Answer:
The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this quesstion:
[tex]\sigma = 1.5, n = 22[/tex]
So
[tex]M = 1.645*\frac{1.5}{\sqrt{22}} = 0.53[/tex]
The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.
PLEASE HELP ME!!! f(x) = x2. What is g(x)?
Answer:
g(x)=3x^2
Step-by-step explanation:
Need Help really difficult
Suppose you work for the Department of Natural Resources and you want to estimate, with 95% confidence, the mean (average) length of all walleye fingerlings in a fish hatchery pond. You take a random sample of 36 fingerlings and determine that the average length is 7.4 inches and the population standard deviation is known to be 1.9 inches.
a. Construct a 95% confidence interval.
b. Interpret the Confidence Interval:
c. If the hatchery supervisor claimed that the average length of the walleye fingerlings fish is more than 7.5 inches, would you agree or disagree?
Answer:
a) [tex]7.4-1.96\frac{1.9}{\sqrt{36}}=6.78[/tex]
[tex]7.4+1.96\frac{1.9}{\sqrt{36}}=8.02[/tex]
b) For this case we can conclude that at 95% of confidence the true mean for the lenght of all welleye fingerprints in a fish hatchery pond is between 6.78 and 8.02
c) For this case since the value of 7.5 is included in the confidence interval we don't have enough evidence to conclude that the true mean is actually higher than 7.5 inches
Step-by-step explanation:
Information given
[tex]\bar X=7/4[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=1.9[/tex] represent the population standard deviation
n=36 represent the sample size
Part a
The confidence interval for the mean is given by :
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]
Replacing the info we got:
[tex]7.4-1.96\frac{1.9}{\sqrt{36}}=6.78[/tex]
[tex]7.4+1.96\frac{1.9}{\sqrt{36}}=8.02[/tex]
Part b
For this case we can conclude that at 95% of confidence the true mean for the lenght of all welleye fingerprints in a fish hatchery pond is between 6.78 and 8.02
Part c
For this case since the value of 7.5 is included in the confidence interval we don't have enough evidence to conclude that the true mean is actually higher than 7.5 inches
A study found that 25% of car owners in Fiji had their cars washed professionally rather than do it themselves. If 18 carowners are randomly selected, find the probability that atmost two people have their cars washed professionally
Answer:
13.5%
Step-by-step explanation:
The probability of interest is the cumulative probability of a binomial probability density function with 18 trials and a probability of success of 0.25. We are interested in the value for x ≤ 2.
CalculatorSuch a calculation can be done "by hand" by adding up the probabilities for 0, 1, and 2 people. (A calculator is needed for the arithmetic.) One may as well use the appropriate function of a calculator to find the probability:
binomcdf(18, 0.25, 2) ≈ 0.135
The probability is about 13.5%.
Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.950.950, point, 95 probability that he will hit it. One day, Samir decides to attempt to hit 101010 such targets in a row.
Assuming that Samir is equally likely to hit each of the 101010 targets, what is the probability that he will miss at least one of them?
Round your answer to the nearest tenth.
Answer:
40.1% probability that he will miss at least one of them
Step-by-step explanation:
For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
0.95 probaiblity of hitting a target
This means that [tex]p = 0.95[/tex]
10 targets
This means that [tex]n = 10[/tex]
What is the probability that he will miss at least one of them?
Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So
[tex]P(X = 10) + P(X < 10) = 1[/tex]
We want P(X < 10). So
[tex]P(X < 10) = 1 - P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]
[tex]P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401[/tex]
40.1% probability that he will miss at least one of them
Question:
Train A arrives at the station at 11:50 AM and leaves the station at 1:50 PM. How long does it stay in the station?
Make a Selection:
A. 1 hr
B. 2 hrs
C. 1 hr 25 min
D. 10 hrs
Need Help With This:
(8x^3 + x^2 - 5) / (x-6)
Answer:
the answer is 8x^2+49x+294+1759/x-6
b/-3+4 is less than 13
Answer:
b < 13
Step-by-step explanation:
Idk what you're asking but I'll try.
