Answer:
Step-by-step explanation:
You need the 6th row of Pascal's triangle which contains the numbers 1, 5, 10, 10, 5, 1
Fill in the expansion as follows, using those numbers and the fact that a = 1 and b = 1:
[tex]1(1a)^5(1b)^0+5(1a)^4(1b)^1+10(1a)^3(1b)^2+10(1a)^2(1b)^3+5(1a)^1(1b)^4+1(1a)^0(1b)^5[/tex]
That simplifies down nicely to
[tex]a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5[/tex]
Those are fun! Pascal's triangle is one of the coolest things ever!
To expand (a+b)^5 using Pascal's Triangle, we can use the Binomial Theorem. The expansion can be written as (a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + (b^5).
To expand the binomial (a+b)^5 using Pascal's Triangle, we will use the Binomial Theorem. According to the theorem, the expansion of (a+b)^n can be written as:
(a+b)^n = (nC0)(a^n)(b^0) + (nC1)(a^(n-1))(b^1) + (nC2)(a^(n-2))(b^2) + ... + (nCn)(a^0)(b^n)
For (a+b)^5, the expansion would be:
(a+b)^5 = (5C0)(a^5)(b^0) + (5C1)(a^4)(b^1) + (5C2)(a^3)(b^2) + (5C3)(a^2)(b^3) + (5C4)(a^1)(b^4) + (5C5)(a^0)(b^5)
Simplifying further, we get:
(a+b)^5 = (a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + (b^5)
A mechanic gives a survey to all of his customers asking them to rate the quality of the service they received. He then keeps track of how many customers return to the shop for additional services during the next six months. Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services. What conclusion can be drawn from this study?
Answer:
Some customers who rate their service as high quality return for additional services.
Step-by-step explanation:
Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services.
This shows than some customers are satisfied overall and return back for additional services.
HELP ASAP PLEASE!!!
List the “DO” and “UNDO” steps you would write to find the inverse of y=x^3+5
If x < 5, then which of the following must be true?
-x < -5
-x > -5
-x < 5
-x > 5
Answer:
B
Step-by-step explanation:
x<5
When we multiply by negative number sign of inequality should be changed also.
x*(-1) > 5*(-1)
-x>-5
For this case we have the following expression:
[tex]x <5[/tex]
By definition we have to:
Let [tex]c <0[/tex]. If [tex]a <b,[/tex] then [tex]ac> bc[/tex]
That is to say:
If we multilate on both sides of the inequality by -1, the sign automatically changes direction.
[tex](-1) (x) <(- 1) (5)\\-x> -5[/tex]
ANswer:
Option B
Use technology or a z-score table to answer the question.
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test.
What percent of students scored below Jake?
Round your answer to the nearest whole number.
A. 33%
B. 57%
C. 63%
D. 72%
Answer:
C
Step-by-step explanation:
First we find the z-score.
z = (x - μ) / σ
z = (520 - 500) / 60
z = 0.33
Using a calculator or z-score table:
P(z < 0.33) = 0.6293
The probability is approximately 63%. Answer C
Answer:
63%
Step-by-step explanation:
63%
What is the reason that the sum of the magnitudes of two vectors and the magnitude of the sum of two vectors not equal? Thank you in advanced
Explanation:
It is the same reason that the distance by road is not the same as the distance "as the crow flies." The two vectors are often not aligned so that the magnitudes both add to directly to the distance from the origin (or the tail of the first vector).
For example, suppose you walk two segments of 1 mile each. If you walk east in both cases, you end up 2 miles east of where you started. (The sum of the vectors is the sum of their magnitudes.)
If you walk east 1 mile and north 1 mile, you end up about 1.4 miles from where you started, not 2 miles. The second "vector" did not add directly to the distance from your starting point.
If you walk east 1 mile, then west 1 mile, you end up exactly where you started. The sum of the vectors is zero, but the sum of their magnitudes is still 2 miles.
The sum of magnitudes of vectors and magnitude of sum of two vectors are not equal due to the directionality property of vectors. The sum of vectors is calculated through the parallelogram rule, accounting both magnitude and direction. It uses the principles of geometry and trigonometry depending on the vectors' alignment.
