Given
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
To find:
a) What was the value of the manuscript 4 years ago?
b) What is the value of the manuscript now?
Explanation:
It is given that,
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
Then, let x be the value of manuscript 4 years ago.
That implies,
[tex]\begin{gathered} 400\%\times4x=1000+x \\ \frac{400}{100}\times4x=1000+x \\ 16x=1000+x \\ 16x-x=1000 \\ 15x=1000 \\ x=\frac{1000}{15} \\ x=\text{ \$}66.67 \end{gathered}[/tex]And, the value of the manuscript now is,
[tex]\begin{gathered} 4x=4(66.67) \\ =\text{ \$}266.67 \end{gathered}[/tex]Hence, the value of the manuscript is $66.67, and the value off the manuscript now is $266.67.
Find mZ1 in the picture below.1(3y² + 2y – 10)(2y² + 7y + 4)
m∠1=29
In this question,
1) Since we have, vertical angles, whose measure are written as polynomials then we can write according to the Vertical angles theorem:
3y² + 2y – 10 =2y² + 7y + 4
3y²-2y² -7y+2y-10-4=0
y²-5y-14=0
1.1) Finding the roots by Sum and Product
S(x) = ___ +___ = -5
P(x) =____ x ___ = -14
x1=-2 or 7
Since our Domain, cannot allow negative numbers, let's keep the positive one 7
2) Moreover to that, m∠1 + 2y² + 7y + 4 = 180º
m∠1 +2(7)²+7(7)+4=180
m∠1 +151 =180
m∠1=180-151
m∠1=29
Suppose y = 6x −5. Find y if:x = −1/6y = ?
To find y, you can follow the steps:
Step 1: Substitute x by -1/6 in the equation.
[tex]\begin{gathered} y=-6x-5 \\ y=6\cdot(-\frac{1}{6})-5 \end{gathered}[/tex]Step 2: Solve the equation.
[tex]\begin{gathered} y=-\frac{6}{6}-5 \\ y=-1-5 \\ y=-6 \end{gathered}[/tex]Answer : y = -6.
Rewrite the equation in standard form. Y+3=-(x-5)
To rewrite the given equation (point slope) into standard form:
1. Remove parentheses: Multiply each term in the parentheses by -1:
[tex]\begin{gathered} y+3=(-1)(x)+(-1)(-5) \\ \\ y+3=-x+5 \end{gathered}[/tex]2. Add x in both sides of the equation:
[tex]\begin{gathered} x+y+3=-x+x+5 \\ x+y+3=5 \end{gathered}[/tex]3. Subtract 3 in both sides of the equation:
[tex]\begin{gathered} x+y+3-3=5-3 \\ x+y=2 \end{gathered}[/tex]Then, the given equation in standard form is: x+y=2Choose ALL answers that describe thequadrilateral DEFGit DE FG,EF | GD, diagonal DF = 16, and diagonalEG=16.
Having two sets of parallel lines means that it can either be a rectangle, a square, a parallelogram, or a rhombus.
Having the diagonals congruent makes this figure either a rectangle or a square.
Since the length of the side is not given, we can only assume that this is a rectangle.
Summarizing it all, quadrilateral DEFG is a parallogram that is a rectangle because of the two pairs of parallel lines, and it has congruent diagonals.
Part 311Use the relationships in circle O to find the missing measures in circle S.1 pointIf WR = 12 units and MN = 8 units, determine MW.Type your answerwMRNePrestipus
From the properties of secant line and the tangent to the circle
If a secant segment and tangent segment are drawn to a circle from the same external point, the length of the tangent segment is the geometric mean between the length of the secant segment and the length of the external part of the secant segment.
