Answers
The simplified form of trigonometric functions by trigonometric formulas are listed below:
Case 1: 0.5√(2 - √3)
Case 2: (0.5√2) / (1 + 0.5√2)
Case 3: sin 6x
Case 4: sin θ
How to simplify and evaluate trigonometric functions
In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:
Case 1
sin 15° = √[(1 - cos 30°) / 2]
sin 15° = √[(1 - √3 / 2) / 2]
sin 15° = √[(2 - √3) / 4]
sin 15° = 0.5√(2 - √3)
Case 2
tan 22.5° = sin 45° / (1 + cos 45°)
tan 22.5° = (0.5√2) / (1 + 0.5√2)
The last two expressions are simplified and evaluated by double angle formulas:
Case 3
2 · sin 3x · cos 3x
sin 6x
Case 4
2 · sin 0.5θ · cos 0.5θ
sin θ
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Related Questions
Simplify: (x^2-5x-36)/(x^3-17x^2+72x)
Group of answer choices
(x+3)/(x-6)
1/(-2x)
(x+4)/(x-8)
(x+4)/(x^2-8x)
Answers
Answer:
(x + 4)/x^2 - 8x)
Step-by-step explanation:
I can’t seem to figure it out
Answers
The dimensions of the circles are as follows
1. Chord AB = 9
2. Chord FG = 6
3. Chord KM = 8
4. Arc length XY = 105 degrees
5. Arc length TU = 85 degrees
6. Arc length TU = 130 degrees
7. QS is the diameter because it bisects the chord and perpendicular to the chord
8. QS is not a diameter because it does not bisect the chord
9. QS is not a diameter because it is not perpendicular the chord
What is the relationship between chord and intercepted arcChords with matching measurements share congruence due to being equidistant from the circle's center.
Congruent radii stem from each chord midpoint, indicating two equivalent right triangles are created; therefore, their respective intercepted arcs also equal in degree measurement.
Therefore, if two chords possess uniform lengths, they will intercept equal degrees along the circle.
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The elevations of four locations are shown in the table. Which statement is true?
Location
New Orleans
Death Valley
Salton Trough
Rio Bravo
Elevation
(meters)
-2
-86
-69
95
New Orleans is closer to sea level than Salton
Trough.
Rio Bravo has a lower elevation than Salton
Trough.
New Orleans has a lower elevation than Death
Valley.
Rio Bravo is closer to sea level than Death
Valley.
Answers
The elevations of four locations.
Hence, the correct option is C.
Based on the elevation
New Orleans has an elevation of -2 meters, which means it is below sea level.Death Valley has an elevation of -86 meters, which means it is also below sea level, but at a lower elevation than New Orleans.Salton Trough has an elevation of -69 meters, which means it is also below sea level, but at a higher elevation than New Orleans.Rio Bravo has an elevation of 95 meters, which means it is above sea level, and thus cannot be closer to sea level than any of the other three locations.Therefore, New Orleans has a lower elevation than Death Valley.
Hence, the correct option is C.
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Use the sine ratio the cones any ratio or the inverse sine to solve for s round each answer to the nearest tenth
Answers
The value of x is given as follows:
x = 13.1 ft.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.We have that the important parameters are given as follows:
Hypotenuse of x.Angle of 57º opposite to the side of length 11.Hence the value of x is obtained as follows:
sin(57º) = 11/x
x = 11/sine of 57 degrees
x = 13.1 ft.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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The value of y varies jointly with the values of x and z. When x=4 and z=9, the value of y is 360.
What is the value of y when x=5 and z=12?
Group of answer choices
170
10
600
450
Answers
Answer:
C
Step-by-step explanation:
y = k * z , where k is any constant
x=4, z=9 , y=360
360 = k (4)(9)
360 = 36 k
k = 360/36
k = 10
y = 10 * z
when x=5 and z = 12
y = 10 (5)(12)
y = 600
A researcher claims that adult males in the U.S. have gotten fatter since 1980, when they weighed 180.4 pounds on average. In 2023, you gather a sample of 10 males and which showed an average of 197.9 pounds. Assume o = 20 and a = .05.
Answers
As our determined t-score (2.77) is larger than the critical t-value (2.262), we disregard the null hypothesis in favor of the alternative one
How to solve
Given data:
The 1980 mean weight (μ) was 180.4 pounds, while the 2023 sample mean weight (x) was 197.9 pounds;
additionally, the sample size (n) was 10 and the sample standard deviation (σ) was 20 pounds.
At a significance level of 0.05, we calculate the t-score by first dividing (x-μ)/(σ/sqrt(n)).
