A health club charges a one time initiation fee of $120.00 plus a membership fee of $30.00 per month. a. Write an expression for the cost function C(x) that gives the total for membership at the health club for x months. b. Draw a graph of the function in (a).c. The health club decided to give it's member an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, use a different color and draw on the same set of axes the cost graph under the plan. d. Determine after how many months the second plan is less expensive for the member. a. C(x) = _______ (Do not factor)
Answers
a.
Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.
The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.
It can be represented by the expression C(x);
[tex]C(x)=120+30x[/tex]b.
Graphing of the function, we would have;
c.
If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;
[tex]F(x)=420+10x[/tex]graphing the above function, we have;
the first plan is represented by the blue line while the second plan is represented by the red line.
d.
The number of months after which the second plan is less expensive is the value of x when the two lines meet.
the two lines meet at point;
[tex](15,570)[/tex]The value of the x coordinate is 15.
So, The number of months after which the second plan is less expensive is
[tex]15\text{ months}[/tex]
Related Questions
2/___=4/18What is the answer to the problem
Answers
Explanation:
These are equivalent fractions, we have to find the missing denominator from the fraction on the left. Since the numerator of the fraction on the right is 4 and the numerator of the fraction on the left is 2, we can see that we have to divide by 2. Therefore 18 divided by 2 is 9. This is the numerat
Answer:
Evaluate( - 4) ^ 3/2
Answers
Answer: 8i
A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw. Fly Read minds Forgetful 6 11 Lazy 5 7 What is the probability that a randomly selected superhero is forgetful and can fly? Simplify any fractions.
Answers
The probability is given the following formula:
Probability = Favorable / total outcomes
In this case, there number of students that selected a forgetfull sperheroe that can fly is 6, the total number of outcomes is 6 + 11 + 5 + 7 = 29, then we get:
Probability = 6 / 29
Then, the probability of selecting a forgetful superheroe that can fly is 6/29
A study done by researchers at a university concluded that 60% of all student athletes in the country have been subjected to 74 repeating the study is based on responses from 1600 athlete what is the margin of error and the 95% confidence interval of the study 
Answers
The marginal error is 0.0240
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
Given,
The percentage of students surveyed = 60%
Number of athletes = 1600
Confidence interval = 95%
We have to find the marginal error and 95% confidence interval of the study;
The following results are obtained from a sample of n people that were surveyed, with a probability of success of π and a level of confidence of 1 - ∝
π ± z [tex]\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Where,
z is the z score with a p value of 1 - ∝/2
Here we have,
n = 1600 and π = 0.6
95% confidence level
So ∝ = 0.05 , z is the value of Z that has a pvalue of 1 - 0.05/2 , so Z = 1.96.
Then, the margin of error is;
M = [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
M = [tex]1.96\sqrt{\frac{0.6.0.4}{1600} }[/tex]
M = 0.0240
M = 2.40 percentage points.
Lower limit of the interval;
π - M = 0.6 - 0.0240 = 0.576
Upper limit of the interval;
π + M = 0.6 + 0.0240 = 0.624
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
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Not sure on how to do this. Could really use some help.
Answers
We will have the following:
We will recall that the surface area of a sphere is given by:
[tex]A_s=4\pi r^2[/tex]So, the surface area of the given sphere will be:
[tex]\begin{gathered} A_s=4\pi(\sqrt{\frac{7}{3.14}})^2\Rightarrow A_s=4(3.14)\ast\frac{7}{3.14} \\ \\ \Rightarrow A_s=4\ast7\Rightarrow A=28 \end{gathered}[/tex]So, the surface area of the sphere will be 28 yd^2.
*The reason we can use "mental math" is that we are using an approximation of pi, which makes it so it cancels with the 3.14 in the denominator after a point; leaving a simple multiplication at the very end.
Laura, Sam, and Miguel served a total of 121 orders Monday at the school cafeteria, Miguel served 7 fewer orders than Laura. Sam served 4 times as manyorders as Miguel. How many orders did they each serve?Number of orders Laura served:Number of orders Sam served:Number of orders Miguel served:
Answers
Let L, S, and M, denote the number of orders served by Laura, Sam, and Mighuel, respectively, on Monday at the school cafeteria.
Given that the total 121 orders were served,
[tex]L+S+M=121\ldots(1)[/tex]Given that Miguel served 7 fewer orders than Laura,
[tex]\begin{gathered} M=L-7 \\ L=M+7 \end{gathered}[/tex]Given that Sam served 4 times as many orders as Miguel,
[tex]\begin{gathered} S=4\cdot M \\ S=4M \end{gathered}[/tex]Substitute the values of 'L' and 'S' in equation (1),
[tex](M+7)+(4M)+M=121[/tex]Simplify the above expression,
[tex]\begin{gathered} M+7+4M+M=121 \\ 6M+7=121 \\ 6M=121-7 \\ M=\frac{121-7}{6} \\ M=19 \end{gathered}[/tex]The corresponding values of L and S will be,
[tex]\begin{gathered} L=19+7=26 \\ S=4\cdot19=76 \end{gathered}[/tex]Thus, Laura served 26 orders, Sam served 76 orders, while MIguel served 19 orders on Monday at the school cafeteria.
