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

The summation of 5 to power of n (where n starts from 1) is determined as 625.

The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.

The given summation expression include;

∑5ⁿ

where;

So we are going to sum the number 5ⁿ 4 times.

The expression becomes;

5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ

where;

n = 1

The summation becomes;

5⁴ⁿ = 5⁴ = 625

Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.

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The population reached in the year 2079 is 1,65,400 and the total population in the year 2081 would be 1,80,623.

To find the population reached in the year 2079, we need to consider the initial population and the growth rate, as well as the number of people who migrated.

The initial population in 2078 was 1,20,000. The population growth rate is 4.5%, which means the population will increase by 4.5% each year.

To calculate the population in 2079, we first need to calculate the increase in population due to the growth rate:

Population increase due to growth rate = 1,20,000 * (4.5/100) = 5,400

Then we add the number of people who migrated:

Total population in 2079 = Initial population + Population increase due to growth rate + Number of migrants

= 1,20,000 + 5,400 + 20,000

= 1,45,400 + 20,000

= 1,65,400

To calculate the total population in the year 2081, we need to consider the growth rate and the population in 2080.

The population in 2080 would be the population in 2079 plus the population increase due to the growth rate:

Population increase due to growth rate in 2080 = 1,65,400 * (4.5/100) = 7,444

Total population in 2080 = 1,65,400 + 7,444

= 1,72,844

To calculate the total population in 2081, we need to consider the growth rate and the population in 2080:

Population increase due to growth rate in 2081 = 1,72,844 * (4.5/100) = 7,779

Total population in 2081 = Population in 2080 + Population increase due to growth rate in 2081

= 1,72,844 + 7,779

= 1,80,623

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Based on the data, we can infer that the park with the highest fee is Coaster City.

To find the value of each park we must take into account the different tables that show the value of each park. In this case we must find the unit value of each park as follows:

Park 1:

Park 2:

Park 3:

In accordance with the above, we can infer that the 2 Coaster City park is the one with the highest rate.

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Answer:

2 * A^(3/2).

Step-by-step explanation:

Given that planet y is twice the mean distance from the sun as planet x, we can denote the mean distance of planet x as "A" and the mean distance of planet y as "2A".

The equation T^2 = A^3 represents the relationship between the orbital period (T) and the mean distance from the sun (A) for a planet.

Let's compare the orbital periods of planet x and planet y using the equation:

For planet x:

T_x^2 = A^3

For planet y:

T_y^2 = (2A)^3 = 8A^3

To find the factor by which the orbital period is increased from planet x to planet y, we can take the square root of both sides of the equation for planet y:

T_y = √(8A^3)

Simplifying the square root:

T_y = √(2^3 * A^3)

= √(2^3) * √(A^3)

= 2 * A^(3/2)

Now, we can express the ratio of the orbital periods as:

T_y / T_x = (2 * A^(3/2)) / T_x

As we can see, the orbital period of planet y is increased by a factor of 2 * A^(3/2) compared to the orbital period of planet x.

Therefore, the factor by which the orbital period is increased from planet x to planet y depends on the value of A (the mean distance from the sun of planet x), specifically, it is 2 * A^(3/2).

Hello!

[tex]7p-13p+4-5p\\\\= 7p-13p-5p+4\\\\= -6p-5p+4\\\\\Large\boxed{= -11p + 4}[/tex]

Answer:

Refer to the step-by-step, follow along carefully.

Step-by-step explanation:

Verify the given identity.

[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)} =\csc(x)(1+\cos^2(x))[/tex]

Pick the more complicated side to manipulate, so the L.H.S.

(1) - Combine the fractions with a common denominator

[tex]\frac{\sin(x)}{1-\cos(x)} -\frac{\sin(x)\cos(x)}{1+\cos(x)}\\\\\Longrightarrow \frac{\sin(x)(1+\cos(x))}{(1-\cos(x))(1+\cos(x))} -\frac{\sin(x)\cos(x)(1-\cos(x))}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos(x)-\sin(x)\cos(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))} \\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}} \\\\[/tex]

(2) - Simplify the denominator

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{(1+\cos(x))(1-\cos(x))}\\\\\Longrightarrow \frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos(x)+\cos(x)-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}}[/tex]

(3) - Apply the following Pythagorean identity to the denominator

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Pythagorean Identity:}}\\\\1-\cos^2(\theta)=\sin^2(\theta)\end{array}\right}[/tex]

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{1-\cos^2(x)}\\\\\Longrightarrow \boxed{\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}}[/tex]

