Answer:
h = 4 units
Step-by-step explanation:
Given equation:
[tex]\text{A}_{\text{trapezoid} } = \dfrac{1}{2}(h)(b_{1} + b_2)[/tex]
Given numerical values:
A = 28b₁ = 6b₂ = 8Plug in all values into the equation and simplify it to find the height:
[tex]\implies \text{28} = \dfrac{1}{2}(h)(6 + 8)[/tex]
[tex]\implies\text{28} = (h)(3 + 4) = 7h[/tex]
[tex]\implies h = \dfrac{28}{7} = 4[/tex]
Therefore, the measure of the height is 4 units.
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What is the median of the numbers 10 6 2 2 8 5 3
Answer:
Step-by-step explanation:
Median: List numbers from smallest to largest. Median is middle number
2 2 3 5 6 8 10
|
5 is in the middle
Median = 5
In the following probability distribution, the random variable
represents the number of activities a parent of a 6th-8th grade student is involved in.
Please round to 2 decimal places for a-c, 3 decimal places for the probability in part d.
X 0 1 2 3 4
P(X) 0.053 0.117 0.258 0.312 0.26
a) Compute and the mean,
, of the random variable
.
2.610
Correct
b) Compute the variance,
, of the random variable
.
c) Compute the standard deviation,
, of the random variable
.
1.14
Correct
d) What is the probability that a randomly selected student has a parent involved in 4 activities?
a) The mean of the random variable is 2.610 (rounded to 2 decimal places).
b) The variance of the random variable is 1.880 (rounded to 3 decimal places).
c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).
d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).
To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.
b) Variance [tex](\sigma^2)[/tex] of the random variable:
Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.
Using the given data:
X: 0 1 2 3 4
P(X): 0.053 0.117 0.258 0.312 0.26
μ (mean): 2.610
Calculating the squared deviations for each value:
[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]
[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]
[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]
[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]
[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]
Summing up the squared deviations:
Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142
Therefore, the variance of the random variable is 16.142.
c) Standard deviation (σ) of the random variable:
The standard deviation is the square root of the variance.
Taking the square root of the variance calculated above:
Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)
d) Probability of a randomly selected student having a parent involved in 4 activities:
The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.
From the given data:
P(X = 4) = 0.26
Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).
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Name the quadrant in which angle 0 must lie for the following to be true.
Answer:
d
Step-by-step explanation:
Find the value of c guaranteed by the Mean Value Theorem……
As per the given equation, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).
To find the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3], we need to determine if the conditions of the Mean Value Theorem are satisfied and then find the value of c.
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).
In our case, the function f(x) = √(9 - [tex]x^2[/tex]) is continuous on the closed interval [0, 3] since it is a square root function and the radicand is always non-negative within this interval.
The function is also differentiable on the open interval (0, 3) since it is the square root of a differentiable function.
To find the value of c, we first calculate f(3) and f(0):
f(3) = √(9 - [tex]3^2[/tex]) = √(9 - 9) = √0 = 0
f(0) = √(9 - [tex]0^2[/tex]) = √(9 - 0) = √9 = 3
Next, we calculate f'(c):
f'(x) = (-2x)/√(9 - x^2)
We want to find the value of c such that f'(c) = (f(3) - f(0))/(3 - 0). Let's substitute the values into the equation:
(-2c)/√(9 - [tex]c^2[/tex]) = (0 - 3)/(3 - 0)
(-2c)/√(9 - [tex]c^2[/tex]) = -1
To solve for c, we can cross-multiply:
-2c = -√(9 - [tex]c^2[/tex])
Squaring both sides:
4c^2 = 9 - [tex]c^2[/tex]
Simplifying:
5[tex]c^2[/tex] = 9
Dividing both sides by 5:
[tex]c^2[/tex] = 9/5
Taking the square root of both sides:
c = ± √(9/5)
Therefore, the value of c guaranteed by the Mean Value Theorem for the function f(x) = √(9 - [tex]x^2[/tex]) over the interval [0, 3] is c = ± √(9/5).
