Answer:
$10,224.30
Step-by-step explanation:
In a statistics course a linear regression equation was computed to predict the final exam score from the score
on the first test. The equation of the least-squares regression line was y=10+0.9x where y represents
the predicted final exam score and x is the score on the first exam.
As per the given equation of the least squares regression line y=10+0.9x the score of Carla's final exam is 95.5.
As given in the question,
Given equation of the least squares regression line is :
y = 10 + 0.9x
Where 'y' shows the predicted final exam score
And 'x' represents the score of the first exam.
Carla's first exam score is equal to 95
Then predicted value 'y' of the Carla's final exam score is given by :
y = 10 + ( 0.9 ) × 95
⇒ y = 10 + 85.5
⇒ y = 95.5
Therefore, the predicted final score of Carla's as per the given least squares regression line is equal to 95.5.
The above question is incomplete, the complete question is :
In a statistics course a linear regression equation was computed to predict the final exam score from the score
on the first test. The equation of the least-squares regression line was y=10+0.9x where y represents the predicted final exam score and x is the score on the first exam.
Carla scored 95 on the first test. What is the predicted value of the Carla's score on the final exam?
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Label the missing angle measures and statements for this diagram.
The missing angle measure is of:
1. 25º.
The missing side length is of:
2. 12 cm.
Triangles ABC and ACD(3) are similar by the AAS theorem.
What are similar triangles?Similar triangles are triangles that share these following two features:
Congruent angle measures.Proportional side lengths.For this problem, we have that the segment SSC is the bisection of angle A, hence:
The missing angle measure is of 25º.The missing side length is of 12 cm.We have two similar angle measures, C and 25º, along with the opposite length, hence the AAS theorem is used.
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In a certain bag, the ratio of red to green to blue marbles is 1:2:3 . There are 5 red marbles. How many blue marbles are there?
Explanation
The ratio 1:2:3 refers to the idea we could have: 1 red, 2 green, 3 blue. The order of the colors is important. Follow the order mentioned in the 1st sentence of the instructions. That order being red:green:blue.
Then the instructions mention that there are actually 5 red (instead of 1 red). This means we multiply each part of the ratio by 5
1*5 = 5 red2*5 = 10 green3*5 = 15 blueThe ratio 1:2:3 scales up to 5:10:15
We see that there are 15 blue marbles
75% of Benny's toy vehicles are trucks if he has 45 trucks how many toy vehicles does Benny have not picked the model that represents the problem how many toy vehicles does Benny have enough
Answer:
Bottom model and has 60 toys in all
Step-by-step explanation:
How to Use a Graphing Calculator to Solve a Word Problem Involving a Local Extremum of a Polynomial Function.
The graphing calculator was used to identify the coordinates of the local extremum point of the polynomial function. This allowed us to find the solution to the word problem by finding the x and y coordinates of the extremum point.
Using a Graphing Calculator to Find the Local Extremum of a Polynomial FunctionBegin by entering the polynomial function into your graphing calculator.Set the calculator to graph the function by pressing the appropriate keys.Observe the graph and locate any local extremum points.Using the calculator’s zoom feature to better view the graph, identify the x-coordinate of the local extremum point.Enter the x-coordinate of the local extremum point into your calculator and press the “Evaluate” key.The calculator will display the y-coordinate of the local extremum point. This is the solution to the word problem.Learn more about Graphing Calculator: https://brainly.com/question/28969437
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A spaceship approaches the Moon along a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of the maximum approach the brake rocket was fired for a short time interval, and the spaceship was transferred into a circular orbit of a Moon satellite. Find how the spaceship velocity modulus increased in the process of braking.
The spaceship's velocity modulus increased due to the firing of the brake rocket in order to transfer the spacecraft into a circular orbit of the Moon satellite.
When approaching the Moon, a spacecraft follows a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of maximum approach, the brake rocket is fired for a short time interval. This causes a decrease in the spacecraft's velocity and an increase in its centripetal force. This, in turn, causes the spacecraft to move away from the Moon and into a circular orbit of a Moon satellite. The increased centripetal force causes the spacecraft to accelerate, and thus its velocity modulus increases. The magnitude of this increase in velocity modulus depends on the duration and power of the brake rocket. In conclusion, the velocity modulus of the spacecraft increases due to the firing of the brake rocket.
