The probability that a randomly selected loan application takes longer than 11 days to process is 0.1587.
The time taken to process a loan application is uniformly distributed between 5 and 17 days.
We need to determine the probability that a random loan application takes longer than 11 days to process.
To compute the probability, we'll first determine the distribution's parameters;
we have: a = 5 (minimum value)b = 17 (maximum value)
Mean: μ = (a+b) / 2 = (5+17) / 2 = 11
Variance: σ2 = (b-a)2/12
= (17-5)2/12
= 12.3333Standard deviation:
σ = 3.516
For the problem, we want to find the probability of a loan application taking more than 11 days to be processed.
In other words, we want to find the probability of the application taking more than one standard deviation from the mean, that is, P(X > μ + σ).
Since the distribution is symmetric, we can also find the probability by calculating P(X < μ - σ) and subtracting the result from 1, since the total probability must be 1.
Using the above formula, we have:
P(X > μ + σ) = P(X > 11 + 3.516)
= P(X > 14.516)
To standardize the value of 14.516, we'll convert it to a z-score, which is z = (X - μ) / σ.
Therefore, we have z = (14.516 - 11) / 3.516 = 1
Since we are dealing with a standard normal distribution, we can use the standard normal distribution table to find the probability associated with z = 1.
From the table, we find that the probability of z being less than 1 is 0.8413;
thus, the probability of z being greater than 1 is 1 - 0.8413 = 0.1587.
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Which set of ordered pairs is NOT A FUNCTION?
(5,3) , 6,3) , (7,3) , (8,3)
(2,1) (3,3) , (4,6) , (2,3)
(1,6) , (8,4) , (3,8) , (7,`)
(9,8), (7,6) , (5,3) , (2,1)
The set of ordered pairs (2,1), (3,3), (4,6), (2,3) is NOT a function because the input value of 2 corresponds to both the output values of 1 and 3.
For a set of ordered pairs to be a function, each input (x-value) must correspond to only one output (y-value). Therefore, if there exists an input (x-value) that corresponds to more than one output (y-value), then the set of ordered pairs is NOT a function.
Let's check each set of ordered pairs:
(5,3), (6,3), (7,3), (8,3): Each input (x-value) corresponds to the output (y-value) of 3. This set of ordered pairs is a function.(2,1), (3,3), (4,6), (2,3): The input value of 2 corresponds to both the output values of 1 and 3. Therefore, this set of ordered pairs is NOT a function.(1,6), (8,4), (3,8), (7,`): The output value for the fourth ordered pair is missing, so we cannot determine whether this set of ordered pairs is a function or not.(9,8), (7,6), (5,3), (2,1): Each input (x-value) corresponds to a unique output (y-value). This set of ordered pairs is a function.Therefore, the set of ordered pairs that is NOT a function is (2,1), (3,3), (4,6), (2,3).
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Let f(x)=3x^2 ÷4x^2+4 and
g(x)= 5x-2÷x+2 then find the following a, fog(3) b, fog(4)
From the given information provided, the value of fog(3) and fog(4) is 0.971 and 27/40 respectively.
a) To find fog(3), we first need to find g(3) and then evaluate f(g(3)).
To find g(3), we substitute x=3 into the formula for g(x):
g(3) = (5(3) - 2)/(3 + 2) = 13/5
Now, we can evaluate f(g(3)) by substituting g(3) into the formula for f(x):
f(g(3)) = f(13/5) = 3(13/5)² / (4(13/5)² + 4) = 0.971
Therefore, fog(3) = 0.971.
b) To find fog(4), we follow the same process. First, we find g(4):
g(4) = (5(4) - 2)/(4 + 2) = 18/6 = 3
Now, we can evaluate f(g(4)) by substituting g(4) into the formula for f(x):
f(g(4)) = f(3) = 3(3)² / (4(3)² + 4) = 27/40
Therefore, fog(4) = 27/40.
