The point −20, 21 is on the terminal arm of an angle = in standard position. Hence, sinФ = 21/29 and cos Ф = -20/29
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Given Data
A (-20 , 21)
We have to find sin = ? and cos = ?
The point is in the fourth quadrant
We have the Opposite side and the Adjacent side
Calculate the hypotenuse
c² = (-20)² + (21)²
c² = 400 + 441
c² = 841
c = 29
Hence,
sinФ = 21/29
cos Ф = -20/29
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A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 16 subjects had a mean wake time of 100.0 min. After treatment, the 16 subjects had a mean wake time of 75.5 min and a standard deviation of 24.2 min. Assume that the 16 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 100.0 min before the treatment? Does the drug appear to be effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.
The 95% confidence interval estimate of the mean wake time is equal to (62.61, 88.39).
Given the following data:
Mean wake time = 75.5 min.Standard deviation = 24.2 min. Number of sample, n = 16.How to construct a 95% confidence interval?Mathematically, a confidence interval of 95% is given by;
α = 1 - 0.95
α = 0.05.
α/2 = 0.05/2 = 0.025.
Also, the degrees of freedom (df) is given by:
Degrees of freedom (df) = n - 1
Degrees of freedom (df) = 16 - 1
Degrees of freedom (df) = 15.
From the Student's t-distribution table, a critical value at t₀.₀₂₅, ₁₅ = 2.131.
Mathematically, the confidence interval for mean is given by:
Mean ± (t-critical × (standard deviation/√(sample size)))
75.5 ± (2.131 × (24.2/√(16))
75.5 ± (2.131 × 6.05)
For the upper end, we have:
75.5 + 12.89 = 88.39
For the lower end, we have:
75.5 - 12.89 = 62.61.
In conclusion, we can deduce that there isn't a significant difference between the mean wake time before and after treatment and as such, this drug isn't effective at the significance level of 0.05.
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Choose the correct answer below:
A- A rate is just a different name for a ratio. The terms are interchangeable
B-a rate refers to the reduced form of a ratio
C-rates are a special type of ratio that always have a 1 in the denominator
D- rates are a special type of ratio used to compare different kinds of quantities
Answer:
C
Step-by-step explanation:
The answer would have to be C cus it can't be A or D
EASY POINTS
Which answer represents the following conditional statement in shorthand?
Answer:
B
Step-by-step explanation:
if it is warm the Megan is swimming
suppose y varies inversely as x and y=12 when x=6 find y if x=8
Answer:
y = 9
Step-by-step explanation:
given that y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 6
12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction
72 = k
y = [tex]\frac{72}{x}[/tex] ← equation of variation
when x = 8 , then
y = [tex]\frac{72}{8}[/tex] = 9
Directions: In this last section, you will answer one problem. Be sure to read the
problem carefully and to answer the question completely. Show your work and circle
your answer. Use any method to solve this problem.
74. A restaurant has a total of 60 tables. Some of the tables can seat 4 people and some
seat 2 people. All of the seats are occupied when there are 160 people seated. How man
tables for 4 are there?
Answer:
40 tables
Step-by-step explanation:
I think lol I'm just guessing. Hope you get it right. If I'm right just remember me as legend or the chosen one.
Nadia has a handful of coins all of which are either dimes or quarters she has a total of 23 coins in her hand and a total of $3.65 worth of coins let D equal the number of dimes Nadia has and like Q represent the number of quarters she has. Must model the solution and show work.
Nadia cannot have 18 dimes and 5 quarters.
The equations that represent the question are:
D + Q = 23 equation 1
0.1d + 0.25q = 3.65 equation 2
The number of dimes is 14 and the number of quarters is 9.
Can Nadia have 18 dimes and 5 quarters?
The equation that represents the total amount of money she has is: 0.1d + 0.25q = 3.65
0.1(18) + 0.25(5) = 3.05
$3.05 is less than 3.65
What are the system of equations that models the situation?D + Q = 23 equation 1
0.1d + 0.25q = 3.65 equation 2
What is the solution to the equation?
Given the above equations, multiply equation 1 by 0.1
0.1d + 0.1q = 2.3 equation 3
Subtract equation 3 from 2
0.15q = 1.35
Divide both sides by 0.15
q = 1.35 / 0.15
q = 9
To determine the value of d, subtract 9 from 23 : 23 - 9 = 14
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PLS HELPPPPPPPPPPPP WILL GIB BRAINLIEST Jimmy Needs to buy 1'000 boxs of Mac n' cheese for a confrecne meeting.