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-2+3c=2x+6+x 8th Grade Math Problem-
Answer:
3c=3x+6
Step-by-step explanation:
-2+3c=2x+6+x
-2+3c=3x+6 First combine the x on the right side.
-2+3c=3x+6
+2 +2 Add 2 to both sides to eliminate 2 on the left side.
3c=3x+6
help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2
All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.
What do you meant by rational expression ?[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$[/tex]
[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$[/tex]
Simplify
[tex]$\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$[/tex]
[tex]$\frac{x-2}{7}=\frac{x-2}{7}$[/tex]
Seven times both sides
[tex]$\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$[/tex]
Simplify
[tex]$x-2=x-2$[/tex]
There is equality between the two sides.
For every x Verify Solutions, true
Search for ill-defined (singularity) points: [tex]$x=-6$[/tex]
Because -6, the equation is undefined.
[tex]x \neq -6[/tex]
Therefore the correct answer is option C ) All real numbers except -6 .
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What is the inverse of function f? f(x) = √x + 7
The inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
What is inverse of function?A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.
Given that the equation of the function is:
f(x) = √x + 7
Covert the given function into an equation:
y = √x + 7
Interchange the variables in the equation:
x = √y + 7
Isolate the value of y.
Subtract, 7 from both sides of the equation:
x - 7 = √y + 7 - 7
x - 7 = √y
Take square on both sides of the equation:
(x-7)² = (√y)²
(x-7)² = y
Replace, y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) = (x-7)^2[/tex]
Hence, the inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
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Hannah makes 5 out of 8 attempted free-throws! What is the average waiting time for Hannah to make her first basket, and what is the probability that she will make a basket on or before her last attempt within her average waiting time?
The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.
Given;
Hannah makes 5 out of 8 attempted free-throws
Now,
The average waiting time of hannah to make her first basket=5/8
The probability of hannah making basket at her last attempt=1/8
The probability of hannah making basket before her last attempt= 2/8
Therefore, the probabilty will be 1/8 and 2/8.
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2. The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s)
when f(x) = g(x)? Explain your answer
Answer: x= -3 and x= -1
Step-by-step explanation:
We can see from table that when x= -3, the f(x) have the same y with g(x). Also when x= -1, the f(x) have the same y with g(x).
Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant.
Coordinates Quadrant
P( , -5/7) IV
The missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant is √(2/7) or √(2/7)
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. If a point P lies on the unit circle, then the distance from the origin to P is 1.
We can use the distance formula to find out the missing coordinate of P.
The distance formula: [tex]d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where (x1, y1) is origin and (x2, y2) is the point P.
Given in the problem that P is in Quadrant IV, then the (x, y)-coordinate is negative.
So we can use the given information and the distance formula to find out the missing coordinate.
[tex]d = \sqrt((x2 - 0)^2 + (y2 - 0)^2) = 1[/tex]
x2 = -5/7, y2 = -5/7
[tex]d = \sqrt((-5/7 - 0)^2 + (-5/7 - 0)^2) = \sqrt((-5/7)^2 + (-5/7)^2) = \sqrt(25/49 + 25/49) = \sqrt(50/49) = \sqrt(2/7) = 1[/tex]
Therefore, the missing x coordinate of P is √(2/7) or √(2/7)
P = (-5/7,√(2/7))
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⚠️QUICK⚠️ ⭐️rewriting exponential expressions⭐️
By exponential expressions 3(5x + 3).(27)x as 3f(x) this we get value 3.5x(27.3,x(x)f) + 3.3(27.3,x(x)f) .
What is exponential expressions?Simply put, exponential expressions are a condensed approach to express powers. The base's frequency of use as a factor is indicated by the exponent.
f(x) = ax, where x is the input variable and is expressed as an exponent, is the formula for an exponential function.
In addition to being dependent on the exponential function, the exponential curve also depends on the value of x. Whenever a>0 and a1 are not equal.
Example :
3(5x + 3).(27)x as 3f(x) : 3.5x(27.3,x(x)f) +3 .3 (27 .3,x(x)f)
Steps
3(5x+3)(27x , 3f(x))
= 3(5x + 3)(27.3,x(x)f)
Apply the distributive law :
a(b + c) = ab + ac
a = 3(27x,3f(x)), b=5x,c = 3
=3(27x,3f(x)). 5x + 3(27x,3f(x)).3
=3.5x(27.3,x(x)f) + 3.3(27.3,x(x)f)
The Complete Question.
