Antonio is working with a new geometric series generated by the equation A(n) =
12(1.5)n-1
S. Help Antonio find the sum of the first 15 terms of the series without just adding them all up. Show your work
below.
6. Help Antonio find the sum of the 16th through the 30th terms of the series. Show your work below.

([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).

To fix \(G\) as a group and set \([g,h]:=g h g^{-1} h^{-1}\), and then set
\[[G,G] := \left\{\left[g_{1}, h_{1}\right] \cdots\left[g_{s}, h_{s}\right]: g_{1}, \ldots, g_{s}, h_{1}, \ldots, h_{s} \in G\right\}\), we can start by noticing that this is a subset of the Cartesian product of \(G\) with itself, and since \(G\) is a group, this subset must also be a group. Therefore, \([G,G]\) is a group, which is the subgroup of \(G \times G\) generated by the set of all commutators \([g,h]\).

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Answer:

Karla Saved for 15 months.

Step-by-step explanation:

Tom saved 60 each month if he saved for 8 months then he made $480. Karla saved 32 each month, each of them saved the same amount, 480 because 480 + 480 = 960. divide 480 by 32 and you'll get 15. therefore Karla saved her money for 15 months.

Hope this helps :)

Answer:

Step-by-step explanation:

9/10

Yes, Laura will have enough money to buy the computer before her brother's birthday.

Cost is the total amount of money, time, and resources required to produce or acquire a product, service, or outcome. It involves the initial outlay of money, time, and resources necessary to produce or acquire something. In addition, it involves any ongoing expenses required to maintain or improve that something. Cost can be a one-time purchase, a long-term investment, or a recurring expense.

At the time of her purchase, Laura had $427 which is $59 short of the $486 computer. She earns $42 each week from babysitting, so if she saves every penny she earns for the next 7 weeks she will have enough money to buy the computer. She will have $294 after the first week of saving, $336 after the second week, $378 after the third week, $420 after the fourth week, $462 after the fifth week, $504 after the sixth week, and $546 after the seventh week. The $546 is more than enough money to purchase the computer before her brother's birthday.

Additionally, the computer's price drops $14 each day, so if Laura waits an extra week to purchase the computer, it will cost her even less. She will have $588 after the eighth week and would only need to spend $400 to purchase the computer.

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The following solutions with regard to resolving or simplifying the radii of the circular pond are given below.

Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters

Part C: The radius of Pond B is 10√2 meters.

Part D: the radius of Pond B is greater than the radius of Pond A.

Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:

164 = 2 × 2 × 41

So, we can write:

√164 = √(2 × 2 × 41) = 2√41

Using this, we can rewrite Step 1 as:

5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:

5 × 10 + 2√41 meters = 50 + 2√41 meters

So, the radius of Pond A is 50 + 2√41 meters.

Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:

25√200/5 meters = 5√200 meters

We can simplify this further by finding the prime factorization of 200:

200 = 2 × 2 × 2 × 5 × 5

So, we can write:

√200 = √(2 × 2 × 2 × 5 × 5)

= 2 × 5√2

Using this, we can rewrite the expression for the radius of Pond B as:

5 × 2 × √2 meters

= 10√2 meters

Thus, the radius of Pond B is 10√2 meters.

Part D: We can compare the radii of the ponds using the original expressions by writing:

√164 < 25√200/5

Simplifying both sides:

2√41 < 10√2

Dividing both sides by 2:

√41 < 5√2

Squaring both sides (since both sides are positive):

41 < 25 × 2

41 < 50

So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.

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Full Question:

Two circular ponds at a botanical garden have the following radii:

Pond A: Sqrt(164) meters;

Pond B: 25Sqrt(200)/5 meters:

Todd simplified the radius of pond A this way:

5sqrt(164)

Step 1: 5sqrt(100) + Sqrt(164) meters

Step 2: 5(10 + 8)

Step 3: 5(18)

Step 4: 90

One of the steps above is incorrect.

Part A: Rewrite the steps so that it is correct

Part B: Using the corrected step from Part A, simplify the radius of Pond A.

Part C: Simplify the expression for the radius of pond B.

Part D: Write an inequality to compare the radii of the ponds, using the original expressions.

