chứng minh rằng S= 5+ 5^2 + 5^3 + ...+ 5^1991 + 5 ^1992 chia hết cho 6

In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.

Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.

Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.

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The full question is:

In the year 2000 the world population was

Answer:

D. 80%

Step-by-step explanation:

15-3 = 12

12/15 = 4/5 = .8

80%

Answer:

70°

Step-by-step explanation:

Because line segment OB and OC are both straight lines, then the measure of angle fromed by this two segments is the same in different locations.

Answer:

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Step-by-step explanation:

Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.

The surface area of the box (excluding the top) is given by:

2(x^2) + 4(x^2) = 6(x^2)

The surface area of the metal top is:

x^2

The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:

6(x^2) + x^2 = 7(x^2)

The cost of the wood for the box is:

5 cents per square inch * 6(x^2) = 30x^2 cents

The cost of the metal for the top is:

12 cents per square inch * x^2 = 12x^2 cents

The total cost of the box is:

30x^2 + 12x^2 = 42x^2 cents

We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:

42x^2 = 3000

Solving for x, we get:

x^2 = 71.429

x ≈ 8.445

Therefore, the maximum volume of the box is:

V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Answer:

A=167⁰, B=13⁰

Step-by-step explanation:

A=167⁰

B=13⁰

I HOPE IT HELPED YOU

Answer:

a° = 167°, b° = 13°

Step-by-step explanation:

since the angles in a triangle add to 180°, we can work out b°

90° (right angle) - 77° = 167°

180° - 167° = 13°

since the angle of a straight line is also 180°, a° would be 180° - 13° which is 167°.

Answer:

18+45x

Step-by-step explanation:

According to the question an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.

Two equations are considered to be comparable when their roots and solutions line up. To create an equivalent equation, the identical quantity, symbol, or expression has to be added to or removed from both of the equation's two sides. We can also create a similar equation by dividing or multiplying each component of an equation with a nonzero value.

given,

To determine which equation would give a bigger value, we can compare the expressions obtained by expanding Equation A and simplifying Equation B.

Expanding Equation A, we get:

A = (C + D) x (C + D) = C² + 2CD + D²

Simplifying Equation B, we get:

B = 2 x (C + D) = 2C + 2D

To compare the values of A and B, let's choose some values for C and D that are greater than zero. Let's choose C = 3 and D = 2.

Plugging these values into Equation A, we get:

A = 3² + 2(3)(2) + 2² = 9 + 12 + 4 = 25

Plugging these values into Equation B, we get:

B = 2(3 + 2) = 2(5) = 10

Since A is greater than B for the values of C = 3 and D = 2, we can conclude that Equation A gives a bigger value than Equation B for positive values of C and D.

Therefore, an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.

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8x + 3 > 2x - 15

8x - 2x > -15 - 3

6x > -18

x > -3

Answer:

x > -3

Step-by-step explanation:

8x + 3 > 2x - 15​

Add -3 and -2x on both sides.

8x - 2x > -15 - 3

6x > -18

Divide 6 into both sides.

x > -18/6

x > -3

Answer:

  $2192.60

Step-by-step explanation:

March 4 is day 63 of the year. So, the amount of tax that Kelly needs to refund to Mason is the tax for the remaining 365 -63 = 302 days of the year.

Kelly will owe Mason ...

  (302/365)($2650) = $2192.6027 ≈ $2192.60

If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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Given two types of geometries are analytic geometry and Euclidean geometry.

Consider analytic geometry.

Analytic geometry, also called coordinate geometry, mathematical subject in which algebraic symbolism and methods are used to represent and solve problems in geometry.

Consider Euclidean geometry.

Euclidean geometry is the study of flat spaces. It describes the relations ship between lines and planes without any numerical measurement.

Answer:

We prefer Analytical geometry because it gives the position of the points in cartesian coordinates. It helps to find the measure of length between points.

Analytical geometry is easier to extend beyond two dimensions.

Consider the triangle, we need to find the angle of the triangle.

According to Euclidean geometry, we can draw triangles by using axioms, but it is difficult to find angles.

According to Analytical geometry, we can find angles by using the coordinates values by using the distance formula and sine law.

Hence I approach Analytical geometry.

The limits of the function for this problem are given as follows:

In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.

At x = -2, we have that:

As the lateral limits are equal, lim x -> -2 f(x) = 3.

At x = 1, we have that:

As the lateral limits are different, the lim x -> 1 f(x) does not exist.

At x = 4, we have that:

As the lateral limits are equal, lim x -> 4 f(x) = -3.

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Answer:

\(m=-\frac{1}{2}\)

Step-by-step explanation:

\(\Delta y=-1,\,\Delta x=2\\\rightarrow \frac{\Delta y}{\Delta x}=\frac{-1}{2}=-\frac{1}{2}\)

\(\Delta\) represents change in both variables, so we calculate the slope this way.

