On solving the question - Use the z distribution if the population variances are known; if not, use the -tdf distribution.
What is population variances?A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.
What is population variance vs standard deviation?The difference between the mean and the mean squared is known as the variance, and the standard deviation is the square root of that difference. Although in different units, both measurements capture the distribution's variability. The same units are used to express standard deviation and the original value.
Use the z distribution if the population variances are known; if not, use the -tdf distribution.
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How many square feet is a 20×20 room?
Answer:
400 square feet
Step-by-step explanation:
the director of a baseball camp estimates that 100 students will enroll if the tuition is $250. for each $20 increase in tuition, eight fewer students will enroll. determine a linear function that will predict the number of students (y) who will enroll at a given tuition (x).
Answer:
Below
Step-by-step explanation:
y = 100 - ( x-250)/20 *8 for every 20 above 250 eight fewer students from the 100 who would enroll at 250 level ( this is for x >= 250...the question says nothing about enrollment change from lowering the price BELOW 250)
In an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books. (a) How many ways can you select and arrange 10 of the 17 books on the shelf? Notice that here we will allow the books to end up in any order. Explain. (b) How many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author? Explain. 6. How many triangles are there with vertices from the points shown below? Note, we are not allowing degenerate triangles - ones with all three vertices on the same line, but we do allow non-right triangles. Explain why your answer is correct. 14. We have seen that the formula for Pln,k) is Your task here is to explain why this is the right formula. (a) Suppose you have 12 chips, each a different color. How many different stacks of 5 chips can you make? Explain your answer and why it is the same as using the formula for P(12,5). (b) Using the scenario of the 12 chips again, what does 12! count? What does 7! count? Explain. (c) Explain why it makes sense to divide 12! by 7! when computing P(12,5) (in terms of the chips). (d) Does your explanation work for numbers other than 12 and 5? Explain the formula P(n,k) = using the variables n and k.
(a) In 70,572,902,400 ways can you select and arrange 10 of the 17 books on the shelf.
(b) In 19,448 ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author.
In the given question, in an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books.
Total number of books = 17
Number of books which self hold = 10
We have to find the following.
(a) We have to find how many ways can you select and arrange 10 of the 17 books on the shelf.
Number of ways to select the 10 books out of 17 books = [tex]^{17}C_{10}[/tex]
Now,
The number of ways of arranging the 10 books = [tex]10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]^{17}C_{10}\times10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]\frac{17!}{10!(17-10)!}\times10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]\frac{17!}{10!7!}\times10![/tex]
Total number of ways of selecting and arranging 10 books out of 17 = [tex]\frac{17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7!}{7!}[/tex]
Total number of ways of selecting and arranging 10 books out of 17 = 17×16×15×14×13×12×11×10×9×8
Total number of ways of selecting and arranging 10 books out of 17 = 70,572,902,400
Hence,
Total number of ways of selecting and arranging 10 books out of 17
(b) We have to find how many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author.
Number of ways to select the 10 books out of 17 books = [tex]^{17}C_{10}[/tex]
Number of ways of arranging the 10 books alphabetically = 1
Total number of ways of arranging 10 books out of 17 in the shelf = [tex]^{17}C_{10}[/tex]
Total number of ways of arranging 10 books out of 17 in the shelf = [tex]\frac{17\times16\times15\times14\times13\times12\times11\times10!}{10!\times7\times6\times5\times4\times3\times2\times1}[/tex]
Total number of ways of arranging 10 books out of 17 in the shelf = 19,448
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Arandomsampleof5weeksshowedthatacruise agency received the following number of weekly specials to the Caribbean: 20, 73, 75, 80, 82. a. Compute the mean, median, and mode. b. Which measure of central tendency best describes the data? c. Comment on the distribution of the data.
The mean is 66, the median is 75 and the mode is None.
