Determine the number of solutions to the following system of equations. Y = -3x2 − 4x 7 3x 2y = 18.
Answers
The correct answer is: "The system of equations has two solutions." This equation represents a parabola in the xy-plane.
To determine the number of solutions to the given system of equations, let's analyze the equations provided:
Equation 1: y = -3x^2 - 4x + 7
Equation 2: 3x + 2y = 18
First, we notice that Equation 1 is a quadratic equation in the form of y = ax^2 + bx + c, where a = -3, b = -4, and c = 7. This equation represents a parabola in the xy-plane.
Next, we look at Equation 2, which is a linear equation in standard form. By rearranging it, we get 2y = -3x + 18, or y = (-3/2)x + 9/2. This equation represents a straight line in the xy-plane.
Now, let's consider the possibilities:
The parabola and line intersect at two points: If the parabola and line intersect at two distinct points, it means there are two solutions to the system of equations.
The parabola and line intersect at one point: If the parabola and line intersect at a single point, it means there is one solution to the system of equations.
The parabola and line do not intersect: If the parabola and line do not intersect at any point, it means there are no solutions to the system of equations.
To determine which case applies, we can graph the equations and observe their intersection. However, without the capability to include a visual graph here, we can still analyze the equations.
Since the first equation represents a downward-opening parabola and the second equation represents a line with a negative slope, it is evident that the parabola and line will intersect at two distinct points. Therefore, the number of solutions to the given system of equations is two.
In conclusion, the correct answer is: "The system of equations has two solutions."
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Related Questions
A house today costs
$300,000. This price will
increase by 95% in
10 years. How much will
the house cost in 10 years?
Answers
Answer:
$585,000. 95% of $300,000 = $285,000. $300,000 + $285,000 = $585,000. hope this helps
Step-by-step explanation:
- Zombie
1) make c the subject of of the formula v=c/4-5
2) Make p the subject of the formula q-p=3p+5
Answers
Answer:
1)c = -v 2)(q-5)/4
Step-by-step explanation:
v = c/4-5
v = c/-1
c = -v
q-p=3p+5
q = 4p+5
q-5 = 4p
p = (q-5)/4
Why do you think that teenagers make up a small percentage of taxpayers overall ?
Answers
The amount of money an adolescent makes, whether from a job, their own business, or investments, determines their tax liabilities and whether they must file a tax return.
What is tax?The selling price and taxpayers' income are factors in the mathematical calculation of taxes. It is a fee levied by the government on residents in order to raise money for public spending and welfare programmes. Direct tax and indirect tax are the two different forms of taxes.
Although the number of teenagers in the United States who are employed has been declining since the late 1970s, many still work and earn money. 1 As a result, the IRS continues to process millions of teen-filed tax returns.
Despite their youth, teens who earn a specific amount of money must pay taxes, just like everyone else. Teenagers and their parents should be aware of the laws that pertain to young people, as well as how various forms of teen income are taxed.
Teenagers aren't exempt from paying income taxes just because of their age or because they are someone else's dependent. The amount of money an adolescent makes, whether from a job, their own business, or investments, determines their tax liabilities and whether they must file a tax return. Teens with investment income are subject to different regulations.Hence, the amount of money an adolescent makes, whether from a job, their own business, or investments, determines their tax liabilities and whether they must file a tax return.
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PLEASE HELP!!
Use the information to answer the question.
A store sells mugs. Each mug costs the same amount. During a sale, the store reduces the price of each mug by $1.75. Wen spends $28.20 on
5 mugs at the sale price
What was the price of I mug before the sale?
Answers
Answer:
$7.39
Step-by-step explanation:
Answer:
7.39
Step-by-step explanation:
1) 28.20 divided by 5 to get what one mug costs at sale price.
28.20 divided by 5= 5.64
2) then add how much they reduced the price by, 1.75.
5.64+1.75= 7.39
Represent the following sentence as an algebraic expression, where "a number" is the letter x. \text{a number raised to the third power.} a number raised to the third power.
Answers
Answer: #x^3
Step-by-step explanation:
"A number " is represented by the letter xA number (x) raised (^) the third power will be,x^3
note: An algebraic expression doesn't have an equal sign (=)
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The weight of each fountain pen manufactured in a factory must be 10g with a tolerance of 2g. Pens that are not within the tolerated weight must be thrown away. Write an inequality that can be used to assess which pens are tolerable (w is the weight of the pen)?