[tex]\frac{b}{1}=b[/tex]
b < 13
Answer:
b > -27.
Step-by-step explanation:
b / -3 + 4 < 13
b/-3 < 13 - 4
b/-3 < 9
-b/ 3 < 9
Multiply both sides by -3 ( the inequality sign will flip):
b > -27
A cone with radius 5 and height 12 has its radius doubled. How many times greater is the volume of the larger cone than the smaller cone? Use a pencil and paper. Explain how the volume of the cone would change if the radius were halved.
Answer:
[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]
Now if we increase the radius by a factor of 2 the new volume would be:
[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]
And we can find the increase factor for the volume like this:
[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]
Then if we increase the radius by 2 the volume increase by a factor of 4
If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.
On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.
Step-by-step explanation:
For this case we have the following info given:
[tex]r = 5 , h =12[/tex]
and we can find the initial volume:
[tex] V = \frac{1}{3} \pi r^2 h[/tex]
And replacing we got:
[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]
Now if we increase the radius by a factor of 2 the new volume would be:
[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]
And we can find the increase factor for the volume like this:
[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]
Then if we increase the radius by 2 the volume increase by a factor of 4
If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.
On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.
Find the point on the curve r(t) = (5Sint)i + (5Cost)j +12tk
at a distance 26pi units along the curve from the point (0,5,0) inthe direction of increasing arc length.
Answer:
Find the point on the curve r(t) = (5Sint)i + (5Cost)j +12tk
at a distance 26pi units along the curve from the point (0,5,0) inthe direction of increasing arc length.
(My attempt):
T comes to be 2pi and when the integral is done and solved to givea value of 26pi and the position comes to be (0,5,24pi). However,this calculation and answer though correct (according to the backof the book) does not involve the use of the fact that at time t=0,the particle is at (0,5,0).
What for is that information given then?
Step-by-step explanation:
Consider the curve r(t) = (5Sint)i + (5Cost)j + (12t)k
Need to find the point on the given curve at a distance 26π unit along the curve from the point (0,5,0) inthe direction of increasing arc length.
Length of a smooth curve is [tex]r(t)=x(t)i+y(t)j+z(t)k, \ \ a\leq t\leq b[/tex] that is traced exactly once as t increase from t = a to t = b, is
[tex]L=\int\limits^b_a \sqrt{(\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2+(\frac{dz}{dt} )^2dt}[/tex]
For the given curve
x(t) = 5 sin t
y(t) = 5 cos t
z(t) = 12t
When t = 0
x(0) = 5 sin 0
= 0
y(0) = 5 cos 0
= 0
z(0) = 12(0)
=0
So, the point (0, 5, 0) corresponds to t = 0
So let t = t₀ correspond to any point (x, y, z) on the curve at a distance of 26pi units from the point t = 0 along the increasing arc length
So, the length of curve from the point t = 0 to t = t₀ is L = 26pi units
Substitute the known value to the arc length formula
[tex]L=\int\limits^b_a \sqrt{(\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2+(\frac{dz}{dt} )^2dt}[/tex]
[tex]26\pi=\int\limits^{t_0}\sqrt{(5 \cos t)6+(-5 \sin t)^2+(12)^2dt}\\\\26\pi=\int\limits^{t_0}_0\sqrt{25 \cos ^2t+25 \sin ^2t+144dt} \\\\26\pi=\int\limits^{t_0}_0 \sqrt{25(\cos^2t+ \sin^2t)+144dt}\\\\26\pi=\int\limits^{t_0}_0\sqrt{25(1)+144dt} \\\\26\pi= \int\limits^{t_0}_0\sqrt{169dt} \\\\26\pi= \int\limits^{t_0}_013 dt\\\\26\pi=13\int\limits^{t_0}_0dt\\\\26\pi=13[t]^{t_0}_0\\\\26\pi=13[t_0-0]\\\\26\pi=13t_0\\\\t_0=\frac{26\pi}{13} \\\\t_0=2\pi[/tex]
