From the table, we see that Julia rolled the die 100 times, and the number of times she rolled a 3 was 45.
The best estimate of the probability of rolling a 3 can be found by dividing the number of times a 3 was rolled by the total number of rolls:
P(rolling a 3) = Number of times 3 was rolled / Total number of rolls
P(rolling a 3) = 45 / 100
P(rolling a 3) = 0.45 or 45%
Therefore, based on Julia's experimental results, the best estimate of the probability of rolling a 3 on her biased die is 0.45 or 45%.
If $5,000 is invested at 9% annual interest compounded quarterly, how long would it take for the account balance to reach $20,000? Round your answer to the nearest tenth.
Using the compound interest formula, it is obtained that it would take approximately 9.9 years for the account balance to reach $20,000.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
We can use the formula for compound interest to solve this problem -
[tex]A = P(1 + \frac{r}{n})^{(nt)}[/tex]
where A is the account balance, P is the principal (the initial investment), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the time (in years).
In this case, we have P = 5000, r = 0.09 (9% annual interest), n = 4 (compounded quarterly), and A = 20000. We want to find t.
Substituting these values into the equation, we get -
[tex]20000 = 5000 \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]
Dividing both sides by 5000, we get -
[tex]4 = \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]
Taking the natural logarithm of both sides, we get -
ln(4) = 4t ln(1 + 0.09/4)
Solving for t, we get -
t = ln(4) / (4 ln(1 + 0.09/4))
Simplifying the equation, we get -
t ≈ 9.9
Therefore, the time value is obtained as 9.9 years.
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what is the value of the expression (-5)-³
Answer:
[tex]\frac{1}{-125}[/tex]
x = -125
Step-by-step explanation:
It shows the steps in the pic you attached so I didn't add those steps.
(-5)(-5)(-5) = -125
if 2^x=x^2 , find x.
Answer:
x = 2 or x = 4
Step-by-step explanation:
The equation:
[tex]2^{x} = x^{2}[/tex]Has two solutions:
x = 2 or x = 4.The values of x can be found by graphing the two functions ([tex]y = 2^{x}[/tex] and [tex]y = x^{2}[/tex]) and finding their points of intersection, or you can use numerical methods to solve the equation.
To check our work, we can simply insert 2 and 4 in as y.
For 2:
[tex]2^{2} = 2^{2}[/tex]You can see that it is the same.
For 4:
[tex]2^{4} = 4^{2}[/tex](2 × 2 × 2 × 2) = (4 × 4)16 = 16They are also the same.
Therefore, x can equal either 2 or 4.
Find the indicated probabilities. Then determine if the event is unusual. Explain your reasoning.
The probability of winning a game of rock-paper-scissors is 1/3 You play nine games of rock-paper-scissors. Find the
probability that the number of games you win is (a) exactly five, (b) more than six, and (c) less than three.
The probability that the number of games you win is (a) exactly five, (b) more than six, and (c) less than three will be 0.196, 0.0082 and 0.056 respectively.
How are probabilities defined?
A probability is indeed a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages spanning form 0% to 100% can be used to describe probabilities.
1/3 of players will succeed in a game of rock-paper-scissors. Choose nine games of rock-paper-scissors, and let X represent the number of victories. With n=9 and p=1/3, X has a random variable.
(a) The likelihood of winning all five games in a row is:
P(X=5) = (9 choose 5)(1/3)⁵(2/3)⁴ = 0.196
Depending on the situation, this likelihood might or might not be seen as uncommon because it is neither extremely high nor extremely low.
(b) The probability of winning more than six games is:
P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9)
= [(9 choose 7)(1/3)⁷(2/3)²] + [(9 choose 8)(1/3)⁸(2/3)¹] + [(9 choose 9)(1/3)⁹(2/3)⁰]
= 0.0082
The fact that this likelihood is so low suggests that winning and over six games is exceptional.
(c) The likelihood of winning two or fewer games is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [(9 choose 0)(1/3)⁰(2/3)⁹] + [(9 choose 1)(1/3)¹(2/3)⁸] + [(9 choose 2)(1/3)²(2/3)⁷]
= 0.056
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The gas/oil ratio for a certain chainsaw is 50 to 1 .
a. How much oil (in gallons) should be mixed with 12 gallons of gasoline?
b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
0.24 gallons of oil should be mixed with 12 gallons of gasoline.
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
Step-by-step explanation:
a. To calculate the amount of oil needed, we need to know the ratio of gas to oil in terms of units. Since 50 parts of gas are mixed with 1 part of oil, we have:
1 gallon of gas / 50 = x gallons of oil
To find x, we substitute the given value of gas (12 gallons) and solve for x:
1 gallon of gas / 50 = x gallons of oil
12 gallons of gas / 50 = x
0.24 gallons of oil = x
Therefore, 0.24 gallons of oil should be mixed with 12 gallons of gasoline.
b. To convert gallons to fluid ounces, we multiply by 128:
0.24 gallons of oil * 128 fluid ounces/gallon = 30.72 fluid ounces of oil
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
PLS HELP , in need to solve by using substitution and with checks
Answer:
(0, 2)Step-by-step explanation:
[tex]\tt y=x+2\\3x+3y=6[/tex]
Substitute y= y=x+2 into 3x+3y=6
[tex]\tt 3x+3(x+2)=6[/tex][tex]\tt 6x+6=6[/tex]Solve for x :-
[tex]\tt 6x+6=6[/tex]Cancel 6 from both sides:-
[tex]\tt 6x=0[/tex]Divide both sides by 6:-
[tex]\tt \cfrac{6x}{6} =\cfrac{0}{6}[/tex][tex]\boxed{\bf x=0}[/tex]Now, Let's solve for y:-
Substitute x = 0 into y=x+2
[tex]\tt y=0+2[/tex][tex]\boxed{\bf y=2}[/tex]Therefore, x = 0 and y = 2.
_________________
Check:-
To check a system of equations by substitution, we plug the values for x and y into the equations, If both simplified are true then your answer is correct.
Equation 1 :-
y = x + 2
(2) = 0 + (2)2=2 ✓Equation 2 :-
3x+3y=6
3(0)+3(2)=60+6=66=6 ✓__________________________
Hope this helps!
the day time temperatures recorded over 5 consecutive days in october were 14.6,15.2,15.8,16.1 . find the average temperature
Answer: 15.54 degrees.
Step-by-step explanation:
To find the average temperature, we need to add up all the temperatures and then divide by the number of days:
Average temperature = (14.6 + 15.2 + 15.8 + 16.1) / 5
= 77.7 / 5
= 15.54
Therefore, the average temperature over the 5 consecutive days in October is approximately 15.54 degrees.
How could mean, median, mode, and range be impacted if a value in a data set changed?
In summary, a change in a value in a data set can have varying impacts on the measures of central tendency and dispersion, depending on the value that was changed and its relationship to the other values in the data set.
Why it is?
The measures of central tendency, such as mean, median, and mode, and the measure of dispersion, range, can be impacted by a change in a value in a data set.
Mean: The mean is calculated by adding all the values in a data set and then dividing by the total number of values. If a value in the data set changes, the sum of the values will change, and thus the mean will also change. The impact of the change on the mean will depend on the value that was changed and how much it differs from the other values in the data set.
Median: The median is the middle value in a data set, when the values are arranged in order. If a value in the data set changes, the position of the median may change, depending on where the new value falls in the order of the values.
Mode: The mode is the value that appears most frequently in a data set. If a value in the data set changes, the mode may change, depending on whether the new value becomes the most frequent value or not.
Range: The range is the difference between the highest and lowest values in a data set. If a value in the data set changes, the range may change, depending on how much the new value differs from the highest or lowest value in the data set.
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URGENT ! 100 POINTS
It's the age of Vikings! You are an archer on a boat approaching the London bridge in England with troops ready to ambush and secure London, England. Your leader yells
to ready your aim to fire as the boat rushes at full speed towards your enemies ahead!
Steadily, you line up the shot and the arrow is launched from your bow into the air with an upward velocity of 60ft/sec. The equation that gives the height (h) of the arrow at any time (t), in seconds, is modeled by:
h(t) = − 16t²+60t + 9.5
How long will it take the arrow to reach the enemy on the bridge and nail him with a
perfect headshot?
(The enemies head is about 45 feet from ground level as he is located on top of the London bridge)
To find out how long it will take for the arrow to hit the enemy on the bridge, we need to find the time when the height of the arrow is 45 feet (the height of the enemy's head above the ground).
So, we can set h(t) equal to 45 and solve for t:
h(t) = − 16t²+60t + 9.5
45 = −16t² + 60t + 9.5
Rearranging the equation, we get:
16t² - 60t - 35.5 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b² - 4ac)) / 2a
where a = 16, b = -60, and c = -35.5
Plugging in the values, we get:
t = (-(-60) ± sqrt((-60)² - 4(16)(-35.5))) / 2(16)
Simplifying the expression inside the square root, we get:
t = (60 ± sqrt(3600 + 2272)) / 32
t = (60 ± sqrt(5872)) / 32
t ≈ 0.81 or t ≈ 3.69
Since we're looking for the time when the arrow hits the enemy, we need to choose the positive solution: t ≈ 3.69 seconds.
Therefore, it will take approximately 3.69 seconds for the arrow to hit the enemy on the bridge with a perfect headshot.
Scientist rope off two evacuation sites. Site A is regular with a length of 60 meters and width of 40 meters. Site B is similar in shape to site A but has a length of 45 meters. How much rope is needed for both sites?
If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
What is amount?Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.
To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).
To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).
It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters. Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
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If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
What is amount?Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.
To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).
To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).
It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters. Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.
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ANSWER BELOW PLEASE!!! ASAP THANK YOU^^!
The equation of the line in slope-intercept form is: y = -25x + 100. A negative slope indicates that the battery percentage is decreasing over time.
Part A:
To write the equation of a line in slope-intercept form, we need to know the slope (m) and y-intercept (b) of the line.
From the given information, we know that the y-intercept is 100 and the x-intercept is 4. This means that after 4 hours, the battery percentage is 0%.
To find the slope, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
Choosing two points on the line, one being the y-intercept (0,100) and the other being the x-intercept (4,0), we can plug in the values:
m = (0 - 100)/(4 - 0) = -25
Therefore, the equation of the line in slope-intercept form is:
y = mx + b
y = -25x + 100
Part B:
To determine the equation, we used the fact that the y-intercept was 100 and the x-intercept was 4. We then found the slope of the line using the slope formula with two points on the line. Plugging the slope and y-intercept into the slope-intercept form equation y = mx + b gives us the final equation.
Part C:
The slope of the line is -25, which means that for every hour that passes, the battery percentage decreases by 25%. Therefore, the slope represents the rate of change of the battery percentage with respect to time. A negative slope indicates that the battery percentage is decreasing over time.
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10 1/3 is how much more than 7 8/9?
Answer:2 4/9
Step-by-step explanation:
multiply. round your answer to the nearest hundredeth: 2.56x0.03=
0.08 rounded for the nearest hundredth
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Given the diagram above, m∠Z is:
A) 180°
B) 120°
C) 60°
D) 30°
Answer:
B. 120o
Step-by-step explanation:
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.
t + 2t = 180
3t = 180
t = 180/3 = 60
m∠Z = 2t = 2(60) = 120
99 times 3 distributive property
Answer:
To use the distributive property to solve 99 x 3, we can write it as:
99 x 3 = (90 + 9) x 3 (decomposing 99 as 90 + 9)
= 90 x 3 + 9 x 3 (using distributive property)
= 270 + 27
= 297
Therefore, 99 times 3 using the distributive property equals 297.
Step-by-step explanation:
A circle has a radius of 21 millimeters.
What is the length of the arc intercepted by a central angle that measures 80°.
Answer:
Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm. Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm².
Step-by-step explanation:
A his herd of cows among his 4 sons he gave one son half the herd a second son one fourth of the herd a third son one fith of the herd and the fourth son 48 cows how many cows were in the herd originally
Answer:
Let the total number of cows in the herd be represented by "x". Then, according to the problem:
The first son received half the herd, or (1/2)x cows.
