Answer:
The answer is "1110, 20.4, and 31.408"
Step-by-step explanation:
For point a:
Given:
[tex]\to mean\ ( \bar{x})=1051\\\\\to standard \ deviation \ (\sigma)=194\\\\\to P(Z<=z)=0.62\\\\\to z=0.3055\\[/tex]
Calculating the SAT score:
[tex]=1051+0.3055 \times 194 \\\\ =1110.267 \approx 1110[/tex]
For point b:
Given:
[tex]\to mean \ \bar{x}=19\\\\ \to standard \ deviation \ (\sigma) =4.7\\\\[/tex]
Calculating the equivalent ACT score:
[tex]=19+0.3055 \times 4.7 \\\\ =20.43585 \approx 20.4[/tex]
For point c:
[tex]\to SAT \ Score =1563\\\\\to z=\frac{(1563-1051)}{194}= \frac{512}{194}=2.64\\\\[/tex]
Calculating equivalent ACT score:
[tex]=19+2.64 \times 4.7 \\\\=31.408[/tex]
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol. How much cholesterol is in each item?
Using a system of equations, the amounts of cholesterol in each item are given as follows:
Egg: 278 mg.Cupcake: 14 mg.Slice of pizza: 11 mg.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables for this problem are given as follows:
Variable x: Amount of cholesterol in an egg.Variable y: Amount of cholesterol in a cupcake.Variable z: Amount of cholesterol in a slice of pizza.By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol, hence:
x + y + z = 303.
3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol, hence:
3y + 4z = 90
y + 1.33z = 30.
By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol, hence:
2x + y = 570.
Then, writing y and z as functions of x:
y = 570 - 2x.z = (30 - y)/1.33 = (30 - 570 + 2x)/1.33 = 1.5x - 406.Then, replacing on the first equation:
x + y + z = 303.
x + 570 - 2x + 1.5x - 406 = 303.
0.5x + 164 = 303.
x = (303 - 164)/0.5
x = 278.
The amounts for the cupcake and the slice of pizza are given as follows:
y = 570 - 2(278) = 14 mg.z = 1.5x - 406 = 1.5(278) - 406 = 11 mg.More can be learned about a system of equations at https://brainly.com/question/24342899
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questions 5 and 6 please!
will give brainliest to whoever answers
90 points
Answer:
5)
rise over run so
5/5 = 1
6)
-2/4 = -0.5
Cycles travel at an the average speed of 20km/h for 1.5 Hours
calculate the distance she travels in 1.5
Answer:
30 km
Step-by-step explanation:
Distance = rate x time
Distance = 20 x 1.5
Distance = 30
[tex]20*1.5=30[/tex] [tex]km[/tex]
Correct answer:-
Avg. speed = [tex]20km/h[/tex]
Time = [tex]1.5 hour[/tex]
Distance traveled in 1.5 hours is Distance = Speed x Time
So,
[tex]D = 20 * 1.5 = 30.[/tex]
reference link-
a cyclist travels at a speed of 20 km per hour how far will he ...https://brainly.in › Math ›
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Using the following accounts and balances, prepare the “Stockholders’ Equity” section of the balance sheet. 60,000 shares of common stock authorized, and 4,000 shares have been reacquired.
Common Stock, $50 par $2,400,000
Paid-In Capital from Sale of Treasury Stock 48,000
Paid-In Capital in Excess of Par—Common Stock 576,000
Retained Earnings 1,368,000
Treasury Stock 25,000
The total Stockholders’ Equity is $4,367,000
Total Stockholders’ EquityCommon Stock, $50 par $2,400,000
Paid-In Capital in Excess of Par—Common Stock $576,000
Paid-In Capital from Sale of Treasury Stock $48,000
Total paid in capital $3,024,000
Retained Earnings $1,368,000
Less Treasury stock $25,000
Total Stockholders’ Equity $4,367,000
Therefore the total Stockholders’ Equity is $4,367,000.
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Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a.
r = 1 + 3 sin theta
c.
r = 1 + 3 cos theta
b.
r = 2 + 2 sin theta
d.
r = 3 + sin theta
Option a. The equation that is used to show the graph of the limacon is given as r = 1 + 3 sin theta.