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She added 3 apples, 5 oranges, 2 pears, 4 plums, and 1 pomegranate. Her daughter grabs a piece of fruit without looking and chooses an apple for breakfast. What was the probability of that happening?
Answer:14
Step-by-step explanation: I added 3 + 5 + 2 + 4 + 1 which gave me 15 and her daughter took 1 fruit so it is 14 fruits left
Determine how many places the following 2 conic intersect at and if they intersect find the point or points of intersection. Solve the system over the real numbers for 19 and 20. x^(2)+y^(2)=34 3x-3y=6
The intersection points of the two conics are therefore[tex](1 + √14, -1 + √14)[/tex]and [tex](1 - √14, -1 - √14).[/tex]Hence, the two conics intersect at two points.
The point or points of intersection and the number of places the following 2 conic intersect is to be determined. The system over the real numbers for [tex]x² + y² = 34 and 3x - 3y = 6[/tex] is to be solved.
To determine how many points the following 2 conic intersect at, the two equations must be solved simultaneously. The points of intersection can then be determined by substituting the value of x or y into the other equation and solving for the remaining variable.The equation 3x - 3y = 6 is the equation of a straight line. Solving the equation for y, [tex]y = x - 2[/tex].
So the line passes through the point (0, -2) and (2, 0) on the x-axis. Now, substitute the value of y into the equation x² + y² = 34 to get[tex]x² + (x - 2)² = 34[/tex], expanding this gives 2x² - 4x - 26 = 0, which simplifies to x² - 2x - 13 = 0.The solution to the quadratic equation [tex]x² - 2x - 13 = 0[/tex] is given as[tex]x = 1 + √14, 1 - √14[/tex]. The corresponding value of y for each x can be calculated by substituting the value of x into the equation y = x - 2.
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What is the area of the following composite figure? Round to the nearest whole.
Answer:
The answer to your problem is 53 in ^2
Hope it helps
Jackie made a poster for the school advertising
the Science Olympiad. She included sample
statistics on the speed of the mousetrap cars
from the previous years. A. If one car raced 8 meters in 1. 5 seconds,
what was its speed?
b. How does this compare to the record time of
10 meters in 2. 32 seconds?
the speed of the car was 5.33 meters per second. Speed = 10 / 2.32 = 4.31 meters per second (rounded to two decimal places) .
a. To find the speed of the car, we use the formula
Speed = Distance / Time
If the car raced 8 meters in 1.5 seconds, we can substitute these values in the formula to get:
Speed = 8 / 1.5 = 5.33 meters per second (rounded to two decimal places)
Therefore, the speed of the car was 5.33 meters per second.
b. The record time of 10 meters in 2.32 seconds gives us a speed of:
Speed = 10 / 2.32 = 4.31 meters per second (rounded to two decimal places)
Comparing this to the speed of the car that raced 8 meters in 1.5 seconds, we see that the car that raced 8 meters was faster, with a speed of 5.33 meters per second compared to the record time of 4.31 meters per second. This suggests that the car that raced 8 meters was well-designed and well-built, and was able to travel a greater distance in a shorter amount of time.
It is important to note, however, that one data point is not enough to draw a firm conclusion about the superiority of one car over another. It is possible that the car that raced 8 meters had a lucky run, or that the car that set the record had a mechanical issue or was not driven to its full potential. To truly compare the performance of different cars, we would need to collect data from multiple trials and multiple cars, and analyze the data using statistical methods to determine which cars consistently perform better.
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what does the greek letter delta that is represented by a ∆ mean?
Answer:
“change” or “the change”
Step-by-step explanation:
The graph below shows the relationship between life expectancy and infant mortality in a random sample of countries.
Answer choices.
Positive linear association
Negative linear association
Non linear association
No association
Answer:
negative linear association
Step-by-step explanation:
The best description of the association between life expectancy and infant mortality rate in the given graph is option B. Countries with higher infant mortality rates tended to have shorter life expectancies.