(4) - Simplify the fraction and split it up

[tex]\frac{\sin(x)+\sin(x)\cos^2(x)}{\sin^2(x)}\\\\\Longrightarrow \frac{1+\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \boxed{\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}}[/tex]

(5) - Apply the following reciprocal identity

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Reciprocal Identitiy:}}\\\\\csc(\theta)=\frac{1}{\sin(\theta)} \end{array}\right}[/tex]

[tex]\frac{1}{\sin(x)}+\frac{\cos^2(x)}{\sin(x)}\\\\\Longrightarrow \csc(x)+\frac{1}{\sin(x)}\cos^2(x) \\\\\Longrightarrow \csc(x)+\csc(x)\cos^2(x) \\\\\therefore \boxed{\boxed{\csc(x)(1+\cos^2(x))}}[/tex]

Thus, the identity is verified.

Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown below.

We have to given that,

Expression to verify is,

⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)

Now, We can simplify as,

⇒ sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x)

⇒ sin x [ 1 / (1 - cos x) - cos x / (1 + cos x)]

⇒ sin x [1 + cos x - cos x (1 - cos x )] / (1 - cos²x)

⇒ sin x [1 + cos x - cos x + cos²x] / sin²x

⇒ (1 + cos²x) / sin x

⇒ cosec x (1 + cos²x)

Thus, Prove of the expression sin x / (1 - cos x) - [sin x cos x ] / (1 + cos x) by using trigonometry formula is shown above.

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Becky contributed $50 towards the building for the aged.

Let's calculate the amounts contributed by each student:

Azar contributed 50% of the total amount:

Amount contributed by Azar = 50% of $200

= (50/100) × $200

= $100

Sunil contributed 25% of the total amount:

Amount contributed by Sunil = 25% of $200

= (25/100) × $200

= $50

Now, we can calculate the amount contributed by Becky:

Total contribution by Azar and Sunil = $100 + $50 = $150

The remaining amount contributed by Becky can be found by subtracting the total contribution by Azar and Sunil from the total amount:

Amount contributed by Becky = Total amount - Total contribution by Azar and Sunil

= $200 - $150

= $50

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Sin 40° = x/16

0.6428 = x/16

x = 0.643 × 16

x = 10.2848

x = 10.28

So, the value of x is 10.28 (C)

That's it :)

The nearest Whole number, the missing dimension (height) of the cylinder is approximately 39 inches.

The missing dimension of the cylinder, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Given that the volume is 10,000π in³ and the diameter of the base is 32 inches, we can determine the radius (r) of the cylinder.

The diameter is twice the radius, so the radius is half of the diameter:

r = 32 inches / 2 = 16 inches

Substituting the known values into the volume formula, we have:

10,000π in³ = π * (16 in)^2 * h

Cancelling out the common factor of π, we get:

10,000 = 16^2 * h

Simplifying further:

10,000 = 256 * h

To isolate h, we divide both sides of the equation by 256:

h = 10,000 / 256

Calculating the value of h:

h ≈ 39.06

Rounded to the nearest whole number, the missing dimension (height) of the cylinder is approximately 39 inches.

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Answer:

Assuming the spinner has 6 equal sectors of different colors, and yellow is only one of those colors, we can say that the probability of the spinner not landing on yellow is 5/6 or approximately 0.8333.

To predict the number of times the spinner will not land on yellow out of 90 spins, we can multiply the probability by the total number of spins:

0.8333 x 90 = 74.997 or approximately 75

Therefore, the best prediction possible for the number of times the spinner will not land on yellow out of 90 spins is 75 times.

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Answer:

 [(5 ± √(29)) ÷ 2]

Step-by-step explanation:

x = [(-b ± √(b² - 4ac)) ÷ 2a]

=  [(-(-5) ± √((-5)² - 4(1)(-1))) ÷ 2(1)]

=  [(5 ± √(25 + 4)) ÷ 2]

=  [(5 ± √(29)) ÷ 2]

The diameter of the hemisphere is 39.1918 feet.

The surface area of a hemisphere is given by the formula:

Surface Area = 2πr²

We have,

surface area of the hemisphere is 768π square feet,

So, 2πr² = 768π

Dividing both sides of the equation by 2π, we get:

r² = 384

To find the diameter, we need to double the radius.

Taking the square root of both sides of the equation, we get:

r = √384

r ≈ 19.5959

Now, Diameter ≈ 2 x 19.5959 ≈ 39.1918

Therefore, the diameter of the hemisphere is 39.1918 feet.

