To be a member at Sal's gym, there is a one-time sign-up fee plus a monthly fee for each month of membership. The table shows the total cost to be a member of the gym for different numbers of months.


Number of Months Total Cost

3 $53. 97

6 $77. 94

12 $125. 88



Create a function that gives the total cost,

C

C

, in dollars, to be a member of the gym given the number of months,

m

m

, of membership.


Enter your function in the space provided

The number of clients that Belvedere train using Plan I if the total training time was 310 minutes will be 2 clients

From the information, Belvedere is a personal trainer and uses two different workout plans with his clients. Plan I takes 50 minutes to complete and Plan Il takes 35 minutes. Belvedere trained 6 clients using Plan Il last weekend.

The number of clients can be given as x.

The number of clients that Belvedere train using Plan I if the total training time was 310 minutes will be:

50x + 35(6) = 310

50x + 210 = 310

Collect the like terms

50x = 310 - 210

50x = 100

Divide

x = 100 / 50

x = 2

The clients are 2.

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The fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.

Divide implies to distribute anything evenly. After learning about whole number division, let's move on to fraction division. The numerator and the denominator are the two components of a fraction. Fractional division is roughly the same as fractional multiplication. When dividing fractions, we multiply the smaller of the two fractions by their reciprocals.

Given that George builds the fence at a rate of 1/3 section per 1/2 hour.

The fraction of fence that George build per hour can be obtained as:

1/3 = 1/2 hour

x = 1 hour

Using the butterfly method for multiplication we have:

x = (1/3) ÷ (1/2)

x = (1/3) × (2)

x = 2/3

Hence, the fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.

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d=2 and (a-1/2)2=2 hence 2a-1=2 hence a=3/2=first term and the common difference=d=2

S1, S2,... Sn can be written as:

A (first term) (first term)

A+r (r is a common difference) (r is a common difference),

A+2r

A+3r

A +(n-1)r

It is possible to calculate the sum as A +A +... +A (n times) + r +2r +3r.... +(n-1)r.

Giving n*A +r*(1+2+3....+n-1)

1+2+3….+n-1= n*(n-1)/2 =n^2 - n/2

The first N terms are added together as follows: n*A + r/2 *n2 - r*n/2

= r/2 *n^2 + (A - r/2)*n

This equals n2 - 2n for any n given the questions, so

A-r/2 = 2 AND r/2 = 1

=> r = 2 and A = 3 with r = 2

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Full question

The sum of the first n terms of an arithmetic sequence is given by Sn= n^2-2n. What are the first term and the common difference?

The equation 12x + 1 = 3(4x + 1) – 2 have infinite solutions

An equation is a mathematical statement that shows that two mathematical expressions are equal. In other terms we say that an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To solve this problem, we can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.

⇒ 12x + 1 = 3(4x + 1) – 2

⇒ 12x + 1 = 12x + 3 – 2

⇒ 12x + 1 = 12x + 1

So that, The equation have infinite solutions.

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This problem have two question:

1) How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) – 2

2) Which of the following shows the graph of y = –(2)x – 1?

we are giving the answer of question no.1

A) The system of equations that you can use to find the number of five-dollar bills and ten-dollar bills are;

x + y = 125

5x + 10y = 990  

B) The number of five-dollar bills are 52 and ten-dollar bills are 73.

The parameters are that the total number of five and ten-dollar bills equals 125 dollars.

Let x denote the number of five dollar bills and let y denote the number of ten dollars bills. Thus;

Total number of bills is;

x + y = 125      --- (1)  

The total value of all bills is $990  

Thus, we have;

5x + 10y = 990  

Divided by 5 into both sides  to get;

x + 2y = 198  ----- (2)

Now solve (1) and (2) for x and y values

Subtract eq (1) from eq (2) to get;

x + 2y - x - y = 198 - 125

y = 73

Substitute y = 73 in (1)

x + 73 = 125

x = 52

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The balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

Let t be the number of seconds since the balloons took off, and Hp(t) and Hg(t) be the altitude of the purple and gold balloons respectively at time t.

We know that:

Hp(t) = 0 + 2.5t (the purple balloon starts at sea level and climbs at a rate of 2.5 m/s)

Hg(t) = 1515 + 222t (the gold balloon starts 1515 m above sea level and climbs at a rate of 2*22 m/s)

We want to find the time t when the balloons are at the same altitude, so we can set Hp(t) = Hg(t) and solve for t:

0 + 2.5t = 1515 + 222t

2.5t = 1515 + 222t

2.5t - 222t = 1515

0.5t = 1515 - 1515

t = 0

So the balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

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The two processes that caused the puddle to form and then disappear were evaporation and infiltration.

Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.

Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.

The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.

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Answer: you can solve for x using the Pythagorean theorem:

Step-by-step explanation. let's say your questing in sides are 12 and 40 what is x. you have side x, y, and h. y=12 h=40. now you solve using the Pythagorean theorem x2 + y2 = h2. (The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).)

Answer:

3x (1 - 3)

Explanation in detail:

= 3x - 9x²

= 3x (1 - 3x) (1 - 3x)

The length of GH is about 7.3 units. The solution has been obtained by using the formula of distance between two points.