[tex]\frac{Whole\text{ Secant}}{\tan gent\text{ Line}}=\frac{\tan gent}{External\text{ Secant Part}}[/tex]
In the given figure we hvae :
Whole secant length (RM),
Tangnt line MN = 8 units
External secant part (WM)
Since RM = WR + WM
RM=12 + WM
Susbtitute the value:
[tex]\begin{gathered} \frac{Whole\text{ Secant}}{\tan gent\text{ Line}}=\frac{\tan gent}{External\text{ Secant Part}} \\ \frac{RM}{MN}=\frac{MN}{MW} \\ \frac{12+MW}{8}=\frac{8}{MW} \\ \text{Apply crossmultiplication:} \\ MW(12+MW)=8\times8 \\ 12MW+(MW)^2=64 \\ \text{ Let MW = x} \\ 12x+x^2=64 \\ x^2+12x-64=0 \\ \text{ Factorize:} \\ x^2+16x-4x-64=0 \\ x(x+16)-4(x+16)=0 \\ (x-4)(x+16)=0 \\ \text{ So, x = 4, -16} \\ \text{ Since measurement cannot be negative thus: x = 4 unit} \\ x\text{ = }MW=4 \end{gathered}[/tex]Answer : MW= 4 units
If 9:x=x:4, then x = 3618246
Answer
Option D is correct.
x = 6
Explanation
9 : x = x : 4
To solve this, we know that ratios can be written in fraction form
(9/x) = (x/4)
[tex]\begin{gathered} \frac{9}{x}=\frac{x}{4} \\ \text{Cross multiply} \\ x^2=9\times4 \\ x^2=36 \end{gathered}[/tex]Take the square root of both sides
√(x²) = √(36)
x = 6
Hope this Helps!!!
5. Solve the system of equations by graphing. y = -x + 2 3x + 3y = 6
Answer:
The system of equations has infinite number of solutions.
The solution to the system of equations is any point on the line of the graph.
Explanation:
Given the system of equations;
[tex]\begin{gathered} y=-x+2 \\ 3x+3y=6 \end{gathered}[/tex]Plotting the two equations using a graph calculator we have;
From the graph, we can observe that the line of the two equations fall on each other.
That means that the equations are the same.
Therefore, the system of equations has infinite number of solutions.
The solution to the system of equations is any point on the line of the graph.
Match the following items.1. (-14) + 81 = 81 + (-14)commutative property of addition312424 +. 15associative property of addition2.(24 + 15)3313 173.= 117 134. -72 + 0 = -72distributive propertymultiplicative inverse5. 101 + (29 +417) = (101 +29) + 417additive identity
The Solution.
1.
[tex](-14)+81=81+(-14)\text{ }\Rightarrow Commutative\text{ property of addition}[/tex]2.
[tex]\frac{1}{3}(24+15)=\frac{1}{3}.24+\frac{1}{3}.15\text{ }\Rightarrow\text{ Distributive property}[/tex]3.
[tex]\frac{13}{17}\times\frac{17}{13}=1\text{ }\Rightarrow Multiplicative\text{ inverse}[/tex]4.
[tex]-72+0=-72\text{ }\Rightarrow\text{ }Additive\text{ Identity}[/tex]5.
Kelly is building a playpen for her dog. The area of the playpen is 22.75 square feet. The length is 6.5 feet and the width is w feet.
w = 3.5 feet
Explanation:Area = 22.75 square feet
length = 6.5 feet
width = w
Since we have beeen given dimensions in the form of length and width, the shape at the play house is a rectangle:
Area of rectangle = length × width
22.75 square feet = 6.5 feet × w
22.75 = 6.5w
divide both sides by 6.5:
22.75/6.5 = 6.5w/6.5
w = 3.5 feet
9. (a) The diagram below, not drawn to scale, shows a circle, where two lines intersect at point C. The points A, B, D and I lie on the circumference of the circle Note that ABDE is a right-angled triangle and BD is the diameter of the circle. A 66° D 78° C E B Determine, giving a reason for your answer, (1) ВСЕ 121 (ii) BDE 121 (iii) DBE 121
(i)
The angle 78° is supplementary to the angle BCE. Then we have:
[tex]\begin{gathered} 78\degree+B\hat{C}E=180\degree \\ B\hat{C}E=180\degree-78\degree \\ B\hat{C}E=102\degree \end{gathered}[/tex](ii)
When the vertex of a angle formed by two segments is located on the circle, the corresponding arc formed by the two segments is the double of the angle. Then we have:
[tex]\begin{gathered} B\hat{A}E=B\hat{D}E=\frac{arc\text{ BR}}{2} \\ B\hat{A}E=66\degree \\ \therefore B\hat{D}E=66\degree \end{gathered}[/tex](iii)
Since BDE is a right triangle, we have:
[tex]\begin{gathered} D\hat{B}E+B\hat{D}E+90\degree=180\degree \\ D\hat{B}E+66\degree+90\degree=180\degree \\ D\hat{B}E=180\degree-90\degree-66\degree \\ D\hat{B}E=24\degree \end{gathered}[/tex]A survey of visitor at national park was conducted to determined the preferred activity. The survey results are shown in the table. Based on this information which prediction about the preferred activity for the next 200 visitors to the park is the most reasonable.