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Find the area of this triangle
The calculated area of the triangle is 38.30 square units
How to find the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
The area of the triangle is calculated as
Area = 1/2absin(c)
Where
a = b = 10
c = 50 degrees
Using the above as a guide, we have the following:
Area = 1/2 * 10 * 10 * sin(50 degrees)
Evaluate
Area = 38.30
Hence, the area of the triangle is 38.30 square units
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please help! show your work or explain to get full credit. (see picture)
1)
The measure of angle A is 45° .
Given,
a= 60
b = 60√2
c = 60
Now the given sides with the dimension is of right angled triangle.
So,
Angle B = 90°
Angle A = 45°
Angle C = 45°
2)
All the six trigonometric functions:
SinФ = 60/60√2
cosФ = 60/60√2
tanФ = 60/60
cosecФ = 60√2/60
secФ = 60√2 /60
cotФ = 60/60
3)
Area of triangle = 1/2 × b× h
Area of triangle = 1/2 *60*60
Area of triangle = 1800 in²
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Choose the function whose graph is given by:
AMMA
+²
OA. y = cos(4x)
OB. y = cos(x)
OC. y = cos(2x)
OD. y = cos(x)
The graph of the function y=cos(x) is shown below:
[Image of the graph of the function y=cos(x)]
The graph of the function y=cos(2x) is shown below:
[Image of the graph of the function y=cos(2x)]
The graph of the function y=cos(4x) is shown below:
[Image of the graph of the function y=cos(4x)]
As you can see, the graph of the function y=cos(4x) is the same as the graph of the function y=cos(x), but it is compressed horizontally by a factor of 4. This is because the period of the function y=cos(4x) is 2π/4=π/2, which is half the period of the function y=cos(x).
Therefore, the correct answer is A.
Define the term inflation
Answer: Inflation is the rise in general level of prices which is determined by the Consumer Price Index (CPI).
The Question is in the Picture, use the Pythagorean theorem to solve and show your work please
Answer:
y=8
Step-by-step explanation:
The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially?
x f(x) g(x)
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243
A f(x), because it eventually exceeds g(x)
B g(x), because it eventually exceeds f(x)
C f(x), because it eventually intersects g(x)
D g(x), because it will not intersect f(x)
The function g(x) is increasing exponentially because it eventually exceeds f(x).
The table shows that as x increases, the values of g(x) increase at a much faster rate compared to the values of f(x).
In fact, the values of g(x) are growing exponentially, as each subsequent value is significantly larger than the previous one.
Therefore, the function g(x) is most likely increasing exponentially.
Thus, g(x) is increasing exponentially because it eventually exceeds f(x).
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The accompanying diagram shows a revolving door with three panels, each of which is 4 feet long. What is the width, w, of the opening between x and y, to the nearest tenth of a foot?
The width, w, of the opening between x and y, is 6.9 ft.
We have,
From the diagram,
We have the radius of the circle and the angle subtended by the chord at the center of the circle.
So,
We can also use the formula.
= 2 x radius x sin(angle/2)
This is the length of the chord.
Now,
radius = 4 ft
angle = 360/3 = 120
Substituting the values.
= 2 x radius x sin(angle/2)
= 2 x 4 x sin (120/2)
= 2 x 4 x sin 60
= 2 x 4 x √3/2
= 4 x √3
= 4 x 1.732
= 6.928
Rounding to the nearest tenth.
= 6.9 ft
Thus,
The width, w, of the opening between x and y, is 6.9 ft.
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Kendra's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 87 caffeinated teas and 13 decaffeinated teas. What percentage of the teas served were caffeinated?
Answer:
Kendra's Tea Shop served 87 caffeinated teas and 13 decaffeinated teas. This means that 87 out of 100 teas served were caffeinated. Therefore, 87% of the teas served were caffeinated.
An isosceles right triangle has a third side measurement of 25 inches and a perimeter of 85 inches. The leg of the dilated triangle measures 6 inches. What is the perimeter of the dilated triangle?
A spherical boulder is 28 feet in diameter and weighs almost 8 tons. Find the volume Use 3.14 for pi
Answer:
V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet
Work Shown:
d = diameter = 28
r = radius = d/2 = 28/2 = 14
V = volume of a sphere
V = (4/3)*pi*r^3
V = (4/3)*3.14*(14)^3
V = 11,488.2133 cubic feet approximately
The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.
need help with this please
The number that belongs in the green box is given as follows:
D. 2.
How to interpret the problem?A quadratic function is given according to the following rule:
y = ax² + bx + c
The solutions are given as follows:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which the discriminant is given as follows:
[tex]\Delta = b^2 - 4ac[/tex]
The number that goes into the green box is then given as follows:
2a = 2(1) = 2.
Meaning that option D is the correct option in the context of this problem.
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Sketch the region enclosed by
y
=
5
x
and
y
=
8
x
2
. Find the area of the region.
Answer:
125/384 ≈ 0.32552
Step-by-step explanation:
You want the area between the curves y = 5x and y = 8x².
AreaThe difference between the curves is ...
f(x) = 5x -8x² = x(5 -8x)
This difference is zero when ...
x = 0
5 -8x = 0 ⇒ x = 5/8
The area will be the integral of f(x) with the limits 0 and 5/8:
[tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]
<95141404393>
The following table gives the number of women age 16 years and older (in
millions) in a country's civilian workforce for selected years from 1950 and
projected to 2050.
Complete parts (a) and (b) below.
CTTS
X+
Women in the
Year Workforce (millions)
1950
1960
1970
1980
1990
2000
18.2
21.3
31.7
45.5
554
65.5
a. Use x as the number of years past January 1st, 1950 to create a cubic model, y, using these data.
y=x²+x+x+
4
(Type integers or decimals rounded to five decimal places.)
Clear all
Women in the
Year Workforce (millions)
2010
2015
2020
2030
2040
2050
75.3
78.1
78.5
80.5
86.6
91.5
Check answer
The cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2
How to calculate the valueLet's set up a system of equations using the given data points:
For x = 0 (year 1950):
18.2 = a(0)³ + b(0)² + c(0) + d ==> d = 18.2
For x = 10 (year 2000):
65.5 = a(10)³ + b(10)² + c(10) + 18.2
For x = 20 (year 2010):
75.3 = a(20)³ + b(20)² + c(20) + 18.2
For x = 25 (year 2015):
78.1 = a(25)³ + b(25)² + c(25) + 18.2
For x = 30 (year 2020):
78.5 = a(30)³ + b(30)² + c(30) + 18.2
For x = 40 (year 2030):
80.5 = a(40)³ + b(40)² + c(40) + 18.2
For x = 50 (year 2040):
86.6 = a(50)³ + b(50)² + c(50) + 18.2
For x = 60 (year 2050):
91.5 = a(60)³ + b(60)² + c(60) + 18.2
Simplifying these equations, we have: d = 18.2
1000a + 100b + 10c + 18.2 = 65.5
8000a + 400b + 20c + 18.2 = 75.3
15625a + 625b + 25c + 18.2 = 78.1
27000a + 900b + 30c + 18.2 = 78.5
64000a + 1600b + 40c + 18.2 = 80.5
125000a + 2500b + 50c + 18.2 = 86.6
216000a + 3600b + 60c + 18.2 = 91.5
We can solve this system of equations to find the coefficients a, b, and c.
Using a cubic regression calculator or a matrix solver, the solution is:
a ≈ 0.00006204
b ≈ 0.00231059
c ≈ -0.10811757
Therefore, the cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2
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Answer all of these pls
1. -3x+7=-8x+47
2. -13x+8=-8x-7
3. 6x+7=3x+19
4. 12x-8=10x+6
5. -7x-4=-10x-10
6. 7x-9=3x-5
7. 3x-9=5x-3
8. 7x-1=5x+5
9. -7x-2=-3x-14
10. -3x-7=-8x-57
Answer:
Sure, I'd be happy to help you solve these equations! Here are the solutions to the equations you provided:
1. -3x+7=-8x+47
Add 8x to both sides: 5x + 7 = 47
Subtract 7 from both sides: 5x = 40
Divide both sides by 5: x = 8
2. -13x+8=-8x-7
Add 13x to both sides: 5x + 8 = -7
Subtract 8 from both sides: 5x = -15
Divide both sides by 5: x = -3
3. 6x+7=3x+19
Subtract 3x from both sides: 3x + 7 = 19
Subtract 7 from both sides: 3x = 12
Divide both sides by 3: x = 4
4. 12x-8=10x+6
Subtract 10x from both sides: 2x - 8 = 6
Add 8 to both sides: 2x = 14
Divide both sides by 2: x = 7
5. -7x-4=-10x-10
Add 10x to both sides: 3x - 4 = -10
Add 4 to both sides: 3x = -6
Divide both sides by 3: x = -2
6. 7x-9=3x-5
Subtract 3x from both sides: 4x - 9 = -5
Add 9 to both sides: 4x = 4
Divide both sides by 4: x = 1
7. 3x-9=5x-3
Subtract 3x from both sides: -6 = 2x - 3
Add 3 to both sides: -3 = 2x
Divide both sides by 2: x = -3/2 or -1.5
8. 7x-1=5x+5
Subtract 5x from both sides: 2x - 1 = 5
Add 1 to both sides: 2x = 6
Divide both sides by 2: x = 3
9. -7x-2=-3x-14
Add 3x to both sides: -4x - 2 = -14
Add 2 to both sides: -4x = -12
Divide both sides by -4: x = 3
10. -3x-7=-8x-57
Add 8x to both sides: 5x - 7 = -57
Add 7 to both sides: 5x = -50
Divide both sides by 5: x = -10
I hope this helps! Let me know if you have any further questions.
Quentin deposited $1,264 into a savings account that earns 2.75% simple interest annually. What will Quentin’s account balance be at the end of 2.5 years? Assume he makes no additional deposits during that time period.
Answer:
I love math
Step-by-step explanation:
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal amount
r = interest rate (as a decimal)
t = time (in years)
In this case, we know that:
P = $1,264
r = 2.75% = 0.0275 (as a decimal)
t = 2.5 years
So, we can plug in these values and solve for I:
I = 1,264 * 0.0275 * 2.5 = $87.55
Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:
Ending balance = $1,264 + $87.55 = $1,351.55
So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.
Write the word
sentence as an
inequality.
A number w plus 4.6
is more than 6.
An inequality is answer:
The inequality that represents the number sentence is given as follows:
w + 4.6 > 6.
What are the inequality symbols?The four most common inequality symbols, and how to interpret them, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. On the coordinate plane, these are the points above the dashed line y = x.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. On the coordinate plane, these are the points below the dashed line y = x.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. On the coordinate plane, these are the points above the continuous line y = x.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. On the coordinate plane, these are the points below the continuous line y = x.A number w plus 4.6 is represented as follows:
w + 4.6.
The amount is more than 6, hence the inequality is given as follows:
w + 4.6 > 6.
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You are willing to pay $5 a pound for dog food. Your local pet store sells dog food at $4 a pound. What is the consumer surplus?
The consumer surplus for the price of the dog food is given as follows:
$1.
How to calculate the consumer surplus?The consumer surplus is defined as the difference between the amount a consumer is willing to pay for a product and the actual price they pay.
The parameters in the context of this problem are given as follows:
The consumer is willing to pay $5 for the pound of dog food.The local pet store sells the pound of dog food for $4.Hence the consumer surplus for the price of the dog food is given as follows:
5 - 4 = $1.
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Determine whether the function represents exponential growth or decay write the base in terms of the rate or decay identify r and interpret the rate of growth or decay y=12,500 (3/4)*
The rate of the decay of the given function is 75 percent.
