Answers
The value of angle XYZ is 0.020 degrees using the cosine function.
What are inverse trigonometric functions?Simply put, inverse trigonometric functions are the opposites of the fundamental trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions. The fields of engineering, physics, geometry, and navigation all heavily utilise the inverse trigonometry functions.
From the given right triangle we observe that:
cos y = 6 / 15 = adjacent side /hypotenuse
y = arccos(6/15)
y = 0.020 degrees
Hence, the value of angle XYZ is 0.020 degrees using the cosine function.
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Related Questions
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Answers
The measure of arc of central angle is 65 degree.
what is Central Angle?According to the definition of a central angle in geometry, it is the angle that the arc of a circle occupies in its centre. The angle's arms are formed by the two radii. Knowing the ratio of the curve to the circle using the central angle is helpful.
Central angle is the angle which is made from the half of the Centre of the circle by the one radius .
First, Congruent arcs in the circle and Congruent arcs have congruent triangles .
We have JEI = 125
So, < GEI = 180- 125 (concurrency property Angle)
= 65
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Avery had $25.40 in her wallet. If she bought lunch with dollars from her wallet, how much money did she have in her wallet after lunch?
A. $18.15
B. $18.30
C. $17.15
Answers
Answer:
Step-by-step explanation:
This question doesn't say how much her lunch cost.
determine the value of cos 2.240 degrees.
needs to be solved in steps like cos 30 = cos (300 -
270)
Answers
Answer - The value of cos 2.240 degrees comes out to be 0.9992.
To determine the value of cos 2.240 degrees, we can use the following steps: Convert the angle from degrees to radians. To do this, we can use the formula: radians = degrees * π/180. Plugging in the given angle, we get: radians = 2.240 * π/180 = 0.0391 radians
Use the cosine function to find the value of cos 2.240 degrees.- The cosine function is defined as cos(x) = adjacent/hypotenuse, where x is the angle in radians.- Plugging in the angle in radians that we found in Step 1, we get: cos(0.0391) = adjacent/hypotenuse
Use a calculator to find the value of cos(0.0391).- Using a calculator, we find that cos(0.0391) = 0.9992. The value of cos 2.240 degrees is 0.9992.
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solve every thing here do not draw anything on the graph
Answers
The median height is less than the mean height.
Option 3 is correct.
What is Median?The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three different metrics are employed in mathematics. The terms are median, mode, and mean. The term "measures of central tendency" refers to these three metrics.
As per the given graph:
Total number of plants = 80
Frequency v/s height of plant is given.
The mean height is 41.9 cm.
To find the median:
Total observations (n) = 25 + 20 + 13 + 10 + 2 + 10
= 80 plants
For median interval:
(n/2) = (80/2)
= 40 plants
Hence, the median interval will be the one where frequency reach 40.
∴ Median lies in the interval of height (30-40) cm.
Hence, the median height is less than the mean height.
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i ijijiijiiiiiiiiiiiiiiiiiiiiiii
Answers
Answer: 1.09 is closer to 1
Which of the statements best describe the origin on the coordinate system?
I. The x- and y-axes intersect at the origin.
II. The origin is the distance from right to left.
III. The point, (0 , 0), is the ordered pair at the origin.
IV. The origin is the distance from top to bottom.
A.
I and III
B.
IV only
C.
I only
D.
II and IV
FIRST ANSWER BRAINLIEST AND 100 POINTS
Answers
Answer:
A, I and III
Step-by-step explanation:
The origin is the point in the center of a graph, where the x- and y-axes intersect. This point is also (0,0).
15% of 35 and show working out.
Answers
Answer: 5.25
Step-by-step explanation:
First, a percent divided by 100 is a decimal.
15% / 100 = 0.15
Next, we are finding 15% of 35. In mathematical terms, "of" usually represents multiplication. We will multiply 0.15 by 35 to find 15% of 35.