The negative linear association between life expectancy and infant mortality rate in the attached graph,
Life Expectancy,
Life expectancy refers to the average number of years a person is expected to live from birth.
In the graph, life expectancy is represented on the vertical axis (y-axis).
Infant Mortality Rate,
Infant mortality rate refers to the number of deaths of infants under one year of age per 1,000 live births.
In the graph, the infant mortality rate is represented on the horizontal axis (x-axis).
Negative Linear Association,
A negative linear association means that as one variable increases, the other variable tends to decrease at a consistent rate.
here, as the infant mortality rate increases (moving right on the x-axis), the life expectancy tends to decrease (moving down on the y-axis).
Interpretation,
Looking at the graph, we can see that countries with higher infant mortality rates are positioned towards the right side of the graph,
and they tend to have shorter life expectancies, which are positioned towards the bottom of the graph.
Conversely, countries with lower infant mortality rates are positioned towards the left side of the graph, and they tend to have longer life expectancies,
which are positioned towards the top of the graph.
Implication,
The negative linear association in the graph indicates that countries with higher rates of infant mortality are likely to have lower life expectancies.
This is because higher infant mortality rates often indicate poorer healthcare systems, lower living standards,
and other factors that can impact life expectancy negatively.
Therefore, based on the graph's trend, we can conclude that the statement B is the best description of the association between life expectancy and infant mortality rate.
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The above question is incomplete , the complete question is :
The Graph Below Shows The Relationship Between Life Expectancy And Infant Mortality Rate In A Random Sample Of Countries.
Which statement is the best description of the association between these variables? Choose all that apply.
A. Countries with higher infant mortality rates tended to have longer life expectancies.
B. Countries with higher infant mortality rates tended to have shorter life expectancies.
C. There is no clear relationship between infant mortality rates and life expectancy.
Attached graph.
write the third column of the matrix as a linear combination of the first two columns, if possible. (if not possible, enter impossible on both answer blanks.) 1 2 17 9 8 63 6 3 21 1 9 6 2 8 3
This is impossible because the third column does not depend on the first two columns.
The third column's values are linear combination of the first two columns. the third column of the matrix as a linear combination of the first two columns, This can be seen by the fact that the third column has values which don't fit the pattern of the first two columns. For example, the first value in the third column (21) is not equal to an any linear combination of the first two columns. Thus, it is impossible to write the third column as a linear combination of the first two columns.
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PLS HELP! WILL MAKE U BRAINLIST!
Find the point of intersection using substitution. DO NOT USE ANOTHER METHOD. Show all your thinking.
Answer:
(-2,-3)
Step-by-step explanation:
3x+y=-9
-3x -3x
y=-3x-9
5x-3(-3x-9)=-1
14x+ 27= -1
-27 -27
14x= -28
/14 /14
x=-2
plug in x
3(-2)+y=-9
-6+y=-9
+6 +6
y=-3
Determine a series of transformations that would map Figure D onto Figure E.
Figure E is a rotated and reflected version of Figure D that has been shifted to the right and up as a result of this transformation sequence.
What is a transformation sequence called?The sequence transformation (which may be dependent on n). This is known as a linear sequence transformation. Nonlinear sequence transformations are nonlinear sequence transformations.
We can use the following transformations to map Figure D onto Figure E:
Figure D should be translated 4 units to the right and 1 unit up.
Figure D should be rotated 90 degrees clockwise around the origin.
Cross the y-axis with the resulting figure.
This transformation sequence results in Figure E, which is a rotated and reflected version of Figure D that has been shifted to the right and up.
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Please help it’s urgent!!! Pls help!!! Will give brainliest!!Tina purchased a new refrigerator
on a payment plan. Four months after purchasing the refrigerator, the balance was $630. Six months after purchasing the refrigerator,
the balance was $520.
Write an equation that models the balance y after t months.
y = _t + _
Answer:
We can use the slope-intercept form of a linear equation to model the balance y after t months, where the slope represents the rate of change of the balance and the y-intercept represents the initial balance.