This gives us the value 17.5/6.32 or 2.77 for the t-score.
Afterward, it is necessary to find the critical t-value with a two-tailed test at a significance level α=0.05 in respect to having 9 degrees of freedom (df = n – 1 = 10 – 1 = 9).
This can be located through either a t-distribution table or an online calculator; the result displays the calculated critical t-value being approximately ±2.262.
As our determined t-score (2.77) is larger than the critical t-value (2.262), we disregard the null hypothesis in favor of the alternative one, signifying there is a glaringly significant disparity between the average mass of grown male adults from 1980 and 2023 which upholds the researcher's statement that since 1980, males in the U.S. have gotten heavier.
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The sports shop has 63 part-time employees and 27 full-time employees. What percentage of
the employees at the sports shop work part-time?
Write your answer using a percent sign (%).
Answers
Answer:
70%
Step-by-step explanation:
63 / (63+27)
63 / 90 = 0.7
Turn 0.7 into a fraction, 70 under 100
Then rewrite the fraction 70 under 100 to 70%
Alondra wrote the following incomplete statement. 4.3 < 4. _____ Which of the following strategies could Alondra use to help her complete the statement? Select all that apply.
A. Write any decimal value with a number greater than 3 in the tenths place
B. Write any decimal value with a number greater than 3 in the hundredths place
C. Write any decimal value greater than 30 hundredths
D. Write any decimal value with 2 digits
E. Write any decimal value with a 3 in the tenths place
Answers
The strategies that Alondra can use to complete the statement include:
A. Write any decimal value with a number greater than 3 in the tenths placeB. Write any decimal value with a number greater than 3 in the hundredths placeC. Write any decimal value greater than 30 hundredthsWhy are these strategies best ?When a decimal number is created by Alondra and possesses 4 or more in the tenths place, it will exceed 4.3, as stated to exemplify decimals including 4.31 or 4.32.
Similarly, if there are 3 units plus a greater number appended behind the second digit after the decimal point (hundredths place). Deriving an outcome extending further than 4.30 can occur for any value above that obtained from inputting the numbers 4 and 3 into their respective positions in a given sequence.
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The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 5.9% per hour.
How many hours does it take for the size of the sample to double?
Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answers
Answer:
11.72 hours
Step-by-step explanation:
In a continuous exponential growth model, the formula for the size of the population at time t is given by:
N(t) = N₀ * e^(rt)
where N₀ is the initial population size, r is the growth rate parameter, and e is the mathematical constant approximately equal to 2.71828.
To find the time it takes for the population size to double, we can set N(t) equal to 2N₀ and solve for t:
2N₀ = N₀ * e^(rt)
Dividing both sides by N₀:
2 = e^(rt)
Taking the natural logarithm of both sides:
ln(2) = rt * ln(e)
Since ln(e) = 1:
ln(2) = rt
Solving for t:
t = ln(2)/r
Substituting the given growth rate parameter of 5.9% per hour:
t = ln(2)/(0.059) ≈ 11.72 hours
Therefore, it takes approximately 11.72 hours for the size of the population to double.
Need help. This please
Answers
The domain of the function in this problem is given as follows:
all real numbers.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
On the graph, the domain of the function is given by the values of x of the function.
A quadratic function has no restrictions on the domain, hence it is defined by all the real values.
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Fill in the missing values to make the equations true.
Answers
Answer:
a)
[tex] log_{7}(3) - log_{7}(5) = log_{7}( \frac{3}{5} ) [/tex]
b)
[tex] log_{3}(11) + log_{3}(2) = log_{3}(22) [/tex]
c)
[tex] - 4 log_{8}(3) = log_{8}( {3}^{ - 4} ) = log_{8}( \frac{1}{ {3}^{4} } ) [/tex]
Directions - Find the sector areas of both the grey and white areas:
*Use 3.14 in place of
285⁰
8 in
in²
in
(round to two decimal places)
(round to two decimal places)
E
Answers
The sector areas of the grey and white areas are 159.09 in² and 41.87 in²
Finding the sector areas of the grey and white areas:From the question, we have the following parameters that can be used in our computation:
Radius, r = 8 inchesCentral angle,= 45 degreesThe area of shaded sector is calculated as
Area = Central angle/360 * π * Radius^2
Substitute the known values in the above equation, so, we have the following representation
Gray = 285/360 * 3.14 * 8^2 = 159.09White = (360 -285)/360 * 3.14 * 8^2 = 41.87Hence, the area is 159.09
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Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter. Write four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon.
Answers
All the four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon are,
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Given that;
Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter.
