Answer:
The trigonometric functions, sin, cos and tan for an angle are the primary functions. The value for cos 60 degrees and other trigonometry ratios for all the degrees 0°, 30°, 45°, 90°, 180° are generally used in trigonometry equations. These trigonometric values are easy to memorize with the help trigonometry table.
Cos 60 Degree Value
In a right-angled triangle, the cosine of ∠α is a ratio of the length of the adjacent side (base) to the ∠α and its hypotenuse, where ∠α is the angle formed between the adjacent side and the hypotenuse.
Cos 60 Degree value
Cosine α = Adjacent Side / Hypotenuse
Cos α = AC / AB
Cos α = b / h
Now, to find the value of cos 60 degrees, let us consider, an equilateral triangle ABC as given below:
Cos 60 Degree
Here, AB = BC = AC and AD is perpendicular bisecting BC into two equal parts.
As we know, cos B = BD/AB
Let us consider the length of each side as 2 units, such as AB = BC = AC = 2 units and BD = CD = 1 unit.
Therefore, the value of cos 60° = BD/AB = ½
In the same way, we can write the value of sin 60° and tan 60° by evaluating the required sides.
In right triangle ABD, by Pythagoras theorem:
AB2 = AD2+ BD2
22 = AD2 + 12
AD2 = 22 -12
AD2 = 4 – 1
AD2 = 3
AD = √3
Now, we have got all the sides of triangle ABD.
Sin 60° = AD/AB = √3/2
Tan 60° = AD/BD = √3 / 1 = √3
We can also write the value of cos 60 degrees in decimal form as:
cos 60° = 1/2 = 0.5
Also, we can write the values of sine, cosine and tangent with respect to all the degrees in a table.
Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.
Angle in Degrees 0 30 45 60 90 180 270 360
Angle in Radians 0 π/6 π/4 π/3 π/2 π 3π/2 2π
Sin 0 1/2 1/√2 √3/2 1 0 -1 0
Cos 1 √3/2 1/√2 1/2 0 -1 0 1
Tan 0 1/√3 1 √3 ∞ 0 ∞ 0
Unit Circle in Trigonometry
It is possible to give the values of trigonometric ratios with respect to radians equivalent to degrees, in case of a unit circle, whose radius is equal to one. The radian for a unit circle is denoted by π. In the below figure, the angle values are represented in degrees instead of radians.
Cos 60 Degree graph
You have learned about cos 60 degrees value along with other degree’s values here now. Also, the derived values for sin and tan with respect to degrees and radians. In the same way, we can find the values for other trigonometric ratios like secant, cosecant and cotangent.
Let us see some example where we can use the value of cos 60 degrees.
Example 1: Find the value of cos 60° + sin 30°.
Solution:
cos 60° + sin 30°
= cos 60° + sin (90° – 60°)
= cos 60° + cos 60°
= (1/2) + (1/2)
= (1 + 1)/2
= 2/2
= 1
Alternatively, cos 60° + sin 30° = (1/2) + (1/2) = (1 + 1)/2 = 2/2 = 1
Example 2: Calculate: 2 sin 60° – 4 cos 60°
Solution:
We know that, sin 60° = √3/2 and cos 60° = 1/2
Thus, 2 sin 60° – 4 cos 60° = 2(√3/2) – 4(1/2)
= √3 – 2
therefore it 3/2
Step-by-step explanation: Peace Out.... Have a good day
PLEASE GIVE MARK BRAINIEST I WORK SO HARD IT TOOK ALL DAY!!!
How to identify whether the word problem is about direct proportion, inverse proportion or partitive proportion?
The identification process of direct proportion, inverse proportion and partitive proportion is show below.
What is proportion?Proportion is comparison of things or magnitudes in terms of size, amount.
In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.
In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.
Partitive proportion is when the division of a quantity into two or more equal or unequal parts.
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find the slope of each line
Answer:
A. 5/3
Step-by-step explanation:
The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point 3 units to the left.
We can model this using rise/run
Rise = 5
Run = 3
5/3
The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”
What is the converse of the original statement?
The converse of the statement that says that If an item is not worth five dimes, then it is not worth two quarters is: If an item is worth five dimes it is worth two quarters.
What is the converse of a statement?By swapping the hypothesis and the conclusion, a statement can be made to mean the opposite. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel." If q, then p is the opposite of "if p, then q."
The converse of a statement may not always have the same truth value as the original. For instance, "All mammals are tigers" is the polar opposite of "All tigers are mammals." This is undoubtedly untrue.
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Samuel is remodeling his basement. One part of the planning involves the flooring. He
knows that he would like both carpet and hardwood but isn't sure how much of each he will
use. The most amount of flooring area he can cover is 2000 square feet. The carpet is $4.50
per square foot, and the hardwood is $8.25 per square foot. Both prices include labor costs.
Samuel has budgeted $10,000 for the flooring.
Write a system of inequalities to represent the maximum amount of flooring needed and
the maximum amount of money Samuel wants to spend.
A system of inequality to represent the maximum amount of flooring needed is c + h ≥ 2000.
A system of inequality to represent the maximum amount of money wants to spend is 4.50c + 8.25h ≥ 10,000.
How to write and solve this inequality?In order to solve this word problem, we would assign variables to the number of square feet of carpet and the number of square feet of hardwood for the given flooring area, and then translate the word problem into an algebraic inequality as follows:
Let the variable c represent the number of square feet of carpet.Let the variable h represent the number of square feet of hardwood.For the maximum amount of flooring needed, we have:
c + h ≥ 2000
For the maximum amount of money, we have:
4.50c + 8.25h ≥ 10,000.
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Weekly
wages at a certain factory
are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$350 and $400.
[ ? ]%
The probability that a worker selected at random makes between $350 and $400 = 0.34134
What is a z score formula?
The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.
By using the z score formula:
z = (x - μ) / σ
Where,
x = raw score
μ = mean
σ = Standard deviation
We are told in the question to find the probability that a worker selected at random makes between $350 and $400
Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.
z1 = (x1 - μ) / σ = (350-400) / 50 = -1
z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0
From tables, P(z <= -1) = 0.15866
P(z <= 0) = 0.5
Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134
Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134
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The state board of education has $5,647 to buy new calculators. each calculator costs $2. after buying as many calculators as it can with its budget, how much money will the state board of education have left over?
By basic arithmetic, the state board of education will have $1 left .
What is meant by basic arithmetic?The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.
Addition, subtraction, multiplication, and division are the four operations employed in arithmetic.
The total amount the state board has = $5647
The cost of calculator = $ 2
The total number of calculators bought = 5647/2
= 2323.5
≈ 2823
So, the cost of 2323 calculators
= 2823 × 2
= 5646
So, the money the state board of education left = $5647 - $5646
= $1
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what are the coefficients in 4x + 8y - 5
Answer:
Step-by-step explanation:
A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.
The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).
15÷(3+13)2
A 2
B 5
C p
D 2 over 5
Answer: D.
Step-by-step explanation:
1/7*5/3 um i need help plese i only have 1 secont
The product of the fractions 1/7*5/3 is 5/21.
The product of the fractions= product of the numerator/product of the denominator.
The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively.
We multiply the 1 and 5, the numerators and 7 and 3 the denominators.
Therefore the product of the fractions is 5/21.
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Answer:
5/21
Step-by-step explanation:
Given problem,
→ (1/7) × (5/3)
Let's solve the problem,
→ (1/7) × (5/3)
→ (1 × 5)/(7 × 3)
→ 5/21
Thus, the answer is 5/21.
Help please, I don't know how to get QS
The complete proof using the AAS congruence postulate and CPCTC is explained below to show that QT ≅ SR.
What is the AAS Congruence Postulate?When two angles of a triangle, and one of its side that is nonincluded are congruent to corresponding two angles and a nonincluded side in the another triangle, then both triangles are congruent by the AAS congruence postulate.
If two triangles are congruent, then all its corresponding parts are also congruent to each other based on the CPCTC theorem.
Below is the two-column proof that proves that side QT is congruent to side SR.
Statement Reasons
1. ∠R ≅ ∠T, QT ≅ SR 1. Given
2. ∠TQS ≅ ∠RSQ 2. Alternate interior angles
3. QS ≅ QS 3. Reflexive property
4. ΔTQS ≅ ΔRSQ 4. AAS
5. QT ≅ SR 5. CPCTC
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It takes 12 minutes per pound to cook a turkey and dinner is at
3:00 pm.
How many hours and minutes is this?
Answer:
The result is 2 hours
Hope this helped!
By rounding each number to 1 significant figure estimate to 6235.1 x 21.5
By rounding each number to 1 significant figure estimate to 6235.1 x 21.5 is 120000.
How can the numbers be rounded up?The concept of significant fiqure is based on the looking for the first non zero number that is resnt in the numbers , and that will be one significant figure, and it goes like that.
Then let us round each of the given fiqures into 1 significant fiqure as instructed:
6235.1 to 1 significant figure will be 6000 , because 6 is the first significant fiqure and the value that follow 6 is less than 5, it can not been approximated
21.5 to 1 significant figure will be 20
Then (6000*20) =120000
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six thousand seven hundred and fifty (6750) people who were free of disease x were enrolled in a cohort study in 1985 and followed with annual exams and interviews through 1995. exposure to factor a was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease x. data from the study at the end of follow-up are shown in the table (below). what is the incidence rate of disease x among persons exposed to factor a?
Option A is the correct choice (0.04)
The incidence rate of disease x among persons exposed to factor a is 0.04
The frequency of a particular incident over a predetermined time period is measured by the incidence rate or incidence. In the corporate world, sampling, surveys, and product testing can all be used to calculate an incidence rate.
Because 120 divided by the total number of exposed people yields the occurrence rate for disease X among those who have been exposed.
The incidence rate would be 4 per 100 people if multiplied by 100, however, this statistic is not specifically specified.
Therefore, those who were exposed to factor a had an incidence risk of disease x of 0.04
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COMPLETE QUESTION:
6,750 people who were free of disease X were enrolled in a cohort study in 1985 and followed by annual exams and interviews through 1995. Exposure to factor A was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease X. Data from the study at the end of the follow-up are shown in the following table. What is the incidence rate of disease X among persons exposed to factor A? Exposure to Factor A People with Disease X People without Disease X Not Exposed 30 3,720 Exposed 120 2,880
Select one:
a. 0.04
b. 0.19
c. 0.25
d. 4.00
e. 5.17
what is the probability that at least nine out of 12 cars have an acceptable emissions level? (round your answer to three decimal places.)
The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.
What is probability?The branch of mathematics which deals with the analysis of random phenomena is called probability. The probability of an event is defined as the ratio of favorable events to the total number of events.
P(E) = F(E)/T(E)
Where P(E) = probability of an event which occur\
F(E) = Number of favorable events
T(E)= Total number of events
Here given that the total number of cars T(E) =12
And the number of cars that have acceptable emissions level F(E) = 4
Hence Probability that at least nine cars have an acceptable emission level
=4/12
= 1/3
= 0.333
The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.
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Teresa estimates that the height of a giraffe in a zoo is 18 feet. In fact, it is 16 feet tall. What is Teresa’s percentage error? Use proportional relationships to solve the problem. Show all your work and round your answer to the nearest tenth.
Answer: 11.1%
Step-by-step explanation:
The formula for percent error is:
|Actual-predicted/predicted| * 100%
In the context of the problem:
Actual = 16 ft
Predicted = 18 ft
Plug these values into the equation:
|16-18/18| * 100% = percent error
11.11% = percent error
If you have any other problems about percent error, you should be able to just plug these values into the formula
wade is skiing on a circular ski trail that has a radius of 0.8 km. wade starts at the 3-o'clock position and travels 2.3 km in the counter-clockwise direction. how many radians does wade sweep out? 2.875 correct radians when wade stops skiing, how many km is wade to the right of the center of the ski trail? .7717 incorrect km when wade stops skiing, how many km is wade above of the center of the ski trail?
The solutions are,
The radians wade sweep out is 2.875 radians.
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
When wade stops skiing, he is 0.003km above the center of the ski trail.
Given that;
Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.
Radius (r) = 0.8km
Distance (s) = 2.3km
Here, we need to find three cases, they are;
Case(I): how many radians does wade sweep out;
The relation between radians and radius is given by,
s = rθ
2.3 = 0.8*θ
θ = 2.3/0.8
θ = 2.875
The radians wade sweep out is 2.875 radians.
Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;
Let, Ф = π - 2.875
Ф = 0.266 radians
Then, x = r*cosФ
x = 0.8*cos(0.266)
x = 0.799
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;
Let, y = r*sinФ
y = 0.8*sin(0.266)
y = 0.003
When wade stops skiing, he is 0.003km above the center of the ski trail.
Therefore, the required solutions are;
The radians wade sweep out is 2.875 radians.
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
When wade stops skiing, he is 0.003km above the center of the ski trail.
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Write an equation of a line that passes through the point (1, -2) and is parallel to the line y = x - 5.
Answer:
y = x - 3
Step-by-step explanation:
y - y1 = m( x - x1 )
y - (-2) = 1 (x - 1)
y + 2 = x - 1
y = x - 3
9. A family ordered 2 large pizzas for lunch. They ate
7
-
8
of one pizza and of the other pizza. What
fraction of a pizza was left for dinner?
118
b. 1/2
d. 12/12
b.
e.
318
334
C.
718
00
10
Answer:
9/16
Step-by-step explanation:
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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Here is a correlation, does it also represent causation? Explain you answer.
The miles driven and the amount of gasoline used.
Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.
What is causation in statistics?The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.
There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.
When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.
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PLEASE HELP!!!Which is an equation in point-slope form for the line that passes through the points (−1,4) and (3,−4)?
100 POINTS!!!!!
Answer:
y - 4 = - 2(x + 1)-------------------------
GivenPoints (-1, 4) and (3, - 4)Find the slopem = (- 4 - 4)/(3 - (-1)) = - 8/4 = - 2Use one of the points and the point-slope formy - y₁ = m(x - x₁)y - 4 = - 2(x - (-1)) ⇒ y - 4 = - 2(x + 1)Which equation has the solution x = 9? Select each correct answer 0 +7=8 24-2x = 13 | | 4 + 5x = 18 0¹²-3=6 02x-3 = 15 3x + 2 = 25
HELP PLS!
For x to be a solution, there must be the quantity x in the equation.
All the equations that contain x are :
+) 24 - 2x = 13
+) 4 + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25
We will solve for the value of x for each of the equation :
+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5
+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8
+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9
+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.
We can see, only the equation 2x-3 = 15 has x=9 as a solution.
Question 2
Which set of rational numbers is arranged from least to greatest?
O
O
O
O
-3.5, 4, 2, 3
11
-3.5, 4,3,2
113
2, 3.
1
4.-3.5
11
4.3.2, -3.5
11
10 pts
Answer:
The second option.
Step-by-step explanation:
We can figure this out by going down each option and checking if it works and is arranged from least to greatest.
The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.
This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.
The second option provides the numbers -3.5, -1/4, 1/3, 2.
This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.
If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.
Please help as I am confused
The region common to both the graphs as shown is the solution set.
What are the system of equations?A system of equations is a collection of two or more equations with a same set of unknowns
Given are the following quadratic inequalities -
x² - 6x - 7 < 0
3x² - 28x + 32 ≤ 0
We have the following quadratic inequalities -
x² - 6x - 7 < 0
3x² - 28x + 32 ≤ 0
We will plot both of them. The common region be the possible set of solutions to the given inequalities. Refer to the graph attached. The region common to both the graphs is the solution set.
Therefore, the region common to both the graphs as shown is the solution set.
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a department store chain is expanding into a new market, and is considering 24 different sites on which to locate 6 stores. assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected? a) 144 b) 96,909,120 c) 168 d) 134,596 e) 30 f) none of the above.
Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways
We can find the number of ways by multiplying the number of possibilities each store can have.
Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites
Therefore the number of ways is:
C = 24 * 23 * 22 * 21 * 20 * 19
C = 9,69,09,120 possibilities
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PLSSSS HELPPP UGRNETLY
The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)
How to determine the GCF of the expressions?From the question, we have the following statement
The greatest common factor of 45 and 27
Rewrite the given expression as follows
This is represented using
45 and 27
Factor out 3 from the expression
So, we have the following representation
15 and 9 => Factored 3
Factor out 3 from the expression
So, we have the following representation
5 and 3 => Factored 3 * 3
So, we have
Factored = 3 * 3 = 9
This represents the GCF
So, the GCF is 9
Factor the expressionIn (a), we have
5 and 3 => Factored 3 * 3
This means that
45 - 27 = 3 * 3(5 - 3)
Evaluate the product
45 - 27 = 9(5 - 3)
Hence, the factored expression is 9(5 - 3)
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how do I solve this?
Answer:
7
Step-by-step explanation: -13(-1) + 36 + 42(-1)
Step 1: -13(-1)= 13
Step 2: 13 + 36= 49
Step 3: 49 + 42(-1)= 49 + (-42)= 7
Solution: 7
suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.4 texts per day. assume a population standard deviation of 33.17 texts per day. compute the p-value. (round your answer to four decimal places.) p-value
The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435
The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.
The parameters are as follows:
The sample mean ([tex]\bar x[/tex]) = 118.4
The population standard deviation ([tex]\sigma[/tex]) = 33.17
The sample size (n) = 30
Calculate the z-score first.
[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]
according to the entire question, x = 128
So, we have:
[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]
As determined by the z table of probability, p = 0.9435395
or p = 0.9435 (approx.)
Consequently, the distribution's p-value is 0.9435.
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PLEASE HELP ASAP express
Answer: 5+3*3(3)-2= 30
Step-by-step explanation: Replacing x with 2 and using PEMDAS
10. A life insurance company found that
among its last 200 claims, there were six
dozen smokers. What is the ratio of smokers
to nonsmokers in this group of claimants?
Write in lowest terms.
for homework .