Tipton Tile has seen an increase in tile sales over the last few weeks. They sold 4,212 square feet of tile to 36 customers last week. If they are expecting between 51 and 59 people to buy tile this week, about how many square feet of tile can they expect to sell?

The probability that the person will not die will be D. 0.99548

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

Since the probability that the person will die is 814/1000000, the probability that the person will not die will be:

= 1 - 452/100000

= 99548/100000

= 0.99548

The correct option is D.

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If the probability that a person will die in the next year is 452/100000, the probability that the person will not die in the next year?

A. 99%

B. 0.99548

C. 0.00452

D. 0.99548

Answer:

Step-by-step explanation:

According to Tylor theorem,

f(x)=f(a)+f′(a)/1!×(x−a)+f′′(a)/2!×(x−a)2+......+fn(a)/n!×(x−a)n

Tylor series for cosx is

1 - x^2/2! + x^4/4! + x^6/6! + ……

cos (0.3) = 1 - 〖(0.3)〗^2/2! + 〖(0.3)〗^4/4!

The R4 valur is fourth derivative of cosx

f’(x) = -sinx

f’’ (x) = -cosx

f’’’ (x) = sinx

f’’’’ (x) = cosx

Here, a = 0, n = 3, x = 0.3

max l f^4l = cos (0.3)

               = 0.9999

lR_4  (x)l ≤ |0.3-0|^(4+1)/4! × 0.9999

              ≤ 0.00015186

               = 1.51786 × 10^(-4)

R_n (x) = cos (0.3) – (1 - 〖(0.3)〗^2/2!-(0.3)^4/4!)

          = 0.0446

The error of approximation R_4  (x) ≤ 1.2 × 10^(-2) and exact value of error R_4 = 0.0446

1) The function that shows the decay is N(t) = 30e^-rt.

2) The percentage rate of decay is 0.98 %.

We know that an element is said to be radioactive if the element can be able to decay spontaneously. The implication of this is that the amount of the element that in the system would continue to be reduced and new daughter nuclei are formed.

We have that;

If the initial mass of the radioactive isotope X has been give to us in the question as 30 g then it follows that we can write the function as;

N(t) = 30e^-rt

N(t) =Mass of the element at time t

r = rate of decay

t = time taken

Since half of the element X would remain after 71 years, we have;

15 = 30e^ -71r

15/30 = e^ -71r

0.5 = e^ -71r

ln 0.5 = -71r

r = ln 0.5/-71

r = 0.0098 or 0.98 %

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Answer:

D

Step-by-step explanation:

b/c

A B and C are not true

Answer:

D

Step-by-step explanation:

We can visualize this by ignoring the constant of 0.3 and remembering the |x| graph.

It has a -x slope when x < 0, and a +x slope when x > 0

The only answer that has a negative slope when x is less than 0 and a positive slope when x is greater than 0 is D.

The 95% confidence interval for p, the proportion of all adults who exercise regularly is (0.46, 0.66).

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given

Sample size(n) = 100

x = 56

Sample proportion (p) = x/n = 56/100 = 0.56

Here, c =  95%, a = 0.95

1-a = 0.05, a/2 = 0.025

Z(a/2) = 1.96

95% confidence interval for p is:

= p-Z(a/2)√{p(1-p)}/n, p+Z(a/2)√{p(1-p)}/n

= 0.56- 1.96√{0.56(1-0.56)}/100, 0.56+1.96√{0.56(1-0.56)}/100

= 0.56 - 0.0972, 0.56+0.0972

= 0.4628, 0.6572

= (0.46, 0.66)

Hence, the 95% confidence interval for p, the proportion of all adults who exercise regularly is (0.46, 0.66).

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equaled the target population. the sample consisted of all veterinarians who returned the questionnaire is None of the answer choices is correct.

The sample in this case consists of all veterinarians who treat horses with Non-Steroidal Anti-Inflammatory Drugs (NSAIDs). The target population for this study would be all veterinarians who treat horses with NSAIDs. Therefore, since the sample is made up of all veterinarians in the target population, the sample equals the target population. None of the answer choices provided is correct in this scenario.

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In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = -1.1

What is standard deviation?

In statistics, the quality deviation could be a live of the quantity of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be about to the mean of the set, whereas a high variance indicates that the values area unit opened up over a wider vary

Main body:

The z score tells us the distance, in terms of standard deviation, the raw score is from the mean. Negative z values are below the mean, while positive ones are above the mean.