0.15 * 35 = 5.25
0.15•35
Solution
5.25
Determine the length and width of a rectangle if the perimeter is
26 and the length is four more than twice the width
Answers
The length and width of the rectangle are 10 and 3, respectively.
Let's use "l" to represent the length of the rectangle and "w" to represent the width. From the problem statement, we've got portions of information:
The perimeter is 26. The formulation for the perimeter of a rectangle is P = 2l + 2w. So we are able to write:
2l + 2w = 26
The length is four extra than twice the width. In equation shape:
l = 2w + four
Now we can use substitution to resolve for the length and width. we will alternative the expression 2w + 4 for l within the first equation:
2(2w + 4) + 2w = 26
Simplifying:
4w + 8 + 2w = 26
6w + 8 = 26
6w = 18
w = 3
So the width of the rectangle is three. To discover the length, we're going to substitute w = 3 into the equation for l:
l = 2w + 4 = 2(3) + 4 = 10
So the length of the rectangle is 10.
Thus, the length and width of the rectangle are 10 and 3, respectively.
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1. Write a function for the graph shown below. There is no stretching or shrinking involved.
Answers
From the graph of the function we determine, [tex]y = 1.(2^{\frac{1}{3}})^x[/tex].
What is an exponential function?A function is said to be an exponential function when the exponent is the independent variable.
Let, The given function be f(x) = abˣ.
Now, At x = 0,
1 = ab⁰.
a = 1.
Again at,
x = 3,
2 = a.b³.
b³ = 2.
b = [tex]2^{\frac{1}{3}[/tex].
Therefore, The given function is, [tex]y = 1.(2^{\frac{1}{3}})^x[/tex].
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(PLS HELP!!)
In the rectangle below, EI=3x+6, EG= 5x + 16, and m
Find the value of x and m ZIHE.
Answers
The value fo x is 4 and the angle is 45 degrees
How to determine the value fo x and the angleFrom the question, we have the following parameters that can be used in our computation:
The rectangle
The diagonals of a rectangle bisect each other
Using the above as a guide, we have the following:
2 * (3x + 6) = 5x + 16
So, we have
6x + 12 = 5x + 16
Evaluate the like terms
x = 4
Next, the diagonals of rectangle bisect the angles
So, we have
IHE = 45 degrees
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If pure water is added to a 15% alcohol solution, what percent alcohol is being added?
Answers
If I understand your question correctly, pure water is 0% alcohol, so by adding water, this will dilute your 15% alcohol solution and lower the percentage of alcohol in the solution.
Many word problems are set up like "You have some amount of 15% alcohol solution and you add some pure water. You end up with some other amount of the diluted mixture. How much 15% alcohol solution and how much pure water were mixed."
For those ones, use 0% alcohol for your pure water.
John and Scott are selling cheesecakes for a school fundraiser. customers can buy new york style cheesecake and so apple cheesecake. John sold 7 new york style cheesecakes and 4 apple cheesecake for a total of $116. Scott sold 8 new York style cheesecake and 12 apple cheesecakes for the total of$244. Find the cost of each of one New York style cheesecake and one apple cheesecake.
Answers
Let
x
represent the
price of one New York style
cheesecake
and
y
the price of
one apple cheesecake
. Based on the information provided, we can construct two equations:
7x + 4y= 116
8x + 12y = 244
We can
solve
for
x
in terms of
y
using the first equation:
7x= 116-4y\sx= (116-4y) / 7
When we plug this expression into the
second equation
for
x
, we get:
8[(116 - 4y) / 7] + 12y = 244
To
eliminate
the fraction,
multiply both sides by 7
.
8(116 - 4y) + 84y = 1708
Extending the parentheses and combining similar terms yields:
928-32y + 84y= 1708
When we simplify, we get the following:
52y = 780
When we
divide both sides by 52
, we get:
y = 15
We now know that
y = 15
; we can use either of the original equations to solve for x:
7x + 4(15) = 116
7x = 56
x = 8
Therefore, one
New York cheesecake costs $8
, and
one apple cheesecake costs $15
.
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How do the factors of a polynomial function relate to the graph of the function?
