Triangle QRS has side lengths r= 24.4 and s= 30.6. Angle Q has a measure of 15°. What is the measure of angle R?
1). 34.2 degrees
2). 123.1 degrees
3).41.9 degrees
4). 9.5 degress
Answers
The measure of angle R is 123.1 degrees.
To find the measure of angle R, we can use the Law of Cosines, which states that c^2 = a^2 + b^2 - 2ab cos(C), where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides. In this case, we want to find the measure of angle R, which is opposite side s, so we'll use s as our value for c.
Explanation 2: Substituting in the given values, we get:
30.6^2 = 24.4^2 + b^2 - 2(24.4)(b) cos(15°)
Simplifying this equation, we get:
b^2 - 48.8b cos(15°) + 310.56 = 0
Using the quadratic formula, we find that:
b = (48.8 cos(15°) ± sqrt((48.8 cos(15°))^2 - 4(1)(310.56))) / (2(1))
Solving for b, we get:
b = 38.83 or b = 9.27
Since we're looking for the measure of angle R, we want to use the larger value of b, which corresponds to the acute angle opposite side r. To find the measure of angle R, we can use the Law of Sines, which states that a/sin(A) = b/sin(B) = c/sin(C), where A, B, and C are the measures of the corresponding angles. Solving for angle R, we get:
24.4/sin(15°) = 38.83/sin(R)
sin(R) = 38.83(sin(15°))/24.4
sin(R) = 0.633
Taking the inverse sine of both sides, we get:
R = 41.9° or R = 138.1°
Since angle Q is acute, we want angle R to be acute as well, so the measure of angle R is 41.9 degrees.
Your question is: What is the measure of angle R in triangle QRS, given side lengths r=24.4, s=30.6, and angle Q=15°?
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Related Questions
Juan lives in San Juan and commutes daily to work at the AMA or on the urban train.
He uses the AMA 70% of the time and 30% of the time he takes the urban train.
When you go to the AMA, you arrive on time for your work 60% of the time.
When you take the urban train, you arrive on time for your work 90% of the time.
What is the probability that arrive on time for work?
What is the probability that you took the train given that it arrived on time?
Round to 2 decimal places
Hint: Tree Diagram
Answers
To calculate the probability of arriving on time for work, we need to consider the two scenarios: taking the AMA or taking the urban train.
Probability of arriving on time when taking the AMA: P(Arrive on time | AMA) = 0.60. P(AMA) = 0.70. Probability of arriving on time when taking the urban train: P(Arrive on time | Urban train) = 0.90. P(Urban train) = 0.30. To calculate the overall probability of arriving on time, we can use the law of total probability: P(Arrive on time) = P(Arrive on time | AMA) * P(AMA) + P(Arrive on time | Urban train) * P(Urban train). P(Arrive on time) = (0.60 * 0.70) + (0.90 * 0.30). P(Arrive on time) = 0.42 + 0.27. P(Arrive on time) = 0.69. Therefore, the probability of arriving on time for work is 0.69 or 69%.To calculate the probability of taking the train given that you arrived on time, we can use Bayes' theorem: P(Take train | Arrive on time) = (P(Arrive on time | Take train) * P(Take train)) / P(Arrive on time). P(Take train | Arrive on time) = (0.90 * 0.30) / 0.69. P(Take train | Arrive on time) = 0.27 / 0.69. P(Take train | Arrive on time) ≈ 0.39.
Therefore, the probability of taking the train given that you arrived on time is approximately 0.39 or 39%, rounded to 2 decimal places.
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How many solutions does the equation 8x-4=10 have ? PLEASE HELP QUICK
Answers
Answer:
one solution
Step-by-step explanation:
8x-4=10
Add 4 to each side
8x - 4+4 = 10+4
8x = 12
Divide by 8
8x/8 = 12/8x
x = 3/2
Answer:
one solution
Step-by-step explanation:
\(8x - 4 = 10 \\ 8x = 10 + 4 \\ 8x = 14 \\ \frac{8x}{8} = \frac{14}{8} \\ x = \frac{7}{4} \)
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A plol of land doubles in size by adding x meters to the length and x meters to the width of the land.
ifihe oniginal plot had an area of 209 by 309 meters, what is the value of x?
Answers
The original plot has an area of 209 x 309 = 64581 square meters.
If x is added to both the length and width, the new area becomes 2 times the original area, which is 2 x 64581 = 129162 square meters.
To solve for x, we can use the formula for the area of a rectangle, which is length x width. If we add x meters to the length and width, the new area can be expressed as (209 + x)(309 + x). We can then set this expression equal to 129162 and solve for x.
(209 + x)(309 + x) = 129162
64,881 + 518x + x^2 = 129,162
x^2 + 518x - 64,281 = 0
Using the quadratic formula, we get:
x = (-518 ± sqrt(518^2 - 4(1)(-64281))) / 2(1)
x = (-518 ± sqrt(33404500)) / 2
x = (-518 ± 5772.13) / 2
The negative value is not meaningful in this context, so we take the positive value:
x = (5772.13 - 518) / 2
x = 2627.065 meters
Therefore, adding 2627.065 meters to both the length and width of the original plot will double its area.
The problem involves finding the value of x, which represents the additional length and width added to the original plot of land to double its size. We know the original area of the plot, which is 209 by 309 meters, and we are given that the area doubles when x meters are added to both the length and width.
To solve for x, we need to use the formula for the area of a rectangle, which is length x width. We can set up an equation using this formula and the given information to solve for x. This equation involves a quadratic expression, so we use the quadratic formula to find the two possible values of x.
We discard the negative value of x, as it is not meaningful in this context, and take the positive value as the answer. This value tells us that adding 2627.065 meters to both the length and width of the original plot will double its area.
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11. a $58 video game is on sale for a 14% discount. what is the price with the discount
Answers
As given by the question
There are given that the price of the video games is $58.
Now,
According to the question, there are given that 14% discount on their game price
So,
The price with discount is:
\(58\times\frac{14}{100}=8.12\)Then,
\(58-8.12=49.88\)Hence, the price with the discount is $49.88
3.7) For a long time period, if a watershed receives 300 mm of
precipitation and has a 200 mm evapotranspiration annually,
determine annual average runofff.
Answers
The annual average runoff for the watershed is 100 mm.
To determine the annual average runoff, we need to calculate the difference between the precipitation and evapotranspiration.
Given:
Precipitation = 300 mm
Evapotranspiration = 200 mm
To find the annual average runoff, we subtract the evapotranspiration from the precipitation:
Annual Average Runoff = Precipitation - Evapotranspiration
Annual Average Runoff = 300 mm - 200 mm
Annual Average Runoff = 100 mm
Therefore, The watershed's average annual runoff is 100 mm.
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which of the at eight o'clock, which of is the angle between the hour and the minute hands
Answers
Answer:
At 8 o'clock angle between the two hands is 120 degree.
Step-by-step explanation:
For even hours, it’s easy. There are 12 numbers on the 360 degree clock face so each number is 30 degrees. Now, if you are after 6 then “the angle” is the other way so for 8:00, 12–8 = 4*30 = 120 degrees.
The problem comes in when you are not at an even hour. At, say, 8:20, the minute hand has moved 120 degrees and the hour hand has moved 1/3 of 30 or 10 degrees so, the angle is now 8*30 - 4*30 + 10 = 240 - 120 +10 = 130 degrees.
At 8:40 the minute hand has moved 8*30 = 240 degrees and the hour hand has moved 2/3 of 30 or 20 degrees so the angle is now 8*30 - 8*30 + 20 = 20 degrees
How do you solve question 8 of geometry worksheet? (Grade 8th)
Answers
Please help me with this question please help
Answers
7. Elle can buy milk at a local farmers'
market for $3.58 per gallon or at the
grocery store for $3.79 for 4 L. Which
is the better buy?
Answers
Answer: They are the same equivalent price, $0.95/liter.
Step-by-step explanation:
Choices: $3.58 per gallon, or $3.79 for 4 L.
========
We need to convert one of the volumes. I'll convert gallons to liters.
By definition, 1 gallon = 3.785 liters
Make this into a conversion factor:
We can make it either:
1) (3.785 liters/gallon), or
2) (1 gallon/3.785 liters)
Now convert the $3.58/gallon into dollars/liter. We'll use the second conversion factor so that gallons cancels out when we multiply:
($3.58/gallon)*(1 gallon/3.785 liters) = $0.95/liter.
The grocery store milk must also be converted to a price expressed per 1 liter:
$3.79 for 4 L
= $0.95/liter.
They are the same equivalent price, $0.95/liter.
HELp show work too pleaseee
Answers
Answer:
its C LOL
Step-by-step explanation:
4x1=4
12x4=48
4/48
what is the value of sin 12 - cos 78
Answers
Answer:
0
Step-by-step explanation:
\(\sin(12\º) - \cos(78\º)\)
Consider the cofunction identity:
\($\boxed{\sin(\theta)=\cos \left(\frac{\pi}{2} - \theta \right)} $\)
\($\boxed{\sin(\theta)=\cos \left(90\º - \theta \right)} $\)
\(\sin(12\º)=\cos(90\º - 12\º)=\cos(78\º)\)
\(\therefore \cos(78\º) - \cos(78\º) = 0\)
The value of Sin 12-cos 78 is 0
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: sin 12 - cos 78 = Sin(90-12)-cos78 but we know sine of any angle = the cosine of any complementary angle
Thus we have Sin78-Cos78=0
Hence, The value of Sin 12-cos 78 is 0
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evaluate the expression without using a calculator. arccot( – √3)
Answers
The inverse cotangent function or arccot is the angle in radians whose cotangent is a given number. Therefore, arccot(-√3) = π - π/6 = 5π/6 or 150°.
To evaluate arccot(-√3), we need to find the angle whose cotangent is -√3. Since cotangent is the reciprocal of a tangent, we can use the identity tan(x) = 1/cot(x) to get the tangent of the angle we are looking for.
In this case, tan(x) = 1/(-√3) = -1/√3.
The angle whose tangent is -1/√3 is -π/6 or -30°, because the tangent function has a period of π or 180°.
Since the range of the arccot function is (0,π), we need to add π or 180° to get the actual angle in the fourth quadrant.
Therefore, arccot(-√3) = π - π/6 = 5π/6 or 150°.
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find the radius of convergence, r, of the series. [infinity] (−1)n xn 2n ln(n) n = 2 r = incorrect: your answer is incorrect.
Answers
The radius of convergence, r, is 2. The series converges for values of x within the interval (-2, 2).
To find the radius of convergence, we can use the ratio test. Consider the series:
∑ (-1)^n * (x^n) / (2^n * ln(n))
Applying the ratio test:
lim |(-1)^(n+1) * (x^(n+1)) / (2^(n+1) * ln(n+1))| / |(-1)^n * (x^n) / (2^n * ln(n))|
= lim |x / 2 * ln(n+1) / ln(n)|
As n approaches infinity, the limit simplifies to:
| x / 2 |
For the series to converge, this limit must be less than 1:
|x / 2| < 1
Solving for x, we have:
-1 < x/2 < 1
Multiplying by 2, we get:
-2 < x < 2
Therefore, the radius of convergence, r, is 2. The series converges for values of x within the interval (-2, 2).
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helppppppppppppppppppppppppppppppppppppp
Answers
Answer: 527.79 m²
Step-by-step explanation:
formula is A = 2πrh + 2πr²
A = 2π x 4 x 17 + 2π x 4²
A = 527.79 m²
4.49 × 10^–3 in standard form?
Answers
Answer:0.0049
Step-by-step explanation: You move the decimal 3 places to the left because its negative which gives you 0.0049
See attachment for math work and answer.
(- x2 + 9xy) – (x2 + 6xy - 8y2) =
Answers
Answer:
(15x- 8y)
Step-by-step explanation:
"y2" was replaced by "y^2"
((0-(x2))+9xy)+(((x2)+6xy)-23y2)
15xy - 8y2
= y • (15x - 8y)
an apple chew was selected 53 times a lemon chew was selected 3 times a peach chew was selected 3 times what's the probability
Answers
The probability that the next chew that Jamar removes from the bag will be an apple chew is of:
0.9 = 90%.
How to calculate the probability?In the context of an experiment, a probability is calculated as the division of the number of desired outcomes in the context of the problem by the number of total outcomes in the context of the experiment.
In this problem, the outcomes are given from the previous experiments, hence we have an experimental probability.
The outcomes are given as follows:
Desired: apple chew = 53 outcomes.Total: 53 + 3 + 3 = 59 outcomes.Then the probability that the next chew that Jamar removes from the bag will be an apple chew is calculated as follows:
p = 53/59 = 0.9 = 90%.
Missing InformationThe problem is given by the image shown at the end of the answer.
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find teh exact value of sin 2x given that sec x = 3/2 and csc y = 3 and x and y are in quadrant 1
Answers
The exact value of \(sin 2x\) is \(4√5/9.\)
Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.
In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)
Also, we know that sin \(2x = 2 sin x cos x.\)
Now, we need to find sin x.
Having sec x = 3/2, we can use the Pythagorean identity
\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)
As x is in the first quadrant, it lies between 0° and 90°.
Therefore, x cannot be negative.
Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)
Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)
Therefore, the exact value of sin 2x is 4√5/9.
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a diver was collecting water samples from a lake. he collected a sample at every 3m, starting at 5m below water surface. the final sample was collected at a depth of 35m.how many sample did he collected
Answers
The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.
We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.
The total depth range is:
35 m - 5 m = 30 m
The distance between each sample is 3 m, so the number of samples is:
(30 m) / (3 m/sample) + 1 = 10 + 1 = 11
Therefore, the diver collected a total of 11 water samples.
Which graph is generated by this table of values?
Answers
Answer:
wheres the rest of the graphs?
Step-by-step explanation:
It’s NOT the first one
Answer:
B
Step-by-step explanation:
you randomly choose one shape from the bag. find the number of ways the event can occur. find the favorable outcomes of the event
Answers
(a) The number of ways that the event can occur is 6.
(b) Probabilities are :
1) 1/2, 2) 1/6 and 3) 1/3.
(a) Given a bag of different shapes.
Total number of shapes = 6
So, if we select one shape from random,
total number of ways that the event can occur = 6
(b) Number of squares in the bag = 3
Probability of choosing a square = 3/6 = 1/2
Number of circles in the bag = 1
Probability of choosing a circle = 1/6
Number of stars in the bag = 2
Probability of choosing a star = 2/6 = 1/3
Hence the required probabilities are found.
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A city planner wants to build a road perpendicular to D Street. What should be the slope of the new road?
Answers
The slope of the new road is zero.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take points from the Graph (5, 0) and (5, 4).
Slope of a line = m = tanθ
where θ is the angle made by the line with the x−axis.
For a line parallel to y−axis ,θ= π/2.
∴m = tan π/2 = undefined
The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.
An horizontal line now has zero slope.
The new road has a zero slope as a result.
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Question 6 Next, you select the basic statistics that can help your team better understand the ratings system in your data. Assume the first part of your code is: trimmed_flavors_df %>% You want to use the summarize() and mean() functions to find the mean rating for your data. Add the code chunk that lets you find the mean value for the variable Rating.
Answers
Based on the ratings system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.
How do you find the mean rating?To find the mean rating, the complete code should be trimmed_flavors_df %>% summarize(mean(Rating)).
This code would allow you to see the mean rating of your data by combining the summarize() and mean() functions such that you can display summary statistics.
Because of the "mean()" function, the statistic that will be displayed is the mean rating which in this case would be 3.185933.
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Gabriel deposits $660 every month into an account earning a monthly interest rate of
0.475%. How much would he have in the account after 16 months, to the nearest
dollar? Use the following formula to determine your answer.
Answers
The future value of the monthly deposit which earns 0.475 monthly interest will be $10,944.67 after 16 months.
How the future value is determined:The future value can be determined using the future value annuity formula or an online finance calculator.
The future value represents the periodic deposits compounded periodically at an interest rate.
N (# of periods) = 16 months
I/Y (Interest per year) = 5.7% (0.475% x 12)
PV (Present Value) = $0
PMT (Periodic Payment) = $660
Results:
Future Value (FV) = $10,944.67
The sum of all periodic payments = $10,560.00
Total Interest = $384.67
Thus, using an online finance calculator, the future value of the monthly deposits is $10,944.67.
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i roll a four-sided die. the possible outcomes are 1, 2, 3, or 4, depending on the number of spots on the side of the die that is face down. this collection of all possible outcomes is called: group of answer choices a census. the probability. the sample space. the distribution.
Answers
The given probability, the collection of all possible outcomes is sample space.
Probability is the statistics term that defines a number that reflects the chance or likelihood that a particular event will occur.
Here we have given that i roll a four-sided die. the possible outcomes are 1, 2, 3, or 4, depending on the number of spots on the side of the die that is face down.
And we need to find collection of all possible outcomes is called.
While we looking into the given question, we know that,
In order to solve this one, we must know the definition of sample space.
The term sample space means a collection or a set of possible outcomes of a random experiment.
According to the definition, here the sample space is the set composed by all the possible outcomes of your random variable.
According this case, the random variable is 4 sided dice,
Therefore the sample space is
S = {1, 2, 3, 4}
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1. Find the probability of picking a yellow marble and an orange
marble when 2 marbles are picked (without replacement)
from a bag containing 2 yellow and 4 orange marbles
Answers
Answer:
4/15
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that the bag contains 2 yellow and 4 orange marbles, the probability of picking a
Yellow marble = 2/(2+4) = 2/6
Orange marble = 4/(2+4) = 4/6
The probability of picking a yellow marble and an orange marble without replacement
= 2/6 * 4/5
= 8/30
= 4/15
A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
Answers
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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Suppose the annual salaries for sales associates from a particular store have a mean of $25,017 and a standard deviation of $2,153. If we don't know anything about the distribution of annual salaries, what is the maximum percentage of salaries below $21,8627 Round your answer to two decimal places and report your response as a percentage (eg; 95. 25).
Answers
The maximum percentage of salaries below $21,862 is 7.36%. This calculation is based on the given mean and standard deviation of annual salaries for sales associates.
In order to find the maximum percentage of salaries below $21,862, we need to determine the z-score associated with this salary value. The z-score measures the number of standard deviations a data point is away from the mean. By calculating the z-score, we can determine the proportion of values below a certain threshold.
To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the threshold salary, μ is the mean, and σ is the standard deviation. Substituting the given values, we get z = (21,862 - 25,017) / 2,153 ≈ -1.48.
Next, we need to find the corresponding cumulative probability associated with this z-score. This can be obtained from a standard normal distribution table or by using statistical software. The cumulative probability for a z-score of -1.48 is approximately 0.0694.
To convert this to a percentage, we multiply the cumulative probability by 100, which gives us 6.94%. However, since we are looking for the maximum percentage of salaries below $21,862, we need to consider the area to the left of the z-score, which represents the salaries below the threshold. Therefore, the maximum percentage of salaries below $21,862 is approximately 7.36%.
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Express the following in the form a + bi, where a and b are real numbers:
\( \sqrt{i} \)
Answers
There were 8 red cars and 12 blue cars in the parking lot what is the ratio of the number of red cars to number of blue cars
Answers
Answer:
2 : 3
Step-by-step explanation:
Hello fellow human!
red : blue - 8 : 12
The ratio is divisible by 4 - (8/4) = 2 ; (12/4) = 3
Hence, 2 : 3