Answers
Alice drew rectangles divided into identical three parts. Following the pattern, she draws four more rectangles. All five rectangles are connected with each other. Her little brother Sam picked a yellow color and colored the first two parts of each rectangle. Find out the shaded part fraction.
How to frame a word problem?1. Pick a central figure for your word puzzle. Decide how many and what kind of things he possesses. The ideal items are those that are simple enough for kids to recognize and, if necessary, sketch.
2. Decide on a supporting character and count the items he owns.
3. After the word puzzle, add a question.
4. Go through your word puzzle and give it a shot. If you feel that your instructions are unclear or that the task is too challenging for your pupils, you should rewrite them.
Now according to the given figure,
Alice drew rectangles divided into identical three parts. Following the pattern, she draws four more rectangles. All five rectangles are connected with each other. Her little brother Sam picked a yellow color and colored the first two parts of each rectangle. Find out the shaded part fraction.
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Related Questions
You and a friend are knitting a scarf that will be 72 inches long. Your friend knits the first 24 inches and then gives you the scarf to finish. You expect to knit at a rate of 8 inches per day.
Answers
At a rate of 8 inches per day, we can work out how long it will take us by doing 48 divide 8, which is 6.
Therefore it would take you 6 days to finish the scarf.
some girls who excelled at math/science in elementary school, during puberty may fear focusing on these may limit popularity or attractiveness as girls.
Answers
It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.
It is unfortunate that some girls may fear focusing on math and science during puberty due to concerns about popularity or attractiveness. However, it is important to remember that excelling in these subjects can lead to numerous opportunities and career paths in the future. It is also important to note that intelligence and academic achievement should be celebrated and valued regardless of gender stereotypes. Schools can play a role in promoting the importance of STEM subjects and encouraging girls to pursue their interests in these areas.
It has been observed that some girls who excelled in math and science during elementary school may develop concerns during puberty that focusing on these subjects might limit their popularity or attractiveness as girls. This could be due to societal stereotypes or peer pressure, which might influence their academic choices and priorities. It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.
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It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.
It is unfortunate that some girls may fear focusing on math and science during puberty due to concerns about popularity or attractiveness. However, it is important to remember that excelling in these subjects can lead to and career paths in the future. It is also important to note that intelligence and academic achievement should be celebrated and valued regardless of gender stereotypes. Schools can play a role in promoting the importance of STEM subjects and encouraging girls to pursue their interests in these areas.
It has been observed that some girls who excelled in math and science during elementary school may develop concerns during puberty that focusing on these subjects might limit their popularity or attractiveness as girls.
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HELP!!! 35 POINTS Solve the equation. −7.8x=−1.56. x=?
Answers
Answer:
x = 0.2
Step-by-step explanation:
-7.8x = -1.56
-1.56/-7.8 = 0.2
x = 0.2
Answer:
\(x =\frac{1}{5}\) or \(0.2\) (they're the same)
Step-by-step explanation:
Divide each side by -7.8, so it now looks like this: x = 0.2A rectangular swimming pool measures 50 meters in length and 25 meters in width. What are the length and width of your scaled drawing with a scale of 1 centimeter represents 5 meters?
Answers
Answer:
10 cm by 5cm
Step-by-step explanation:
We know that for every 5 meters, there will be 1 centimeter. The pool is 50 meters by 25 meters. So to find this in terms of centimters, divide by 5 to get 10 cm by 5 cm.
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
1, 1, 6, 10, 10, 11, 12, 14, 15, 18, 20, 20, 20, 20, 20
Donations to charity
1-5 has 2
6-10 has 3
11-15 has 4
16-20 has 6
Donations in dollars
Which measure of center should the charity use to accurately represent the data? Explain your answer.
