The ElA predicts that the United States has 216 billion barrels of crude oil reserves left. If 4 billion barrels are extracted each year, and extraction grows by 0.5% per year, how long will the reserves last?

The function y = 18(0.914)^m is having exponential decay. The decay percent of this function is 8.6%

Consider the function:

[tex]y = a(1\pm r)^m[/tex]

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %

If there is negative sign, then there is exponential decay happening by r fraction or 100r %

For this case, the exponential growth/decay function given is:

[tex]y = 18(0.914)^m[/tex]

That means, there is multiplication of (0.914) for each growth/decay.

We can rewrite 0.914 as:

0.914 = 1 - 0.086

This shows decay as multiplication with 0 < quantity < 1 makes the number less in magnitude.

A quantity times (1 - 0.086) = that quantity - that quantity times 0.086

and we can write 0.086 = 8.6/100 = 8.6%

Thus, we're decreasing 8.6% each time from a quantity when we multiply that quantity with (1-0.086)

Thus, there is exponential(exponential because of the presence of variable 'm' as exponent in the given function) decay of 8.6%.

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Answer:

1 mm Hg per year

Explanation:

Here equation : y = x + 95

Comparing with slope intercept formula: y = mx + b

                                    where m is slope and b is y-intercept

Slope determines the increase per year.

Equation given

Comapre to slope intercept form y=mx+b

Rate of change=Slope=1mm HG /year

Using the given discrete probability distribution, it is found that the probability that a randomly selected student has a grade higher than a C is given by:

P(X > 2).

From the table, it is given by:

Grades A and B are greater than C, hence the probability of getting a grade higher than C is given by:

P(X > C) = P(X = A) + P(X = B) = P(X = 3) + P(X = 4) = P(X > 2).

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Answer:

3/20

Step-by-step explanation:

3y - 4

hope it helps...!!!

Answer:

210.8 (mean for Luis), 241.5 (mean for Darcy)

Step-by-step explanation:

Luis 178 + 213 + 198 + 245 + 236 + 198 + 221 + 253 + 189 + 177 = 2108

2108/10 = 210.8 (mean for Luis)

Darcy 231 + 210 + 245 + 259 + 286 + 245 + 231 + 244 + 236 + 228 = 2415

2415/10 = 241.5 (mean for Darcy)

Answer:

To find the median number of words in Darcy’s essays, first arrange the values in the data set in ascending order:

210, 228, 231, 231, 236, 244, 245, 245, 259, 286.

Because the number of values in the data set is an even number (10), the median is the mean of the two middle values, the fifth and sixth values, in the data set. The fifth and sixth values are 236 and 244, respectively. So,

median

.

The median number of words in Darcy's essays is 240.

Step-by-step explanation:

Answer:

b=-30;c=41

Step-by-step explanation:

I don't really know how to explain it... Vertex form, so factor out 5, divide by two, that has to be three. so .1b=3, b=30... opposite of the square of 3 times 5 add c=-4, so -45+c=-4, c=41. Just learn vertex form, and complete the perfect square. Good luck!

Answer:

x= 29

Step-by-step explanation:

use Pythagoras because it has a right angle and 2 sides length is given.

when the hypoteneus(side opposite the right angle) is the value you are finding out you use the equation : x²+y²=hypoteneus² (Pythagoras)

then you sub in the values you are given

(21)² + (20)² = hypoteneus²

them take the square root (²) to the opposite side to find the hypoteneus

square root (441+400) = hypoteneus

now you can put into a calculator and you get the value

hypoteneus =29 (for reference to hypoteneus is the same as X-the value you are looking for)

therefore, x=29

for extra reference, say you want to work out a side that is not the hypotenues you use the formula ,

(side u looking for)² = (hypotenues)² - (other side given)²

Answer:

x = 29

Step-by-step explanation:

To find x, we can use the Pythagorean theorem.

a^2 + b^2 = c^2

21^2 + 20^2 = x^2

441 + 400 = x^2

841 = x^2

[tex]\sqrt{841}[/tex] = [tex]\sqrt{x^2}[/tex]

29 = x

Answer:Im pretty sure the slope is 2.

Step-by-step explanation:

Answer:

20 inmates should leave

Step-by-step explanation:

A camp having 80 inmates, has food sufficient for 70 days.

total=80*70

How many inmates should leave after 10 days so that the

remaining food lasts another 80 days?

the food served for 10 days to 80 inmates

10*80

let x be inmates leave after 10 days food last for 80 days

(80-x)*80

Total=food served for 10 days+x inmates left after 10 days

80*70=10*80+(80-x)*80

70=10+80-x

x=90-70

x=20

Answer:

5x - 9

Step-by-step explanation:

2x -(-3x + 9)                

2x + 3x - 9)                  DISTRIBUTE -1

5x - 9                           COMBINE LIKE TERMS

Answer:

6 and -1

Step-by-step explanation:

If you take the equation and set it to be 0, you can find the input values that make it 0.

[tex]x^2-5x-6=0[/tex]

Since this is a quadratic, equation you can use the quadratic formula with the values:

The quadratic formula is:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

If you plug the values for a, b, and c, you get:

x = 6 and x = -1

Answer:

*select all that apply*

All of these are true

Step-by-step explanation:

Answer choice A:

We-Haul: c = 0.45m + 20

You-Haul: c = 1m

--> TRUE

Answer Choice B:

the y-intercept is the upfront charge bc the charge for "per mile" is attached to "mx" and the "b" (y-intercept) is the upfront charge

--> TRUE

Answer choice C:

We-Haul -

c = 0.45(38) + 20 = $37.10

You-Haul -

c = 1m = $38.00

--> TRUE

answer choice D:

We-Haul -

c = 0.45(35.36) + 20 = $35.91

You-Haul -

c = 1m = $35.36

Since the two costs are very close to being the same, I think this is a true statement also

--> TRUE

Answer choice E:

You-Haul's rate is 1 mph whereas We-Haul's rate is 0.45mph. You-Haul's rate is 0.55 larger than We-Haul's

--> TRUE

Hope this helps :)

The difference, to the nearest gram, of the masses of the rectangular

prisms  is 1393.2 grams.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

Joe has a rectangular prism made of aluminum and a rectangular prism made of lead.