Something like z = 2.5 indicates we're 2.5 standard deviation units above the mean.

Something like z = -1.1 indicates we're 1.1 standard deviation units below the mean.

The value z = 0 itself is the center of the standard normal distribution (it's the mean mu).

The sigma value for the standard normal Z distribution is sigma = 1

sigma = population standard deviation

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for a study cvaluating the difference among three treatments with a separate sample of n-10 for cach treatment,the kruska-walis test statistic would have df - 2(3-1)=2

The Kruskal-Wallis test statistic has a degrees of freedom (df) equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1).The Kruskal-Wallis test statistic is a non-parametric test used to compare the means of a set of independent samples. In this case, we have three separate samples of n-10 for each treatment. To calculate the Kruskal-Wallis test statistic, we need to first calculate the sum of the ranks for each sample and then subtract the expected sum of ranks for each sample. The df for the Kruskal-Wallis test statistic is equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1). Finally, the Kruskal-Wallis test statistic is calculated by dividing the calculated sum of ranks by the expected sum of ranks and multiplying by the df. This will give us the Kruskal-Wallis test statistic for the data set.

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The exponential growth function that models the population growth of the given city is P(t) = P(0) x e^rt and the population of the city in 2016 is 328,029.39.

The population of the city in 2000 (t=0) = 145,210

The population of the city in 2010 (t=10) = 219,185

Rate of growth for 10 years = ((219185 - 145210)/145210) x 100

Rate of growth for 10 years = 50.943%

Rate of growth per year = Rate of growth for 10 years/10

Rate of growth per year = (50.943/10)%

Rate of growth per year = 5.094%

According to the exponential growth function,

P(t) = P(0) x e^rt

Population in 2016 (t=16) is:

P(16) = 145210 x e^((5.094/100) x 16)

P(16) = 145210 x 2.259

P(16) = 328029.39

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Answer:

2 × 2 × 7

Step-by-step explanation:

start dividing by the lowest prime and work up until 1 is reached

28 ÷ 2 = 14

14 ÷ 2 = 7

7 ÷ 7 = 1

then

28 = 2 × 2 × 7 = 2² × 7

Answer:

------------------------------

Simplify:

Answer:

[tex] \sf \red{c) \: 16} \: is \: the \: answer.[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf →6 + \frac{3}{8} [/tex]

Changing error in problem,

[tex] \sf →6 \div \frac{3}{8} [/tex]

Let's solve the problem,

[tex] \sf →6 \div \frac{3}{8} [/tex]

[tex] \sf →6 \times \frac{8}{3} [/tex]

[tex] \sf → \frac{(6 \times 8)}{3} [/tex]

[tex] \sf → \frac{48}{3} [/tex]

[tex] \sf \: →16 \:[/tex]

Hence, the answer is 16.

The builder must pay the bank $6005.66. for further details read below.

A mortgage is a type of loan used to purchase or maintain a home, land, or other types of real estate.

For the given problem We must determine the present value of all the relaxations granted to us over the first two years in order to determine how much the builder must pay the bank for this buydown payment. The output and Excel formulae are listed below.

Monthly payment    726.96

Monthly interest rate   10.%/12

Relaxation value in 1st year:

Amount reduced     C2*50%

No. of months    12

present value    PV(C3,C7, -C6)

Relaxation value in 2nd year:

The amount reduced       C2*25%

No. of months    12

present value    PV(C3,C12, -c11)

Present value today     C13/(1+ C 3)^12

Present value of buy option     C14 + C8

Therefore, the buydown option's current value is $6005.66. In order to provide this option to the customers, the builder must pay the bank $6005.66.

b. It is advised to take advantage of this option since the benefit the house buyer would get, or its current value exceeds the additional cost. Benefits to the purchaser of this option include. The benefit to the buyer equals the Present Value of the BuyDown Option - Additional Payment

Buyer benefit is equal to 6005.66 - 5000, or 1005.66$.

So, if a buyer received this option, he would profit $1005.66. It is thus advised to purchase real estate using this buydown option.

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Hello,

The probability that both number generators generate the number 5 is (1/10) * (1/10) = 1/100 = 0.01 or 1%.

This is because the probability of an event occurring is the product of the probabilities of each event occurring independently. In this case, the probability of the first generator generating the number 5 is 1/10 and the probability of the second generator generating the number 5 is also 1/10, so the probability of both events occurring is (1/10) * (1/10) = 1/100.