1. The median of 14 is the most accurate to use since the data is skewed
2. The mean of 13.2 is the most accurate to use since the data is skewed
3. The median of 13.2 is the most accurate to o use to show that they need more money
4. The mean of 14 is the most accurate to use to show that they have plenty of money
Answers
The measure of center the charity should use to accurately represent the data of its typical donation receipts is 2. The mean of 13.2 is the most accurate to use since the data is skewed.
What are the measures of central tendency?The typical measures of central tendency are the mode, the median, and the mean.
The mode refers to the most occurring data value, the median describes the middle value, while the mean is the average value.
Ordered Data Values:1, 1, 6, 10, 10, 11, 12, 14, 15, 18, 20, 20, 20, 20, 20
Total value = 198
The number of items = 15
Mean = 13.2 (198 ÷ 15)
Median = 14 (the middle value)
HistogramDonations to charity
1-5 has 2
6-10 has 3
11-15 has 4
16-20 has 6
Donations in dollars
Mode = 20 (occurred 6 times)
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which is the greatest common factor for 15 and 18
Answers
Answer:
3 is the GCF for 15 and 18
Step-by-step explanation:
Q) GCF for 15 and 18?
Possible factors are,
→ 15 = 3 × 5
→ 18 = 2 × 3 × 3
Common factor is,
→ 3 (in 15 and 18)
Hence, 3 is the GCF for 15 and 18.
Alex, jas and stef each get a student loan to help with living expenses. they decide to allocate two fifths of their loans for food, and one-sixth for travel. what fraction of their student loan will be left to spend?
Answers
The fraction of their student loan will be left to spend is half of their loan.
A number expressed quotient, in which numerator is divided by denominator is called a fraction.
Let the loan amount be $100.
Expenses for food is given that two fifths of their loan
i.e.
= 2/5 × 100
= $40
Now,
Remaining part will be = $100- $40 = $60
So,
Expenses for travel are given that one sixth of their loan,
i.e.
= 1/6 × 60
= $10
So,
Remaining part will be = $60 - $10 = $50
Hence, the fraction of their student loan will be left to spend is half of their loan.
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Write the equation of the line through the point (2,4) that is parallel to the line 3x-2y=18. Write the answer in slope-intercept form.
Answers
To find the equation of the line (line 1) that passes through the points (2,4) and is parallel to the line 3x - 2y = 18 (line 2), you can follow the steps above.
Step 1) Write the equation of line 2 in the slope-intercept form.
A general equation for the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
So, let's isolate y in line 2:
3x - 2y = 18
3y - 18 =2y
2y = 3x - 18
y = 3/2x - 18/2
y = 3/2x - 9
Step 2) Find the slope of line 1.
Since line 1 and 2 are parallel, they have the same slope.
So,
\(m_1=m_2=\frac{3}{2}\)Step 3) Find the y-intercept (b) for line 1.
The equation for line 1 is
\(y=\frac{3}{2}x+b\)To find b, we substitute the point (2,4) in the equation:
\(\begin{gathered} y=\frac{3}{2}x+b \\ 4=\frac{3}{2}\cdot2+b \\ 4=\frac{6}{2}+b \\ 4=3+b \\ 4-3=b \\ b=1 \end{gathered}\)Step 4) Write the equation of the line.
Since you found m and b, you can write the equation of the line:
\(y=\frac{3}{2}x+1\)Answer:
\(y=\frac{3}{2}x+1\)Compare two functions: f(x) shown in the table below and g(x) which is described in the following way: Darya is 2 miles east of home and begins jogging east at a constant rate of 5 miles per hour. Let g(x) be her distance away from home and x be the time she has been jogging in hours.
Which of the following statements is NOT true?
f(x) is an exponential function whose base is 3.
f(x) is an exponential growth function that will keep growing larger.
g(x) is an exponential function because Darya keeps getting farther away from home.
g(x) is a linear function because Darya is jogging at a steady rate.