Josh wants to use Rockaway Hall, the Groove Guru Band, and PJ's Party Supplies. Josh has a total of
650 dollars and wants to invite 25 people. His friend told him he would be able to afford the band for 4 hours. Is that true?
Answers
1) Assume that x is the number of hours and that y is the total cost. To model, write an equation. 2) Tutoring his friend in geometry is the second way he can get money.
One of the first areas of mathematics is geometry, along with arithmetic.
What is the Bernoulli inequality?A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used. It contains a few helpful variations, including those for any integer r 0 and real number x > 1. If x 0 and r 2, the inequality is strictly true.A statement about raising a number to a natural power is made by the binomial inequality: and. It can be easily demonstrated by induction and is essentially a condensed version of the binomial theorem.A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used.To learn more about Bernoulli inequality refer to:
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Which of the following graphs represent the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
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The Solution:
Given:
[tex]\begin{gathered} f(x)=x^2+2x+2 \\ \\ g(x)=-x^2+2x+4 \end{gathered}[/tex]We are required to determine the graphs of the given functions.
Below is the graph of the function:
Thus, the correct answer is:
Hello! I need a little bit of help with this question please. (This information is not from an open test, it is a book as I'm studying for the ASVAB I am going to take later on.)
Answers
Given:
[tex]\sqrt{100}-\sqrt{64}[/tex]To find:
We need to solve this sum and find the final answer
Step-by-step solution:
To solve this problem, we need to know the square root of 100 and 64.
√100 = 10
√64 = 8
[tex]\begin{gathered} =\sqrt{100}-\sqrt{64} \\ \\ =10\text{ - 8} \\ \\ =2 \end{gathered}[/tex]Final answer:
Thus 2 (Option A) is the correct answer.
Order the lengths from least to greatest 19in 1yd 2ft 32in
Answers
19 in
1 yd
2ft
32 in
First, we have to convert all the length into a unique unit:
For example, inches:
Since
1 ft = 12 inches
2 ft = 2 x12 = 22 inches
1yd = 36 inches
Now, we have to order from least to greatest:
19 in-22in -32in-36in
In the original units:
19 in , 2ft, 32in ,1yd
Identify all points and line segments in the picture below.Points: A, B, C, DLine segments: AB, BC, CD, AD, BD, ACPoints: A, B, C, DLine segments: AD, AC, DC, BOPoints: A, B, C, DLine segments: AB, AD, AC, DC, BCPoints: A, BLine segments: AB, AC, DC, BC
Answers
Option C
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
what is the slope of the line shown graohed belowzero5undefined-5
Answers
Answer: undefined
The slope of this graph is undefined because it does not run on the horizontal
Since, slope = y2 - y1 / x2 - x1
Therefore, x2 - x1 = 0
Slope = y2 - y1 / 0 = undefined
In a test of the effectiveness of garlic for lowering cholesterol, 48 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 5.3 and a standard deviation of 19.6. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
Answers
1) The 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment is 5.3 ± 5.6.
2) Regarding the effectiveness of garlic in reducing LDL cholesterol, the confidence interval suggests A. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
What is the confidence interval estimate?The confidence interval estimate shows us the mean estimate plus or minus the margin of error (or variation in the estimate).
On the other hand, the margin of error is the difference between the actual and projected results in a random sample.
The number of subjects treated with garlic, n = 48
The mean changes in LDL cholesterol level = 5.3
The standard deviation = 19.6
The 95% confidence interval gives a Z-score of 1.96
The margin of error = Z-score x standard deviation/√n
= 1.96 x 19.6/√48
= 1.96 x 19.6/6.9
= 1.96 x 2.84
= 5.6
Lower Limit = Mean - Margin of Error
= 5.3 - 5.6
= -0.3
Upper Limit = Mean + Margin of Error
= 5.3 + 5.6
= 10.9
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Question Completion with Answer Options:2. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
A.The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
B.The confidence interval limits do not contain0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
C.The confidence interval limits do not contain0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
D.The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
3/4 square foot in 1/2 hour what is the unit rate as mixed number
Answers
Answer:
[tex]\text{1 }\frac{1}{2}[/tex]Explanation:
The unit rate is:
3/4 divided by 1/2
[tex]\begin{gathered} \frac{3}{4}\times\frac{2}{1} \\ \\ =\frac{3}{2} \end{gathered}[/tex]As a mixed fraction, it is
[tex]\text{1 }\frac{1}{2}[/tex]which is the solution of 3(t + 1) = 6 - 13.5?A <-5.5B t2-5.5Ci< 5.5D (>55
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} 3\mleft(t+1\mright)\le6t-13.5 \\ 3t+3\le6t-13.5 \\ \text{Put like terms together, we have:} \\ 3+13.5\le6t-3t \\ 16.5\le3t \\ \frac{16.5}{3}\le\frac{3t}{3} \\ 5.5\le t\Rightarrow t\ge5.5 \\ \therefore t\ge5.5 \end{gathered}[/tex]Therefore, D is the correct answer
Solve the inequalities|4x + 5| + 2 > 10
Answers
We have to solve this inequality:
[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.
