12. Suppose sin is theta= 20/29 and tan theta < 0. Find the values of the six trigonometric functions for the angle theta.
Answers
The values of the six trigonometric functions for the angle θ are:
sin θ = 20/29
cos θ = -21/29
tan θ = -20/21
csc θ = 29/20
sec θ = -29/21
cot θ = -21/20
We are given sin θ = 20/29 and tan θ < 0, which means that the angle θ is in the third quadrant, where sine is positive and tangent is negative. Using the Pythagorean identity, we can find the cosine of θ:
cos² θ = 1 - sin² θ
cos² θ = 1 - (20/29)²
cos θ = -21/29 (since cosine is negative in the third quadrant)
Using the tangent ratio, we can find the tangent of θ:
tan θ = sin θ / cos θ
tan θ = (20/29) / (-21/29)
tan θ = -20/21
Now we can find the remaining three trigonometric functions using the definitions:
csc θ = 1 / sin θ = 29/20
sec θ = 1 / cos θ = -29/21
cot θ = 1 / tan θ = -21/20
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Related Questions
Suppose 20% of 300 students choose recycling. How many students choose
recycling? Explain how you found your answer.
Answers
Answer:
around 60 kids chose to recycle
Step-by-step explanation:
20% of 300 = 60
Answer:
60
Step-by-step explanation:
20% of 300
= \(\frac{20}{100}\) × 300
= 0.2 × 300
= 60
Your parents took your family out to dinner . Your parents want to give you the server a 15% tip . If the total amount of the dinner was $42.00 , what will be the amount of the tip ?
Answers
Answer:
The tip will be $6.30
x-2y=4 in slope intercept form
Answers
Answer:
y = 1/2x - 2
Step-by-step explanation:
Slope intercept form:
y = mx + b
x - 2y = 4
-2y = -x + 4
2y = x - 4
y = 1/2x - 2
Slope intercept form: y = mx + b
y= answer, y-value
m=slope
x= independent variable, x-value
b= y-intercept (0,b)
x-2y=4
1. Isolate 2y by adding x to both sides of the equation: 2y = 4+x
2. Isolate y by dividing 2 to both sides of the equation: y = 2+(1/2)x
3. Rearrange in slope intercept form.
y=(1/2)x + 2
PLEASE HELP I will Mark Brainlist its A Math Question thank you
Answers
Answer:
The correct answer is the second alternative!
john missed 4 problems on a test but did 75% of them correctly. how many problems were there in the test? john missed 4 problems on a test but did 75% of them correctly. how many problems were there in the test?
Answers
From the given information, upon calculation , there were 16 problems in the test.
Let's assume the total number of problems in the test as 'x'. We know that John missed 4 problems, so the number of problems he answered correctly is 'x - 4'. It is also given that he did 75% of the problems correctly, which can be represented as 0.75x.
Equating these two expressions, we can form the equation:
x - 4 = 0.75x
To solve this equation, we can subtract 0.75x from both sides:
0.25x - 4 = 0
Next, we add 4 to both sides of the equation:
0.25x = 4
To isolate 'x', we divide both sides by 0.25:
x = 4 / 0.25
Simplifying the division, we find:
x = 16
Therefore, there were 16 problems in the test.
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a rational expression is undefined if the numerator is zero T/F
Answers
The given statement "a rational expression is undefined if the numerator is zero" is false because a rational expression is undefined if the denominator is zero, not the numerator.
When the denominator of a rational expression becomes zero, the expression becomes undefined because division by zero is not defined in mathematics.
If the numerator of a rational expression is zero, it does not make the expression undefined. Instead, it results in the value of the expression being zero, regardless of the value of the denominator.
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juan owns 7 pairs of pants, 5 shirts, 6 ties, and 8 jackets. how many different outfits can he wear to school if he must wear one of each item?
Answers
Answer: I believe he could wear 768 outfits
Step-by-step explanation: I had a similar question consisting of the same numbers.
Darnell and emma are college students . darnell currently has 22 credits and he plans on taking 6 credits per semester . emma has 4 credits and plans to take 12 credits per semester . after how many semesters , s will darnell and emma have the same number of credits ?
Answers
After 3 semesters Darnell and Emma have same number of credits as 40.
Given,
Current credit score of Darnell = 22
Current credit score of Emma = 4
Darnell plans to score a credit per semester = 6
Emma plans to score a credit per semester = 12
Now, we have to find that after how many semesters will Darnell and Emma have the same number of credits .
