WORTH 50 POINTS 4. Tom decided to join Platinum Gym because of its new equipment. At the grand opening, the manager announced that 124 people had signed up for gym membership. As part of the grand opening event, the manager waived the registration fee for 50 random people.
(a) Write an expression to represent how much money Platinum Gym will make from the grand opening memberships. Simplify the expression and label any variables.
(b) After 6 months, how much money will Platinum Gym have made from the original 124 people who joined at the grand opening, assuming that all 124 people are still members? Show your work.

The speed of Natalie in miles per hour is 1.2 mph.

The given parameters;

The speed of Natalie in miles per hour is obtained by dividing the distance covered by Natalie by the time of motion.

The value of this speed is  calculated as;

[tex]speed = \frac{distance }{time} \\\\speed = \frac{3/5}{1/2} = \frac{3\times 2}{5} = \frac{6}{5} = 1.2 \ mph[/tex]

Thus, the speed of Natalie in miles per hour is 1.2 mph.

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Final answer:

The selling price for the running shoes should be $40.79 to include the cost price of $22.29 and the desired profit of $18.50.

Explanation:

To calculate the selling price of the running shoes to achieve a desired profit of $18.50, we simply add the cost of the shoes to the desired profit.

The cost of the shoes is $22.29, and the store owner wants to make a profit of $18.50.

Therefore, the selling price should be:

Cost of shoes: $22.29

Desired profit: +$18.50

Total selling price: $40.79

The store owner should set the selling price at $40.79 to make a profit of $18.50 on the pair of running shoes.

Relations are subsets of products A×BA×B where AA is the domain and BB the codomain of the relation.

A function ff is a relation with a special property: for each a∈Aa∈A there is a unique b∈Bb∈B s.t. ⟨a,b⟩∈f⟨a,b⟩∈f.

This unique bb is denoted as f(a)f(a) and the 'range' of function ff is the set {f(a)∣a∈A}⊆B{f(a)∣a∈A}⊆B.

You could also use the notation {b∈B∣∃a∈A[⟨a,b⟩∈f]}{b∈B∣∃a∈A[⟨a,b⟩∈f]}

Applying that on a relation RR it becomes {b∈B∣∃a∈A[⟨a,b⟩∈R]}{b∈B∣∃a∈A[⟨a,b⟩∈R]}

That set can be labeled as the range of relation RR.

Answer:

A. C=2.50v

B. C=2.50x22

C=55

Step-by-step explanation:

list all the possible numbers:

10 - cant be divisible by 0

11 - can be divided by 1 and 1

12 - can be divided by 1 and 2

13 - cant be divided by 3

14 - cant be divided by 4

15 - can be divided by 1 and 5

16 - cant be divided by 6

17 - cant be divided by 7

18 - cant be divided by 8

19 - cant be divided by 9

20 - cant be divided by 0

21 - cant be divided by 2

22 can be divided by 2 and 2

23 - cant be divided by 3

24 - can be divided by 2 and 4

 the numbers are  11, 12, 15,  22 and 24

Answer: The Answer is 16

The system of equations x+3y+5z=45, 6x-3y+2z=-10, -2x+3y+8z=72 can be solved algebraically to get the values x=6, y=12, z=-1.

First, we can combine the first and the second equations and the first and third equations to cancel out y.

Doing so, we get: x+3y+5z+6x-3y+2z=45-10 and x+3y+5z-2x+3y+8z=45+72

The new equations simplify to 7x+7z=35 and -x+13z=117

Next, we can divide the first new equation by 7 to get x+z=5. Subtract x from both sides to get z=5-x.

Substitute z=5-x into the second equation to find the value of x.

Performing these substitutions gives x=6. Substituting x=6 back into the equation z=5-x gives z=-1.

Finally, we substitute x=6 and z=-1 back into the original equations to solve for y: y=(45-6-5(-1))/3 = 12

So, x=6, y=12, z=-1 are the solutions to the system of equations.

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The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52).

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

y = − 56x − 4

Let x = 1, the value of y will be

y = − 56 (1) − 4

y = − 56 − 4

y = − 60

Let x = − 1, the value of y will be

y = − 56(−1) − 4

y = 56 − 4

y = 52

The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52). Then the diagram of the line is given below.

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Answer:

8(10) + 8(9)

2(9) + 2(3)

Step-by-step explanation:

The result of the expression 42-24 divided by 6, calculated using the 'Order of Operations' rule, is 38.

You've asked to solve this mathematical expression: 42-24 divided by 6. To do this correctly, we must follow the 'Order of Operations,' often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In your problem, the operations are Subtraction and Division. Following the PEMDAS rule, we perform Division before Subtraction. Therefore, first perform 24 divided by 6, which is 4. Then, subtract that result from 42. In the end, 42 minus 4 gives us 38 as the final answer.

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Answer:

[tex]52.5\ miles[/tex]

Step-by-step explanation:

we know that

The scale on the map is equal to

[tex]\frac{2}{15}\frac{cm}{miles}[/tex]

so

by proportion

Find how many miles are [tex]7\ cm[/tex] on the map

[tex]\frac{2}{15}\frac{cm}{miles}=\frac{7}{x}\frac{cm}{miles}\\ \\x=15*7/2\\ \\x=52.5\ miles[/tex]

Answer:32.39

Step-by-step explanation: cost of movie is 19.9

Cost of earphone is 12.49

Adding both cost is 19.9+12.49

=32.39

The cost before tax deduction is 32.39

The value of -4 squared (-4^2) is -16 because the exponent only applies to 4, not the negative sign. To include the negative in the exponent, use parentheses like (-4)^2 = 16.

The value of -4^2 is -16. This is because the exponent applies only to the number 4 and not the negative sign in front of the 4. In other words, -4^2 means -(4*4) which is -16. To make the negative part of the base, the operation should be placed in parentheses like (-4)^2 = 16.

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The complete question is given below:

The value of -4^2 is _____.  

A hiker has the following items:

A sleeping bag that weighs 3.4 lb

A Camping bag that weighs 4.6 lb

And a water bottle that weighs 2.2 lb.

The expression would be:

3.4x + 4.6x + 2.2x = x

Where x is the weight that each x hikers are carrying.

You just need to add the three items and the answer would be 10.2 pounds.

We want to find the total weight that each hiker carries by adding the weights of all individual items that they carry. And then we want an expression for the total weight that x hikers carry.

These items can be seen in the image at the end of the answer.

We will see that the total weight carried by x hikers is given by:

W(x) = (10.2lb)*x

--------------------------------

First, let's find the weight that each hiker carries.

Each hiker carries:

The total weight is:

T = 3.4 lb + 4.6 lb + 2.2 lb = 10.2 lb

Then if each hiker carries 10.2 lb of weight, and there are x hikers, the total weight carried by them will be x times 10.2 lb

We have:

W(x) = (10.2lb)*x

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Answer: The share would be approximately $285, $175, $141 respectively.

Step-by-step explanation:

Since we have given that

Number of box tops collected by Mr. Aceves's class = 3760

Number of box tops collected by Mrs. Baca's class = 2301

Number of box tops collected by Mr, Canyon's class = 1855

We first find the ration of box tops of Mr. Aceves, Mrs. Baca and Mr. Canyon respectively:

3760:2301:1855

Total = 3760+2301+1855=7916

Total amount to be share among them as a prize = $600

Mr. Aceves's share is given by

[tex]\dfrac{3760}{7916}\times 600\\\\=284.99\\\\\approx 285[/tex]

Mrs. Baca's share is given by

[tex]\dfrac{2301}{7916}\times 600\\\\=175.08\\\\\approx 175[/tex]

Mr. Canyon's share is given by

[tex]\dfrac{1855}{7916}\times 600\\\\=140.60\\\\\approx 141[/tex]

Hence, the share would be approximately $285, $175, $141 respectively.