Suppose that the world's current oil reserves is R = 2200 billion barrels. If, on average, the total reserves
are decreasing by 15 billion barrels of oil each year, answer the following:
A.) Give a linear equation for the total remaining oil reserves, R, in billions of barrels, in terms off, the
number of years since now. (Be sure to use the correct variable.)
R=-15t+2200
B.) 15 years from now, the total oil reserves will be 1975
✓billions 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 146.60
x years from now.
(Round your answer to two decimal places.)
age instructor

Answers

Answer 1

Answer:

54637737636553363666


Related Questions

Copy and complete the pattern in the table

Answers

The pattern in the table should be completed as follows;

Number of                      1          3        9       27        81

students with pets

Total number                  3         9        27     81        243

of students

A ratio that compares the number of blue squares to the total number of squares is 3 : 4.

What is a proportional relationship?

In Mathematics and Geometry, a proportional relationship can be modeled or represented by the following mathematical equation:

y = kx

Where:

y represents the x-variable​.x represents the y-variable.k is the constant of proportionality.

Next, we would find the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/1 = 9/3

Constant of proportionality, k = 3.

y = 3x

81 = 3x

x = 27

x = 9/3

x = 3

y = 3(81)

y = 243

For the ratio of blue squares to total squares, we have:

18/24 = 3/4 = 3 : 4

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1. The Roth Family took out a $215,000 with a 15-year mortgage at an APR of 5.4%. The
monthly payment was $1,850. What will be their total interest charges after 15 years?

Answers

The total interest charges to the Roth Family, after 15 years, given the monthly payment would be $ 118, 000

How to find the total interest charges ?

First, find the total amount paid over the 15 years by the Roth Family to be :

= Number of years x Monthly payment x Number of months per year

= 15 x 1, 850 x 12

= $ 333, 000

The total interest charges that the Roth Family paid would be :

= Total amount paid after 15 years - Total amount borrowed as mortgage

= 333, 000 - 215, 000

= $ 118, 000

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least common denominator of -3/a and 1/4a^2

Answers

Answer:

-12a-1/4a2

Step-by-step explanation:

What number is equal to 13 ones and 62 hundredths

Answers

Answer:13.6

Step-by-step explanation:

Need Help ASAP. Thank you in advance :)

Answers

The value of x, considering the vertical angles in this problem, is given as follows:

x = 11.

What are vertical angles?

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles for this problem are given as follows:

(x + 7)º.(2x - 4)º.

As the vertical angles are congruent, the value of x is obtained as follows:

2x - 4 = x + 7

x = 11.

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Write and solve an equation to find the value of x.

Answers

The value of x for each item is given as follows:

28. x = 5.

29. x = 3.44.

How to obtain the value of x in each item?

For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:

16x = 10 x 8

16x = 80

x = 5.

For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:

10(x + 10) = 12(12 + 25)

10x + 100 = 444

10x = 344

x = 3.44.

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Calculate the unknown length, x, in the shape below.
If your answer is a decimal, give it to 1 d.p.
8
8 cm
area = 55 cm²
area=178.2 cm²
15 cm

Answers

The triangles are similar triangles. Then the value of 'x' will be 27 cm.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

From the above theorem, the equation is given as,

(x/15)² = 178.2 / 55

Simplify the equation, then we have

(x/15)² = 3.24

x/15 = 1.8

x = 27 cm

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Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
14√2
14
45
14√2
14√3
45
7√2 7√3

Answers

The legs of the big triangle are 14 units and the legs of the small triangle are 7√2 units

How to determine the lengths of the missing segments

From the question, we have the following parameters that can be used in our computation:

The right triangles

The right triangles are special triangles with acute angles of 45 degrees

This means that the relationship between the legs and the hypotenuse of the triangles is

Hypotenuse = Leg√2

Leg = Hypotenuse/√2

Using the above as a guide, we have the following:

Leg = 14√2/√2

Leg = 14

i.e. the legs of the big triangle are 14 units

Leg = 14/√2

Leg = 7√2

i.e. the legs of the small triangle are 7√2 units

See attachment for the triangles

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Answer:

Step-by-step explanation:

PLS HELP MARKING AS BRAINLIST

Answers

Answer:

108 sq ft

Step-by-step explanation:

The formulas are given in the bottom right.