The center or typical value of a dataset is represented by summary statistics known as measures of central tendency. These metrics, such as the mean, median, and mode, are examples. These statistics, often known as the central location of a distribution, show where the majority of values in a distribution fall.
Given,
No. of observations = 5
Mean = Total observations/ no. of observations = 20+73+75+80+82/5 = 66
Median = Middle most observation arranged from smallest to largest = 75
Mode = Observation which occurs at least twice = None
Mean describes the data the best because it takes the average of all the given data.
The distribution of the data set is scattered and the shape of the frequency graph is going upwards.
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Find the distance between the two points rounding to the nearest tenth (if necessary). (1,−6) and (−8,−4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.2[/tex]
in which section of the graph does the actual solution to the system lie? 1 2 3 4; consider this system of inequalities. x + y โค โ3 y < which graph shows the solution for this system?; modeling with systems of linear inequalities ; consider the system of inequalities and its graph; consider the system of inequalities and its graph y x/4; a school is planning for an addition; which graph represents the system of inequalities y 34x 2y โ 1 โฅ 2x; which graph represents the solution set of the system of inequalities? (x+y 12y โฅxโ4)
The graph of the system of inequalities y ≤ –0.75x , y ≤ 3x – 2 is attached.
Actual solution of the inequalities in the graph is shown by common shaded region of both the inequalities below A(-0.533 , 0.4 ).
As shown in the question,
Given system of inequalities are :
y ≤ –0.75x
y ≤ 3x – 2
Graph of the inequalities is attached.
For first inequality :
y ≤ –0.75x
When x = 0
y ≤ 0
when y =0 ⇒ x ≤ 0
For second inequality :
y ≤ 3x – 2
x = 0⇒ y ≤ -2
when y =0 ⇒x ≥ 2/3
Actual solution by converting into equalities
y = -0.75x
Substitute in second equation
-0.75x = 3x -2
⇒ 3.75x =2
⇒ x= 0.5333
⇒ y= -0.4
Graph below ( 0.533 , -0.4 ) represents the actual solution.
Therefore, the actual solution of the attached graph of the inequalities is region below ( 0.533 , -0.4 ) common shaded region.
The complete question is :
Consider the system of inequalities and its graph. y ≤ –0.75x , y ≤ 3x – 2 In which section of the graph does the actual solution to the system lie? 1 2 3 4.
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Which of the following equations is modeled by the counters inside the rectangle?
A. 12 ÷ 3 = 4
B. (-12) ÷ (-3) = -4
C. 12 ÷ (-3) = -4
D. (-12) ÷ 3 = -4
PLEASE ANSWER FAST!
The equation which represents the counters inside the rectangle is,
12 ÷ 3 = 4.
What is equation?
Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.
In the given diagram there is a rectangle containing 4 counters.
Each counter containing 3 red balls.
So, the total number of red balls are 4 x 3 = 12.
From this the equation which represents the counters inside the rectangle is,
12 ÷ 3 = 4.
Hence, the equation which represents the counters inside the rectangle is, 12 ÷ 3 = 4.
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TRUE OR FALSE in html5, it is only possible to check a form for valid inputs (say within a given range) once the data has been submitted to the server.
The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.
HTML5
HTML5 is a markup language used for structuring and presenting content on the World Wide Web. It is the fifth and final major HTML version that is a World Wide Web Consortium recommendation. The current specification is known as the HTML Living Standard.
On-premises servers
On-premises servers refer to the group of servers that are under the control of a private entity. This is not like the traditional cloud computing method where resources can be leased to third-party service providers.
The use of the term, on-premises refers to the local installation of these resources as against the cloud type where the resource is on the vendor's server and a client can reach the software via their internet browsers.
Hypertext Markup Language revision 5 (HTML5) is markup language for the structure and presentation of World Wide Web contents. HTML5 supports the traditional HTML and XHTML-style syntax and other new features in its markup, New APIs, XHTML and error handling.
The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.