How to solve for the equationWe have these ppoints [-5,5] by [-5,5]
The limacoin is used to represent a shape that may appear like that of a snail.
This is written in the form of
r = a ± b sin θ
and
r = a ± b cos θ
Given that we have the ± sign, the curve that is at the top of the horizontal; line is the + sign and the one below is the -
If a/b < 1 then a circle is within the circle that was formed as a graph.
Hence from the description that we have given here, the graph has the forms of
r = a + b sin θ
This is the equation that can be used to suit the form r = 1 + 3 sin theta
Hence option a is right.
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someone please help me find the value of x
Hello,
5x² = 90/2
5x² = 45
x² = 45/5
x² = 9
x = √9 or x = -√9
x = 3 or x = -3
I need help with this geometry question asap!
No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.
When are Two Lines Proven to be Parallel to each other?Two lines that are cut across by a transversal can be proven to be parallel to each other if:
The alternate interior angles along the transversal and on the two lines are congruent [alternate interior angles theorem].The alternate exterior angles along the transversal and on the two lines are congruent [alternate exterior angles theorem].The same-side interior angles along the transversal and on the two lines are supplementary [same-side interior angles theorem].The corresponding angles along the transversal and on the two lines are congruent [corresponding angles theorem].Thus, given the following information:
m∠2 = 115°
m∠15 = 115°
With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.
In summary, we can conclude that:
D. None of the options are correct.
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The box plot below shows the total amount of time, in minutes, the students of a class surf the Internet every day: Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)
Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)
Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)
The pieces of information that is provided by the box plots are the median and first quartile.
The piece of information that is not provided by the box plots is the mean.
The interquartile range is 22.50.
An outlier would distort the values of the median and the quartiles.
What is a box plot?
A box plot is used to study the distribution and level of a set of scores. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the quartiles is the interquartile range.
Interquartile range = 60 - 37.50 = 22.50
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Gene is tossing a normal quarter. He tosses the quarter 12 times and it lands on heads 9 times. If Gene tosses the quarter again, what is the probability that it lands on tails? Input your answer in fraction form.
Answer:
1/2
Step-by-step explanation:
This is an independent event. It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes. There are only 2 outcomes: heads or tails. I am only looking for one of those outcomes, so 1/2.
Solve for v. -8=-2/v
According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.
–4, –3, 2, 3, 4
Which are actual roots of f(x)?
–4 and 3
–4, 2, and 3
–3 and 4
–3, 2, and 4
The actual roots of f(x) are -4 and 3
How to determine the actual roots?The function is given as:
f(x) = 2x^2 + 2x – 24.
Expand the function
f(x) = 2x^2 + 8x- 6x – 24.
Factorize the function
f(x) = 2x(x + 4) - 6(x + 4)
Factor out x + 4
f(x) = (x + 4)(2x - 6)
Set to 0
(x + 4)(2x - 6) = 0
Solve for x
x = -4 and 2x = 6
This gives
x = -4 and x = 3
Hence, the actual roots of f(x) are -4 and 3
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Answer:
A
Step-by-step explanation:
Got 100 on test
20 pts and brainliest
The two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.
Hence, option C is the correct answer.
What are the solutions to the quadratic equation?Given the equation; 9x² + 4 = 0
First, we subtract 4 from both sides.
9x² + 4 = 0
9x² = -4
x² = -4/9
Take the square roots of both sides
x = ±√(-4/9)
Rewrite -4/9 as (2i/3)²
x = ±√(2i/3)²
x = ±(2i/3)
Hence,
x = 2i/3, -2i/3
Therefore the two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.
Hence, option C is the correct answer.
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Answer:
but it says ill get 10 only
Step-by-step explanation:
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².
How to interpret the graph?The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.
This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:
x⁴
x - a
(x - b)²
In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².
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Name the following polynomial: 4x^2 +8+16 cubic polynomial quartic trinomial quadratic trinomial cubic trinomial
The polynomial is quadratic trinomial
How to name the polynomial?The polynomial function is given as:
4x^2+ 8x +16
The highest power in the above polynomial is 2.
