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Using geometric sequence concepts, it is found that:

a) The rule is: [tex]P_n = 750000(0.5)^{n-1}[/tex].

b) An exponential relationship exists between the two variables.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

A geometric sequence represents an exponential relationship between the variables.

In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:

[tex]a_1 = 750000, q = 0.5[/tex].

Hence the nth term of the sequence is given by:

[tex]P_n = 750000(0.5)^{n-1}[/tex]

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Answer:

As you wish love, 2sqrt x 3sqrt8 = 12sqrt6

Step-by-step explanation:

2sqrt3x3sqrt8

Simplify,

2sqrt3 x 3 x 2sqrt2

Evalutate,

12sqrt6

Answer:

Corresponding

Step-by-step explanation:

So, we know that 1&2, 3&4, 5&6, and 7&8 all equal 180 degrees in their pairs. 7&3 are corresponding angles that are less than 90 degrees on their own. We don't know the degrees of each angle, so we can't say their exact angle.

(I know I didn't give the second answer, if you elaborate, maybe I can understand what it's asking better)

Hope this helped!

Answer:

-> Corresponding

-> Are equal

Explanation:

        First, we will find where angles 3 and 7 are at. See attached. Since they are in corresponding places on both lines, these angles are corresponding angles.

        We know that corresponding angles have the same measurement, so their measures will be equal, or in other words, congruent.

Answer:

she bought 7 packs of paper

Step-by-step explanation:

12.74/p = 7

Answer:

∠ FLW = 112°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ FLW is an exterior angle of the triangle , then

∠ FLW = x + 32 , that is

2x - 48 = x + 32 ( subtract x from both sides )

x - 48 = 32 ( add 32 to both sides )

x = 80

Then

∠ FLW = 2x - 48 = 2(80) - 48 = 160 - 48 = 112°

Answer:

C

Step-by-step explanation:

given a triangle with 2 sides and the angle between them given, then the area (A) is calculated as

A = [tex]\frac{1}{2}[/tex] bc sinA

the 2 sides are b = 4, c = 6 and ∠ A = 35° , then

A = [tex]\frac{1}{2}[/tex] × 4 × 6 × sin35° = 12 × sin35° ≈ 6.9 m² ( to the nearest tenth )

Answer:

If the angles are 9 degrees 6 degrees and 12 degrees it is acute

Step-by-step explanation:

if the roots of the polynomial function are -9 and 7 - i, then the other factor of the polynomial function is x - (7  + i)

The roots of the polynomial function are given as:

-9 and 7 - i

The root is 7 - i is a complex number.

This means that its conjugate must also be a root of the factor.

The conjugate of 7 - i is 7 + i

So, we have:

x = 7 + i

Equate to 0

x - (7  + i) = 0

Hence, the other factor of the function is x - (7  + i)

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Answer:

A on edge 23

Step-by-step explanation:

trust me bro

Answer:

BC = 25 in

AN = 12 in

BN = 16 in

NC = 9 in

Formulas:

Pythagorean Theorem

[tex]c^2 = a^2 + b^2[/tex]

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Area of triangle

[tex]A = \frac{1}{2}bh[/tex]

A ... area of triangle

b ... base (one of the sides of the triangle)

h ... height perpendicular to base

Step-by-step explanation:

Given:

A = 90°

AB = 20 in

AC = 15 in

See attached picture.

1) BC

To find BC we can use Pythagorean theorem, since ABC is a right triangle. We have the lengths of two legs (AB, AC) and we are finding the hypotenuse.

[tex]c^2 = a^2 + b^2\\\text{BC}^2 = \text{AB}^2 + \text{AC}^2\\\text{BC}^2 = 20^2 + 15^2\\\text{BC}^2 = 625\\\sqrt{\text{BC}^2} = \sqrt{625}\\\text{BC} = 25 \text{ in}[/tex]

2) AN

AN is the height corresponding to base BC. To find it we can use formula for the area of the triangle. But first let's find the area of the triangle.

Notice how AB is perpendicular to AC. We can use AB as base and AC as height.

