PLEASE I NEED AN ANSWER ASAP THIS EXAM IS TIMED!!!!!
In the equation y = 3/4x + 5 , identify the slope and y-intercept.
slope =
Y-Intercept =
Answer:
Step-by-step explanation:
S is3/4
Intercept is 5
find the equation of a circle with a point at ( 10 , - 4 ) and a point at ( -2 , - 4 )
Answer:
Solution given:
letA=(10,-4)
B=(-2,-4)
centre[C](h,k)=\(\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)\)
radius=\(\sqrt{(4-10)²+(-4+4)²}=6\)units
we have
Equation of a circle is;
(x-h)²+(y-k)²=r²
(x-4)²+(y+4)²=36
or.
x²-8x+16+y²+8y+16=36
x²-8x+8y+y²=36-32
x²-8x+8y+y²=4
The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.
Answer:
\( \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36\)
Step-by-step explanation:
the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter
since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle
remember midpoint formula,
\( \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)\)
let,
\( \displaystyle x _{1} = 10\)\( \displaystyle x _{2} = - 2\)\( \displaystyle y _{1} = - 4\)\( \displaystyle y _{2} = -4\)thus substitute:
\( \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)\)
simplify addition:
\( \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)\)
simplify division:
\( \rm\displaystyle M = \left( 4, - 4 \right)\)
so the centre of the circle is (4,-4)
since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is
\( \displaystyle r = 4 - ( - 2)\)
simplify which yields:
\( \displaystyle\boxed{ r =6}\)
recall the equation of circle
\( \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} \)
we acquire that,
h=4k=-4r=6therefore substitute:
\( \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} \)
simplify:
\( \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36\)
and we are done!
also refer the attachment
(the graph is web resource of desmos)
Leona and Fred are friendly competitors in high school. Both are about to take the ACT college entrance examination. They agree that if one of them scores 5 or more points better than the other, the loser will buy the winner a pizza. Suppose that in fact Fred and Leona have equal ability, so that each score varies Normally with mean 24 and standard deviation 2. (The variation is due to luck in guessing and the accident of the specific questions being familiar to the student.) The two scores are independent. What is the probability that the scores differ by 5 or more points in either direction?
If Leona and Fred are friendly competitors in high school. the probability that the scores differ by 5 or more points in either direction is: 0.0771.
How to find the probability?Let F = Fred
Let L= Leona
In a situation where F and L are respective score , F - L is has this distribution N(0, √2² + 2²)
Now let find the Probability
P(Fred score 5 point more than Leona) + P(Leona score 5 point more than Fred)
= P(F-L>5) +P(L-F>5) = P(Z> 5-0/√8) + P(Z> 0-5/√8)
P(Z>1.7678)+ =P(Z< -1.7678)
=2P(Z>1.7678)
=2(0.03854)
=0.0771
Therefore the probability is 0.0771.
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Helppp, 60 points!!!
Answer:
the answer is c
Step-by-step explanation:
please mark this answer as brainliest
Answer:
The answer is c
Step-by-step explanation:
By moving 5 units to the right you lend at x-1 y-3
How much money will it cost you to drive a diesel tractor trailer truck 175.0 miles if it gets 8.500 miles per gallon and diesel fuel costs $3.599/gallon
To calculate the cost of driving a diesel tractor trailer truck for 175.0 miles, we need to determine the number of gallons of fuel required and then multiply it by the cost per gallon.
Calculate the number of gallons of fuel needed. Given that the truck gets 8.500 miles per gallon, we divide the total distance (175.0 miles) by the fuel efficiency: 175.0 miles / 8.500 miles per gallon
= 20.59 gallons (approximately)
Calculate the cost of the fuel.Since diesel fuel costs $3.599 per gallon, we multiply the number of gallons needed by the cost per gallon: 20.59 gallons x $3.599/gallon = $73.89 (approximately) Therefore, it will cost you approximately $73.89 to drive the diesel tractor trailer truck for 175.0 miles, assuming it gets 8.500 miles per gallon and diesel fuel costs $3.599 per gallon.
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Suppose that
f(x) = 5 x^6 - 3 x^5.
