest system. We have to use the given formula, I = p.r.t to solve this problem.

a) James wants to have earned $7,592 amount of interest in 16 years. So, here the time period is 16 years and the interest rate is 9.04% and we have to find the principal amount.

I = p. 16. ( 9.04% )

Amount of interest = $ 7592

Time period = 16 years

rate of interest = 9.04 %

7592 = p . 16 . ( 904/10000 )

p = 75920000/ 16 . 904

or , p = $5,248.89 ≈ $5249

James have to invest $5,248.89 to earn $7,592 amount of interest in 16 years .

b) We have to use the given formula to find the value of p or the principal amount of money .

Rate of interest = 8.63% or .0863

time period = 24 years

Interest = $8613

We can write ,

p = I / r.t

p = 8613 / 24 . ( .0863 ) = $ 4,158.458 = $ 4,158.46

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Round to the nearest ten
thousand.
123,045,067

Answers

Answer: 123050000

Step-by-step explanation:

don't take this down again :)

What is 961 divided by 48???

Answers

Answer:

20.02

Step-by-step explanation:

maths calc

What is the domain and range of this function

Answers

I can’t see the problem. You have to upload it

What is the least common multiple of 70, 60, and 50?

60

180

210

2,100

210,000

Answers

The least common multiple of 70,60,and 50 is 2,100 :))

Which fraction is greater, 35/109 or 36/104?? To explain your answer, use our definition of fraction along with reasoning other than finding common denominators, common numerators, cross-multiplying, or converting to decimals.

Answers

The greater proportion is 36/104 since 34.62% is greater than 32.11%.

What is percentage?

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) indicates the hundredth part; consequently, 100 percent represents the complete amount and 200 percent specifies times the supplied quantity.

According to the given data:

Given fractions are = 35/109 and 36/104

finding the greater fraction we express them as a percentages:

So the first fraction will be:

(35/109 ) * 100

= 3500/109

= 32.11%

For the second equation:

(36/104) * 100

= 3600/104

= 34.62%

The greater proportion is 36/104 since 34.62% is greater than 32.11%.

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please help ill mark you brainly thanks

Answers

Answer:

the answer is c(4)

Step-by-step explanation:

30/2=15

30/3=10

30/4= not an interger(7.5)

30/5=6

30/6=5

this is the reason why c is not an interger because all other is a whole number while c is a decimal

Which is the best description of range?
The repeated values in the input set.
The -values on a graph.
The connection between sets of values.
The input values of a function.

Answers

The best description of range is (b) The y-values on a graph.

How to determine the best description of range?

A graph is characterized by the following concepts:

DomainRange

The domain of a function is the set of input values of the graph

On the other hand, the range of a function is the set of output values of the graph

This in other word means that the range is the y-values on a graph.

Hence, the best description of range is (b) The y-values on a graph.