The given function is y=12,500(3/4)ˣ
This function represents exponential decay with a base of (3/4). The rate of decay, "r", is equal to 3/4. This means that the value of the function decreases by a factor of 3/4 every time the independent variable increases by 1. Thus, the rate of decay is 3/4 or 75%.
Therefore, the rate of the decay of the given function is 75 percent.
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The PTO is selling raffle tickets to raise money for classroom supplies. There is 1 winning ticket out of the 150 tickets sold. The winner gets a prize worth $200.
Round your answers to the nearest cent.
Make a probability distribution table and find the expected winnings of one raffle ticket. $?
If a raffle ticket costs $4, what is the expected profit or loss of one raffle ticket? (Enter a negative number for a loss) $?
Answer:
Expected winnings = $1.33
Expected profit or loss = -$2.67
Step-by-step explanation:
Winning Probability Prize Value
Yes 1/150 $200
No 149/150 $0
Expected winnings of one raffle ticket:
Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)
Expected winnings = (1/150 x $200) + (149/150 x $0)
Expected winnings = $1.33
If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:
Expected profit or loss = Expected winnings - Cost of ticket
Expected profit or loss = $1.33 - $4
Expected profit or loss = -$2.67
Solve for X
20x+30
28x-10
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Statement:Corresponding angles are equal.Solution:20x + 30 = 28x - 10 (Corresponding angles)
Add 10 to both sides20x + 30 + 10 = 28x
20x + 40 = 28x
Subtract 20x from both sides40 = 28x - 20x
40 = 8x
Divide both sides by 85 = x
OR
x = 5[tex]\rule[225]{225}{2}[/tex]
An airplane is cruising at a rate of 550 miles per hour. Write an equation that shows the relationship between the number of hours of cruising, x, and the number of miles traveled, y.
Answer: y = 550x
Step-by-step explanation:
a function is in the form g(x)= ax2 + d. if a is greater than 1 and d is positive, which could be the graph of g(x) ?
hello
to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file
What are the x-intercepts of the quadratic function? (1 point)
parabola going down from the left and passing through the point negative 3 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 6 and 2 comma 0
(0, −3) and (0, 2)
(0, −6) and (0, 6)
(−3, 0) and (2, 0)
(−6, 0) and (6, 0)
Answer:
The x-intercepts are (-3, 0) and (2, 0).
p: 10 > 7 q: 10 > 5
p →q
F F → T
T F → F
F T → T
T T → T
Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).
Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:
If p and q are both False (F), then p → q is True (T).
If p is True (T) and q is False (F), then p → q is False (F).
If p is False (F) and q is True (T), then p → q is True (T).
If p and q are both True (T), then p → q is True (T).
Given your propositions:
P: 10 > 7
Q: 10 > 5
P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.
Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.
An apartment building has 9 apartments that are being rented. The data shows the monthly rent for each apartment.
$1,710 $1,515 $1,410 $1,435 $1,555 $1,595 $1,690 $1,575 $1,640
Create a stem display for this data.
The stem display for the data, given the monthly rent and the apartment building is:
$14 | 10 15 35
$15 | 15 55 75 95
$16 | 40 90
How to make the stem display ?To create a stem display, we first divide the data into groups of tens. The first group is $ 1400 -$ 1499, the second group is $ 1500 - $1599 , and so on. Next, we write the units digit of each number in the appropriate group.
For example, the number 1,710 is in the $ 1500 - $ 1599 group, so we write a 1 in the 15 column. Finally, we count the number of numbers in each group. There are three numbers in the $ 1400 - $ 1499 group, two numbers in the $ 1500 - $ 1599 group, and three numbers in the $ 1600 - $ 1699 group.
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i need help can someone help me
The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the sine of angle 41°
sin 41° = 2.5/x {opposite/hypotenuse}
x = 2.5/sin 41° {cross multiplication}
x = 3.8106
Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
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