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Sara has agreed to help with her younger sister's science fair experiment. Her sister planted string beans in two pots. She is
using a different fertilizer in each pot to see which one will grow the tallest plant. Currently, plant A is 4 inches tall and
grows 2/3 inch per day, while plant B is 9 inches tall and grows 1/2 inch per day. If the plants continue growing at these rates
in how many days will the two plants be the same height? Which plant will be tallest in six weeks? Write a system of
equations and solve.
Answer: plants are same height in 30 days; Plant A is tallest in 6 weeks
Step-by-step explanation:
x = number of days
4 + (2/3)x = 9 + (1/2)x
(2/3)x - (1/2)x = 9 - 4
(1/6)x = 5
x = 30, number of days for Plant A and Plant B to be same height.
6 wks = 42 days
Plant A in 42 days: 4 + (2/3)(42) = 32 inches
Plant B in 42 days: 9 + (1/2)(42) = 30 inches
HELP !
The Manchester novelty shop borrowed $205,000 from the bank to pay for new merchandise. The bank lent the money at 6 percent ordinary interest for 45 days. Find the interest owned and the maturity value of the loan.
The interest owned and the maturity value of the loan is $217,300.
What is meant by interest?Simple interest is calculated using the following formula. PRT/100 is the formula for simple interest (SI). In this case, the principal amount is P, the interest rate is R, and the interest period is T. The total sum that must be paid consists of the principal amount plus basic interest, or P + SI.
The interest rate for the loan is denoted by this proportion. When you deposit money in a high-yield savings account, for instance, a bank will give you interest. Simple interest examples include monthly-amortized auto loans and store installment loans; both have a dipping loan balance with each monthly payment as well as a dipping interest rate.
Principal amount=205,000
Given that the interest is 6%
=205000(6/100)
=12300
The maturity amount of loan is:
=205000+12300
=$217300
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A study assessing the effect of anxiety (low vs. high) and stress (low vs. moderate vs. high) on test performance uses = 10 in each treatment condition. In this study, N = 20
a. 20
b. 10
c. 30
d. 60
In this study assessing the effect of anxiety (low vs. high) and stress (low vs. moderate vs. high) is at N = 20.
With respect to
n [tex]\leq[/tex] 0.05 N
Given:
If n = 10
10/0.05 [tex]\leq[/tex] N
n = 10
=> 2 Treatments
=> N = 20
This is the study of the effect of anxiety (low vs. high) and stress (low vs. moderate vs. high) on test performance uses = 10 in each treatment condition.
Thus, one-way ANOVA, when Fx = 1
One-way analysis of variance (ANOVA) is used to determine whether there are statistically significant differences between the means of three or more independent (unrelated) groups. This guide provides a brief introduction to one-way ANOVA, including test assumptions and when to use this test.
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A car moving at a constant speed passes the timing device at T equals 0 after 8 seconds the car has traveled 840 ft what linear function in the form y equals mx + b represents the distance in feet d, the car has traveled any number of seconds, t, after passing the timing device
Answer:
Answer
d = 840t + 0
Consider a population with data values of:
12, 8, 28, 22, 12, 30, 14.
The population standard deviation is closest to: ____.
a) 8.64.
b) 64.00.
c) 74.67.
d) 8.00.
Answer:
D)8.00
σ = √64
= 8
which of the following equations could be the result of using substitution to solve the system
Therefore the solution of the equations could be the result of using substitution is 2[tex]y^{2}[/tex]-6 -y=0
What is equation?In English, an equation is defined as a properly written formula that consists of two expressions joined by an equals sign, while cognates of the word in other languages may have slightly different meanings. For instance, in French, the word "équation" means "thing with one or more variables."
Given two equations are
x=[tex]y^{2}[/tex]-1 and 2x-y=4
We must select an equation from the list of possibilities that may be obtained by utilizing substitution to resolve the problem.
We substitute x in terms of y because the supplied equation is in terms of y.
