Larry Lazy purchased a one year membership at a local fitness center at the beginning of the year. It cost him $150. He goes twice a week for the first three months (13 weeks) of the year, but then goes only once a month for the rest of the year.
How much does each visit to the center cost?
If he continued going twice a week all year, how much would each visit cost?
Answer:
A. $4.29
B. $1.44
Step-by-step explanation:
A. We have been given that Larry goes to gym twice a week for 13 weeks. Let us multiply 13 by 2 to find the number of times Larry visited the gym for first 3 months.
[tex]\text{The number of Larry's visits to gym for the first 3 months}=13\times 2=26[/tex]
Since there are 12 months in a year, then Larry has gone to gym only 9 times for rest of month as 12-3=9.
Now let us add 26 and 9 to get the total number of Larry's visits to gym.
[tex]\text{Larry's total visits to gym}=26+9[/tex]
[tex]\text{Larry's total visits to gym}=35[/tex]
Now let us divide total cost (150) by total number of visits (35) to get the each visit's cost.
[tex]\text{Each visit's cost}=\frac{150}{35}[/tex]
[tex]\text{Each visit's cost}=4.2857142857142857\approx 4.29[/tex]
Therefore, each visit to the center costs $4.29 to Larry.
B. If Larry continued going twice a week all year, then total number of Larry's visits to center will be 52 times 2.
[tex]\text{Larry's total visits to center}=52\times 2[/tex]
[tex]\text{Larry's total visits to center}=104[/tex]
Now let us divide total cost (150) by total visits (104) to find the cost of each visit.
[tex]\text{Each visit's cost}=\frac{150}{104}[/tex]
[tex]\text{Each visit's cost}=1.4423076923076923\approx 1.44[/tex]
Therefore, If Larry continued going twice a week all year, it would cost him $1.44 for each visit.
50 points!! help with justification of these steps please
Caitlyn needs to solve the equation: 2(3x+1)=3(2-x). She solves for x in 5 steps:
6x+2 = 6 - 3x
2 = 6 - 9x
-4 = -9x
4/9 = x
x = 4/9
What is the justification for each of the steps that Caitlyn took? Give the Algebraic Property for each step.
Answer:
combining like terms
Step-by-step explanation:
Is the square root of 38 rational or irrational?
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1. The tables below show the values of y corresponding to different values of x:
Table A
x 3 2 1
y 1 0 0
Table B
x 3 5 4
y −2 1 1
Which statement is true for the tables?
Both Table A and Table B represent functions.
Both Table A and Table B do not represent functions.
Table A does not represent a function, but Table B represents a function.
Table A represents a function, but Table B does not represent a function.
2. Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) + 4?
The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Both Table A and Table B in the question represent functions, as each x value corresponds to exactly one y value in both tables. The operation of replacing the graph of f(x) with f(x) + 4 results in a vertical shift of the graph 4 units upward.
The subject of the question involves interpreting the data sets presented in Table A and Table B and understanding the behavior of functions. According to the definition, a function is a mathematical relationship wherein each input (x) corresponds to exactly one output (y).
Now, let's determine which tables represent functions. Table A: each 'x' corresponds to exactly one 'y', so this represents a function.
For Table B, each 'x' also corresponds to exactly one 'y', so this also represents a function.
This means both Table A and Table B represent functions.
As for the second question, the operation of replacing the graph of f(x) with f(x) + 4 will result in the graph shifting 4 units upward. The vertical shift is a result of adding 4 to the entire function f(x).
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If you are using this figure to prove the isosceles triangle theorem which of the following would be the best strategy
If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.
∠P≅∠Q∠P≅∠Q
Proof:
Let SS be the midpoint of PQ¯¯¯¯¯PQ¯ .
Join RR and SS .
Since SS is the midpoint of PQ¯¯¯¯¯PQ¯ , PS¯¯¯¯¯≅QS¯¯¯¯¯PS¯≅QS¯ .
By Reflexive Property ,
RS¯¯¯¯¯≅RS¯¯¯¯¯RS¯≅RS¯
It is given that PR¯¯¯¯¯≅RQ¯¯¯¯¯PR¯≅RQ¯
Therefore, by SSS ,
ΔPRS≅ΔQRSΔPRS≅ΔQRS
Since corresponding parts of congruent triangles are congruent,
∠P≅∠Q∠P≅∠Q
The converse of the Isosceles Triangle Theorem is also true.
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
If ∠A≅∠B∠A≅∠B , then AC¯¯¯¯¯≅BC¯¯¯¯¯AC¯≅BC¯ .
If you purchase 100 items that cost $.25 each, how much would the items cost all together?
It takes 36 minutes for 7 people to paint 4 walls. How many minutes does it take 9 people to paint 7 walls?
Zoe, Latoya, Christina, and Rhoda each used a different method to verify that
-2(3x - 12) = -6x + 24
Whose method can be used to verify that the distributive property was correctly applied to the expression?