What is distance between two points?

The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation

[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]  is used to calculate the distance between two points. One can use this formula to get the separation between any two points on an x-y plane or coordinate plane.

We are given two points as G(-9,-4) and H(-2,-6)

Using the distance formula,

[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]

[tex]d=\sqrt{(-2 +9)^{2} + (-6 +4)^{2} }[/tex]

[tex]d=\sqrt{(7)^{2} + (-2)^{2} }[/tex]

[tex]d=\sqrt{49 + 4 }[/tex]

[tex]d=\sqrt{53 }[/tex]

d = 7.3 units

Hence, the length of GH is about 7.3 units.

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In a scenario when X is replaced with (x-3) then it means that the value of x will be reduced by 3 units.

This is referred to as the process which involves the replacement of a word , number or phrase with another when performing different types of operations.

During an arithmetic operation and X is replaced with (x-3), then it means that the value of X will be reduced by 3 units and an example is given below:

Let's assume X is 5 and we substitute it with (x-3) will therefore become (5-3) = 2. This depicts that there has been a reduction by 3 units thereby making it the correct choice.

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a. More than 3,000 people are killed yearly in crashes involving large trucks or buses.

The stopping distance of a large truck or bus is determined by calculating the kinetic energy (K) of the vehicle, the coefficient of friction (μ) between the road and the tires, and the weight (W) of the vehicle. The formula for calculating the stopping distance is K = (μ * W2) / 2g, where g is the acceleration due to gravity. This means that the heavier the vehicle and the lower the coefficient of friction, the longer the stopping distance. Since large trucks and buses are heavier than cars, they have a longer stopping distance and are more likely to be involved in fatal crashes.

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The ascending order of the given data is-

80g < 12254g < 0. 845kg <  1. 2kg.

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The calculator short hand notations are;

a) -4E3

b) -3E4

c) 3E4

d) 4E3

We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.

It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.

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Answer: You have a 1/6 chance to roll a 2 when you role a dice since there is 6 sides

Step-by-step explanation:

a. The length of x is 4 cm.

b. The area of the shaded face in the triangle prism is 36 cm².

The net of the triangular prism shows that the shaded face is a rectangle.

The side labelled x is the same as the side of the triangular face with a side of 4 cm, when the net of the triangular prism is folded.

Therefore:

a. Length of x = 4 cm

b. Area of shaded face = area of rectangle = length × width

= 9 × 4

= 36 cm²

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The member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

What is Equation of a straight line ?

The equation of a straight line as follows : y = mx+c where m is slope of a straight line and c is y-intercept.

Given that the equation of the line of best fit is given by

Let x represents the amount of time in minutes.

Let y represents the temperature in degrees Fahrenheit.

From the equation of line of best fit, it is obvious that the temperature that a person can tolerate is 173 degrees Fahrenheit at 0 minutes.

Because the y - intercept represents the temperature when the x - value is zero.

So,  the member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

Therefore, The member can tolerate a temperature of 173° Fahrenheit for 0 minutes

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This type of data is cross-sectional data.

In statistics and econometrics, cross-sectional data, or a cross-section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.

Time series data, in which the same small-scale or aggregate entity is seen multiple times in time, differs from cross-sectional data. A different kind of data called panel data (also known as longitudinal data) combines the concepts of cross-sectional and time series data and examines how the topics (firms, people, etc.) develop throughout a time series. Panel data differs from cross-sectional data that has been pooled over time.

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Using exponents rule the missing term in the equation 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____ is found to be 7^(-29).

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The given expression is - 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____

Let the missing term be x.

Then the equation is -

7^(-147) × 7^(98) = 7^(18) × 7^(-38) × x

Since, the base of the exponents is same, so apply the operations on the powers of the base.

The exponent rule is - a^(b) × a^(c) = a^(b + c)

Write the equation according to the rule -

7^(-147 + 98) = 7^(18 - 38) × x

Now perform the arithmetic operation of addition and subtraction -

7^(-147 + 98) = 7^(18 - 38) × x

7^(-49) = 7^(-20) × x

The exponent rule is - a^(b) / a^(c) = a^(b - c)

Write the equation according to the rule -

x = [7^(-49)] / [7^(-20)]

x = 7^[-49 - (-20)]

x = 7^(-49 + 20)

x = 7^(-29)

Therefore, the missing term is x = 7^(-29).

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Select the correct answer from the drop-down menu. Find the missing term. 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____

Answer:

5:38 am

Step-by-step explanation:

Since the train arrived at it's final destination at 12:28 pm and it took two hours to get there. Subtract two hours from the final destination time and it's 10:28 am. Then it took 4 hours and 50 minutes to arrive to Wildgrove, so subtract four hours of the time when the train arrived. It is now 6:28 am. Subtract fifty minutes from that and you would get 5:38 am.

p.s. There are time calculators online if you need an answer if this is kinda hard to understand

The value of x in the figure is 20

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Given;

Ratio of first line segment = 4.4/6.3

Ratio of other line segment= 14.08/x

Now, to find the value of x

4.4/6.3 = 14.08/x

4.4x= 14.08x6.3

x=14.08x6.3/4.4

x=20.16

Therefore, according to ratio x will be equal to 20

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The simplify of given equation 11k/ (55k^2+ 22k) is 1/(5k+2).

