Alexa plans to join a members-only speaker series for $50. As a member, she will pay just $12.50 for each event she attends. Alexa has budgeted $100 to become and member and attend these events. How many events can she afford to attend?

hey, I checked on desmos, which is a calculator for this type of stuff, and got 1.8,5.2. So I think that's one solution. Sorry if wrong.

Answer: 1468.17

Step-by-step explanation:

Answer:

The equation of the proportional relationship can be written as y = (2/3)x.

Step-by-step explanation:

This equation is derived by using the fact that the slope of the relationship between x and y is 2/3. The slope of a line can be expressed as the ratio of the change in y to the change in x, which is represented by (delta y) / (delta x).

Since the slope is 2/3, the change in y for a unit change in x can be expressed as 2/3 * x. This relationship can then be written in terms of x and y by solving for y:

y = (2/3) * x.

In this equation, y is directly proportional to x with a constant of proportionality equal to 2/3.

Answer:

0.5236 radians per minute

or

0.00872665 radians per second

Step-by-step explanation:

Let's first define angular speed

Angular speed is the rate at which an object changes it angles which we measure in radians in a given time. Angular speed has a magnitude (a value only whereas velocity is a vector with speed and direction)

The angular speed, ω of an object is given by the formula
ω = θ/t

where  θ is the angle in radians
1 full revolution is 360° or 2π radians

t = time taken for completing θ radians of rotation

We are given that the Ferris wheel completes 1 full revolution in 12 minutes

1 full revolution = 2π radians

t = 12 minutes

Angular speed = ω = θ/t =  2π/12 radians/minute

ω = 0.5236 radians per minute

or in radians per second

ω = 0.5236/60 = 0.00872665 radians per second

The coordinates of the image of quadrilateral DEFG after being reflected about the origin include the following:

D' = (9, 5).

E' = (-5, -4).

F' = (6, 2).

G' = (-4, -2).

In Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

Generally speaking, reflecting a point about the origin is a a type of transformation which causes both the x-coordinate and the y-coordinate to become negated (the signs are changed);

(x, y)                              →               (-x, -y)

Ordered pair D  = (-9, -5) →   Ordered pair D' = (9, 5).

Ordered pair E  = (5, 4) →   Ordered pair E' = (-5, -4).

Ordered pair F  = (-6, -2) →   Ordered pair F' = (6, 2).

Ordered pair G  = (4, 2) →   Ordered pair G' = (-4, -2).

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Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.

Graphing the correlation between two additional variables is the most common way to use a chart to present data. It is also permitted to use hand-drawn or digitally generated diagrams. Go three pieces up and 2 types to the right starting at the origin. Displaying the numbers for rows 2, 3, and 4 on the standard system is crucial. Make sure to be very clear in what you say.

Here,

Given :

A figure having pre image and post image ,

We have to find in which quadrant the pre image is located,

So,

In order to find that,

We see the image are in quadrant II and quadrant III

Since ,

After II quadrant III quadrant comes,

Thus , Pre image is located in II quadrant.

Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.

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The terms, when sorted into groups of " like terms " gives:

Like terms :

Unlike terms :

To sort a set of algebraic terms into groups of like terms, you must look for terms that have identical variables and exponents. These terms can be combined and simplified using the rules of addition and subtraction. in this scenario, they include: - 7 y ² and y ², 0. 5 kt and - 10 kt, 6 and 9.

Terms that have different variables or exponents are considered unlike terms and cannot be combined in this way. They include : - 4 p and p ², 5 x and 5, 3 ad and 2 bd .

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Answer:

Step-by-step explanation:

divide $43.74 by 6 = 7.29 per pair

linear function

x=5+n

given:

height of tree = 5ft

growth per month = 1ft

Find:

equation:

Computation:

asume:

New height of x

number of month = n

x=5+1(n)

x=5+n

hope this helped.

Answer:

6000 bushels per hour.

Step-by-step explanation:

Let's assume that the rate at which the conveyor unloads wheat is proportional to its width.

If a 14-inch conveyor unloads 4000 bushels per hour, we can write this as:

Rate = 4000 bushels/hour * (Width of conveyor) / 14 inches

Now, if we want to find the rate at which an 21-inch conveyor would unload wheat, we can simply plug in the width into the equation:

Rate = 4000 bushels/hour * (21 inches) / 14 inches

Rate = 6000 bushels/hour

Therefore, an 21-inch-wide conveyor would unload 6000 bushels per hour.

