Tom and his best friend, Edward, are seeking to join a gym. Tom saw on television that
Platinum Gym was having a grand opening in a few months and is considering a
membership there. Platinum Gym charges a one-time registration fee of $60, and
membership is $20 monthly. Tom's best friend, Edward, says he plans to join Super Fit
because it only charges $10 monthly with a one-time registration fee of $150.

(a) Write an expression to represent the membership cost of Platinum Gym for x
months.

(b) Write an expression to represent the membership cost of Super Fit for x months.

(d) Is there a membership period for which Tom and Edward would pay the same
amount? If so, how long would this membership be and how much would it cost? Show
your work (2 points for showing work, 1 points for answer).

Answer:

A

Step-by-step explanation:

18/16=1.125

54/50=1.05

Therefore, Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50. So A is the correct answer.

Hope that helped!

The angle that is a vertical angle to AEB is CED.

When we have the intersection of two lines, we define the vertical angles as the pair of angles that share a vertex and don't share sides.

So these angles are only connected by the vertex.

So a vertical angle to AEB should also have the vertex E, and no common sides to AEB, the only angle that meets that requiriment is CED.

Then we conclude that the vertical angle to AEB is CED.

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Answer:

corresponding Angles

Step-by-step explanation:

2x+16=3x-7

16-7=3x-2x

9=x

Answer:

x = 23

Step-by-step explanation:

The two angles shown in the diagram are corresponding angles. Therefore, the angles are congruent. 2x + 16 = 3x - 7; simplify to get x = 23

Answer: f(-5)=-11 g(-3)=-52

Step-by-step explanation:

Answer:2

Step-by-step explanation: To solve the equation -2 1/3x = -1 3/4, we need to isolate the variable x on one side and simplify the equation.

First, we need to convert both sides to have the same denominator. We can choose the least common multiple of 3 and 4, which is 12.

-2 1/3x = -1 3/4

-2 1/3 * 4/4 * x = -1 3/4 * 3/3

-8/3 x = -5 1/3

Next, we isolate x by dividing both sides by -8/3:

(-8/3) x / (-8/3) = -5 1/3 / (-8/3)

x = (5 1/3) / (8/3)

x = (5 1/3) * (3/8)

Finally, we simplify the fraction to get the final solution:

x = (5 1/3) * (3/8)

x = (5 * 3 + 1 * 3) / 8

x = 16 / 8

x = 2

Therefore, the solution to the equation -2 1/3x = -1 3/4 is x = 2.

The equation for the discounted price should be:

A' = $25*(1 - 20%/100%) = $20

If we have an initial value A, and we decrease it by X (a percentage) then:

The discounted amount is:

D = A*(X/100%)

The new value is:

A' = A*(1 - X/100%)

So, if the initial value is $25 and there is a discount of the 20%, the new value of the item will be:

A' = $25*(1 - 20%/100%)

A' = $25*(1 -0.2)

A' = $25*0.8 = $20

That is the correctly discounted price.

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The height of his kite on this blustery day if an angle of elevation is 40°, 64.3 meter

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

Edward is flying a kite on a beautiful sunny day at the beach,

An angle of elevation of 40°

kite string let out = 100 meter

The height of his kite = ?

Suppose, height  = h

if we consider horizontal distance of kite from the Edward and Vertical distance from the Edward

It will form a right angle triangle

Now, we can use sine formula in the right angle triangle,

α =  40°

L  = 100 meter

h  = ?

It is known that,

sinα  = height/hypotenuse  

sin40° =  h/100

h  = 0.643 x 100

    =  64.3

Hence, the height of kite is 64.3 meter

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Answer:

0.00000016

Step-by-step explanation:

Raise 0.02 to the power of 4.

0.000000256.

The expression (0.02)^4 represents the fourth power of 0.02. In mathematical terms, "^" symbol is used to indicate exponentiation, so (0.02)^4 is equal to 0.02 multiplied by itself 4 times.

To calculate this expression, we can multiply 0.02 by itself 4 times:

0.02 * 0.02 * 0.02 * 0.02 = (0.02)^4 = 0.000000256

So, the result of (0.02)^4 is approximately equal to 0.000000256.

For the graph of the cubic root function, the function has no intercept.

The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.

Given the graph of the cubic root function,

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

the function of the graph is y = ∛x

when x = 0, y = 0

the function does not have any intercept.

Hence option C is correct.