(A) Find all critical numbers of f. If there are no critical numbers, enter 'NONE'.
Critical numbers =
(B) Use interval notation to indicate where f(x) is increasing.
Note: Use 'INF' for \infty, '-INF' for -\infty, and use 'U' for the union symbol.
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'.
x values of local maxima =
(E) Find the x-coordinates of all local minima of f. Note: If there are no local minima, enter 'NONE'.
x values of local minima =
(F) Use interval notation to indicate where f(x) is concave up.
Concave up:
(G) Use interval notation to indicate where f(x) is concave down.
Concave down:
(H) List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'.
x values of inflection points =
(I) Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'.
Horizontal asymptotes y =
(J) Find all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'.
Vertical asymptotes x =
The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point
f(x) = 5x⁶ - 3x⁵
differentiation w.r.t x
=> f'(x) = 30x⁵ - 15x⁴
Putting f'(x) = 0
30x⁵ - 15x⁴ = 0
=> x⁴(30x - 15) =0
=> 30x - 15 = 0
=> x = 15/30
=> x = 0.5 , 0
Critical number is 0.5 , 0
(B) To find where f(x) is increasing
for x > 0.5 ,
(30x-15) > 0 => x⁴(30x - 15) > 0
Therefore , f(x) is increasing at ( 0.5 , ∞ )
(C)To find where f(x) is decreasing
for x < 0.5 ,
(30x-15) < 0 => x⁴(30x - 15) < 0
Therefore , f(x) is decreasing at ( -∞ , 0.5)
(D) Differentiation f'(x) again w.r.t to x
f'(x) = 30x⁵ - 15x⁴
f"(X) = 150x⁴ - 60x³
Substituting critical values of x
=> 150(0.5)⁴ - 60(0.5)³
=>9.375 - 7.5
=> -1.875 < 0 , Hence , x = 0.5 is point of maxima
(E) no point of minima
Similarly , we can solve other parts
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write the equation of each line in slope intercept form
The equation of each line in slope intercept form y = 2x + 3,x = 4
The equation of a line in slope-intercept form (y = mx + b), the slope (m) and the y-intercept (b). The slope-intercept form is a convenient way to express a linear equation.
Equation of a line with slope m and y-intercept b:
y = mx + b
Equation of a vertical line:
For a vertical line with x = c, where c is a constant, the slope is undefined (since the line is vertical) and the equation becomes:
x = c
An example for each case:
Example with given slope and y-intercept:
Slope (m) = 2
y-intercept (b) = 3
Equation: y = 2x + 3
Example with a vertical line:
For a vertical line passing through x = 4:
Equation: x = 4
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Answer:
y=mx+b
Step-by-step explanation:
Use the method of cylindrical shells to find the volume of the solid generated by rotating the region bounded by the curves y=cos(πx/2), y=0, x=0, and x=1 about the y-axis
Answer:
1,45 cubic units
Step-by-step explanation:
The method of cylindrical shells demands that the volume of the solid is given by:
\(V=2\pi\int_a^b xf(x)dx\) (1)
In this case you have that f(x) is:
\(f(x)=cos(\frac{\pi}{2}x)\)
a = 0
b = 1
First, you solve the integral, by parts:
\(\int xf(x)dx=\int xcos(\frac{\pi}{2}x)dx=x(\frac{2}{\pi})sin(\frac{\pi}{2}x)-\int (\frac{2}{\pi})sin(\frac{\pi}{2}x)dx\\\\=(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)+C\)
Next, you calculate the volume of the solid, by replacing the solution to the integral in the equation (1):
\(V=2\pi[(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)]_0^1\\\\V=2\pi[(\frac{2}{\pi})-(\frac{2}{\pi})^2]=1,45u^3\)
hence, the volume of the solid generated is 1,45 cubic units
A) Tell which measure of central tendency best describes the data.
Time spent on the internet (min/day): 75,38,43,120,65,48,52.
B) Tell which measure of central tendency best describes the data.
Weight of books (oz): 12,10,9,15,16,10.
A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.
The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.
B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.
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Construct a line parallel to the given line through point P.