For the triangles*, the base = 8 ft. The height = 6 feet.

Area = (bh)/2.

Area = (8*6)/2 = (48)/2 = 24 sq ft.

There are two of those identical triangles. 24+24 = 48.

(*Another way to look at this is to say that the base = 8+8 = 16. Area = (bh)/2 = (16*6)/2 = 96/2 = 48. It doesn't matter, mathematically. I can't tell if they have tried to show this as 2 triangles or one.)

For the bottom rectangle, area = length x width = 6*10 = 60 sq ft.


Add them up! 24 + 24 + 60 = 108 sq ft.

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Help me please! Thanks

Answers

The identification of the polygon that are given in the diagram above would be =

Polygon 1 = Isosceles trapezoid

polygon 2 = parallelogram

polygon 3 = Rectangle

polygon 4 = Rhombus

polygon 5 = Square

polygon 6 = trapezoid

What are the properties of the polynomials given above?

Isosceles trapezoid : This is the type that of polygon in which the the top and base are not equal in length, but they are parallel to each other.

Parallelogram : This is defined as the type of polygon that has two pairs of parallel sides.

Rectangle : This has two pairs of sides that are equal and opposite.

Rhombus: All the sides are equal in length with its opposite angles equal .

Square: All sides are equal in length but and all angles are equal to 90°.

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Solve the inequality for y.
-3>9-6y
Simplify your answer as much as possible.

Answers

Answer:

  y > 2

Step-by-step explanation:

You want the solution to the inequality ...

  -3 > 9 -6y

Solution

We can add 6y+3 to both sides. This gives ...

  6y > 12

Dividing by 6 tells us the solution for y:

  y > 2

__

Additional comment

We could have solved by subtracting 9 to get ...

  -12 > -6y

Then dividing by -6 reverses the inequality symbol:

  2 < y

We avoid the issue with negative number multiplication or division by making the y-term positive in our solution process.

<95141404393>

Question 5 Joy is a 52-year-old nurse who earns a salary of R286 500 per annum. She contributes 7% of her annua salary to a pension fund. She only has her 2 daughters listed as a dependents on her medical aid. Sh is concerned that the R4000 monthly income tax deduction is too much.​

Answers

Determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.

To assess whether the monthly income tax deduction of R4000 is too much for Joy, we need to calculate her annual income tax liability and compare it to the deduction.

First, let's calculate the amount Joy contributes to her pension fund annually:

Pension fund contribution = 7% of annual salary

Pension fund contribution = 7/100 * R286,500

Pension fund contribution = R20,055

Next, we need to determine Joy's taxable income by subtracting her pension fund contribution from her annual salary:

Taxable income = Annual salary - Pension fund contribution

Taxable income = R286,500 - R20,055

Taxable income = R266,445

Now, we can calculate the income tax liability based on the South African income tax brackets for the 2023 tax year. Please note that tax brackets are subject to change, so it's essential to verify with the latest tax regulations.

According to the current tax brackets, the tax rates for the 2023 tax year are as follows:

18% on the first R216,200 of taxable income

26% on the portion of taxable income between R216,201 and R337,800

31% on the portion of taxable income between R337,801 and R467,500

36% on the portion of taxable income between R467,501 and R613,600

39% on the portion of taxable income above R613,601

Using these tax rates, we can calculate the income tax liability:

Tax liability = (18% * amount within first bracket) + (26% * amount within second bracket) + (31% * amount within third bracket) + (36% * amount within fourth bracket) + (39% * amount within fifth bracket)

First, let's calculate the amounts within each tax bracket:

Amount within first bracket = min(Taxable income, R216,200)

Amount within second bracket = min(max(Taxable income - R216,200, 0), R337,800 - R216,201)

Amount within third bracket = min(max(Taxable income - R337,800, 0), R467,500 - R337,801)

Amount within fourth bracket = min(max(Taxable income - R467,500, 0), R613,600 - R467,501)

Amount within fifth bracket = max(Taxable income - R613,600, 0)

Now, let's substitute the values and calculate the income tax liability:

Tax liability = (18% * min(Taxable income, R216,200)) + (26% * min(max(Taxable income - R216,200, 0), R337,800 - R216,201)) + (31% * min(max(Taxable income - R337,800, 0), R467,500 - R337,801)) + (36% * min(max(Taxable income - R467,500, 0), R613,600 - R467,501)) + (39% * max(Taxable income - R613,600, 0))

By calculating this equation, you can determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.

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Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points. Which of the following equations can be used to determine how many points Patrick earned?

5 + 6 = 14 + y
6y + 5 = 14
5y + 6 = 14
5 + 6 + y = 14

Answers

The equation can be used to determine how many points Patrick earned is ;5 + 6 + y = 14.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.  4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Billy, Kip, and Patrick earned a combined 14 points during their team's game. Billy earned 5 points and Kip earned 6 points.

We can determine the direct answer by taking Billy and Kip's points and subtracting it from the total combined points.

That will give us 11, which means Patrick earned 3 points.

The equation we can use to represent this is ;5 + 6 + y = 14.

100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!

Answers

The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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A right circular cylinder has a surface area of 112 π. If the height of the cylinder is 10, find the diameter of the base.

Answers

If the height of the cylinder is 10, the diameter of the base of the cylinder is 8 units.

A right circular cylinder has two congruent circular bases and a curved surface area. To find the diameter of the base, we need to first find the radius of the base.

Let's begin by using the given information to write an equation. The surface area of a cylinder is given by the formula:

Surface Area = 2πr² + 2πrh

where r is the radius of the base and h is the height of the cylinder.

We are given that the surface area of the cylinder is 112π and the height is 10. Substituting these values, we get:

112π = 2πr² + 2πr(10)

Simplifying the equation by dividing both sides by 2π, we get:

56 = r² + 10r

Now we have a quadratic equation in terms of r. We can solve this equation by using factoring, completing the square, or the quadratic formula. Let's use factoring:

r² + 10r - 56 = 0

(r + 14)(r - 4) = 0

The solutions are r = -14 and r = 4. Since the radius cannot be negative, the radius of the base is 4.

The diameter of the base is twice the radius, so the diameter is 8.

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Factor completely, then place the answer in the proper location on the grid.

9x4 -225y8

Answers

The factored expressions of 9x⁴ - 225y⁸ is (3x² + 15y⁴)(3x² - 15y⁴)

How to factor the expressions completely

From the question, we have the following parameters that can be used in our computation:

9x⁴ - 225y⁸

²⁴

For the expression, we can apply the difference of two squares

Where

9x⁴ = (3x²)²

225y⁸ = (15y⁴)²

Using the above as a guide, we have the following:

9x⁴ - 225y⁸ = (3x²)² - (15y⁴)²

So, we have

9x⁴ - 225y⁸ = (3x² + 15y⁴)(3x² - 15y⁴)

Hence, the factored expressions is 9x⁴ - 225y⁸ = (3x² + 15y⁴)(3x² - 15y⁴)

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NEED THIS SOLVED ASAP!!!!!!!!!!!! I AM GIVING 15 POINTS

Arm Span (inches) / Height (inches)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41 40
46 50
58 61

Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word-processing document. (Recommend me this software so I can do this part).

Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word-processing document.

Answers

The scatter plot for the above data and it's line of best fit is attached accordingly. You may achieve this result using Microsoft Excel.