The point corresponding to [tex]t_0 = 2\pi[/tex]
when t = 0
[tex]x(2\pi)=5 \sin (2\pi)\\\\=0\\\\y(2\pi)=5 \cos (2\pi)\\\\=5(1)=5\\\\z(2\pi)=12(2\pi)\\\\=24\pi[/tex]
Therefore the point corresponding to [tex]t_0 = 2\pi[/tex] is [tex](0,5,24\pi)[/tex]
Hence, the required point on the given curve at distance 26\pi units along the curve from the point (0,5,0) in the direction of increasing arc length is [tex](0,5,24\pi)[/tex]
Keep gettin this one wrong please help
Answer:
30 Nickels and 188 Pennies
Step-by-step explanation:
okay, so to set up the equation first, we have to assign each coin a variable, let's call them p and n:
P= number of pennies
N= number of nickels
the value of a penny is 1 cent, so 1P, and the value of a nickel is 5 cents, so 5N
The problem states that he has 218 coins, meaning that the total number of pennies and nickels adds up to 218:
P + N = 218
the total value of the coins is $3.38, so that would mean that 1P + 5N has to equal $3.38:
1P + 5N = 338
Okay, so now that we have our equations let's solve them using elimination:
we have to get a common coefficient between both equations, so let's multiply our first equation by 5:
P x 5 = 5P
N x 5 = 5N
218 x 5 = 1090
so, now we can solve by elimination:
5P + 5N = 1090
1P + 5N = 338
the N's cancel out:
4P = 752
divide both sides by 4:
P = 188
okay, so if theres a total of 218 coins, subtract 188 from 218:
218 - 188 = 30
so, there are 30 nickels and 188 pennies.
check our work:
5 x 30 = 150
1 × 188 = 188
150 + 188 = 338
338 = 338
I hope this helps! :)
Could someone please give me the answer to this?
Answer:
? = 8.77
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opposite/ hypotenuse
sin 20 = 3/?
? = 3 / sin 20
? =8.7714132
To the nearest hundredth
? = 8.77
We can use the trigonometric function [ sin theta = opposite/hypotenuse ] to solve.
sin(20) = 3/hypotenuse
hypotenuse = 3/sin(20)
hypotenuse = 8.7714...
Round to the nearest hundredth.
8.7714... → 8.77
Therefore, the answer is 8.77
Best of Luck!
At a school fair, each student spins the spinner, which is equally likely to land on each of the four sectors. The spinner shows how many tokens the student wins or loses. What is the expected number of tokens that a student will win on each spin
Answer:
3 tokens.
Step-by-step explanation:
We need the roulette image, therefore we will suppose one that I will leave as an attached image:
The main thing to keep in mind in this case is that the probabilities are the same, therefore you don't have to take that into account, just operate with the values of each sector, therefore the expected value would be:
expected value = profit - loss
expected value = (5 + 5) - (4 + 3)
expected value = 10 - 7 = 3
This means that the number of tokens waiting for the student to earn for each spin is 3 tokens.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. -4<x<2
Step-by-step explanation:
The highest x point is -4 and lowest peak is 2
Answer:
B. -4 ≤ x ≤ 2
Step-by-step explanation:
→Basically, the question is asking, "At what point is the line on the graph decreasing?"
→Looking at the graph, you can see that when x = -4, that's when the line on the graph starts to decrease. The line continues to decrease, until it reaches the point where x = 2.
This makes the correct answer "B. -4 ≤ x ≤ 2."
Please answer this correctly
Answer:
42 13/20 km
Step-by-step explanation:
10 3/10+9 7/20+14 7/10+ 8 9/20=41+ (6+7+14+9)/20=41 + 1 13/20= 42 13/20 km
On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32. Round your answer to four decimal places.
