Answer:
Step-by-step explanation:
The equation of this circle is (x - 3)^2 + (y - 3)^2 = 12^2.
Let's substitute the coordinates of the given point and compare the results to the above equation: do they produce a correct statement?
(-6 - 3)^2 + (-5 - 3)^2 = ?
9^2 + 8^2 = 145
Because r = 12, the above result would need to be 144, not 145, if the given point were actually on the circle. We must conclude that (-6, -5) lies just outside the circle.
81 + 64 = 144
What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%
Answer: 35%
Step-by-step explanation:
If no is 10, 10 x 0.65 = 6.5. OR
10 - 35% of 10 = 6.5
Multiplying by 0.65 is the same as decreasing by 35%
Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.
Let the number is 'a' and percentage decrease is 'b',
Expression for the given statement will be,
a × 0.65 = a - (b% of a)
[tex]0.65a=a(1-\frac{b}{100})[/tex]
[tex]0.65=1-\frac{b}{100}[/tex]
[tex]\frac{b}{100}=1-0.65[/tex]
[tex]b=100(0.35)[/tex]
[tex]b=35[/tex]
Therefore, Multiplying by 0.65 is the same as decreasing by 35%.
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A number is chosen at random from the first 100 positive integers. Find the probability that the number is a multiple of 7
Answer:
Dear user,
Answer to your query is provided below
Probability = 7/50
Step-by-step explanation:
Total no. Of positive integers = 100
Multiple of 7 - 7,14,21,28,35,42,49,56,63,70,77,84,91,98
Total multiples of 7 = 14
Probability = 14/100 = 7/50
I won 5 tickets to the Red Sox. I have 9 friends but I can only bring 4 of them. In how many ways can I form team?
Answer:
189
Step-by-step explanation:
9 choose 4 = (9 x 8 x 7 x 6 )/(4 x 3 x 2 x 1)=189
:D 189 ways
Answer:189
Step-by-step explanation:
Please answer this correctly
Answer:
4 because 6th floor has no office
Answer:
5 floors
Step-by-step explanation:
Fewer than 80 makes it 0-79
So,
0-79 => 5 floors
As a property owner, you want to fence a garden which is adjacent to a road. The fencing next to the road must be stronger and cost $6 per foot. The fencing on the other sides cost $4 per foot. The area of garden is 2400 square feet.
Required:
Find a function that models the cost of fencing the garden.
Answer:
[tex]C(x)=\dfrac{10x^2+19200}{x}[/tex]
Step-by-step explanation:
Let the dimension of the garden be x and y
Area of the graden =xy
Since the area of garden is 2400 square feet.
xy=2400
Making y the subject, we have:
[tex]y=\dfrac{2400}{x}[/tex]
Let the side next to the road =x
Cost of fencing Next to the road =$6Cost of the other three sides = $4Therefore, total cost of fencing the garden,
C(x,y)=6x+4x+4y+4y
C(x,y)=10x+8y
Substituting [tex]y=\dfrac{2400}{x}[/tex] derived earlier, we have:
[tex]C(x)=10x+8(\frac{2400}{x})\\C(x)=\dfrac{10x^2+19200}{x}[/tex]
Therefore, a function that models the cost of fencing the garden is:
[tex]C(x)=\dfrac{10x^2+19200}{x}[/tex]
What is the kinetic energy of a 19 kg dog that is running at a speed of 7.1 m/s (about 16 mi/h)
Answer:
K.E = 67.5 J
Step-by-step explanation:
K.E = 1/2 mv^2
= 0.5 x 19 x 7.1
= 67.5 J
Best Regards!
The commute time for people in a city has an exponential distribution with an average of 0.66 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.55 and 1.1 hours? Answer: (round to 3 decimal places)
Answer:
[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]
And replacing we got:
[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]
[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]
And rounded the answer would be 0.246
Step-by-step explanation:
For this case we can define the random variable X as "The commute time for people in a city" and for this case the distribution of X is given by:
[tex] X \sim exp (\lambda = \frac{1}{0.66}= 1.515)[/tex]
And for this case we want to find the following probability:
[tex] P(0.55 <X<1.1)[/tex]
And we can use the cumulative distribution function given by:
[tex] F(x) =1- e^{-\lambda x}[/tex]
And using this formula we got:
[tex] P(0.55 <X<1.1)= F(1.1) -F(0.55) [/tex]
And replacing we got:
[tex] P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})[/tex]
[tex] P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457[/tex]
And rounded the answer would be 0.246
An oarsman can row his boat 3 mph in still water. He sets out on the Illinois River, which flows at 5 mph. We are interested in what an observer on shore measures. 14) When the man heads the boat directly downstream and rows as fast as he can, how fast does the observer on shore see the boat going
Answer:
The speed from the observer is 8 mph.
Step-by-step explanation:
When the boat is going downstream with full force, its speed will be the one the oarsman can row on still water added by the flow of the river. In this case he can row the boat at speed of 3 mph, while the stream is 5 mph, so the speed from the observer standpoint is:
[tex]speed = 3 + 5\\speed = 8 \text{ mph}[/tex]
The speed from the observer is 8 mph.
Please answer this correctly
Answer:
The range will decrease by 1
Step-by-step explanation:
Range: Largest no. - Smallest no.
The range with the original numbers is 7 -1 =6
The range when 1 is replaced by 6,the smallest no. becomes 2 which makes the range 7-2= 5
So 1st range - 2nd range =6 - 5 = 1
I just need reassurance
Answer:
i believe the answer is 286°
Step-by-step explanation:
a minor arc=to the central angle's measure.
a circle has 360°
so 360-74=286
What is simplified expression for the expression below
Answer:
4(x+8) + 5(x-3)
= 4x + 32 + 5x - 15
= 9x + 17
Answer:
9x+17
Step-by-step explanation:
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A researcher has noted that the repair times of a sample of 15 new lawn mowers has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all its new lawn mowers is:_______
a) 8.58 to 39.79
b) 1.64 to 1.96
c) 4 to 16
d) 4 to 15
It is known that the number of hours a student sleeps per night has a normal distribution. The sleeping time in hours of a random sample of 8 students is given below. See Attached Excel for Data. Compute a 98% confidence interval for the true mean time a student sleeps per night and fill in the blanks appropriately. We have 98 % confidence that the true mean time a student sleeps per night is between and hours. (round to 3 decimal places)
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
It is known that the number of hours a student sleeps per night has a normal distribution. The sleeping time in hours of a random sample of 8 students is given below. 7.4, 6.2, 8.5, 6.3, 5.4, 5.5, 6.3, 8.3 Compute a 98% confidence interval for the true mean time a student sleeps per night and fill in the blanks appropriately. We have 98% confidence that the true mean time a student sleeps per night is between _____ and ____ hours. (Keep 3 decimal places)
Solution:
Mean = (7.4 + 6.2 + 8.5 + 6.3 + 5.4 + 5.5 + 6.3 + 8.3)/8 = 6.7375
Standard deviation = √(summation(x - mean)²/n
Summation(x - mean)² = (7.4 - 6.7375)^2 + (6.2 - 6.7375)^2 + (8.5 - 6.7375)^2 + (6.3 - 6.7375)^2 + (5.4 - 6.7375)^2 + (5.5 - 6.7375)^2 + (6.3 - 6.7375)^2 + (8.3 - 6.7375)^2 = 9.97875
Standard deviation = √(9.97875/8
s = 1.12
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
sample standard deviation
number of samples
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 8 - 1 = 7
Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99
Looking at the t distribution table,
z = 2.998
Margin of error = 2.998 × 1.12/√8
= 1.19
the lower limit of this confidence interval is
6.738 - 1.19 = 5.548
the upper limit of this confidence interval is
6.738 + 1.19 = 7.928
We have 98 % confidence that the true mean time a student sleeps per night is between 5.548 hours and 7.928 hours.
In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The complement of A is a. all new customers. b. all new customers whose accounts are between 31 and 60 days past due. c. all accounts fewer than 31 or more than 60 days past due. d. all accounts from new customers and all accounts that are from 31 to 60 days past due.
Answer:
c. all accounts fewer than 31 or more than 60 days past due.
Step-by-step explanation:
The Universal Set is the set of all past due accounts.
Event A = the event that the account is between 31 and 60 days past due.
Event B = the event that the account is that of a new customer.
Therefore, the complement of A will be the event of all the accounts fewer than 31 or more than 60 days past due.
The correct option is C.
Please answer this correctly
Answer:
Pillows:
Blankets:
Pet Beds:
Step-by-step explanation:
18 + 45 + 27 = 90 (there are 90 students)
18 out of 90 = 20%
45 out of 90 = 50%
27 out of 90 = 30%
Hope this helps!
On Tuesday , the wait to ride the roller coaster was 40 minutes. The roller coaster is the fastest ride at the fair .The line of people waiting was 100 meters long . How long would you expect to wait if the line 50 meters long.
Answer:
You would expect to wait 20 minutes if the line was 50 meters long.
Step-by-step explanation:
This question can be solved using a rule of three.
The line of people waiting was 100 meters, and the wait was 40 minutes. How long the wait would have been if the line was of 50 meters?
100m - 40 min
50m - x min
[tex]100x = 50*40[/tex]
[tex]x = \frac{50*40}{100}[/tex]
[tex]x = 20[/tex]
You would expect to wait 20 minutes if the line was 50 meters long.
there are three witches and three children they were going to cross the river with a boat that can carry only two people and if a mother lives her child alone the another witches will kill her son.how will the witches and children cross the river?
Answer:
It will take to long to type it all but i think i figured it out. The children would have to take several trips. 2 kids would go, then one kid goes back to get the other kid, crosses again, then goes back, gets out, and two witches go (the parents of the kids on the other side), leaving one set of witch and child still needing to cross. One of the children on the other side brings the boat back and picks up the left over kid, now just one witch needing to cross, the two kids cross then the one kid with his mother on the other side takes the boat back again to get his mom.
And then when it gets to the other side the witch there eats it
Step-by-step explanation:
To safely cross the river, the witches and children can follow these steps:
Two witches (W1 and W2) cross the river, leaving one witch (W3) behind.
W1 returns alone to the starting side.
W1 and one child (C1) cross the river, leaving C1 on the other side.
W2 takes two children (C2 and C3) across the river, leaving them on the starting side.
W1 and W3 cross the river, leaving C2 and C3 behind.
W1 returns alone to the other side.
W1 and C1 cross the river, leaving W3 on the other side.
W2 and W3 cross the river.
W2 returns alone to the starting side.
W2 and C2 cross the river, leaving C3 behind.
W1 and C3 cross the river
How will the witches and children cross the river?To solve this puzzle, the witches and children can follow these steps to cross the river without any harm coming to the children:
Two witches cross the river: Two witches (W1 and W2) row the boat to the other side of the river, leaving one witch (W3) on the starting side.
One witch returns alone: W1 leaves the other witch (W2) on the other side and rows back alone to the starting side of the river.
One witch and one child cross the river: W1 takes one child (C1) with her and they both row across the river to the other side. W1 leaves C1 on the other side and rows back alone to the starting side.
Two children cross the river: W2, who has been waiting on the other side, takes two children (C2 and C3) and rows across the river to the starting side. W2 leaves C2 and C3 on the starting side and rows back alone to the other side.
Two witches cross the river: W1 returns to the other side and picks up the remaining witch (W3). They both row across the river to the starting side, leaving C2 and C3 on the other side.
One witch returns alone: W1 rows back alone to the other side.
One witch and one child cross the river: W1 takes C1 and rows across the river to the starting side, leaving W3 on the other side.
Two witches cross the river: W2 returns to the starting side and picks up W3. They both row across the river to the other side.
One witch returns alone: W2 rows back alone to the starting side.
One witch and one child cross the river: W2 takes C2 and rows across the river to the other side, leaving C3 on the starting side.
Two children cross the river: W1 returns to the starting side and picks up C3. They both row across the river to the other side.
Now, all three witches and all three children have safely crossed the river without any harm coming to the children.
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What is the factorization of the trinomial below?
-x2+ x + 42
Answer:
-(x + 6)(x - 7)
Step-by-step explanation:
The expression that we have can also be expressed in the following way:
- (x ^ 2 - x - 42)
Now to factorize we must find two numbers that multiplied by -42 and the sum of these numbers by -1.
these numbers are: -7 and 6
-7 * 6 = -42
-7 + 6 = -1
Thus:
- (x + 6) (x - 7)
Find the equation of a line perpendicular to 4x – 4y = -4 that contains the point (-5, -2).
Answer:
Y = -X - 7
Step-by-step explanation:
y-y1 =m(x-x1)
y-(-2)= -1(x-(-5)
y+2 = -1(x+5)
Solve for y
subtract 2 from both sides
y=-x-5-2
Y = -x-7
In a lottery game, a player picks 7 numbers from 1 to 53. If 6 of the 7 numbers match those drawn, the player wins second prize. What is the probability of winning this prize?
The probability of winning the prize is [tex]P = \frac{1}{99,884,400}[/tex].
Given data:
To calculate the probability of winning the second prize in the lottery game, determine the number of successful outcomes (matching 6 out of 7 numbers) and divide it by the total number of possible outcomes.
The number of possible outcomes can be calculated using the combination formula:
[tex]C(n, r) = \frac{n!} {(r!(n-r)!)}[/tex]
where n is the total number of options (53 numbers in this case) and r is the number of selections (7 numbers in this case).
[tex]C(53, 7) = \frac{53!} {(7!(53-7)!)}[/tex]
[tex]C(53, 7) = \frac{53!}{ (7!46!)}[/tex]
The number of successful outcomes is 1, as there is only one way to match exactly 6 out of the 7 numbers drawn.
Therefore, the probability of winning the second prize is:
Probability = Number of successful outcomes / Total number of outcomes
Probability = 1 / C(53, 7)
C(53, 7) ≈ 99,884,400
Thus, the probability of winning the second prize is approximately:
[tex]P = \frac{1}{99,884,400}[/tex]
Hence, winning the second prize in the lottery game is highly unlikely.
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HELP HELP HELP PLEASE!!!!!
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $31. The total cost to rent 6 chairs and 5 tables is $59
What is the cost to rent each chair and each table?
Answer:
The rental of each chair is $2.75
The rental of each table is $8.5
Step-by-step explanation:
Let's name the unknowns "c" for the cost of each chair rental, and "t" for the cost of each table rental.
Now we can create the equations that represent the statements:
a) "The total cost to rent 2 chairs and 3 tables is $31."
2 c + 3 t = 31
b) "The total cost to rent 6 chairs and 5 tables is $59."
6 c + 5 t = 59
now we have a system of two equations and two unknowns that we proceed to solve via the elimination method by multiplying the first equation we got by "-3" so by adding it term by term to the second equation, we eliminate the variable "c" and solve for "t":
(-3) 2 c + (-3) 3 t = (-3) 31
-6 c - 9 t = -93
6 c + 5 t = 59
both these equations added give:
0 - 4 t = -34
t = 34/4 = 8.5
So each table rental is $8.5
now we find the rental price of a chair by using any of the equations:
2 c + 3 t = 31
2 c + 3 (8.5) = 31
2 c + 25.5 = 31
2 c = 5.5
c = 5.5/2
c = $2.75
c. How much longer does Sana spend in the bathroom than Ali ? Mother Showers, washes and dries hair, brushes teeth ¾ hour Father Showers, shaves, brushes teeth 50 minutes Ali Showers, brushes teeth 20 minutes Sana Takes a bath, brushes teeth ½ hour Grand father Showers, shaves 35 minutes Grand mother Takes a bath, brushes teeth 40 minutes
Answer:
Sana takes 10 minutes longer than Ali in bathroom
Step-by-step explanation:
Given:
Ali Showers, brushes teeth 20 minutes
Thus, Ali takes 20 minutes time in bathroom
Sana Takes a bath, brushes teeth ½ hour
1 hour has 60 minutes
1/2 hour has 60/2=30 minutes
Thus, Sana takes 30 minutes time in bathroom.
Time, taken more by sana than Ali = 30 minutes - 20 minutes = 10 minutes
.
Thus, Sana takes 10 minutes longer than Ali in bathroom.
figure a~figure b:figure a r=4 ft figure b r =2 ft v=352 cu ft fing the volume of figure b for a final exam due at midnight, will fail year, help.
A brewery distributes beer in cans labeled 12 oz. The Bureau of Weights and Measures randomly selects 36 cans, measures their contents, and obtains a sample mean of 11.82 oz. Assume that σ is known to be 0.38 oz. At 0.01 significance level, can we conclude that the brewery is cheating consumers? Please show all 4 steps of the classical approach clearly.
Answer:
Hypothesis
Null hypothesis:[tex]\mu = 12[/tex]
Alternative hypothesis:[tex]\mu \neq 12[/tex]
Statistic
[tex]t=\frac{11.82-12}{\frac{0.38}{\sqrt{36}}}=-2.84[/tex]
[tex]df=n-1=36-1=35[/tex]
P value
The p value for this case would be given by:
[tex]p_v =2*P(t_{(35)}<-2.84)=0.0075[/tex]
Conclusion
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 12 oz.
Step-by-step explanation:
Information given
[tex]\bar X=11.82[/tex] represent the sample mean
[tex]s=0.38[/tex] represent the sample standard deviation
[tex]n=36[/tex] sample size
[tex]\mu_o =12[/tex] represent the value to verify
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to verify
We want to cehck if the true mean is 12 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 12[/tex]
Alternative hypothesis:[tex]\mu \neq 12[/tex]
Statistic
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{11.82-12}{\frac{0.38}{\sqrt{36}}}=-2.84[/tex]
The degrees of freedom are given by:
[tex]df=n-1=36-1=35[/tex]
P value
The p value for this case would be given by:
[tex]p_v =2*P(t_{(35)}<-2.84)=0.0075[/tex]
Conclusion
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 12 oz.
Create a set of data that shows temperature highs for 10 days and satisfies each condition below:
Mean: 72
Median: 74
Mode: 68
Range: 21
72*10=720 so all the numbers would need to add to 720
the median is 74 so you need to have both 75 and 76 in the set
the mode is 68 so that need to be in at least twice
and the range is 21 so the largest number-21=smallest number
57, 68, 68, 68, 75, 76, 76, 77, 77, 78
A set of data that shows temperature highs for 10 days is 57, 68, 68, 68, 75, 76, 76, 77, 77, and 78.
Given that, create a set of data that shows temperature highs for 10 days.
What are the Mean Median and Mode?Mean, median and mode are all measures of central tendency in statistics. In different ways, they each tell us what value in a data set is typical or representative of the data set.
The mean is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.
The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers.
The mode is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set. The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode.
Now,
72×10=720 so all the numbers would need to add to 720.
The median is 74 so you need to have both 75 and 76 in the set.
The model is 68 so that needs to be in at least twice.
The range is 21 so the largest number-21=smallest number
57, 68, 68, 68, 75, 76, 76, 77, 77, 78
Therefore, a set of data that shows temperature highs for 10 days is 57, 68, 68, 68, 75, 76, 76, 77, 77, and 78.
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(a) A company that makes crayons is trying to decide which colors to include in a promotional mini-box of crayons. The company can choose the mini-box colors from its collection of colors. How many mini-boxes are possible?
Complete Question
The complete question is shown on the first uploaded image
Answer:
The number of color are possible [tex]\left n} \atop }} \right. C _r = 1215450[/tex]
Step-by-step explanation:
From the question we are told that
The number of colors is r = 4
The sample size n = 75
The number of color that are possible can be mathematically evaluated as
[tex]\left n} \atop }} \right. C _r = \frac{n !}{ (n-r)! r!}[/tex]
substituting values
[tex]\left n} \atop }} \right. C _r = \frac{75 !}{ (75-4)! 4!}[/tex]
[tex]\left n} \atop }} \right. C _r = \frac{75 !}{ (71)! 4 !}[/tex]
[tex]\left n} \atop }} \right. C _r = \frac{75 *74 * 73* 72 * 71!}{ (71)! (4*3*2 *1)}[/tex]
[tex]\left n} \atop }} \right. C _r = 1215450[/tex]
Which lists the ratios in order from least to greatest 2:9,1:6,7:36
Answer:
1:6, 7:36, 2:9
Step-by-step explanation:
2 : 9 → 8 : 36
1 : 6 → 6 : 36
7 : 36
Least → Greatest
1:6, 7:36, 2:9
An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
Answer:
72
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Calculating Angle Measures
In the diagram,
Which statements about the diagram are true? Check
all that apply.
Answer:
Options (3), (4), and (5).
Step-by-step explanation:
From the figure attached,
∠JKM is a straight angle on a segment JKM.
PK is a perpendicular drawn on segment JKM at point K.
Option (1). [tex]\overrightarrow{KQ}[/tex] is a angle bisector
Not True.
Option (2). ∠LKQ is bisected.
Not True.
Option (3). m∠JKL = 45°
Since [tex]\overrightarrow{KL}[/tex] is an angle bisector of angle JKP which is equal to 90°.
True.
Option (4). m∠MKQ + m∠PKQ = m∠PKM
True.
Option (5). [tex]\overrightarrow{PK}[/tex] is a angle bisector.
Since [tex]\overrightarrow{PK}[/tex] is an angle bisector of straight angle JKM.
True.
Option (6). ∠JKL ≅ ∠QKM
Not True.
Therefore, options (3), (4) and (5) are correct.
In a certain clothing store, 6 shirts and 3 ties cost $79.50, and 3 shirts and 2 ties cost $41. Determine the cost of each shirt.
Answer: $12
Step-by-step explanation:
For this problem, we can use system of equations to solve. Let's use x for shirts and y for ties.
Equation 1
6x+3y=79.5
This equation comes from the first sentence. 79.5 is the total cost.
Equation 2
3x+2y=41
This equation comes from the second part of the first sentence. 41 is the total cost.
Since we are looking for the cost of each shirt, let's use the elimination method to eliminate y. First, we need to multiply both equations to that the y in both equations equal each other.
2(6x+3y=79.5)
3(3x+2y=41)
Now that we have chosen a common number, we can multiply.
12x+6y=159
9x+6y=123
We can now subtract both equations to cancel out y.
3x=36
Divide to get x alone.
x=12
Each shirt costs $12.