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The quadratic equation shown in the graph is:

y = x² + 2x - 8

Here we want to find the graph of the given quadratic equation, where we only know the zeros of it.

Remember that if a quadratic equation has the zeros:

x = a

x = b

Then we can write it as:

y = (x - a)*(x - b)

Here the zeros are:

x = -4

x = 2

Then we can write:

y = (x + 4)*(x - 2)

Expanding that we will get the standard form:

y = x² + 4x - 2x - 8

y = x² + 2x - 8

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Answer:

(2x + 3)(x - 5)

Step-by-step explanation:

2x² - 7x - 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

the factors are - 10 and + 3

use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

= (2x + 3)(x - 5) ← in factored form

Blank 1 is 3

Blank 2 is 5

Answer:

There are 20 blue fish in the aquarium.

Step-by-step explanation:

If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.

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

In order to expand the properties of logarithms log981x:

log981x = log98 + log1x

One must know that loga + logb = log(ab), and loga + logb = log(ab) may also be represented as loga(b) or logab.

Using this property, we can simplify the expression further:

log981x = log98 + log1x = log9 + log8 + log1 + logx

We know that log9 = 2 and log1 = 0, so we can simplify even further:

log981x = log9 + log8 + log1 + logx = 2 + log8 + 0 + logx = 2 + log8x.

Therefore, the expanded value would be log981x to 2 + log8x.

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Step-by-step explanation:

To solve this problem, we need to calculate the probability of the first student being a boy and the second student being a girl.

There are a total of 13 boys and 15 girls in the class, making a total of 28 students.

The probability of the first student being a boy is given by:

P(boy) = Number of boys / Total number of students = 13 / 28

After the first student is selected, there are now 27 students remaining (since one student has already been selected). Out of these 27 students, there are still 15 girls remaining.

The probability of the second student being a girl, given that the first student was a boy, is given by:

P(girl|boy) = Number of girls / Remaining number of students = 15 / 27

To find the probability of both events occurring (the first student being a boy and the second student being a girl), we multiply the individual probabilities:

P(boy and girl) = P(boy) * P(girl|boy) = (13/28) * (15/27)

Calculating this expression:

P(boy and girl) ≈ 0.2041

Therefore, the probability that the first student is a boy and the second student is a girl is approximately 0.2041 or 20.41%.

The statement "If dom(f) = Χ, then f is an n-ary functionon X" means that if the domain   of the function f is equal to the set X, then f is considered an n-ary function on X.

In other words, for each element in X,   the function f can take n arguments or inputs to produce aunique output. The term "n-ary" indicates the number of arguments that the function can accept.

A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is anothername for a statement. The main point is that there should be no uncertainty.

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Answer:

The statement "If dom(f) = X, then f is an n-ary function on X" means that if the domain of a function f is equal to the set X, then f is a function that takes n arguments or inputs from the set X, where the value of n depends on the specific function.

Step-by-step explanation:

The statement "If dom(f) = X", then f is an n-ary function on X" means that if the domain of the function f is equal to the set X, then f is an n-ary function on X.

Here's a breakdown of the terms used in the statement:

- dom(f): The domain of a function f refers to the set of all possible input values for the function. It represents the set of values for which the function is defined.

- X: In this context, X represents a set. It could be any set, and it serves as the domain for the function f.

- n-ary function: An n-ary function is a function that takes n arguments or inputs. The value of n represents the number of inputs the function expects.

Therefore, the statement is saying that if the domain of the function f is equal to the set X, then f is an n-ary function on X. It implies that the function f takes n inputs from the set X, where n is determined by the specific function.

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Answer: (4x-12) + ( 1/2x y -10) = 6

Step-by-step explanation:

First, input 4 for x and 6 for y into the equation so it looks like this:

(4(4)-12) + (1/2(4)(6)-10)

Now solve inside the parentheses starting with the first one. 4 * 4 = 16 so the inside of the first parentheses should look like (16 - 12) which equals 4.

For the second set of parentheses, 1/2 * 4 * 6 = 12, so the inside of that parentheses would look like (12 - 10), which equals 2.

At this point, the equation should look like this: (4) + (2). If you add those two together, your answer should be 6.

Answer:

Step-by-step explanation:

the of of 50 percent of people is married

The correct statement regarding the association in the scatter plot is given as follows:

Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.

There can either be a positive association between variables or a negative association between variables, as follows:

In this problem, we have a decreasing scatter plot, hence there is a negative association between the variables.