----

The function represented by the series is [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]

The interval of convergence of the series is ( - 1, 1 )

As per the question the given function is:

[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k$$[/tex]

[tex]$$\sum_{n=0}^{\infty} a r^n=\frac{1}{1-r}$$[/tex]

[tex]$$\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$[/tex]

[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\frac{1}{1-\frac{x^2+3}{4}} \\& =\frac{1}{\frac{4-x^2-3}{4}} \\& =\frac{4}{1-x^2}\end{aligned}$$[/tex]

Thus, [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]

[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k=\sum_{k=0}^{\infty} \frac{\left(x^2+3\right)^k}{4^k}$$[/tex]

[tex]$$\begin{aligned}L & =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)^{k+1}}{4^{k+1}} \frac{4^k}{\left(x^2+3\right)^k}\right| \\& =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)}{4}\right| \\& =\left|\frac{\left(x^2+3\right)}{4}\right|\end{aligned}$$[/tex]

The series will converge, if L<1

[tex]$$\begin{array}{ll} & \left|\frac{\left(x^2+3\right)}{4}\right| < 1 \\ & \frac{\left(x^2+3\right)}{4} < 1 \\ & x^2+3 < 4 \\\end{array}[/tex]

[tex]& x^2 < 1 \\[/tex]

 |x| < 1

 -1 < x < 1

Substitute the values of 'x' in the given function

At, x = - 1

[tex]\begin{aligned} \\\qquad \begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(-1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}\end{aligned}$$[/tex]

Also, at x = 1

[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}$$[/tex]

Thus, the interval of convergence is ( - 1, 1 )

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Answer:1=t

2=flase

3=flase

4=flase

5=true

6=true

7flase

8=true

Step-by-step explanation:i spelt false wrong lol

A square-based pyramid has a total of five faces. Four of the faces are triangles and one of the faces is a square. The surface area of a square-based pyramid is the total area of all its sides.

hope this helps!! :D

Answer:

1/9

Step-by-step explanation:

PLEASE MARK AS BRAINLIEST

Answer: The voting district that contributed the most to the test statistic is District B.

Step-by-step explanation:

How do you calculate the contribution of each voting district to the test statistic?

The contribution of each voting district to the test statistic is calculated by taking the difference between the observed and expected values for that district, squaring it, and then dividing it by the expected value. In this case, the contribution for District A is (58-46.80)^2/46.80 = 2.68, the contribution for District B is (22-32.40)^2/32.40 = 3.34, the contribution for District C is (12-18)^2/18 = 2.00, and the contribution for District D is (28-22.80)^2/22.80 = 1.19. Therefore, District B contributed the most to the test statistic.

The chi-square goodness-of-fit test compares observed and expected values to determine if they are significantly different from each other. The test statistic is calculated by summing the squared differences between the observed and expected values, divided by the expected values. The larger the difference between the observed and expected values, the larger the contribution to the test statistic. In this case, District B had the largest difference between the observed and expected values, therefore it had the greatest impact on the overall test statistic.

District B contributed the most to the test statistic because it had the highest value in the "Components" column. The formula for the chi-square goodness-of-fit test is (Observed - Expected)^2 / Expected, and the resulting value for District B is 3.34, which is the highest of the four districts. Therefore, District B had the biggest deviation from the hypothesized proportions.

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Answer: Voting district B contributed the most to the test statistic.

Step-by-step explanation:

How do you determine each voting district's contribution to the test statistic?

By subtracting the observed value from the predicted value for each voting district, square rooting the result, and then dividing the result by the expected value, the contribution of each voting district to the test statistic is determined. In this instance, the contributions for Districts A, B, C, and D are as follows:

District A's contribution is (58-46.80)²/46.80 = 2.68; District B's contribution is (22-32.40)²/32.40 = 3.34; District C's contribution is (12-18)²/18 = 2.00; and District D's contribution is (28-22.80)²/22.80 = 1.19. As a result, District B was most responsible for the test statistic.

In order to assess if actual and expected values differ significantly from one another, the chi-square goodness-of-fit test compares observed and expected values. The test statistic is determined by multiplying the expected values by the total of the squared discrepancies between the actual and predicted values. The contribution to the test statistic increases as the gap between observed and predicted values widens. In this instance, District B's largest disparity between actual and predicted values had the biggest effect on the test statistic as a whole.

