Jean's bedroom is 13 feet by 13 feet. She has chosen a carpet which costs $28.60 per square yard. This
includes installation.
to carpet her room -what’s the cost of the carpet for the room ?
Answers
Answer:
$4,833.40
Step-by-step explanation:
First find the area of the room.
A = lw
A = (13)(13)
A = 169\(ft^{2}\)
It cost 28.60 per square foot. Multiply these numbers together.
169(28.60) = 4833.40
Related Questions
PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answers
Answer:
7z + 17
Step-by-step explanation:
Like terms
All the numbers without letters are like terms
All the numbers with letters are like terms
Since we have 2 numbers without letters, we'll combine those.
15 + 2 = 17
Since there's only one number with letters, we can keep it the same since there's no others to combine it with
7z + 17
you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answers
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
4.) Rotate the image 90 degrees counter-clockwise about the origin. (x,y) -> (-y, x)
Answers
Answer:
is rotation of 90° counterclockwise about origin and hence it is the correct answer.Step-by-step explanation:
Convert 49° Celsius to degrees Fahrenheit using the following formula: F = {C+32 O A. 506.5°F OB. 196.2°F C. 94.6°F OD. 2237°F O E. 120.2°F
Answers
Answer:
Step-by-step explanation:
F = 9/5C + 32
Putting value
9/5(49) + 32
88.2 + 32
= 120.2°F
Option E is the correct answer
The Celsius temperature 49 in Fahrenheit is 120 F.
To convert Celsius to Fahrenheit, you can use the formula:
F = (C × 9/5) + 32
Let's calculate the conversion using the given Celsius value:
C = Celsius temperature
F = (C × 9/5) + 32
F= (49 x 9/5)+ 32
F= 88.2 + 32
F = 120.2 F
Thus, Celsius temperature 49 in Fahrenheit is 120 F.
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Assumptions: Tax depreciation is straight-line over three years. Pre-tax salvage value is 25 in Year 3 and 50 if the asset is scrapped in Year 2. Tax on salvage value is 40% of the difference between salvage value and book value of the investment. The cost of capital is 20%.
Answers
Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.
To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:
Assumptions:
Tax depreciation is straight-line over five years.
Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.
Tax on salvage value is 30% of the difference between salvage value and book value of the investment.
The cost of capital is 12%.
Given:
Initial investment cost = $50,000
Useful life of the equipment = 5 years
To calculate the depreciation expense each year, we divide the initial investment by the useful life:
Depreciation expense per year = Initial investment / Useful life
Depreciation expense per year = $50,000 / 5 = $10,000
Now, let's calculate the book value at the end of each year:
Year 1:
Book value = Initial investment - Depreciation expense per year
Book value \(= $50,000 - $10,000 = $40,000\)
Year 2:
Book value = Initial investment - (2 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (2 \times$10,000) = $30,000\)
Year 3:
Book value = Initial investment - (3 \(\times\) Depreciation expense per year)
Book value = $50,000 - (3 \(\times\) $10,000) = $20,000
Year 4:
Book value = Initial investment - (4 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (4 \times $10,000) = $10,000\)
Year 5:
Book value = Initial investment - (5 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (5 \times $10,000) = $0\)
Based on the assumptions, the salvage value is $10,000 in Year 5.
If the asset is scrapped in Year 4, the salvage value is $15,000.
To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:
Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)
For Year 5:
Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)
For Year 4 (if scrapped):
Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)
Now, let's calculate the after-tax cash flows for each year:
Year 1:
After-tax cash flow = Depreciation expense per year - Tax on salvage value
After-tax cash flow = $10,000 - $0 = $10,000
Year 2:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 3:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 4 (if scrapped):
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $15,000 - $1,500 = $13,500
Year 5:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $10,000 - $3,000 = $7,000
Now, let's calculate the net present value (NPV) using the cost of capital of 12%.
We will discount each year's after-tax cash flow to its present value using the formula:
\(PV = CF / (1 + r)^t\)
Where:
PV = Present value
CF = Cash flow
r = Discount rate (cost of capital)
t = Time period (year)
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment
Let's calculate the NPV:
PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)
PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)
PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)
PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)
PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)
NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000
NPV = $22,954.24 - $50,000
NPV = -$27,045.76
The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.
Therefore, the investment may not be favorable.
Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.
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The complete question may be like :
Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.
You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.
Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.
A bakery can make 72 cheesecakes for every 6 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses? A Cheesecakes Cheesecakes Cream Cheese (blocks) Cream Cheese (blocks) 12 12 1 1 13 13 2 2 14 14 3 3 B Cheesecakes Cheesecakes Cream Cheese (blocks) Cream Cheese (blocks) 12 12 1 1 24 24 13 13 36 36 25 25 C Cheesecakes Cheesecakes Cream Cheese (blocks) Cream Cheese (blocks) 72 72 6 6 78 78 12 12 84 84 18 18 D Cheesecakes Cheesecakes Cream Cheese (blocks) Cream Cheese (blocks) 72 72 6 6 84 84 7 7 96 96 8 8
Answers
The table that represents the relationship between the number of cheesecakes the bakery makes & the number of blocks of cream cheese the bakery uses is option- D, found using unitary-method.
What is unitary-method?
The unitary method is used to evaluate the value of a single unit or object, and then we can evaluate the necessary value by multiplying the single unit value. The unitary method involves determining the value of a single unit before determining the value of the necessary quantity of units. In the unitary method, the value of one unit quantity is determined before the values of the other units are determined. Direct variation and inverse variation are the two forms of variations.
Given that number of cheesecakes that can be made using 6 blocks of cream cheese is 72 cheesecakes
6 blocks of cheese= 72 cheesecakes
1 block of cheese = 72 ÷ 6 cheesecakes
= 12 cheesecakes.
2 blocks of cheese= 12 x 2 cheesecakes
=24 cheesecakes
3 blocks of cheese = 12 x 3 cheesecakes
= 36 cheesecakes
6 blocks of cheese = 12 x 6 cheesecakes
=72 cheesecakes
7 blocks of cheese = 12 x 7 cheesecakes
=84 cheesecakes
8 blocks of cheese = 12 x 8 cheesecakes
=96 cheesecakes
12 blocks of cheese = 12 x 12 cheesecakes
=144 cheesecakes
13 blocks of cheese = 12 x 13 cheesecakes
=156 cheesecakes
18 blocks of cheese = 12 x 18 cheesecakes
=216 cheesecakes
25 blocks of cheese = 12 x 25 cheesecakes
=300 cheesecakes
The option in which the cheesecakes directly variate with cheese blocks is option -D
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Refer to the attachment for the options.
8. A pyramid has a volume of 8 cubic feet. The height is 2 feet. The base is rectangular. Give possible dimensions for the length and width of the base.
Answers
Answer:
base = 12 ft²
The base could be 3 ft x 4 ft, 6 ft x 2 ft, etc. (any numbers multiplied together = 12)
Step-by-step explanation:
volume = 1/3bh
8 = 1/3b(2)
multiply both sides of the equation by 3:
24 = 2b
b = 12 ft²
in the coordinate plane, ABCD has vertices with coordinates A(1,-1), B(-5,3), C(-3,6),
and D(3,2)
Answers
Answer:
C
Step-by-step explanation:
Calculate the missing angles a, b, c, and d in the diagram below, giving a reason for each answer
Answers
Answer:
see below and attachment
Step-by-step explanation:
a=30°
because, the marked angle of 30° is an alternate interior angle to angle a. Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.
b=50°
because the marked angle of 50° is a vertical angle to angle b. Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.
c=50°
because the marked angle of 50° is a corresponding angle (same side angle) to angle c. These corresponding angles are congruent because the 2 horizontal lines are parallel.
d=100°
because the 3 interior angles of a triangle must add up to 180°. We have 30°, 50°, so the last angle must be 100°. We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°. We have angle a as 30°, angle c as 50°, so angle d must be 100°.
Hope this helps! See attachment for visual.
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
3.
The Moy family budgeted $32,650 to remodel their kitchen. They spent
$43,987. How much more or less is the amount spent than the amount
budgeted?
A $11,337 more
B $11,337 less
C $17,887 more
D $17,887 less
Answers
Answer:
A
Step-by-step explanation:
43987-32650= 11337
And it’s more
Which table represents a linear function?