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The volume of the given figure which is the sum of two rectangular prism would be = 1,490cm³

The formula the is used to calculate the volume of a rectangular prism = v= length×width×height

There are two rectangular prism:

For the smaller prism;

where;

length= 6cm

height= 2cm

width= 5cm

volume = 6×2×5= 60cm³

For the larger prism;

length= 22cm

height= 5cm

width= 13cm

volume = 22×5×13 = 1,430cm³

The total volume of the figure = 1430 +60 = 1,490cm³

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Answer:154

Step-by-step explanation:

12+12=24 24+1=25 25-10=15

The measure of angles for questions 19) and 20) are x = 32° and x = 115° respectively using the triangle sum and exterior angle theorem.

question 19 has 2 isosceles triangles and the measure of x can be derived by equating one of the base angles of the smaller triangle to the sum of its 2 opposite angles as follows;

let y be one of the base angles of the smaller triangle so that;

2y = 180 - 56 {sum of interior angles of a triangle}

2y = 124

y = 62

hence;

62 = x + x {exterior angle of a triangle equals the sum of its two opposite angles}

2x = 62

x = 31°

For question 20, we first find the two opposite angles of x as follows;

180 -(62 + 50) = 68

180 - (53 + 80) = 47

x = 68 + 47

x = 115°

Therefore, the measure of angles for questions 19) and 20) are x = 32° and x = 115° respectively using the triangle sum and exterior angle theorem.

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Answer: All values/solutions of P must be greater than 2 to be true to the inequality 10p-8>12

Step-by-step explanation:

When solving inequalities, we treat it like an equation, solving for the variable, in this case, p.

10p - 8 > 12

Lets isolate p

10p - 8 > 12

       +8   +8

10p > 20

/10     /10

p > 2

After solving, we now know that all values of P must be greater than 2.

Answer: x=7

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Rate1 = 1 pool / 85 min = 1/85

rate2 = 1 / 40

now find how long it will take with the combined rates

pool / (rates) = time

1 / ( 1/85 + 1/40)   = 27.2 min

The value of x in the given proportion is determined as 10.56.

The value of x in the given proportion is calculated by applying the following equation as shown below.

1650 = x ( 156.25 )

where;

The value of x in the given expression is calculated as follows;

x = ( 1650 ) / ( 156.25 )

x = 10.56

Thus, the value of x in the proportion is obtained by dividing both sides of the equation by 156.25 and thereby making the unknown ( x ) the subject of the formula.

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Saving account is an example of a demand account.

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The circumference of the circle is 54. 64 mm. Option B

It is important to note that the formula for calculating the circumference of a circle is expressed as;

C = 2πr

Given that the parameters are;

From the information given, we have that;

Circumference = 2 × 3.14 × 8.7

Now, multiply the values, we get;

Circumference = 54. 636

Approximate to two decimal place, we get;

Circumference = 54. 64 mm

Hence, the value is 54. 64 mm

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Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767

There are several applications for facial recognition technology, including security and surveillance, access control, marketing, and social media. The most popular type of facial recognition technology makes use of biometrics, which track and examine the physical and behavioral traits of individuals.

When issuing identity documents, facial recognition is utilized, most frequently in conjunction with other biometric technology like fingerprints (preventing ID fraud and identity theft). At border crossings, face match is used to match the portrait on a digital biometric passport with the owner's face.

If the server needs all of the 10 million functioning to operate as intended, the overall reliability of the system is given by the product of each component's individual reliability:

S = [tex]c_{1} * c_{2} * c_{3} * c_{4} * c_{5} * c_{6} * c_{7} * c_{8} * c_{9} * c_{10} *[/tex]

If the system needs to have a reliability of 0.93, and all components have the same reliability, the required reliability for the components is:

20 = [tex]c^{10}[/tex]

c = [tex]\sqrt[10]{20}[/tex]

c = 1.34928284767

Therefore,

Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767

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Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767

There are several applications for facial recognition technology, including security and surveillance, access control, marketing, and social media. The most popular type of facial recognition technology makes use of biometrics, which track and examine the physical and behavioral traits of individuals.

When issuing identity documents, facial recognition is utilized, most frequently in conjunction with other biometric technology like fingerprints (preventing ID fraud and identity theft). At border crossings, face match is used to match the portrait on a digital biometric passport with the owner's face.