Answers
f(x) is an exponential function whose output increases exponentially as the input increases, while g(x) is a linear function whose output increases in a constant rate as the input increases.
f(x) is an exponential function, meaning that the output increases exponentially as the input increases. In the table, when x is 1, the output is 3, when x is 2, the output is 9, and when x is 3, the output is 27. This shows that the output increases exponentially as the input increases.
On the other hand, g(x) is a linear function, meaning that the output increases in a constant rate as the input increases. For example, if Darya has been jogging for 1 hour, she will be 2 miles east of home, and if she has been jogging for 2 hours, she will be 7 miles east of home (5 miles per hour x 2 hours). This shows that her distance away from home increases in a constant rate as the input (time) increases.
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Suppose an insurance company wants to determine the average speed of cars passing through an intersection. They randomly selected 85 cars and found their average speed to be 42 miles per hour with standard deviation of 4.2 miles per hour. A 90% confidence interval for the average speed of all the cars passing through the intersection is
Answers
The 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.
To calculate the confidence interval, we can use the formula:
Confidence interval = Sample mean ± (Critical value * Standard error)
Given that the sample mean is 42 miles per hour and the standard deviation is 4.2 miles per hour, we need to determine the critical value and the standard error.
Since we have a sample size of 85, we can use the t-distribution with (n-1) degrees of freedom to find the critical value. With a 90% confidence level, the corresponding critical value for a two-tailed test is approximately 1.66.
The standard error is calculated as the standard deviation divided by the square root of the sample size:
Standard error = (Standard deviation) / √(Sample size)
Standard error = 4.2 / √85 ≈ 0.456
Now we can plug in the values into the confidence interval formula:
Confidence interval = 42 ± (1.66 * 0.456)
Confidence interval ≈ (41.29, 42.71)
Therefore, the 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.
Based on the given data and calculations, we can conclude that with 90% confidence, the average speed of all the cars passing through the intersection falls within the range of 41.29 to 42.71 miles per hour.
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in 5-8, find each reciprocal. 5/9 8 7/3 1/12
Answers
the answer
155
324
5/9 (87/3(1/12)= 155/324
The perimeter of the figure below is 60.7 ft. Find the length of the missing side. 7.2 ft 4.1 ft 4.1 ft 4.1 ft 4.1 ft 12.8 ft ? 1.9 ft 1.9 ft 7.2 ft (Note: diagram is NOT to scale)
Answers
we know that
The perimeter of the figure is equal to the sum of its length sides
so
P=7.2(2)+4.1(2)+4.1(2)+12.8+1.9(2)+x
Combine like terms
P=47.4+x
Remember that
P=60.7 ft
substitute
60.7=47.4+x
x=60.7-47.4
x=13.3 ft
therefore
the answer is
13.3 ftwhat is x-y=-5 in slope intercept form
Answers
Answer:
y = x + 5
Step-by-step explanation:
x - y = - 5
-y = -x - 5
-(-y = - x - 5)
y = x + 5
In Gwinnett, the sales tax is 6%. You buy a watch that costs $45.50. What is the TOTAL cost including tax?.
Answers
Answer: $48.23
Step-by-step explanation: %6 is equal to 0.06 so you can multiply the price of the watch by 1.06 because that is the base price plus the sales tax. That gets you $48.23
Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and o=17.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed.)
Answers
To explain the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and o=17.
8, assuming the population is normally distributed, we can use the formula:$$n=\left(\frac{z_{\alpha/2}\times \sigma}{E}\right)^2$$Where;α = 1 – 0.99 = 0.01 and zα/2 is the z-score for the critical value of α/2 for a 99% confidence level. Using the Z table, z0.005 = 2.576.σ is the population standard deviation, which is given as 17.8, and E is the margin of error, which is 1.Therefore;$$n=\left(\frac{2.576\times 17.8}{1}\right)^2 = (45.48)^2 \approx 2071$$
Hence, a 99% confidence level requires a sample size of 2071, rounded up to the nearest whole number. Therefore, the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and o=17.8 is 2071.