Explanation:The reason that the sum of the magnitudes of two vectors and the magnitude of the sum of two vectors is not equal lies in basic properties of vectors, specifically, the directionality of vectors. When you add two vectors, you are applying the parallelogram rule, which considers both the magnitude and direction of the vectors. Because the sum of vectors results in a resultant vector based on their geometrical arrangement, the magnitude of the resultant vector is not simply a sum of original magnitudes but a composition governed by rules of geometry and trigonometry.
To put it simply, if two vectors are aligned in the same or opposite direction, the magnitude of their sum or difference will be the sum or difference of their magnitudes. But if the vectors are at an angle (neither parallel nor anti-parallel), the magnitude of the sum will be less than the sum of the individual magnitudes, due to the Pythagorean theorem applied in the parallelogram rule.
For example, If you have vectors A and B and they happen to make a right angle (perpendicular), the magnitude of the sum (Resultant vector) will be √(A²+B²), not A + B. The sum of the magnitudes would be aligned along one line while the magnitude of the sum would be along the hypotenuse of the right triangle formed by vectors, hence the difference.
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What is the mean absolute deviation of the data set?
{12, 10, 10, 8, 6, 7, 7, 12}
.1
.2
.6
.9
Answer:
the mean absolute deviation of the data set is 2.
Step-by-step explanation:
To calculate the mean absolute deviation of a data set, we need to follow the following steps:
Step 1: Calculate the mean.
Step 2: Calculate how far away each data point is from the mean (always keeping a possitive distance).
Step 3: Calculate the mean of the deviations.
Step 1: The mean of the data set is:
Mean = (12 + 10 + 10 + 8 + 6+ 7 + 7 + 12)/8 = 72/8 = 9
Step 2:
{12 -9, 10-9, 10-9, 9-8, 9-6, 9-7, 9-7, 12-9} = {3, 1, 1, 1, 3, 2, 2, 3}
Step 3: (3 + 1 + 1 + 1 + 3 + 2 + 2 + 3)/8 = 2
In conclusion, the mean absolute deviation of the data set is 2. Which corresponds to the option B.
Find the area of the regular polygon. Round to the nearest tenth. Please & Thank You!
A=259.8 cm^2 is the correct answer
There are two bags of marbles. Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from Bag A and one black marble from Bag B.
a. 3/20
b. 1/26
c. 17/20
d. 1/10
A) 3/20 would be the answer
Melody has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was $0, but this was her balance for only the first 15 days of the billing cycle. She then made a purchase that increased her balance to $4800, and her balance stayed this amount for the remainder of the billing cycle. If her credit card's APR is 29%, how much was Melody charged in interest for the billing cycle? A. $57.21 B. $0 C. $139.20 D. $114.41
Answer:
The answer is B $0.00
Step-by-step explanation:
Answer:
The answer is 0%
Step-by-step explanation:
Previous Balance Method uses the "previous" balance, that is, the balance from the month before.
Here it is given that Melody's balance at the beginning of the billing cycle is $0.
So, this means she has to pay interest on $0 (the previous month balance)
And for the rest balance, she will pay the next month.
Therefore, the answer is 0%
PLEASE HELP : Which line could be the graph of the points in the table?
Answer:
see below
Step-by-step explanation:
As x gets larger, y gets smaller. Only one of the graphs has that characteristic.
Line of the graph (3) could be the graph of the points in the table.
To determine which line could be the graph of the points in the table, we can plot the points and then draw a line that passes through all three points.
The line that passes through all three points is the line that intersects the y-axis at 0 and has a slope of −2.
Therefore, the line that could be the graph of the points in the table is:
y = -2x
We can check our answer by substituting the points from the table into the equation. If the points satisfy the equation, then the equation is a possible graph of the points.
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When all three points are connected, triangle PQR will be a right triangle. At which coordinates must R be located?
A) (-6,3)
B) (-3,3)
C) (0,3)
D) (5,3)
b) u gotta each R point w p & q and see which one would give u a right triangle, which is b
Answer:
your answer should be (-3,3)
Step-by-step explanation:
brainliest pls
Math Question please help
Answer:
Step-by-step explanation:a+b
ANSWER
B. y=8x +1200
EXPLANATION
If the family's well pumps on average 8 gallons of water per minute, then the unit rate of change is 8.