[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{AB} \times \text{AC}\\\\A = \frac{1}{2} \times 20 \times 15\\\\A = 150 \text{ in}^2[/tex]

Now that we have area, we can use BC as base and AN as height and solve for AN.

[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{BC} \times \text{AN}\\\\150 = \frac{1}{2} \times 25 \times \text{AN}\\\\\ 300 = 25 \times \text{AN}\\\\12 = \text{AN}\\\\\text{AN} = 12 \text{ in}[/tex]

3) BN

Let's use Pythagorean theorem in right triangle ABN. Hypotenuse is AB.

[tex]c^2 = a^2 + b^2\\\text{AB}^2 = \text{AN}^2 + \text{BN}^2\\20^2 = 12^2 + \text{BN}^2\\400 = 144 + \text{BN}^2\\256 = \text{BN}^2\\\sqrt{256} = \sqrt{\text{BN}^2}\\16 \text{ in} = \text{BN}[/tex]

4) NC

We know the lengths of BC an BN, so we can just subtract.

[tex]\text{NC} = \text{BC} - \text{BN}\\\text{NC} = 25 - 16\\\text{NC} = 9 \text{ in}[/tex]

Answer:

25

Step-by-step explanation:

(x+5)(x+5) = x^2 + 10x + 25

Answer:

25

Step-by-step explanation:

The number that goes in the blank is 25.

The constant must have two factors that multiply to equal the constant and add to equal the coefficient.

The number of ways Laura will wear a pair of mittens, a scarf, and a jacket will be 36.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

Laura will wear a pair of mittens, a scarf, and a jacket as she leaves the house.

She has two pairs of mittens to choose from, six scarves chosen from, and three jackets to choose from.

Then the number of ways will be

Number of ways = ²C₁ x ⁶C₁ x ³C₁

Number of ways = 2 x 6 x 3

Number of ways = 36

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Answer:

B

Step-by-step explanation:

Do the math

5x1 is 5

4x1 is 4

35÷7 is 5

28÷7 is 4

Hope this helps

Answer:

The second table.

Step-by-step explanation:

4 sweaters for every 5 T-shirts is a ratio of 4/5, which is equal to 0.8. That means that every ratio in the table should also be equal to 0.8 since they are all different versions of 4/5. In the second table, 4/5 = 0.8, 8/10 = 0.8, 28/35 = 0.8, and 32/40 = 0.8, so it is the second table.

An inscribed angle (like angle RTS) is half its intercepted arc.

Angle RTS = 51

Then, we just have a triangle to look at. Remember that the interior angles of a triangle add up to 180.

67 + 51 + x = 180

118 + x = 180

x = 62

Answer: angle RST = 62 degrees

Hope this helps!

We will see that:

h(g(g(x)) = -78 + 24x

Which means that the statement is false.

Here we have that:

g(x) = 13 - 2x

h(x) = 6x

Now we want to find the composition of functions:

h(g(g(x))

First, let's find g(g(x)) = 13 - 2*g(x) = 13 - 2*(13 - 2x) = 13 - 26 + 4x

g(g(x)) = -13 + 4x

Now let's evaluate h(x) in that:

h(g(g(x)) = 6*g(g(x)) = 6*(-13 + 4x) = -78 + 24x

This is not equal to what we have in the question, so we conclude that the statement is false.

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The function that would best model the progression of points in the given scatter plot is: D. an exponential function.

If a function is an exponential function, as the x-value increases, the value of y approaches infinity, or as x-value decreases, the value of y approaches 0.

The graph given is a typical example of how an exponential function graph behaves.

Therefore, the best model for the progression of points is: D. an exponential function.

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The formula would you use to calculate the floor space of Firm 3's structure is πr²h.

It should be noted that the formula that can be used on this scenario will be:

= πr²h

where,

h = 60

r = 70/2 = 35

The volume will be:

= πr²h

= 3.14 × 35² × 60

= 230790 feet ³

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Answer:

about 4 or 8

Step-by-step explanation:

Answer: 4 schools

Step-by-step explanation:

The breadth of your books are perpendicular to the length because they meet at right angles.

The shape of a book is a rectangle. A rectangle has four enclosure. This means they are formed by 4 lines.

The opposite sides are equal in length.