The initial balance (y-intercept) is the amount Tina borrowed to buy the refrigerator, which we don't know. But we can find the slope using the two data points provided:
Four months: balance = $630
Six months: balance = $520
The change in the balance over the two-month period is:
$520 - $630 = -$110
The slope of the line is the rate of change of the balance per month, which is:
slope = Δy/Δt = (-$110)/(6-4) = -$55/month
Using the point-slope form of a linear equation, we can plug in one of the data points to find the y-intercept:
y - 630 = -$55(t - 4)
y - 630 = -$55t + 220
y = -$55t + 850
Therefore, the equation that models the balance y after t months is:
y = -$55t + 850.
Which lines are parallel? check all that apply. lines b, c, d, e, f are cut by transversal a. clockwise from top left, the angles formed by lines b and a are blank, 89.5 degrees, blank, blank; by lines c and a are blank, blank, blank, 91.5 degrees; by lines d and a are blank, blank, 89.5 degrees, blank; by lines e and a are 88.5 degrees, blank, blank, blank; by lines f and a are blank, blank, 90.5 degrees, blank. b is parallel to f b is parallel to d c is parallel to e c is parallel to d d is parallel to f e is parallel to f
The lines which are parallel are given below :
Line b is parallel to line f, line b is parallel to line d, line c is parallel to line e, line c is parallel to line d and line d is parallel to line f.
Line b is parallel to line f because they both have a pair of alternate angles that are congruent which is 89.5 degrees and 90.5 degrees.
Line b is parallel to line d because they both have a pair of alternate angles that are congruent at 89.5 degrees.
Line c is parallel to line e because they both have a pair of alternate angles that are congruent at 91.5 degrees.
Line c is parallel to line d because they both have a pair of alternate angles that are congruent: 89.5 degrees.
Line d is parallel to line f since they have corresponding angles of 89.5 degrees and 90.5 degrees, respectively
Therefore, the correct answer is :
Line b is parallel to line f, line b is parallel to line d, line c is parallel to line e, line c is parallel to line d and line d is parallel to line f.
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There are 6 cups of oatmeal in a container. Stella eats ¼ cup of oatmeal every day for breakfast. In how many days will Stella finish all the oatmeal in the container?
It will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.
The container has 6 cups of oatmeal and Stella eats 1/4 cup every day for breakfast.
To find the number of days it will take Stella to finish all the oatmeal, we can use the formula:
Number of days = Total amount of oatmeal ÷ Amount of oatmeal consumed per dayTotal amount of oatmeal in the container = 6 cups
Amount of oatmeal consumed by Stella per day = 1/4 cup
Number of days = 6 cups ÷ 1/4 cup = 24 daysTherefore, it will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.
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HELP ME PLS! Brainlist :)
SHOW HOW U GOT IT AND SHOW ALL STEPS! IF CORRECT WILL MAKE U BRAINLIST!
Answer:
surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...
Surface Area of Triangular Prism - Formula, Examples
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Complete the following proof.
Given: mXOY = m WOV
m -- YZ = m --ZW
Prove: m -- XZ = m -- ZV
Since mXOY = mWOV, we can form the following equations so, m--XZ = m--ZV.
What is equation?An equation is a mathematical statement that states the equality of two expressions. It usually consists of two terms, with an equals sign between them, representing the relationship between the terms. Equations are often used to describe relationships between variables, such as in physics and chemistry, and can be used to calculate unknown values.
Proof:
Since mXOY = mWOV, we can form the following equations:
m--YZ = m--ZW (Given)
Subtract both sides of the equation by m to get:
YZ = ZW
Then, multiply both sides of the equation by X to get:
XZ = XW
Now, substitute Y for V and W for V in the equation to get:
XZ = ZV
Finally, subtract both sides of the equation by m to get:
m--XZ = m--ZV
Therefore, m--XZ = m--ZV.
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A town has a population of 109,500 and grows at a rate of 7.4% every year. Which equation represents the town's population after 2 years?