Answer:

m=-1/2

Step-by-step explanation:

Use slope formula: \(m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}\)

The amount saved weekly is 2000/w and the duration to save $10000 is 5w

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

Emergency fund = $10,000

Rule = 50/30/20 rule

According to the 50/30/20 rule of budget, we have

Savings = 20

This means that

Savings = 20/100 * Emergency fund

Substitute the known values in the above equation, so, we have the following representation

Savings = 20/100 * 10000

Evaluate

Savings = 2000

The weekly amount is

Weekly savings = Savings/Number of weeks

So, we have

Weekly savings = 2000/w

We have

Weekly savings = 2000/w

To save $10,000, we have

Duration = 10000/(2000/w)

Evaluate

Duration = 5w

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Answer:

4.78

Step-by-step explanation:

4.78

 ×13

36.14

Answer: 5 and 6

Step-by-step explanation:

X^2 - 11 = (X-1)^2

X^2 - 11 = X^2-2X+1

X^2 - X^2 + 2X = 11+1

2X = 12

X = 6

The preceding number is 5

(6)(6)=36 and (5)(5)=25

36-25=11

The number required is 6

If the number is multiplied by itself, it becomes x²

If the result is 11 greater than the preceding number when it is multiplied by itself is expressed as:

x² - 11  = (x - 1)²

x² - 11 = x² - 2x + 1

2x = 11 + 1

2x = 12

x = 6

Hence the number required is 6

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Answer:

\(x^{1}\) or x

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\)

then

\(\frac{x^{\frac{3}{2} } }{x^{\frac{1}{2} } }\)

= \(x^{(\frac{3}{2}-\frac{1}{2}) }\)

= \(x^{1}\)

= x

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

x = 2 or x = 4

Step-by-step explanation:

The equation:

Has two solutions:

The values of x can be found by graphing the two functions (\(y = 2^{x}\) and \(y = x^{2}\)) and finding their points of intersection, or you can use numerical methods to solve the equation.

To check our work, we can simply insert 2 and 4 in as y.

For 2:

You can see that it is the same.

For 4:

They are also the same.

Therefore, x can equal either 2 or 4.

Answer:

x=6

Step-by-step explanation:

9-3=6 or 6+3=9

Answer:

13.25

Step-by-step explanation:

1. you have to subract the cost of the drink:

94.25-1.50=92.75

2.you have to divide to get the individual cost of pizzas by doing

92.75÷7=13.25

so therefore your answer is 13.25 per pizza

Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

Answer:

A

Step-by-step explanation:

3x^2 - 8x + 4 = 0

x= [-b +or- square root (b^2 - 4ac)] ÷ 2a

= [-(-8) +or- square root (-8)^2 - 4(3)(4)] ÷ 2(3)

= [8 +or- square root 16] ÷ 6

= 2 or 2/3

The values of x that satisfy the equation 3x² - 8x + 4 = 0 are x = 2/3 and x = 2.

The correct option is A.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

We can solve the equation 3x² - 8x + 4 = 0 using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a,

where a = 3, b = -8, and c = 4.

Substituting these values, we get:

x = (-(-8) ± √((-8)² - 4(3)(4))) / 2(3)

Simplifying:

x = (8 ± √(64 - 48)) / 6

x = (8 ± √(16)) / 6

x = (8 ± 4) / 6

So the solutions are:

x = 2/3 or x = 2

Therefore, x = 2/3 or x = 2.

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Answer:

3,168 cal= 2lbs of Ice Cream

Step-by-step explanation:

I need to fin how many calories are in two pounds of that ceratin ice cream.

594cal/6=99cal

99cal=1 oz

16oz x 2 = 32oz

99 x 32 = 3,168 cal

There is 3,168 cal in two pounds of ceratin ice cream.

The length of JK is 18.333.

Since MN is parallel to JK, the angles formed by JLN and MLK are equal. Therefore, we can use the Triangle Proportionality Theorem, which states that if a line parallel to one side of a triangle divides the other two sides proportionally, then the triangles are similar.

Using the Triangle Proportionality Theorem, we can set up the following proportion:

\($\frac{LK}{JL} = \frac{MN}{LN}$\)

Therefore,

\($\frac{7.2}{13.2} = \frac{10}{6}$\)

We can cross-multiply to solve for JK:

\($7.2 \cdot 6 = 13.2 \cdot 10$\\$43.2 = 132$\\$JK = \frac{132}{7.2} = 18.333$\)

Therefore, the length of JK is 18.333.

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The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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Answer:

24.012

Step-by-step explanation:

y=kx^2

54=81k

k=54/81

k=0.667

y=kx^2

y=0.667×36

y=24.012

its false ik this because im one of the boyzz

Answer:

r=ln3/10

Step-by-step explanation:

The daily rate is given by 3 to the power x divided by 10.

We have given that a sample of bacteria is growing at a continuously compounding rate.

The sample triples in 10 days.

The daily rate of the bacteria growth is. exponential growth is in the form

y = abˣ

where y, x are variables.

a is the initial value

Sample triples, in 10 days. therefore the value of b=3.

Therefore we get,

\(y=3a^{\frac{x}{10}\)

\(y=a3^{\frac{x}{10}\)

Therefore the daily rate is given by \(3^{\frac{x}{10}\).

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