The sides of the book has a pair of breadth and a pair of length.

The breadth and length are straight lines.

When this straight line meets, it forms a right angle(90 degrees). This means the breadth and the length are perpendicular to each other.

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flip over the line, then slide up

Answer:

[tex]volume \: = 1130.4 {m}^{3} [/tex]

Step-by-step explanation:

The formula to find the volume of a cylinder is:

[tex]v = \pi {r}^{2} h \\ basically \:it \:is\: the\: area \:of \:the \:circular \\ \:base\: \times\: \:height \:of \:the \:cylinder[/tex]

Note that the radius is half the diameter (12), therefore the radius is 6*

According to the diagram we know that:

[tex]\pi = 3.14 \: \: \: r = 6 \: \: \: h = 10 \\ \\v = \pi {r}^{2} h\\ \\ v = (3.14)( {6}^{2} )(10) \\ \\ v = (3.14)(360) \\ \\ v = 1130.4 {m}^{3} [/tex]

Answer:

"=" and "<"

Step-by-step explanation:

|9| = |-9|

|9| and |-9| indicates the absolute value of 9 so we use equality sign

7.5 = 7.50

7.5 is equal to 7.50 adding zeros to the right side of an expression won't change its quantity

For example:

I say I have 7.5 dollars and my friend says he has 7 dollars and 50 cent

We have same amount of money.

-3.31 is smaller than -3.13 because it's further from point zero in number line so we use < for this expressions.

Step-by-step explanation:

1. find P of semicircle

perimeter of a semicircle = pi×r+d

=3.14×5+10

=25.7

2.find P of rectangle

P=10×4=40cm

3. add P of semicircle and P of rectangle

25.7+40=65.7cm

Answer:

I hope this helps................

Answer:

terminal point is at (0, -1) and sin 0 = -1

Step-by-step explanation:

In a unit circle the radius of the circle is 1 so

- we know the points where the circle intersects the x-axis and y-axis as a (x , y) coordinates.

(1, 0) where we start on the positive x-axis and where angle is 0°

(0, 1) where we go counterclockwise and where angle is 90°

(-1, 0) where we go continue counterclockwise and where angle is 180°

(0, -1) where we stop in our problem because the angle is 270°

-we also know that x= cos O and y= sin O so the coordinates (x, y) are really

(cos O, sinO)

Given:

        0 = 270°

    sin 0 = sin 270°

sin 270°  =  -1

The terminal point is at (0, -1) and sin 0 = -1

The number of minutes that she practiced in a day will be 175 minutes per day.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Yaritza practices the piano for 875 minutes in 5 weeks.

The number of minutes that she practiced in a day will be given as,

Rate = 875 / 5

Rate = 175 minutes per day

The number of minutes that she practiced in a day will be 175 minutes per day.

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Answer:

1/8 or 12.5 percent

Step-by-step explanation:

So You first draw the red marble you have a 25 percent chance of that or 1/4 then you draw a green so just add 4 to the denominator!

Hope this helps!

Answer:

Step-by-step explanation:

Conversion

A % can always be changed into a decimal by dividing by one hundred. In this case

decimal = 36.2/100 = 0.262 \\

Answer: 0.262

Answer:

181/500

Step-by-step explanation:

Answer:

Item #1

[tex]-\frac{27}{8}[/tex] fraction form

[tex]- 3.375[/tex] decimal form

[tex]-3\frac{3}{8}[/tex] mixed number

Item #2

$7.98 (rounded to nearest cent)

According to the standard sound intensity model, the intensity of a 70-dB sound is equal to an amount of 1 × 10⁻⁵ watts per square meter.

The sound intensity (L), in decibels, is the intensity of a sound relative to a reference value, whose formula is described below:

L = 10 · ㏒ (I/I')

Where:

If we know that L = 70 dB and I' = 1 × 10⁻¹² W/m², then the sound intensity is:

70 = 10 · ㏒ (I/10⁻¹²)

10⁷ = l/10⁻¹²

I = 10⁻⁵ W/m²

According to the standard sound intensity model, the intensity of a 70-dB sound is equal to an amount of 1 × 10⁻⁵ watts per square meter.

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