If the server needs all of the 10 million functioning to operate as intended, the overall reliability of the system is given by the product of each component's individual reliability:

S =

If the system needs to have a reliability of 0.93, and all components have the same reliability, the required reliability for the components is:

20 =

c =

c = 1.34928284767

Therefore,

Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767

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The graph represents this system of inequalities:

F. y ≤ −x + 4

G. y ≤ 3x − 1

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line of f(x) which passes through the points (0, 4) and (4, 0) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (4 - 0)/(0 - 4)(x - 4)

y - 0 = -1(x - 4)

y = -x + 4

Therefore, an inequality representing the line of f(x) is y ≤ -x + 4

For the line of g(x), we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-1) = (5 - (-1))/(2 - 0)(x - 0)

y + 1 = 3(x - 0)

y = 3x - 1

Therefore, an inequality which represents the line of g(x) is y ≤ 3x - 1.

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Complete Question:

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line. The graph represents which system of inequalities?

y ≤ −3x − 1

y ≤ −x − 4

y > −3x + 1

y ≤ −x − 4

y < 3x − 1

y ≤ −x + 4

y ≤ 3x − 1

y ≥ −x + 4

The probability that a randomly selected person from the city will be a woman is 17,000 / 190,000, or approximately 0.089.

1. Calculate the total number of women: 17,000

2. Calculate the total population of the city: 190,000

3. Divide the number of women by the total population: 17,000 / 190,000

4. The probability is approximately 0.089

The probability that a randomly selected person from the city will be a woman is 17,000 / 190,000, or approximately 0.089.

The probability that a randomly selected person from the city of Akron, Ohio will be a woman is 0.089. This means that out of every 100 people, approximately 8.9 of them will be female. The city has a population of 190,000 and 17,000 of them are female. This means that approximately 8.9 percent of the city's population is female.

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Dani collecting rainwater in a 1 litre jug. So much water did Dani collect on Wedneday is 530 ml.

These are the specified parameters:

Monday = 220 ml

Tuesday = 1/4 litre

Wednesday = 0.1 litre

Fill the jug = 1 liter

A lot of water that has not been collected

= Fill the jug - (monday + tuesday + wednesday)

= 1 litre - (220 ml + 1/4 litre + 0.1 litre)

= (1 × 1000) ml - (220 ml + (1/4 × 1000) ml + (0.1 × 1000) ml)

= 1000 ml - (220 ml + 250 ml + 100 ml)

= 1000 ml - 570 ml

= 430 ml

Much water did Dani collect on Wedneday

= 0.1 litre + 430 ml

= 100 ml + 430 ml

= 530 ml

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The best first step to begin to simplify the equation -2(x + 3) = -10​ is:

Dividing both sides of the equation by -2 to get x + 3 = 5

As per the given data, the equation is given by -2(x + 3) = -10

We have to determine the best first step in solving the equation:

-2(x + 3) = -10​

Firstly we start by distributing -2 in the bracket (x + 3)

-2x - 6 = -10

Or

-2(x + 3) = -10​

Also if we divide both sides of the equation by -2, we get

x + 3 = 5

Now, we can easily solve the equation.

Hence, the first best step to begin to simplify the equation -2(x + 3) = -10​ is:

Distributing -2 in the bracket (x+3)

We get -2x -6 = -10

Or Dividing both sides of the equation by -2

We get x + 3 = 5

Here in options given x + 3 = 5

Hence option (c) is correct.

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The event that "a or b but not both" P{(A∩B) ∪ (A ∩B)}

= P(A∩B) + P(A∩B) - P(A∩B∩A ∩B)

In this question, we will use the addition rule of the probability to calculate the required probability. The probability is a positive quantity from zero to one inclusively. The negative probability of an event does not exist

This is for independent events

P(A U B): This is A or B or both:

P(A n B): This is A and B.

P(A U B) = P(A) + P(B) - P(A n B)

P( A n B) = P(A) x P(B)

Hence:

A or B but not both:

P(A U B) = P(A) + P(B) - P(A n B) - P(A n B) = P(A) + P(B) - 2 x P(A n B)

can also be written in terms of the conditional probability P(A|B)

So we can write

P{(A∩B) ∪ (A ∩B)}

= P(A∩B) + P(A∩B) - P(A∩B∩A ∩B)

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The root of the expression is 3/4

The index form of a number can be described as that number written in the nature of an exponential expression.

They are also forms that are written as a single numbers raised to another number.

Exponents explains the number of times to multiply the base of by itself to simply or evaluate the expression.

Note that the cube root of a number is the value which when multiplied by itself thrice gives the original value.