Answer:

5564+746655754673346

The Surface area of Figure is  496 ft².

The Volume of Figure is 608 ft³.

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

Surface Area of Pyramid

= Base area + 1/2 x P x l

= 64 + 1/2 x 32 x 3

= 64 + 16 x 3

= 112 ft²

and, Volume of Pyramid

= 1/2 x 64 x 3

= 96 ft³

So, total Surface Area

= 112 + 384

= 496 ft²

and, The total volume

= 96 + 512

= 608 ft³

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Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

In the image, the triangles are congruent to each other by the Side-Angle-Side Congruence Theorem (SAS).

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

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90, 000 will be the total number of different phone extensions.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, A company wants to have ​5-digit phone extensions with the first digit not being zero.

This problem is an application of the Basic Counting Rule which was discussed above. We want to compute the number of different 5-digit phone extensions.

there are 10 different digits, which are 0,1,2,3,4,5,6,7,8,9. The first digit can't be 0.

There are 9 choices for the first digit. For each choice of the first digit, there are 10 choices for the second digit. For each choice of the first and second digits, there are 10 choices for the third digit, and so on.

According to the Basic Counting Rule, we know that the total number of phone extensions is the product of the number of ways to choose each digit (the product of the 6 above numbers).

the total number of different phone extensions is = 9 *10 *10 *10 *10

therefore, the total number of different phone extensions is = 90,000.

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(AUB) will be equal to {2,4,6,7,6,10,11, .....even numbers). The empty set, or 0, is one of the most significant sets in mathematics.

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolized by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

A set with no elements is referred to as a null set or empty set.  The null set is the intersection of two disjoint sets, or sets that have no elements in common.

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The expression that represents the cube root of 1+i​ is ∛(1 + i)

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

The cube root of 1+i​

In mathematics and algebra, the cube root is represented as ∛

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

The cube root of 1+i​ is ∛(1 + i)

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Step-by-step explanation:

(n+1)! = (n+1)n(n-1)(n-2)...×3×2

16n! = 16n(n-1)(n-2)...×3×2

16(n-1)! = 16(n-1)(n-2)...×3×2

we can now divide both sides by (n-1)! and get

(n+1)n = 16n + 16

n² + n = 16n + 16

n² - 15n - 16 = 0

1×n² - 15n - 16 = 0

we try to bring this into a form

(n + a)(n - b)

one factor has to contain "-", because we have "-16".

and because -15 = 1 - 16, we see that

a = 1

b = 16

n² - 15n - 16 = (n + 1)(n - 16)

and that is 0, when at least one of the factors is 0, because 0×... = 0.

so, the solutions are

n = -1

n = 16

n = -1 does not make any sense for n!

so, n = 16 is the solution.

The completion of the equation to find w, the number of weeks until Ashely and Tanner have the same amount in their savings accounts is 25w + 450 = 40w + 200.

An equation is a mathematical statement claiming that two or more mathematical expressions are equivalent or equal.

Equations are depicted with the equation symbol (=) to show equality of the expressions.

                                       Ashely  Tanner

Savings                            $450    $200

Planned weekly deposits $25      $40

Let the number of weeks to save equal amounts = w

Ashely's total savings in w weeks = 25w + 450 ... Equation 1

Tanner's total savings in w weeks = 40w + 200 ... Equation 2

For the two friends to have an equal amount, Equation 1 must equal Equation 2:

25w + 450 = 40w + 200

-15w = -250

w = 16.67

Thus, for Ashely's and Tanner's savings to become equal in amount, it would take 16.67 weeks.

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Answer:

modal class is 70 - 79

Step-by-step explanation:

the modal class is the interval which occurs most often

in this case 70 - 79 occurs 6 times

then modal class is 70 - 79

Answer:

4. y = 3x

Step-by-step explanation:

A proportional relationship is one in which the ratio of two variables is always constant. This is also known as direct proportion.