This represents quadratic
The number of terms in the above polynomial is 3
This represents trinomial
Hence, the polynomial is quadratic trinomial
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a. P is equal to the set containing t,v,c and d
b. the set consisting of the elements 2 and 6 is a proper subset of [ 2,6,8,12}
c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6}
a.P is equal to the set containing t,v,c and d
p=
The answers to the questions are:
a. p = { t, v, c, q}
b. {2, 6} ⊂ {2,6,8,12}
c. {0, 3} ⊄ {3,2,4,6}
How to write the mathematical expression s using mathematical symbols.To represent sets we use
p = { }
Hence
a. p = { t, v, c, q}
b. If 2 and 6 is a proper subset of [ 2,6,8,12},
This can be represented as
{2, 6} ⊂ {2,6,8,12}
c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6} is written as
{0, 3} ⊄ {3,2,4,6}
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(1)
Determine the equation of the line passing through the point (0; -1) and
parallel to the -axis. Do you remember what the gradient of this line is?
(2)
Determine the equation of the line passing through the point(-1;0) and
parallel to the -axis. Do you remember what the gradient of this line is?
We know that,
slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]
Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )
So,
Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]
Now,
The required line equaqtion is given by,
==> y−y 1 = m(x-x1)
==> y−1=1(x−0)
==> y−1=x
==> y=x+1
Suppose y varies inversely with x, and y = 36 when x=112
What inverse variation equation relates x and y ?
The inverse variation equation that relates x and y is x = 4032 / y.
What is the equation that relates x and y?if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
The equation that represents inverse proportion : x = b/y
where b = constant of proportionality
112 = b /36
b = 36 x 112 = 4032
The equation : x = 4032 / y
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A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.
1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x − d)] + c.
-
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.
A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3. Here, amplitude of the graph is 5, value of k is π/40, d is π/2 and c is 3.
Developing the Equation of a Cosine Graph
The given information constitutes the following,
Diameter = 10 m
⇒ Radius, r = 5 m
Time, t = 80 s
Height above the ground, h = 2 m
Thus, we can infer that,
Amplitude, A = 5 m
Period, T = 80 s
Minimum height = 2 m
The cosine function is given as,
a cos [k(x − d)] + c
Here, A is amplitude
B is cycles from 0 to 2π and thus period = 2π/k
d is horizontal shift
c is vertical shift (displacement)
Now, 2π/k = 80
⇒ k = 2π/80 = π/40
The value of c is given as,
c = Amplitude - Minimum height
c = 5 - 2
c = 3
For a shift to the left by π/2 gives, we have,
d = π/2
Thus, the desired equation of the drawn cosine graph is,
y = 5 cos [( π/40)(x - (π/2))] + 3
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Jackson invested $4,200 in an account paying an interest rate of 9 1/2 compounded continuously. Julia invested $4,200 in an account paying an interest rate of 8 7/8 compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Julia's money to double than for Jackson's money to double?
It would Julia 0.60 years more to double the initial investment.
What is future value?
Future value means the initial investment multiplied by 2 since the future value is meant to double.
The formula for future value of a continuously interest rate is provided below:
FV=PV*e^(rt)
FV=future value=$4,200*2=$8,400
PV=initial investment=$4,200
e=exponential constant=2.7182818
r=interest rate=9.5%
t=number of years it takes for the investment to double=unknown
$8,400=$4,200*2.7182818^(9.5%*t)
$8,400/$4,200=2.7182818^(0.095t)
2=2.7182818^0.095t
take log of both sides
ln(2)=0.095t* ln(2.7182818)
0.095t=ln(2)/ln(2.7182818)
0.095t=0.69314718781684800
t=0.69314718781684800/0.095
t=7.30 years
The future value when interest is compounded quarterly is shown thus:
FV=PV*(1+r/4)^(N*4)
FV=$8,400
PV=$4,200
r=8 7/8%
r=8.875%
N=the number of years it would take for the initial investment to double=unknown
$8,400=$4,200*(1+8.875%/4)^(N4)
$8,400=$4,200*(1+0.0221875)^(N4)
$8,400/$4,200=(1+0.0221875)^(N4)
2=(1+0.0221875)^(N4)
2=(1.0221875)^(N4)
take log of both sides
ln(2)=N4*ln(1.0221875)
N4=ln(2)/ln(1.0221875)
N4=31.5857423180125
N=31.5857423180125/4
N=7.90
Difference in years=7.90-7.30
difference in years=0.60 years
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Select the symbol = (equal to) or ≠ (not equal to) to make the expression true.
{0} ? { }
Answer:
=
Step-by-step explanation:
{0}={} because 0 means that there is nothing and in null set too, there is no elements.
Part II: Use the formula from Part I to find the midpoint of the
segment with endpoints at (-2,-1) and (0, 9). Show your work.
PLS
Answer: (-1, 4)
Step-by-step explanation:
[tex]\left(\frac{-2+0}{2}, \frac{-1+9}{2} \right)=\boxed{(-1, 4)}[/tex]
(-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9). This can be obtained by using the formula for finding the midpoint of a line segment.
Find the midpoint of the line segment:When the end points of a line segment are known, the mid point of the line segment is calculated using the midpoint formula,
Midpoint formula,
[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]
(x₁, y₁) and (x₂, y₂) are the endpoints of the line segment.
⇒ This means that, the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is [tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex].
From the question it is given that,
(x₁, y₁) = (-2,-1) (x₂, y₂) = (0, 9)are the endpoints of the line segment.
By using the Midpoint formula we get,
[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](\frac{-2+0 }{2},\frac{-1+9}{2})[/tex]
[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](-1, 4)[/tex]
Hence (-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9).
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Graph the image of the polygon after a reflection in the line y = t.
Answer:
see the attached
Step-by-step explanation:
Reflection over a line moves each point so that the segment between it and its image has the reflection line as its perpendicular bisector.
Reflection over y=xThe line of reflection y=x has the effect of swapping the x- and y-coordinates:
(x, y) ⇒ (y, x) . . . . . reflection in y=x
For example, point C(2, 3) moves to point C'(3, 2).
The attachment shows the reflected figure.
a infant grew 2/4 inches in the first month 7/4 inches in the third month . first find the total inches the infant grew over the three months . then find the difference in the infants from the second month to the third month
The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.
How to compute the fraction?First month = 2/4 inches
Second month = 1 inch
Third month = 7/4 inches.
The total inches the infant grew over the three months will be;
= 2/4 + 1 + 7/4
= 3 1/4 inches.
The difference in the infants from the second month to the third month will be:
= 7/4 - 1
= 3/4 inches.
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If P(En F) = 0.036, P(E|F) = 0.09, and P(F|E) = 0.1, then (a) P(E) = (b) P(F) = = (c) P(EUF) (d) Are the events E and Findependent? =
The events E and F are not independent
How to determine the probabilities?The given parameters are:
P(E n F) = 0.036
P(E|F) = 0.09
P(F|E) = 0.1
To calculate P(E), we use:
P(F|E) = P(E n F)/P(E)
This gives
P(E) = P(E n F)/P(F|E)
So, we have:
P(E) = 0.036/0.1
Evaluate
P(E) = 0.36
To calculate P(F), we use:
P(E|F) = P(E n F)/P(F)
This gives
P(F) = P(E n F)/P(E|F)
So, we have:
P(F) = 0.036/0.09
Evaluate
P(F) = 0.4
To calculate P(E U F), we use
P(E U F) = P(E) + P(F) - P(E n F)
So, we have:
P(E U F) = 0.36 + 0.4 - 0.036
Evaluate
P(E U F) = 0.724
The events E and F are independent if
P(E n F) = P(E) * P(F)
This gives
0.036 = 0.36 * 0.4
Evaluate
0.036 = 0.144 --- false
Hence, the events E and F are not independent
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This is the photo for the last question
All the angles required to complete each sentence are:
m ∠ 4 = 60, m ∠ 2 = 120m ∠ 3 = 110, m ∠ 4 = 70m ∠ 2 = x, m ∠ 1 = 180 - xHow to find measures of missing angles by Euclidean geometry
In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:
If m ∠ 5 = 60, then m ∠ 4 = 60 by alternal internal angles between parallel lines and m ∠ 2 = 120 by supplementary angles.If m ∠ 7 = 110, then m ∠ 3 = 110 by corresponding angles between parallel lines and m ∠ 4 = 70 by supplementary angles. If m ∠ 6 = x, then m ∠ 2 = x by corresponding angles and m ∠ 1 = 180 - x by supplementary angles.To learn more on angles: https://brainly.com/question/7116550
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f(x)=2^x. What is g(x)?