This implies that, the slope of the linear equation that models this situation is
[tex]m = 8[/tex]
It was also given that, the well's tank had 1200 gallons of water in the morning.
This implies that the y-intercept of the straight line is
[tex]b = 1200[/tex]
The equation is given by:
[tex]y = mx + b[/tex]
We substitute the values to obtain:
[tex]y = 8x + 1200[/tex]
The amount of water in the tank, y after it has been pumping for x minutes is
[tex]y = 8x + 1200[/tex]
Find the circumference or distance around a circus ring (circle) with a diameter of 100 feel. Use 3.14 for pi
Use Formula C= pi(d) so that would be 3.14 x 100 = 314
Answer:
the circumference is 314.16
When two six-sided dice are rolled, there are 36 possible outcomes. a. Find the probability that the sum is not 4. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. b. Find the probability that the sum is greater than 5. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. Round the fraction
The probability of not getting a sum of 4 when rolling two six-sided dice is 33/36 or 92%. The probability of getting a sum greater than 5 when rolling two six-sided dice is 13/18 or approximately 72%.
Explanation:The subject area for this question is in Mathematics, specifically probability. The question asks to determine the probability of a sum not being 4, and of a sum being greater than 5 when two six-sided dice are rolled.
(a) The possibilities of getting a sum of 4 are (1,3), (2,2), and (3,1). That's 3 possibilities out of a total of 36, therefore the probability of not getting a sum of 4 is 1 - (3/36) = 33/36 (in simplified form) and as a percentage that's approximately 92%.
(b) The possibilities of getting a sum greater than 5 are (2,4),(3,3),(3,4),(4,2),(4,3),(4,4),(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5), and (6,6). That's 26 possibilities out of 36, therefore the probability of getting a sum greater than 5 is 26/36 or 13/18 in simplest form, and as a percentage that's approximately 72%.
In this way, understanding of probability and how to calculate it properly can help in accurately determining outcomes in different scenarios.
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The probability of the sum not being 4 is (36 - 3) / 36, and the probability of the sum being greater than 5 is 21 / 36.
Explanation:When two six-sided dice are rolled, there are 36 possible outcomes. To find the probability that the sum is not 4, we need to calculate the number of outcomes where the sum is not 4 and divide it by the total number of outcomes.
There are 3 outcomes with a sum of 4, so the probability is (36 - 3) / 36.
To find the probability that the sum is greater than 5, we need to calculate the number of outcomes where the sum is greater than 5 and divide it by the total number of outcomes.
There are 21 outcomes with a sum greater than 5, so the probability is 21 / 36.
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What is the maximum number of possible solutions for the system shown below?
[tex]x^2-4y^2=16[/tex]
[tex]x^2+y^2=36[/tex]
A. 1
B. 4
C. 3
D. 2
Answer:
4
Step-by-step explanation:
Which of the following equations describes the graph?
Answer:
y = 1/2x^2 - 2x + 1
Step-by-step explanation:
The equation of the parabola in vertex form is y = 1/2 (x - 2)^2 - 1. By finding the vertex at (2,-1) we plug in the point into the formula y = a(x-h)^2 + k. To convert it to standard form like the equations listed, multiply through the distributive property to clear the parenthesis.
y = 1/2 (x-2)(x-2) - 1
y = 1/2 (x^2 - 4x + 4) - 1
y = 1/2x^2 - 2x + 2 - 1
y = 1/2x^2 - 2x + 1
At the beginning of year 1, Lisa invests $500 at an annual compound interest
rate of 3%. She makes no deposits to or withdrawals from the account.
Which explicit formula can be used to find the account's balance at the
beginning of year 6? What is the balance?