Answers
Answer:
C
Step-by-step explanation:
C is the only function that have a consistent decrease while A is a trigonometric function, B is a non linear function, D is an exponential function
Find the lateral area, surface area and volume of the cube
Answers
Answer:
Lateral Area = 13 x 13 x 4 = 676 ft²
Surface area = 13 x 13 x 6 = 1014 ft²
Volume = 13 x 13 x 13 = 2197 ft³
Find the equation of a line that is vertical through (1,3)
Answers
Answer:
x=1
Step-by-step explanation:
What percentage is 14 of 28? *
75%
60%
50%
45%
Answers
The answer for the percentage of 14 and 28 is 50%.
Because 28/14= 1/2= 50%
9. (a) (b) (c) (d) (e) Bako is twice as old as he was five years ago. His mother was then six times as old as he was. She is now 35 years old. How old is Bako? 10 How old was his mother when Bako was five? How old will Bako be when his mother is 50? How old was Bako's mother when he was born? What is the difference between Bako's age and his mother's?
Answers
Answer:
(a) Bako is 10 years old
(b) His mother was 30 years old when Bako was 5
(c) Bako will be 25 years old when his mother is 50
(d) Bako's mother was 25 years old when he was born
(e) The difference between Bako's age & his mother's is 25 years
Step-by-step explanation:
Let Bako's age five years ago be x years
Presently, Bako is 2x years old (according to the 1st statement)
Normal, Bako's present age should have been (x + 5) years; since he was x years old 5 years ago.
This simply means that Bako's present age is BOTH 2x years & (x + 5) years.
We have to equate them since they mean the same thing (Bako's present age)
x + 5 = 2x
2x - x = 5
Therefore x = 5 years
Remember that x signified Bako's age five years ago... This simply means that Bako's age five years ago was 5 years.
This simply means that Bako's age now is 10 years old.
His mother was then six times 5 years = 30 years old (from the 2nd statement).
If Bako was 5 years old five years ago and his mother was 30 years old... It simply means that Bako was born ten years ago when his mother was 25 years old.
This simply means that Bako's mother is older than him with 25 years.
Therefore, Bako will be 25 years old when his mother is 50 years old
Write the ratio:
10
to
68
as a fraction in lowest terms.
Answers
Answer:
5/34
Step-by-step explanation:
change 10:68 into 10/68, then divide by 2/2 to get 5/34.
Gina is going to buy 100 stickers
Answers
Gina should buy from Stickers4u.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Gina is going to buy 100 stickers.
If she buys from the shop - Stickers4u,
then the cost is,
= 100/25 x 2.15
= 4 x 2.15
= 8.6.
And if she buys from the World stationary,
then the cost is,
= (100 - 50)/10 x 1.65
= 5 x 1.65
= 8.25
Therefore, she should buy from Stickers4u.
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For the figure shown on the right, find the value of the variable and the measures of the angles.
Q
(2x+38)
(x-10)
X = 38
mZP
ZP-O
What would be the m
Answers
Answer:
38-10=28
Step-by-step explanation:
The angle labeled is x-10.
Since we know x is 38, subtract!
38-10=28
Mark brainliest please!
There were two containers of beads. The ratio of the number beads in the first
container to that in the second container was 7:11 at first. When 12 beads
were transferred to the second container, the ratio became 1: 2. How many
beads were in the first container at first?
Answers
The number of beads in the first container at first was:
7x = 7(12) = 84
So, there were 84 beads in the first container at first.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Let's assume that the number of beads in the first container at first is 7x, and the number of beads in the second container at first is 11x, where x is some positive constant.
After 12 beads are transferred from the first container to the second container, the number of beads in the first container becomes 7x - 12, and the number of beads in the second container becomes 11x + 12.
The ratio of the number of beads in the first container to the second container becomes 1:2, so we can write:
(7x - 12) / (11x + 12) = 1/2
Cross-multiplying gives:
14x - 24 = 11x + 12
Simplifying, we get:
3x = 36
x = 12
Therefore, the number of beads in the first container at first was:
7x = 7(12) = 84
So, there were 84 beads in the first container at first.