From 2x-y=4
x=4+y/2
Substitute x=4+y/2 in other equation
We get,
=> x=[tex]y^{2}[/tex]-1
=> 4+y/2 =[tex]y^{2}[/tex]-1
=>4+y=2[tex]y^{2}[/tex]-2
=>2[tex]y^{2}[/tex]-6 -y=0
Therefore the solution of the equations could be the result of using substitution is 2[tex]y^{2}[/tex]-6 -y=0
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[-1(4x-2) -5] [-1 2 -5]
[0 (3z-9) (y-1)] [0 3 2] value y?
The value of y is 4.
What is The value of y?Generally, To find the value of y in the expression [0 (3z-9) (y-1)], we need to isolate y. To do this, we can start by combining like terms:
[-1(4x-2) -5] [-1 2 -5] [0 (3z-9) (y-1)] [0 3 2]
Becomes:
[-4x + 2 - 5] [0 3 2]
Then we can rearrange the terms to get:
[-4x - 5 + 2] [0 2 + 3]
This simplifies to:
[-4x - 3] [5]
Finally, we can isolate y by dividing both sides by 2:
[-4x - 3] / 2 = 5 / 2
This gives us:
y = (5/2) + 3/2
Simplifying, we find that y = 4.
Therefore, the value of y in the expression [0 (3z-9) (y-1)] is 4.
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Find the sum of following two quantities if the number is reprensented by x
i. Seven multiplied by the sum of nine and a number.
ii. The sum of four and the number.
The sum of two (63 + 7x) and (4 + x) quantities will be 8x + 67.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let 'x' be the number.
The first number is given as,
⇒ 7(9 + x)
⇒ 63 + 7x
The second number is given as,
⇒ 4 + x
Then the sum of two numbers is given as,
⇒ 63 + 7x + 4 + x
⇒ 8x + 67
The sum of two (63 + 7x) and (4 + x) quantities will be 8x + 67.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The values of the trigonometric functions sin(∅) and cos(∅) are -1/2 and [tex]\frac{\sqrt{3} }{2}[/tex] respectively.
What are trigonometric functions?The trigonometric functions and identities are the ratio of sides of a right-angled triangle. The sides of a right triangle are the perpendicular side, hypotenuse, and base, which are used to calculate the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulae.
if ∅ = [tex]\frac{11\pi }{6}[/tex] rad converting to degree
we know that [tex]\pi[/tex] rad = 180°
which means ∅ in degrees = 11/6 x 180 which is 330°
sin(330) = -1/2
cos(330) = [tex]\frac{\sqrt{3} }{2}[/tex]
In conclusion, the function values of the sin(∅) and cos(∅) are -1/2 and [tex]\frac{\sqrt{3} }{2}[/tex]
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wendy has a monopoly in the retailing of motor homes. she can sell five per week at a price of $21,000 each. if she wants to sell six, she must charge $20,000 each. the marginal revenue of selling the sixth motor home is: -$5,000 -$1,000 $15,000 $20,000
She may sell five of them each week for $21,000. She needs to ask for $20,000 for each unit if she wants to sell six. The marginal revenue of selling the sixth motor home is -$5000. Here option A is the correct answer.
If demand is price inelastic, then raising the price will decrease income. If price increases elastic, lowering the price will boost earnings.
Demand is considered to be elastic if an increase in price results in a loss in overall income because the quantity required is significantly impacted by the price rise. Depending on whether they are requirements or wants, the marketplace. in other words, may have varying elasticities (accessories).
Thus, a fall in revenue because of a rise in price
= (20,000 - $21,000) × (5)
= -$5000
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a thief uses a bag of sand to replace a gold statue that sits on a weight-sensitive, alarmed pedestal. the bag of sand and the statue have exactly the same volume, 1.90 ll. (assume that the mass of the bag is negligible.) part a calculate the mass of each object. (densityofgold
4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
Given that,
A gold statue that is perched on a pedestal with a weight-sensitive alarm is replaced by a thief using a bag of sand. The statue and the bag of sand have the exact same volume, 1.55 L.