Given the expression;

[tex]\sqrt[3]{\frac{27}{y} }[/tex]

Find the cube root

3/4

Hence, the value is 3/4

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f(-2) and f(2) does not exist. Limit when x tend to -2, 0 and 4 does not exist. f(0) = 5 and f(4) = -1. Limit when x tend to 2 converges to 0.5.

f(-2) does not exist as shown in the figure there is no definite value at -2. Also limit does not exist at x = -2 as right limit approaches positive infinity where left limit approaches negative infinity.

f(0) equals 5 and not 3.5 as we can see that at 3.5 it is a hole implying it is not defined, while at 5 it is a solid dot. Limit does not exist at f(0) as the left limit approaches 3.5 and the right limit approaches 5.

f(2) does not exist as there is a hole at that point in the graph. Limit as x tend to 2 approaches 0.5 as both right and left limit approaches 0.5.

f(4) equals -1 as the solid dot is at that point. As x tend to 4 the limit diverges to positive infinity implying the limit does not exist.

--The question is not readable, answering to the question below and graph attached--

"Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.)

(a) f(−2)

(b) lim x→−2 f(x)

(c) f(0)

(d) lim x→0 f(x)

(e) f(2)

(f) lim x→2 f(x) 0.5

(g) f(4)

(h) lim x→4 f(x) "

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The length of the line through the center that touches two points on the edge of the circle.

The spikes extending from one end to the other end through the center of a bicycle wheel are an illustration of diameter. We may compare this to the diameter of a circle, as the diameter is the line segment that runs from one end of the circle to the other, passing through the center.

The diameter of a circle goes from edge to edge and cuts through the center, whereas the radius travels from center to edge. The diameter of a circle divides the form in half.Every circle have infinite no. of diameter.

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The product of the given expressions is 2x squared + 7x minus 4.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expressions are 2x - 1 and x + 4.

We have to multiply both the expressions.

(2x - 1) (x + 4) = (2x . x) + (-1 . x) + (2x . 4) + (-1 . 4)

                      = 2x² - x + 8x - 4

Adding the like terms together,

(2x - 1) (x + 4) = 2x² + 7x - 4

Hence the multiplication of the given expression gives the expression 2x² + 7x - 4.

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The conversion from torr to atm involves multiplying the torr value by a conversion factor of 1/760. This is because 1 atm is equal to 760 torr.

Given, that convert torr to atm.

Atmosphere (atm) and torr are both units of pressure measurement. Torr is a unit of pressure in the centimeter-gram-second (CGS) system, while atm is a unit of pressure in the International System of Units (SI).

The conversion from torr to atm involves multiplying the torr value by a conversion factor of 1/760. This is because 1 atm is equal to 760 torr.

For example:

To convert 2.77 atm to torr, multiply 2.77 by 760, which gives 2,108 torr.  In conclusion, 2.77 atm is equal to 2,108 torr.

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The probability of winning chess tournament is 0.375.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Let A₁ be the event of playing an opponent of type i.

A₁ = playing the half of the opponent pool where the probability of winning

P (winning∣A₁) = 0.3

A₂ = playing the half of the opponent pool type 2, where the probability of winning P(winning∣A₂) = 0.4

A₃ = playing the half of the opponent pool type 3, where the probability of winning P(winning∣A₃) =0.5

By total probability theorem, we get,

P(winning)=P(A₁) P(winning∣A₁) +P(A₂) P(winning∣A₂) +P(A₃) P(winning∣A₃)

P(winning)=50%×0.3+25%×0.4+25%×0.5

P(winning)=0.375.

The probability of winning chess tournament is 0.375.

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The probability of winning the game depends on the type of opponent. If the opponent is of type 1, the probability of winning is 0.3; type 2, 0.4; and type 3, 0.5.

The probability of winning the game depends on the type of opponent. There are three types of opponents: type 1, type 2, and type 3. Against type 1 opponents, the probability of winning is 0.3. Against type 2 opponents, the probability of winning is 0.4. Against type 3 opponents, the probability of winning is 0.5. As the opponent is chosen randomly, the probability of winning is the average of all three probabilities. This means that the probability of winning the game is 0.4. To calculate this, we first add the probabilities of winning against each type of opponent: 0.3 + 0.4 + 0.5 = 1.2. We then divide this result by the number of opponent types (3): 1.2/3 = 0.4. This means that the probability of winning the game is 0.4.

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