A.) Zoe's method
B.) Latoy's Method
C.) Christina's Method
D.) Rhoda's Method
Answer:
D) Rhoda's Method
Step-by-step explanation:
-2(3x - 12)
Using the distributive property a(b - c) = ab - ac
-2(3x -12) = -2(3x) -2(-12)
= -6x + 24
Which means-2(3x - 12) and -6x + 24 are equal.
To check this, we have to substitute the same x value for both the expression and evaluate them.
Both expression will have the same value.
Therefore, Rhoda is correct.
Thank you.
how many decimal places should be in the answer if 2.214 is added to 6.3
If y=1/2 when x=2, find y when x=3, given that y varies directly with x
Find the best of a parallelogram if the area is 10 cm2 and the height in 2cm
Two times antonio's age plus three times sarah's age equals 34. Sarah's age is also 5 times antonio's age. how old is sarah
Maria, bill, and change sent a total of 71 text messages during the weekend. change sent 2 times as many messages as bill. maria sent 7 more messages than bill. how many messages did they each send?
If your bank charges an out-of-network service fee of $3.00, and you withdraw $20 from each of three out-of-network atms, how much money in total will be removed from your account?
a. $60
b. $63
c. $69
d. $120
The amount of the money that is in total removed from the account would be $69.
As per the question, the bank charges an out-of-network service fee of $3.00, and you withdraw $20 from each of three out-of-network ATMs, how much money in total will be removed from your account is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Amount withdrew from the ATM three times,
= 3 × 20
= $60
The total service fee charged on out of network 3 times
= 3 × 3
= $9
Now, total money withdrew from the account = 60 + 9 = $69
Thus, the amount of money that is in total removed from the account would be $69.
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The total amount of money that will be removed from your account is $9.00.
Explanation:To find the total amount of money that will be removed from your account, you need to multiply the out-of-network service fee by the number of withdrawals you made. In this case, the out-of-network service fee is $3.00 and you made three withdrawals. So, the total amount of money that will be removed from your account is $3.00 x 3 = $9.00.
Write an inequality that represents the sentences:
What is the product of g and 2 is less than -6
Which binomial is not a devisor of x^3-11x^2+16x+84?
x + 4
Further explanationGiven:
The expression x³ - 11x² + 16x + 84
Question:
Which binomial is not a divisor of x³ - 11x² + 16x + 84?
x + 2x + 4x - 6x - 7The Process:
This is a problem about Remainder Theorem.
If x = a or (x - a) is one of the roots or factors (divisors) of the function f (x), then f(a) = 0.
Let us test one by one of the options available into the polynomial function.
[tex]\boxed{ \ x + 2 \ } \rightarrow \boxed{ \ x = -2 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (-2)^3 - 11(-2)^2 + 16(-2) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow -8 - 44 - 32 + 84 = 0 \ }[/tex][tex]\boxed{ \ x + 4 \ } \rightarrow \boxed{ \ x = -4 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (-4)^3 - 11(-4)^2 + 16(-4) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow -64 - 176 - 32 + 84 = -188 \ }[/tex][tex]\boxed{ \ x - 6 \ } \rightarrow \boxed{ \ x = 6 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (6)^3 - 11(6)^2 + 16(6) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow 216 - 396 + 96 + 84 = 0 \ }[/tex][tex]\boxed{ \ x - 7 \ } \rightarrow \boxed{ \ x = 7 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (7)^3 - 11(7)^2 + 16(7) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow 343 - 539 + 112 + 84 = 0 \ }[/tex]From the test results above, it was clearly observed that (x + 4) is not a divisor of x³ - 11x² + 16x + 84 because [tex]\boxed{ \ f (-4) \neq 0 \ }[/tex].
- - - - - - - - - -
Alternative Steps
We will use Horner's rule for polynomial division in finding factors as well as divisors.
To begin, let us try x = -2 to see if it is one of the roots of x³ - 11x² + 16x + 84. The complete process can be seen in the attached picture.Since there is no remainder when x³ - 11x² + 16x + 84 is divided by (x + 2), this binomial is a divisor (or a factor). The quotient is obtained x² - 13x + 42. After factorization, we get (x - 6) dan (x - 7 as factors and also the divisor.Learn moreThe remainder theorem https://brainly.com/question/9500387A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 https://brainly.com/question/12700460 The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2.How do you solve: -1= 5+x/6
Solve the inequality (show your work):
-5/2(3x + 4) < 6 - 3x
-5/2 (3x+4)<6-3x distribute
-15/2 x-10<6-3x move -15/2 to the other side by adding it to 3x
-10<6+9/2 x move 6 over by subtracting it from -10
-16<9/2 x divide 9/2 by 16 (or multiply 2/9)
-32/9<x
You are planning to volunteer at a zoo that is 60 miles from your home. you can either take stephanie's car, which gets 20 miles to the gallon
Penny translate a trapezoid so that one of the vertices is at the origin. if the pre-image has a perimeter of 44 units what is the perimeter of the image
Translations are part of rigid motions which also include reflection and rotation. For these three, we can then assume that neither the perimeter nor the area of an object would change. This means that, once an object is translated it is not biased or distorted (either enlarged or diminished). Thus, making the perimeter of the original and the image are equal. So for this problem, the perimeter of the image would be the same as the pre-image, and that would be 44 units.
