Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Sidney wants to take group fitness classes at a nearby gym, but needs to start by selecting a
membership plan. With the first membership plan, Sidney can pay $36 per month, plus $2 for
each group class she attends. Alternately, she can get the second membership plan and pay
$35 per month plus $3 per class. If Sidney attends a certain number of classes in a month,
the two membership plans end up costing the same total amount. How many classes per
month is that? What is that total amount?
If Sidney attends
Submit
classes per month, each membership plan costs $

The simplified expression is 2187.

Given expression:

expression 3 with the exponent 4 multiplying  3 with the exponent of 3.

= [tex]3^{4} *3^{3}[/tex]

we know that,

if base are equal exponents are added.

= [tex]3^{4+3}[/tex]

= [tex]3^{7}[/tex]

= 3*3*3*3*3*3*3

= 9*3*3*3*3*3

= 27*3*3*3*3

= 81*3*3*3

= 243*3*3

= 729*3

= 2187.

Therefore the simplified expression is 2187.

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1.) Yes,it will fit because volume of the base ball is 13.36 cubic inch and the volume of box is 64 cubic inch which greater than the volume of baseball .

2) The ratio of the side length of box B to the side length of box

A is 1.472 inche : 6 inch.

What is cube ?

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

What is circumference?

The circumference is the distance that surrounds a circle. We can measure the circumference of the earth by measuring the distance that we will have to walk all the way around the world.

To check whether the baseball is will till in the box we will check the maximum value of circumference.

⇒  [tex]2\pi r[/tex] = 9.25

⇒ [tex]r = \frac{9.25}{2\pi}[/tex]

⇒[tex]r = 1.472 in.[/tex]

Volume of the baseball [tex]= \frac{4}{3} \pi x^{3}[/tex]

                                      [tex]= \frac{4}{3}\times \pi\times (1.472)^3 in^3[/tex]

                                      [tex]= 13.36\ in^3 < 64 \ in^3\\[/tex]

So, it will fit inside the box.

2.)[tex]\sqrt[3]{216} = 6 \ (\therefore V = a^3)[/tex]

The length of each side of the box is 6 inches.

and the ratio of the side length of box B to the side length of box

A:

1.472 in : 6 inches

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Answer:

6x+97

Step-by-step explanation:

Hint: 3 sides of a triangle adds up to 180*.

((i know ur gonna clown on me for not giving the answer(i know the answer :d)but trust me the if u get da hint, ull solve it fine)

The AGI and taxable income is $23,670 and $11,270

How to calculate AGI(Adjusted gross income) ?

The AGI calculation can be done as,

We have given that,

Gross income = $23670

1 Exemption = $12400

Adjustment = 0

Deduction = 0

Find AGI and Taxable income

AGI = Adjusted gross income

we know,

AGI = Total income - Any deduction or any adjustment  

AGI = ($23,670 + $12400)  - (0 + 0)

AGI = $36070

Now, Calculate taxable income

Taxable income = Gross income - 1 Exemption

                           = $23670 - $12400

                           = $11,270

Hence, the AGI and taxable income is $36,070 and $11,270

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Answer: D is the answer

Step-by-step explanation:

$23,670 and $11,270

The percent of the number is 0.5% when the number is 1/200.

Given that,

We have to find the percent of the number 1/200.

A percentage is a number or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the symbol "%" or just "percent" or "pct."

Take the number.

1/200

Multiply by 100

1/200×100

We get

1/2

In decimal we get

0.5%

Or

Convert the number to decimal.

1/200= 0.005

Multiply 0.005 by 100 to convert to a percentage.

0.005×100

Simplify

0.5%

Therefore, The percent of the number is 0.5% when the number is 1/200.

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The measurement of the distance from the tip of the slice of pizza to the crust is the radius.

The diameter of the pizza is 12 inches and the circumference is 37.7 inches

A slice of pizza is cut from the middle of the pizza to the crust. It is therefore cut from the middle of the pizza (circle) to the edge of the pizza (circle).

This is the radius because the radius is the straight - line distance from the edge of the middle of a circle to the edge.