O A. A(n) = 500 (1 + 0.03)(n = 1); $579.64
O B. A(n) = 500 + (0.03+500) -1); $584.50
O C. A(n) = 500 + (n - 1)(0.03 . 500); $575.00
O D. A(n) = 500 - (1 +0.03), $597.03
Answer:
the actual answer is a(n)= 500 * ( 1 + 0.03) ^(n - 1) ;$579.64
Step-by-step explanation:
( Help Please )
A farmer is searching his farmland, looking for a missing horse that went grazing in the field of newly cut hay. He finds himself on the opposite corner of where he started and wants to return to his truck as soon as possible. The field is 450 yd by 600 yd. How far will he walk if he walks diagonally across the field, and how much distance will he save instead of walking around the field? Explain your answer. Make sure to use the Pythagorean Theorem when solving this word problem.
Answer:
750 yards
Step-by-step explanation:
I entered the area of the field into a Pythagorean Theorem Calculator and it concluded that the diagonal length of the field would be approximately 750 yard.
Answer:
300 yd saved
Step-by-step explanation:
The length of the diagonal of the field is found using the Pythagorean Theorem and is
d = √( 450 yd)² + ( 600 yd)² ) = √562500 yd² = 750 yd is the diagonal distance. If, on the other hand, the farmer walks the length and width of the perimeter of the field, that would be 450 yd + 600 yd, or 1050 yd.
The farmer could spare himself 1050 - 750, or 300 yd, of walking if he crosses the field along a diagonal.
What is the value of a in the equation , when ?
3
15
21
39
Answer:
15
Step-by-step explanation:
5 times 15 is 75
10 times 3 is 30
75 -30 = 45
Answer:
The value of a is 15
Step-by-step explanation:
Given the equation
[tex]5a-10b=45[/tex]
we have to find the value of a when b is 3
[tex]5a-10b=45[/tex]
Substitute b=3, we get
[tex]5a-10(3)=45[/tex]
[tex]5a-30=45[/tex]
[tex]5a=45+30=75[/tex]
[tex]a=\frac{75}{5}=15[/tex]
Hence, the value of a is 15
27.) FEMALE LAWYERS There are 1,094,751 active lawyers living
in the United States. If 71.4% of these lawyers are male, find
(a) the percent of the lawyers who are female and (b) the number
of lawyers who are female. Round to the nearest whole number.
Answer:
28.6%; 313,099
Step-by-step explanation:
Lawyers are either male or female, so if 71.4% are male, then 100% minus that are female.
100% - 71.4% = 28.6%
28.6% of 1,094,751 is:
0.286 × 1094751 = 313098.786
Rounded to the nearest whole number, there are 313,099 female lawyers.
Evaluate sin(Arcos(-9/√145)).
Use the fact that [tex]\sin x = \sqrt{1-\cos^2 x}[/tex] to solve it.
[tex]\sin(\arccos(-\frac{9}{\sqrt{145}}))=\sqrt{1-\cos^2(\arccos(-\frac{9}{\sqrt{145}}))} =\\= \sqrt{1-(-\frac{9}{\sqrt{145}})^2}=\frac{8}{\sqrt{145}}[/tex]
Answer:
a
Step-by-step explanation:
Bill is doing a fundraiser for soccer. He needs at least $100 worth. Candy bars cost two dollars each insurance cost $10 each Hemist sell more than four candy bars
Bill needs to sell more than 45 candy bars to reach his fundraising goal of $100, after factoring in his insurance cost.
Explanation:Bill is trying to raise a minimum of $100 for soccer. If each candy bar is priced at $2 and he has an insurance cost of $10, we can start calculating how much product he needs to sell to reach his goal.
Firstly, we subtract the insurance cost from the total he needs to raise. This is because the insurance cost is a fixed cost that he needs to cover regardless of the number of candy bars sold. Hence, $100 - $10 = $90.
Now, the remaining $90 needs to be covered by selling candy bars. As each candy bar costs $2, we divide $90 by $2 to find out how many candy bars he needs to sell. Therefore, $90 ÷ $2 = 45 candy bars.
This shows that Bill needs to sell more than 45 candy bars to reach his goal, taking into account his initial fixed insurance cost.
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PLEASE HELP ME!! WILL GIVE BRAINLIEST!
Daniela has a rectangular yard with a pool in the shape of a semicircle. How many square feet of grass does Daniela need to cover her yard, but not the pool?