∠T has a cosine ratio of 15/17.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

PQR and STU are the similar triangles.

With the help of cosine function we can find the measure of T.

Cosine = Adjacent side/ hypotenuse

The adjacent side is thirty and hypotenuse is thirty four.

Plug in these values in the above formula.

∠T=30/34

Divide numerator and denominator by 2

∠T=15/17

Hence, ∠T has a cosine ratio of 15/17.

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Answer: 8 times per minute

Step-by-step explanation: 50 (1-84%) = 8

Answer:

tgv7cutc

Step-by-step explanation:

txr. thh5d tdhg6643gchctc

Answer:

3 people

Step-by-step explanation:

Add 25.25 and 8.75 together which is $34 so then you $34 by 3 and get 102 so then you add tax. So only three people would be able to go.

Answer:A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Answer:

sin 45°= x/110 ft

sin45° * 110 = x

Step-by-step explanation:

try it i dont have calculator here

The value of x is 9 and the sides are 28,8

what is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always is 180 degrees.

From the given figure ,

we can say that the two triangles are similar ,

21 / 3x+1  =  6 / x-1

21 ( x-1) = 6 (3x+1)

21x - 21 = 18x + 6

21x - 18x = 21 + 6

3x = 27

x = 9

3x + 1 = 3* 9 + 1 = 28

x-1 = 9-1 = 8

Therefore, The value of x is 9 and the sides are 28,8

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The solutions to the equation z^2 = -361 are:

z = ±19i and z = ±19i*(-1)^k, k = 0 or 1.

To find all n complex solutions of the equation x^n = k, where k is a complex number, we can use the polar form of complex numbers. If we write k in polar form as k = re^(iθ), where r = |k| is the modulus of k and θ = arg(k) is the argument of k, then we can write x in polar form as x = ρe^(iφ), where ρ = |x| is the modulus of x and φ = arg(x) is the argument of x.

Substituting these polar forms into the equation x^n = k, we get:

(ρe^(iφ))^n = re^(iθ)

Taking the modulus of both sides, we get:

|ρ^n| = |r|

Since r is a complex number, its modulus is a positive real number, so we can write r = Re^(i0) in polar form, where R = |r|.

Substituting this into the equation above, we get:

|ρ^n| = R

Taking the argument of both sides, we get:

nφ = 0 + 2πk

where k is an integer. Solving for φ, we get:

φ = (2π*k) / n

Substituting this expression for φ back into the polar form of x, we get:

x = ρe^(i(2π*k)/n)

where ρ is a positive real number. This gives us n complex solutions for x, which are:

x = ρe^(i(2π*k)/n), k = 0, 1, 2, ..., n-1.

Now let's apply this method to solve the equation z^2 = -361.

Writing -361 in polar form, we have:

-361 = 361e^(iπ)

Taking the square root of both sides, we get:

z = ±sqrt(361)e^(iπ/2 + iπk)

where k = 0 or 1. Simplifying, we get:

z = ±19e^(i(π/2 + π*k))

So the solutions to the equation z^2 = -361 are:

z = ±19i and z = ±19i*(-1)^k, k = 0 or 1.

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To find the total distance Henri hiked, we can multiply the distance he hiked each day (7/10 mile) by the number of days he hiked (9 days):

Total distance = (7/10) mile/day * 9 days

We can simplify this expression by multiplying the fractions and then multiplying by 9:

Total distance = (7/10) * 9 mile

Total distance = 63/10 mile

Therefore, the equation equivalent to the total amount hiked is:

Total distance = 63/10 mile

or, if we prefer to write the distance in decimal form:

Total distance = 6.3 miles

The probability of at most one price hike in one year is 0 + 0 = 0.

No price hikes in a randomly selected one and a half year:

The probability of no price hikes in one year is 0, since the average is 4. Therefore, the probability of no price hikes in one and a half years is also 0.

Four price hikes in 2 years:

The average number of price hikes in one year is 4, so the average number of price hikes in 2 years is 8. The probability of exactly 4 price hikes in 2 years is therefore 0, since it is less than the average.

At most one price hike in one year:

The probability of at most one price hike in one year is the sum of the probabilities of 0 and 1 price hikes. The probability of 0 price hikes is 0, as mentioned before. The probability of 1 price hike is also 0, since it is less than the average of 4. Therefore, the probability of at most one price hike in one year is 0 + 0 = 0.