Given:
A survey of visitors at a national park is shown in the table.
a) The number of visitors who preferred champing is 28.
The number of visitors who preferred hiking tails is 22.
And The number of visitors who preferred champing is 6 more than visitors who preferred hiking tails.
Option a) is incorrect.
b) Hiking trails - water sports= 22-14=8
c) Water sports - biking trails = 14-16= -2
Option c) is incorrect.
d)
[tex]\begin{gathered} \text{Camping}=2\times water\text{ sports} \\ =2\times14 \\ =28 \end{gathered}[/tex]From the given options b) and d) shows the correct predictions.
Amoung these two options most reasonable is option d) for next 200 visitors.
10÷5+10-9×1110 / 5 + 10 - 9 * 11 equals what
Follow the order to solve polynomials
1. Powers and roots
2. Divisions and products
3. Sums and substractions
[tex]\begin{gathered} \frac{10}{5}+10-9\cdot11 \\ 2+10-99 \\ 12-99 \\ -87 \end{gathered}[/tex]The answer is -87
Look at the graph of f(x). Which of the following are true? Select all that apply. 2 answers
Answer:
Explanation:
Answer:
A. [tex]f(x)[/tex] is [tex]y=sec(x-\pi )[/tex] shifted 6 units up.
C. [tex]f(x)[/tex] is [tex]y=sec(x)+6[/tex] shifted [tex]\pi[/tex] units to the left.
Step-by-step explanation:
If you guessed the answer to this question, or did not answer, go back and review how to write to equation of a trigonometric function.
Your welcome...
What are the leading coefficient and degree of the polynomial?-8u^6-15+4u+18u^9
The degree of a polynomial is given by the higher exponent of the variable.
In this polynomial, we have terms with the variable with exponents 6, 0, 1 and 9.
Therefore the degree of the polynomial is 9.
The leading coefficient is the number that multiplies the variable with a higher exponent.
The leading term is 18u^9, so the leading coefficient is 18.
Which method of finding probabilities do you prefer: lists, binompdf, binomcdf, nCr, etc.? Why?
For BinomPDF and BinomCDF we have a distribution that gives you the probability to have some number of successes, the difference is that PDF gives you only one specific number of successes, and the CDF gives you a range of successes probabilities.
Lists are the basic form to find a probability, you have to write all the cases and count the different groups of them, then divide by the total of cases.
NCR and NPR are the classic counting method to reach the number of combinations or permutations that a situation could have, is very useful and very quick to calculate the interest data or the number of combinations that may have a group of cases.
14. To surf the internet at the Airport costs $20,40 for 20 minutes and it costs $26.25 for 35minutes. How much would it cost to surf the internet for exactly 55 minutes.
Cost = $20.40 / 20 min
Cost = $26.25 / 35 min
To calculate the cost to suft 55 min just add the previous values given
Cost = 20.40 + 26.25
= $46.65
17 * 7*20000000000000
Here, we want to multiply the given terms
The best way to go about this
Answer: 2.38e+15
Step-by-step explanation:
Use the sample data and confidence level given below to complete parts (a) through (d)A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1047 and x = 545 whosaid "yes." Use a 95% confidence level.A. find the best point of estimate of the population of portion p.B. Identify the value of the margin of error E. (E= round to four decimal places as needed.)C. Construct the confidence interval. (
a. The best point of estimate of the population of portion p is given by the formula:
[tex]p^{\prime}=\frac{x}{n}[/tex]where x is the number of successes x=545 and n is the sample n=1047.
