Answer:
The relationship ⇒ 25x + 40y = 12,250
Step-by-step explanation:
The number of student memberships = x
The number of adult memberships = y
The monthly membership fee for a student = $25
The monthly membership fee for an adult = $40
The total fee = 25x + 40y
Al's Athletic Club receives $12,250 in membership fees for the month of January.
So, the relationship between x and y is:
25x + 40y = 12,250
For every 2 student memberships (2x$25=$50), there were 305 adult memberships.
To represent the relationship between the number of student memberships (2) and the number of adult memberships (y) at Al's Athletic Club for the month of January, we can use an equation based on the given information. Let's assume that there were 2 student memberships and y adult memberships in January. The monthly membership fees for students and adults are $25 and $40, respectively. The total membership fees collected for the month were $12,250.
The total fees can be represented as:
Total Fees = (Number of Student Memberships * Monthly Fee for Student) + (Number of Adult Memberships * Monthly Fee for Adult)
Using the given information, we can write the equation:
$12,250 = (2 * $25) + (y * $40)
Now, we can simplify this equation:
$12,250 = $50 + $40y
To isolate the variable y, we can subtract $50 from both sides of the equation:
$12,250 - $50 = $40y
$12,200 = $40y
Now, divide both sides by $40 to find the relationship:
y = $12,200 / $40
y = 305
So, the relationship between the number of student memberships (2) and the number of adult memberships (y) for the month of January is represented by the equation y = 305. This means there were 305 adult memberships in January for every 2 student memberships.
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I owe my friend Miguel $4.00. I also owe my friend Gloria $7.50. Which equation correctly shows this relationship?
A. -4 - 7.50 = 11.50
B. 7.50 - 4 = 3.50
C. 4 + (-7.50) = -3.50
D. -4 + (-7.50) = -11.50
(-4+6i) + (-6-2i)
How do I solve
Answer:
(-4+(-6))+(6i-2i)
(-10+4i)
Answer:
-10+4i = -2(5-2i)
Step-by-step explanation:
(-4+6i) + (-6-2i)
Collecting like terms
(-4-6) + (6i-2i)
-10+4i
-2(5-2i)
24 ⅗ + 43 x (8 ⅕ - 2)
Answer: -14/5
Step-by-step explanation:
24 ⅗ + 43 x (8 ⅕ - 2)
= 72/5 + 43 * (8/5 - 2)
= 72/5 + 43 * (8 - 10/5)
= 72/5 + 43 * (-2/5)
= 72/5 - 86/5
= -14/5
if (x +5) -2(4x-1)=0 what is the value of x
Answer: x=1
Step-by-step explanation:
(X+5)-2(4x-1)=0
(-2•4x) (-2•-1)
X+5-8x+2=0
X-8x+5+2=0
(5+2)=7
X-8x=-7
-7x= -7
X=1
Simplifying the given expression (x +5) -2(4x-1)=0 we get the solution of this expression is x = 1.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
The given expression,
(x +5) -2(4x-1)=0
Distributing the number inside the bracket we get,
x + 5 - 8x + 2 =0
Simplifying the like terms,
-7x + 7 = 0
Subtract 7 on both sides,
-7x = -7
Divide by -7 on both sides we get,
x = 1
Hence,
The solution of the expression is x = 1.
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9+ (- 3/4+1.25)-6 please help you need to evaluate the solution
answer: 9+(-3/4+1.25)-6= 3.5
Answer:
Step-by-step explanation:
9+ (- 3/4+1.25)-6 = 9 + (-0.75 + 1.25) - 6
= 9 + 0.50 - 6
= 3.50
Estimate what’s 32.27/7
Answer:
The answer we can solving the above division is 4.61
Step-by-step explanation:
Given:
The given divider is 7 and the given dividend is 32.27.
To find:
Quotient and remainder
Formula:
The basic division formula that we all know is,
Quotient + Remainder/Divisor = Dividend/Divisor
where we know both dividend and divisor.
By using normal division method we get,
= 32.37/7
= 4.61
Thus we got the quotient as four and remainder as six.
