The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.
What is trigοnοmetry?Relatiοnships between cubic splines and mathematics When the disciplines οf astrοphysics were cοmbined, it is thοught that the subject was bοrn in the third century B.C. Precise mathematical techniques can be used tο sοlve a large number οf geοmetric equatiοns οr tο identify the οutcοmes οf calculatiοns invοlving them. The study οf the six fundamental trigοnοmetric functiοns is knοwn as trigοnοmetry. They gο by many different names and abbreviatiοns, such as sine, dispersiοn, angle, οblique, etc (csc).
Here,
cοs(b) Plus sin(b) = 1
Using the equatiοn, we can find the sοlutiοn fοr cοs(b) in terms οf sin(b):
cοs(2b) = (1 - sin(2b)) (b)
Inputting this intο the fοrmula fοr tan(b), we οbtain:
Tan is equal tο sin(b)/√(1 - sin2(b)).
When we square bοth sides and multiply by the remainder, we get:
(Tan(b)) / (1 + (Tan(b))) Equals sin2(b)
By simplifying and substituting tan(b) = sin(A)/cοs(A), we οbtain:
the fοrmula fοr sin2(b) is (sin(A))/((cοs(A))² + (sin(A))²)
Inputting the numbers we previοusly discοvered fοr sin(A) and cοs(A), we οbtain:
=> sin²(b) = (3/5)
=> sin² / ((4/5)
=> sin² + (3/5)²)
=> sin²(b) = 9/25 / (16/25 + 9/25)
=> sin²(b) = 9/25 / 25/25
=> sin²(b) = 9/25 sin(b) = +/- 3/5
Sin(b), which is pοsitive in the first regiοn, results in:
sin(b) = 3/5
As a result, sin(b) = 3/5 if tan(A) = 3/4.
Therefοre, The sοlutiοn tο the given prοblem οf trigοnοmetry cοmes οut tο be sin(b) = 3/5 if tan(A) = 3/4.
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Yamilet works in a jewelry store and receives 12% commission when she makes a sale. how much commIssuing will she receive for selling an $8,125 ring
Answer: To find out how much commission Yamilet will receive for selling an $8,125 ring, we need to multiply the price of the ring by her commission rate, which is 12% or 0.12 in decimal form.
Commission = Price of ring x Commission rate
Commission = $8,125 x 0.12
Commission = $975
Therefore, Yamilet will receive a commission of $975 for selling an $8,125 ring.
Step-by-step explanation:
Is (0, 6) a solution to the equation y = -x + 6?
Yes or No
Answer:
Yes
Step-by-step explanation:
We just need to (0,6) in the equation to see if it gives a true answer or not!
y = -x + 6
6 = 0 + 6
6 = 6
So, (0,6) is a solution to the equation y = -x + 6
K
The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total
amount due at time t.
P = $9000, r = 5.5%, t = 8 months
The future value is $
(Simplify your answer. Type an integer or a decimal.)
ew an example
Get more help.
Clear all
Check answer
orrect
Answer:
the future value or total amount due at the end of 8 months is $9,330.00
Step-by-step explanation:
To find the future value of a loan that is borrowed at a simple interest rate, we use the formula:
A = P(1 + rt)
where A is the future value or total amount due, P is the principal or initial amount borrowed, r is the simple interest rate as a decimal, and t is the time period in years.
In this case, the principal is $9000, the simple interest rate is 5.5% or 0.055 as a decimal, and the time period is 8 months or 8/12 = 2/3 years.
Substituting these values into the formula, we get:
A = 9000(1 + 0.055 × 2/3)
= 9000(1.0375)
= $9,330.00
Therefore, the future value or total amount due at the end of 8 months is $9,330.00
we know that a year has 12 months, so 8 months is really 8/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\to \frac{8}{12}\dotfill &\frac{2}{3} \end{cases} \\\\\\ A = 9000[1+(0.055)(\frac{2}{3})] \implies A = 9330[/tex]
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 38 and 54?
By answering the supplied question, we may infer that the response is standard deviation As a result, 95% of requests for lightbulb replacements with a total number between 38 and 54 are in this range.
What is standard deviation?A statistic known as standard deviation may be used to indicate the variation or variability of a set of statistics. A low standard deviation means that the values tend to be closer to the established mean whereas a large standard deviation shows that the values are widely spread. The standard deviation serves as a gauge for how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is low, and are more scattered when the standard deviation is high. Standard deviation is a measurement of the data set's average variability. It displays the standard deviation of each score with respect to the mean.
The rule states approximately:
One standard deviation from the mean is shared by 68% of the requests.
The average request is within two standard deviations in 95% of cases.
The average request falls within three standard deviations in 99.7% of cases.
a mean three standard deviations away:
38 8 = 30 to 46 with one standard deviation
two standard deviations: 22 to 54 for 38 2(8)
38 3(8) = 14 to 62 for three standard deviations
We know that almost 95% of the requests fall within this range since we are interested in the proportion of requests between 38 and 54, which is within two standard deviations of the mean. As a result, 95% of requests for lightbulb replacements with a total number between 38 and 54 are in this range.
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Answer this in this hour or no points.
A spinner has 3 equal sections colored blue, orange, and red. Determine the sample space for spinning the spinner two times.
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Blue Red
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Orange Blue
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Red Blue
Red Orange
Orange Blue
Orange Red
If the spinner is spinning two times then the sample space becomes { BB,B0,BR,OB,OO,OR,RB,RO,RR}.
What is sample space?In probability a sample space is a set of possible number of outcomes of a random experiment.
A spinner has three equal sections blue(B), orange(O), red(R).
The sample space will be
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Hence, If the spinner is spinning two times then the sample space becomes { BB, B0, BR, OB, OO, OR, RB, RO, RR}.
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Mark is doing a course.There are 5 tests on the course. He needs a mean score of 10 to pass. In his first 4 tests his mean score is 12. What score does he need in the 5th test to pass the course
Mark needs a score of 2 on the 5th test to pass the course
How to calculate the mean score needed by Mark to pass the courseLet X be the score Mark needs to get on the fifth test to pass the course.
To find X, we can use the formula for the mean of five numbers:
(mean of 5 numbers) = (sum of the 5 numbers) / 5
We know that Mark needs a mean score of 10 to pass, so:
10 = (total score on all 5 tests) / 5
Multiplying both sides by 5, we get:
50 = total score on all 5 tests
We also know that Mark's mean score on the first four tests is 12, so:
(mean score on the first four tests) = (total score on the first four tests) / 4
12 = (total score on the first four tests) / 4
total score on the first four tests = 48
To pass the course with a mean score of 10, Mark needs a total score of 50, and he has already scored 48 on the first four tests. Therefore, he needs to score:
X = 50 - 48
X = 2
Mark needs a score of 2 on the fifth test to pass the course with a mean score of 10.
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Calculate the height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees. Round your answer to the nearest cm. Include a diagram.
The height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees is 131.30 cm.
What connection exists in trigonometry between the angle of elevation and the tangent function?The tangent function in trigonometry describes the relationship between an angle's adjacent and opposing sides. The angle of elevation is the angle formed by a horizontal line and a line leading from the observer's eye to a higher-than-horizontal object. When calculating an object's height with the tangent function, we utilize the angle of elevation and the length of the neighbouring side (in this example, the slanted height) to get the length of the opposing side (the height). As a result, the height of the object increases with increasing tangent value and elevation angle.
Given that, a roof has slanted height of 325 cm and an angle of elevation of 22 degrees.
Using the trigonometric functions:
tan(22) = h / 325
h = 325 * tan(22)
h ≈ 131.30 cm
Hence, the height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees is 131.30 cm.
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Emmy watson is buying a new oven for 915.00. She made a down payment of 20% and financed the remainder. How much did she finance
Answer:
$732.00
Step-by-step explanation:
Down payment 20% of 915.00
20% = 0.2
915 x 0.2 = $183.00
Down payment = $183.00
Financed the remainder:
915.00 - 183.00 = $732.00
So, she finance $732.00
A triangle has sides with lengths of 9 yards, 17 yards, and 18 yards. Is it a right triangle?
Answer:
No
Step-by-step explanation:
from Pythagoras theorem, if the triangle is right angled square of largest side should be equal to sum of the squares of smaller two sides. the square of largest side is 18^2= 324
9^2=81 and the last side is 17^2= 289
81+ 289= 370
This triangle is NOT a right triangle.
PLEASE HELP !!!What is the area of a cross section that passes through the center of a sphere with a diameter of 7 centimeters? Express your answer in terms of π.
.
just find the area of a circle which is
pi times 3.5 squared. 3.5 is the radius because 7 is the diameter
On a grid, a middle school is located at (-5, 3), and a library is located at (2, 3). If 1 unit represents 1 mile on the grid, how far is the library from the middle school, in miles?
Answer: To find the distance between two points on a grid, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates of the middle school are (-5, 3), and the coordinates of the library are (2, 3). So we have:
distance = sqrt((2 - (-5))^2 + (3 - 3)^2)
distance = sqrt((2 + 5)^2 + 0^2)
distance = sqrt(7^2)
distance = 7
Therefore, the library is 7 miles away from the middle school.
Step-by-step explanation:
During a lab experiment, the temperature of a liquid changes from 6.4°F to 10.75°F.
What is the percent of increase in the temperature of the liquid?
Enter your answer in the box as a percent rounded to the nearest hundredth. Help pls
Answer:
67.97%
Step-by-step explanation:
Answer:
67.97%
Step-by-step explanation:
J
14
20
K
22.4
AKLS-
T
32
L
Similar By:
S
Determine if the triangles are similar. If similar.state how and complete the similarity statement
Answer:
triangles, we can determine if these triangles can be proven similar by using the SSS Similarity ... use AA Similarity to prove the triangles are similar.
4.
A principal estimated that 100 students attended the school's play. Select
all of the statements that could represent this estimate.
65% of 150 students
24% of 394 students
52% of 140 students
78% of 211 students
the jacket is
Answer:
Step-by-step explanation:
The statement "65% of 150 students" could represent the estimate that 100 students attended the school's play.
To see this, we can calculate 65% of 150:
0.65 x 150 = 97.5
Since 97.5 is close to 100, it is possible that the estimate was based on 65% of 150 students.
The other statements do not come close to 100, so they are not likely to represent the estimate that 100 students attended the school's play.
Simplify the radical: √32x
(I understand how to simplify radicals I just don’t know how to do it with an unknown variable in it)
The expression when evaluated is 4√2x
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
√32x
Express 32 as the product of 16 and 2
So, we have
√32x = √(16 * 2x)
Take the LCM of 16
So, we have the following representation
√32x = 4√2x
Hence, the solution is 4√2x
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Which of these cannot be an r2-value?
The value given that cannot be an r ² value is A. - 0.75.
What is the r ² value ?The r² value, also known as the coefficient of determination, is a statistical measure that represents the proportion of variance in the dependent variable that can be explained by the independent variable(s). It is a value between 0 and 1, with higher values indicating a better fit of the regression model to the data.
It is not possible for the r² value to be negative because it is the square of the correlation coefficient. - 0.75 cannot possibly be a value of r ² as a result.
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Pleaseeee yelp meeeeee
Answer:
x ≤ 6.8
Step-by-step explanation:
1.25x + 6.50 ≤ 15
1.25x ≤ 8.5
x ≤ 6.8
So, the answer is x ≤ 6.8
Answer:
Below
Step-by-step explanation:
1.25x + 6.50 <= 15 SUBTRACT 6.50 from both sides of the equation
1.25x ≤ 8.50 DIVIDE both sides by 1.25
x ≤ 6.8
Amira has 27 feet of ribbon to make 5 braided bracelets.How much ribbon goes to each bracelet
27 ÷ 5 = 5.4
∴ 5.4 feet of ribbon goes to each bracelet.
HELPPPP!
You are washing cars for a fundraiser and have reservations for 30 cars to be washed. You realize that it will take 4 people 8 hours to wash all the cars. Exactly how long will it take 6 people to wash all the cars? If you only have 2 hours and 40 minutes to wash all the cars how many people will you need?
Answer:
How long will it take 6 people to wash all the cars? 5 hours 20 minutes
If you only have 2 hours and 40 minutes to wash all the cars how many people will you need? 12 people
Step-by-step explanation:
The important thing to realize here is that the time taken to wash x cars is inversely proportional to the number of people
That is represented mathematically as
y ∝ 1/x
The more the number of people, the less time it takes
We can write this as a proportionality equation:
y = k/x
where k is referred to as the constant of proportionality
We have the information: 4 people take 8 hours.
Plugging these two values into the equation
4 = k/8
k = 4 x 8 = 32 hours
So it takes 1 person 32 hours to wash all the cars
If there were 6 people instead
6 = 32/h where h is the time taken for 6 people to wash 30 cars
h = 32/6 = 16/3 hours = 5 1/3 hours
= 5 hours and 20 minutes
2 hours and 40 minutes = 2 40/60 hours = 2 2/3 hours
Converting to improper fraction
2 2/3 = (2 x 3 + 2)/3 = 8/3 hours
Plugging this value of x into the equation gives
y = 32/(8/3)
32 ÷ 8/3 is computed by flipping the fraction and multiplying
32 ÷ 8/3 = 32 x 3/8 = 12 people
Which statement sentence is true?
A) 0.35 > 0.36
B) 0.3 < 0.04
C) 0.3 > 0.20
D) 0.75 < 0.7
Answer: C
Step-by-step explanation: 0.3 is greater than 0.20
0.3 could be 0.30 or 0.35 or even 0.31, depends.
Avery earned $130.20 at her job when she worked for 6 hours. How. Much money did she earn each hour? I need helpppppp!!
Answer:
She got $21.70 an hour
Step-by-step explanation:
130.20/6= 21.7
Estimate a 20% tip on a dinner bill of $169.86 by first rounding the bill amount to the nearest ten dollars
The 20% percentage of bill $169.86 is $33.9.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.
Here the total bill amount= $169.86
The percentage for tip is 20%.
Then the tip amount = 20% of bill
=> 20% of 169.86
=> 20% × 169.86
=> [tex]\frac{20}{100}\times 169.86[/tex]
=> $33.9
Hence the bill amount is $33.9.
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Can anyone help me with this question
The relative maximum from the given graph is (2, 0). Therefore, options B, C, D and E are the correct answers
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
From the given graph,
The zeros of function are x=-3, x=2 and x=5.
So, the number of zeros are 3 and the degree of the polynomial is 3.
The relative maximum from the given graph is (2, 0).
The leading coefficient test tells us that the graph rises or falls depending on whether the leading terms are positive or negative.
Here, the leading coefficient is negative.
The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as the graph multiplicity.
Here, the multiplicity is 2.
Therefore, options B, C, D and E are the correct answers
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Kailyn has 4 days to complete 100 mins in mindplay and wants to split the time evenly over those days . Which inequality can she use to decide at least how many minutes she must complete each day
The inequality Kailyn can use to ensure that she completes at least 25 minutes of Mindplay each day over 4 days to complete a total of 100 minutes is x ≥ 25.
What is inequality ?
An inequality is a mathematical statement that compares two values or expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
To split the 100 minutes evenly over 4 days, Kailyn would need to complete at least 25 minutes each day.
To express this mathematically as an inequality, you can use the greater than or equal to symbol (≥) to indicate that Kailyn must complete at least 25 minutes each day:
Let x be the number of minutes Kailyn completes each day. Then the inequality would be:
x ≥ 25
This means that Kailyn must complete at least 25 minutes of Mindplay each day to ensure that she completes all 100 minutes in the given 4 days.
Therefore, the inequality Kailyn can use to ensure that she completes at least 25 minutes of Mindplay each day over 4 days to complete a total of 100 minutes is x ≥ 25.
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How can you determine how many solutions a quadratic function has?
Determining how many x-intercepts the graph has
O Determining how many y-intercepts the graph has
Looking to see if the function opens downward
Looking to see if the function opens upward
Determing how many x intercepts the graph has, as those are the points when y = 0.
Griffin read 27 books about animals and 6 books
about space. How many books did he read?
Answer:
33 27 plus 6 = 33
Step-by-step explanation:
Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
The graph of the rational equation is solved and f ( x ) = 1/ ( x + 2 ) ( x - 5 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 1/ ( x + 2 ) ( x - 5 )
The function will have increasingly large values as the denominator approaches zero. When x -2, the denominator is positive and the function tends to the upside. When x -2 x 5, the function is negative. When x 5, the function becomes positive once more.
Hence , the rational function is f ( x ) = 1/ ( x + 2 ) ( x - 5 )
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The complete question is attached below :
Which of the following rational functions is graphed below?
A. F(x) =(x-2)/(x+5)
B. F(x) =1/(x-2)(x + 5)
C. F(x) =1/(2x + 5)
D. F(x)= 1/(x+2)(x-5)
12. A mosaic wall is divided into 100 equal
Name
sections. If 30 sections are reserved for
orange tiles and 40 sections are reserved
for blue tiles, what fraction of the mosaic
wall is left for other colors?
Answer:
There are 30 + 40 = 70 sections reserved for orange and blue tiles. This means there are 100 - 70 = 30 sections left for other colors.
To express the fraction of the mosaic wall left for other colors, we can write:
30 sections left / 100 total sections = 3/10
Therefore, the fraction of the mosaic wall left for other colors is 3/10.
Electricity bills in a certain city have mean $ 106.27 . Assume the bills are normally distributed with standard deviation $ 17.15 . Find the value that separates the lower 40 % of the bills from the rest.
Write only a number as your answer. Round to two decimal places (for example: 42.81). Do not write any units.
Answer:
Step-by-step explanation:
To find the value that separates the lower 40% of the bills from the rest, we need to find the z-score corresponding to the 40th percentile of the standard normal distribution, and then use this z-score to find the corresponding value in the distribution of electricity bills.
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 40th percentile is approximately -0.25.
To find the corresponding value in the distribution of electricity bills, we can use the formula:
z = (x - mu) / sigma
where z is the z-score, x is the corresponding value in the distribution, mu is the mean, and sigma is the standard deviation.
Rearranging this formula to solve for x, we get:
x = mu + z * sigma
Substituting the given values, we get:
x = 106.27 + (-0.25) * 17.15
x = 101.63
Therefore, the value that separates the lower 40% of the electricity bills from the rest is approximately $101.63.
Pamela is 15 years younger than Jiri. The sum of their ages is 81. What is Jiri's age?
Answer:
Jiri is 48 years old
Step-by-step explanation:
STEP 1
Let Jill's age be equal to: x
Let Pamela's age be equal to :Jiri's age(x) - 15
STEP 2
Total sumof Jiri and Pamela's age= 81
Sum= Pamela's age + Jiri's age
81 = (x-15) + x
81 =x -15 + x
81 = x+x -15
81= 2x -15
Collect like terms
81 + 15= 2x ( recall - changes to + when crossing the =)
96=2x
Divide both sides by 2
96/2 =2x/2
48 = x
Recall Jiri's age is equal to x
Hence Jiri's age is equal to 48