If the radius is 6 inches, the diameter is:

= radius x 2

= 6 x 2

= 12 inches

The circumference is:

= π x diameter

= 22/7 x 12

= 37.7 inches

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Using Combination formula, total 2,24,070 ways to make a math team of 14 selected students in which consist of 8 seniors and 6 juniors.

We have following information,

total number of seniors in math club = 15

total number of juniors in math club = 11

total number of students in math club = 26

A math team of 14 students be choosen from maths club such that it consists 8 seniors and 6 juniors .

Number of ways to choose 8 seniors out of 15 seniors = ¹⁵C₈ = 485

Number of ways to choose 6 juniors out of 11 juniors = ¹¹C₆ = 462

Number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors

= 485 × 462 = 2,24,070

Hence, the number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors is 2,24,070..

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Given the equation x² + y² + 4x - 8y + 11 = 0, the center of the circle is (-2, 4).

The standard form of the equation of circle is given by

(x - h)² + (y - k)² = r²

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x² + y² + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h² + k² - r².

If the equation of the circle in general form is x² + y² + 4x - 8y + 11 = 0, then the coefficients are:

D = 4

E = -8

F = 11

If D = -2h and D = 4, then

4 = -2h

h = -2

If E = -2k and E = -8, then

-8 = -2k

k = 4

Hence, the center of the circle is (h, k) = (-2, 4).

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Answer:

Step-by-step explanation:

Answer x = 4 or x = -4.

Explanation: you can make what is called a 3-4-5 triangle. The base in this case is 3(from -2 to -5 there is 3 units), the hypotenuse is 5(length given in the question) therefore the height (also known as the y coordinate) is 4 or -4 if you flip the triangle.

The value e = 0.869 indicates that the ellipse is more elongated that circular.

Given,

x²/12+y²/49 = 1

We will compare with x²/a² + y²/b² = 1 where a<b

Coordinate of center = (0,0)

Here a²=12 and b²=49

We know that the formula of eccentricity(e)

e=√(1-(a²/b²))

= √(1-(12/49))

= √37/7

=0.869

Therefore e=√37/7 = 0.869

Therefore this value indicates that the ellipse is more elongated that circular.

In mathematics, an ellipse is a plane bend encompassing two central focuses, to such an extent that for all focuses on the bend, the amount of the two distances to the central focuses is a consistent. It sums up a circle, which is the extraordinary kind of oval wherein the two focal points are something similar.

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The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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Step-by-step explanation:

The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5.  That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f.  For example, if  x = 2, the point (2, 20) is on the graph of  f  but the point (2, 16) is on the graph of  p (so it lies under the point (2, 20).

The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of  f  and it is reflected over the x-axis.  The negative coefficient -1 is doing that.  The values of the function  p(x)  are opposite sign to values of  f(x).

The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of   p  lie farther away from the x-axis than points on the graph of  f(x).

the graph above is the graph of a Cubic function, namely a polynomial with a degree of "3", and the behaviour is that it comes from the bottom from -infinity goes up up get to a smooth flat or horizontal plateau then it keeps on going right back up, its slope is never negative.

now, Cubic functions do not have a "vertex" as in a U-turn sense or a peak-sense.

The meaning of the x-value when y=90 means that Anthony will use 3.1 hours.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The relationship that can be represented by the equation y=57+7.4x,

where

y represents the expected quiz score

x represents hours spent on homework that week.

When y = 90, the value of x will be:

y=57+7.4x

57 + 7.4x = 90

Collect like terms

7.4x = 90 - 57

7.4x = 23

Divide

x = 23/7.4

x = 3.1

He'll use 3.1 hours.

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Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15

If the choir has learned 9 classical songs;

Equate the ratio of the number of modern songs to the number of classical songs

5 : 3 = x : 9

5/3 = x/9

5 × 9 = 3 × x

45 = 3x

divide both sides by 3

x = 45/3

x = 15

In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15

Complete question:

Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.

If the choir has learned 9 classical songs, how many modern songs have they learned?

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The distance up the house the ladder will reach after pulling it 10 feet further from the base of the house is 43.9 ft.

The ladder is set against the side of the house so that it reaches up 48 feet.  Shaniece grabs the ladder at its base and pulls it 10 feet farther from the house.