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kate pays $203 in advance on her account at the athletic club. Each time she uses the club, $9 is deducted from the account. Find the remaining in the account after 12 visits
Answers
Answer:
95
Step-by-step explanation:
The equation to solving this would be 203 - (9 multiply 12). If you multiply 9 and 12 you get 108. Minus 108 from 203 and you get 95.
Solve the following equation for hh. Be sure to take into account whether a letter is capitalized or not
Answers
Answer:
Divide each term by J and simplify.
h = m /J
Step-by-step explanation:
I hope this helps! Have a great day!
b) In a certain weight lifting machine, a weight of 1 kN is lifted by an effort of 25 N. While the weight moves up by 100 mm, the point of application of effort moves by 8 m. Find mechanical advantage, velocity ratio and efficiency of the machine
Answers
The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.
The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.
The problem has provided the following information:
Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m
We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage
The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;
Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;
Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5
Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.
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Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval.
I NEED HELP ASAP
Answers
Each interval that represents the behavior of the function are shown below:
0 < x < 4: increasing.
4 < x < 6: decreasing.
6 < x < 8: increasing.
8 < x < 10: decreasing.
10 < x < 14: neither increasing or decreasing.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
First, we need to know when the function is increasing, and when is decreasing.
It is because greater x-values correspond to higher y-values that a function increases. On the other side, a function decrements when lower y-values are associated with greater x-values. The function will move in the graph in an upward direction when it is rising and in a downward direction when it is decreasing.
So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.
All these interpretations we can expressed using math language, specifically inequalities:
0 < x < 4: increasing.
4 < x < 6: decreasing.
6 < x < 8: increasing.
8 < x < 10: decreasing.
10 < x < 14: neither increasing or decreasing.
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Complete question:
what is inequalities
Answers
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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Which equation has the steepest graph?
Answer Choices:
y = 2x + 4
y = -4x – 1
y = 1/2 x + 10
y = 5x + 2
Answers
Answer:
y = 5x + 2
Step-by-step explanation:
in order to find if a line is steeper, you need to look at the slope
the greater the slope, the steeper the line will be
y = 2x + 4
y = -4x - 1
y = 1/2x + 10
y = 5x + 2
out of all of these options, y = 5x + 2 has the largest slope. this means that it is the steepest one.
There are total 52 flowers name the multiples of 4 in this..
Answers
Answer: multiples of 4 are -4,8,12,16,20,24,28,32,36,40,44,48,52
Step-by-step explanation:
4x1=4
4x2=8
4x3=12
4x4=16
4x5=20
4x6=24
4x7=28
4x8=32
4x9=36
4x10=40
4x11=44
4x12=48
4x13=52
Answer:
208
Step-by-step explanation:
52×4=208
How to calculate your bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour. Also, You will need to deduct Federal Income Tax (11.9%) , State Income Tax (3.6%), F.I.C.A (7.65%), and professional dues. Lastly you will need to look determine whether or not you will be able to pay your monthly car insurance bill of $200.00?
Answers
To calculate your bi-weekly paycheck, follow these steps:
Step 1: Calculate the gross earnings:
Multiply the number of hours worked per week by the hourly rate.
20 hours/week * $9.00/hour = $180.00/week
Step 2: Calculate the total earnings for two weeks:
Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.
$180.00/week * 2 weeks = $360.00
Step 3: Calculate the deductions:
Calculate each deduction separately and subtract them from the gross earnings.
Federal Income Tax: $360.00 * 11.9% = $42.84
State Income Tax: $360.00 * 3.6% = $12.96
F.I.C.A: $360.00 * 7.65% = $27.54
Professional Dues: Amount varies depending on the specific dues.
Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues
Step 4: Calculate the net earnings:
Subtract the total deductions from the gross earnings.
Net Earnings = Gross Earnings - Total Deductions
Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.
It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.
Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.
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k (x) = 6x + 100
k(-5) = ?
Answers
Answer:
im not super sure but i think its 70
Step-by-step explanation:
Can someone help please
ASAP
Answers
Answer:
see explanation
Step-by-step explanation:
using the tangent ratio in the right triangle
tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then
∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )
tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then
∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )
AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )