The exact values of the six trigonometric functions for the point (x, y) = (20, 21) are listed below:
sin θ = 21 / 29, cos θ = 20 / 29, tan θ = 21 / 20, cot θ = 20 / 21, sec θ = 29 / 20, csc θ = 29 / 21
How to determine the exact six trigonometric functions related to a point in rectangular format
Points in rectangular format are points of the form (x, y), where x and y represent the position of the point respect to the origin and along the respective orthogonal axis.
The line segment between the origin and that point represents the hypotenuse of a right triangle. Then, we can determine the six trigonometric functions by using the following formulae:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
If we know that x = 20 and y = 21, then the exact values of the trigonometric functions are:
sin θ = 21 / √(20² + 21²)
sin θ = 21 / 29
cos θ = 20 / √(20² + 21²)
cos θ = 20 / 29
tan θ = 21 / 20
cot θ = 20 / 21
sec θ = √(20² + 21²) / 20
sec θ = 29 / 20
csc θ = √(20² + 21²) / 21
csc θ = 29 / 21
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can somebody please solve this if you send picture please send good quality
Explain+how+you+csn+use+similar+triangles+to+find+a+missing+measurement.++Write+a(n)+that+uses+the+missing+measurement+because+the+++are++
You can use similar triangles to find missing measures according to proportional relationships.
What are similar triangles?Similar triangles are two triangles that share these two features listed as follows:
Same angle measures.Proportional side lengths.The second feature, the proportional side lengths, is what is used to find the missing measures, as proportional relationships are built according to them.
When two triangles are similar, the equivalent side lengths have to be identified for the two triangles, and those are the sides that have the same angle measures.
Then, for the two triangles, the equivalent sides will have proportional lengths, and then these equations will involve a missing length. Then cross multiplication is applied and the equation can be solved for the missing length.
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y≥x²+2x-8 factor the quadratic equation to find x intercepts
The factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)
What is meant by quadratic equation?A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown value and a, b, and c represent known numbers. In general, a = 0; equations with a = 0 are considered degenerate because the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, and they can be distinguished by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.
To find x-intercept y=0
y≥x²+2x-8
x²+2x-8≥0
x²+4x-2x-8≥0
x(x+4)-2(x+4)≥0
(x-2)(x+4)≥0
∴x≥-4, x≥2
∴(-∞, -4]∪[2, ∞)
Therefore, the factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)
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Solve the following equation for y. 3y - 7(y + 5) = y - 35 Also Show your work Describe and show each step taken.
A. y = 0
B. y = 1
C. y = 2
D. All real values for y are correct solutions.
The equation is,
→ 3y - 7(y + 5) = y - 35
Now the value of y will be,
→ 3y - 7(y + 5) = y - 35
→ 3y - 7y - 35 = y - 35
→ -4y - y = -35 + 35
→ -5y = 0
→ y = 0/-5
→ [ y = 0 ]
Hence, option (a) is correct.
let x be the exam grade of a random student taking calculus 1 at uiuc. suppose professor smith takes a random sample of 140 students from the calculus 1 class to see how they did on the exam. in his sample, he got a mean of 86 and a standard deviation of 11. approximate the probability that (the sample mean) would be higher than 88.4 or smaller than 84.4?
The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = 86
sample size, n = 140
standard deviation, σ = 11
The probability
P(z > 88.4) + P(z < 84.4)
z score for z < 88.4
z = (88.4 - 86) / 11
= 0.21818 p value = 0.41364
z score for z < 84.4
z = (84.4 - 86) / 11
= -0.14545
p value for z < -0.14545 = 0.44218
The probability required = 0.41364 + 0.44218 = 0.85582
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To keep in shape, Leah exercises at a track near her home. She requires 84 minutes to do 8 laps running and 10 laps walking. In contrast, she requires 66 minutes to do 2 laps running and 10 laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Leah take to complete a lap? Leah takes minutes to run a lap and minutes to walk a lap.
Using a system of equations, it is found that:
Leah takes 3 minutes to run a lap and 6 minutes to walk a lap.
What is the system of equations?The variables of the system of equations are presented as follows:
Variable x: time required to complete a lap running.Variable y: time required to complete a lap walking.She requires 84 minutes to do 8 laps running and 10 laps walking, hence the first equation is:
8x + 10y = 84.
She requires 66 minutes to do 2 laps running and 10 laps walking, hence the second equation is:
2x + 10y = 66.
Simplifying by 2, we have that:
x + 5y = 33.
x = 33 - 5y.
Replacing in the first equation, we can find the time it takes to walk a lap, as follows:
8(33 - 5y) + 10y = 84.
264 - 40y + 10y = 84
30y = 180
y = 180/30
y = 6 minutes.
Then the time it takes to run a lap is obtained as follows:
x = 33 - 5y = 33 - 5(6) = 33 - 30 = 3 minutes.
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a cashier cannot tell the difference between cilantro and parsley. customers would only buy either cilantro or parsley. he knows that 20% of his customers prefer parsley. these customers will buy parsley 40% of the time when shopping. otherwise, they wouldn't buy either herb. 40% of his customers prefer cilantro and will buy cilantro 15% of the time when shopping. otherwise, they wouldn't buy either herb. the other 40% of his customers don't prefer, and thus don't buy, either herb. given the next customer buys one of the two herbs, what is the probability it is parsley?
Probability that customer buy parsley given buy any of two herb
= 0.5714
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Parsley ( 0.4 , 0.6 )
buy = B ∩ P = 0.08
Don't buy = DB ∩ P = 0.12
Cilantro = ( 0.15 , 0.85 )
buy = B ∩ C = 0.06
Don't buy = DB ∩ C = 0.34
Don't buy anything = DB = 0.4
P( Buy anything ) = P(B∩P) + P( B ∩ C )
= 0.08 + 0.06 = 0.14
Now, P( P/B) = P( P ∩ B)/P(B)
= 0.08/0.14 = 4/7 = 0.5714
Hence, probability that customer buy parsley given buy any of two herb
= 0.5714
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Hey, I haven't been able to get any of these right, I wasn't a there the day we learned this and i'm needing help getting the rest of it done before 3:00. Could any of you please help me out on this, it'd mean a lot!
The correct graph for each of the equations are respectively;
5) Graph C
6) Graph A
7) Graph B
How to Interpret Linear Equation Graphs?The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
5) We are given the linear equation as;
-9x + 3y = 0
3y = 9x + 0
y = 3x + 0
The slope is 3 and y-intercept is zero. Thus, the correct graph for this function is; Graph C
6) We are given the linear equation as;
4x - 6y = 12
Rearranging we have;
6y = 4x - 12
y = ⁴/₆x - 2
y = ²/₃x - 2
Thus, slope is 2/3 and y-intercept is -2. The correct graph is graph A
7) The correct graph of the function 25x - 10y = -50 is the graph B.
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A biology class examined some flowers in a local meadow. They saw 60 flowers, of which 70% were perennials. How many perennial flowers did the students see?
The number of perennials flower from 60 flowers seen by the students with of which 70% were perennials flowers is 42.
What is perennial flower?Perennials Flowers are plants that live more than two years.
To calculate the amount of perennial flowers seen by the students, we use the techniques of percentage.
Using the formula,
P = N(q)/100............. Equation 1Where:
P = Number of perennial flowers seen by the studentsN = Total number of flowers seenq = Percentage of perennials flowers from the total number of flowers seen.From the question,
Given:
N = 60 flowersq = 70%Substitute these values into equation 1
P = (60×70)/100P = 42.Hence, the number of perennials flower is 42.
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Can somone help me with this will mark u brainliest
Answer: 2[tex]\sqrt{2}[/tex]
Step-by-step explanation: First plug in the value, which is [tex]\sqrt{8}[/tex]
Then divided to 2[tex]\sqrt{2}[/tex]
the length length of a species of plants is normally distributed with expected value 60 cm. it is known from past experience that seventy five percent of theses flowers have length between 50 and 70 cm. what can we say about the standard deviation of the length of this plant?
The standard deviation of the length of this plant be 25.
m = 60(mean)
Let the standard deviation be s,
As, the probability for 50<x<70 be 0.75
Z = (x−m)/s
for x=50,
Z=0
for x=70,
Z=(70−50)/s=20/s
Now, the probability for 50<x<70 be,
P(50<x<70) = 0.75
In the standard form 0<z<(20/s)
using Z-table, the area from 0 to 20/s,
= 0.75
s = 25
Hence, the standard deviation of the length of this plant be 25.
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what value of x will make the triangles similar by the sss similarity theorem? what value of x will make the triangles similar by the sss similarity theorem? 15.9 59 77 96.8
By applying the SSS similarity theorem, the value of x that will make the provided triangles similar is 77.
SSS Similarity Theorem: What is it?
The SSS similarity theorem is used to determine whether or not two triangles are similar.
The side-side-side, or SSS. According to this theorem, triangles are comparable if all three sides of one triangle are proportional to the three equivalent sides of another triangle.
The first triangle's sides in the example figure are 35, 20, and 20. The second triangle has sides x, 44, and 44.