The height of the ladder on the house can be computed as follows:

The situation form two right angle triangle.

The initial distance of the base of the ladder from the house can be calculated as follows;

using Pythagoras's theorem,

b² = 50² - 48²

b = √2500 - 2304

b = √196

b = 14 ft.

Therefore, the initial distance of the ladder from the base of the house is 14 feet.

Let's find the height of the ladder on the house after pulling it 10 ft further.

using Pythagoras's theorem,

b² = 50² - 24²

b = √2500 - 576

b = √1924

b = 43.8634243989

b = 43.9 ft

Therefore,

height of the ladder up the house = 43.9 ft

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x = y = 48 , by using angle sum property of triangle.

What are the properties of triangle?

A triangle's characteristics are:

1. Three sides, three angles, and three vertices make up a triangle.

2. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

3. Any two triangle sides can add up to a length that is longer than the third side.

4. The greatest side of a triangle is the side that faces the largest angle.

5. The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.

In the given triangle , two sides of the triangle are equal and we know angle opposite to equal sides are equal therefore both angle x and y are equal.

Now, Using angle sum property of triangle

x + y + 84 = 180 degree

x + x + 84 = 180

2x + 84 = 180

2x = 180 - 84

2x = 96

x = 96/2  

x = 48

Similary , y = 48 as x and y are equal.

Therefore, x = y = 48

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The formula for w in terms of p and l is w = (p - 2l)/2

Numbers, symbols and operators grouped together that show the value of something.

Given that, an expression p = 2l + 2w

Solving for w, we get,

w = (p - 2l)/2

Hence, The formula for w in terms of p and l is w = (p - 2l)/2

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(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

A scatter plot is a graph of the given points or given data.

(a)

To make a scatter plot of the data, plot the points (x,y) on a graph.

To draw the line of fit, draw a line such that the distance between the line and the plotted points is minimum.

(b) The line passes through points (7.3,0)and (0,18).

The equation of the line is given by:

[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]

Substitutes the points (x₁,y₁) = (7.3,0) and (x₂,y₂)=(0,18) into the above equation:

[tex]y-0=\frac{18-0}{0-7.3}(x-7.3)\\y=-2.5(x-7.3)\\y=-2.5x+18.3[/tex]

(c) The slope of a line of the form y=mx+c is m.

Therefore, the slope of the line y=-2.5x+18.3 is m = -2.5.

The slope indicates the change in y with respect to the change in x.

Therefore, the slope -2.5 indicates that the gamer losses 2.5 every week after getting a new game.

Hence,

(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

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It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.

We are asked the probability that an applicant scores below 552.

Now, using the formula of probability, we get

P(X < 552) = 0.8329

when the mean is given i.e. 460 and standard deviation is given i.e. 80.

Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

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Step-by-step explanation:

as the graph shows :

4x + 12x = 320

16x = 320

x = 20

Answer:

A $1.20

Step-by-step explanation:

Answer:   A) $1.20

Step-by-step explanation:   To get 10% of a number, you just need to divide by 10, so 12 ÷ 10 = 1.2.

f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....

8.3, 10.4, 12.5, 14.6,...

The given sequence is a arithmetic sequence.

The first term is 8.3

The common difference is 2.1

The nth term of arithmetic sequence aₙ=a+(n-1)d

the nth term of this sequence=8.3+(n-1)2.1

f(n)=8.3+(n-1)2.1

Hence, f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.

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a) These ramp dimensions do not meet the ADA guidelines.

b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.

The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:

The ratio between the vertical change to the horizontal change is of:

3/15 = 1/5.

Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.

If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:

As the ratio would be of:

3/39 = 1/13 < 1/12.

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The distance covered by second cyclist is, 9 + (3/4)b miles.

What is speed?

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

Given: Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions.

The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.

Speed of first cyclist = 12 miles per hour.

Speed of second cyclist = 12 + b miles per hour.

Since, distance = speed x time

The distance covered by the second cyclist in 45 minutes is,

45 minutes = 45/60 = 3/4 hour.

Therefore, distance covered by second cyclist is,

=  (12 + b) x 3/4 = 9 + 3b/4 miles.

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