Replace these values in the formula and find p:
[tex]p^{\prime}=\frac{545}{1047}=0.521[/tex]b. The value of the margin of error E is given by the following formula:
[tex]E=(z_{\alpha/2})\cdot(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}})[/tex]Where z is the z-score at the alfa divided by 2, q'=1-p'.
As the confidence level is 95%=0.95, then alfa is 1-0.95=0.05, and alfa/2=0.025
The z-score at 0.025 is 1.96.
Replace the known values in the formula and solve for E:
[tex]\begin{gathered} E=1.96\cdot\sqrt[]{\frac{0.521\cdot(1-0.521)}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.521\cdot0.479}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.2496}{1047}} \\ E=1.96\cdot\sqrt[]{0.0002} \\ E=1.96\cdot0.0154 \\ E=0.0303 \end{gathered}[/tex]c. The confidence interval is then:
[tex]\begin{gathered} (p^{\prime}-E,p^{\prime}+E)=(0.521-0.0303,0.521+0.0303) \\ \text{Confidence interval=}(0.490,0.551) \end{gathered}[/tex]d. We estimate with a 95% confidence that between 49% and 55.1% of the people felt vulnerable to identity theft.
If the spinner is spun, what is the probability that the spinner will land on a multiple of 4?
Answer: A
Step-by-step explanation:
There are 10 possible outcomes on the spinner listed 1-10.
The multiples of 4 are 4, 8, 12, 16, and so on.
On the spinner, there are only 4 and 8 (of the multiples), and out of the 10 outcomes, that's 2/10 of them both.
If you multiply that fraction by 10 (we multiply by 10 since 2/10 isn't on the answer choices, also a number over 100 is also a percent)
that gives us 20/100, or 20%.
Hope that helps!
what represents the factorization of the trinomial below?[tex] {x}^{2} - x - 20[/tex]
The expression given is,
[tex]x^2-x-20[/tex]Factorize the expression above
[tex]\begin{gathered} Break\text{ the expressions into two groups} \\ \left(x^2+4x\right)+\left(-5x-20\right) \\ Factorize\text{ out the common terms} \\ =x\left(x+4\right)-5\left(x+4\right) \\ \mathrm{Factor\:out\:common\:term\:}x+4 \\ =\left(x+4\right)\left(x-5\right) \end{gathered}[/tex]Hence, the answer is
[tex]\left(x+4\right)\left(x-5\right)[/tex]Countries represented at each festival 6 5 4 Number of festivals 3 N 1 0 0-5 6-11 12-17 18-23 24-29 Number of countries How many festivals had 12 or more countries represented.
11 festivals
Explanation
to find the nunmber of festivals that had 12 or more countries, sum the festivals for all values in number of countries greather than 12, it its
[tex]\begin{gathered} \text{column 3 (12-17)=5 festivals} \\ \text{column 4(18-23)=4 festivals} \\ column5(24-29)=2\text{ festivals} \\ so,\text{ the total of festivals for 12 or more countries is} \\ \text{total}=5+4+2 \\ total=11\text{ festivals} \end{gathered}[/tex]I hope this helps you
7. Translate the following Marco has $6 less than Ann has
Solution:
Let x represent the amount Marco has,
let y represent the amount Ann has.
Given that Marcos has $6 less than Ann has, this implies that
[tex]\begin{gathered} x=y-6 \\ \end{gathered}[/tex]Ann has
[tex]y[/tex]Marco has
[tex]y-6[/tex]A swim team consist of seven boys and four girls a relay team of four swimmers is chosen at random from the team members what is the probability that three boys are selected for the relay team given that the first selection was a girl express your answer as a fraction in lowest terms or a decimal rounded to the nearest million
At start, we have:
- 7 boys
- 4 girls
It is given that the first selection was a girl. Since there were 4 girls, there is 3 left to be picked. So we have:
- 1 girl picked
- 7 boys to be picked
- 3 girls to be picked
We want the next 3 pickes to be boys.