Here,
Current credit score of Darnell = 22
Current credit score of Emma = 4
After 1 semester,Credit score of Darnell = 22 + 6 = 28
Credit score of Emma = 4 + 12 = 16
After 2 semester,Credit score of Darnell = 28 + 6 = 34
Credit score of Emma = 16 + 12 = 28
After 3 semester,Credit score of Darnell = 34 + 6 = 40
Credit score of Emma = 28 + 12 = 40
That is,
After 3 semesters Darnell and Emma have same number of credits as 40
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1) A radio station runs a promotion at an auto show with a money box with14 $25 tickets, 12 $5 tickets, and 10 $1 tickets. The box contains an additional 20 "dummy" tickets with no value. Find the probability that three $25 prizes are chosen. The probability that three $25 prizes are chosen is____
(Round to five decimal places as needed.)
2) A radio station runs a promotion at an auto show with a money box with 15 $100 tickets,13 $50 tickets, and 12 $25 tickets. The box contains an additional 20 "dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that exactly two $100 prizes and no other money winners are chosen
The probability that exactly two $100 prizes and no other money winners are chosen is____?
(Round to four decimal places as needed.)
3) A radio station runs a promotion at an auto show with a money box with 14 $25 tickets,11 $5 tickets, and 13 $11 tickets. The box contains an additional 20 "dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that all three tickets have no value. The probability that all three tickets drawn have no money value is___?(Round to four decimal places as needed.)
4) A manufacturing company performs a quality-control analysis on the ceramic tile it produces. Suppose a batch of 21 tiles has 7defective tiles. If 4 tiles are sampled at random, what is the probability that exactly 1 of the sampled tiles is defective?
How many ways can 4 tiles be selected from 21 tiles? ____ways
(Type a whole number.)
The probability that exactly 1 of the sampled tiles is defective is_____?
(Round to four decimal places as needed.)
5) A shipment of 8 computers contains 4 with defects. Find the probability that a sample of size 4, drawn from the 8, will not contain a defective computer. What is the probability that a sample of 4 of the 8 computers will not contain a defective computer?______?
(Type an integer or a simplified fraction.)
Answers
1. The probability that three $25 prizes are chosen is approximately 0.01314.
2. The probability that exactly two $100 prizes and no other money winners are chosen is approximately 0.6123.
3. The probability that all three tickets drawn have no money value is approximately 0.0468.
4. The probability that exactly 1 of the sampled tiles is defective is approximately 0.4268.
5. The probability that a sample of 4 of the 8 computers will not contain a defective computer is 1/70.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
1) To find the probability that three $25 prizes are chosen, we need to calculate the probability of selecting three $25 tickets from the total tickets available.
Total number of tickets: 14 ( $25 tickets) + 12 ($5 tickets) + 10 ($1 tickets) + 20 (dummy tickets) = 56 tickets
Number of ways to choose three $25 tickets: C(14, 3) = 14! / (3! * (14-3)!) = 364
Total number of ways to choose three tickets from the total: C(56, 3) = 56! / (3! * (56-3)!) = 27720
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 364 / 27720 = 0.01314 (rounded to five decimal places)
Therefore, the probability that three $25 prizes are chosen is approximately 0.01314.
2) To find the probability that exactly two $100 prizes and no other money winners are chosen, we need to calculate the probability of selecting two $100 tickets and one dummy ticket.
Total number of tickets: 15 ($100 tickets) + 13 ($50 tickets) + 12 ($25 tickets) + 20 (dummy tickets) = 60 tickets
Number of ways to choose two $100 tickets: C(15, 2) = 15! / (2! * (15-2)!) = 105
Number of ways to choose one dummy ticket: C(20, 1) = 20
Total number of ways to choose three tickets from the total: C(60, 3) = 60! / (3! * (60-3)!) = 34220
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (105 * 20) / 34220 = 0.6123 (rounded to four decimal places)
Therefore, the probability that exactly two $100 prizes and no other money winners are chosen is approximately 0.6123.
3) To find the probability that all three tickets have no value (dummy tickets), we need to calculate the probability of selecting three dummy tickets.
Total number of tickets: 14 ($25 tickets) + 11 ($5 tickets) + 13 ($11 tickets) + 20 (dummy tickets) = 58 tickets
Number of ways to choose three dummy tickets: C(20, 3) = 20! / (3! * (20-3)!) = 1140
Total number of ways to choose three tickets from the total: C(58, 3) = 58! / (3! * (58-3)!) = 24360
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1140 / 24360 = 0.0468 (rounded to four decimal places)
Therefore, the probability that all three tickets drawn have no money value is approximately 0.0468.