Answer:
Step-by-step explanation:
you didn’t post the given line.
if it’s parallel, that means they have the same slope.
all you need is in the photo
Answer:
2
Step-by-step explanation:
8% - 8/100 = 0.08
0.08 x 25 = 2
Which of the following statements best describes what a p-value is in terms of hypothesis testing?
Group of answer choices
It measures the probability that the null hypothesis is true
It measures the probability that the null hypothesis is not true
It is a measure of the strength of the evidence against the null hypothesis
It provides quantifiable proof that a hypothesis is true
The statement that best describes what a p-value is in terms of hypothesis testing is: It is a measure of the strength of the evidence against the null hypothesis.
What is a p-value?
In statistics, the p-value is the likelihood of obtaining the observed results of a test, or anything more extreme, assuming that the null hypothesis is true.
The null hypothesis is a statistical hypothesis that assumes that the statistical data used in the analysis are insignificant and that the observed differences can only be due to chance.
The p-value is a critical measure in hypothesis testing since it determines the statistical importance of the evidence against the null hypothesis.
The p-value is a percentage value that ranges from 0 to 1.
When p ≤ 0.05, we reject the null hypothesis because the observed evidence is statistically significant. If p > 0.05, we accept the null hypothesis because the observed evidence is not statistically significant.
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the following parts guide you through finding the distribution of ˆθ. (a) show that c −1h¯ has a gamma nα, β nc distribution. write its density.
The density of \(\(c - \frac{1}{\bar{h}}\) is given by: \\\[f(x) = \frac{1}{\Gamma(n\alpha)\beta^{n\alpha}} x^{n\alpha - 1} e^{-\frac{x}{\beta}}\]\)
To find the distribution of \(\(\hat{\theta}\), we are given that \(c - \frac{1}{\bar{h}}\) has a gamma \(n\alpha, \beta\)\) distribution. The gamma distribution is defined as:
\(\[f(x) = \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha - 1} e^{-\frac{x}{\beta}}\]\)
where\(\(\Gamma(\alpha)\)\) is the gamma function.
Now, let's find the density of\(\(c - \frac{1}{\bar{h}}\). Since \(c - \frac{1}{\bar{h}}\) has a gamma \(n\alpha, \beta\) distribution, we have:\[f(x) = \frac{1}{\Gamma(n\alpha)\beta^{n\alpha}} x^{n\alpha - 1} e^{-\frac{x}{\beta}}\]\)
where \(\(n\alpha\) is the shape parameter and \(\beta\)\) is the scale parameter.
Therefore, the density of \(\(c - \frac{1}{\bar{h}}\) is given by:\[f(x) = \frac{1}{\Gamma(n\alpha)\beta^{n\alpha}} x^{n\alpha - 1} e^{-\frac{x}{\beta}}\]This is the desired density for the distribution of \(c - \frac{1}{\bar{h}}\).\)
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By using the properties of the gamma distribution and substituting the given parameters, we have derived the density function for c−1h¯, which follows a gamma nα, βnc distribution.
To find the distribution of ˆθ, we are given that c−1h¯ follows a gamma nα, βnc distribution. Let's break down the problem step by step.
1. We know that c−1h¯ follows a gamma nα, βnc distribution. The gamma distribution is defined as:
\(\(f(x) = \frac{(\beta^\alpha \cdot x^{\alpha-1} \cdot e^{-\beta x})}{\Gamma(\alpha)}\)\)
where α > 0 is the shape parameter, β > 0 is the rate parameter, x > 0 is the random variable, and Γ(α) is the gamma function.
2. To find the density of c−1h¯, we substitute the given parameters nα and βnc into the gamma distribution formula. So the density of c−1h¯ is:
\(\(f(c−1h¯) = \frac{(\beta^\alpha \cdot (c−1h¯)^{\alpha-1} \cdot e^{-\beta(c−1h¯)})}{\Gamma(\alpha)}\)\)
3. Simplifying the expression, we have:
\(\(f(c−1h¯) = \frac{(\beta^\alpha \cdot (c−1)^{\alpha-1} \cdot h¯^{\alpha-1} \cdot e^{-\beta(c−1h¯)})}{\Gamma(\alpha)}\)\)
4. Hence, we have shown that c−1h¯ has a gamma nα, βnc distribution, and its density is given by:
\(\(f(c−1h¯) = \frac{(\beta^\alpha \cdot (c−1)^{\alpha-1} \cdot h¯^{\alpha-1} \cdot e^{-\beta(c−1h¯)})}{\Gamma(\alpha)}\)\)
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-15-3w = 4w-2w
H is it a infinite solution or no solution
The solution is an infinite solution.