Answer:
0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 28, \sigma = 5[/tex]
Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
This is the pvalue of Z when X = 32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 28}{5}[/tex]
[tex]Z = 0.8[/tex]
[tex]Z = 0.8[/tex] has a pvalue of 0.7881
0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.
you invested $22,000 in two accounts paying 4% and 9% annual interest. if the total interest earned for the year was $1180, how much was invested at each rate
Answer:
Amount invested at 4% is $16,000
Amount invested at 9% is $6,000
Step-by-step explanation:
Let one vestment be x
if total investment is $22,000 then
other investment will $22,000 - x
simple interest earned in any year is given by
SI = p*r*t/100
where SI is the interest earned
t is the time period of investment
r is the rate of annual interest
_____________________________________
interest on one account 4%
p = x
t = 1 year
SI = x*4*1/100 = 4x/100
_____________________________
interest on one account 9%
p = 22,000 - x
t = 1 year
SI = (22,000 - x)*9*1/100 = (198000 - 9x)/100
_____________________________________
it is given that total interest earned was $1180
thus sum of SI calculated for the 9% and 4% investment will be equal to 1180
4x/100 + (198000 - 9x)/100 = 1180
=> (4x+198000 - 9x)/100 = 1180
=> 198000 - 5x = 1180*100
=> -5x = 118,000 - 198000
=> -5x = -80,000
=> x = -80,000/-5 = 16,000
Thus,
Amount invested at 4% is $16,000
Amount invested at 9% is $(22,000 - 16,000) = $6,000
Spend some time looking at the vehicles on the road. Look at the first 40 vehicles that drive by. Take note of the number of vehicles that are cars (sedans). Use the data you collect to construct confidence interval estimates of the proportion of vehicles that are cars (rather than trucks, vans, etc). Report your confidence interval to the group. Why might people get different results? Is your sample likely a good representation of the total population of all vehicles? Why or why not?
Answer:
The confidence interval is ( 0.225952516, 0.474047484)
People will get different results because, the amount of sedans may be dependent on the area in which the data is taken.
No, the sample is not really a good representation of the whole population of vehicles, since only a certain area was sampled or experimented.
Step-by-step explanation:
Solution
Given that:
From the experiment we discovered that out of 40 vehicles, 14 of them were sedans.
Let us note that:
p^ = It is the point estimate of the population proportion
Where,
n=/n = 0.35
We also check for the standard error of p, sp:
which is,
sp =√{p^ (1-p^)/n] =0.075415516
Thus,
for the the critical z, we have the following:
α/2 = 0.05
So,
z (α)/2 = 1.644853627
Thus,
For lower bound = p^ - z(α/2) * sp = 0.225952516
For upper bound = p^ + z(α/2)* sp = 0.474047484
Hence,
The confidence interval becomes: ( 0.225952516, 0.474047484)
Find the volume of a come with the radius of 80 and the height of 21. Please show step by step
Answer:
= 140800 cubic (ft/meters/yards/cm/inches)
Step-by-step explanation:
For Cone
radius (r) = 80
height (h) = 21
Volume Of Cone
= π r² h/3
= 22/7 x 80 x 80 x 21/3
= 22 x 80 x 80
= 22 x 6400
= 11 x 12800
= 140800 cubic (ft/meters/yards/cm/inches)
Mrs. DeMarco wants to estimate the length of her porch so she knows how much paint to buy. What is the best benchmark for her to use? *
Answer:
Without any multiple choice options i would have to guess square feet.
Step-by-step explanation:
The marked price of a water cooler is $ 500. The shopkeeper offers an off-season discount of 15% on it. Find the discount.
Answer:
75 dollars
Step-by-step explanation:
You know that 500=100%, so we can set up the following
15%(500/100%) = 75
so the discount 75 dollars
A certain car traveling 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. In approximately what distance would the car stop had it been going 105.4 mph?