Due to having the highest value in the "Components" column, District B had the greatest impact on the test statistic. (Observed - Expected)² / Expected is the formula for the chi-square goodness-of-fit test, and the result for District B, which is the highest of the four districts, is 3.34.

District B therefore, showed the greatest departure from the predicted proportions.

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Answer:

Second option (Plot 3-17i. Scale by ✓2/4 .Rotate 45° clockwise.)

Step-by-step explanation:

Given below in the picture.

I hope my answer helps you.

The gallons of gas that she would need to travel 162 miles will be 4374 gallons.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mackenzie's car used 4 gallons to travel 108 miles. The rate will be:

= 108 / 4

= 27 miles per gallon

The gallons of gas that she would need to travel 162 miles will be:

= 162 × 27

= 4374 gallons.

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Answer:

m = -4 ; c = 3

Step-by-step explanation:

m is the number that multiplies x

c is the number without letters

Answer:

1. To find the probability that a randomly selected test has a score of 90 or higher, we need to find the z-score corresponding to a score of 90 and then use the standard normal table to find the probability that a score is greater than or equal to this value. To find the z-score, we can use the formula:

z = (x - mean) / standard deviation

where x is the score we are interested in, mean is the average score, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:

z = (90 - 75) / 8 = 1.875

Rounding this value to the nearest hundredth, we get z = 1.88. Looking up this value in the standard normal table, we find that the probability that a score is greater than or equal to 1.88 is 0.9637. Therefore, the probability that a randomly selected test has a score of 90 or higher is 0.9637.

2. To find the probability that the grill will last less than 3 years, we need to find the z-score corresponding to a life of 3 years and then use the standard normal table to find the probability that a life is less than this value. To find the z-score, we can use the formula:

z = (x - mean) / standard deviation

where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:

z = (3 - 3.5) / 0.35 = -1.43

Rounding this value to the nearest hundredth, we get z = -1.43. Looking up this value in the standard normal table, we find that the probability that a life is less than -1.43 is 0.0747. Therefore, the probability that the grill will last less than 3 years is 0.0747.

3. To find the probability that the ambulance will respond within 6 to 8 minutes, we need to find the z-scores corresponding to a response time of 6 and 8 minutes, respectively, and then use the standard normal table to find the probability that a response time is between these two values. To find the z-score, we can use the formula:

z = (x - mean) / standard deviation

where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:

z1 = (6 - 7.5) / 2.5 = -0.6

z2 = (8 - 7.5) / 2.5 = 0.2

Rounding these values to the nearest hundredth, we get z1 = -0.6 and z2 = 0.2. Looking up these values in the standard normal table, we find that the probability that a response time is less than -0.6 is 0.2743 and the probability that a response time is less than 0.2 is 0.5398. Therefore, the probability that a response time is between -0.6 and 0.2 is 0.5398 - 0.2743 = 0.2655. Therefore, the probability that the ambulance will respond within 6 to 8 minutes is 0.2655.

1. The probability that a randomly selected test has a score of 90 or higher is 0.0301.

2. The probability that the grill will last less than 3 years is 0.0764.

3. The probability that an ambulance will respond within 6 to 8 minutes is 0.1465.

In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:

Z-score, z = (x - μ)/σ

Where:

Part 1.

By substituting the given parameters, we have the following:

Z-score, z = (90 - 75)/8

Z-score, z = 1.88

Based on the standardized normal distribution table, the required probability is given by:

P(Z ≥ 1.88) = 1 - P(x < Z)

P(Z ≥ 1.88) = 1 - 0.9699

Probability = 0.0301.

Part 2.

By substituting the given parameters, we have the following:

Z-score, z = (3 - 3.5)/0.35

Z-score, z = -1.43

Based on the standardized normal distribution table, the required probability is given by:

P(Z < -1.43) = 1 - P(x > Z)

P(Z < -1.43) = 1 - 0.9236

Probability = 0.0764.

Part 3.

At 6 minutes, we have:

Z-score, z = (6 - 7.5)/2.5

Z-score, z = -0.6

At 8 minutes, we have:

Z-score, z = (8 - 7.5)/2.5

Z-score, z = 0.2

Based on the standardized normal distribution table, the required probability is given by:

P(6 < x < 8) = P(-0.6 < z < 0.2)

P(-0.6 < z < 0.2) = P(z < 0.2) - P(z < -0.6)

P(-0.6 < z < 0.2) = 0.42074 - 0.27425

P(-0.6 < z < 0.2) = 0.1465.