So, according to the SSS similarity theorem,
x/35 = 44/20
x =44 *35 /20
x =77
By applying the SSS similarity theorem, the value of x that will make the provided triangles similar is 77.
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Answer:28
Step-by-step explanation:
a rancher plans to use 170 yards of fencing to enclose a rectangular corral and to divide it into two parts with a fence parallel to the shorter sides of the corral. find the dimensions of the corral if its area is to be 1200 square yards.
The dimensions of recangle is = 30 yrds.
What is the area of rectangle?Any shape's area can be calculated by counting how many unit squares will fit inside of it. A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area.Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangular floor's area.acc to our question-
2000 = 160x - 3x^23x^2 -160x + 2000 = 0x = [160 +- sqrt(160^2 - 4*3*2000)]/6x = [160 +- sqrt(1600)]/6Positive solution:x = [160 + 40]/6x = 200/6x = 33 1/3 yrds. (side);Learn more about area of rectangle click here:
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What is the solution of the inequality -8(x + 7.5) ≤ 10?
Step-by-step explanation:
-8(x + 7.5) ≤ 10?
expand left side:
-8x - 60 ≤ 10
subtract 60 to both sides:
-8x - 60 + 60 ≤ 10 + 60
-8x ≤ 70
dive both sides by -8: (Remember when dividing by a negative number, you flip the direction of the inequality sign)
-8x/-8 ≥ 70/-8
x ≥ -35/4
reduce right side:
x ≥ -35/4 or x ≥ -8.75 [depends on if you need fractional or decimal format]
so in set builder format: [-35/4 , ∞) or [-8.75 , ∞) [depends on if you need fractional or decimal format]
Suppose the temperature in your town is 88°F and rising 1.5°F every hour, h. In how many hours will the temperature be over 100°F? Write an inequality representing the situation. Solve the inequality.
Determine the distance between the points (−2, −3) and (2, 0). 2 units 4 units 5 units 10 units
The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x 2 - x 1) 2 + (y 2 - y 1) 2. where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The order of the points does not matter for the formula as long as the points chosen are consistent.
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Answer:
it is 5 units!
the population etiologic fraction is a measure of the proportion of the disease rate in a population attributable to the exposure of interest. this measure of effect is influenced by:
The relative risk of the disease influences this measure of effect in exposed individuals versus unexposed individuals and the prevalence of exposure in the population.
As stated, the population etiology fraction measures the disease rate in a population attributable to the exposure of interest. A measure that is primarily determined by the exposure caused by a particular disease. Therefore, it may be influenced by the relative risk of the disease in exposed individuals versus unexposed individuals, as well as the prevalence in the population of the exposure.
An epidemiological tool is the Population Attributable Risk, also called the Etiologic Fraction or Attributable Fraction. Efforts to eliminate a given risk factor would be expected to reduce the attributable risk to a specific percentage. The attributable risk of disease is calculated by combining the relative risk for a given exposure with the prevalence of the exposure in the population.
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Place a. Point on the number line to show the value that is 1/10 of 0.5
The value of 1/10 of 0.5 lies between 0.1 and 0.2
What is Number line?A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
Given:
Point on the number line to show the value that is 1/10 of 0.5
So, 1/10 of 0.5
= 1/10 x 0.5
= 0.05
Hence, the value of 1/10 of 0.5 lies between 0.1 and 0.2
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Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
The cars are 315 miles apart 1.5 hours after they start moving. Use the answer
from part (c) to write an equation.
find the value of the expression when a=2 and b=7
The value of the expression when a=2 and b=7 is 41.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, the expression given is 3a + 5b and we want to find the value of the expression when a=2 and b=7.
This will be illustrated thus:
= 3a + 5b
= 3(2) + 5(7)
= 6 + 35
= 41
The value is 41.
The complete question is given below.
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Complete question
The expression given is 3a + 5b. Find the value of the expression when a=2 and b=7
events which can never occur together in probability theories then it is classified as? a. mutually exclusive events b. collectively exclusive events c. mutually exhaustive events d. none of these
In probability theories, events which can never occur together are classified as "mutually exclusive events" that is option A.
What is mutually exclusive event?Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, serve as an obvious illustration. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot get both outcomes. Since they do not occur at the same time, such events are also known as disjoint events.
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Maria was memorizing her lines for a play. There were 8 pages to memorize, and she had 4 lines on each page. How many lines did Maria memorize in all?
Given the circle below with chords ST and UV. Find the length of TW. Round to the nearest tenth if necessary.
Answer:
TW = 16.8
Step-by-step explanation:
When two chords of a circle intersect inside the circle, then the product of the lengths of the chords of one segment equals the product of the lengths of the segments of the other chord.