How to plot scatter plot on Microsoft Excel

Enter your data into two columns in an Excel worksheet. For example, in columns A and B, enter the years and corresponding life expectancies from your given data.

Select the data range by clicking and dragging over the cells containing the data.

Go to the "Insert" tab in the Excel ribbon.

In the "Charts" group, click on the "Scatter" chart type. Choose the scatter plot style that suits your preference (e.g., "Scatter with Straight Lines").

A scatter plot will be created on your worksheet.

Right-  click on any data point on the scatter plot and choose "Add Trendline" from the context menu.

In the  "Format Trendline" pane  that appears on the right side of the screen, select the "Linear"  trendline option.

Check the box for  "Display Equation on Chart" if you want to show the equation of the line of best fit on the  chart.

You can further customize the appearance of the scatter plot and the trendline using various chart formatting options in Excel.

Your scatter plot with the line of best fit is now plotted on Excel.

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A paint machine dispenses dye into paint cans to create different shades of paint. The
amount of dye dispensed into a can is known to have a normal distribution with a mean of 5
milliliters and a standard deviation of 0.4 milliliters. Find the dye amount that represents the
99th percentile of the distribution.
Select one:
O a. 4.1 milliliters
O b. 5.9 milliliters.
O c. 4.9 milliliters
O d. 5.1 milliliters

Answers

Answer:

  b. 5.9 mL

Step-by-step explanation:

You want the value that represents the 99th percentile of a normal distribution with a mean of 5 mL and a standard deviation of 0.4 mL.

Inverse normal

The inverse of the normal CDF function is used to find the X value for a given area. Here, we want X such that P(x < X) = 0.99 for μ = 5 and σ = 0.4.

The attached calculator output shows that is about X = 5.9305. Rounded to 1 decimal place, the volume is ...

  5.9 mL

<95141404393>

(2x^2-9x-5) \div(x-5)

Answers

Answer:2x+1

Step-by-step explanation:


1/5 ( x - 10 ) = 4/5

Answers

The value of x is 14

What are fractions?

Fractions are described as expression that shows the part of a whole number, a whole variable. a whole element.

The different types of fractions are listed as;

Improper fractionsProper fractionsMixed fractionsSimple fractionsComplex fractions

From the information given, we have that;

1/5 ( x - 10 ) = 4/5

This is written as;

(x -10)/5 = 4/5

cross multiply the values, we have;

5(x-10) = 20

expand the bracket

5x - 50 = 20

Collect like terms

5x = 70

Divide the values

x =14

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Currently it is estimated that 3 out of every 1000 Californians are infected with
coronavirus. The so-called rapid "antigen" test for coronavirus has a very low false
positive rate of just 0.05, but has a high false negative rate of 0.2. The so-called
PCR test is more reliable: it has an even lower false positive rate than the antigen
test, namely only 0.001, but even more importantly its false negative rate is much
lower at 0.01.
What is the probability that you have a coronavirus infection conditional on your
PCR test has coming back positive?

Answers

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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The exponential model A=433.4e^0.032t describes the​ population, A, of a country in​ millions, t years after 2003. Use the model to determine when the population of the country will be 796 million.

The population of the country will be 796 million in

​(Round to the nearest year as​ needed.)

Answers

The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

[tex]A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}[/tex]

Divide both sides by 433.4:

[tex]e^{(0.032t)} = 1.836[/tex]

Take the natural logarithm of both sides:

[tex]ln(e^{(0.032t)}) = ln(1.836)[/tex]

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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Lines y and z are parallel.
Parallel lines are cut by transversals s and t. The angles formed by lines s, t, and y, clockwise from top left, are blank, blank, (10 x + 5) degrees, blank, (4 x minus 7) degrees, blank; formed by s and z are 65 degrees, 1, blank, blank; formed by z and t are 2, blank, blank, blank.
What is the measure of angle 2?
6 degrees
11 degrees
28 degrees
37 degrees

Answers

The measure of Angle 2 is 17 degrees.