Riding an exercise bike burns 6 calories per min how many calories will a person burn if he/she bikes for 23 1/2 minuets
Answer: 141
Step-by-step explanation:
23 1/2 *6=141
Cynthia has the choice of taking out a 25-year loan for $155,000 at 4.4%
interest, compounded monthly, or the same loan at 20 years for a higher
monthly payment. If she would pay a total of $100,831 in interest on the 25-
year loan, how much in total would she pay in interest on the 20-year loan?
Answer:
D. Less than $100,831
Step-by-step explanation:
There is an equation for calculating monthly payment:
x = p • r • (1+r)^n / (1+r)^n - 1
It may seem a bit complicated, but let's explain it step by step:
- p is the amount of loan, in this case $155,000
- r is monthly interest rate, in this case (4.4/12) / 100, which is 0.00367
- n is the number of months for paying back, or in this case 20 • 12 = 240
Now that we know all the values, all that's left is to plug them in and solve it on the calculator:
x = 155,000 • 0.00367 • (1.00367^240) / (1.00367^240) - 1
x = $972.27
So, the monthly payment is around $972.3. We now multiply it by the number of months to get total payment:
$973.3 • 240 = $233,352
So, the total amount, loan plus interest, is 233,352 dollars.
To only find amount of interest, we simply subtract loan from total amount:
$233,352 - $155,000 = $78,352
Complete the statements about the cone.
-The height is___
units.
-The radius is___
units.
-The volume is___
Pi cubic units.
Answer:
The height is 6 units.
The radius is 8 units.
The volume is 128 Pi cubic units
Step-by-step explanation:
The height is 6 units.
Use Pythagorean Theorem to find the radius.
6² + x² = 10²
36 + x² = 100
-36 -36
x² = 64
x = 8
V = πr²h/3
V = π(8)²6/3
V = π(64)2
V = 128π
Answer:
6,8,128
Step-by-step explanation:
PLEASE!!! NEED HELP ASAP!!! 50 PTS AND BRAINLIEST!!!
1) There are at least 3 ways to show that 2 functions are inverses. However, only ONE method is a valid proof. Although Methods A and B might convince you that the functions are inverses, they are NOT acceptable methods to verify that functions are inverses. Complete the work for each method below:
Method A: Given () = 3 − 4 and () = +4/3
Show that these are inverse functions by finding ^−1 () and showing that it is the same as ().
Method B: Given () = 3 − 4 and () = +4/3
Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)
Method C: Given () = 3 − 4 and () = +4/3
Verify that these are inverse functions by showing that (()) = AND (()) =
The notation that we use really depends upon the problem. In most cases either is acceptable.
For the two functions that we started off this section with we could write either of the following two sets of notation.
f(x)=3x−2f−1(x)=x3+23g(x)=x3+23g−1(x)=3x−2f(x)=3x−2f−1(x)=x3+23g(x)=x3+23g−1(x)=3x−2
Now, be careful with the notation for inverses. The “-1” is NOT an exponent despite the fact that is sure does look like one! When dealing with inverse functions we’ve got to remember that
f−1(x)≠1f(x)f−1(x)≠1f(x)
This is one of the more common mistakes that students make when first studying inverse functions.
The process for finding the inverse of a function is a fairly simple one although there is a couple of steps that can on occasion be somewhat messy. Here is the process
That’s the process. Most of the steps are not all that bad but as mentioned in the process there are a couple of steps that we really need to be careful with.
In the verification step we technically really do need to check that both (f∘f−1)(x)=x(f∘f−1)(x)=x and (f−1∘f)(x)=x(f−1∘f)(x)=x are true. For all the functions that we are going to be looking at in this section if one is true then the other will also be true. However, there are functions (they are far beyond the scope of this course however) for which it is possible for only of these to be true. This is brought up because in all the problems here we will be just checking one of them. We just need to always remember that technically we should check both.
There is one final topic that we need to address quickly before we leave this section. There is an interesting relationship between the graph of a function and its inverse.
Here is the graph of the function and inverse from the first two examples. We’ll not deal with the final example since that is a function that we haven’t really talked about graphing yet.
In both cases we can see that the graph of the inverse is a reflection of the actual function about the line y=xy=x. This will always be the case with the graphs of a function and its inverse.
https://tutorial.math.lamar.edu/classes/alg/inversefunctions.aspx
Mrs. Lin is sewing costumes for her grandchildren. She is making 3 lion costumes, 1 zebra costume, and 2 bear costumes. Fabric costs $7.49 per yard. How much fabric does Mrs. Lin need?