We have to calculate the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
We know that,
Mass of gold = Volume × Density
= 1.55×1000 cc × 19.3
= 29915 grams
= 29.915 Kg
Mass of sand = 1.55×1000×3
= 4650g
= 4.65 Kg
Volume = 1.55 L
= 1.55 × 1000 cc
= 1550 cc
Mass = Volume × Density
Mass of gold = 1550 × 19.3
= 29915 grams
= 29.915 kg
Mass of sand = 1550 × 3
= 4650 grams
= 4.65 kg
Therefore, 4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
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57 students choose to attend one of three after school activities: football, tennis or running.
There are 26 boys.
24 students choose football, of which 15 are girls.
18 students choose tennis.
3 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
The probability that the randomly selected student will chose running can be written as 12/57.
How can the the probability this student chose running be calculated?The concept used is the probability which is the likelyhood of an event to take place.
Total number of students was given as 57
Total number of boys that was given was 26
Total number of girls can be written as 57-26=31`
Number of Girls that chose football can be written as 15
Number of boys that chose football can be wriitten as 9
Number of students that chose Tennis can be written as 18
Now, number of students that chose running will be;
Number of students that chose running = 57 - (24 + 18) = 15
Therefopre, probability that a randomly selected student chose running = 15/57
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"F(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i"
Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.
What is function?Function is a relation or expression involving one or more variables.
The zeros are:
x = 3/2
x = -3/2
x = (3/2)*i
x = (-3/2)*i
First, for a given function f(x), we define the zeros as the values of x such that:
f(x) = 0.
Then we must solve:
f(x) = 16*x^4 - 81 = 0
Solving this for x leads to:
16*x^4 = 81
x^4 = 81/16
x^2 = ±√(81/16) = 9/4
x = ±√±(9/4) = ±3/2 and ±(3/2)*i
So there are 4 zeros, and these are:
x = 3/2
x = -3/2
x = (3/2)*i
x = (-3/2)*i
Where the two complex zeros come from evaluating the second square root on
-9/4.
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7. Segment A'B' is parallel to
segment AB. (Lesson 3-11)
a. What is the length of
segment A'B'?
2
B'
b. What is the length of C 3
segment B'B?
A'
B
6
12
A
a) The length of segment A'B' is given as follows: 4 units.
b) The length of segment B'B is given as follows: 4 units.
How to obtain the missing lenghts?The two similar triangles in this problem are given as follows:
ABC and A'B'C'.
Then side lengths of ABC are given as follows:
12, 9 and 2 + x.
The equivalent side lengths on triangle A'B'C' are given as follows:
y, 3 and 2.
When the triangles are similar, the side lengths are proportional, hence the following equation is built:
12/y = 9/3 = 2+x/2.
Then the length of segment A'B' is obtained as follows:
12/y = 9/3
12/y = 3
3y = 12
y = 12/3
y = 4.
The length of segment B'B is x, hence it is obtained as follows:
9/3 = 2+x/2.
2 + x = 6
x = 4 units.
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The heights (in cm) of 17 students are, 106,110,123,125,117,120,112, 115,110,120,115, 102, 115,115,109,115 and 101. Find the mean and median of the above data.
brainiest marked
Answer:To find the mean of the heights of the 17 students, we need to add up all of the heights and divide the sum by the number of students. The sum of the heights is 1777 cm, and when we divide this by 17, we get a mean height of 104 cm.
To find the median of the heights of the 17 students, we first need to put the heights in order from least to greatest. The heights in order are 101,102,106,109,110,110,112,115,115,115,115,115,117,120,120,123,125. There are 17 students, so the median is the height of the 9th student, which is 115 cm.
Step-by-step explanation:
Graham graphs the following system of equations to determine its solution.
2x + 4y = 12
2x - y = 2
What is the correct solution?
Please explain step by step to get marked as brainliest!
Answer:
x=2 and y=2
Step-by-step explanation:
2x=12-4y
x=12-4y/2
x=6-2y
substitute equation on in two
2(6-2y)-y=2
12-4y-y=2
12-5y=2
5y=12-2
5y=10
y=10/5
y=2
substitute in the equation 6-2(2)=2
y=2 and x=2
Use a graph to show the relationship between the time and the distance traveled
Answer:
I don't know the answer of this questions
Which of the following terms appear in the expansion of (x + y)10? The letter a in each term represents a real constant. ax3y7, ay5, ax5, ax5y
In the binomial expression (x + y)^10, the term that will appear in the expansion of expression is ax^3y^7.
Binomial expression refers to the algebraic expression which contains two terms. These expressions are expanded using binomial theorem. According to the theorem, it is possible to expand the binomial (x + y)^n into a sum involving terms of the form ax^by^c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. Hence, for the given expression, the term which will appear in the expansion of binomial would have variables whose sum of power would be equal to the power of the expression i.e., the sum of the power would be 10. Hence, ax3y7 would appear in the expansion as the sum 3+7=10.
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Calculate the given limit using the outstanding limits................
Answer:
Step-by-step explanation:
A translation is applied to the triangle formed by the points A(−1, 4) , B(−1, 10) , and C(3, 6) . The image is the triangle that has vertices A′(3, 4) , B′(3, 10) , and C′(7, 6) . Select the phrase from the drop-down menu to correctly describe the translation.
Answer:
The triangle was translated to the right by 4 points.
Step-by-step explanation:
If you look at the coordinates, the Y value does not change at all when comparing the original image to the translated image. Only the x value was translated. Since the problem told you it was a translation you can pick a point and subtract the value of the original image from the value of the translated image. If your answer to the subtraction problem is positive, the image moved to up or to the right (for the x-axis), if it is negative then your image moved down or to the left . Up and down is for translations along the Y-axis, and left and right are for translations along the X-axis. This works for both X and Y values. I know I just dumped a bunch of words on you, so to show you lets use points C and C'. C has an X value is 3 and C' has an X value of 7.
Subtract C (3) from C' (7) and that'll give you an answer of 4. Since the answer is positive it will move up or to the right. Since we used the X value, it moved to the right.
If you need a better explanation let me know and I'll try my best.
The angle
θ
1
θ
1
theta, start subscript, 1, end subscript is located in Quadrant
II
IIstart text, I, I, end text, and
sin
(
θ
1
)
=
9
41
sin(θ
1
)=
41
9
sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 9, divided by, 41, end fraction .
What is the value of
cos
(
θ
1
)
cos(θ
1
)cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Express your answer exactly.
cos
(
θ
1
)
=
cos(θ
1
)=
The value of cosθ₁ is -40/41 when angle θ₁ is located in quadrant II and sinθ₁=9/41.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that angle θ₁ is located in quadrant II and sinθ₁=9/41.
We need to find the value of cosθ₁.
We know that sinθ is opposite side/hypotenuse .
opposite side=9 and hypotenuse is 41.
By pythagoras theorem we find the adjacent side.
41²=9²+x²
41²-9²=x²
1681-81=x²
Taking square root on both sides
x=40
So adjacent side is 40.
cosθ₁=Adj/hyp
=40/41
Since it is in second quadrant the value of cosθ₁ will be -40/41.
Hence, angle θ₁ is located in quadrant II and sinθ₁=9/41 then value of cosθ₁ is -40/41.
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name the additive inverse of 5 + i
The additive inverse of 5 + i is (-5) + (-1)
what is additive Inverse?
To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
Given:
5 + I
As, the additive inverse is the opposite sign of the given number.
For example, if the number is -6 and we have to find its additive inverse.
So, the additive inverse will be 6.
Similarly for 5 + i ;
the additive inverse is (-5) + (-1)
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