The second son received one fourth of the herd, or (1/4)x cows.
The third son received one fifth of the herd, or (1/5)x cows.
The fourth son received 48 cows.
We can write an equation to represent the total number of cows in the herd:
(1/2)x + (1/4)x + (1/5)x + 48 = x
To solve for "x", we can start by simplifying the fractions:
5/10x + 2/10x + 2/10x + 48 = x
Combining like terms, we get:
9/10x + 48 = x
Subtracting 9/10x from both sides, we get:
48 = 1/10x
Multiplying both sides by 10, we get:
x = 480
Therefore, the original herd had 480 cows.
An item is regularly priced at $80 . It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regular price
Assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 25 adult smartphone users are randomly selected, find the probability that exactly 20 of them use their smartphones in meetings or classes.
Answer:
The probability that exactly 20 out of 25 adult smartphone users use their smartphones in meetings or classes is approximately 0.002.
Question 9
The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube.
Match the equation for how to solve for the side length of a cube to its description.
Drag the equation into the box to match the description.
The equation for solving the side length of a cube is s = ∛V, where s is the side length of the cube, and V is the volume.
The equation for solving the side length of a cube can be expressed as s = ∛V, where s is the side length of the cube, and V is the volume. This equation can be used to calculate the side length of a cube when the volume is known. For example, if the volume of a cube is 125 cubic units, the side length can be calculated by substituting 125 for V and solving the equation: s = ∛125 = 5. This means that the side length of the cube is 5 units.
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Given
f(x, y) = 2x2 + 2xy + y2 + 2x − 5,
find all points at which
∂f
∂x
= 0 and
∂f
∂y
= 0
simultaneously.
Answer:
Step-by-step explanation:
To find the critical points of the function f(x,y), we need to find all points where both partial derivatives ∂f/∂x and ∂f/∂y are equal to zero.
We first find ∂f/∂x by differentiating f(x,y) with respect to x and treating y as a constant:
∂f/∂x = 4x + 2y + 2
We then find ∂f/∂y by differentiating f(x,y) with respect to y and treating x as a constant:
∂f/∂y = 2x + 2y
To find the critical points, we need to solve the following system of equations simultaneously:
4x + 2y + 2 = 0
2x + 2y = 0
We can solve the second equation for y:
2y = -2x
y = -x
Substituting this into the first equation, we get:
4x + 2(-x) + 2 = 0
2x + 2 = 0
2x = -2
x = -1
Substituting x = -1 into y = -x, we get:
y = -(-1) = 1
Therefore, the critical point is (-1,1).
To verify that this point is a minimum, we can use the second partial derivative test. We first find the second partial derivatives:
∂²f/∂x² = 4
∂²f/∂y² = 2
∂²f/∂x∂y = 2
The discriminant of the Hessian matrix is:
∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = (42) - (22) = 4
Since the discriminant is positive and the second partial derivative with respect to x is positive, the critical point (-1,1) is a local minimum.
Therefore, the point (-1,1) is the only critical point of the function f(x,y), and it is a local minimum.
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms. 5z + 2z³ + 3z4 Standard form: Degree: Leading coefficient: Classification:
The given polynomial written in standard form is: 3z⁴ + 2z³ + 5z
Degree: 4
Leading Coefficient: 3
Classification: Trinomial
How to write polynomial in standard form?Writing a polynomial in standard form simply means that we put the term with the highest exponent in it first and then the one with the second highest exponents second, and so on.
The polynomial we are given is: 5z + 2z³ + 3z4
Writing it in standard form gives us:
3z⁴ + 2z³ + 5z
The degree of the polynomial is defined as the value of the exponent in the leading term (if we are assuming a single variable). Thus, this given polynomial is of degree 4.
The leading coefficient is the number that the first term is multiplied by and in this problem that would be 3.
There are three terms in the given polynomial (the first term is 3z⁴, the second term is 2z³, and the 3rd term is 5z). Thus, it is a trinomial.
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Calculate the volume of sand needed to fill the long jump pit to a depth of 0,07m
Answer:
Step-by-step explanation:
To calculate the volume of sand needed to fill the long jump pit to a depth of 0.07 meters, we need to know the length and width of the pit.
Assuming that the long jump pit is a rectangular prism, we can use the formula:
Volume = length x width x depth
Let's say the length of the pit is 8 meters and the width is 3 meters. Then the volume of sand needed to fill the pit to a depth of 0.07 meters would be:
Volume = 8m x 3m x 0.07m
Volume = 1.68 cubic meters
Therefore, we would need 1.68 cubic meters of sand to fill the long jump pit to a depth of 0.07 meters.
Find the equation of the line that passes through the given point and has the given slope. (Use x as your variable.) (-9,- 9 ) , m = 0
The linear equation that passes through (-9, -9) and has the slope m = 0 is:
y = -9
How to find the equation of the line?A general linear equation can be written in slope-intercept form as.
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we want to find the equation of a line that passes through (-9, -9) and that has the slope m = 0.
Repplacing the slope we will get:
y = 0*x + b
And no we want it to pass throug (-9, -9), replacing these values we will get:
-9 = 0*-9 + b
-9 = b
Then the linear equation is:
y = -9
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Solve the equation. x2 = 16
Answer:
I hope that this answers your question!
Fuel wood is measured in cords. The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.
Hannah measures a pile of wood to be 14 ft long by 20 ft wide.
Which equation can be used to determine the number of cords in a pile of wood h ft tall?
The equation that is used to determine the number of cords in a pile of wood h ft tallis is the number of cords = 280×h×128.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.
Given that
The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.
The length of the wood pile is 14 ft and the wide is 20 ft.
The product of length and width is lw = 14×20 = 280 ft².
Putting lw= 280 in the equation number of cords=lwh128:
number of cords = 280×h×128
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Please help will mark Brainly
Answer:
B. linear
Step-by-step explanation:
x y
0 9
1 9 + 8
2 9 + 2(8)
3 9 + 3(8)
4 9 + 4(8)
=> linear function
You deposit $50,000 into a bank account that earns 2.5% simple interest annually.
How much will be in the account at the end of 4 years?
Step-by-step explanation:
To calculate the amount of money in the account at the end of 4 years, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
t = Time period (in years)
Plugging in the given values, we get:
I = $50,000 * 0.025 * 4
I = $5,000
This means that over the course of 4 years, the account will earn $5,000 in interest.
To find the total amount in the account at the end of 4 years, we simply add the interest earned to the initial deposit:
Total amount = $50,000 + $5,000
Total amount = $55,000
Therefore, at the end of 4 years, there will be $55,000 in the account if you deposit $50,000 into a bank account that earns 2.5% simple interest annually.
Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
Step-by-step explanation:
tan(19°) = 7425/d1
tan(37°) = 7425/d2
Solving for d1 and d2, we get:
d1 = 7425/tan(19°) ≈ 22977.6 feet
d2 = 7425/tan(37°) ≈ 13060.2 feet
Therefore, the distance the plane traveled from point A to point B is:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
In ΔLMN, l = 150 inches, n = 890 inches and ∠N=61°. Find all possible values of ∠L, to the nearest 10th of a degree.
The possible values of ∠L are 118.9 degrees (rounded to 10th of a degree).
What is a triangle?A polygon with three sides and three angles is a triangle. It is one of the simplest geometric shapes.
To find the measure of angle L in ΔLMN, we can use the fact that the sum of the angles in a triangle is 180 degrees:
∠L + ∠M + ∠N = 180
We know that ∠N = 61 degrees, so we can substitute that value in and simplify:
∠L + ∠M + 61 = 180
∠L + ∠M = 119
We also know that the length of LM is 150 inches and the length of LN is 890 inches. We can use the Law of Cosines to find the measure of angle M:
cos M = (150² + 890² - LM²) / (2 × 150 × 890)
cos M = 0.999989 (rounded to 6 decimal places)
M = cos⁻¹(0.999989)
M ≈ 0.00114 radians
M ≈ 0.0655 degrees (rounded to 10th of a degree)
Now we can substitute the value of M into the equation we derived earlier and solve for angle L:
∠L + 0.0655 + 61 = 180
∠L = 118.9345
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