The function g(x) is g(x)= (3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 3 to form g(x).
This means that:
g(x) = f(3x)
So, we have:
g(x)= (3x)^2
Hence, the function g(x) is g(x)= (3x)^2
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An athlete has 75% of winning the race if he is not injured. If he is injured, his probability of winning the race is only 15%. If the total chances of winning is 51%, what is the probability that he gets injured?
Answer:
X = 'is the athlete injured' (X in {0,1})
Y = 'the athlete wins' (Y in {0,1})
P(Y=1|X=0) = 0.75
P(Y=1|X=1) = 0.15
P(Y=1) = 0.51
We are looking for P(X=1) - P(Y=1) = P(Y=1|X=0)*(1-P(X=1)) + P(Y=1|X=1)*P(X=1)
The above equation should provide you with the answer 0.4!
Step-by-step explanation:
A compression wave is moving away from an explosion at 100 ft/sec. How fast is the volume within the spherical compression wave increasing in t = 4 seconds? You will need the formula for the volume of a sphere! *Leave π in your answer do not convert to a decimal!
The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.
Volume of a sphereGiven:
dr/dt=100 ft/sec
When: t=4 seconds, radius(r)=400ft
Hence:
Volume of a sphere (V)=4/3πr³
dv/dt=4/3π.3r² dr/dt
dv/dt=4πr²dt/dr
When t=4 seconds
dv/dt=4π×(100×4)²×100 cubic ft/sec
dv/dt=4π×(400)²×100 cubic ft/sec
dv/dt=64000000π cubic ft/sec
Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.
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Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let PP represent Jeremiah's total pay on a day on which he sells xx dollars worth of computers. The table below has select values showing the linear relationship between xx and P.P. Determine how many dollars worth of computers Jeremiah would have to sell in order to get paid $130 on a given day.
Jeremiah has to sell 5000 dollars worth of computers to get paid $130 on a given day. Using the linear equation, the required value is calculated.
What is a linear equation?An equation in which if the highest degree of the variable is 1(one), then that equation is said to be a linear equation.
General form: ax + b = c; where the power of the variable x is 1.
Calculation:It is given that,
Jeremiah makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day.
Consider,
P - as total pay on a day, x - as the number of dollars worth of computers, B - as basic pay, and C - as commission percentage.
So, the linear equation that relates x and P is,
P = Cx + B ...(i)
On substituting the values from the given table we get,
122.5 = C(4500) + B ...(ii)
160 = C(7000) + B ...(iii)
175 = C(8000) + B ...(iv)
By solving equations (iii) and (iv), we get
C = 15/1000 = 0.015
B = 55
Finding x value when P = $130:
We have P = Cx + B. Then for P = 130,
130 = Cx + B
We know C = 0.015 and B = 55
On substituting these values,
130 = (0.015) x + 55
⇒ 0.015x = 130 - 55 = 75
∴ x = 75/0.015 = 5000
Therefore, the required computers are 5000 dollars worth.
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Disclaimer: The given question on the portal was incomplete. Here is the complete question.
Question: Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Jeremiah's total payments on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how many dollars worth of computers Jeremiah would have to sell to get paid $130 on a given day.
Table:
x: 4500, 7000, 8000
P: 122.5, 160, 175
respectively.
Which of the following equations represents F(x)= x4 reflected across the line
y = x?
OA. F(x)=√x
OB. F(x)=√x
OC. F(x)=-4x
OD. F(x) = ±**
The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.
For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).
In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.
The function can be shown as:
y = f(x) = x⁴,
or, x⁴ = y,
or, [tex]x = \pm\sqrt[4]{y}[/tex]
Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].
Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.
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The complete question is:
"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?
A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]
B. [tex]F(x)= \sqrt[4]{x}[/tex]
C. [tex]F(x)= \pm x^4[/tex]
D. [tex]F(x)=- \sqrt[4]{x}[/tex] "