Each rectangular prism has a height of 6 cm, length of 9 cm, and width of 3 cm.

The volume of a rectangular prism made of aluminum  = (length x width x height)

= [tex]6 \times 9\times 3\\\\162[/tex]

The volume of a rectangular prism made of lead= (length x width x height)

= 162 cubic cm

We know that mass = density x volume

The density of aluminum is approximately 2.70.

mass = 2.70 x 162

          = 437.4 grams

The density of lead is approximately 11.3 cm3

mass = 11.3 x 162

          = 1830.6 grams

The difference, to the nearest gram, of the masses of the rectangular

prisms  1830.6 - 437.4  = 1393.2 grams

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Answer:

the answer is (3,4)

Step-by-step explanation:

because if you check wich quadrant it is in and you check the number you can see which one it is. x,y that is how it goes so 3,4 should be correct if you line them up.

Answer:

40

Step-by-step explanation:

16+24=40

40-16=24

Answer:

a = 40

Step-by-step explanation:

Add 16 on both sides

a - 16 + 16 = 24 + 16

a = 24 +16 = 40

a = 40

Verification

LHS = a - 16  a = 40

40 - 16 = 24

RHS = 24

Both LHS and RHS are same so, our answer is correct.

Answer:

3 tons

Step-by-step explanation:

1 ton = 2000 pounds

3 x 2000= 6,000 pounds

6000 > 5999

Answer:

42.5 ft squared

Step-by-step explanation:

hope this helped brah

Answer:

D

Step-by-step explanation:

The scale factor would be x1/2

12÷2=6 16÷2=8 24÷2=12

Answer:

D. don't know how? but the answer is in no.D

Step-by-step explanation:

divided 2

Answer:

Step-by-step explanation:

Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the x-axis and time on the y-axis. The slope will be 2.2 at every point along her bike ride.

Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5

Answer:

-18^6

Step-by-step explanation:

(-18^2)^3   = -18^(2*3)  =  -18^6

Answer:

60

Step-by-step explanation:

TOTAL SURFACE AREA = AREA OF SQUARE+2×(AREA OF TRIANGLE)

=(6×6)+2×(1/2×6×4)

=36+24=60 square inches

I hope it helped you

Answer:

The area of the full figure is 60 square inches.

Step-by-step explanation:

There are 4 triangles and one square in this figure. We can start by figuring out the area of the middle square, which would be [tex]6*6=36[/tex] because we know the sides are all 6 inches.

Next, we can look at the triangles and see that their hypotenuses (the longest sides) are all the same length, that being 5 inches. This means that we only need to find the length of the third side and then multiply the area of one triangle by 4 to get the area of all the triangles.

The pythagorean theorem states that in any right triangle, [tex]a^2 +b^2=c^2[/tex], with [tex]c^2[/tex] being the length of the hypotenuse. Since we know the length of the hypotenuse is 5 and one of the legs of the triangle is 4, we can insert this into the equation: [tex]a^2+4^2=5^2[/tex], which when simplified all the way gives us that [tex]a=3[/tex].

Since a right triangle is half of a rectangle, the easiest way to find the area of the triangle is to multiply the measures of the two legs together and then divide by two: [tex](3*4)/2=6[/tex]. Therefore, we know that each triangle in the picture has an area of 6.

Finally, you need to add all of the areas together to find the area of the full figure: [tex]36+6+6+6+6=60 in^2[/tex]

The area of the full figure is 60 square inches.

Hope this helps! :)

Answer:

arc = 7.5π units

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

the angle subtended at the centre by the arc is 360° - 90° = 270° , then

arc = 2π × 5 × [tex]\frac{270}{360}[/tex]

     = 10π × [tex]\frac{3}{4}[/tex]

     = [tex]\frac{30\pi }{4}[/tex]

     = 7.5π

Answer:

Letting f represent the value of the flower and b represent the value of the butterfly, we have f = 20 and b = -53.

Step-by-step explanation:

7f + 2b = 34 ------> 7f + 2b = 34

3f + b = 7-----------> 6f + 2b = 14

-----------------

f = 20, b = -53

Answer:

Option D, [tex]x =[/tex] ± [tex]4/13[/tex]

Step-by-step explanation:

Step 1:  Add 16 to both sides

[tex]169x^2 - 16 = 0[/tex]

[tex]169x^2 - 16 + 16= 0 + 16[/tex]

[tex]169x^2 = 16[/tex]

Step 2:  Divide 169 from both sides

[tex]\frac{169x^2}{169} = \frac{16}{169}[/tex]

[tex]x^2 = 0.09467[/tex]

Step 3:  Square root both sides

[tex]\sqrt{x^2} = \sqrt{0.09467}[/tex]

[tex]x =[/tex] ± [tex]0.30769[/tex]

[tex]x =[/tex] ± [tex]4/13[/tex]

Answer:  Option D, [tex]x =[/tex] ± [tex]4/13[/tex]

Answer:

your answer is 280

Step-by-step explanation:

Because you already know what X and Y are all you will have to do is plug them in

10 (10 + 2(9))

2*9= 18

10 (10 + 18)

10+18= 28

10(28)

280