Given,

[tex]\frac{11x}{55^{2}+22k }[/tex]  We have to simplify in rational expression

The common factor is 11. So, we have to pick the common factor from the equation.

= [tex]\frac{11x}{55^{2}+22k }[/tex]

= [tex]\frac{1}{5x + 2}[/tex]

Therefore the simplification of given equation is 1/(5k+2).

Reasonable expressions resemble fractions with variable denominators (and often numerators too). An example of a rational expression is x 2 x + 3 dfracx2x+3 x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction.

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The required function that represent the given situation is y = 10x + 350.

In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.

Rental fee is $350 for the first week and $10 for each additional day or any portion of a day.

So, The equation that represent this problem is;

Let cost y (in dollars) to rent the dumpster for x days.

y = 350 + 10x (y in dollar)

y = 10x + 350

Here, slope of function is 10 and y- intersect is 350.

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Where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.

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She left the 1/6 yards pipes.

Now, According to the question:

Rose bought a length of 4/6 copper pipe.

She used 1/2 yard to repair a water line in her house.

To find how much pipe does she have left?

Pipes available = 4/6 yards

Pipes used = 1/2 yards

Pipes left = total pipes bought - she doesn't suit that way

Pipes left = Total pipes available - pipes used

= 4/6 yards - 1/2 Yards

= 4-3/6

= 1/6 yards

Pipes left = 1/6 yards

Hence,  She left the 1/6 yards pipes.

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The given question is incomplete, complete question is:

Rose bought a length of 4/6 copper pipe. She used 1/2 yard to repair a water line in her house. How much pipe does she have left? Solve this problem any way.

The length of every median in an equilateral triangle whose side length is 5 is; 4.33

In geometry, a median of a triangle is defined as a line segment joining a vertex to the midpoint of the opposite side which therefore bisects that side.

This tells us that every single triangle has exactly three medians, with one from each vertex, and as a result they all intersect each other at the centroid of the triangle.

The median joins a vertex and the opposite side's midpoint. Thus;

side = 5

half side = 5/2 = 2.5

Using Pythagoras theorem;

a² + b² = c²

Thus;

2.5² + b² = 5²

b² = 18.75

b = √18.75

b ≈ 4.33

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The speed required to obtain this decrease in travel time is 360 mph.

Formula between speed, distance, and travel time

v = d/t

The formula to calculate distance is

d = v × t

In the first condition

d₁ = v₁ × t₁

720 = v × t₁

t₁ = 720/v

In the second condition

d₂ = v₂ × t₂

720 = (v + 40) (t₁ - 0.2)

720 = (v + 40) (720/v - 0.2)

720 = v (720/v - 0.2) + 40 (720/v - 0.2)

720 = 720 - 0.2v + 28,800/v - 8

0.2v + 8 - 28,800/v + 720 - 720 = 0

0.2v + 8 - 28,800/v = 0

0.2v² + 8v - 28,800 = 0

v² + 40v - 144,000 = 0

Factorize quadratic equations

v² + 40v - 144,000 = 0

v² + 400v - 360v - 144,000 = 0

v (v + 400) - 360 (v + 400) = 0

(v + 400) (v - 360) = 0

v + 400 = 0   or   v - 360 = 0

v = - 400              v = 360 mph

(negative speed is impossible)

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The required value of side q is  117. 05 cm for the triangle ΔQRS.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle  ΔQRS, r = 83 cm, mm∠R=161° and mm∠S=5°

To find the length of the side q,

The third angle can be calculated using the angle sum property as;

angle Q + angle R + angle S = 180 degrees

angle Q + 161 degrees + 5 = 180 degrees

angle Q = 180 - (166) degrees

angle Q = 14 degrees

To find the length of q we shall apply the Sine rule.

q / Sin Q = r / Sin R

q / Sin 14 = 83 / Sin 161

Now  cross multiplication we will get;

q = (83 x Sin 14 ) / Sin 161

q = 117. 05 cm (approximately)

So,  the length of q is  117. 05 cm.

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4 m/s is the final speed of the 3.0 kg cart.

When two bodies of different masses move together each other and have a head-on collision, they travel in the same or different directions after a collision. This phenomenon is called the conservation of momentum.

The external force is not working here, so the initial momentum is equal to the final momentum. For elastic collision, the final velocities are different for both bodies.

m₁u₁ +m₂u₂ = m₁v₁ +m₂v₂

A 2.0  kg cart moving right at 5.0  m/s on a frictionless track collides with a 3.0 kg cart initially at rest. The 2.0 kg cart has the final speed of 1.0 m/s  to the left.

Substitute the values, m₁ = 2kg, m₂ =3kg, u₁ =5 m/s and u₂ =0 m/s, then the final velocity will be

3x0 +2x5 = -2x1 + 3v₂

v₂ = 4 m/s

Thus, the final velocity 3.0  kg cart is  4 m/s.

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