There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
sin²x = (sec x - cos x) / sec x is,
sin²x + cos²x = 1
(proved)
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
sin²x = (sec x - cos x) / sec x
We will prove that,
sin²x + cos²x = 1
sec x = 1/cos x
Now,
sec x - cos x
= 1/cos x - cos x
= (1 - cos²x) / cos x
Now,
sin²x = (1 - cos²x) / [(cos x) x 1/cos x]
sin²x = 1 - cos²x
sin²x + cos²x = 1
Proved
Thus,
sin²x = (sec x - cos x) / sec x is,
sin²x + cos²x = 1
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Evaluate the expression and enter your answer in the box below.
|42|
Answer:
42
Step-by-step explanation:
because the distance between 42 and zero is 42
Find the GCF if 8 and 15
A.1
B.2
C.3
D.5
1 is the greatest common factor of 8 and 15 .
What is GCF ?GCF stand for greatest common factor.It is a set of numbers is the largest factor that each and all the number share. GCF is also often used to find the common denominator.
First we need to write common factor of each number.
The common factors of 8 = ( 1,2,4,8)
The common factor of 15= (1,3,5,15)
1 is the only one common factor here which is divides both 8 and 15.
So 1 is the only and GCF of 8 and 15.
Thus, 1 is the right answer.
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josh and dan each want to save $600 to attend a sports camp. josh has saved 60% of the amount. dan $320 .who saved more money?
what number solud you multipluy both sides by to solve for x
The amount of money that Josh has is more than the amount of money that Dan has.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Josh and Dan each need to save $600 to go to a games camp. Josh around has saved 60% of the amount. Dan has $320.
The amount of money that Josh has is given as,
⇒ 60% x $600
⇒ 0.6 x $600
⇒ $360
The amount of money that Josh has is more than the amount of money that Dan has.
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Ernesto guesses there are 69 marbles in a jar, but there are actually 60.
What is the percent error in Ernesto's guess?
Answer:
15%
Step-by-step explanation:
Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:
60 = 100%
68 = x
x = 69x100/60
x = 115
That means 69 is 115% of 60, which means that the error is of:
115 - 100 = 15%
Hope this helps, have a great day! :D
Hey y’all can y’all help me again
Answer:
Answer
Step-by-step explanation:
10. is (-1,0)
12. is (3,0)
14. is (1,0)
all of the following increase the width of a confidence interval except a. decreased sample size b. increased sample size c. increased confidence level d. increased variation
The width of a confidence interval increase except increased sample size , the correct option is (b) .
In the question,
it is asked that which option will decrease the width of a confidence interval ,
we know that the ,
the decrease in sample size increases the width of the confidence interval , and
the increased confidence interval also leads to increase in width of confidence interval , and
the increase in variation also leads to increase in the width of the confidence interval .
So , the only option that decreases the width of the confidence interval is increased sample size
that is increase in sample sizes causes smaller confidence interval.
Therefore , the correct option is (b) .
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What is 35.7 divided by 0.07
Answer:
510
Step-by-step explanation:
Answer: The answer is 510
Step-by-step explanation:
35.7/0.07 = 510
Jordan and his children went into a grocery store and he bought $13.50 worth of apples and mangos. Each apple costs $1.50 and each mango costs $0.75. He bought 6 more mangos than apples. Determine the number of apples and the number of mangos that Jordan bought.
The number of apples and the number of mangos that Jordan bought is
8 apples and 2 mangoesHow to find the amount Jordan boughtThe worth of apple and mango is $13.50
Each apple costs $1.50 and each mango costs $0.75
let the amount of apple by x then amount of mangoes be y. such that
1.50x + 0.75y = 13.50
6 more mangoes than apples this means that
x = y + 6
x - y = 6
the two equations formed are
1.50x + 0.75y = 13.50
x - y = 6
solving the simultaneous equation gives
x = 8
y = 2
The number of apples bought is 8 and the number of mangoes bought is 2
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Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k. What test can you use to check whether the true average is 59k?.
To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted.
What is an Average?
In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.
It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.
When we analyze the given question, we find that,
The total number of students were 49,
The true average was found to be 59k,
and the Sample average is found to be 44k.
Thus, in the present question we will use the One- sample T-test.
We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.
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let n be a three digit positive integer with all different signs. what can we say about the difference between n and its reverse
By using the expanded form of a number, it can be concluded that
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
What is expanded form of a number?
Every number can be written as a sum of the place value of its digit. This is known as expanded form of a number
Let the three digit positive integer be n = abc where a, b and c are distinct positive integers
n can be written as 100a + 10b + c
Its reverse is n' = cba
n' can be written as 100c + 10b + a
Difference between the number and its reverse
= 100a + 10b + c - 100c - 10b -a
= 99a - 99c
= 99(a - c)
= Since a and c are distinct, a - c [tex]\neq[/tex] 0
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
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Zahra used a 40% discount coupon while purchusing new clothes . her total bill , after discount , was AED 600. What was the original amount of the bill?
Answer:
AED 1000
Step-by-step explanation:
The price is 600 after 40% discount
if original price is ,
100% : x = 60% : 600
1 : x = 0.6 : 600
600 = 0.6x
x = 1000
if the measure of an interior angle of a regular polygon is 120 degrees, how many sides does the polygon have?
Answer:
6 sides
Step-by-step explanation:
since the measure of an interior angle of a polygon can be found with the formula 180(n-2) / n where n is the number of sides we can substitute 120 to the answer and cross multiply to find that
120n = 180(n-2)
120n = 180n-360
360 = 60n
n = 6
a family begins a car trip at 2:00pm. at 5:00pm, the car has traveled a total of 80 miles. use the mean value theorem to explain why
In one hour, the car covered a distance of 26.66 miles
Given,
The time when the trip begins = 2.00 pm
Distance travelled till 5.00 pm = 80 miles
Here,
Mean value Theorem;-
The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a, b] if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).
The Mean Value Theorem is as follows. F is constant over I if f′(x)=0 over a period I. If f′(x)=g′(x) over I for two differentiable functions f and g, then f(x)=g(x)+C for some constant C.
Here,
2 pm to 5 pm = 3 hours
80 miles in 3 hours
That is,
80/3 = 26.66 miles per hour
That is,
The car travelled a distance of 26.66 miles in an hour.
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|-2c-3| > -4
Absolute value inequality
The solutions of the absolute value inequality.
|-2c-3| > -4
are all the real numbers.
How to solve the absolute value inequality?Here we have a really trivial inequality, which is:
|-2c - 3| > -4
Notice that we have an absolute value there, and the absolute value is defined as:
|x| = x if x ≥ 0
|x| = -x if x < 0
Then the absolute value |x| is always equal to or larger than zero, so:
|x| > -4
Is true for any value of x.
Then our inequality:
|-2c - 3| > -4
Is true for any value of c, because the left side is always equal to or larger than 0, and 0 > -4
So c can be any real number.
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A cardboard carrying box has the dimensions shown below. How many square inches of cardboard are needed to make the box?
A goalie makes 15 saves in 5 games. What is the unit rate of saves per game?
Answer:
Step-by-step explanation:
15/5= how many saves per game
1 game = 3 saves
Answer:
The unit rate is 3 saves per game.
Step-by-step explanation:
15 / 5 = 3
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Question 5 of 15
Solve: 6+ x/2 = 1/4(x − 4) – 1
OA. There are infinitely many solutions.
OB. x=-16
OC. x= 32
OD. X=-32
PLEASE HELP ME HURRY❗️❗️❗️❗️❕
Answer: x= -32
Step-by-step explanation:
6+x/2=1/4(x-4)-1
6 +x/2 = 1/4x -1 -1 distribute
6+ x/2 = 1/4x -2 combine like terms
(6+x/2) = (1/4x -2) Find GCF for denominator
4(6+x/2) = 4(1/4x -2) GCF is 4 so multiply by 4 on both sides
24 +x = x-8 add 8 on both sides
32+x=x subtract x
32=-x divide by -1 on both sides
-32= x
Anna and Derek are both electricians.
Anna uses the function f(x)=70x+100 to determine the charge to her customers, where x represents the number of hours of labor.
The table shows what Derek charges a customer for x hours of labor.
x (hours) 0 1 2 3 4
cost ($) 70 170 270 370 470
Which electrician charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements.
Anna charges $100 for an initial fee, Derek charges $100 for an initial fee. Derek charges less for an initial fee
How to determine the initial fees?The equation is given as
f(x) = 70x + 100 ---- Anna
Also, we have
Derek
x (hours) 0 1 2 3 4
cost ($) 70 170 270 370 470
Set x = 0, to calculate the initial fees
So, we have
Anna: f(0) = 70(0) + 100
Evaluate
Anna: f(0) = 100
For Derek, we have
Cost = $70, when x = 0
Hence, Derek charges less for an initial fee
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Are the following lines parallel, perpendicular, or neither?
y = 3(x + 7)
y + 5 = -1/3x
O parallel
O perpendicular
O neither
Answer:
perpendicular
Step-by-step explanation:
Find the slope for both lines and compare. Same slope would mean parallel. Different slopes means intersecting lines. But specifically if the slopes are opposite sign and reciprocals (one is flipped over from the other) then they are perpendicular.
Put them in slope-intercept form to find the slope.
y = mx + b
m is the slope (number by the x)
y = 3(x+7)
distribute the 3.
y = 3x + 21
This line has a slope of 3.
y + 5 = -1/3 x
y = -1/3 x - 5
This line has a slope of -1/3.
-1/3 and 3 are negative reciprocals. They have opposite signs. Also 1/3 is just 3 but flipped over. They are perpendicular.
a person casts a shadow that aligns with a shadow of a tree. the person is 5.5 feet tall and casts a shadow 8.25 feet long. the trees shadow measures 22.5 feet long
Part A: write and equation you can use to find the trees hight.
Part B: How tall is the tree? How far is the person standing from the tree?
An equation that can be used to determine the tree's height is 22.5/8.25 = x/5.5.
The height of this tree is equal to 15 feet.
The distance of this person from the tree is equal to 14.25 feet.
What are the properties of similar triangles?In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Additionally, two (2) geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Now, we can write an equation that can be used to determine the tree's height. Since the ratio of the corresponding sides of similar triangles are equal in magnitude, we have the following mathematical expression (equation):
22.5/8.25 = x/5.5
Where:
x represents the height of the tree.
How tall is the tree?22.5/8.25 = x/5.5
Cross-multiplying, we have:
8.25x = 22.5 × 5.5
8.25x = 123.75
x = 123.75/8.25
x = 15 feet.
How far is the person standing from the tree?The distance of this person from the tree can be calculated as follows;
Distance = Length of tree's shadow - Length of person's shadow
Distance = 22.5 - 8.25
Distance = 14.25 feet.
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Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.
Option B, The center 95% of players had an average weight of 151 pounds.
Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.
So, let x represent a football player's weight.
X ≅ N(200, (25)²)
The minimal weight of the center 95% of the members is
P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)
P(X > 95) = P(-4.2 < z)
P(X > 95) = - P(z < -4.2)
P(X > 95) = 0.1512
The needed percentage is 0.1512 × 100 = 151.2 percent.
A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
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How is a constant term different than a variable for an expression that represents a real word situation
A constant does not change its value over time. A variable, on the other hand, changes its value dependent on the equation.
What is a tern!?A term is either a number, a variable, or the product of a number and a variable. A coefficient is your term's numerical factor. A constant term is one that only contains a number. In other words, a constant term contains no variables.
Constants are algebraic expression terms that only contain numbers. That is, they are the terms that do not have variables. We call them constants because their value never changes because the term contains no variables that can change its value.
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(03.06 MC)
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work. (4 points)
A) The data models a geometric sequence
B) Using a recursive formula, the time she will complete station 5 is; 2
C) Using a explicit formula, the time she will complete station 9 is; 512
How to find the Recursive Formula?A) From the given coordinates (1, 3), (2, 6), (3, 12), (4, 24), we can say that when x increases by 1, y is multiplied by 2. Thus, as the quotient between consecutive terms is the same, the data depicts a geometric sequence.
B) The recursive formula for a geometric sequence with common ratio r and first term a₁ is given by the formula:
f(n) = a₁(r)ⁿ⁻¹
Since a₁ = 2 and r = 1, then we have;
f(1) = 2(1)¹⁻¹
f(1) = 2
f(5) = 2
C) The explicit formula from the calculations above will be;
aₙ = 2ⁿ
Thus;
a₉ = 2⁹
a₉ = 512
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What is the value of the rational expression below when x is equal to 5?
15-x
x-10
OA. 10
O.B. -2
OC. 2
O D. -10
Answer: A. 10
Step-by-step explanation:
Plug in x which is 5 to equation 1
15-5=10
Plug in x which is 5 to equation 2
5-10= -5
POSSIBLE POINTS: 20
A prestigious program accepts 2 out of every 9 applicants per yer. If the program accepted 360 applicants, how many applicants were NOT accepted?
A.1260
B.1620
C.2520
D.3240
E.3600
The correct option is A. It can be solved by the concept of ratio and proportion.
What is ratio?
It is the way of representation of a quantity relative to the other quantity. Its symbol is :. For example size of 2 relative to 5 is represented by 2:5 or 2/5.
Total number of applicantas = 9
Accepted applicants = 2
Not accepted applicants = 9-2 = 7
Take the ratio of accepted to the not accepted applicants = 2/7
Now, if new not accepted applicants are x then accepted applicants are 360. To keep the ratio constant, the following equation must be satisfied:
[tex]\frac{2}{7}=\frac{360}{x}\\x=\frac{7}{2}\times 360\\x=1260[/tex]
Hence, the correct option is A. It can be solved by the concept of ratio and proportion.
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Pennylvania ha 51 mile of coat along Lake Erie and 57 mile horeline along the Delaware Etuary. The total ditance around Pennylvania i about 1000 mile. How much of that ditance around Pennylvania i not horeline?
the total distance around Pennsylvania is not shoreline will be 892 miles.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Pennsylvania has 51 miles of coast along Lake Erie and a 57-mile shoreline along the Delaware Estuary.
The total distance around Pennsylvania is about 1000 miles.
So the distance around Pennsylvania is not shoreline will be 1000-(57+51) = 892miles
Hence, the total distance around Pennsylvania is not shoreline will be 892 miles.
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you roll two fair dice. find the probability that the first die is a 6 given that the minimum of the two numbers is a 4.
Step-by-step explanation:
answers is 1 and 2 by 3
all the best
The probability of getting the 6 on the first die given that the minimum of two numbers is 0.11.
What is the probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Given that Two dice are rolled.
Then the sample space (n) = 36
Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}
Probability = 4/36
= 0.11
Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 0.11.
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in base 10, the number 2013 ends in the digit 3. in base 9, on the other hand, the same number is written as (2676)9 and ends in the digit 6. for how many positive integers b does the base-b-representation of 2013 end in the digit 3?
As described in number system the of positive integers is 13
what is number system ?
A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or other symbols to represent the numbers in a given set in a standardised way. In different numeral systems, the same set of symbols may represent various numbers.
Solution:
we want the integers b such that
2013 = 3 ( modb)
=> b is a factor of 2010
since 2010 has 2 * 3 * 5* 67 it has
(1+1)(1+1)(1+1)(1+1) = 16 factors
since b cannot equal to 1, 2, or 3, as these cannot have 3 in there base representation, our answer is 16 - 3 =13.
therefore the number of positive integers is 13
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You spin the spinner and flip a coin. Find the probability of the compound event.
The spinner is divided into 5 equal regions with numbers 1,2,3,4,and 5
The probability of spinning an even number and flipping heads is
The probability of spinning an even number and flipping heads is 1/5
How to determine the probability?The sections on the spinner are given as
Sample space (sections) = {1, 2, 3, 4, 5}
These sections mean that
P(Even number) = Count of even numbers/Number of sections
So, we have the following representation
P(Even number) = 2/5
Also, we have
Coin = {H, T}
This means that
P(Head) = 1/2
So, we have the probability equation
P(Even and Head) = P(Even) * P(Head)
This gives
P(Even and Head) = 2/5 * 1/2
Evaluate
P(Even and Head) = 1/5
So, the probability is 1/5
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The soup pot is 8. 5 inches tall with a radius of 4 inches. What is the volume of the soup pot? answer choices are rounded to the nearest tenth cubic inch.
The volume of the soup pot is 427.04 inches³
The soup pot is 8. 5 inches tall with a radius of 4 inches
We need to find the volume of the soup pot
What is volume?
Volume, is defined as the space that a body occupies. it is the ratio of the mass of object to its density.
Volume of cylinder = 3.14r²h
Where r represents the radius of the cylinder and h represents the height of the cylinder.
Volume of cylinder = 3.14 x 4 x 4 x 8.5
Volume = 427.04 inches³
Thus, the required volume of the soup pot when it is s 8. 5 inches tall with a radius of 4 inches is 427.04 inches³
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