Answers
A game room has three circular targets to play darts with. Target A has a diameter of 14 inches, Target B has a radius of 10 inches, and target C has a circumference of 18π inches.
A. Which target is the largest? Justify your answer using the lengths of the radii of all three targets.
B. What is the circumference, in inches, of target A? Use 3.14 to approximate it.
C. What is the area, in square inches, of target C? Use 3.14 to approximate it.
Answers
(A). The largest target is Target B since it has the widest radius. (B). The size of Object A is around 44 inches around. (C). Target C has a surface area of around 254 square inches.
What does the term "circumference" mean?The length of a circle and perhaps other circular geometric object is referred to as its circumference. Anything in a double circular shape that is linear in one dimension is the perimeter.
A). We must contrast the radii of the three objects in order to compare their sizes.
Target A consists of a radius of 7 inches and a width of 14 inches.
The radius of Target B is 10 inches.
Target C has a circumference of 18π inches, so we can use the formula C = 2πr to find its radius:
18π = 2πr
r = 9 inches
Target B is the main market since it has the greatest radius.
B). The circumference of a circle is given by the formula C = 2πr, where r is the radius. For Target A, r = 7 inches, so:
C = 2πr
C = 2π(7)
C ≈ 44 inches (using 3.14 to approximate)
Target A's circumference is therefore around 44 inches.
C). The area of a circle is given by the formula A = πr², where r is the radius. For Target C, we know its circumference is 18π inches, so we can use the formula for circumference to find its radius:
C = 2πr
18π = 2πr
r = 9 inches
Target C's area is as follows because of its 9-inch radius:
A = πr²
A = π(9)²
A ≈ 254 square inches (using 3.14 to approximate)
Target C therefore has a surface area of around 254 square inches.
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1. Sharon is interested in learning about the returns to schooling. She finds a dataset with information on earnings, education, gender, age, experience and quarter and year of birth collected from a random sample of individuals. She uses this data to estimate the following Mincer earnings regression using ordinary least squares: Log Y = a + b*S + c*female + d* experience + h*experience2+u Where S is the individual's years of schooling; female takes the value of 1 if the individual is female and 0 if female. Experience is in years. The Table below provides the coefficients and standard errors that she obtained. Coefficient Std error a 6.561 2.650 b 0.074 0.025 c -0.121 0.041
d 0.075 0.033 h -0.021 0.013 a) Sharon shows you this table and asks for your help in interpreting the coefficients. From this table, what is the magnitude of the OLS estimate of the return to an additional year of schooling? Is this statistically significant at the 5% level of significance? Note that the critical value for the t-distribution for a two- sided test with 5% level of significance is 1.96. (10 marks) b) Sharon thinks that this is the true return to schooling. Is she correct? Explain your answer. (20 marks) c) Sharon learns that individuals in this data started school on the January after their 6th birthdays. They were also obliged to stay in school until their 16th birthdays. Could Sharon use this to obtain the true return to schooling? Explain your answer. (30 marks)
Answers
The OLS estimate of the return to an additional year of schooling is 0.074. This means that for every additional year of schooling, the individual's earnings will increase by 7.4%. This is statistically significant at the 5% level of significance because the t-value is 0.074/0.025 = 2.96, which is greater than the critical value of 1.96.
However, Sharon is not correct in thinking that this is the true return to schooling. This is because there may be other factors that affect earnings that are not included in the model, such as ability or family background. These omitted variables can bias the estimate of the return to schooling.
Sharon could use the information about the starting age and compulsory schooling age to obtain the true return to schooling. This is because these rules create exogenous variation in the amount of schooling that individuals receive. She could use this exogenous variation to estimate the causal effect of schooling on earnings by using an instrumental variables approach. By using the starting age and compulsory schooling age as instruments for years of schooling, she could obtain an unbiased estimate of the true return to schooling.
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Order the given steps for the perpendicular bisector construction of the segment below.