Overall, the probability of no price hikes in a randomly selected one and a half year, four price hikes in 2 years, and at most one price hike in one year are all 0, since they are all less than the average number of price hikes.

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The radius of the circle is approximately 5.861 cm, and the area of the circle is approximately 107.76 cm².

A regular polygon is one that has an equal number of sides and angles. Each vertex of a regular polygon is located on a shared circle known as the circumscribed circle or circumcircle. A circumscribed circle or circumcircle of the polygon, on the other hand, is any circle that goes through every vertex of the polygon. The circumradius of the polygon is the circumference of the circle. The circumradius is the distance from the centre to any vertex of a regular polygon with n sides, and the circumcircle's centre coincides with the polygon's centre.

Given that, the hexagon is regular, angle AOB is 60 degrees.

The side AB is given as 8cm.

Using trigonometric functions we have:

h = r * cos(30 degrees) = (√(3)/2) * r.

Now using the Pythagoras theorem:

OB² = AB² - h².

Substituting the value of h:

OB² = 8² - (√(3)/2)² * r².

OB² = 64 - (3/4) * r².

OB = √(64 - (3/4) * r²).

Here, OB is equal to the radius of the circle.

r = √(64 - (3/4) * r²) = 5.861 cm.

The area of the circle, we can use the formula:

Area = π * r²

Hence, the radius of the circle is approximately 5.861 cm, and the area of the circle is approximately 107.76 cm².

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The model is a good fit because the data are randomly distributed above and below the x-axis.

In Mathematics, a residual value can be defined as a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).

Generally speaking, the independent variable (fitted values) are generally plotted on the x-axis of a residual plot (scatter plot) while the residual value is plotted on y-axis of a residual plot (scatter plot).

Additionally, a line of best fit simply refers to a trend line on a residual plot (scatter plot) and the given model represents a good fit because the data set are randomly distributed below and above the x-axis.

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The measures of the angles in the triangle are A = 6.17°,B = 11.50°, C = 162.33° and that's the solution to the triangle using the Law of Sines.

To solve the triangle using the Law of Sines, we can use the following formula:

(a/sin A) = (b/sin B) = (c/sin C)

First, let's convert the given angle B from degrees and minutes to decimal form:

B = 11° 30' = 11.5°

Next, we can plug in the given values into the formula and solve for the unknowns:

(3.7/sin A) = (6.5/sin 11.5°)

Cross-multiplying and rearranging gives us:

sin A = (3.7 * sin 11.5°) / 6.5

Using a calculator, we can find the value of sin A:

sin A = 0.1076

Now, we can use the inverse sine function to find the measure of angle A:

A = sin^-1(0.1076) = 6.17°

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C:

C = 180° - A - B = 180° - 6.17° - 11.5° = 162.33°

So, the measures of the angles in the triangle are:

A = 6.17°
B = 11.5°
C = 162.33°

Round your answers to two decimal places, we have:

A = 6.17°
B = 11.50°
C = 162.33°

And that's the solution to the triangle using the Law of Sines.

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The answers are explained in the solution below.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given are some operation based on multiplication,

1) 26 x 3/4 = 78/4

2) 9 x 7/10 = 63/10

3) 2/5 x 32 = 64/5

4) 1/8 x 400 = 400/8 = 50

5) 15 x 4/5 = 60/5 = 12

6) 3/11 x 66 = 198/66 = 18

7) 45 x 3/8 = 135/8

8) 3/10 x 12 = 36/10 = 18/5

9) 55 x 2/5 = 110/5 = 22

10) 5/6 x 40 = 200/6 = 100/3

11) 7/9 x 54 = 378/54 = 7

12) 600 x 5/12 = 3000/12

= 250

13) 2/3 x 21 = 42/3 = 14

14) 500 x 3/5 = 1500/5 = 300

15) 72 x 5/8 = 360/8 = 45

16) 2/9 x 35 = 70/9

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The measure of arc AE is 77 degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to find the measure of the arc AE.

The measure of BC is 38 degrees.

The measure of DE is 103 degrees.

The value of p is 77 degrees which is measure of CD.