In the context of geometric transformations, the shape and size do not change, only position. Therefore, if the trapezoid's pre-image has a perimeter of 44 units, the image, as a result of translation, will have the same perimeter of 44 units.
Explanation:In the context of geometric transformations like translations, rotations, or reflections, the shape and size of the object do not change--only its position does. The pre-image and the image are congruent, so their perimeters are the same.
In the situation described in your question, Penny's trapezoid is translated so that one of its vertices is at the origin. Because a translation is a type of isometry (a transformation that preserves distance), the shape of the trapezoid and the lengths of its sides will not change in the translation process. As a result, if the perimeter of the pre-image is 44 units, then the perimeter of the image will also be 44 units, regardless of where the vertices are located.
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what is 165.2 diveded by 3 times 10 plus 65 minus 82 divided by 100 times 65 plus 1
Answer: 563.37 hahaha
Step-by-step explanation:
Determine whether each conjecture is true or false given: n is a real number
Conjecture: n^2 (squared) is a nonnegative number
The conjecture that any real number squared is a nonnegative number is correct. This is because squaring a positive number gives a positive result, squaring a negative number also gives a positive result, and squaring zero equals 0, which is nonnegative.
Explanation:This mathematical conjecture proposes that for any real number, when squared, the result is a nonnegative number. Given n is a real number, the conjecture n^2 is a nonnegative number is indeed true. In mathematics, a real number is considered nonnegative if it is greater than or equal to zero.
To provide more insight, let's look at a few examples: If we take a positive number such as 3, and you square it (3^2), you get 9, which is a positive number. Equally, if you take a negative number like -3 and square it (-3^2), you get 9 again, which is also a positive number. Even if you take the number zero (which is neither positive nor negative) and square it, you get 0, which is still considered nonnegative. Thus, any real number when squared is always a nonnegative number.
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Let f(x) = 4 – x^2-, g(x) = 2 – x. Find (f + g)(x) and its domain.
in 35 days a person saved $70 what was the person's average daily savings
The person's average daily savings is $2.00. The correct answer is option b $2.00.
Step 1
To find the average daily savings, we need to divide the total amount saved by the number of days over which the savings occurred.
Calculation:
1. Total savings: $70
2. Number of days: 35 days
Step 2
The average daily savings is calculated as:
[tex]\[\text{Average daily savings} = \frac{\text{Total savings}}{\text{Number of days}} = \frac{70}{35} = 2\][/tex]
The person's average daily savings is $2.00.
Complete question : In 35 days, a person saved $70. What was the person's average daily savings?
a $0.70
b $2.00
c $1.50
d $1.05
e $2.33
f none of these
Luis has a $10 bill and three $5 bills. He spends $12.75 on the entrance fee to an amusement park and $8.50 on snacks. How much money doe she have left
Answer:
She has a total of $3.75 left
Step-by-step explanation:
Step 1
Express the amount of money Luis had in the beginning as follows;
A=E+R
where;
A=initial amount he had at the beginning
E=total expenditure
R=total remainder after spending
In our case;
A=(1×10)+(3×5)=$25
E=Amount spent at amusement park+amount spent on snacks
E=(12.75+8.50)=$21.25
R=unknown=r
Step 2
Substitute the values in the expression and solve for A;
25=21.25+r
r=25-21.25=3.75
r=3.75
She has a total of $3.75 left
Kaitlin brought 7 cans of cola to a party. lisa brought 18 packs of cola, and each pack had 6 cans. how many cans did they bring in all?
One number is three more than twice another, the sum of the numbers is 12. find the two numbers
The area of the conference table in Mr. Nathan’s office must be no more than 175 ft2. If the length of the table is 18 ft more than the width, x, which interval can be the possible widths?
What is the surface area of a sphere with a radius of 13 units?
Answer:
676pi units ^2
Step-by-step explanation:
apex
The surface area of a sphere with a radius of 13 units is 676π²
What is surface area?explaination;
Given radius = 13 units
surface area of a sphere = 4πr²
= 4 * 13*13 π²
676π² answer.
The surface area is the sum of the areas of all its faces.The areas of the base, top, and lateral surfaces i.e all sides of the object. It is measured using different area formulas and measured in square units and then adding all the areas. The surface area of a solid object is a measure of the total area that the surface of the object covers.The floor region of a strong object is a measure of the full vicinity that the floor of the item occupies. The mathematical definition of surface vicinity within the presence of curved surfaces is extensively extra involved than the definition of arc length of 1-dimensional curves, or of the floor area for polyhedra for which the surface place is the sum of the areas of its faces. clean surfaces, such as a sphere, are assigned floor region using their representation as parametric surfaces. The definition of floor area is based totally on methods of infinitesimal calculus and includes partial derivatives and double integration.
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Jenna has $50 to spend at a local crafts fair. The entrance price for the fair is $10. At a pottery stand, Jenna finds some cups that she likes that are $4.50 each. what is the maximum number of cups she can buy?