The probability that the first pick will be a boy is the number of boys to be picked from over the total team left to be picked from. We have 7 boys and a total of 7 + 3 = 10 members, so:
[tex]P_1=\frac{7}{10}[/tex]Next, we want another pick of boy, but now we have got only
- 6 boys
- 3 girls
So, the probability of the second pick to be boy is:
[tex]P_2=\frac{6}{9}[/tex]And for the third, we have:
- 5 boys
- 3 girls
Probability of
[tex]P_3=\frac{5}{8}[/tex]Since we want these three to occur, the final probability is the product of them:
[tex]P=P_1\cdot P_2\cdot P_3=\frac{7}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}=\frac{7}{1}\cdot\frac{1}{3}\cdot\frac{1}{8}=\frac{7}{24}[/tex]So, the answer as a fraction in the lowest form is:
[tex]\frac{7}{24}[/tex]cam you show me the conversion from mm to cm to m to dm to km please
To determine the conversion from mm to cm to m to dm to km:
[tex]\begin{gathered} \operatorname{mm}\text{ => Millimtere} \\ \operatorname{cm}=>\text{centimetre} \\ m\Rightarrow\text{ metre} \\ dm\Rightarrow\text{ decimetre} \\ \operatorname{km}-\text{kilometre} \end{gathered}[/tex]Conversion from mm to cm =
[tex]10\text{ mm }\Rightarrow\text{ 1 cm}[/tex]Conversion from cm to m
[tex]100\operatorname{cm}\Rightarrow\text{ 1m}[/tex]Conversion from m to dm
[tex]1m\Rightarrow\text{ 10dm}[/tex]Conversion from dm to km
[tex]10000dm\Rightarrow\text{ }1\text{ km}[/tex]Hence the correct conversion are
10 mm = 1 cm
100 mm = 1 dm
1000 mm = 1 mm
1000000 mm = 1 km
I hope you are having a blessed day. Question is attached as a screenshot. Thank you :)
Solution:
Given the graphs of
[tex]\begin{gathered} y=x, \\ y=-x+4, \\ y=0 \end{gathered}[/tex]to be as plotted below:
The region ABC is bounded as shown above.
To find its area, the region ABC takes the shape of a triangle. Thus, we are to evaluate the area of the triangle ABC.
Step 1: Evaluate the midpoint between the distance AB.
The midpoint (x,y) of the distance AB is evaluated as
[tex]\begin{gathered} (x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{where} \\ x_1=0,y_1=0,x_2=2,y_2=2 \\ \text{thus,} \\ (x,y)=(\frac{0+2}{2},\frac{0+2}{2}) \\ =(1,1) \end{gathered}[/tex]Thus, the midpoint of the distance AB is (1,1).
Step 2: Evaluate the height of the region (triangle).
The height of the region is the same as the distance between points A and the midpoint of the distance AB.
Thus,
The distance is evaluated as
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ x_1=2,y_1=2,x_2=1,y_2=1 \\ \text{thus,} \\ d=\sqrt[]{(1_{}-2_{})^2+(1_{}-2_{})^2} \\ =\sqrt[]{(-1_{})^2+(-1_{})^2} \\ =\sqrt[]{1+1} \\ d=\sqrt[]{2} \end{gathered}[/tex]Step 3: Evaluate the distance between points B and C.
The distance is evaluated similarly as
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ x_1=0,y_1=0,x_2=4,y_2=0 \\ \text{thus,} \\ d=\sqrt[]{(4_{}-0_{})^2+(0_{}-0_{})^2} \\ =\sqrt[]{4^2+0^2} \\ d=4\text{ units} \end{gathered}[/tex]Step 4: Evaluate the area of the triangle ABC.
Given that the distance BC is 4 units and the height of the region is √2 units, the area of the region ABC is evaluated as the area of the triangle ABC.
Thus,
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times4\times\sqrt[]{2} \\ \Rightarrow Area\text{ =2}\sqrt[]{2} \end{gathered}[/tex]Hence, the area of the region is
[tex]2\sqrt[]{2}[/tex]The fourth option is the correct answer.
Which equations can you solve to find the value of m choose all that apply
m = 7.50 + 12.50
m - 7.50 = 12.50
Explanation:Cost of the book = $7.50
Amount remaining on the gift card = $12.50
m = Amount on the gift card in dollars when Salim received it
Amount on the gift card in dollars when Salim received it = Cost of the book + Amount remaining on the gift card
m = $7.50 + $12.50
m = 7.50 + 12.50
Another form of the equation:
subtract 7.5 from both sides:
m - 7.50 = 7.50 - 7.50 + 12.50
m - 7.50 = 12.50
Hence, equation that can be used to solve m:
m = 7.50 + 12.50
m - 7.50 = 12.50
12. On Monday, a museum had 150 visitors. On
Tuesday, it had 260 visitors.
a. Choose Efficient Methods Estimate the
percent change in the number of visitors to
the museum.
b. About how many people would have to visit
the museum on Wednesday to have the same
percent change from Tuesday to Wednesday
as from Monday to Tuesday? Explain your
answer.
a. The percent change in the number of visitors to the museum is 73.33%
b. The people that would have to visit the museum on Wednesday to have the same
percent change is 450.
How to calculate the percentage?From the information given, on Monday, a museum had 150 visitors. On Tuesday, it had 260 visitors. It should be noted that the increase will be:
= 260 - 150
= 110
The percentage increase will be:
= Increase in value / Original value × 100
= 110/150 × 100
= 73.33%
The number of people that should visit in Wednesday will be:
= 260 + (73.33% × 260)
= 260 + 190
= 450
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
A ball is thrown from an initial height of 3 meters with an initial upward velocity of 30 m/s. The ball’s height h (in meters) after t seconds is given by the following. h=3+30t-5t^2 Find all values of t for which the ball’s height is 13 meters. Round your answer(s) to the nearest hundredth.
Answer:
The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]Explanation:
The function of the ball's height h (in meters) is given as;
[tex]h=3+30t-5t^2[/tex]the value of time t for which the ball's height is 13 meters, can be derived by substituting h=13 into the function of h.
[tex]\begin{gathered} h=3+30t-5t^2 \\ 13=3+30t-5t^2 \\ 3+30t-5t^2=13 \end{gathered}[/tex]subtract 13 from both sides and solve the quadratic equation;
[tex]\begin{gathered} 3+30t-5t^2-13=13-13 \\ -5t^2+30t-10=0 \end{gathered}[/tex]solving the quadratic equation, using the quadratic formula;
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ t=\frac{-30\pm\sqrt{30^2-4\times-5\times-10}}{2\times-5} \\ t=\frac{-30\pm\sqrt{900-200}}{-10} \\ t=\frac{-30\pm\sqrt{700}}{-10} \\ t=0.3542=0.35 \\ or \\ t=5.64575=5.65 \end{gathered}[/tex]The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]see attached for question and diagram
Given: D = (1,3) and E = (3,-3)
The graph of DE is as following:
a) Translation (0,2) then reflection on x-axis
So, at first move 2 units upward t hen reflect across x-axis
Note: the rule of reflection across x-axis: (x,y) to (x,-y)
the final result in green color
B) reflection in x-axis then clock wise rotation
(1,3) to (1,-3) to (-3 , -1)
(3,-3) to (3,3) to (3,-3)
Note : reflection cross x-axis will give the red dash line
Then make rotation for the red dash line will give the green line
A person who wants to get in shape goes to a local gym that advertises 31 training sessions for $1908. Find the cost of 133 training sessions. Round your answer to the nearest cent.
According to the given data we have the following:
31 training sessions=$1908
In order to calculate the cost of 133 training sessions we would have to apply the 3 rule.
So, if 31 training sessions__________________$1908
133 training sessions______________________x
Therefore, x=(133 training sessions*$1908)/31 training sessions
x=$253,764/31 training sessions
x=$8,186
The cost of 133 training sessions would be $8,186