Answer:
279 m
Step-by-step explanation:
Work by friction = change in kinetic energy
Fd = ½ mv²
d ∝ v²
d / 29 m = (105.4 mph)² / (34.0 mph)²
d = 279 m
A worker is paid $2,350 monthly and has $468 withheld from each monthly paycheck. Which of the following is her annual net salary
Joe and Janna leave home at the same time, traveling in opposite directions. Joe
drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will
they be 510 miles apart?
O a) 7 hours
Ob) 6 hours
Oc) 4 hours
Od) 5 hours
Answer:
B
Step-by-step explanation:
because if you do 40 times 6 and 45 times 6 you get 270 and 240 and you add them up for 510
Is the sequence arithmetic? (Yes or no) If yes, please also give its common difference. 14) -2.8, -2.2, -1.6, -1.0
Answer:
Yes
The common difference is .6
Step-by-step explanation:
Take the second term and subtract the first term
-2.2 - (-2.8)
-2.2+ 2.8 = .6
Take the third term and subtract the second
-1.6 - (-2.2)
1.6 +2.2
The common difference is .6
Answer:
Yes
Step-by-step explanation:
-2.8, -2.2, -1.6, -1.0
-2.2-(-2.8)= -1.6 - (-2.2)= -1 - (-1.6)= 0.6
This is AP with first term -2.8 and common difference 0.6
what would be the answer for this.
Answer & Step-by-step explanation:
We are given that m∠1 = m∠2. We are to prove that line l is parallel to line m. So, let's make a proof. Your first statement should always be the given statement. You are given the statements. All we have to do is find the reasons for those statements.
m∠1 = m∠2 → Givenm∠1 = m∠3 → Vertical angles are equalm∠2 = m∠3 → Substitutionl ║m → If corresponding angles are equal, then lines are parallelThe triangle shown below has an area of 16 units2.
Find z.
4
2
units
Answer:
8 units
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
16 = 1/2 (4)*x
16 = 2x
Divide each side by 2
16/2 = 2x/2
8 =x
Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?
Q'(4, 4), P'(0, 0), R'(-4, -8), S'(8, -4)
Q'(1, 1), P'(0, 0), R'(-1, -2), S'(2, -1)
Q'(4, 4), P'(2, 2), R'(0, -2), S'(6, 0)
Q'(0, 0), P'(-2, -2), R'(-4, -6), S'(2, -4)
Answer:
B
Step-by-step explanation:
The coordinates of quadrilateral Q'P'R'S' is
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
To perform a dilation centered at the origin with a scale factor of 2, we need to multiply the x and y coordinates of each vertex by 2.
So starting with the coordinates of quadrilateral QPRS:
Q(2, 4), P(0, 0), R(-2, -4), S(4, -2)
Multiplying each coordinate by 2, we get:
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4)
Therefore,
The coordinates of quadrilateral Q'P'R'S' is
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).
Learn more about scale factors here:
https://brainly.com/question/20759556
#SPJ3
The complete question.
Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?
Where
The coordinates of PQRS are:
Q = (2, 4), P = (0, 0), R = (-2, -4), S = (4, -2).
Find the roots of the quadratic equation 3y² - 4y+1=0 By
i) completing the square method
ii) the formula
Answer:
i) [tex] 3y^2 -4y +1=0[/tex]
We can divide both sides of the equation by 3 and we got:
[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]
Now we can complete the square and we got:
[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]
[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]
We take square root on both sides and we got:
[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]
And the solutions for y are:
[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]
[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]
ii) [tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And with [tex] a = 3, b=-4 and c =1[/tex] we got:
[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]
And we got:
[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]
Step-by-step explanation:
Part i
For this case we have the following function given:
[tex] 3y^2 -4y +1=0[/tex]
We can divide both sides of the equation by 3 and we got:
[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]
Now we can complete the square and we got:
[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]
[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]
We take square root on both sides and we got:
[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]
And the solutions for y are:
[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]
[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]
Part ii
We can use the quadratic formula:
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And with [tex] a = 3, b=-4 and c =1[/tex] we got:
[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]
And we got:
[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]