Answers
Answer: kdsl.dmcs
Step-by-step explanation:
A MBA student is interested to investigate the "Factors affecting employee turnover intention in private organizations in Bahrain". The sample consists of 78 employees from different private organizations in Bahrain. Based on literature review, he has identified 8 constructs; each construct to be measured with interrelated statements (items) using 7-point balanced Likert Scale in Part B of the questionnaire. These constructs (unobserved variables) are: Job-satisfaction (JS), Inter-personal relationship (IR), Work Environment (WE), Work Stress (WS), Financial Compensation (FC), Administrative Support (AS), and independent variable as Turn-over intention (TI). Part A of the questionnaire include some basic questions on nominal scale such as, Years of Experience (4 groups: less than 5 years; 5 – 10 Years; 10-15 Years; Above 15 Years), Job-level (3 levels: Executive Management, Middle Management, Staffs), Organization Type (2 groups: Service/Manufacturing). Part C of the questionnaire includes questions related to demographic information such as Gender, Marital Status, Age Group, Education Level.
Questions:
a. Frame any 2 Research Questions considering the basic information provided in Part A and Part B of the questionnaire as stated above
b. Frame any 2 meaningful hypotheses that you believe could be interesting to investigate considering the information provided in Part C and Part B of the questionnaire as stated above [(write down both Null (H0) and Alternative (H1)]
c. One sample t test was performed to measure if the mean response of the employees on each construct stated in Part B of the questionnaire stated above differ from neutral point (4). Descriptive statistics and Inferential statistics are reported in Tables below.
i. Interpret the findings (concluding about the entire population of the study) on employees’ perception.
ii. On which underlying factors employees think most alike?
iii. On which underlying factors employees think most differently?
iv. Write down any one hypothesis related to the test performed (write both H0 and H1)
v. Write any one research question that is answered through this test
One sample t test (Test Value = 4)
Factor t df Sig. (2-tailed) Mean Difference
JS 6.429 77 0.001 0.849
OC 7.721 77 0.002 1.059
IR 13.816 77 0 1.696
WE 8.58 77 0 1.118
WS 4.121 77 0 0.626
FC -1.043 77 0.3 -0.173
AS 3.57 77 0.001 0.467
TI 1.849 77 0.068 0.343
one sample statistic
n Mean SD
OC 78 5.059 1.211
IR 78 5.696 1.084
WE 78 5.118 1.151
WS 78 4.626 1.341
FC 78 3.827 1.466
AS 78 4.467 1.154
TI 78 4.343 1.638
Answers
Answer:
a. Two research questions that can be framed based on the information provided in Part A and Part B of the questionnaire are:
1. What is the relationship between years of experience and turnover intention among employees in private organizations in Bahrain?
2. What is the relationship between job level and job satisfaction among employees in private organizations in Bahrain?
b. Two meaningful hypotheses that can be framed based on the information provided in Part C and Part B of the questionnaire are:
H0: There is no relationship between gender and work stress among employees in private organizations in Bahrain.
H1: There is a relationship between gender and work stress among employees in private organizations in Bahrain.
H0: There is no relationship between education level and financial compensation among employees in private organizations in Bahrain.
H1: There is a relationship between education level and financial compensation among employees in private organizations in Bahrain.
c. i. The findings from the one sample t test indicate that employees' perceptions differ significantly from the neutral point (4) on the constructs of job satisfaction (JS), organizational commitment (OC), inter-personal relationship (IR), work environment (WE), and work stress (WS). However, there is no significant difference between employees' perceptions and the neutral point on the constructs of financial compensation (FC) and administrative support (AS).
ii. Employees think most alike on the construct of inter-personal relationship (IR), as indicated by the highest mean difference (1.696) and the highest t value (13.816).
iii. Employees think most differently on the construct of financial compensation (FC), as indicated by the lowest mean difference (-0.173) and the lowest t value (-1.043).
iv. One hypothesis related to the test performed is:
H0: There is no difference between employees' perceptions of job satisfaction and the neutral point.