Answer:
rtetrt343444
Step-by-step explanation:
rewrew
Mrs. Lin needs a total of [tex]6 \frac{13}{24} \text{ yards}[/tex] yards of fabric for all the costumes.
To find out how much fabric Mrs. Lin needs for all the costumes, we need to calculate the total yardage required for each type of costume and then sum them up.
Given:
- Bear costume requires 2 1/4 yards.
- Lion costume requires 1 2/3 yards.
- Zebra costume requires 2 5/8 yards.
Let's calculate the total yardage required for each type of costume:
1. Bear costume:
[tex]\[ \text{Yardage for bear} = 2 \frac{1}{4} \text{ yards} \][/tex]
2. Lion costume:
[tex]\[ \text{Yardage for lion} = 1 \frac{2}{3} \text{ yards} \][/tex]
3. Zebra costume:
[tex]\[ \text{Yardage for zebra} = 2 \frac{5}{8} \text{ yards} \][/tex]
Now, let's convert all these mixed numbers into improper fractions:
1. Bear costume:
[tex]\[ \text{Yardage for bear} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ yards} \][/tex]
2. Lion costume:
[tex]\[ \text{Yardage for lion} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \text{ yards} \][/tex]
3. Zebra costume:
[tex]\[ \text{Yardage for zebra} = 2 + \frac{5}{8} = \frac{16}{8} + \frac{5}{8} = \frac{21}{8} \text{ yards} \][/tex]
Now, let's sum up the yardages for all the costumes:
[tex]\[ \text{Total yardage} = \text{Yardage for bear} + \text{Yardage for lion} + \text{Yardage for zebra} \][/tex]
[tex]\[ \text{Total yardage} = \frac{9}{4} + \frac{5}{3} + \frac{21}{8} \text{ yards} \][/tex]
To add these fractions, we need to find a common denominator, which is 24:
[tex]\[ \text{Total yardage} = \frac{9 \times 6}{4 \times 6} + \frac{5 \times 8}{3 \times 8} + \frac{21 \times 3}{8 \times 3} \][/tex]
[tex]\[ \text{Total yardage} = \frac{54}{24} + \frac{40}{24} + \frac{63}{24} \][/tex]
Now, let's add the fractions:
[tex]\[ \text{Total yardage} = \frac{54 + 40 + 63}{24} \][/tex]
[tex]\[ \text{Total yardage} = \frac{157}{24} \][/tex]
Now, let's convert the improper fraction to a mixed number:
[tex]\[ \text{Total yardage} = 6 \frac{13}{24} \text{ yards} \][/tex]
So, Mrs. Lin needs a total of [tex]6 \frac{13}{24} \text{ yards}[/tex] yards of fabric for all the costumes.
complete question given below:
Mrs. Lin is sewing costumes for her grandchildren. She is making three lion costumes, one zebra costume, and two bear costumes. Fabric costs $7.49 per yard. How much fabric does Mrs. Lin need?
Bear= 2 1/4 yards
Lion= 1 2/3 yards
Zebra= 2 5/8 yards
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION :::(((((
A typical traffic signal is programmed on a timer so that it is red 50% of the time, green 42% of the time, and yellow 8% of the time. The bulbs for each color are LED and are designed to last 100,000 hours. How many years does each color light last? Give your answer in years and months (rounded to the nearest month). What is the problem asking? What do we know? How did you solve the problem? Explain your steps.
Please answer this question for me
The problem is asking to identify how many years would each color light last. We know that a red light turns on 50% of the time, a green light is 42% of the time, and yellow is 8% of the time. Each light lasts 100,000 hours.
Although this question gives a lot of information, we really don't need the percentages of the lights. They simply are there to throw you off. Each light lasts 100,000 hours. We will use the following conversions:
1 day = 24 hours
1 year = 365 days
100,000 hours divided by 24 hours = 4166.67 days
4166.67 days divided by 365 days = 11.4 years (the 4 is 4 months).