Answers
According to the information given, the absolute value inequality that can be used to assess which pens are tolerable is:
\(|w - 10| \leq 2\)
The absolute value function measures the distance of a point to the origin, and is defined by:
\(|x| = x, x \geq 0\)\(|x| = -x, x < 0\)The weight must be of 10g, with a tolerance of 2g, which means that the absolute value of the difference between the weight w and 10g must be of at most 2g, hence the inequality is:
\(|w - 10| \leq 2\)
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Theorem 7.1.2 (Calculations with the Fourier transform)
Given f € L¹(R), the following hold:
(i) If f is an even function, then
f(y) = 2 [infinity]J0 f(x) cos(2πxy)dx.
(ii) If f is an odd function, then
f(y) = -2i [infinity]J0 f(x) sin(2πxy)dx.
Answers
(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.
(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.
The Fourier transform pair for a function f(x) is defined as follows:
F(k) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx
f(x) = (1/2π) ∫[-∞,∞] F(k) \(e^{2\pi iyx}\) dk
Now let's prove the given properties:
(i) If f is an even function, then f(y) = 2∫[0,∞] f(x) cos(2πxy) dx.
To prove this, we start with the Fourier transform pair and substitute y for k in the Fourier transform of f(x):
F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx
Since f(x) is even, we can rewrite the integral as follows:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[-∞,0] f(x) \(e^{2\pi iyx}\) dx
Since f(x) is even, f(x) = f(-x), and by substituting -x for x in the second integral, we get:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[0,∞] f(-x) \(e^{2\pi iyx}\)dx
Using the property that cos(x) = (\(e^{ ix}\) + \(e^{- ix}\))/2, we can rewrite the above expression as:
F(y) = ∫[0,∞] f(x) (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dx
Now, using the definition of the inverse Fourier transform, we can write f(y) as follows:
f(y) = (1/2π) ∫[-∞,∞] F(y) \(e^{2\pi iyx}\) dy
Substituting F(y) with the expression derived above:
f(y) = (1/2π) ∫[-∞,∞] ∫[0,∞] f(x) \(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\)/2 dx dy
Interchanging the order of integration and evaluating the integral with respect to y, we get:
f(y) = (1/2π) ∫[0,∞] f(x) ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy dx
Since ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy = 2πδ(x), where δ(x) is the Dirac delta function, we have:
f(y) = (1/2) ∫[0,∞] f(x) 2πδ(x) dx
f(y) = 2 ∫[0,∞] f(x) δ(x) dx
f(y) = 2f(0) (since the Dirac delta function evaluates to 1 at x=0)
Therefore, f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx, which proves property (i).
(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.
The proof for this property follows a similar approach as the one for even functions.
Starting with the Fourier transform pair and substituting y for k in the Fourier transform of f(x):
F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx
Since f(x) is odd, we can rewrite the integral as follows:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx - ∫[-∞,0] f(x) \(e^{-2\pi iyx}\) dx
Using the property that sin(x) = (\(e^{ ix}\) - \(e^{-ix}\))/2i, we can rewrite the above expression as:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) - \(e^{2\pi iyx}\)/2i dx
Now, following the same steps as in the proof for even functions, we can show that
f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx
This completes the proof of property (ii).
In summary:
(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.
(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.
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Jim is running on a trail that is five fourths of a mile long. So far he has run two thirds of the trail. How many miles has he run so far?
Answers
Answer:
Jim has run
5/6 of a mile so far.
plese pick me branilest
Which set of numbers has the same greatest
common factor of 48 and 108?
A:32 and 60
B: 72 and 90
C:16 and 96
D:60 and 84
Answers
Answer: a
Step-by-step explanation:
A cylinder with a radius of 10 mi and a height of 8 mi. What is the volume of the figure? Round your answers to the nearest
tenth, if necessary.
а
2306.4mi3
b
1818.9mi3
c
2513.3mi3
d
15205.3mi?
Answers
Answer:
C
Step-by-step explanation:
cylinder volume is πr²h so when you do the math you get c
Assume that p is a relation that contains the points (3, -4). What other point must be included in the relation if p is:1. symmetric about the x-axis?2. symmetric about the y-axis?
Answers
The point needed for the relation is \(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.
The point needed for the relation is \(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.