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1.4 Classify the systems as being either discrete or continuous: (a) Electrical capacitor (You are interested in modeling the amount of current in a capacitor at any time t). (b) On-line gaming system. (You are interested in modeling the number of people playing Halo 4 at any time t.) (c) An airport. (You are interested in modeling the percentage of flights that depart late on any given day).
(a) Any number could represent the amount of current flowing through the capacitor in decimal form. So that the electric capacitor is Continuous.
(b) There are exactly that many players. So On-line gaming system is Discrete.
(c) The number of flights or their proportion depend on the aircraft, which are expressed as whole numbers. So an airport is continuous.
In the question, we have to classify the systems as being either discrete or continuous:
Discrete data, often known as discrete values, is information that only accepts specific values. This type of data, which typically takes the form of whole numbers or integers, can be counted and has a finite set of possible values.
Data that can be measured is referred to as continuous data. There are an endless number of alternative possibilities for the values in this data, which are not fixed.
Nevertheless, the main distinction between discrete and continuous data is that the former has a finite value that can be counted while the latter has an infinite range of possible values that can be measured.
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The diagram below shows the dimensions of a can of tomatoes. HELP!! TYY
A can of tomatoes is shown. A dashed line across the top of the can is labeled nine centimeters. The height of the can is labeled twelve and four tenths centimeters.
How much tin was used to make the can rounded to the nearest square centimeter? Use 3.14 for π.
Enter the correct answer in the box.
_______cm^2
The amount of tin was used to make the can of cylindrical can is 478 cm²
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.
The surface area of cylindrical can = 2π(radius * height + radius²)
From the image:
radius = 9 cm/2 = 4.5 cm, height = 12.4 cm
Hence, substituting:
The surface area of cylindrical can = 2(3.14)(4.5 * 12.4 + 4.5²) = 478 cm²
The surface area of cylindrical can is 478 cm²
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What does x equal???
here is ur answer seeee now
Sets
A, B, C
are subsets of the universal set
U
.
These sets are defined as follows.
U = f, g, h, p, q, r, x, y, z
A = f, g, p, q
B = g, h, q, x, y
C = p, q, x, y, z
Find
C ∩ (B’ ∪ A) =
.
What is roster form
∅
.
The required roster form of the given sets are C ∩ (B’ ∪ A) = {p, q}.
What is the roster form of a set?The roster form of a set is defined as a set that can be represented mathematically in a precise way using a roster notation. In a roster notation, if the set has more than one element, a comma is used to denote the separation between every pair of elements.
The given sets are defined as follows:
U = {f, g, h, p, q, r, x, y, z}
A = {f, g, p, q}
B = {g, h, q, x, y}
C = {p, q, x, y, z}
The complement of set B is the set of all elements in the universal set U that are not in set B.
U = {f, g, h, p, q, r, x, y, z}
B = {g, h, q, x, y}
B’ = {f, p, r, z}
The union of set B' and A is the set of all elements that are in set B' or in set A.
A = {f, g, p, q}
B’ = {f, p, r, z}
B’ ∪ A = {f, g, p, q, r, z}
The intersection of set C and (B’ ∪ A) is the set of all elements that are in both set C and set (B’ ∪ A).
C = {p, q, x, y, z}
B’ ∪ A = {f, g, p, q, r, z}
C ∩ (B’ ∪ A) = {p, q}
So, C ∩ (B’ ∪ A) = {p, q}
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A rock is thrown upward with a velocity of 18 meters per second from the top of a 36 meter high cliff, and it misses the cliff on the way back down. when will the rock be 4 meters from the water, below? round your answer to two decimal places.
The time that is taken to fall is 3.1 s.
What is the time required?In this case, we have been told that A rock is thrown upward with a velocity of 18 meters per second from the top of a 36 meter high cliff, and it misses the cliff on the way back down.
We have to know that the maximum height that the rock has attained by the use of the formula;
v^2 = u^2 - 2gh
v = final velocity
u = initial velocity
g = acceleration
h= distance
v = 0 m/s at the maximum height
h = u^2/2g
h = (18)^2/2 * 9.8
h = 324/19.6
h = 16.5 m
The height from the cliff upwards is; 16.5 m + 36 m = 52.5 m
The distance that is covered when falling is; 52.5 m - 4 m = 48.5 m
If it is falling then it is dropped from a height and u = 0 m/s
h = 1/2gt^2
48.5 = 0.5 * 9.8 * t^2
t = √48.5/0.5 * 9.8
t = 3.1 s
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Rate of change In gallons of gas per year from 1995 to 1997???!?