Each box costs 50.Cent how much money will he have to buy.
After u figure out The answer divide that by the by 56.
A 84712 = FIRST.... 84712 ÷ = 393893.329432112
B 50000 = FIRST.... 50000 ÷ = 892.857142857
C 43792 = FIRST.... 9382784 ÷ = 94923.2232
D 37263 = FIRST.... 8438493 ÷ = 4095923.31
PART B
The answer you just figured out find out how much cents that equals in dollars
A 5000
B 2123
C 3282
D 3921
Answer:
its 500$ to buy 1000 mac and cheese at 50 cent a piece so im asuming the answer is A
Step-by-step explanation:
Trey deposits 5000 into an account that pays simple interest at an annual rate of 2%. he does not make any more deposits. he makes no withdrawals until the end of 6 years when he withdraws all the money
The simple interest Trey earns if he makes no additional deposit or withdrawal for a period of 6 years is 600
How to calculate simple interest?Principal = 5,000Rate = 2%= 2/100
= 0.02
Time = 6 yearsSimple interest = principal × rate × time
= 5000 × 0.02 × 6
= 600
Therefore, the simple interest Trey earns if he makes no additional deposit or withdrawal for a period of 6 years is 600
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Solve this problem, and identify the percent, amount, and base. What percent 60 of 15 is ?
Answer:
Step-by-step explanation:
'
A. 56
B. 154
C. 210
D. 252
Option A
Evaluate 5x – 2y + (7x – y) for x = 7 and y = –2. 90 –18 –45 63
The value of the expression 5x – 2y + (7x – y) when x = 7 and y = -2 is 90
How to evaluate the expression?The expression is given as:
5x – 2y + (7x – y)
Substitute x = 7 and y = –2 in the above expression
5 * 7 - 2 * -2 + (7 * 7 + 2)
Evaluate the expression
90
Hence, the value of the expression 5x – 2y + (7x – y) when x = 7 and y = -2 is 90
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2007 Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700 Aaron Priest had a taxable income of $165,000. He figured his tax from the single taxpayer table above. 1. Find his earned income level. 2. Entered the base amount. = $ 3. Found the amount over $ = $ 4. Multiplied line 3 by % = $ 5. Added Lines 2 and 4 = $ 6. Computed his monthly withholding would be = $
Answer:
$160850
Step-by-step explanation:
84102 - 1052=?
pasagot po pls with solution
Answer:
83050
Step-by-step explanation:
that's the answer to the question
If a city with a population of 283,900 doubles in size every 66 years, what will the population be 198 years from now
PLEASE HELP
The population after 198 years from now will be 2,270,200.
What is an exponent?Let a be the initial value and x be the power of the exponent function. Then the exponent is given as,
[tex]\rm y = 283,900\times (2)^{x/198}[/tex]
The population after 198 years from now will be calculated as,
[tex]\rm y = 283,900 \times (2)^{198/66}[/tex]
Simplify the equation, then we have
y = 283,900 x 8
y = 2,270,200
The population after 198 years will be 2,270,200.
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Theo's friend made a display with dimensions that were each half as long as those theo used. what is the approximate mass of theo's friends display
Answer:
great question buddy and I wish you the most
Step-by-step explanation:
x-y=b^2/2=2
Can someone help me with this problem?
The volume of the fourth doll based on the information given will be 549cm³.
How to calculate the volume?The formula to use will be:
= πr²h
where,
Volume = 8cm³
Diameter = 2.1
Radius = 2.1/2 = 1.05cm
Therefore, 8 = (3.14 × 1.05² × h)
h = 8/(3.14 × 1.05²)
h = 2.31 cm.
The scale factor used is:
= 3.36/2.1
= 1.6
Therefore, the diameter of the fourth doll will be:
= 2.1 × 1.6³
= 8.6
Radius will be:
= 8.6/2 = 4.3.