In this exercise we are supposed to determine the coordinates of a point P under an assumption of rigid transformation. Now, we must use the following symmetry transformations:
Reflection about the x-axis
\(S'(x,y) = S(x,y) - 2\cdot (0, s_{y})\) (1)
Reflection about the y-axis
\(S'(x,y) = S(x,y) - 2\cdot (s_{x}, 0)\) (2)
Where:
\(S(x,y)\) - Original point.\(S' (x,y)\) - Reflected point. \(s_{x}, s_{y}\) - Coordinates of point S.If we know that \(P'(x,y) = (3, -4)\), the coordinates for each reflection are, respectively:
Reflection about the x-axis
\(P(x,y) = (3,-4) - 2\cdot (0, -4)\)
\(P(x,y) = (3, 4)\)
\(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.
Reflection about the y-axis
\(P(x,y) = (3, -4) - 2\cdot (3, 0)\)
\(P(x,y) = (-3, -4)\)
\(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.
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(a) Simplify 53 x 56 by following these step: i. Rewrite with each exponential written explicitly (so 53 becomes 5 x 5 x 5). ii. You should have just a bunch of 5's multiplied together. Express as a single exponential. (b) Simplify (23)4 by following these step: i. Explicitly write this as 23 times itself four times. ii. Rewrite, replacing each 23 with 2 x 2 x 2. iii. You should have just a bunch of 2's multiplied together. Express as a single exponential. (c) For each of (a) and (b), discuss a general rule of exponents
Answers
(a) 53 x 56 simplifies to \(5^9\). (b) (23)4 simplifies to \(2^{12\). (c) When multiplying numbers with the same base, you combine their exponents by adding them. When we have an exponent raised to another exponent, the rule dictates that we multiply the exponents together.
(a) To simplify 53 x 56, let's follow the steps provided:
i. Rewrite 53 as 5 x 5 x 5 and 56 as 5 x 5 x 5 x 5 x 5 x 5.
So, 53 x 56 becomes (5 x 5 x 5) x (5 x 5 x 5 x 5 x 5 x 5).
ii. Now, we can express this as a single exponential by combining the like terms:
53 x 56 = (5 x 5 x 5) x (5 x 5 x 5 x 5 x 5 x 5)
= (5³) x (5⁶).
Therefore, 53 x 56 can be simplified to 5³⁺⁶ or 5⁹.
(b) Let's simplify (23)4 using the provided steps:
i. Explicitly writing 23 four times, we have 23 x 23 x 23 x 23.
ii. Now, let's replace each 23 with 2 x 2 x 2:
(2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2).
iii. We can simplify this expression by combining the like terms:
(2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2)
\(= 2^{(3+3+3+3)\)
\(= 2^{3*4}=2^{12.\)
So, (23)4 can be simplified to \(2^{12\).
(c) The general rule of exponents we can observe from these examples is as follows:
For (a), (a), when we multiply two numbers with the same base but different exponents, we can simplify the expression by adding the exponents:
\(a^m\) x \(a^n = a^{(m+n)\).
For (b), when we raise a power to another power, we can simplify by multiplying the exponents.: \((a^m)^n\) = a^(m x n).
These rules help us simplify expressions with exponents and make calculations more efficient.
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PLEASE LOOK AT PHOTO! WHOEVER ANSWERS CORRECTLY I WILL MARK BRAINIEST!!
Answers
Answer:
33 degree
Step-by-step explanation:
Let m1 be x
m2= x+1
A/Q
--> m1+m2= 67
--> x+x+1= 67
--> 2x+1=67
--> 2x= 67-1
--> 2x=66
--> x= 66/2
--> x= 33
So, m1= 33 degree
PLEASE MARK ME AS BRAINLIEST:)
Perform average value and RMS value calculations of:
-5 sin (500t+45°) + 4 V
Answers
The average value and RMS value calculations of the given waveform \(-5 \sin(500t + 45°) + 4V\) can be performed. To calculate the average value and RMS value of the given waveform.
To calculate the average value and RMS value of the given waveform, we need to first determine the mathematical representation of the waveform. The given waveform is a sinusoidal function with an amplitude of 5 and an angular frequency of 500 radians per second, phase-shifted by 45 degrees and offset by +4V.
The average value of a waveform is calculated by integrating the waveform over one period and dividing by the period. Since the waveform is a sine function, its average value over one period is zero, as the positive and negative values cancel each other out.
The RMS (Root Mean Square) value of a waveform is calculated by taking the square root of the average of the squared values of the waveform over one period. For a sine function, the RMS value is equal to the amplitude divided by the square root of 2. Therefore, the RMS value of the given waveform is \(\frac{5}{\sqrt{2}} \approx 3.54V\).
