the third term of an arithmetic sequence is 7 and the twelfth term in 106. what is the one hundredth term of the sequence

Answer:

  y > 2

Step-by-step explanation:

You want the solution to the inequality ...

  -3 > 9 -6y

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.

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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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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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Answer:13.6

Step-by-step explanation:

Answer: x= 10

Step-by-step explanation:

2x+4=24

2x=24-4

2x=20

x=10

Answer:

Step-by-step explanation:

2x+4=4

subtract 4 from both sides

2x=0

divide by 2 on both sides

x=0

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

x = 11.

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:

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

2x - 4 = x + 7

x = 11.

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a. The number of possible access codes. The number of different codes available is 343.

b. The probability of randomly selecting the correct access code on the first try is 0.003

a. To find the number of possible access codes. The number of different codes available is:

= 7* 7* 7

= 343

(b) The probability of randomly selecting the correct access code is nnothingwill be:

P = 1/343

= 0.003

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The access code for a safe consists of three digits. Each digit can be any number from 0 through 6 , and each digit can be repeated. Complete parts (a) through (c). a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing . (b) What is the probability of randomly selecting the correct access code on the first try?

Cos = 20/27 = 0.7407

so

angle that stream makes with the road = 42.2

answer

42 (Round only your final answer to the nearest degree)

Answer:

Love helping people so here's the answer :)

Step-by-step explanation:

A square pyramid has 5 faces: 1 square base and 4 triangular faces. The surface area of the pyramid is the sum of the areas of all its faces.

The area of the square base is 1 * 1 = 1 square inch.

The area of each triangular face is (1/2) * base * height = (1/2) * 1 * 2 = 1 square inch.

Since there are 4 triangular faces, the total area of the triangular faces is 4 * 1 = 4 square inches.

Therefore, the surface area of the pyramid is 1 + 4 = 5 square inches.

The total height of the flyer at any time after deploying the wingsuit would be;

y = -3x + 200 + (-4.9t² + 420),

Now, Based on the given information, we can use the two functions to determine the height of the wingsuit flyer at a particular time.

During the freefall, the height of the flyer can be calculated using the function

y = -4.9x² + 420.

Let's say the flyer falls freely for t seconds before deploying the wingsuit.

Therefore, the height at the moment of deploying the wingsuit would be,

y = -4.9t² + 420.

After deploying the wingsuit, the height of the flyer is given by the function

y = -3x + 200.

We can combine these two functions to get the total height of the flyer at any given time after deploying the wingsuit.

So, the total height of the flyer at any time after deploying the wingsuit would be;

y = -3x + 200 + (-4.9t² + 420),

where x is the time after deploying the wingsuit and t is the time of freefall before deploying the wingsuit.

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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.

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

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:

Answer:

B.   {1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}

Step-by-step explanation:

The intersection of two sets is a set containing the elements that are present in both sets.

{1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}

The contrapositive of the original conditional statement is B. If a number does not have a negative cube root, then the number is not negative.

In logic, the contrapositive of a conditional statement is a logically equivalent statement that switches the positions of the hypothesis and the conclusion, while also negating both.

The contrapositive maintains the logical validity of the original statement. If the original statement is true, then the contrapositive is also true, and vice versa.  "If a number is negative, then it has a negative cube root." The contrapositive of this statement would be: "If a number does not have a negative cube root, then the number is not negative."

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Answer:

Step-by-step explanation:

3: ANSWER = 864

4; ANSWER = I DONT KNOW TNH YOU JUST HAVE TO MULTIPLY AMD THEN SUBRACT BOTH

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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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

Answer:

id ont givea

efijhaoieuvbhzoiubhoewivbawzoufhbealivjhbr

Step-by-step explanation:

idsifui piuh vSeth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

k bro i gochu

the answer is 84 man,

do good on ur hw

also can i get a pizza

Answer:

3/8 = (3 + AD)/20

8(3 + AD) = 60

24 + 8AD = 60

8AD = 36

A = 4 1/2

B is the correct answer.

Answer:2x+1

Step-by-step explanation:

The fraction represented by the point between 1 and 2 on the number line is 5/3.

If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.

The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.

Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.

                              2

Thus, the point A corresponds to the mixed fraction 1 -

                                                                                     3

 2                             5

1 -  = (1*3)+2 / 3 =  -

 3                             3

So, the fraction represented by the point between 1 and 2 on the number line is 5/3.

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The calculated value of the unit rate of the situation is (c) $12 per hour

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

$60.00 in 5 hours

This means that

Time = 5 hours

Total costs = $60.00

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

Unit rate = Total costs / time

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

Unit rate = 60.00/5

Evaluate

Unit rate = 12

Hence, the unit rate of the situation is (c) $12 per hour

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Answer:

A. Because it would simplify this equation.

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

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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Answer: 2x2 + 1000 x 1000 = 1000004

Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also

Answer:

1000004

Step-by-step explanation:

First we do can separate it into the parentheses: (2*2) + (1000*1000)

= 4 + 1000000

= 1000004

Answer:

36

Step-by-step explanation:

48/8 = 6. 6*6 = 36.