What is an infinite solution?An infinite solution can be defined as a solution with both sides equal to each other
Given the expression;
-15 - 3w = 4w - 2w
Let's simply the expression
Collect like terms
- 3w - 4w + 2w = 15
Add or subtract like terms
-5w = 15
Make 'w' the subject
w = 15/ -5
w = -3
Thus, the solution is an infinite solution.
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a ship is 50 miles from a lighthouse. the bearing of the lighthouse from the ship is n 30 w. the ship travels due east and calculates the bearing to the lighthouse n 40 w. how far is the ship from the lighthouse after traveling due east?
The initial 50 miles distance from the lighthouse and the N 30° W and N 40° W bearing of the ship before and after traveling due east, using the law of sines, indicates.
After travelling due east the ship is approximately 56.53 miles from the lighthouse.What is the law of sines?The law of sines states that in a triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for each of the three sides of the triangle.
The distance of the ship from the lighthouse = 50 miles
Bearing of the lighthouse from the ship = N 30° W
The direction in which the ship travels = due east
The new bearing to the lighthouse = N 40° W
In the triangle formed by the initial and new locations of the ship and the lighthouse, the interior angles, A, B, C are;
m∠A = 30° + 90° = 120°
m∠B = 90° - 40° = 50°
Therefore; m∠C = 180° - (120° + 50°) = 10°
Angle opposite the initial distance of the ship from the lighthouse = ∠B = 50°
The angle opposite the new distance of the ship from the lighthouse = m∠A = 120°
The law of sines indicate that we have;
\(\dfrac{50}{sin(50^{\circ})} = \dfrac{New \, distance}{sin(120^{\circ})}\)
50 × sin(120°) = The new distance of the lighthouse × sin(50°)
The new distance of the lighthouse = 50 × sin(120°)/(sin(50°)) ≈ 56.53
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In a class of 25 pupils, if 15 are females. Calculate the ratio of males : total
Answer:
2:5
Step-by-step explanation:
15 are female. 10 must be male.
Out of 25 pupils, 10 are male, so it's 10:25, or 2:5
Hello, So I cam across this question and im really confused on how to comeplete it. Please could someone help me?
Answer:
89
Step-by-step explanation:
Using the rule for alternate angles, angle ACD is also 39 degrees.
After finding this, we now have the 2 angles in the triangle: 50 and 39 .
Using this we can calculate the value of the angle adjacent to x: 180 - (50+39) = 91.
X and the adjacent angle are on a straight line so they add up to 180.
so, x = 180 - 91 = 89
Hope this helps.
Please mark brainiest.
Can someone pls help me
18/24=0.75
?/80=.75
80x.75=?
?=60
5x+10=60
-10 -10
5x=50
/5 /5
x=10
sub x in for 10
10x5=50+10=60
C.X=10
Which technique most clearly minimizes the likelihood that any outcome differences between the experimental and control conditions can be attributed to age or personality differences in research participants?.
The technique that most clearly minimizes the likelihood that any outcome differences between the experimental and control groups is e. random assignment.
What is random assignment?A methodology used to divide research participants into two groups—the treatment group, also known as the experimental group, and the control group—by randomization is known as random assignment, also known as random placement.
Every research volunteer has an equal chance of being assigned to any of the groups thanks to this randomization mechanism.
In studies, random assignment is a method used to divide participants into different research groups with similar characteristics so that the groups are equal at the start of the investigation.
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Which technique most clearly minimizes the likelihood that any outcome differences between the experimental and control groups can be attributed to age or personality differences in research participants?
a. the double-blind procedure
b. statistical measurement
c. replication
d. operational definitions
e. random assignment
Work out
m
and
c
for the line:
y
=
3
−
x
Answer:
3x
Step-by-step explanation:
m= -1 , c=3
that is the answer for ur question. hope it helped
Please help explain my answer!!