The arc CD is opposite to the AE

Which makes the measure of AE is vertical to P.

They are equal

Hence, the measure of arc AE is 77 degrees.

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The area οf the cοmpοsite shape is 541 square meters.

Cοmpοsite shapes refer tο 2D shapes that are made up οf twο οr mοre simple shapes. These simple shapes can be cοmbined tο fοrm a mοre cοmplex shape.

Tο find the area οf this cοmpοsite shape, we need tο divide it intο smaller shapes and add up their areas. Let's divide it intο twο rectangles and a triangle:

First rectangle:

Length = 18 m

Width = 11 m

Area = length x width = 18 m x 11 m = 198 m²

Secοnd rectangle

Length = 14 m

Width = 20 m

Area = length x width = 14 m x 20 m = 280 m²

Triangle:

Base = 14 m

Height = 9 m (we can find this by subtracting the height οf the tοp rectangle frοm the height οf the entire shape: 20 m - 11 m = 9 m)

Area = (base x height) / 2 = (14 m x 9 m) / 2 = 63 m²

Nοw we add up the areas οf the three shapes tο get the tοtal area οf the cοmpοsite shape:

Tοtal area = 198 m² + 280 m² + 63 m² = 541 m²

Hence, the area οf the cοmpοsite shape is 541 square meters.

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Answer:

6

Step-by-step explanation:

24h/6g= 4 hours per gaurd

Using Pythagoras Theorem, The height of the screen is approximately 27.18 inches.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

We can use the Pythagorean theorem to solve this problem. Let's call the height of the screen "h". Then, according to the Pythagorean theorem, we have:

[tex]h^2 + 32^2 = 42^2[/tex]

Simplifying this equation, we get:

[tex]h^2 + 1024 = 1764[/tex]

Subtracting 1024 from both sides, we get:

[tex]h^2 = 740[/tex]

Taking the square root of both sides, we get:

[tex]h = \sqrt{(740)}[/tex]

Using a calculator to approximate the square root, we get:

h ≈ 27.18 inches

Hence, the height of the screen is approximately 27.18 inches.

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The value of x in the chord is 4.8 units

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

The circle

Next, we calculate the radius using each chord using the Pythagoras theorem

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

r² = x² + (37/2)²

r² = 13² + (28/2)²

By substitution, we have

x² + (37/2)² = 13² + (28/2)²

So, we have

x² = -(37/2)² + 13² + (28/2)²

Evaluate

x² = 22.75

Take the square root

x = 4.8

Hence, the value of x is 4.8 units

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Shante rides at an average speed of 9.33 miles per hour.

We need to determine how many miles Shante rode per hour. We can set up an equation to solve this problem:

3 hours x M (miles per hour) = 29 miles

7 hours x M = 65 miles

We can then solve this equation to find out the number of miles she rode per hour:

3M = 29

M = 29/3

M = 9.67 miles per hour.

Therefore, Shante rode at an average rate of 9.67 miles per hour.

Now, we can find her average speed by dividing the total distance she has traveled by the total time she has traveled:

Therefore, Shante rides at an average speed of 9.33 miles per hour.

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Answer: 11.1 ft

Step-by-step explanation:

Answer:

Hey I would love to help you but can you just add the photo of the graph? That would help a lot!

Step-by-step explanation:

The probability of Heather getting exactly 12 out of 15 correct can be found using the binomial probability formula:

P(X = 12) = (15 choose 12) * (0.87)^12 * (0.13)^3
= (15! / (12! * 3!)) * (0.87)^12 * (0.13)^3
= 455 * 0.087 * 0.0022
= 0.0828

Therefore, the probability of Heather getting exactly 12 out of 15 correct is 0.0828, or 8.28%.

To round this answer to two decimal places, we can use the following formula:

0.0828 * 100 = 8.28%

So the final answer is 8.28%.

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Answer:

To simplify this expression, we first need to evaluate the expression inside the parentheses:

10 - 9 + 6 = 7

Now we can substitute this value back into the original expression:

10 + 28 ÷ 7 (7) = 10 + 4(7) (since 28 ÷ 7 = 4)

= 10 + 28

= 38

Therefore, 10 + 28 divided by 7 (10-9+6) equals 38.