4) To find the probability that exactly 1 of the sampled tiles is defective, we need to calculate the probability of selecting 1 defective tile and 3 non-defective tiles.
Total number of tiles: 21 tiles
Number of ways to choose 1 defective tile: C(7, 1) = 7
Number of ways to choose 3 non-defective tiles: C(14, 3) = 14! / (3! * (14-3)!) = 364
Total number of ways to choose 4 tiles from the total: C(21, 4) = 21! / (4! * (21-4)!) = 5985
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (7 * 364) / 5985 = 0.4268 (rounded to four decimal places)
Therefore, the probability that exactly 1 of the sampled tiles is defective is approximately 0.4268.
5) To find the probability that a sample of size 4 drawn from the 8 computers will not contain a defective computer, we need to calculate the probability of selecting 4 non-defective computers.
Total number of computers: 8 computers
Number of ways to choose 4 non-defective computers: C(4, 4) = 1
Total number of ways to choose 4 computers from the total: C(8, 4) = 8! / (4! * (8-4)!) = 70
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 70 = 1/70
Therefore, the probability that a sample of 4 of the 8 computers will not contain a defective computer is 1/70.
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In Europe, surveyors often measure angles in grads. There are 100 grads in one-quarter of a circle. How many grads are there in 1.85 radians?
Answers
There are approximately 118.3205236 grads in 1.85 radians.
One complete circle is equal to 360° or 2π radians.
Since there are 100 grads in one-quarter of a circle, there are 400 grads in one complete circle.
The following formula is used to convert radians to grads:x grad = x × 200 / π grad
So, to convert 1.85 radians to grads, we substitute x = 1.85 in the formula as follows:
x grad = 1.85 × 200 / π grad≈ 118.3205236 grad
Therefore, there are approximately 118.3205236 grads in 1.85 radians.
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What value of x makes the two expressions below equal? Give your answer as a decimal. 7x-5 First expression 5x+8 Second expression
Answers
Answer:
x = 6.5
Step-by-step explanation:
For the two expressions to be equal, we'll set them equal to each other and solve.
7x - 5 = 5x + 8
Subtract 5x from both sides.
2x - 5 = 8
Add 5 to both sides.
2x = 13
Divide both sides by 2.
x = 13/2
Divide to find the decimal answer.
x = 6.5
On Monday, a local hamburger shop sold a combined total of 588 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
Answers
the answer would be 147.I hope this helps you
Step-by-step explanation:
4h=588
h=588÷4
What ordered pair represents the total number of fish they each caught after four hours?
Answers
do any of y’all know how to do number 7?
Answers
Answer:
f(-3) = 2
f(-1) = 2
f(8) = 1
Step-by-step explanation:
Yep! For any function f(x), you find the y value corresponding the x value. For example, in this question, it asks us to find f(-3). Therefore, you go to the line, x = -3, and see where it intersect the function (the y value). Your answer would be the y value.
The value corresponding to f(-3) seems to be 2.
The value corresponding to f(-1) seems to be -2.
The value corresponding to f(8) seems to be 1.
an asphalt parking lot is in the shape of a trapezoid if it costs 1.75 per square yard to seal an asphalt surface find the cost to seal the parking lot
Answers
Answer:
The answer would be $1995
Step-by-step explanation:
Trust me
Maya runs 7 miles in 50 minutes. At the same rate, how many miles would she run in 75 minutes
Answers
Answer:
10.5 miles
Step-by-step explanation:
what is (5 over 3/4 divided by 1/16) plus 4 over 1/2
Answers
Answer:
114.666666666666667
Step-by-step explanation:
what is 6pints equal to in cups ?
Answers
Answer: 12 cups
Step-by-step explanation:
Answer:
12 cups
Step-by-step explanation:
1 pint = 2 cups
6 pints = 6 × 2 cups = 12 cups
Listed below are the results of 16 independent trials that attempted to measure quantity Q. Calculate the average value and give an uncertainty range where you can be 95% sure that the true value of Q lies within.41.31440.08741.24840.19640.28441.15238.85236.40137.94139.22139.03538.40440.68341.56842.17542.319calculate the absolute value of the difference in the two estimates of q with an uncertainty range at a 95onfidence interval. make sure you do all calculations with unrounded values.
Answers
Note that the absolute value of the difference in the two estimates of Q with an uncertainty range at a 95% confidence interval is 1.052.
What is the rationale for the above response?To find the average value of Q, we simply add up all the values and divide by the number of trials:
Average value of Q = (41.314 + 40.087 + 41.248 + 40.196 + 40.284 + 41.152 + 38.852 + 36.401 + 37.941 + 39.221 + 39.035 + 38.404 + 40.683 + 41.568 + 42.175 + 42.319)/16
= 39.976
Next, to find the uncertainty range where we can be 95% sure that the true value of Q lies within, we need to find the standard error of the mean. The formula gives this:
Standard error of the mean = standard deviation / √(n)
where n is the number of trials. We can find the standard deviation using the formula:
Standard deviation = √(Σ(Qi - Q_avg)² / (n-1))
where Qi is the value of Q for the ith trial.
Using these formulas, we find:
Standard deviation = 1.549
Standard error of the mean = 0.387
To find the uncertainty range, we say:
Uncertainty range = t-value * standard error of the mean
= 2.131 * 0.387
= 0.826
Therefore, we can be 95% sure that the true value of Q lies within the range:
39.976 ± 0.826
Now, to calculate the absolute value of the difference in the two estimates of Q with an uncertainty range at a 95% confidence interval, we can simply add the uncertainty ranges of the two estimates and take the absolute value of the difference:
|Q1 - Q2| = |39.976 ± 0.826 - 40| + |39.976 ± 0.826 - 39.8|
= 0.826 + 0.226
= 1.052
Therefore, the absolute value of the difference in the two estimates of Q with an uncertainty range at a 95% confidence interval is 1.052.
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How does the formula for the sample mean differ from the formula for the Population mean?
Answers
The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).
The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.
The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :
The mean formula is written thus :
Population mean = Σx / N
Sample mean = Σx / n
Where, x = set of values.
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how much did she spend on food for the party?
Answers
Answer:
Step-by-step explanation:
You can write and equation for this problem.
as 20.27-2.01x= The left money for food.
x: is two.
SO applying the number to the equation:
20.27-4.02= Food money
$16.25 is the answer
What is the addition and subtraction rule with significant figures? Please give some specific examples.
Answers
When adding or subtracting numbers with significant figures, the result should be rounded to the least precise decimal place of the measurements involved.
How do you round the result when adding or subtracting significant figures?When performing addition or subtraction operations with numbers that have different levels of precision, it is important to ensure that the result is reported with the appropriate number of significant figures.
The rule states that the result should be rounded to the least precise decimal place among the measurements involved in the calculation.
For example, consider the addition of 53.5 and 46.5. Both numbers have one decimal place, so the sum should also be reported with one decimal place.
Adding the numbers gives us 100, but when applying the rule, we round the result to 100.0 to reflect the precision of the original measurements.
Similarly, if we subtracted 46.5 from 53.5, the result would still have one decimal place: 7.0.
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Solve for x:
5x+1=6x+9
Answers
Answer: -8
Step-by-step explanation:
For large parties at a seafood restaurant, a tip of 18% is automatically included on the bill. Jerome’s family went out for his grandmother’s 75th birthday. Their bill came to $268.21 before tip. Calculate the amount of tip that will be charged and the total amount after tip. Round to the nearest cent if necessary .
Answers
Answer:
tip=48.28
total cost =316.49
Step-by-step explanation:
tip = 48.28
Total + tip= 316.49
grog writes every possible arrangement of the digits 2,4,6 with a decimal point between two digits Find the sum of every number less than 4.4 than grogg writes
Answers
First, let's list all the possible arrangements of the digits 2, 4, and 6 with a decimal point between two digits: - 2.4.6
- 2.6.4
- 4.2.6
- 4.6.2
- 6.2.4
- 6.4.2
Now, we need to find the sum of every number less than 4.4 than grogg writes. This means we need to add up all the numbers that are less than 4.4 and are also less than each of the six numbers on our list.
Let's start with the first number on our list, 2.4.6. The numbers that are less than 4.4 and less than 2.4.6 are:
- 2.4
- 2.6
So we add those two numbers together: 2.4 + 2.6 = 5, That's the sum for the first number on our list. Now we can repeat this process for each of the other five numbers on our list, and add up all the sums at the end. For 2.6.4, the numbers less than 4.4 and less than 2.6.4 are: - 2.6 .
So the sum for 2.6.4 is: 2.6, For 4.2.6, the numbers less than 4.4 and less than 4.2.6 are:
- 4.2
- 4.6, So the sum for 4.2.6 is: 4.2 + 4.6 = 8.8, For 4.6.2, the numbers less than 4.4 and less than 4.6.2 are:
- 4.2
- 4.6
So the sum for 4.6.2 is:
4.2 + 4.6 = 8.8
For 6.2.4, the numbers less than 4.4 and less than 6.2.4 are:
- None
There are no numbers less than 4.4 and less than 6.2.4, so the sum for 6.2.4 is 0.
Finally, for 6.4.2, the numbers less than 4.4 and less than 6.4.2 are:
- None
Again, there are no numbers less than 4.4 and less than 6.4.2, so the sum for 6.4.2 is 0.
Now we can add up all the sums: 5 + 2.6 + 8.8 + 8.8 + 0 + 0 = 25.2
So the sum of every number less than 4.4 than grogg writes is 25.2.
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12 1/2 - (-4 1/2) = ?
Answers
Answer:
17
Step-by-step explanation:
12 1/2-(-4 1/2)
12 1/2+ 4 1/2
17
A cab company charges a $3 boarding rate in addition to its meter which is $2 for every mile. What is the equation?
Please give an actual answer
Answers
1. Given: Line segment with endpoints A(‒6,6) and B(6,‒3).
Prove: If the coordinates of Y is (2,0), prove that Y is two-thirds of the way from A to B.
Answers
Y is two-thirds of the way from A to B because the ratio of the distances AY to AB is 2/3.
To prove that Y is two-thirds of the way from A to B, we need to show that the ratio of the distances AY to AB is 2/3.
Calculate the distance between points A and B using the distance formula:
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
AB = √[(6 - (-6))² + ((-3) - 6)²]
AB = √[12² + (-9)²]
AB = √[144 + 81]
AB = √225
AB = 15
Calculate the distance between points A and Y:
AY = √[(x₂ - x₁)² + (y₂ - y₁)²]
AY = √[(2 - (-6))² + (0 - 6)²]
AY = √[8² + (-6)²]
AY = √[64 + 36]
AY = √100
AY = 10
Calculate the ratio of AY to AB:
Ratio = AY / AB
Ratio = 10 / 15
Ratio = 2/3
Since the ratio of AY to AB is 2/3, we can conclude that Y is two-thirds of the way from A to B.
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Examine the equation-5|1 + 8x| + 9 = -116A: Determine how many solutions this equation has and justify your responseB: Determine what your solutions are for this equation
Answers
Part A
The equation has two solutions since it is an absolute equation.
Part B
Given the equation:
\(-5|8x+1|+9=-116\)First, subtract 9 from both sides.
\(\begin{gathered} -5|8x+1+9-9=-116-9 \\ -5|8x+1|=-125 \end{gathered}\)Next, we divide both sides by -5.
\(\begin{gathered} \frac{-5\mleft(|8x+1|\mright)}{-5}=\frac{-125}{-5} \\ |8x+1|=25 \end{gathered}\)We then solve the absolute value.
\(\begin{gathered} 8x+1=25\text{ or }8x+1=-25 \\ 8x=-1+25\text{ or }8x=-1-25 \\ 8x=24\text{ or }8x=-26 \\ x=\frac{24}{8}\text{ or }x=\frac{-26}{8} \\ x=3\text{ or }-\frac{13}{4} \end{gathered}\)The solutions for this equation are 3 or -13/4.
Claire buys furniture to the value of R35 000. she pays a 15% cash deposit and signs a hire purchase agreement for the balance. the interest rate will be 13% per annum and she will pay off the loan over a period of 3 years. what is the value of the deposit?
Answers
Answer:
Total amount = R41 337.50
Step-by-step explanation:
The value of the deposit is 15% of the total purchase price:
Deposit = 15/100 x R35 000
Deposit = R5 250
To calculate the balance that Claire will have to pay off, we need to subtract the deposit from the total purchase price:
Balance = Total purchase price - Deposit
Balance = R35 000 - R5 250
Balance = R29 750
To calculate the interest that Claire will have to pay on the balance, we can use the formula:
Interest = Principal x Rate x Time
where:
Principal is the amount of the balance
Rate is the annual interest rate (13%)
Time is the duration of the loan in years (3)
So, the interest that Claire will have to pay is:
Interest = R29 750 x 0.13 x 3
Interest = R11 587.50
Therefore, the total amount that Claire will have to pay back over the 3-year period is:
Total amount = Balance + Interest
Total amount = R29 750 + R11 587.50
Total amount = R41 337.50
Note that this assumes that the interest is calculated annually and added to the balance at the end of each year. In reality, the interest may be calculated differently depending on the terms of the hire purchase agreement.