Here,
TW × WS = UW × WV
TW × 30 = 18 × 28
TW = (18 × 28)/30
TW = 16.8
The value of TW is 16.8 in a circle.
What is a chord of a circle?The product of all the chord values of one segment, where two chords from a circle cross from within the circle, equaled the product of the chord measures of each additional segment. The value of the cord will be the distance with respect to the circle that is present in the circle.
The value of WS = 30
The value of UV = 18
The value of WV = 28
The value of TW is:
TW × WS = UW × WV
TW × 30 = 18 × 28
TW = (18 × 28)/30
TW = 16.8
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Help? Fractions/visual
3/3 * 3/4 is fraction of green color .
What is fraction in math?
Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.green colored boxes = 3
blue colored boxes = 3
fraction of green = 3/3 * 3/4
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please help with this im strugglingggggggg
The dimensions of the kennel and the size of the cylinder indicates;
4.1.1. The two 3D objects which the figure consists of are a triangular prism that lays on top of a rectangular prism at the bottom.
4.1.2. The area of the wood needed to build the dog kennel is approximately 2.85 m²
4.1.3. The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers
4.2. The new height of the water in the container will be approximately 18 cm.
What is the surface area of a solid?The surface area of a solid is found by adding together the area of the surfaces that enclose the solid.
4.1.1. The two 3D objects in the figure are;
A triangular prismA rectangular prism4.1.2. The amount of wood needed is found by finding the surface area, A, of the dog kennel as follows;
A = 2×80×60+2×50×60+50×80+2×0.5×80×40+2×√(40²+40²)×50
A = 22800 + 80·√2×50 = 22800 + 4000·√2
The amount of wood needed = (22800 + 4000·√2) cm²
1 m² = 10,000 cm²
(22800 + 4000·√2) cm² = ((22800 + 4000·√2))/10,000 m²
((22800 + 4000·√2)) cm² = (2.28 + 0.4·√2) m² ≈ 2.85 m²
The amount of wood needed is approximately 2.85 m²4.1.3. 500 milliliters of paint is enough to for 1.5 m² area
The number of containers of paint containers required, n, is therefore;
[tex]n = \dfrac{(2.28 + 0.4\cdot \sqrt{2}) \, m^2 }{1.5 \, m^2/container} = (1.52+0.\overline 6\cdot\sqrt{2} ) \, containers \approx 2 \, containers[/tex]
The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers4.2 Diameter of the base of the water container = 20 cm
Radius of the base = (20 ÷ 2) cm = 10 cm
Height of water in the container = 15 cm
Volume of water added = 1,000 cm³
The new height will be 15 + (1,000/(π×10²)) = (15 + 10/π) cm ≈ 18 cm
The height of the water in the container will rise to approximately 18 centimeters
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If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 3.
The probability is
The probability that the sum of the dice is 9 is, 4/33.
What is dice?
Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.
Let two fair dice are rolled.
So the possible number of outcomes are,
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4,6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
There are total 36 outcomes.
There are 33 outcomes with sum greater than 3.
The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).
Hence, the probability that the sum of the dice is 9 is, 4/33.
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Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:[tex]x2{12}5\\ =18[/tex]
Rhombus EFGH is rotated 90° counterclockwise about vertex G. How many pairs of parallel sides does the rotated figure have?
The number of pairs of the parallel lines after the rotation is 2
How to determine the number of pairs of the parallel lines?The transformation is described by
Rotation by 90° counterclockwise about vertex G
There are four types of transformation, and they are:
DilationRotationReflectionTranslationAs a general rule of rotation:
When a shape, line or an angle is rotated, the size of the properties in the rotated figure remains unchanged
Before rotation, a rhombus has two pairs of parallel sides
This means that the parallel sides would remain parallel after rotation
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find the number that is 33 greater than twice the opposite of itself
Answer:
11
Step-by-step explanation:
x = 2(-x) + 33
x = -2x + 33
x + 2x = 33
3x = 33
3/3 x = 33/3
x = 11
Write an equation in point-slope form for the line that passes through the
point with the given slope.
(-6, -3), m = -1
Answer:
( y + 3 ) = - ( x + 6 )
Step-by-step explanation:
The Equation of Line in Point-Slope Form is
[tex](y-y_1)=m(x-x_1)\\where\ m \is \ the \ slope\ and \ (x_1 , y_1) \ is \ any \ point \ on \ the \ line[/tex]
So by Substitution by the Givens
( y - (-3) ) = -1( x - (-6) )
( y + 3 ) = - ( x + 6 )
Glad to Help