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area of equilateral triangle =

[tex]( \sqrt{3 } \div 4) \times a {}^{2} [/tex]

(C) area = 84.9 in²

The height of the average fourth grader is 135 cm 21 mm

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

Birth age = 45 cm 7 mm

Average fourth grader = three times as tall

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

Average fourth grader = 3 * Birth age

So, we have

Average fourth grader = 3 * 45 cm 7 mm

Evaluate

Average fourth grader = 135 cm 21 mm

Hence, the height of the average fourth grader is 135 cm 21 mm

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Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

The required answer are :

6. The transformation from the graph of f to the graph of r in equation (6) involves compressing the graph horizontally by a factor of 5/2.

7. The transformation from the graph of f to the graph of r in equation (7) involves stretching the graph vertically by a factor of 6.

8.  The transformation from the graph of f to the graph of r in equation (8) involves shifting the graph horizontally to the right by 3 units.

9. The transformation from the graph of f to the graph of r in equation (9) involves compressing the graph horizontally by a factor of 4/3.

10.  The transformation from the graph of f to the graph of r in equation (10) involves shrinking the graph vertically by a factor of 1/2.

11.  The transformation from the graph of f to the graph of r in equation (11) involves shifting the graph vertically upward by 3 units.

In formula form: r(x) = f(2/5x)

This transformation causes the graph of r to become narrower compared to the graph of f, as it is compressed horizontally. The rate at which x-values change is increased, resulting in a steeper slope. The overall shape and direction of the graph remain the same, but it is narrower and more compact.

Therefore, the transformation from the graph of f to the graph of r in equation (6) involves compressing the graph horizontally by a factor of 5/2. This means that every x-coordinate in the graph of f is multiplied by 2/5 to obtain the corresponding x-coordinate in the graph of r. The vertical positioning of the graph remains unchanged.

In formula form: r(x) = 6f(x)

This transformation causes the graph of r to become taller compared to the graph of f, as it is stretched vertically. The rate at which y-values change is increased, resulting in a steeper slope. The overall shape and direction of the graph remain the same, but it is taller and more elongated.

Therefore, the transformation from the graph of f to the graph of r in equation (7) involves stretching the graph vertically by a factor of 6. This means that every y-coordinate in the graph of f is multiplied by 6 to obtain the corresponding y-coordinate in the graph of r. The horizontal positioning of the graph remains unchanged.

In formula form: g(x) = f(x - 3)

This transformation causes the entire graph of f to shift to the right by 3 units. Every point on the graph of f moves horizontally to the right, maintaining the same vertical position. The overall shape and slope of the graph remain the same, but it is shifted to the right.

Therefore, the transformation from the graph of f to the graph of r in equation (8) involves shifting the graph horizontally to the right by 3 units. This means that each x-coordinate in the graph of f is increased by 3 to obtain the corresponding x-coordinate in the graph of r. The vertical positioning of the graph remains unchanged.

In formula form: g(x) = f(4/3x)

This transformation causes the graph of r to become narrower compared to the graph of f, as it is compressed horizontally. The rate at which x-values change is increased, resulting in a steeper slope. The overall shape and direction of the graph remain the same, but it is narrower and more compact.

Therefore, the transformation from the graph of f to the graph of r in equation (9) involves compressing the graph horizontally by a factor of 4/3. This means that every x-coordinate in the graph of f is multiplied by 4/3 to obtain the corresponding x-coordinate in the graph of r. The vertical positioning of the graph remains unchanged.

In formula form: g(x) = 1/2 f(x)

This transformation causes the graph of r to become shorter compared to the graph of f, as it is vertically shrunk. The rate at which y-values change is decreased, resulting in a flatter slope. The overall shape and direction of the graph remain the same, but it is shorter and more compact.

The transformation from the graph of f to the graph of r in equation (10) involves shrinking the graph vertically by a factor of 1/2. This means that every y-coordinate in the graph of f is multiplied by 1/2 to obtain the corresponding y-coordinate in the graph of r. The horizontal positioning of the graph remains unchanged.

In formula form: g(x) = f(x) + 3

This transformation causes the entire graph of f to shift upward by 3 units. Every point on the graph of f moves vertically upward, maintaining the same horizontal position. The overall shape and slope of the graph remain the same, but it is shifted upward.

The transformation from the graph of f to the graph of r in equation (11) involves shifting the graph vertically upward by 3 units. This means that every y-coordinate in the graph of f is increased by 3 to obtain the corresponding y-coordinate in the graph of r. The horizontal positioning of the graph remains unchanged.

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