Why does a compass point towards the earth's geographic North Pole?
My answer:
Because that's where Earth's south magnetic pole is located and they attract.
Make sure to explain your answer.
Help!
The correct answers are that Earth’s North Pole is close to the magnetic south pole, magnets allowed to move freely align themselves to point north, and the north pole on a compass is attracted to Earth’s south pole. I really hope this helps you!!
Proving the Parallelogram Diagram Theorem
Given: ABCD is a Parallelogram. Diagonals AC,BD intersect at E.
Prove AE = CE and BE =DE
THE AWNSWERS ARE IN THE PICTURE FROM 4 DOWN SOME POSTED A PICTURE WITH THE 4 UP HERE TO HELP :)
Answer:
Did you learn about equal rectangles? we can prove AEB and CED are equal, which results in what we need to prove here
AE = CE and BE = DE. This can be proved with the help of the properties of congruent triangles.
What is a parallelogram?'A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.'
According to the given problem,
ABCD is a parallelogram.
We know,
BC ║ AD and BC ≅ AD
From, the properties of a parallelogram,
∠CBD = ∠ADB
∠BCA = ∠DAC
We know, two lines are parallel and alternate interior angles of the parallelogram are equal.
Also, Δ BEC ≅ ΔAED (Angle-Side-Angle)
Therefore, AE ≅ CE ( The properties of congruent triangles )
BE ≅ DE ( The properties of congruent triangles )
Hence, we can conclude, in the parallelogram ABCD, AE = CE and BE = DE from the properties of congruent triangles.
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Please help! Make you brainliest and 15 points!
Answer:
b value is 3
rise = 3 run = -2
another point could be (2,0)
Step-by-step explanation:
Find the volume of the sphere.
Either enter an exact answer in terms of \piπpi or use \dfrac{22}{7}
7
22
start fraction, 22, divided by, 7, end fraction for \piπpi.
The volume of sphere is 1437.33 if the given radius is 7 .
What is Surface area of sphere ?
Surface area of sphere can be defined as the product of four , pi and square of radius. And here the value of pi could be 3.14 or 22/7 .
Given ,
Volume of a sphere = 4/3πr³
π = 22/7
r = 7
Volume of a sphere = 4/3πr³
= 4/3 * 22/7 * 7³
= 4/3 * 22/7 * 7 * 7 * 7
= (4 * 22 * 7 * 7 * 7) / (3 * 7)
= 30,184/21
= 1437.3333333333
Volume of a sphere = 1,437.33
Therefore, the volume of sphere is 1437.33 if the given radius is 7 .
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A carton has a length of 2 teet, width of 1teet
, and height of 1. teet. What is the volume of the carton?
03
cubic feet
cubic feet
5
O
cubic feet
5
-
0713
cubic feet
Answer:
432/120 or 18/5 or 3 3/5
Step-by-step explanation:
Once you multiply all the fractions, you get 432/120
Then you simplify to the furthest
Find the measure of an angle that is complementary to one find a Measure that is complementary to to name a pair of adjacent complementary angles
Answer:
1) 25deg. Angle EGF
2) 25deg. Angle BGC
3) Angle 2 and BGC or Angle 1 and EGF
If the ratio between the radii of two spheres is 3:7, what is the ratio of
their volumes?
A. 27:343
B. 9:49
C. 9:7
D. 21:49
Answer:
A
Step-by-step explanation:
Ratio of volume is ratio of the radius raised to the power 3.
The ratio of the volume of the spheres is 27 : 343
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
The ratio of the radii of two spheres is 3:7.
Therefore, if the smaller sphere has a radius of 3x, then the larger sphere has a radius of 7x.