Now,
Here are four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon:
⇒ (1, 5) (2, 10) (3, 15) (4, 20)
Hence, In each pair, the first number represents the side length of the pentagon, and the second number represents the perimeter of the pentagon.
And, If you add 1 to the side length in each pair, you'll see that the perimeter increases by 5, just as Fernando learned in math class.
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20 Per Question, Algebra 2, Thanks :)
Answers
The fraction in factored form is determined as (x - 8)(x + 10) / (x - 10)(x + 8).
What is the quotient of the division?
The quotient of the division is calculated as follows;
( x² - 3x - 40 )/ (x² + 8x - 20) ÷ (x² + 13x + 40)/(x² + 12x + 20)
Factorize each of the expressions;
x² - 3x - 40
= x² + 5x - 8x - 40
= x(x + 5) - 8(x + 5)
= (x + 5)(x - 8)
x² + 8x - 20
= x² + 2x - 10x - 20
= x(x + 2) - 10(x + 2)
= (x + 2)(x - 10)
x² + 13x + 40
= x² + 5x + 8x + 40
= x(x + 5) + 8(x + 5)
= (x + 5)(x + 8)
x² + 12x + 20
= x² + 2x + 10x + 20
= x(x + 2) + 10(x + 2)
= (x + 2)(x + 10)
The fraction in factored form is written as;
(x + 5)(x - 8)/(x + 2)(x - 10) ÷ (x + 5)(x + 8)/(x + 2)(x + 10)
(x + 5)(x - 8)/(x + 2)(x - 10) x (x + 2)(x + 10)/(x + 5)(x + 8)
= (x - 8)(x + 10) / (x - 10)(x + 8)
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On average, 66% of the days in Seattle, Washington, are cloudy or rainy. Describe a model that you could use to simulate this situation.
Answers
Since on average, 66% of the days in Seattle, Washington, are cloudy or rainy, a model that could be used to simulate this situation is an experimental probability model of about 2/3.
How to describe a model that you could use to simulate this situation?In this scenario and exercise, you are to required to describe a model that you could be used to simulate a situation in which 66% of the days in Seattle, Washington, are cloudy or rainy on an average.
In this context, we can reasonably infer and logically deduce that the most accurate and feasible model to use would be an experimental probability model of about 2/3;
66% = 66/100 = 33/50 ≈ 2/3.
In conclusion, you should select two (2) red marbles that each represent cloudy or rainy days and one (1) blue marble that represent non-cloudy or non-rainy days, and then pick one marble randomly. Repeat several times in order to determine experimental probability that a day would either be cloudy or rainy.
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Una versión muy simplificada de una tabla de insumo-producto para la economía de Israel en 1958 divide dicha economía en tres sectores agricultura, manufactura y energía con los si-guientes resultados.
a) ¿Cuántas unidades de producción agrícola se requieren para obtener una unidad de produc-to agrícola?
b) ¿Cuántas unidades de producción agrícola se requieren para obtener 200 000 unidades de productos de esta naturaleza?
c) ¿Cuántas unidades de producción agrícola se requieren para obtener 50 000 unidades de energía?
d) ¿Cuántas unidades de energía se requieren para obtener 50 000 unidades de productos agrí-colas?
Answers
Note that:
a) 1 unit of agricultural production required to obtain 1 agricultural product.
b) 200,000 units of agricultural production are required to obtain 1 of agricultural product.
c) 22,727 units of agricultural production are required to obtain 50,000 units of energy.
d) we need 27,825 units of energy to produce 50,000 units of agricultural products.
How did we get the aabove answer?a) According to the table, the coefficient of production for agriculture is 0.293, that is
0.293 units of agricultural production = a unit of agricultural product.
b) To obtain 200,000 units of agricultural products we say
0.293 x 200,000,= 58,600 units of agricultural production.
c) the coefficient of production for energy with respect to agriculture is 0.044,
that is ,
0.044 units of agricultural production = a unit of energy.
So
50,000 units of energy,=
0.044 by 50,000,
= 2,200 units of agricultural production.
d) To obtain 50,000 units of agricultural products
use the Leontief inverse of the input-output table, which is simply the inverse of the coefficient matrix.
[ 3.4175 -0.2345 -0.5565 ]
[-0.1894 4.8264 -0.2114 ]
[-0.3074 0.1772 4.8324 ]
[ (3.4175 x0) + (-0.2345 x 0) + (-0.5565 x 50,000) ]
[ (-0.1894 x0) + (4.8264x 0) + (-0.2114 x50,000) ]
[ (-0.3074 x0) + (0.1772 x0) + (4.8324 x50,000) ]
[ -27,825 ]
[ -10,570 ]
[ 241,620 ]
Thus, we need 27,825 units of energy to produce 50,000 units of agricultural products.