Simplify 15 × 1316 in decimal form
Answer:
i multiplied them together and the result is 19740 but in decimal it would be 19740.0
Final answer:
To simplify 15 × 1316, you multiply to get 19740, which is rounded to 19700 when limited to three significant figures.
Explanation:
To simplify the expression 15 × 1316 in decimal form, you need to perform basic multiplication. Multiplying 15 times 1316 gives you a result of 19740.
However, to express this answer in terms of significant figures, specifically limiting to three significant figures, you would round this number to 19700, as the number 740 does not contribute to the first three significant digits.
A local grocery store kept track of the types of items sold in 2 hours. Express the ratio that compares the amount of produce sold to the total number of grocery items sold.
Answer:
Step-by-step explanation:
Tracking sales in a small convenience store does not require sophisticated sales monitoring software or expensive computer equipment, although basic point of sale software can save time and prevent mathematical errors. Daily monitoring of inventory, saving sales receipts and using a simple spreadsheet may be all you need to track sales. Depending on the size of your store and foot traffic the store receives each day, tracking sales may take only an hour or so each day.
Ashley had a summer lemonade stand where she sold small cups of lemonade for 41.25 AND LARGE CUPS FOR $2.50. If Ashley solf a total of 155 cups of lemonade for $265, how many cups of each tpe did she sell?
Question:
Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each did she sell
Answer:
The number of small cups of lemonades is 98
The number of Large cups of lemonades is 57
Step-by-step explanation:
Given:
Cost of small lemonade cups = $1.25
Cost of large Lemonade cups = $2.50
Total number of lemonade cups = 155 cups
The total cost for which the lemonade is sold = $265
To Find:
Number of each types of lemonade sold = ?
Solution:
Let the number of small cups of lemonade sold be x
the number of large cups of lemonade sold be y
Then according to the question,
x+y = 155-----------------------------(1)
Then the amount earned by selling small and large lemonade cups is $265
Then
1.25x+2.50y = 265------------------(2)
From (1)
y = 155-x----------------------------------(3)
Substituting (3) in (2), we get
1.25x+ (155-x)2.50 = 265
1.25 + (387.5 -2.50x) =265
-1.25x + 387.5 = 265
-1.25x= 265 -387.5
-1.25x = -122.5
[tex]x = \frac{-122.5}{-1.25}[/tex]
x= 98--------------------------------(4)
Substituting (4) in (3)
y = 155-98
y =57
Brainliest for best answer. No stupid answers please!
Answer:
They both have the same slope.
They have different y- intercepts.
They have no solution.
Please let me know, if I am right or wrong. I try my best to give correct answers
Answer:
A
Step-by-step explanation:
The standard equation is
y = mx + c
Where m is the slope and c is the y intercept
The 1st equation y = -2x + 1/4
Comparing with standard equation
the slope m = -2 and c = 1/4
The 2nd equation y = -2x - 1/4
Comparing with standard equation
the slope m = -2 and c = -1/4
To check if it as a solution
y = -2x + 1/4.......(1)
y = -2x - 1/4........(2)
Substracting (2) from (1)
y - y = -2x + 2x + 1/4 + 1/4
No solution since both x and y were eliminated
(It's a fraction). 5/2 + 5/7
Answer:
3 3/14
Step-by-step explanation:
First look for the LCM of the denominators 2 Andy 7. The LCM is 14.
then , divide the denominators by 14 and add the results to the numerators of both fractions divided by 14.
you‘ll have something like this 35+10/14
=45/14
= 3 3/14
=
A train leaves a station and travels north at a speed of 45 mph. Two hours later, a second train leaves on a parallel track and travels north at 75 mph. How far from the station will they meet?
Both trains will meet in 3 hours.
Step-by-step explanation:
Given,
Speed of train A = 45 mph
Distance covered in two hours = 2*45 = 90 miles
Let,
x be the number of hours for both trains.
A(x) = 45x+90
Speed of train B = 75 mph
B(x) = 75x
For same distance;
A(x) = B(x)
[tex]45x+90=75x\\90=75x-45x\\90=30x\\30x=90[/tex]
Dividing both sides by 30
[tex]\frac{30x}{30}=\frac{90}{30}\\x=3[/tex]
Both trains will meet in 3 hours.
