Final answer:
By setting up and solving an equation based on the monthly membership and per-session training costs at both Silver Gym and Fit Factor, it's determined that Sarah would need to buy 3 personal training sessions for the total cost at the two gyms to be equal.
Explanation:
To find how many personal training sessions Sarah would have to buy to make the total cost at Silver Gym and Fit Factor equal, we'll set up an equation. Let x be the number of personal training sessions.
At Silver Gym, the total cost is $45 (membership) + $25x (personal training sessions).
At Fit Factor, the total cost is $75 (membership) + $15x (personal training sessions).
Setting these two expressions equal to each other gives us the equation:
45 + 25x = 75 + 15x.
To solve for x, first subtract 15x from both sides, giving: 10x = 30. Then divide both sides by 10 to isolate x, resulting in x = 3.
Therefore, Sarah would have to buy 3 personal training sessions in one month for the total costs at both gyms to be equal.
Answer:
3 sessions
Step-by-step explanation:
You want to know the number of personal training sessions Sarah would have to buy to make the total costs the same at Silver Gym and Fit Factor. Silver Gym costs $45 per month and $25 per session, while Fit Factor costs $75 per month and $15 per session.
DifferencesSilver Gym costs $25 -15 = $10 more per personal training session, but $75 -45 = $30 less for the monthly fee. This means it takes $30/$10 = 3 sessions for the difference in fees to be made up by the difference in session costs.
Sarah would have to buy 3 sessions for the total cost to be the same.
EquationsIf you need to see this using equations, we can write the cost equations as ...
S = 45 +25x . . . . . . . . cost for x sessions at Silver Gym
F = 75 +15x . . . . . . . . . cost for x sessions at Fit Factor
Setting these equal, we have ...
S = F
45 +25x = 75 +15x
25x -15x = 75 -45 . . . . . . . subtract 45+15x from both sides
10x = 30
x = 30/10 = 3 . . . . sessions for equal cost
Sarah would have to buy 3 sessions for the total cost to be the same.
__
Additional comment
These "break even" problems usually have a higher fixed cost associated with a lower per use cost, and vice versa. The costs are the same when the number of uses, multiplied by the difference in use cost, comes to the same amount as the difference in fixed costs. Here, the $10 difference in session cost, times 3 sessions, is equal to the $30 difference in monthly membership fee.
Anthony ‘s family went out to dinner. They left at the. Time 5:05 pm any they returned home at 6:52p.m
How long was Anthony ‘s family gone
Write a story problem to represent 5 divided by 1/4
The problem can be seen below, we will see that the quotient between the given numbers is 20.
How to write the problem?Here we want to divide 5 by 1/4.
An example of this can be: Assume that you have $5, and you want to buy pieces of wood (to make little houses for birds) such that each piece costs $(1/4).
How many pieces can you buy?
To solve this, we need to take the quotient between 5 and (1/4), this gives:
[tex]\frac{5}{1/4} = 20[/tex]
You can buy 20 pieces.
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Your doctor told you to eat 25 grams of fiber each day.
You had 4 grams of fiber for breakfast.
What percent of the 25 grams of fiber have you eaten so far?
Consider the expression 4n3 + 3n2 + 2n + 1. What is the coefficient of n2?
Answer:
Coefficient of n² is 3.
Step-by-step explanation:
Given : 4n³ + 3n² + 2n + 1.
To find : What is the coefficient of n².
Solution : We have given 4n³ + 3n² + 2n + 1.
Coefficient : A numerical or constant quantity placed before and multiplying the variable in an algebraic expression
Example : 4 in 4x² .
In 4n³ + 3n² + 2n + 1.
Coefficient of n² is 3.
Therefore, Coefficient of n² is 3.
The bus will leave Norfolk, VA at 6:00 a.m. on Thursday. The distance from Norfolk to New York City is 350 miles. The average speed of the bus is 50 miles per hour. 1.Determine how long it will take the charter bus to arrive in New York City. Represent the distance traveled every hour in a table of values.
Melanie eats 1.5 pounds of cereal each week. Which model below best represents the number of pounds of cereal she eats in .5 weeks?
Jessie set up a lemonade stand for three days. On Saturday she sold 10 and 2/3 gallons of lemonade. On Sunday she sold 3 and 1/3 gallons mor3 than she sold on Saturday. On Monday she sold 2 and 2/3 gallons less than she sold on Sunday. How many gallons of lemonade did jessie sell on Monday
Jessie set up a lemonade stand for three days.
On Saturday she sold 10 and 2/3 gallons of lemonade = 10+2/3 = 32/3 gallons
On Sunday she sold 3 and 1/3 gallons more than she sold on Saturday
Lemonade sold on Sunday = 32/3 + 3 and 1/3 gallons
= 32/3 + 10/3 = 42/3 gallons = 14 gallons
On Monday she sold 2 and 2/3 gallons less than she sold on Sunday
Lemonade sold on Monday = 14 - 2 and 2/3 gallons
= 42/3 - 8/3 = 34/3 gallons
Therefore, Jessica sold 11 and 1/3 gallons of lemonade on Monday
What is 6x – 8 = 4 written as a system?
A. y = 6x – 8
y = –4
B. y = 6x – 8
y = 4
C. y = –6x + 8
y = 4
6x – 8 = 4 written as a system y = 6x – 8, y = 4. So, option B) is correct.
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given,
6x-8=4
For A) Given system
y = 6x – 8.....................1
y = –4.....................2
Substituting y=-4 in eq 1
-4=6x – 8
6x – 8=-4, which is not the same as the given equation.
For B) Given system
y = 6x – 8.....................3
y = 4.....................4
Substituting y=4 in eq 3
4=6x – 8
6x – 8=4, which is the same as the given equation.
For C) Given system
y = -6x +8.....................5
y = 4.....................6
Substituting y=4 in eq 5
4=-6x + 8
-6x +8=4, which is the same as the given equation.
Thus, 6x – 8 = 4 written as a system y = 6x – 8, y = 4. So, option B) is correct.
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how do you solve each absolute value by graphing
What is the b in 8b=5.6
Thomas wrote the equation y equals 3x + 3/4 when Sandra her equation they discovered that her equation had all the same Solutions at Thomas's equation which equation could be Sandra's
Is y = 0 the asymptote of all functions of the form f(x) = ab^x? Explain your reasoning.
Final answer:
No, y = 0 is not the asymptote of all functions of the form f(x) = ab^x. The y = 0 line is called the x-axis and is only an asymptote for certain functions. Functions of the form f(x) = ab^x do not have y = 0 as an asymptote.
Explanation:
No, y = 0 is not the asymptote of all functions of the form f(x) = ab^x. The y = 0 line is called the x-axis and is only an asymptote for certain functions. In order for a function to have y = 0 as an asymptote, the limit of the function as x approaches infinity or negative infinity would need to be 0. For example, the function f(x) = 1/x has y = 0 as an asymptote because as x approaches infinity or negative infinity, the function approaches 0. However, functions of the form f(x) = ab^x do not have y = 0 as an asymptote because as x approaches infinity or negative infinity, the value of the function either approaches infinity or approaches 0, depending on the values of a and b.
Write an inequality to represent this situation: Nina wants to take at least $15 to the movies. How did you decide which inequality symbol to use?
A hot air balloon descends at a rate of 320 ft per minute for 3 minutes use integers to calculate represent the balloons total change in altitude
A rectangular prism has a length of 112 meters, a width of 3 meters, and a height of 512 meters.
Enter the volume of the prism as a mixed number in simplest form in the box.
Answer:
[tex]Volume=24\frac{3}{4}m^3[/tex]
Step-by-step explanation:
The volume of a rectangular prism is calculated using the formula;
[tex]Volume=l \times w\times h[/tex]
where [tex]l=1\frac{1}{2}m[/tex] is the length, [tex]w=3m[/tex], is the width and [tex]h=5\frac{1}{2} m[/tex] is the height of the rectangular prism.
We substitute all these values into the formula to obtain
[tex]Volume=1\frac{1}{2} \times 3\times 5\frac{1}{2}[/tex]
Convert to improper fractions to get;
[tex]Volume=\frac{3}{2}\times 3\times \frac{11}{2}[/tex]
[tex]Volume=\frac{99}{4}[/tex]
[tex]Volume=24\frac{3}{4}m^3[/tex]
Marta bought new fish for her home aquarium. She bought 3 guppies and 2 platies for a total of $13.95. Hank also bought guppies and platies for his aquarium. He bought 3 guppies and 4 platies for a total of $18.33. Find the price of a guppy and the price of a platy.
The price of a guppy and the price of a platy are $3.19 and $2.19 respectively.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions. Equation: A declaration that two expressions with variables or integers are equal.