Answer:
126305.622 is the town's population after 2 years on percentage 7.4.
Step-by-step explanation:
Answer:
you will asume this rate is constant. so put it into y=mx+b form y=1.74*2+109,500
Step-by-step explanation:
Examine the system of equations.
2x − 4y = 6,
x − 2y = 3
How many solutions does this system of equations have?
Answer:
infinitely many solutions
Step-by-step explanation:
When you put the equations in desmos, the lines are the same therefore it has infinitely many solutions.
Answer:
✔️ c) infinitely many
Step-by-step explanation:
the probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw. what is the probability that he will break a chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking? multiple choice question.
The probability that the arborist will break a saw chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking is 0.007
We are given the probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw.
The time that he spends on each saw are 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking.
Let us find the probability that he will break a chain when he uses the small climbing saw.
P(small climbing saw) = 1/2P(Break a chain using small climbing saw) = 0.004
Using the medium limbing saw: P(medium limbing saw) = 3/8P(Break a chain using medium limbing saw) = 0.008
Using the large felling and bucking saw: P(large felling and bucking saw) = 1/8P(Break a chain using large felling and bucking saw) = 0.04
Now, to find the probability that he will break a chain on a day, we use the weighted average. Probability is a weighted average because the probability of breaking the saw chain is different for each saw that he uses.
Hence, the probability that he breaks a saw chain when he uses each saw is weighted according to how much time he spends on that saw.
P = P(small climbing saw)* P(Break a chain using small climbing saw) + P(medium limbing saw) * P(Break a chain using medium limbing saw) + P(large felling and bucking saw) * P(Break a chain using large felling and bucking saw)P = (1/2 * 0.004) + (3/8 * 0.008) + (1/8 * 0.04)P = 0.007
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What is the value of x^0 assuming x ≠ 0?
The value of any number raised to the power of 0 is always 1, irrespective of the value of x, as long as x is not 0. So, x^0 = 1.
Write a cosine function that has an amplitude of 3, a midline of y = 4 and a period of 2/3
Answer:
[tex]y=3cos(3\pi x)+4[/tex]
Step-by-step explanation:
[tex]f(x)=cos(x)\\[/tex]
[tex]A(f(Bx+C)+D)[/tex]
The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.
[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]
[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]
I hope this helps
A boat is heading towards a lighthouse, where Dominic is watching from a vertical distance of 114 feet above the water. Dominic measures an angle of depression to the boat at point � A to be 6 ∘ ∘ . At some later time, Dominic takes another measurement and finds the angle of depression to the boat (now at point � B) to be 32 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is approximately 1363.7 feet.
How to solveUsing slope concept:
tan(θ1) = h/d
tan(θ2) = h/(d+x), where x is the distance from point A to the boat when Dominic measured the angle of depression at point B.
We can rearrange these equations to solve for h and x:
h = d*tan(θ1)
h = (d+x)*tan(θ2)
d*tan(θ1) = (d+x)*tan(θ2)
d*(tan(θ1)-tan(θ2)) = x*tan(θ2)
d = x*tan(θ2)/(tan(θ1)-tan(θ2))
Substituting the given values, we get:
d = x*tan(32°)/(tan(6°)-tan(32°))
Using a calculator, we can evaluate this expression to get:
d ≈ 1363.7 feet
Therefore, the distance from point A to point B is approximately 1363.7 feet.
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kendrick lamar is incredibly story teller but i dont like his music like when he raps fast thats unpelasent
An American rapper, is known for his poetic, and complex lyrical style.
How Kendrick Lamar becomes a story teller?Kendrick Lamar is a highly talented storyteller, however, some people may not like his music when he raps quickly as it can be unpleasant.What are the aspects of Kendrick Lamar's music?
An American rapper, is known for his highly poetic, socially conscious, and complex lyrical style.
However, his musical talent has been highly praised by critics and audiences alike.