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begin{tabular}{|r|l|r|r|} \hline 3 & Below are your numerical inputs for the problem: \\ \hline 4 & Initial Cost (\$) & 390000 \\ \hline 5 & Year 1 Revenues (\$) & 192000 \\ \hline 6 & Year 1 Costs (\$) & 125000 \\ \hline 7 & Inflation & 2.75% \\ \hline 8 & Project Duration (years) & 6 \\ \hline 9 & Depreciation Method & \\ \hline 10 & Tax Rate & \\ \hline 11 & Net Working Capital (\% oft+1 Revenues) & MACRS \\ \hline 12 & Salvage Value (\$) & 28.00% \\ \hline 13 & Cost of Capital & 15.00% & 245000 \\ \hline \end{tabular} How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.
Answers
Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.
To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:
OCF = Year 1 Revenues - Year 1 Costs
OCF = $192,000 - $125,000
OCF = $67,000
To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.
The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:
Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues
Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.
The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:
ATSV = Salvage Value percentage * Initial Cost
ATSV = 28% * $390,000
ATSV = $109,200
To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.
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The complete question is:
Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000 7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.
The ratio of men to women working for a company is 5 to 6. If there are 102 women working for the company, what is the total number of employees?
Answers
Answer:
187 people
Step-by-step explanation:
5 to 6 is the same as 5/6. 5 is the men and 6 is the women. We know that there are 102 women so we can arrange this equation.
\(\frac{5}{6}\) = \(\frac{x}{102}\)
Re-arrange the equation to find x, or the number of men in the company.
\(\frac{(102*5)}{6}\) = x
x = 82
We have found the number of men in the company. Now add the number of men and women.
102 + 82 = 187
187 total people!
Answer: 187 employees
Step-by-step explanation:
ratio of men to women: 5:6
number women working for company: 102
to work out the number of men working for the company, you must first find out what you have to multiply 6 by to get to 102
therefore you do 102/6 which is 17
now you do 17x5 to work out how many men are working for the company which is 85
total number of employees: 102+85=187
Find the volume of a cone with a base radius of 5 cm and a height of 12 cm. Use the value 3.14 for it, and do not do any rounding. Be sure to include the correct unit in your answer.
Answers
The volume of a cone can be calculated using the formula V = 1/3 * π * r^2 * h, where V is the volume, π is the mathematical constant pi, r is the base radius, and h is the height of the cone. Substituting the given values, we get V = 1/3 * 3.14 * 5^2 * 12.
Now, we can simplify the equation by performing the arithmetic operations in the correct order of operations, which is multiplication before division, and then addition or subtraction. First, we need to calculate 5^2, which is 25. Then, we can multiply 25 by 12, which gives us 300. Finally, we can multiply 300 by 3.14 and divide by 3 to get the volume of the cone. The answer is approximately 157.08 cubic centimetres.
Therefore, the volume of the cone with a base radius of 5 cm and a height of 12 cm is approximately 157.08 cubic centimetres. It is important to include the correct unit, which is cubic centimetres, as volume is a three-dimensional quantity that represents the amount of space inside a shape.
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Please help me on this!
Answers
Answer:
linear
Step-by-step explanation:
Answer:
bec97 is right it is linear
Step-by-step explanation:
y = 10 + 2x
Have a nice day! :)
Mia bought a wedge with a central angle of pie/2 radians and radius of 6 inches. What is the area of the top surface of this wedge
Answers
The area of the top surface of the wedge is 9 × pi square inches.
To find the area of the top surface of the wedge, we first need to find the area of the whole circle with radius 6 inches. The formula for the area of a circle is A = pi × \(r^2\), where A is the area and r is the radius.
So, A = pi × \((6)^2\) = 36 × pi square inches.
Since the central angle of the wedge is pi/2 radians, we can find the fraction of the circle that is represented by the wedge by dividing pi/2 by 2 × pi (the total number of radians in a circle).
