The total amount of the purchase was ...
... $2.50 + 3c = $5.05
This equation can be solved by subtracting 2.50 and dividing by 3. Both these operations are done to both sides of the equation in accordance with the rules of equality.
... 3c = $2.55
... c = $0.85
The cost of a bag of chips was $0.85.
The cost of a bag of chips can be found by subtracting the juice price from the total cost and then dividing by the number of chip bags. This gives us an answer of $0.85 per bag.
Explanation:To solve this problem, we need to subtract the cost of the juice from the total cost, then divide that answer by the total number of chip bags bought to find the cost of one bag. First, we subtract the juice price ($2.50) from the total spent ($5.05), which gives us $2.55. This is the total cost of the chips. Then, we divide that $2.55 by the number of chip bags bought (which is three) to find the cost of one bag. This can be represented by the equation: c = (total cost - juice price) / number of chip bags, or c = ($5.05 - $2.50) / 3. Calculating this, we find that c equals $0.85, so a bag of chips costs $0.85.
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Help me with this please!
Angles B and C are alternate interior angles where transversal BC cuts parallel lines AB and CD. Thus angles B and C are equal. Angle B is 65°.
Angle AEC is the exterior angle opposite interior angles A and B, which means its value is the sum of angles A and B.
∠AEC = ∠A +∠B = 47° +65°
∠AEC = 112°
EASY BRAINLIEST! **PLEASE HELP**
A set of stairs is being built as shown. What is the height of the stair?
The stair is inches _____ high.
To find the answer,we need to first find the legth of the not given side of triangle by using Pythagoras theorem:
[tex] = \sqrt{{15 }^{2} -{ 9 }^{2} } \\ = \sqrt{144 }\\ = 12[/tex]
Therefore the side length is 12in.
Therefore the answer 12 in.
The total height of the stair is equivalent to 36 inches.
What is Pythagoras theorem?Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular.
We can write the formula for Pythagoras theorem as -
(hypotenuse)² = (base)² + (perpendicular)²
We can write the height of the stairs as -
h = 3 x √(15² - 9²)
h = 3 x √(225 - 81)
h = 3 x √144
h = 3 x 12
h = 36 inches
Therefore, the total height of the stair is equivalent to 36 inches.
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It takes 18 electricians 35 days to wire a new housing subdivision. How many days would 28 electricians require to do the same job?
Assuming one electrician-day is the same as another, the total job is ...
... (18 electricians)×(35 days) = 630 electrician·days
When that work is split among 28 electricians, it can be expected to take ...
... (630 electrician·days)/(28 electricians) = 22.5 days
Given x less than y, compare the following expressions and determine which is greater: 2x-y;2y-x. Explain your answer
Let's form the difference of the two expressions and see what we can learn.
(2y -x) -(2x -y) = 2y -x -2x +y = 3y -3x = 3(y -x)
Since y > x, this is positive, so 2y -x is greater than 2x -y.
How many Mondays would there be in 171 school days?
There are 5 days to a school week: Monday, Tuesday, Wednesday, Thursday and Friday.
Divide number of school days by 5 to find the number of weeks:
171 / 5 = 34.2 weeks.
The weeks start with Monday, so there would be 35 Mondays. ( 34 full weeks and the partial week would begin with a Monday)
Divide 171 by 7 (as there are 7 days in each week), obtaining 24.4. There's one Monday in every 7 days, so in 168 days there'd be exactly 24 Mondays, and in 171 days there'd still be exactly 24 Mondays, with 3 days left over.
PLEEEAAASSSEEE HEEEELLLPPP!!!
For ΔABC, ∠A = 4x - 4, ∠B = 6x - 1, and ∠C = 8x - 13. If ΔABC undergoes a dilation by a scale factor of 2 to create ΔA'B'C' with ∠A' = 51 - x, ∠B' = 4x + 21, and ∠C' = 6x + 9, which confirms that ΔABC∼ΔA'B'C by the AA criterion?
A) ∠A = ∠A' = 44° and ∠B = ∠B' = 71°
B) ∠A = ∠A' = 36° and ∠C = ∠C' = 67°
C) ∠B = ∠B' = 59° and ∠C = ∠C' = 67°
D) ∠B = ∠B' = 65° and ∠C = ∠C' = 75°
The angle in the dilated figure is the same as the original angle in each case, a fact that should be confirmed by the way the answer choices are shown.
∠A = ∠A'
... 4x -4 = 51 -x
... 5x = 55
... x = 11
∠A = 4·11 -4 = 40 . . . . . . doesn't match any offered choice
___
∠B = ∠B'
... 6x -1 = 4x +21
... 2x = 22
... x = 11
... ∠B = 6·11 -1
... ∠B = ∠B' = 65 . . . . . matches selection D)
_____
∠C = ∠C'
... 8x -13 = 6x +9
... 2x = 22
... x = 11
... ∠C = 6·11 +9 = 75
... ∠C = ∠C' = 75 . . . . . matches selection D)
(2x^2+4x-3)+(2x^2+4x-3) show work
If you want to simplify this, you can add the coefficients of like terms.
... = x²(2+2) +x(4+4) +(-3-3)
... = 4x² +8x -6
_____
Since both of the parts of the sum are the same, this expression can be rewritten using the distributive property:
... = 2(2x² +4x =3)
_____
The sum can also be rewritten to vertex form.
... = 4(x² +2x) -6
... = 4(x² +2x +1) -6 -4(1)
... = 4(x +1)² -10
This is an expression describing a parabola with vertex (-1, -10) and a vertical scale factor of 4. It has roots (x-intercepts) at -1±√2.5.
On a recent test, Shawna was given the following problem:
Shawna's work is shown below:
1. a2+72=252
2. a2+14=50
3. a2=36
4. a=6 m
In which step did Shawna make an error?
Step 1. She incorrectly applied the Pythagorean theorem.
Step 2. She incorrectly squared the numbers.
Step 3. She incorrectly isolated a2
Step 4. She incorrectly solved for a.
Answer: Step 2. She incorrectly squared the numbers.
Solution:
The correct steps are:
1. a^2+7^2=25^2
2. a^2+49=625
3. a^2=576
4. a=24
In which step did Shawna make an error?
Step 2. She incorrectly squared the numbers.
Since, we are given right angled triangle
so, we use pythagoras theorem to find 'a'
step-1:
Using pythagoras theorem
[tex]a^2+7^2=25^2[/tex]
step-2:
we know that
[tex]7^2=7\times 7 =49[/tex]
[tex]25^2=25\times 25 =625[/tex]
so, we get
[tex]a^2+49=625[/tex]
she made error in second step
step-3:
Subtract both sides by 49
[tex]a^2+49-49=625-49[/tex]
[tex]a^2=576[/tex]
step-4:
Take sqrt both sides
we get
[tex]a=24[/tex]
so,
Answer is:
Step 2. She incorrectly squared the numbers.
PLZZZ HELP WITH 2 PROBLEMS
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. y= 1/3 x− 2/3
Given the graph of a line y=−x.Write an equation of a line which is perpendicular and goes through the point (8,2).
Answer:
1. (0, -2/3), (2, 0)
2. y = x-6
Step-by-step explanation:
1. Since the equation is in slope-intercept form, you know the y-intercept is -2/3. The x-coordinate there is 0, so the ordered pair is (0, -2/3).
Substituting y=0 into the equation gives the value of the x-intercept.
... 0 = 1/3x -2/3
... 0 = x - 2 . . . . . multiply by 3
... 2 = x . . . . . . . . add 2
The x-intercept is (2, 0).
2. The given line has slope -1, so the perpendicular line has a slope that is the negative reciprocal of that: -1/-1 = 1. Then the point-slope equation of the line can be written ...
... y = 1(x -8) +2
... y = x - 6 . . . . simplify
(1)
to find the intercepts
• let x = 0, in the equation for y-intercept
• let y = 0, in the equation for x-intercept
x = 0 : y = - [tex]\frac{2}{3}[/tex] → (0, - [tex]\frac{2}{3}[/tex]) ← y-intercept
y = 0 : [tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = 0 ( multiply by 3 )
x - 2 = 0 → x = 2 → (2, 0 ) ← x- intercept
(2)
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - x is in this form with slope m = - 1
the slope of a perpendicular line = - [tex]\frac{1}{m}[/tex] = 1
the partial equation of the perpendicular line is
y = x + c
to find c substitute (8, 2 ) into the partial equation
2 = 8 + c → c = 2 - 8 = - 6
y = x - 6 ← equation of perpendicular line
Helpp!!!Evaluate the piecewise function at the indicated values from the domain:
Answer:
f(-1) = -1 . . . . matches the last selection
Step-by-step explanation:
When evaluating piecewise functions, the first step is to determine the applicable piece. The argument -1 is in the range of the middle definition, (-2, 1). So, the function value is ...
... (-1)³ = -1
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B.
Part (a)
The variable y is the dependent variable and the variable x is the independent variable.
Part (b)
The cost of one ticket is $0.75. Therefore, the cost of 18 tickets will be:
[tex]0.75\times 18=13.5[/tex] dollars
Now, we know that Kendall spent her money only on ride tickets and fair admission and that she spent a total of $33.50.
Therefore, the price of the fair admission is: $33.50-$13.50=$20
If we use y to represent the total cost and x to represent the number of ride tickets, the linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission can be written as:
[tex]y=0.75x+20[/tex]......Equation 1
Part (c)
The above equation is logical because, in general, the total cost of the rides will depend upon the number of ride tickets bought and that will be 0.75x. Now, even if one does not take any rides, that is when x=0, they still will have to pay for the fair admission, and thus their total cost, y=$20.
Likewise, any "additional" cost will depend upon the number of ride tickets bought as already suggested. Thus, the total cost will be the sum of the total ride ticket cost and the fixed fair admission cost. Thus, the above Equation 1 is the correct representative linear equation of the question given.
50 POINTS!
What is the reason for each step in the solution of the equation?
3(x+2)=4x+1
Drag and drop the reasons into the boxes to correctly complete the table.
(15 Points)
Find the derivative of each of the following (inverse function)
[tex]f(x) = x^2 arctan(x)[/tex]
[tex]f(x) = xarcsin(1-x^2)[/tex]
ANSWER 1
Note that,
[tex]f(u)=tan^{-1}(u)[/tex]
is the same as
[tex]f(u)=arctan(u)[/tex]
We apply the product rule.
[tex]f(x)=x^2tan^{-1}(x)[/tex]
So we keep the second function and differentiate the first,plus we keep the first function and differentiate the second.
[tex]f'(x)=(x^2)'tan^{-1}(x)+x^2(tan^{-1}(x))' [/tex]
Recall that,
If
[tex]f(u)=tan^{-1}(u)[/tex]
Then,
[tex]f'(u)=\frac{1}{1+u^2}} \times u'[/tex]
This implies that,
[tex]f'(x)=2xtan^{-1}(x)+\frac{x^2}{x^2+1} [/tex]
ANSWER 2
We apply the product rule and the chain rules of differentiation here.
[tex]f(x)=xsin^{-1}(1-x^2)[/tex]
[tex]f'(x)=x'sin^{-1}(1-x^2)+x(sin^{-1}(1-x^2))' [/tex]
Recall that,
If
[tex]f(u)=sin^{-1}(u)[/tex]
Then,
[tex]f'(u)=\frac{1}{\sqrt{1-u^2}} \times u'[/tex]
This implies that,
[tex]f'(x)=sin^{-1}(1-x^2)+x \times \frac{1}{\sqrt{1-(1-x^2)^2}}\times (-2x) [/tex]
[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-(1-2x^2+x^4)}} [/tex]
[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-1+2x^2-x^4}}[/tex]
[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{2x^2-x^4}}[/tex]
the area of a rectangular wall of a barn is 117 square feet. its length is 4 feet longer than the width. find the length and width of the wall of the barn?
Area is the product of length and width. If you assume the dimensions are integers, you are looking for factors of 117 that differ by 4.
117 = 1×117 = 3×39 = 9×13
These last two factors differ by 4, so we know the dimensions of the barn are ...
... 9 ft wide by 13 ft long
help me with this equations please
We know:
The product of two negative numbers is positive.