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D
114°
A
в
56°
C
HURRRRRYYY PLEASEEEE
The calculated value of the angle x is 58 degrees
How to calculate the value of xfrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the sum of opposite external angles, we have the following equation
114 = 56 + x
When the like terms are evaluated, we have
x = 114 - 56
Evaluate
x = 58
Hence, the value of x is 58
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4cd - 5cd + 3c + 8d simplify
Answer:
-cd+3c+8d
Step-by-step explanation:
4cd - 5cd + 3c + 8d
Combine like terms
(4cd - 5cd) + 3c + 8d
-cd+3c+8d
Answer:
3c + 8d - cd
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 4cd - 5cd + 3c + 8d
Let's simplify the expression,
→ 4cd - 5cd + 3c + 8d
→ 3c + 8d + 4cd - 5cd
→ (3c) + (8d) + (4cd - 5cd)
→ 3c + 8d + (-cd)
→ 3c + 8d - cd
Hence, answer is 3c + 8d - cd.
Help em fin the answer
Answer:
1 ft per 4 seconds
120 seconds
72 seconds
Step-by-step explanation:
The length of the shadow of a pole having 20m height is 20√3m. Find the length of the shadow of a pole of height 25√3m at the Same time.
The length of the shadow of the second pole is 75 meters, was solved by using the concept of similar triangles.
What is the concept of similar triangles?The concept of similar triangles is based on the idea that if two triangles have the same shape but different sizes, they are called similar triangles. This means that their corresponding angles are equal and their corresponding sides are in proportion.
What are triangles?A triangle is a 2-dimensional geometric shape with three sides, three angles, and three vertices. It is one of the basic shapes in geometry and is used to describe many real-world objects and phenomena.
In the given question,
Length of shadow of first pole / Height of first pole = Length of shadow of second pole / Height of second pole
Substituting the given values, we get:
20√3 / 20 = x / 25√3
Simplifying, we get:
x = (20√3 / 20) * 25√3
x = 25*3
x = 75
Therefore, the length of the shadow of the second pole is 75 meters.
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For a school field trip, a charter bus company charges a $50 reservation fee for the group, plus an additional $12 per student. Let n
represent the number of students going on the field trip.
The expression that best represents the total cost of the charter bus for the field trip is 12n + 50
Which expression best represents the total cost of the charterThe total cost of the charter bus for the field trip consists of a $50 reservation fee and an additional $12 per student.
If n represents the number of students going on the field trip, then the expression for the total cost can be written as:
Total cost = 12n + 50
This expression represents the variable cost of the charter bus, which depends on the number of students going on the field trip.
The fixed cost of $50 is added to the variable cost to give the total cost.
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the average rent in a city is $1,510 per month with a standard deviation of $210. assume rent follows the normal distribution. [you may find it useful to reference the z table.] a. what percentage of rents are between $1,300 and $1,720?
The percentage of rents between $1,300 and $1,720 is 34.13%.
To calculate this, we need to use the z-score formula to convert the rent range into a z-score range. The z-score formula is (x-μ)/σ, where x is the rent range, μ is the mean rent and σ is the standard deviation.
To calculate the lower z-score, the formula becomes (1300-1510)/210 = -1.19.
To calculate the higher z-score, the formula becomes (1720-1510)/210 = 1.14. The z-score of -1.19 to 1.14 corresponds to 34.13% according to the z-table. Therefore, 34.13% of rents are between $1,300 and $1,720.
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this is simple i dont need no words js the work pls and thankyou <33
Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
Unpacking the expression we have,
[tex](\sqrt{x})(\sqrt[4]{x})[/tex]
Its better to work with this in terms of exponents so we rewrite the expression as [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}[/tex]. (cause [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]) This can be a little tricky when learning it for the first time.
Then by the exponent sum rule [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}=x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex] (more straightforward, you probably know this from class).
I assume this is what you mean by rational exponent form. But you could also write it as [tex]\sqrt[4]{x^3}[/tex].