The ratio of the volumes of the two spheres is given by:
(Volume of smaller sphere) : (Volume of larger sphere) = (4/3)π(3x)³ : (4/3)π(7x)³
Simplifying the above expression, we get:
(Volume of smaller sphere) : (Volume of larger sphere) = 27 : 343
Hence , the ratio of the volumes of the two spheres is 27 : 343
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In finance, we need to do partial observations of data and estimate the data generating process (DGP) -- for example, log-normal returns. Sometimes, we can observe only the data points of a certain process, but we don't know what is the function generating the process. Consider the following graph is a plot of the f ′
(x), of a function f(x) given. What is the underlaying function ( f(x −
i)) that is the generator of the observed points in the plot f ′
(x −
i), for points x −
1=−1,x −
2=−0.9,…,x −
n=1?
The underlying function f(x - i) that generates the observed points f'(x - i) in the plot can be determined by integrating the observed points. By integrating f'(x - i), we can obtain f(x - i) up to a constant of integration.
The constant of integration can be determined by incorporating additional information or constraints related to the problem or by considering the behavior of the function at a specific point.
To find the underlying function f(x - i) that generates the observed points f'(x - i), we need to integrate the observed points.
Integration is the reverse process of differentiation, so by integrating f'(x - i), we can recover f(x - i) up to a constant of integration.
The constant of integration arises because integration does not provide a unique solution.
The constant represents an arbitrary additive term that can vary depending on the specific problem or additional constraints.
To determine the constant of integration, we may need additional information or consider specific conditions related to the problem.
It is also important to note that the accuracy of estimating the underlying function f(x - i) depends on the quality and quantity of the observed data points f'(x - i). More data points and precise measurements can lead to a better estimation of the underlying function.
Additionally, the behavior of the function at a specific point can provide valuable insights for determining the constant of integration and refining the estimation of the underlying function.
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If F(x) = 5x + 4, which of the following is the inverse of F(x)? A. F-1(x) = 4 – 5x B. F-1(x) = C. F-1(x) = D. F-1(x) = 5x – 4
Answer:
5x-4
Step-by-step explanation:
A store has issued two different coupons for its customers to use. One coupon gives customers $25 off their purchase price, and the other coupon gives customers 35% off of their purchase. The store allows customers to use both coupons and choose which coupon to apply first. For this context, ignore sales tax. Let f be the function that inputs a cost in dollars) and outputs the cost after applying the "$25 off" coupon, and let g be the function that inputs a cost in dollars) and outputs the cost after applying the "35% off" coupon. a. A customer purchases an item for $140 and asks the cashier to apply the "$25 off" coupon first, followed by the "35% off" coupon. What is the cost of the item after the two coupons are applied? b. A customer purchases an item for $140 and asks the cashier to apply the "$25 off" coupon first, followed by the "35% off" coupon. Use function notation to represent the cost of the item in dollars) after the two coupons are applied. c. A customer purchase an item for $140 and asks the cashier to apply the "35% off" coupon first, followed by the "$25 off" coupon. What is the cost of the item after the two coupons are applied? d. A customer purchases an item for $140 and asks the cashier to apply the "35% off" coupon first, followed by the "$25 off" coupon. Use function notation to represent the cost of the item in dollars) after the two coupons are applied.
On a purchase of $140, if $25 off coupon is applied followed by 35% off coupon, a) the cost will be $74.75, b) the functional representation will be
g°f = 0.65x - 16.25 : x = $140 . If 35% off coupon is applied followed by $25 off coupon, c) the cost will be $66 and d) functional representation will be f°g = 0.65x - 25 : x = 140
Here we are given two functions f and g.
f reduces the cost by $25 and g is the function that reduces it by 35%. This means that it will make the amount equivalent to 65% of the original.
Now f will be
f(x) = x - 25
g(x) = 0.65x
a)
The cost before applying the coupons is $140.
Now after applying finction f and reducing 25$ we get
$140 - $25
= $115
Now after applying 35% off coupon, the cost will be 65% of the previous one.
Hence the final cost will be
65/100 X 115
= $74.75
b)
Here we need to use function notation to represent the cost after the two coupons are applied.
Here it will clearly be g°f
Hence it will be
g°f = 0.65(x - 25) : x = $140
or, g°f = 0.65x - 16.25 : x = $140
c)
Here we will first apply the 35% off coupon to get
0.65 X 140
= $91
Now applying the $25 off coupon will give us
$66
d)
Now, here we will see that we will get the function
f°g = 0.65x - 25 : x = 140
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