Therefore
(-12)(12)(-6.3)(-0.2)(-15.9) = (-12)(-6.3) (-0.2)(-15.9)(12) > 0 ANSWER
(12)(-6.3)(-0.2)(-15.9) < 0
(-12)(12)(-6.3)(-0.2)(-15.9)(0) = 0
(12)(12)(6.3)(0.2)(-15.9) < 0
What is the interquartile range (IQR) of the following data set 17 16 21 15 25 22 18 23 17
IQR = 6
First locate the median [tex]Q_{2}[/tex] at the centre of the data arranged in ascending order. Then locate the lower and upper quartiles [tex]Q_{1}[/tex] and [tex]Q_{3}[/tex] located at the centre of the data to the left and right of the median.
Note that if any of the above are not whole values then they are the average of the values either side of the centre.
rearrange data in ascending order
15 16 ↓17 17 18 21 22 ↓23 25
↑
[tex]Q_{2}[/tex] = 18
[tex]Q_{1}[/tex] = [tex]\frac{16+17}{2}[/tex] = 16.5
[tex]Q_{3}[/tex] = [tex]\frac{22+23}{2}[/tex] = 22.5
IQR = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 22.5 - 16.5 = 6
Final answer:
The interquartile range (IQR) for the given data set is calculated by first arranging the data in ascending order, finding the first and third quartiles (Q1 and Q3), and subtracting Q1 from Q3. The correct IQR for this data set, following this methodology, is 6, not the mistakenly provided 7.
Explanation:
The question asks about calculating the interquartile range (IQR) of a given data set. The IQR is important because it measures the middle 50% spread of data, pinpointing where the bulk of values lie, and helps in identifying potential outliers. To compute the IQR, we first need to organize the data in ascending order, then find the first quartile (Q1) and the third quartile (Q3), and finally subtract Q1 from Q3 (IQR = Q3 - Q1).
For the provided data set: 17, 16, 21, 15, 25, 22, 18, 23, 17:
Arrange data in ascending order: 15, 16, 17, 17, 18, 21, 22, 23, 25.
Find the median (Q2), which is 18 in this case as it's the middle value.
Q1 is the median of the first half (excluding the middle value if odd number of data), so Q1 = 16.5.
Q3 is the median of the second half, hence Q3 = 22.5.
Therefore, IQR = Q3 - Q1 = 22.5 - 16.5 = 6.
Contrary to the mistaken calculation of IQR as 9 - 2 = 7 provided in the reference, the computed IQR for this data set, following the correct methodology, is 6.
What’s the answer to this? Help ASAP!
Grace made tables of values to solve a system of equations. First, she found that the x-value of the solution was between 0 and 1, and then she found that it was between 0.5 and 1. Next, she made this table.
Answer: C
Step-by-step explanation:
Answer:
OPtion C is correct answer.
Step-by-step explanation:
Given that there is a system of equations as
y =-4x+3 and y =3x+1
Table is prepared with side by side values of y for a given x
From the table we are to find the solution of the system
On analysing the table we find that the difference between two y's is
0.5, -0.2, -0.9, -1.6, -2.3,-3
Hence we select the one which shows minimum difference i.e. -0.2
For this, x = 0.6
When x =0.6, y shows two values as 0.6 and 0.8
So we approximate y value as average of these two i.e. 0.7
So solution is
(0.6, 0.7)
50/22 rounded to the hundredth
Divide 50 by 22: 2.27272727...
Round up to hundredth and your final answer is 2.27
hope that helps :)
Mrs.Palmer bought one pair of goggles, one bathing suit, and one beach towel for each of her three daughters.Suppose she had $18 left after buying the swimming items.Write an equation to determine the amount Mrs.Palmer originally had to spend on each daughter.
To find the amount Mrs. Palmer originally had to spend on each daughter, we set up the equation as (x - 18) / 3 = y, where x is the total money she initially had and y indicates the amount spent on each daughter.
Let's denote the total amount Mrs. Palmer originally had as x.
We know she spent this on buying swimming items for her three daughters and had $18 left afterwards.
This infers that the total money she spent is (x - 18) dollars.
Since each daughter received a pair of goggles, a bathing suit, and a beach towel, this means she used this money to buy three sets of swimming items.
Therefore, the amount of money she spent on each daughter is equal to (x - 18)/3.
The equation to find out what x (the amount Mrs. Palmer originally had) is therefore:
(x - 18) / 3 = y
where y represents the amount she spends on each daughter.
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Need help please!
Write a paragraph proof for the following conjecture.
Given: QS bisects < PQR
m < PQS = 45*
Prove PQR is a raight triangle
(1) QS bisecting <PQR implies <PQS = <SQR
(2) <PQS=45 deg and (1) imply <SQR also = 45 deg
(3) from (2) it follows that <PQR = <PQS + <SQR = 45 + 45 deg = 90 deg and therefore the triangle is right-angled
Find the measures of the angles of a triangle whose angles have a measure of x, 1/2x, and 1/6x. Also, what kind of triangle is it?
the sum of the angles in a triangle = 180°, thus
x + [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{6}[/tex] x = 180
multiply through by 6
6x + 3x + x = 1080
10x = 1080 ( divide both sides by 10 )
x = 108
the angles are 108°, 54° and 18°
Since all the angles are different and the largest is 108°
The triangle is an obtuse scalene triangle
The measures of the angles of the triangle are approximately 108 degrees, 54 degrees, and 18 degrees. This type of triangle is a scalene triangle, as all of its angles are different.
Explanation:To find the measures of the angles of a triangle whose angles are x, 1/2x, and 1/6x, we will use the fact that the sum of the angles in a triangle is always 180 degrees. The equation representing this is:
x + 1/2x + 1/6x = 180
Combine like terms:
1.6667x = 180
Then solve for x:
x ≈ 108 degrees
Now plug x into the original angle measures to get:
Angle 1 = 108 degrees
Angle 2 = 1/2x = 54 degrees
Angle 3 = 1/6x = 18 degrees
Lastly, in terms of the type of triangle, this is a scalene triangle because all of its angles are different.
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Use the continuous change function A(t) = Pe^rt to answer the question.
You invest $10,500 in an account that grows 3.75% each year. What will be your investment amount after 9 years?
A.
$14,715.12
B.
$14781.48
C.
$15,049.96
A
note that r = 3.75% = 0.0375
A(9) = 10500 × [tex]e^{0.0375(9)}[/tex] = 10500 × [tex]e^{0.3375}[/tex] = 14, 715.12
We are given formula for continuous change function A(t) = Pe^rt.
We need to find the value of $10,500 investment amount grows 3.75% each year after 9 years.
Plugging values of P=10500
r= 3.75% = 0.0375 and
t=9 in given formula.
We get
[tex]A(9) = 10500e^{0.0375\times 9}[/tex]
Let us simplify it now.
[tex]e^{0.0375\times 9}=e^{0.3375}=1.40144[/tex]
[tex]=10500\times \:1.40144\dots[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:10500\times \:1.40144\dots =14715.11589\dots[/tex]
Rounding it to the nearest cents.
=14715.12.
Therefore, $14715.12 will be investment amount $10,500 after 9 years.Is this correct need help please answer quickly
Every 3 feet is $18. 18 divided by 3 equals 6.
24 divided by 6 equals 4. (So the second one is correct)
30 divided by 6 is 5, so the answer is not 30. it'd be 36.
48 divided by 6 is 8, so it is not 7.
72 divided by 6 is 12. But 6 multiplied by 9 equals 52. So, your answer is 52.
Hoped this helped,
-Anime
On a map of Chicago, 1cm represents 100m. Select all statements that express the same scale. A. 5cm on the map represents 50m in Chicago. B. 1mm on the map represents 10m in Chicago. C. 1km in Chicago is represented by 10cm on the map. D. 100cm in Chicago is represented by 1m on the map.
Answers: The statement that express the same scale are Options B and C.
Solution:
A. 5 cm on the map represents 50 m in Chicago?
Rule of three:
1 cm represents 100 m
5 cm represents x
x=(5 cm).(100 m) / (1 cm)
x=500 m
5 cm on the map represents 500 m in Chicago.
The statement A doesn't express the same scale.
B. 1 mm on the map represents 10 m in Chicago?
1 mm = 0.1 cm
Rule of three:
1 cm represents 100 m
0.1 cm represents x
x=(0.1 cm).(100 m) / (1 cm)
x=10 m
1 mm = 0.1 cm on the map represents 10 m in Chicago.
The statement B expresses the same scale.
C. 1 km in Chicago is represented by 10 cm on the map?
1 km = 1,000 m
Rule of three:
1 cm represents 100 m
x represents 1,000 m
x=(1 cm).(1,000 m) / (100 m)
x=10 cm
1 km = 1,000 m in Chicago is represented by 10 cm on the map.
The statement C expresses the same scale.
D. 100 cm in Chicago is represented by 1 m on the map?
100 cm = 1 m
Rule of three:
1 cm represents 100 m
x represents 1 m
x=(1 cm).(1 m) / (100 m)
x=0.01 cm
100 cm = 1 m in Chicago is represented by 0.01 cm on the map.
The statement D doesn't express the same scale.
Answer:
a,b,c d is incorrect but a,b,c is right
Step-by-step explanation:
just took the test
Compute the following volume and surface area. A rectangular pyramid has a base measuring 4 in. on each side and an altitude of 6 in. What is its volume? cubic inches
32 inches³
the volume V of a pyramid = [tex]\frac{1}{3}[/tex] × area of base × height
area of base = 4² = 16 and h = 6
V = [tex]\frac{1}{3}[/tex] × 16 × 6 = 32
Mr. Spencer has 7 1/5 L of juice. Do you wanna support equal amounts of juice into three punch bowls. How many liters of juice should he poured to each bowl
Into each bowl, he will pour
... (1/3)×(7 1/5) = (1/3)×(6 6/5) = 2 2/5 . . . liters of juice
_____
Here, we have elected to rewrite 7 1/5 as 6 6/5 so each part of the number (whole number, fraction) will be divisible by 3.
You may have been taught to convert 7 1/5 to an improper fraction before doing the multiplication. That method looks like ...
... (1/3)×(36/5) = 12/5 = 2 2/5 . . . . same result
an angle measures 2 degrees more than 3 times it’s complement. find the measure of its complement.
If the angle is 90 degrees, then the complement would be 27, because 90 / 3 = 30, and 30 - 3 = 27. Basically, you divide the angle by 3 and subtract 3 to find the complement if this is the case.
Answer:
22⁰
Step-by-step explanation:
Angle = x
Complement = 90 - x
Given:
x = 3 (90 - x) + 2
x = 270 - 3x + 2
4x = 272
x = 68
Complement = 90 - 68 = 22⁰
N-6.47=4.32 what is the unknown number for N?
N = 10.79
isolate N by adding 6.47 to both sides of the equation
N = 4.32 + 6.47 = 10.79
The unknown number N in the equation N - 6.47 = 4.32 is found to be 10.79 when we add 6.47 to both sides of the equation.
To solve for the unknown number N in the equation N - 6.47 = 4.32, we must isolate the variable N on one side of the equation. We do this by adding 6.47 to both sides of the equation:
N - 6.47 + 6.47 = 4.32 + 6.47
This simplifies to:
N = 10.79
The unknown number N is therefore 10.79. When providing the final answer, we must make sure that it is reported with the correct number of significant figures, which in this case are three significant figures.
An amusement park offers a yearly membership of $275 that allows for free parking and admission to the park. Members can also use the water park for an additional $5 per day. Nonmembers pay $6 for parking, $15 for admission, and $9 for the waterpark.
Write and solve an equation to find the number of visits it would take for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.
The yearly membership cost plus the cost per visit was set equal to the non-member cost per visit, and solving the equation gave us the result.
We need to find the number of visits it would take for the total cost of a member and a non-member to be the same if they both use the waterpark at each visit. Let's denote the number of visits as x.
The yearly membership cost is $275, and each visit to the waterpark costs an additional $5 for a member. So, for x visits, the total cost for a member is:
Member cost = $275 + $5x
Non-members pay $6 for parking, $15 for admission to the park, and $9 for the waterpark per visit. Therefore, the total cost for a non-member is:
Non-member cost = ($6 + $15 + $9)x = $30x
Setting both costs equal to find the number of visits where the costs are the same:
$275 + $5x = $30x
Now we solve for x:
$275 = $30x - $5x
$275 = $25x
x = $275/$25
x = 11
Therefore, it would take 11 visits for the total cost to be the same for a member and a non-member if they both use the waterpark at each visit.