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Check the picture below.

We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets. The correspondence a function.

The symbol for an ordered pair is (INPUT, OUTPUT): The relation denotes the connection between the input and output.

For the stated question-

We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets.

One student is related to one facility.

Thus, correspondence given forms a function.

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The confidence interval for the population mean at significance level is

2.724<μ<30.76 .

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Population standard deviation: σ = 0.45

Sample size: n = 25

Sample Mean: x= 2.90

Х=2.90 represent the sample mean for the sample  

μ population mean (variable of interest)

σ = 0.45 represent the population standard deviation

n=25 represent the sample size  

We have the following distribution for the random variable:

X≈N(μ,σ =0.45)

And by the central theorem we know that the distribution for the sample mean is given by:

X≈N( μ, [tex]\frac{σ}{\sqrt{n} }[/tex])

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha =0.05[/tex] and[tex]\frac{\alpha }{2} =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)" and we see that

Z₁ =±1.96

Now we have everything in order to replace into formula:

[tex]2.90-1.96\frac{0.45}{\sqrt{25} }=2.724[/tex]

[tex]2.90+1.96\frac{0.45}{\sqrt{25} }=3.076[/tex]

So on this case the 95% confidence interval would be given by (2.724:3.076) .

At a significance level, the population mean's confidence interval is 2.724–30.76.

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a) The type of function that can be used to describe the value of each house is:

b) The functions that define the value of each house are given as follows:

For House 1, the change each year is a percentage, as follows:

312519.92/303417.30 = 303417.30/294580 = 1.03.

Hence, considering the initial value of $294,580, the exponential function is defined as follows:

H1(x) = 294580(1.03)^x.

For House 2, the change each year is a fixed amount, as follows:

313,000 - 304,000 = 304,000 - 295,000 = 9,000.

Hence, considering the initial value of 295,000, the linear function is defined as follows:

H2(x) = 295,000 + 9,000x.

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The polar coordinates of the points are: A(√29,68.1°),B(√45,-63.4°),C(√97,66.0°),D(√65,7.12°)

consider A=(2,5)

To find the polar coordinates we have the formula:

[tex]r=\sqrt{x^2+y^2} and tan^{-1} (\frac{y}{x} )----------(1)[/tex]

Assume that x=2,y=5 and substitute in equation(1)

r=√2^2+5^2 and tan^-1(5/2)

r=√4+25 and tan^-1(2.5)

r=(√29,68.1°)

For point B =(3,-6)

Assume that x=3,y=-6 and substitute in equation(1)

r=√3^3+(-6)^2 and tan^-1(-6/2)

r=√9+36 and tan^-1(-2)

r=(√45,-63.9°)

For point C=(-4,9)

Assume that x=-4,y=9 and substitute in equation(1)

r=√(-4)^2+9^2 and tan^-1(9/-4)

r=√16+81 and tan^-1(2.25)

r=(√97,66.0°)

For the point D=(-8,-1)

Assume that x=-8,y=-1 and substitute in equation(1)

r=√(-8)^2+(-1)^2 and tan^-1(-1/-8)

r=√64+1 ,7.12°

r=(√65,7.12°)

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Confidence interval for the population mean time σ for computer repairs is [98.05 , 89.850].

What is confidence interval?

A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for an exact proportion of times.

Main body:

According to question:

N = 110

X bar = 93.9 minutes

σ = 16.9 minutes

value for 99% confidence interval = 2.576

C.I. = x bar ± z*s/√n

C.I. = 93.9 ± 2.576 *16.9 /√110

C.I. = 93.9 ± 4.150

C.I. = [98.05 , 89.850]

Hence , confidence interval for the population mean time σ for computer repairs is [98.05 , 89.850].

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a) The equation of a vertical line is x = k, where k is the x-coordinate of the point where the line intersects the y-axis. In this case, the point where the line intersects the y-axis is (2, -65), so the equation of the line is x = 2. The slope of a vertical line is undefined, since it has no slope.

b) The equation of a horizontal line is y = k, where k is the y-coordinate of the point where the line intersects the x-axis. In this case, the point where the line intersects the x-axis is (-2, 4), so the equation of the line is y = 4. The slope of a horizontal line is 0, since it has no slope.

m=(C-12)/a

According to question

C=12+a*m

⇒C-12=a*m

⇒(C-12)/a=m

∴Equation to solve for the number of minutes , m = (C-12)/a

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