The rate of change In gallons of gas per year from 1995 to 1997 is: C. Δg/Δt = 4 gal/year.
How to calculate the rate of change?In Geometry, the rate of change of the data in this table can be calculated by using this mathematical equation;
Rate of change (slope), m = (Change in y-axis, Δg)/(Change in x-axis, Δt)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (1995, 1997).Points on the y-coordinate = (530, 538).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), Δg/Δt = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), Δg/Δt = (538 - 530)/(1997 - 1995)
Rate of change (slope), Δg/Δt = 8/2
Rate of change (slope), Δg/Δt = 4 gallon/year.
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Consider a function f defined as follows: f(x)=(x-3)^2, x belongs to [1,2]. Is f invertible in the domain [1,2]? If yes, find the inverse of the function.
(Looking for an complete explanation on how to prove invertible, probably by showing the function is one-to-one and then determining the inverse. )
The inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider the function f(x)=(x-3)²
Where x belongs to [1, 2]
f(x)=x²+9-6x
y=x²+9-6x
Interchange the variables.
x=y²+9-6y
y=3+√18+x
y=3-√18+x
Relace y with f⁻¹(x)
f⁻¹(x)=3+√18+x, 3-√18+x
Hence, the inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
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f(x) 2x + 7 and g(x) = 3x - 12, find f(g(-4))
Step-by-step explanation:
g(-4) = 3(-4)-12
= -24
f(g(-4)) = f(-24)
f(-24) = 2(-24)+7
= -41
i don't know it is true i'm just trying:)
Consider a pool of six I/O buffers. Assume that any buffer is just as likely to be available or occupied as any other. Compute the probabilities associated with the following events:
A = At least two but no more than five buffers occupied.
B = At least three but no more than five buffers occupied.
C = All buffers available or an even number of buffers occupied.
D = At least one of the events A, B, and C occurs.
The associated probabilities are A = At least two but no more than five buffers occupied.
There are a total of 2^6 = 64 possible outcomes when rolling 6 dice.
To find the probability of event A, we need to find the number of outcomes where at least two but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where two, three, four, or five buffers are occupied and subtracting the probabilities where six or zero buffers are occupied.
The probability of two buffers being occupied is (6 choose 2)(1/64) = 15/64
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)(1/64) = 6/64
So the probability of event A is (15/64) + (20/64) + (15/64) + (6/64) = 56/64.
B = At least three but no more than five buffers occupied.
To find the probability of event B, we need to find the number of outcomes where at least three but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where three, four, or five buffers are occupied and subtracting the probability where six buffers are occupied.
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)*(1/64) = 6/64
So the probability of event B is (20/64) + (15/64
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Write the polynomial that represents the perimeter of the figure pictured below.
The polynomial that represents the perimeter of the figure is 3x
How to determine the perimeter of the triangleFrom the question, we have the following parameters that can be used in our computation:
Side length = x
Triangle type = equilateral triangle
See attachment for the figure
The perimeter of an equilateral triangle can be calculated as
P = 3 * side length
substitute the known values in the above equation, so, we have the following representation
P = 3 * x
So, we have the following representation
P =3x
Hence, the perimeter expression is 3x
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Opportunity cost and production possibilities
Shen is a talented artist who sells hand-crafted goods on his website. Shen currently crafts and sells both crochet hats and baskets. He spends 8 hours
a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good.
Answer:
I'm not understanding can you say it in a similar way?
Answer:
Step-by-step explanation:
Opportunity cost and production possibilities
Shen is a talented artist who sells hand-crafted goods on his website. Shen currently crafts and sells both crochet hats and baskets. He spends 8 hours
a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good
Write a function in a factored form that could represent the situation below:
A Polynomial function has zeros at 1, -2 and 5 (all multiplicity 2).
The polynomial equation with the given zeros is something like:
p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²
How to find the function that can represent the situation?Remember that for a polynomial of degree a with the zeros {x₁, x₂, ...} the polynomial can be written as:
p(x) = a*(x - x₁)*(x - x₂)*...