In summary, the average value of the given waveform is zero, while the RMS value is approximately 3.54V.
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Kyle earns $6 per hour babysitting. Select the answer that shows the dollars Kyle will earn babysitting for h hours and for 4 hours.
Answers
Answer: Kyle will earn 6h dollars babysitting for h hours, and 6 x 4 = 24 dollars babysitting for 4 hours.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Mateo’s school is selling tickets to the spring musical. On the first day of ticket sales the school sold 30 adult tickets and 90 children’s tickets for $750.00. The school made $670.00 on the second day by selling 80 adult tickets and 50 children tickets. What is the price of one adult ticket and one children ticket?
Answers
Answer:
Kids: 6.25
Adults: Also 6.25
Step-by-step explanation:
So I focused on the first day more. I noticed that 1/4 of the people who attended were kids, and that leaves it with 3/4 people which were adults.
25% (or 1/4) of 750 is 187.5
So 75% of 750 is 562.5
187.5+562.5=750 so we are on the right path
If the ticket for kids totaled 187.5 and 30 students got it, then the price for the ticket is 187.5/30=x and x equals 6.25
If the ticket for adults totaled 562.5 and 90 people got it, then the price is 562.5/90=y and y equals 6.25.
Checking if i'm correct:
6.25*30=187.5
6.25*90=562.5
187.5+562.5= 750
i probably didnt make it as clear im only in 7th grade, but hopefully this was the answer you were looking for
if the number of times you take the test were independent of the chance you fail what could that mean?
Answers
if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.
The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.
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If total employee benefits are calculated as a percentage of their gross pay whitch of the following employees receive the largest percentage of their gross pay in employee benefits
Answers
The employee that receives the largest percentage of their gross pay in employee benefits is Marcel.
The percentage of employee benefits to total gross pay for each worker has to be determined.
Percentage = (total job benefits / gross pay) x 100
Emily: (33,600 / 32,600) x 100 = 103.07%
Jack: (34,700 / 33,700) x 100 = 102.97%
Judy: (33,900 / 33,400) x 100 = 101.5%
Marcel: (34,000 / 32,900) x 100 = 103.43%
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Please find attached a complete question
yesterday, Linda traveled 128 miles to visit her uncle. Her car used for gallons of gasoline. If Linda's car uses gasoline at the same rate, how many gallons of gasoline will her car used today when she travels 432 miles?
Answers
Answer:
Linda car will use 13.5 gallons
Step-by-step explanation:
PLease help me thank you if you do have a good day
Answers
Answer:
acceleration
Step-by-step explanation:
use POE:
the object is moving because the graph is not a straight line
the object is not slowing down because the graph is going up
there is not a constant speed because the line is exponential not linear
the only one left is a. acceleration
Every morning, a deli offers a “commuter special” in which customers can select a pastry, beverage, and a copy of one of the local papers and pay $1.00. Their options are listed in the table.
Commuter Special
Pastry
Beverage
Paper
Donut
Coffee
The Times
Brownie
Milk
The Herald
Muffin
Tea
Scone
Orange Juice
Croissant
Last Tuesday, the deli did not have any muffins. How did that affect the number of possible combinations?
It decreased the number of combinations by 1.
It decreased the number of combinations by 4.
It decreased the number of combinations by 8.
It decreased the number of combinations by 10.
Answers
Raul has a figure made up of 100 congruent squares. He shaded
40
100
of the squares yellow and the other
60
100
of the squares green. Select the decimal expression from the drop-down menu to correctly complete the sentence. The decimal expression
Choose. Compares the yellow and green parts of Raul’s figur
Answers
The correct answer to the given question about colored congruent squares is option A) 0.4 < 0.6
This is because Raul shaded 40/100 of the squares yellow, which can also be written as 0.4 as a decimal. He shaded the other 60/100 of the squares green, which can also be written as 0.6 as a decimal. Therefore, we can compare the two decimals and say that 0.4 is less than 0.6. To show how we find the answer 0.4 < 0.6, we can follow these steps:
Recall that Raul shaded 40/100 of the squares yellow and the other 60/100 of the squares green.Convert the fractions to decimals by dividing the numerator by the denominator: 40/100 = 0.4 and 60/100 = 0.6.Compare the two decimals: 0.4 is less than 0.6.Write the answer using the less than symbol: 0.4 < 0.6.
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Complete Question
Raul has a figure made up of 100 congruent squares. He shaded 40/ 100 of the squares yellow and the other 60/100 of the squares green. Select the decimal expression from the following
0.4 <0.6
0.04 < 0.06
0.4 = 0.6
0.04 = 0.06
0.4 > 0.6
0.04 > 0.06
The table shows male and female life expectancy in several countries.
(the screenshot)
What is the value of r, the correlation coefficient?
Round your answer to the nearest hundredth.
Answers
Answer:
chase ur breath smells like hotdog water, hamzah you cant dance, claire you cant sing, and hailey ur my bestfriend u know that. yeah bestfriend *winks*
Step-by-step explanation:
Find the Slope!!Giving brainliest!!
Answers
Answer:
3/2
Step-by-step explanation:
Given the functions below, find f(2)-g(-7).
Will give brainliest :))
Answers
Answer:
49
There u go :)
Answer:
Given the functions below, f(2) - g(-7) is -34.
Step-by-step explanation:
f(2) - g(-7)
First solve f(2).
f(x) = -|3 - 8x|
Substitute variable.
f(2) = -|3 - 8(2)|
Multiply.
f(2) = -|3 - 16|
Subtract 16 from 3.
f(2) = -|-13|
Apply absolute value.
f(2) = -13
Now solve g(-7).
g(x) = x² + 4x
Substitute variable.
g(-7) = (-7)² + 4(-7)
Raise -7 to the second power.
g(-7) = 49 + 4(-7)
Multiply 4 and -7.
g(-7) = 49 - 28
Subtract 28 from 49.
g(-7) = 21
Now with those values, lets go back to our original equation.
f(2) - g(-7)
Substitute known values.
-13 - 21
Subtract 21 from -13.
-34.
Write a possible recursive rule and then find a7 for { 7,12,17,22,27}
Answers
Start from 7, then add 5 each time.
a7 is 7 plus 30, or 37.
please help h(-6)= -x^2+8
Answers
Answer:
take a break kid you must enjoy life :(
Step-by-step explanation:
For triangle ABC with sides a,b and c the law of cosines statesc^2=in which of the following cases must the law of cosines be used to solve a triangle?ASA SSS SAS SSA
Answers
The law of cosines is used to solve a triangle when one of the following cases is given SSA, SSS, or SAS.
In the SSA (side-side-angle) case, two sides and a non-included angle are given, and we need to find the third side and remaining angles. However, there can be two possible triangles, one or none depending on the size of the non-included angle and the length of the given sides.
In the SSS (side-side-side) case, all three sides of a triangle are given, and we need to find the three angles. This can be solved using the law of cosines to find any of the angles, and then the law of sines to find the other two.
In the SAS (side-angle-side) case, two sides and an included angle are given, and we need to find the third side and remaining angles. This can be solved using the law of cosines to find the missing side and then the law of sines to find the remaining angles.
The ASA (angle-side-angle) case can be solved using the law of sines or the law of cosines, depending on the given information.
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what is the relationship between student's t distribution and the standard normal distribution? student's t will approach to standard normal distribution as the sample size approachs 0 student's t will approach to standard normal distribution as the sample size approachs infinite standard normal distribution will approach to student's t distribution as the sample size approachs 0 standard normal distribution will approach to student's t distribution as the sample size approachs infinite
Answers
The correct relationship between Student's t-distribution and the standard normal distribution is option B: as the sample size approaches infinity, the Student's t-distribution approaches the standard normal distribution.
The sample mean's estimation of the population mean is less precise and the sample mean's distribution is more erratic when the sample size is small. Because the distribution of t-values is more skewed as a result, the student's t-distribution has thicker tails than the traditional normal distribution.
The sample mean's distribution, however, narrows as sample size increases, making it a more precise reflection of the population mean. The student's t-distribution resembles the traditional normal distribution as a result of the narrowing of the t-value distribution.
For the ordinary normal distribution to accurately approximate the student's t-distribution in practice, a sample size of 30 or more is frequently thought to be sufficient.
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Correct question:
what is the relationship between student's t distribution and the standard normal distribution?
student's t will approach to standard normal distribution as the sample size approachs 0.
student's t will approach to standard normal distribution as the sample size approachs infinite
standard normal distribution will approach to student's t distribution as the sample size approachs 0
standard normal distribution will approach to student's t distribution as the sample size approachs infinite.
what is \(\sqrt[n]{x}\)
Answers
n
√
a
x
=
a
x
n
a
x
n
=
a
x
n
to rewrite
n
√
x
x
n
as
x
1
n
x
1
n
.
x
1
n