Out of the given options, the equation that shows a proportional relationship is:

4. y = 3x

In this equation, the ratio of y to x (y/x) is always 3, so the relationship between y and x is proportional. As x increases, y also increases at a constant rate, and as x decreases, y decreases at a constant rate. This type of relationship is often represented by the equation y = kx, where k is the constant of proportionality.

by trigonometry the magnitude of the force P so that the resultant force exerted on the stake is vertical. The magnitude of the force is 196.6 N.

When a force system acts on an item, the difference between the forces is referred to as the Resultant force. When an item is under the influence of two or more forces, the combined force may be calculated by adding up the separate forces. The forces in all directions will be the same for all the forces if they are all acting in the same direction. The SI unit for resultant force is the Newton.

Given that,

α = 30°

Using the triangle rule, and the law of sines:

120 N / Sin 30° = P / Sin 25°

or, P =  (Sin 25° /  Sin 30°) × 120

or, P = 101.428 N

or, P = 101.4 N

and also, θ = 180 - 25 - 30

θ = 125°

the value of resultant is:

120 N / Sin 30° = R / Sin 25°

or, R = 196.6 N

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It is not possible to make the statement true for one value of x, as the two linear functions have the same slope.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

The functions for this problem are defined as follows:

As the two functions have the same slope, there are two possible number of solutions.

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Step-by-step explanation:

The expression that is the factored form of 10x - 25 using the greatest common factor is option A: 5(2x - 5).

To factor the expression, we need to find the greatest common factor of the terms, which in this case is 5. We then write the expression as a product of 5 and a second expression with the remaining terms:

10x - 25 = 5 * (2x - 5)

So, option A is the correct answer.

The line's equation is y = 3x - 3 with the z-intercept (-1, 0) and the y-intercept (0, -3).

What do intercepts mean? The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.

Put x = 0 and work out y to determine the y-intercept. The purpose will be (0, y). Set y = 0 and solve for x to determine the x-intercept. The purpose will be (x, 0).

It gives both a slope and an intercept, hence the name "slope intercept form." Thus, this is your slope. You can move by keeping in mind that slope is rise over run.

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A correct answer is option (B) 7.78%. so, the interest rate is  7.78% being charged in her lease.

What is the interest rate?

Interest rate is the amount charged over and above the principal amount by the lender from the borrower. In terms of the receiver, a person who deposits money to any bank or financial institution also earns additional income considering the time value of money, termed as interest received by the depositor.

The interest rate in a lease can be calculated using the money factor, which is essentially a type of interest rate used in auto leasing.

To calculate the interest rate from the money factor, multiply the money factor by 2400.

In this case, the money factor is 0.00324, so the interest rate would be:

0.00324 * 2400 = 7.776%

Therefore, the correct answer is option (B) 7.78%. so, the interest rate is  7.78% being charged in her lease.

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A correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

The money factor, which is essentially a sort of interest rate utilized in auto leasing, can be used to compute the interest rate in a lease.

By multiplying it by 2400, you can determine the interest rate from the money element.

Given that the money component in this situation is 0.00324, the interest rate would be:

The result of three consecutive conversions from an interest rate to a money factor is 2400 (1/2 × 1/12 × 1/100). 6/2400 = 0.0025 money factor, which can be multiplied by the entire amount borrowed to see how much the monthly interest would be roughly.

(1/2 × 1/12 × 1/100). 6/2400 = 0.0025

0.00324 × 2400 = 7.776%

Therefore, the correct answer is option (B) 7.78%. so, the interest rate is  7.78% being charged in her lease.

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Answer:

C = 5x+6

Step-by-step explanation:

one of the properties of triangle is the supplemental angle of B = sum of the other 2 angles

so 11x+1=6x-5+c

C = 5x+6

Answer:

706.86

Step-by-step explanation:

The area of the sign will be found with the formula πr^2

r = 15 since the radius is half of the diameter

π(15)^2 = 706.86

Answer:

707 square inches.

Step-by-step explanation:

The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. The diameter of a circle is equal to twice the radius, so we can find the radius by dividing the diameter by 2.

In this case, the diameter of the circular railroad-crossing sign is 30 inches, so the radius is 30/2 = 15 inches.

So, the area of the sign is A = π * 15^2 = π * 225 = 706.86 square inches.

Rounding to the nearest whole number, the area of the sign is 707 square inches.