Here we don't know the leading coefficient, and we know that the zeros are:
{1, 1, -2, -2, 5, 5}
These appear twice because all have a multiplicity of 2.
Then the equation is:
p(x) = a*(x - 1)*(x - 1)*(x + 2)*(x + 2)*(x - 5)*(x - 5)
p(x) = a*(x - 1)²*(x + 2)²*(x - 5)²
Where a can be any real number different than zero.
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Given the function: y(x) = 4x ^ 3 + 3x ^ 2 - 3x . Evaluate the change in y between x = 5 and x = 9
The change in y between x = 5 and x = 9 is 2572.
What is a function?
An assignment of a Y element to every X element constitutes a function from X to Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.
Here, the function is given as y(x) = 4x ^ 3 + 3x ^ 2 - 3x.
we'll find the value of given function i.e. y when x = 5 and 9.
when x = 5, y(5) = 4(5) ^ 3 + 3(5) ^ 2 - 3(5)
= 4(125) + 3(25) - 15
= 500 + 75 - 15
= 560.
when x = 9, y(9) = 4(9) ^ 3 + 3(9) ^ 2 - 3(9)
= 4(729) + 3(81) - 27
= 2916 + 243 - 27
= 3132.
So, the change in y is 2572 (3132 - 560).
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What is the following difference?? PLSS help
The simplified expression is ab∛ 3ab².
The correct option is (C).
What are Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])
Now, factorizing the terms as
192ab² = 2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b
81 [tex]a^4b^5[/tex] = 3 x 3 x 3 x 3 x a x a x a x a x b x b x b x b x b
So, 2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])
= 2ab (∛2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b) -5(∛3 x 3 x 3 x 3 x a x a x a x
a x b x b x b x b x b)
= 2ab ( 2 x 2 ∛ 3 x a x b x b) -5( 3 x a x b ∛3 x a x b x b )
= 8ab ∛ 3ab² - 15ab∛ 3ab²
= -7ab ∛ 3ab²
Hence, the simplified expression is ab∛ 3ab².
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Two angles are supplementary if the sun of their measures is 180 degrees find two supplementary angles such that one is 150 degrees more than 1/5 of the others
The two supplementary angles are 155 and 25.
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given;
Two angles are supplementary
One is 150 degrees more than 1/5 of the others
Let one angle be x
Then the other angle will be x/5+150
Now,
x+ x/5+150=180
6x/5+150=180
6x/5=180-150
6x/5=30
x=150/6
x=25
Other angle= x/5+150=25/5+150
=155
Therefore, the angles will be 155 and 25.
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find the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2. (source: hmmt)
The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.
The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2 can be calculated using the following formula:
Range = Maximum Value - Minimum Value
The expression inside the parentheses can be simplified to 3cos2a cos4a + 3sin2a sin4a and the expression inside the exponential can be simplified to tan2a (1 / cos2a - sin2a). This gives us the expression
Range = 3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)
To calculate the maximum and minimum values, we can use derivatives to find the critical points of the expression. Taking the first derivative with respect to a, we get
d/da (3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)) = 0
Solving this equation gives us the critical points of a = ±7t/6. Using these values, we can calculate the maximum and minimum values of the expression.
Maximum Value = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6)
Minimum Value = 3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6)
Finally, using the formula for the range, we can calculate the range of the expression to be
Range = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6) - (3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6))
This expression gives us the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.
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Question 5 Piecewise graphs. Graph each of the given functions. Be sure to clearly indicate possible points that may be significant. 2 (a) f(x) = x^2 +1
The function f(x) = x^2 + 1 can be graphed using the coordinates (x, y) where x is the x-coordinate, and y is the y-coordinate.
This function can be written as y = x^2 + 1. Using this equation, we can plot the graph of the function. To plot the graph, we need to plot points on the x-axis and y-axis. The x-axis is the horizontal line and the y-axis is the vertical line.
For example, let us take a point x = 0. Substituting x = 0 in the equation f(x) = x^2 + 1, we get y = 0^2 + 1, which is equal to 1. So, we can plot the point (0,1) on the graph. Similarly, we can plot the point (1,2), (2,5), (3,10), (4,17), (5,26), and so on.
By plotting all these points, we can get the graph of the function f(x) = x^2 + 1. This graph is a parabola with vertex at (0,1). It is an increasing function, which means that as the value of x increases, the value of y also increases. The graph is also symmetric about the y-axis.
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