Answer:
A D F
Step-by-step explanation:
Area of rectangle: 80*45=3600
Area of semi-circle: ((60/2)^2)/2*pi=1413
Total area of grass=3600-1413=2187
Find the unknown angle measure by solving for the given variable
Answer choices are: 125, 35, 40, and 140.
A straight line is 180°. So you can do:
(15x - 4) + (5x - 8) = 180 Simplify
20x - 12 = 180
20x = 192 Find the value of x
x = 9.6
m∠ABD = 15x - 4 Plug in x = 9.6
m∠ABD = 15(9.6) - 4 = 144 - 4 = 140°
m∠DBC = 5x - 8 Plug in 9.6
m∠DBC = 5(9.6) - 8 = 48 - 8 = 40°
Final answer:
To find the unknown angle, use the trig identity sin(90° - x) = cos x, ensure the calculator is in radian mode, and check if the answer is reasonable.
Explanation:
To find the unknown angle measure in the given problem, we need to use the trigonometric identity sin(90° - x) = cos x. This identity is useful when dealing with right-angled triangles and can help in finding missing angles when other angles or sides are known.
First, we need to identify the known values within the problem and the given equation. Assuming we are looking for value 'a', we then solve the equation by substituting the appropriate known values into it. After that, we need to ensure that our calculator is set to radian mode, as the instructions suggest that angle measurements should be in radians.
After obtaining the numerical solution, it is important to check if the answer is reasonable and makes sense within the context of the problem.
If pizzas cost $9.83 per pizza, estimate how much money you would need to buy 18 of them.
Your answer does not need to be exact, so please do NOT use a calculator and please do not put a $ sign in your answer.
Answer:
180
Step-by-step explanation:
because it doesn't has to be exact you can do: 10 × 18 = 180
Answer:
180
Step-by-step explanation:
This is a good question to keep in mind. When you do use a calculator the answer to this estimate will tell you if your work on the calculator is correct.
round the cost of the pizza to 10
18 * 10 = 180 dollars. So you should get an answer that is under 180 dollars -- about 3 dollars short. (0.17 * 18 which is another guess).
Now pick up your calculator and do the math. It comes to 176.94
If you do any grocery shopping, this is a good skill to have.
A parking garage has a total of 87 parking spaces. If there are 3 levels in the garage and each level has an equal number of parking spaces. How many parking spaces are on each level
Divide total parking spaces by number of levels.
87 / 3 = 29
There are 29 parking spaces on each level.
To find out how many parking spaces are on each level of a garage with 87 total spaces and 3 levels, divide the total number of parking spaces (87) by the number of levels (3) to get 29 parking spaces per level.
If a parking garage has a total of 87 parking spaces and there are 3 levels in the garage with an equal number of parking spaces on each level, to find out how many parking spaces are on each level, we need to divide the total number of parking spaces by the number of levels.
Here is the step-by-step calculation:
Count the total number of parking spaces: 87.Count the total number of levels: 3.Divide the total number of parking spaces by the number of levels: 87 parking spaces/ 3 levels = 29 parking spaces per level.Therefore, there are 29 parking spaces on each level in the garage.
A walking path is shaped like a rectangle with a width 7 times its length l. what is a simplified expression for the distance between opposite corners of the walking path?
Answer:
The simplified expression is d = (5√2) L
Step-by-step explanation:
* Lets explain the problem
- A walking path is shaped like a rectangle
- The width of the rectangle is 7 times its length L
∵ The length of the rectangle is L
∵ The width is 7 times the length
∴ The width of the rectangle is 7L
- The distance between the opposite corners represented by the
diagonal of the rectangle
- The length , the width and the diagonal formed a right triangle
- Its hypotenuse is the diagonal of the rectangle
- Its two legs are the length and the width of the rectangle
* Now we have right triangle use the Pythagoras Theorem to find
the hypotenuse
∵ The length , the width and the diagonal of the rectangle are the
sides of a right triangle
∵ The diagonal is the hypotenuse (h) of the triangle
∵ hypotenuse = √[L² + W²]
∵ The length = L and the width = 7L
∴ h = √[(L)² + (7L)²] = √[L² + 49L²] = √[50L²]
∵ √50 = 5√2
∵ √(L²) = L
∴ h = 5√2 L
∵ The diagonal of the rectangle is the distance between the
opposite corners
∴ The distance between the opposite corners is (5√2) L
* The simplified expression is d = (5√2) L, where L is the length
of the rectangle
To find the distance between opposite corners of the walking path, which is shaped like a rectangle, we need to determine the length of the diagonal.