When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:
[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:
[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.
We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).
Answer: (-∞, -3.25) ∪ (0.75, ∞)
A random sample of CGCC students found that 19% say math is their favorite subject with a margin of error of 2.5 percentage points.a) What is the confidence interval? % to %b) What does the confidence interval mean?
Answers
If 19% say that math is their favorite subject, with a margin of error of 2.5%, then the confidence of interval is:
[tex]\begin{gathered} Confidence\text{ of interval= 19\% math }\pm\text{ 2.5\% margin of error} \\ Confidence\text{ of interval= 16.5\% to 21.5\%} \end{gathered}[/tex]b) The confidence of interval is the range of values in which you think the study or the values are going to fall between if anyone redo the study, it doesn't contain the margin of error because this percentage means the probability that the values aren't going to fall between the confidence of interval.
the jar's inner dimensions are approximately a rectangular prism with dimensions of 14cm by 12cm by 28cm. George estimates that the lowest amount of marbles possible to fill the jar 225 marbles and the highest amount is approximately 489 marbles. what is the reasonable lower limit and upper limit for the amount of marbles in the jar according to Fermi?
Answers
Given: the dimensions of the rectangular prism is 14 x 12 x 28 in cm
Here are the numbers of times 13 people ate out last month.5, 3, 4, 6, 3, 4, 5, 6, 4, 7, 3, 7, 6Find the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."No modeX?.
Answers
The mode is the number that appears most or occurs most frequently. Therefore, the mode of the data set below can be calculated below
[tex]5,3,4,6,3,4,5,6,4,7,3,7,6[/tex]Let's rearrange the data
[tex]3,3,3,4,4,4,5,5,6,6,6,7,7[/tex]The mode will be
[tex]\mleft\lbrace3,4,6\mright\rbrace[/tex]The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
Answers
4149000000 is the approximation age of oldest rock. The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest."
What is approximation age?The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest." The closest estimate you can make without knowing something's exact size or measurement is called an approximation.
Despite the fact that approximation is most usually used in relation to numbers, it is also regularly used in relation to mathematical functions, forms, and physical laws. In science, the term "approximation" can refer to using a less complex method or model when the proper one is challenging to use.
For this, sampling techniques like Markov chain Monte Carlo and significance sampling as well as variationally methods like mean-field approximations and assumed density filtering have been used.
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drag the location of each ordered pair after a reflection over the x axis stated. then, drag the correct algebraic representation of the reflection to the white box. answer choices: (y, x), (-2,-6),(x,-y),(-3,-2),(5,8),(-5,-8),(-x, y),(-6,-6),(-6,-1),(2,-6),(6,-1),(3,2),(-x, -y),(-7,-2),(6,-6),(7,2)
Answers
Reflection over the x-axis transform the point (x, y) into (x, -y)
Applying this rule to the vertex of the triangle ABC, we get:
A(-6, 6) → A'(-6, -6)
B(-2, 6) → B'(-2, -6)
C(-6, 1) → C'(-6, -1)
Algebraic representation: (x, -y)
kmarks Solve the following system of equations graphically on the set of axes below 1 y 22 - 4 y = -X – 7 Plot two lines by clicking the graph. Click a line to delete il. y 10 9 8 7 6 5 4 3 2. 1 5 6 7 8 9 10
Answers
Explanation:
For the first line :
1. Draw a line which has a slope of 1 /2
2. Adjust the line so that it has a y-intercept of -4.
For the second line:
1. Draw a line which has a slope of -1
2. Adjust this line so that it has a y-intercept of -7.
Finally, find the point where the two lines intersect.
The coordinates of the point of intersection are the solution to our system.
To get a line which has a slope 1/2, you start from (0, -4 ) and then move 2 units to the right and then 1 unit up.
At the end of 2008, the number of text messages sent one month was
110.4 billion. If 270.3 million people used text messaging, about how
many did each person send that month? Round to the nearest whole
number.
Answers
The average number of text messages sent during the month by each person was 408.