Keywords: function, division
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Susan uses a credit card with an APR of 22.2%. What is the monthly percentage rate on the card?
Answer:
1.85 %
Explanation:
APR refers to the "Annual Percentage Rate." This refers to the rate that is being charged to the borrower on a yearly basis.
It is very easy to get the monthly percentage rate once you know the APR. All you have to do is to divide the APR by the total number of months.
In the situation above, we just have to divide the APR of 22.2% by 12 (number of months on one year).
22.2% ÷ 12 months = 1.85 % per month (this is the monthly percentage rate on the card. Thus, this is the answer.a sprinkler in a backyard turns through 180 degrees. the sprinkler has turned 96 degrees so far. how many more degrees will the sprinkler turn through to reach 180 degrees?
What 2 numbers multiply to get -12 and add up to get 11
Answer:
12 and -1
Step-by-step explanation:
12(-1) = -12
12 + (-1) = 11
What is the inverse of the function f(x) = 2x – 10?
Answer:
f^-1 (x)=1/2x+5
Step-by-step explanation:
y=2x-10
x=2y-10
2y=x+10
y=1/2x+10/2
y=1/2x+5
How to tell the ordered pair represent an exponential function
Exponential functions include numbers that are doubled. For example, an ordered pair such as (2, 4), (3, 8), (4, 16) the y values are doubled, so it is an exponential funcion.
If y is an nonnegative , would it be describing a inequality or interval notation?
How do you graph Y is less than 3/4 X +2
Solve the equation. Simplify your answer if possible.
((x+2)/5)+((x+1)/3)=((x-3)/10)-2
Answer:
The solved given equation
[tex](\frac{x+2}{5})+(\frac{x+1}{3})=(\frac{x-3}{10})-2[/tex] is x=-7
Step-by-step explanation:
Given equation is [tex](\frac{x+2}{5})+(\frac{x+1}{3})=(\frac{x-3}{10})-2[/tex]
To solve the given equation as below :
[tex](\frac{x+2}{5})+(\frac{x+1}{3})=(\frac{x-3}{10})-2[/tex] ( by using the distributive property )
[tex]\frac{3x+6+5x+5}{15}=\frac{x-3-20}{10}[/tex] ( adding the like terms )
[tex]\frac{8x+11}{15}=\frac{x-23}{10}[/tex]
Multiply into (10(15) on both sides we get
[tex]\frac{8x+11}{15}\times (10)(15)=\frac{x-23}{10}\times (10)(15)[/tex]
[tex](8x+11)\times (10)=(x-23)\times (15)[/tex] ( by using the distributive property )
[tex]80x+110-15x+345=0[/tex] ( adding the like terms )
[tex]65x+455=0[/tex]
[tex]65x=-455[/tex]
[tex]x=-\frac{455}{65}[/tex]
Therefore x=-7
Therefore the solved given equation is x=-7
2(x−3)=(x−1)+7
x = ___
Answer:
x=12
Step-by-step explanation:
Answer:
x = 12
Add 6 to both sides, simplify then subtract x from both sides
Expression equivalent to 5(3m + n)
Answer:
Step-by-step explanation:
5(3m + n) = 15m + 5n
Final answer:
The expression equivalent to 5(3m + n) is found by applying the distributive property, resulting in 15m + 5n, where the 5 is multiplied by each term inside the parentheses.
Explanation:
The expression 5(3m + n) is an example of the distributive property in algebra. To find an expression equivalent to this, we need to distribute the 5 across the terms inside the parentheses. This means we multiply 5 by each term inside the parentheses.
Multiply 5 by 3m, which gives us 15m.Multiply 5 by n, which gives us 5n.Putting these two results together, the equivalent expression is 15m + 5n. This is a straightforward application of the distributive property, which is a fundamental concept in algebra.
When graphing two systems the break even point:
A. is the point of intersection of the two lines
B. includes the points greater than the line
C. includes points less than the line
Question 3(Multiple Choice Worth 3 points)
(06.04)
What is the value of 4 + 5x when x = 3?
11
O 12
017
0 19
19
June
Help me and I will mark you the brainlest
Answer:
19
Step-by-step explanation:
4+5x
Since x=3
4+5(3)
4+15
19