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PLEASE HELP I WILL GIVE 20 POINTS
Data:
Record the data from each trial in the data chart below. Be sure to fill in the chart completely.
Test One
Parent 1: FF
Parent 2: Ff
Phenotype ratio:
________ : ________
short fur : long fur
Test Two
Parent 1: Ff
Parent 2: Ff
Phenotype ratio:
________ : ________
short fur : long fur
Test Three
Parent 1: ff
Parent 2: ff
Phenotype ratio:
________ : ________
short fur : long fur
Conclusion:
Your conclusion will include a summary of the lab results and an interpretation of the results. Please write in complete sentences.
Which genotype(s) and phenotype for fur length are dominant?
Which genotype(s) and phenotype for fur length are recessive?
If you have a hamster with short fur, what possible genotypes could the hamster have?
If you have a hamster with long fur, what possible genotypes could the hamster have?
Did your data support your hypotheses? Use evidence to support your answer for each test.
Test One:
Test Two:
Test Three:
Which hamsters are the parents of the mystery hamster? Include evidence to prove that they are the correct parents.
Answers
Answer:
Answer: Test One
Parent 1: FF
Parent 2: FF
Phenotype ratio:
short fur: long fur
Test Two
Parent 1: Ff
Parent 2: FF
Phenotype ratio:
short fur: long fur
Test Three
Parent l: ff
Parent 2: ff
Phenotype ratio:
short fur: long fur
Step-by-step explanation:
Answer: Test One
Parent 1: FF
Parent 2: FF
Phenotype ratio:
short fur: long fur
Test Two
Parent 1: Ff
Parent 2: FF
Phenotype ratio:
short fur: long fur
Test Three
Parent l: ff
Parent 2: ff
Phenotype ratio:
short fur: long fur
This data set represents the widths in yards of pieces of fabric used by a sewing group.
What is the mean of this data set?
{1 1/3, 1/4, 2/3, 1/2, 1 1/4}
Enter your answer as a fraction in simplest form in the box.
Answers
Answer:
[tex] \frac{4}{5} [/tex]
Which graph shows the correct solution to the linear-quadratic system of inequalities below?
{y<0.5x^2+1
5x-2y>=-10}
Answers
The graph of the linear and quadratic equation is attached below
What is the graph of linear and quadratic equationsA linear and quadratic system can be represented by a line and a parabola in the xy-plane. Each intersection of the line and the parabola represents a solution to the system.
A line and a parabola can intersect zero, one, or two times, which means a linear and quadratic system can have zero, one, or two solutions.
If a graph of the system is not provided, then the ability to quickly draw graphs based on equations is essential.
However, in this problem, we have the equation given and we can easily draw the graph using a graphing calculator.
The solution to the problem is attached below;
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What is the volume of a cylinder, in cubic ft, with a height of oft and a base diameter
of 16ft? Round to the nearest tenths place please:3
Answers
the volume of a cylinder is 2009. 6 cubic feet
How to determine the volumeThe formula for calculating the volume of a cylinder is expressed as;
V = πr²h
Given that the parameters in the equation are;
V is the volume of the cylinder.r is the radius of the cylinder.h is the height of the cylinder.From the information given, we have that;
Diameter = 2 radius
Substitute the values
Radius = 8ft
Then,
Volume = 3.14 × (8)² × 10
Find the square
Volume = 3.14 × 64 × 10
Multiply the values
Volume = 2009. 6 ft³
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Students are making lemonade from a powdered lemon drink mix. Jonathan mixes 2 cups of water and 7 teaspoons of powdered lemon mix. Maya mixes 1 cup of water and 7 teaspoons of powdered lemon mix. Whose mix will be more lemony?
Group of answer choices
Maya’s mix will be more lemony.
Jonathan’s mix will be more lemony.
The two mixes will be equally lemony.
Answers
Answer: Maya’s mix will be more lemony.
Step-by-step explanation:
We see that both Jonathan and Maya mix 7 teaspoons of the powdered lemon mix. Since we are finding whose mix will be more lemony, we need to find the person who added less water since their mixture will be less diluted.
This leads us to Maya, she only added 1 cup of water while Jonathan added 2 cups of water. Maya's mixture will have a higher concentration since she has a higher ratio of lemon to water than Jonathan.
Multiply 6 × 3 then divide by 2 how do you simplify that expression
Answers
Answer:
6 × 3 = 18
18 ÷ 2 = 9
Therefore, the expression 6 × 3 ÷ 2 simplifies to 9
Step-by-step explanation:
To simplify the expression, we follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right.There
are no parentheses or exponents,so we multiply 6 by 3 to give us 18.
Then we divide 18 by 2 to give us 9.
There for the Expression simplifies to 9.
HOPE IT HELPS.
PLEASE MARK ❣️‼️ ME AS BRAINLIEST .
simple interest see question
Answers
Answer:
P((1 + r)^6) = 1,675.80
P((1 + r)^5) = 1,606.50
------------------------------
b) 1 + r = 266/255, so r = 11/255 = .04 = 4%
a) P((1 + 11/255)^5) = 1,606.50
P = $1,300.69
determine the volume of the composite figure below. round to the hundredths place if needed.
Answers
The volume of the composite figure is calculated as:
= 1,894.2 cm³
What is the Volume of the Composite Figure?The volume of the composite figure can be calculated using:
Volume = volume of rectangular prism + 1/2(volume of cylinder)
Volume of rectangular prism = length * width * height
length = 15 cm
width = 2(6) = 12 cm
height = 10 cm
Volume of rectangular prism = 15 * 12 * 10 = 1,800 cm³
Volume of half Cylinder = 1/2(πr²h)
r = 6 cm
h = 10 cm
π = 3.14
Volume of half Cylinder = 1/2(πr²h) = 1/2 * 3.14 * 6 * 10 = 94.20 cm³
Volume of the composite figure = 1,800 + 94.20 = 1,894.2 cm³
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Please help ASAP math question
Answers
The possible values of x, given the number of bets are $54,999, $14,999, and -$1.
The expected winnings would be -$0.97.
How to find the expected winning ?The possible values of the net winning would be the amount you win at net if you win first prize, second prize, or nothing.
The possible values would therefore be:
$54,999, $14,999, and -$1.
These show that if you win the first or second prize, you will deduct the $ 1 you bet. And if you win nothing, you would have lost $ 1.
The expected winnings would be:
= ∑ ( Probability of event x Potential net win / loss)
= ( 1 / 3, 000, 000 x 54, 999 ) + ( 2 / 3, 000, 000 x 14, 999 ) + ( 2,999, 997 / 3, 000, 000 x - 1 )
= - $ 0.97
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
hope this helps !!
Answer: It's 30.
Step-by-step explanation: The dot at 200 on "Amount Spent" is also right between 20 and 40. Which is 30, your answer.
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?B)
B) 23 – 6x – 24 = x – 15
C) –1 – 6x = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answers
The step that indicates the addition property of equality while solving the equation -1 - 6x = x - 15 is : (b) -1 - 6x + 15 = x - 15 + 15.
The "addition-property" of equality states that if we add the same quantity to both sides of an equation, the equation remains true.
In the equation -1 - 6x = x - 15, we need to isolate the variable term 'x'.
To isolate variable "x", we are adding 15 to both sides of the equation, which is the addition property of equality. This step simplifies the equation and isolate the variable "x" on one side.
So, we get, -1 - 6x + 15 = x - 15 + 15,
Therefore, the correct step indicating the "addition-property" is (b).
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The given question is incomplete, the complete, the complete question is
Which of the following steps indicates the addition property of equality while solving the equation -1 - 6x = x - 15?
(a) x = 14/2
(b) -1 - 6x + 15 = x - 15 + 15
(c) -1 - 6x = x - 15
(d) 23 - 6x - 24 = x - 15
What is the length of the DF? (Round to the tenths place)
Answers
The length of DF in the triangle DEF is 10.8 units
The given triangle is DEF
We have to find the length of side DF
We know that the tan function is a ratio of opposite side and adjacent side
tan 42 = DF/12
0.9 =DF/12
DF=12×0.9
DF=10.8
Hence, the length of DF in the triangle DEF is 10.8 units
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please help me i don’t understand how to make the parabola wider
Answers
Answer:
The smaller the coefficient (the number in front of the x), the wider the parabola
Step-by-step explanation:
the pH of a liquid is measure of how acidic or basic it is. the concentration of hydrogen ions in a liquid is labeled [H+]. use the formula pH=-log[H+] to find the pH level, to the nearest tenth, of a liquid with [H+] about 4.3 x 10^-14
13.4
14.6
-13.4
-14.6
any other answers from the Exponential and Logarithmic functions unit test part one? really struggling, offering 20 points and brainliest
Answers
pH = -log(4.3 x 10^-14)
pH = -(-13.37)
pH = 13.4
Therefore, the pH level of the liquid with [H+] about 4.3 x 10^-14 is 13.4 to the nearest tenth.