Given:
Marta bought 3 guppies and 2 platies for a total of $13.95,
Hank bought 3 guppies and 4 platies for a total of $18.33,
Write the equation of the above statements as shown below,
3g + 2p = 13.95
3g + 4p = 18.33
Here, g is the price of guppies and p is the price of platies,
Solve the above equation by elimination as shown below,
3g + 2p - (3g + 4p) = 13.95 - 18.33 (Subtract equation from each other)
3g + 2p - 3g - 4p = -4.38
- 2p = -4.38
p = 4.38 / 2
p = $2.19 and,
3g = 18.33 - 4 × 2.19
3g = 9.57
g = 9.57 / 3
g = $3.19
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A cube has a surface area of 486 square meters. What is the volume of the cube.
Which expression is equivalent to i^233
Answer: the answer is i
Step-by-step explanation:
What is the domain of the square root function graphed below?
Answer:
x greater than or equal to 3
Step-by-step explanation:
got it right on quiz
Anyone please help solving this maths problems not sure if I did it right. Thanks.
what is between 3/8 in a number line
Rachel opened a savings account 6 years ago. The account earns 8% interest, compounded monthly. If the current balance is $1,000.00, how much did she deposit initially?
The cost of a television is $429.99 after sales tax is added. If the sales tax is 7.5%, what was the cost of the television before sales tax was added? (A) $377.74 (B) $389.46 (C) $397.74 (D) $399.99 (E) $459.27
The original cost of the television before a 7.5% sales tax was added, which made the total $429.99, is optionD. $399.99.
The question is asking to find the original cost of a television before sales tax was added. Given that the final cost after including the 7.5% sales tax is $429.99, we need to find the price before this tax was applied. To calculate this, we first convert the percentage to a decimal, which is 0.075, and then create an equation to represent the relationship between the original price (let's call it x) and the total cost with tax. The equation would be x + 0.075x = $429.99. This is equivalent to 1.075x = $429.99. Solving for x gives us the original price of the TV before tax.
To solve for x, we would divide both sides by 1.075, which is the combined total of the original price and the tax. x = $429.99 / 1.075. This calculation gives us the original price of the TV, which turns out to be $399.99, which is option (D).
You may use any word processing program or Web 2.0 tool to present your argument, but you must include the following: A summary of your argument. The summary should begin with the argument statement you chose. In addition, provide at least three reasons why the method you chose is better than the other method and at least three reasons why the other method is not better. This summary can have a lot of opinion in it and should be persuasive and argumentative. A list of at least two resources used. Resources may include interviews with professionals and/or URLs of websites. Remember, you may gather ideas from research, but you must explain the ideas yourself.
In summary, an effective argumentative essay includes a clear thesis statement followed by logically structured reasons supported by a mix of well-researched evidence and personal knowledge, ensuring a persuasive and objective argument.
Students tasked with creating an argumentative essay must focus on developing a persuasive argument. The essay should begin with a summary of the argument that clearly states the main thesis. Following this, at least three reasons should be provided to support why the adopted approach is superior, using logical and persuasive evidence, such as statistics, expert opinions, and relevant examples. Contrary to this, the reasons why the alternative method is less effective should also be articulated. The Rule of 3 is a strategic approach where the contentions made to support an opinion are outlined in three clear points, enabling a structured and convincing argument to be presented.
To successfully make an argument in a position paper, it is crucial to provide a paragraph for each reason, starting with a clear topic sentence and backed by well-researched evidence. This can include research findings, personal knowledge, and a variety of evidence to ensure the argument is perceived as objective. An informal approach may also be used to frame the debate, maintaining relevance and ensuring engagement with the topic.
Finally, it's vital to use reliable resources to supplement the argument. A combination of research from credible sources and well-prepared reasoning constructs an objective and persuasive document that clearly distinguishes the author's ideas from those presented in the referenced texts.
i don’t know how to do this. can someone please help me :)
8n+3n-n+3n+5n I need help with this
To see how costly it would be for other people to complete a similar cycling tour, you decide to work out two averages and compare.
Group A
Person 1: $500
Person 2: $600
Person 3: $900
Person 4: $450
The average amount spent by members of cycle group A was $
Group B
Person 1: $700
Person 2: $500
Person 3: $680
Person 4: $500
The average amount spent by members of cycle group B was $
what is the solution to this equation x-16=-8
The solution to the equation x - 16 = -8 is x = 8.
We have,
To solve the equation x - 16 = -8, we want to isolate the variable x on one side of the equation.
First, let's add 16 to both sides of the equation:
x - 16 + 16 = -8 + 16
This simplifies to:
x = 8
Therefore,
The solution to the equation x - 16 = -8 is x = 8.
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A rectangle has a perimeter of 48 feet and a length of 14 ft which equation can you solve to find the width
Answer: 2n + 28 = 48
Step-by-step explanation: Got it right on TTM
What is the value of x in this number sentence?
32 = 17 + x