H1: There is a difference between employees' perceptions of job satisfaction and the neutral point.
v. One research question that is answered through this test is: Do employees' perceptions of job satisfaction differ significantly from the neutral point?
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What is the % of the votes did MRS Naido receive write the answers to theearst wholw%
Answers
Based on these numbers, M Venkaiah Naidu secured around 68% of the valid votes cast, while Gopalkrishna Gandhi received around 32%.
In the vice-presidential election, M Venkaiah Naidu received 516 valid votes, while his opponent Gopalkrishna Gandhi received 244 valid votes. The total number of valid votes cast was 760, which is the sum of the votes received by the two candidates.
It's worth noting that the 68% figure only represents the proportion of valid votes cast, which excludes any abstentions or spoiled ballots. Additionally, this percentage reflects the support M Venkaiah Naidu received among the MPs who voted and may not necessarily reflect the views of the general public or the broader electorate.
Overall, M Venkaiah Naidu's victory in the election was decisive, with a difference of 272 valid votes between him and Gopalkrishna Gandhi, which was greater than the latter's total number of votes.
Complete question:
According to BJP sources, around two dozen MPs from opposing parties disobeyed their leaders and supported M Venkaiah Naidu for vice president of the NDA. Against the estimated 495 votes of pledged support, Mr. Naidu received 516 votes.
With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to the opposition's Gopalkrishna Gandhi, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.
What is the % of the votes did MRS Naido receive to write the answers to the east wholw%
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The interior angles of the pentagon
he has drawn are all less than 180°.
Ben attempts to express the
interior angles of his pentagon
using algebra.
His expressions are
xᵒ, (x +40)°, (2x − 30)°,
3(x - 40) and 3xº
Show that Ben is incorrect.
Input note: include the angle sum
of a pentagon, the value of x and
the size of any angles that don't
meet the criteria set out in the
question.
Ben is incorrect because…
Answers
All of Ben's expressions are erroneous since none of them equal the number 108 degrees. The correct equation is (n-2) x 180 / n.
What is the equation of interior angle in a regular polygon?A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides or edges are created by connecting end to end segments of a straight line to create a closed shape. Vertex or corners refers to the intersection of two line segments, which produces an angle.
In a regular polygon, where n is the number of sides, the formula for measuring an interior angle is (n-2) x 180 / n.
An internal angle in a pentagon has a measure of (5-2) x 180 / 5 = 108 degrees.
Substituting the angle in Ben's expression:
xᵒ + (x + 40)° + (2x - 30)° + 3(x - 40)° + 3x°
9x - 27° = 108
We observe that none of the value of x results in 108 degrees.
Hence, all of Ben's expressions are erroneous since none of them equal the number 108 degrees.
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(8+5)/(y+6) how can this expressions best be described A. this is a quotient of two sums B. this is a difference of a quotient C. this is a sum and a difference D. this is a product of two sums (8+5)/(y+6)
Answers
In response to the aforementioned query, we may say that As a result, expressions the response is A. A quotient of two sums is this.
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
It is better to refer to the phrase (8+5)/(y+6) as "a quotient of two sums" since it divides the sum of 8 and 5 by the sum of y and 6.
As a result, the response is A. A quotient of two sums is this.
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What is the common ratio of this geometric sequence
Answers
Answer: 3
Step-by-step explanation:
Each number is being multiplied by 3 to get the next number
Answer:
The common ratio is 3
Step-by-step explanation:
Since this is a geometric sequence you know you will be either adding or dividing. If you do 3159/3 you get 1053 and if you divide 1053 by 3 you get 351. So therefore the common ratio of this sequence is 3
I'm assuming this problem is going left to right. Right?
PLEASE HELP IM TIMED!
Answers
The value for the function f(g(-2)) is obtained as f(g(-2)) = 0.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph for the function y = f(x) is given.
The graph for the function y = g(x) is given.
We need to evaluate the function f(g(-2)).