What is the average?The average is the total number of a data set divided by the number of items on the data set.
The average is the same as the mean, which is a central value of a data set.
The total number of text messages sent in a month in 2008 = 110.4 billion
(110,400,000,000)
The total number of people using text messaging = 270.3 million (270,300,000)
Average text messages per person = 408. 44 (110,400,000,000/270,300,000)
Thus, we can conclude that, on average, each person in the population texted 408 messages per month in 2008.
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Solve for w.4w+6= -22Simplify your answer as much as possible.W8DDХ5?
Answers
w= -7
Explanation
[tex]\begin{gathered} 4w+6=-22 \\ \end{gathered}[/tex]
Step 1
The addition property of equality and subtraction property of equality are similar. Adding or subtracting the same number to or from both sides of an equation keeps both sides equal, so we can use this fact to isolate w
a) subtract 6 in both sides of the equation
[tex]\begin{gathered} 4w+6=-22 \\ 4w+6-6=-22-6 \\ 4w=-28 \\ \end{gathered}[/tex]Step 2
The division property of equality states that when we divide both sides of an equation by the same number, the two sides remain equal.so
b) divide both sides by 4
[tex]\begin{gathered} 4w=-28 \\ \frac{4w}{4}=\frac{-28}{4} \\ w=-7 \end{gathered}[/tex]therefore, the answer is
w= -7
I hope this helps you
write the function below in slope. Show ALL the steps and type the answer.
Answers
This is a simple question to solve. First, let's take a look at a slope-intercept form equation as follows:
Once we know how a slope-intercept form looks like all we need to do is to simplify our equation to find that as follows:
And that is our slope-intercept form:
What is the answer and how do I solve this
Answers
A parent absolute value function f(x) = |x| is plotted as
We can change the appearance of this absolute value function based on what we add to the absolute value function and the constant accompanied by it.
Let's start with shifting the plot from |x| to |x+1|. If we add +1 to x inside an absolute value function, the parent absolute value function will shift one unit to the left. This shifting is represented by the red dotted plot on the figure below.
We now multiply a constant -3 on the absolute value function |x+1|. Multiplying a negative number to the absolute value function results in mirroring the absolute value function via the x-axis. Then, the plot will be compressed by a factor of 1/3. We now have
Hence, the final plot for the given absolute value function y = -3|x+1| is
Use the distributive property and simplify: 3n+4-5(n+6)
Answers
By distributing the number -5 into the parentheses, we have
[tex]3n+4-5n-30[/tex]Now, by collecting similar terms, we get
[tex]-2n-26[/tex]Therefore, the answer is: -2n-26
Evaluate the logarithmLog 6 1/36
Answers
Answer:
-2
Explanation:
By properties of logarithms, the logarithm of a fraction is equal to the difference of logarithms, so
[tex]\log _6(\frac{1}{36})=\log _61-\log _636[/tex]Now, log₆(1) = 0 and log₆36 = 2, so
[tex]\begin{gathered} \log _6(\frac{1}{36})=0-2 \\ \log _6(\frac{1}{36})=-2 \end{gathered}[/tex]Therefore, the answer is -2
used to name a point
Answers
Answer:
It is represented by a dot and named by a capital letter
Step-by-step explanation:
O GRAPHS AND FUNCTIONSIdentifying solutions to a linear equation in two variables
Answers
Given:
Function is:
[tex]9x+2y=13[/tex]Find-:
Check for solution
Explanation-:
The value of "y" is:
[tex]\begin{gathered} 9x+2y=13 \\ \\ 2y=13-9x \\ \\ y=\frac{13-9x}{2} \end{gathered}[/tex]For (0,8)
Check value of "y" at x = 0 then,
[tex]\begin{gathered} x=0 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(0)}{2} \\ \\ y=\frac{13-0}{2} \\ \\ y=\frac{13}{2} \\ \\ y=6.5 \end{gathered}[/tex]So (0,8) it is not a solution.
Check (3,-7) the value of "x" is 3
[tex]\begin{gathered} x=3 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(3)}{2} \\ \\ y=\frac{13-27}{2} \\ \\ y=-\frac{14}{2} \\ \\ y=-7 \end{gathered}[/tex]So (3,-7) is the solution of function.
Check for (1 , 2) value of "x" is 1.
[tex]\begin{gathered} x=1 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9}{2} \\ \\ y=\frac{4}{2} \\ \\ y=2 \end{gathered}[/tex]So, (1,2) is the solution.
Check for (4,-5) the value of "x" is 4.
[tex]\begin{gathered} x=4 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(4)}{2} \\ \\ y=\frac{13-36}{2} \\ \\ y=-\frac{23}{2} \\ \\ y=-11.5 \end{gathered}[/tex]So, (4,-5) is not a solution