So, the fraction of the circle represented by the wedge is pi/2 / 2 × pi = 1/4.
To find the area of the top surface of the wedge, we simply multiply the area of the whole circle by this fraction:
Area of top surface = (1/4) × 36 × pi = 9 × pi square inches.
Therefore, the area of the top surface of the wedge is 9 × pi square inches.
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Write an algebraic expression that represents each verbal expression: 6 times a number plus 3
Answers
\(\huge \text{Hello there! :)}\)
Answer:
The algebraic expression is as followed:
➛ \(\huge \text{6(n+3)}\)Step-by-step explanation:
Given the following question:
➛ 6 × a number➛6 × n➛plus 3 ➛ equals6(n+3)what is a algebraic expression?It's an equation built up by integers, variables, and many different operations like addition and subtraction.In this case 6 and 3 are the integersn is the variable6 times and + 3 are the operationsAll form together to make a algebraic expression.Hope this Helps! :)If you have any doubts about my answer please let me know.
\(-Nature-\)
\(\huge \text{Thanks for choosing Brainly! :)}\)
The hypotenuse of a right triangle measures 16 cm and one of its legs measures 4 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
a2 + b2 = c2
42 + b2 = 162
16 + b2 = 256
- 16
b2 = 256
square root of 256 is the answer which is 15.5
The measure of the other leg of right angled triangle is 15.5cm
What is Pythagoras theorem?The Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
According to the question
In a right angled triangle
Hypotenuse = 16 cm
Base = 4 cm
measure of the other leg or perpendicular is
Now ,
By applying Pythagoras theorem
\(Hypotenuse^{2} = Base^{2} + Perpendicular^{2}\)
substituting the values
\(16^{2} = 4^{2} + Perpendicular^{2}\)
256 = 16 \(+ Perpendicular^{2}\)
240 = \(Perpendicular^{2}\)
applying square root both side
Perpendicular = 15.5 cm
Hence, the measure of the other leg of right angled triangle is 15.5cm
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What is the quotient of 6 and 2?
?
-12.
1
12.
0
12.
0 12.
Answers
Answer:
-12
Step-by-step explanation:
I got it right on edgen
What is the sum of the first 32 terms in the arithmetic
series 3 + 10 + 17 + …?
Answers
Answer:
30
Step-by-step explanation:
Stamps come in boxes of six envelopes come in boxes of 21 Cindy wants to purchase the smallest number of stands and envelopes so that she will have exactly one envelope first how many boxes of stamps and envelopes should Cindy purchase
Answers
Answer: To find the smallest number of stamp boxes and envelope boxes that Cindy should purchase to have exactly one envelope first, we need to determine the least common multiple (LCM) of 6 and 21.
The LCM is the smallest multiple that both numbers have in common.
Prime factorize each number to find the LCM:
6 = 2 * 3
21 = 3 * 7
The LCM is the product of the highest powers of all the prime factors:
LCM = 2 * 3 * 7 = 42
Therefore, Cindy should purchase 42 boxes of stamps and 42 boxes of envelopes in order to have exactly one envelope first.
a joint probability is the . a. sum of the probabilities of two events b. probability of the intersection of two events c. sum of the probabilities of two independent events d. probability of the union of two events
Answers
Option B. It defines the joint probability as the probability of the intersection of two events.
A joint probability refers to the probability of two or more events occurring simultaneously. In other words, it is the probability that two or more events will occur together.
The joint probability of two events A and B is denoted as P(A ∩ B), which represents the probability of the intersection of events A and B. This is the probability that both A and B occur at the same time.
For example, if we toss a coin and roll a dice, the probability of getting heads on the coin and a 4 on the dice would be the joint probability of these two events occurring together. This joint probability can be calculated by multiplying the probability of getting heads (1/2) and the probability of rolling a 4 (1/6), giving a joint probability of 1/12.
Therefore, option (b) is the correct answer, as it defines the joint probability as the probability of the intersection of two events.