Given that the width is 7 times the length (l), we can represent the width of the rectangle as \(7l\).
Let's denote the length of the rectangle by \(l\) and the width by \(w\). According to the information, \(w = 7l\).
Now, to find the length of the diagonal, we use the Pythagorean theorem, which states that for a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For our rectangle, the diagonal forms the hypotenuse, and the length and width are the other two sides of the right-angled triangle. Thus, if we denote the diagonal by \(d\), the Pythagorean theorem gives us:
\(d^2 = l^2 + w^2\)
Substituting the expression for the width:
\(d^2 = l^2 + (7l)^2\)
\(d^2 = l^2 + 49l^2\)
\(d^2 = 50l^2\)
To find \(d\), we take the square root of both sides:
\(d = \sqrt{50l^2}\)
Since \(50\) can be broken down into \(25 \times 2\) and \(25\) is a perfect square, we can simplify the square root as follows:
\(d = \sqrt{25 \times 2 \times l^2}\)
\(d = \sqrt{25} \times \sqrt{2} \times \sqrt{l^2}\)
\(d = 5l \times \sqrt{2}\)
So the simplified expression for the distance between opposite corners of the walking path is:
\(d = 5l\sqrt{2}\)
Match each property with the appropriate example.
1.
4(x - 2) = 4x - 8
2.
(4+2) + 8 = 4 + (2+8)
3.
4 * 2 = 2 * 4
4.
4 * 1 = 4
a.
Commutative property
b.
Distributive property
c.
Associative property
d.
Identity property
Answer:
1. Distrubutive 2. Associative 3. Commutative 4. Identity
Step-by-step explanation:
1. Distributive property 2. Associative property
3. Identity property 4. Commutative property
For this case we have that by definition:
the distributive property establishes that:[tex]a (b + c) = ab + ac[/tex]
So:
[tex]4 (x-2) = 4x-8[/tex]
State the distributive property.
The associative property states:[tex]a + (b + c) = (a + b) + c[/tex]
So:
[tex](4 + 2) + 8 = 4 + (2 + 8)[/tex]
Enunciates the associative property
The commutative property establishes that the order of the factors does not alter the product.[tex]a * b = b * a[/tex]
So:
[tex]4 * 2 = 2 * 4[/tex]
Enunciates the commutative property
The Identity property establishes that every number multiplied by 1 gives the same number. So:[tex]4 * 1 = 4[/tex]
State identity property
Answer:
Distributive property
Associative property
Commutative property
Identity property
Which of the following is not a solution for the inequality 3x +2 < 12?
A. x = 2
B. x = 2.5
C. x = 3
D. x = 3.5
Answer:
Step-by-step explanation:
3x + 2 < 12
3x < 10
x < 10/3
x < 3 1/3
D. x = 3.5, because 3.5 > 3 1/3 and x can't be bigger than 3 1/3
Answer:
3.5
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
3 x + 2 < 12
( -2 from both sides )
3 x < 10
( ÷ 3 from both sides )
x < 3.33333333333
So x is less than 3.33333333333 but the question asks which is not a solution and 3.5 is greater than 3.33333333333 so 3.5 is your answer
Find the value of x. Round the length to the nearest tenth
A.) 9.0 yd
B.) 15.6 yd
C.) 31.2 yd
D.) 10.4 yd
the answer will be B
Answer:
D.) 10.4 yd
Step-by-step explanation:
In the given figure the alternate angles are equal and hence a right angle triangle with one of its angle as 30 degree is formed .
For angle 30 degrees adjacent side is 18 yard and opposite side is x.
Tan of an angle is equal to [tex]\frac{opposite}{adjacent}[/tex]
[tex]Tan 30=\frac{x}{18}[/tex]
x=Tan 30 (18)
x= 10.39
x= 10.4 yard (rounded to tenth place)
Option D is the right answer.