The height of the fourth doll will be:
= 2.31 × 1.6³
= 9.46
The volume of the fourth doll will be:
= 3.14 × 4.3² × 9.46
= 549cm³
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-6x +3>-39
sombody pls do this problem
Answer:
x>-7
Step-by-step explanation:
Answer:
x>-7
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
If the volume of a cube is 64 cubic inches, find the length of one edge
A rectangle has a width of 46 centimeters and a perimeter of 210 centimeters. What is the rectangles length?
Answer:
59 cm
Step-by-step explanation:
First, we can do 46x2=92 to find one part of the perimeter. 210-92=118. 118/2=59. So the length is 59.
Today only a table is being sold for $364.89. This is 38% of its regular price. What was the price yesterday
Answer:
$960.24
Step-by-step explanation:
Hello!
Let the regular price be x.
38% of x = 0.38x
0.38x = 364.89
Solve for x0.38x = 364.89x = 364.89/0.38x = 960.2368421053 ≈ 960.24The price of the table yesterday was around $960.24.
Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. The equation y = 15 + 110x – 16x2 can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint: If the pumpkin hits the ground, its height is 0 feet.)
Answer:
See below
Step-by-step explanation:
y = - 16x^2 + 110x + 15 is a dome shaped parabola
max will occur at x = -b/2a = - 110/(2*-16) = 3 7/16 seconds
using this value in the equation results in y = 204 units (feet?)
Height = 0 = -16x^2 +110x + 15 use quadratic formula
with a = -16 b = 110 c = 15 to find 7 seconds
Confirmed as of 12.14.22
Here you go! Please mark Brainliest! Tysm if you do and have a great holiday!
__________
1. $11.50
2. Distributive Property
3. x ->-4 and x -< 3
4. x = 0 or x = -3/2
5. D = all real numbers
R = {y | y -> 0}
6. y = 12/13x - 10/13
slope: 12/13; y-intercept: -10/13
7. y - 3 = 4/9 (x - 9)
8. (1/4, -7); x = 1/4; translated to the right 1/4 unit and down 7 units.
9. Graph C (representing the inequality y -< x/2 - 3)
10. Graph C (representing the system {x -> 0, y -< -1/8x + 5, y -> 5/8x - 1)
11. [ -12 -13 13 | -15]
[ 7 -10 -3 | 11]
[ 7 14 5 | -5]
12. Graph C (representing y = 3(x - 3)^2 + 3)
13. The pumpkin's maximum height is 204.06 feet and it hits the ground after 7.01 seconds.
14. 4x^2 + 3x - 6
15. 7/2 -+ sqrt17/2
16. -15
17. (0,3), (3,0)
18. -3. -2. 2
19. Graph C (Goes vertically down, up, then down again.)
20. -6, -2
21. 2, -2, 4i, -4i
22. s^4 + 15s^4 v + 90s^3 v^2 + 270s^2 b^3 + 405sv^4 + 243v^5
23. y = x - 2
24. f(x) = 295(1.07)^x; 338
25. y = 497(1/2)^38x; 462.029 kg
26. 4
27. 1.03
28. 4.55
29. r = Q/8s^2
30. x = 2
31. Constant of variation: -1/3
x = -63
32. (-1, 7, 5)
33. (x + 4)(6x + 7
______________________________________________
The equation that models the current water temperature t of the swimming pool is t -6=78 which best describes the error made when solving for the current temperature
I am 6 foot and 4 inches what is my height in metres?12 inches=to 1 foot and 1 foot=to 30 cm
Answer:
1.9 m
Step-by-step explanation:
1 ft = 30 cm (approximately)
12 in. = 1 ft
100 cm = 1 m
Find the height in ft:
4 in. / 12 in/ft = 1/3 ft
6 ft 4 in. = 6 ft + 1/3 ft = 6 1/3 ft
Convert ft to cm:
6 1/3 ft × 30 cm/ft = 190 cm
Convert cm to m:
190 cm × 1 m / 100 cm = 1.9 m
NO LINKS!!! Please help me with this problem
Answer:
1. 0.75
2. 0.15
3. 1
Step-by-step explanation:
1. P(student is female) = 1 - 0.25 = 0.75
2. P(student is male and does not walk to school) = 0.25 × 0.6 = 0.15
3. P(student walks to school or does not walk to school) = 0.4 + 0.6 = 1
Answer:
The sum of the probabilities of all possible outcomes is 1.