From the graph of y = g(x) the value for g(-2) is obtained as -
g(-2) = 1
So, now we have -
f(g(-2)) = f(1)
From the graph of y = f(x) the value for f(1) is obtained as -
f(1) = 0
Therefore, the value is obtained as 0.
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Help me pleaseeeeeeee
Answers
26. The equation in slope-intercept form is y = 3x + 20.
27. The equation in slope-intercept form is y = (1/4)x - 11.
30. The equation in point-slope form is y - (-3) = -6(x - 2)
31. The equation in slope-intercept form is y = -6x + 9.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
26.
y-8 = 3(x+4)
y - 8 = 3x + 12 (distribute the 3)
y = 3x + 12 + 8 (add 8 to both sides)
y = 3x + 20
The equation in slope-intercept form is y = 3x + 20.
27.
y+5= (1/4)(x-24)
y + 5 = (1/4)x - 6
y = (1/4)x - 6 - 5
y = (1/4)x - 11
The equation in slope-intercept form is y = (1/4)x - 11.
To find the equation of a line with a slope of -6 that goes through (2,-3), we can use the point-slope form.
Point-slope form:
y - y₁ = m(x - x₁) where m is the slope and (x₁,y₁) is the point
Substituting m = -6, x₁ = 2, and y₁ = -3, we get:
y - (-3) = -6(x - 2)
y + 3 = -6x + 12
y = -6x + 9
The equation in slope-intercept form is y = -6x + 9.
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In ΔFGH, f = 67 inches, mm∠G=66° and mm∠H=30°. Find the length of g, to the nearest inch.
Answers
The length of side 'g' is approximately 61.54 inches.
What is triangle?A triangle is a 2-dimensional geometric shape that consists of three line segments or sides and three angles. It is one of the simplest polygonal shapes and is often used in mathematics and geometry to illustrate basic concepts such as area, perimeter, angles, and congruence.
To find the length of side 'g' of ΔFGH, we can use the Law of Sines, which relates the lengths of the sides of a triangle to the sine of their opposite angles. The Law of Sines states that:
a/sin(A) = b/sin(B) = c/sin(C)
Here the lengths of the sides of a ΔABC are a, b, and c, and A, B, and C are the opposite angles.
In this case, we know that the length of side 'f' is 67 inches, and the measures of angles, G and H are 66° and 30° respectively. Let's assume the length of ∠G side is 'g'. Then, using the Sin Law, we can write:
f/sin(F) = g/sin(G) = h/sin(H)
Substituting the given values, we get:
67/sin(F) = g/sin(66) = h/sin(30)
Solving for 'g', we have:
67/sin(F) = g/sin(66°)
g = 67 * {sin(66°) / sin(F)}
To find the measure of angle F, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:
F = 180° - G - H
F = 180 - 66° - 30°
F = 84°
Substituting this value into the equation for 'g', we get:
g = 67 * sin(66°) / sin(84°)
putting the values from Sin table: Sin(66°) = 0.913 and Sin(84°) = 0.994
g = 61.54 inches
Therefore, the length of side 'g' is approximately 61.54 inches.
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4)
xyz
y2
2
at x = 3, y=−1, z = 2
Answers
1)Substituting the given values, we get:
xyz = 3(-1)(2) = -6
Therefore, when x=3, y=-1, and z=2, the value of xyz is -6.
2)y^2 = (-1)^2 = 1
Therefore, when x = 3, y = -1, and z = 2, y^2 = 1.
3) 2
Given f(x) = x – x^2 and g(x) = 4x – 2 Remember to document your steps so that someone reading your solution can understand what you did how your work results in the answers you give
(a)simplify f(-3)
(b)simplify g(x^2)/2
(c)simplify f(g(x))
(d)simplify g(g(x))-x
Answers
We have the following answers:
(a)[tex]f(-3) = -12[/tex](b) [tex]g(x^2)/2 = 2x^2 - 1[/tex] (c) [tex]f(g(x)) = -16x^2 + 20x - 6[/tex](d) [tex]g(g(x)) - x = 15x - 10[/tex]Solution:
(a) To simplify [tex]f(-3)[/tex], we need to plug in [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f(x) = x - x^2[/tex]:
[tex]f(-3) = (-3) - (-3)^2\\f(-3) = -3 - 9\\f(-3) = -12[/tex]
(b) To simplify [tex]g(x^2)/2[/tex], we need to plug in [tex]x^2[/tex] for [tex]x[/tex] in the function[tex]g(x) = 4x - 2[/tex], and then divide the result by 2:
[tex]g(x^2)/2 = (4(x^2) - 2)/2\\g(x^2)/2 = (4x^2 - 2)/2\\g(x^2)/2 = 2x^2 - 1[/tex]
(c) To simplify [tex]f(g(x))[/tex], we need to plug in the function [tex]g(x) = 4x - 2[/tex] for [tex]x[/tex] in the function[tex]f(x) = x - x^2[/tex]:
[tex]f(g(x)) = (4x - 2) - (4x - 2)^2\\f(g(x)) = 4x - 2 - (16x^2 - 16x + 4)\\f(g(x)) = -16x^2 + 20x - 6[/tex]
(d) To simplify [tex]g(g(x)) - x[/tex], we need to plug in the function [tex]g(x) = 4x - 2[/tex] for [tex]x[/tex] in the function [tex]g(x) = 4x - 2[/tex], and then subtract x from the result:
[tex]g(g(x)) - x = (4(4x - 2) - 2) - x\\g(g(x)) - x = (16x - 8 - 2) - x\\g(g(x)) - x = 15x - 10[/tex]
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The net below shows four equilateral
triangles. What is the total surface area of the
triangular pyramid in square feet?
8 ft
12 ft
Answers
The total surface area of the triangular pyramid is 107 * [tex]\sqrt(3)[/tex]square feet.
What is a triangular pyramid?Take a triangle. This is a base. Now take 3 triangles such that each of them are connected to one-one side of the first triangle and when they're taken together, they form a closed object, called as a triangular pyramid.
We are given that;
The length of median from outer triangle to side of the inner triangle is 8 ft
Side of inner equilateral triangle is 12 ft
Now,
First, we can find the height of the outer equilateral triangle using the Pythagorean theorem:
a^2 + (m/2)^2 = b^2
where a is half the length of the side of the inner triangle (6 ft), m is the length of the median (8 ft), and b is the length of the side of the outer triangle (unknown).
b^2 = 6^2 + 8^2/4
b^2 = 36 + 4
b^2 = 40
b = sqrt(40)
b = 2 * sqrt(10)
So the height of the outer triangle is:
h = b * sqrt(3)/2
h = sqrt(30)
Now we can find the area of each equilateral triangle using the formula:
A = (sqrt(3)/4) * s^2
where A is the area and s is the length of the side.
For the inner triangle:
A_inner = (sqrt(3)/4) * 12^2
A_inner = 36 * sqrt(3)
For the outer triangle:
[tex]A_outer = (\sqrt(3)/4) * (2 * \sqrt(10))^2A_outer = 5 * \sqrt(3)[/tex]
Now we can find the area of the base, which is just the area of the inner equilateral triangle:
A_base = A_inner
A_base = 36 * [tex]\sqrt(3)[/tex]
Finally, we can find the surface area of the triangular pyramid by adding the areas of the four triangles and the base:
SA = A_inner + 3 * A_outer + A_base
[tex]SA = 36 * \sqrt(3) + 3 * 5 * \sqrt(3) + 36 * \sqrt(3)SA = 107 * \sqrt(3)[/tex]
Therefore, the surface area of the triangular pyramid will be 107 * [tex]\sqrt(3)[/tex]square feet.
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Which exponential function is equivalent to the geometric sequence
Answers
The exponential function that is equivalent to the geometric sequence, aₙ = 9.5 × 5ⁿ is A. f(n) = (0.95)5ⁿ.
What is an exponential function?An exponential function is a mathematical function that calculates the exponential growth or decay of a data set.
There are two types of exponential functions: exponential growth and exponential decay.
The function f(x) = bx where b > 1 represents exponential growth function while f(x) = bx when 0 < b < 1, represents an exponential decay function.
Thus, the equivalent exponential function is Option A.
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For a function f(x) and a particular input value x=a, then we may write the difference quotient as
(f(a+h)−f(a))/h
where h≠0.
Now, let Q(x)=3x^2+5x+10 and consider the input value a=3. We could now write the difference quotient as
(Q(3+h)−Q(3))/h
where h≠0h≠0.
Use this difference quotient to calculate the average rate of change of f(x) from x=3 to x=3+h for the following particular values of h.
When h=0.2, the average rate of change of Q(x) is?
Answers
The average rate of change of Q(x) from x=3 to x=3+h for h=0.2 is 21.2.
To find the average rate of change of Q(x) from x=3 to x=3+h, we need to plug in the values of h and a into the difference quotient and simplify.
When h=0.2, the difference quotient becomes:
(Q(3+0.2)−Q(3))/0.2
= (Q(3.2)−Q(3))/0.2
= ((3(3.2)^2+5(3.2)+10)−(3(3)^2+5(3)+10))/0.2
= ((30.24+16+10)−(27+15+10))/0.2
= (56.24-52)/0.2
= 4.24/0.2
= 21.2
Therefore, when h=0.2, the average rate of change of Q(x) is 21.2.
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A box contains 5 balls numbered 1, 2, . . . , 5. In each trial
we remove one ball without replacement. Let X be the total number
of trials until all odd numbered balls are removed. Find V ar(3X +
2022
Answers
The variance of 3X + 2022 is -26.
The variable X in this scenario contains the total number of trials until all odd numbered balls are removed from the box without replacement. In order to find the variance of 3X + 2022, we can use the formula for the variance of a linear transformation: V ar(aX + b) = a^2V ar(X).
In this case, a = 3 and b = 2022, so the formula becomes: V ar(3X + 2022) = 3^2V ar(X) = 9V ar(X).
To find the variance of X, we can use the formula for the variance of a discrete random variable: V ar(X) = E(X^2) - [E(X)]^2.
Since X is the total number of trials until all odd numbered balls are removed, we can find E(X) by calculating the expected value of the number of trials until each odd numbered ball is removed. This can be done using the formula for the expected value of a geometric random variable: E(X) = 1/p, where p is the probability of success.
For the first odd numbered ball, the probability of success is 3/5, so E(X) = 1/(3/5) = 5/3. For the second odd numbered ball, the probability of success is 2/4, so E(X) = 1/(2/4) = 4/2 = 2. For the third odd numbered ball, the probability of success is 1/3, so E(X) = 1/(1/3) = 3/1 = 3.
Therefore, the expected value of X is E(X) = 5/3 + 2 + 3 = 14/3.
To find E(X^2), we can use the formula for the expected value of the square of a geometric random variable: E(X^2) = (2 - p)/p^2.
For the first odd numbered ball, E(X^2) = (2 - 3/5)/(3/5)^2 = (10/5 - 3/5)/(9/25) = 7/5 * 25/9 = 35/9. For the second odd numbered ball, E(X^2) = (2 - 2/4)/(2/4)^2 = (8/4 - 2/4)/(4/16) = 6/4 * 16/4 = 24/4 = 6. For the third odd numbered ball, E(X^2) = (2 - 1/3)/(1/3)^2 = (6/3 - 1/3)/(1/9) = 5/3 * 9/1 = 15.
Therefore, the expected value of X^2 is E(X^2) = 35/9 + 6 + 15 = 170/9.
Now we can find the variance of X: V ar(X) = E(X^2) - [E(X)]^2 = 170/9 - (14/3)^2 = 170/9 - 196/9 = -26/9.
Finally, we can find the variance of 3X + 2022: V ar(3X + 2022) = 9V ar(X) = 9(-26/9) = -26.
Therefore, the variance of 3X + 2022 is -26.
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