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A submarine 50.2 m below the surface of the ocean goes up 15.6 m. Then it goes down 35.7 m. What is the
submarine's new position relative to the surface of the ocean? Show your work.
Help Please?
Answers
Answer:
70.3
EXPLANATION:
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What multiplication equattion can be used to explain the solution to 15 / 1/3
Answers
Step-by-step explanation:
15 / (1/3) is equal to 15 x 3/1 = 15 x 3 = 45
Reciprocal of 1/3 = 3/1
So, the multiplication equation that explains the solution is:
15 * (3/1) = 45
Therefore, 15 divided by 1/3 is equal to 45.
what is the probability that does not exceed 35 minutes?
Answers
The probability that a clock is on 35 minutes in a day is extremely low.
This is because a day is made up of 24 hours, or 1440 minutes. Even if a clock was set to stay on one minute for each hour, it would only be on for 24 minutes. Therefore, it is highly unlikely that a clock would be on for 35 minutes in a day.
In order for a clock to be on for 35 minutes in a day, it would have to be set to a specific time, or it would have to be reset multiple times throughout the day.
For example, if a clock was set to 5:35 PM and then reset to 5:35 AM the next day, it would be on for 35 minutes. However, this is an extremely unlikely scenario that would require someone to manually reset the clock each day. As such, the probability of a clock being on 35 minutes in a day is extremely low.
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Complete question:
what is the probability that a clock is on 35 minutes in a day?
given that sin y= -2/3, cos x= -1/5, x in quadrant two, y in quadrant three, find the exact values of sin( x y), tan (x y), and the quadrant of x y
Answers
To determine the quadrant of x y, we need to find the signs of sin(x y) and cos(x y). Since sin(x y) is negative and cos(x y) is positive, we know that x y is in the fourth quadrant.
Since sin y= -2/3 and y is in the third quadrant, we know that the adjacent side is negative and the opposite side is negative in the following right triangle:
|
| /|
2 | / |
| / |
|/ y|
-----------
-3
Using the Pythagorean theorem, we can find the hypotenuse:
|
| /|
2 | / |
| / |
|/ y| 2^2 + (-3)^2 = 13
-----------
-3
So the sine and cosine of y can be found as:
sin y = -2/3
cos y = -sqrt(1 - sin^2 y) = -sqrt(1 - 4/9) = -sqrt(5/9) = -sqrt(5)/3
Since cos x = -1/5 and x is in the second quadrant, we know that the adjacent side is negative and the opposite side is positive in the following right triangle:
|
| /|
| / |
| / |
x |/ |
-----------
-5
Using the Pythagorean theorem, we can find the hypotenuse:
|
| /|
| / |
| / |
x |/ | x^2 + 5^2 = 26
-----------
-5
So the sine and cosine of x can be found as:
sin x = sqrt(1 - cos^2 x) = sqrt(1 - 1/25) = 2sqrt(6)/5
cos x = -1/5
Now, we can use the identities sin(x y) = sin x cos y + cos x sin y and tan(x y) = sin(x y) / cos(x y) to find sin(x y) and tan(x y):
sin(x y) = sin x cos y + cos x sin y = (2sqrt(6)/5)(-sqrt(5)/3) + (-1/5)(-2/3)
= (-2sqrt(30) - 2) / 15
cos(x y) = cos x cos y - sin x sin y = (-1/5)(-sqrt(5)/3) - (2sqrt(6)/5)(-2/3)
= (2sqrt(30) - sqrt(5)) / 15
tan(x y) = sin(x y) / cos(x y) = [(-2sqrt(30) - 2) / 15] / [(2sqrt(30) - sqrt(5)) / 15]
= (-2sqrt(30) - 2) / (2sqrt(30) - sqrt(5))
To determine the quadrant of x y, we need to find the signs of sin(x y) and cos(x y). Since sin(x y) is negative and cos(x y) is positive, we know that x y is in the fourth quadrant.
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