The measure of angle 2,  the relationships between the given angles formed by the parallel lines and transversals.

1. The angles formed by lines s, t, and y, clockwise from top left, are:

  - Blank

  - Blank

  - (10x + 5) degrees

  - Blank

  - (4x - 7) degrees

  - Blank

2. The angles formed by s and z are:

  - 65 degrees

  - 1

  - Blank

  - Blank

3. The angles formed by z and t are:

  - 2

  - Blank

  - Blank

  - Blank

From the given information, we can deduce the following:

- Angle 1 is congruent to the angle formed by z and t (corresponding angles).

- Angle (10x + 5) degrees is congruent to angle 65 degrees (alternate interior angles).

- Angle (4x - 7) degrees is congruent to angle 2 (alternate interior angles).

Therefore, we can set up the following equations:

65 = 10x + 5     (Equation 1)

2 = 4x - 7       (Equation 2)

Solving Equation 1:

65 - 5 = 10x

60 = 10x

x = 6

Substituting x = 6 into Equation 2:

2 = 4(6) - 7

2 = 24 - 7

2 = 17

Hence, the measure of angle 2 is 17 degrees.

Therefore, the correct answer is:Angle 2 = 17 degrees.

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On Saturday, a local hamburger shop sold a combined total of 234 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?

Answers

Answer:

78

Step-by-step explanation:

Let the number of hamburgers sold = x.

Then, the number of cheeseburgers sold = 2x.

Total number of sales: x + 2x = 3x

Total number of sales: 234

3x = 234

x = 78

Answer: 78

What is the quotient of the expression
O7a³ + ab + 3
O7a³ + ab - 3
O7a³ + 4ab+
+8
O7a³+4ab-8
28a b+4a²b²-12ab?
4ab

Answers

The quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).

How to find the quotient

By dividing each term of the numerator by 4ab:

(7a³ + ab + 3) / (7a³ + ab - 3) ÷ 4ab

= (7a³ / 4ab) + (ab / 4ab) + (3 / 4ab)

Simplifying each term individually:

= (7/4a²) + (1/4b) + (3/4ab)

Thus, the quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).

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Expand & simplify.

23p - 3( 2k + 14p ) + 5( 6k - p )

Answers

Answer:

23p -6k - 42p + 30k - 5p

23p - 42p - 5p + 30k - 6k

23p - 47p + 24k

-24p + 24k

24(- p + k)

24( k - p)

Answer:

The answer is

60p + 24k

Step-by-step explanation:

1: Expand

=23p - 6k + 42p + 30k - 5p

step2: collect like terms

=42p + 23p - 5p - 6k + 30k

step 3: add/subtract them to get your answer

=60p + 24k

your answer☝

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer:

A. All sides of a rhombus are congruent, so if DK = 8, then KL = 8.

B. The diagonals of a rhombus are perpendicular to each other, so if angle KAL = 2x - 8, then we have:

2x - 8 = 90

2x = 98, so x = 49.

C. All sides of a rhombus are congruent, so if DM = 5y + 2 and DK = 3y + 6, then we have:

5y + 2 = 3y + 6

2y = 4, so y = 2, and KL = 5(2) + 2 = 12.

For the matrix D shown below, determine the value of the element d12. If the element is not defined, click the undefined button. D = [-3 -8 6 -4] Answer:​

Answers

The calculated value of the element d₁₂ is -8

How to determine the value of the element d₁₂

From the question, we have the following parameters that can be used in our computation:

The matrix D given as

D = [-3 -8 6 -4]

The element d₁₂ represents the element located at the first row and the second column

In this case, the element located at the first row and the second column is -8

Using the above as a guide, we have the following:

d₁₂ = -8

Hence, the value of the element d₁₂ is -8

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Answers

Answer is B. This is because the ratio between 12 and 10 is 1.5. You find this from dividing 10 from 12. Therefore, BE is 1 and a half
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