Given:
Male students = 25% = 0.25Students who walk to school = 40% = 0.4Therefore:
Female students = 1 - 0.25 = 0.75Part (a)
[tex]\begin{aligned}\sf P(\textsf{female}) & = 1 - 0.25\\ & = 0.75\\ & = 75\%\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}\sf P(\textsf{does not walk to school}) & = 1 - 0.4\\ & = 0.6\\ & = 60\%\end{aligned}[/tex]
[tex]\begin{aligned}\implies\sf P(\textsf{student is male and does not walk to school}) & = 0.25 \times 0.6\\ & = 0.15\\ & = 15\%\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}\implies\sf P(\textsf{student walks to school or does not walk to school}) & = 0.4+0.6\\ & = 1\\ & = 100\%\end{aligned}[/tex]
Solve: x = 27
A) X= 3
B) X = 3 and x = -3
C) X = 9
D) X = 9 and x = -9
Answer:
A) x=3
Step-by-step explanation:
I guess it's : [tex]x^{3} =27[/tex]
[tex]x^{3} =27[/tex]
[tex]x=\sqrt[3]{27}[/tex]
[tex]x = 3[/tex]
Lines AB and CD are parallel. The coordinates of point A are (-2,5), the coordinates of point B are (6,3), and the coordinates of point D are (8,5).
The equation of line CD is y =
Equation of the line CD is equals to [tex]y = \frac{-x}{4} +7[/tex].
What are parallel lines?" Parallel lines are defined as the lines in the same plane never intersect with each other. They are equidistant to each other in the same plane."
Formula used
[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
According to the question,
Given,
Coordinates of A [tex](x_{1},y_{1})[/tex] = ( -2 , 5)
Coordinates of B [tex](x_{2},y_{2})[/tex] = ( 6 , 3)
Substitute the value to get the slope of line AB we get,
[tex]Slope of line AB 'm_{1}' =\frac{3-5}{6-(-2)}[/tex]
⇒ [tex]m_{1} = \frac{-2}{8}[/tex]
[tex]= \frac{-1}{4}[/tex]
Coordinates of C [tex](x_{1},y_{1})[/tex] = ( x ,y)
Coordinates of B [tex](x_{2},y_{2})[/tex] = ( 8,5)
Substitute the value to get the slope of line CD we get,
[tex]Slope of line CD 'm_{2}' =\frac{5-y}{8-x}[/tex]
Lines AB and CD are parallel.
Slope of parallel lines are equal.
Therefore,
[tex]m_{2} = m_{1}[/tex]
⇒ [tex]\frac{5-y}{8-x}[/tex] [tex]= \frac{-1}{4}[/tex]
⇒[tex]5-y = \frac{-1}{4} (8-x)[/tex]
⇒ [tex]y = \frac{-x}{4} +7[/tex]
Hence, equation of the line CD is equals to [tex]y = \frac{-x}{4} +7[/tex].
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In the cycle-plane, what is the y-intercept of the graph of the equation y=6 (x-0.5) (x+3)
The y-intercept of the graph of the equation y = 6 (x - 0.5) (x + 3) will be negative 9.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The parabolic equation of the function is given below.
y = 6 (x - 0.5) (x + 3)
Then the y-intercept of the graph of the equation y = 6 (x - 0.5) (x + 3) will be
We know that for the y-intercept, the value of x is zero. Then we have
y = 6 (x - 0.5) (x + 3)
y = 6 (0 - 0.5)(0 + 3)
y = 6 (-0.5)(3)
y = -9
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2. Which statement about like terms is true?
O All equations have like terms.
Only equations with the variable x have like terms.
O Some equations do not have like terms.
O No equations have like terms.
Answer:
All equations have like terms
Which of the following is an identity?
sin²x sec²x +1 = tan²x cosec²x is an Identity and therefore Option C is an Identity.
What is a Trigonometric Identity ?Trigonometric Identities are based on Trigonometric ratios , these are useful in conversion of the ratios into each other and to solve the problems of Trigonometry.
There are four Identities Given
Among them Option C is an Identity because on solving it
sin²x sec²x +1 = tan²x cosec²x
(sin²x/cos²x) +1 = sin²x / (sin²x cos²x)
sin²x +cos²x = 1
Which is an Identity and
therefore Option C is an Identity.
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XO
0
1
2
3
4
5
6
f(x)
15
20
25
30
35
чо
45
Answer:
56
Step-by-step explanation: