Answer:
The correct answer is:
The samples are independent because there is not a natural pairing between the two samples. (d.)
Step-by-step explanation:
Paired samples or dependent samples are samples in which natural matching or coupling occur, thus creating a data set where data from one sample is uniquely paired to another sample because they are from related groups. Examples are: pre-test/post-test data gotten before and after an intervention, samples from siblings, twins, couples etc.
On the other hand, independent or unpaired samples are those data sets that are gotten from unrelated groups, these type of samples are gotten by matching randomly sampling two unrelated groups without first matching the subjects. In our example, the sample from randomly selected women and men are not paired and unrelated, hence they are independent samples.
The samples are independent because there is not a natural pairing between the two samples. Hence, option (D) is correct.
Let us understand both the events in a systematic manner to answer this question.
Independent Events:
The simple way to understand the events, If the events are not related to each other, then the events are independent of each other. If one event is dependent on another then it is not an independent event.
Example:
Event 1: Toss a coin.
Event 2: Roll a die.
Both the events are independent of each other.
Dependent Events:
The simple way to understand the events, If the events are related to each other, then the events are independent of each other. If one event is dependent on another then it is not an independent event.
Example:
Event 1: Toss a coin.
Event 2: If head appears then roll a die.
Both the events are dependent on each other.
Thus, the samples are independent because there is not a natural pairing between the two samples.
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If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire tub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.
Answer:
46.2÷m=x
Step-by-step explanation:
u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).
16.5/min
time = m
gallons / minutes = rate
46.2 = 16.5 (m)
46.2 / 16.5 = 16.5 (m) / 16.5
2.8 = minutes
bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab
Answer:
[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]
Step-by-step explanation:
Bananas represented by b
1 banana costs $4 so b bananas will cost $ 4 b
Apples represented by a
1 apples costs 0.60 $ so a apples will cost $ 0.60 a
Totally, they will cost:
=> $ (4 b + 0.60 a)
Answer:
hiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
When determining the sample size necessary for estimating the true population mean, which factor is NOT considered when sampling with replacement
Answer:
Population Size
Step-by-step explanation:
When sampling with replacement, we can expect that the population size will remain the same. Sampling with replacement occurs when a unit or subject for research is chosen from a population at random. This chosen unit can be returned to the population and another random selection done with the possibility that a unit that was chosen before could be chosen again. So in applying this system of selection, the population size is not taken into consideration. When samples are chosen in this form, it can be referred to as a simple random sample.
So, when determining the sample size necessary for estimating the true population mean, using the sampling with replacement method, the population size is not considered.
i need help quick!!!
Answer: A,C, and D
Step-by-step explanation:
Answer:
the answer to this question may be option B, C and D
Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling?
Answer:
20kg
Step-by-step explanation:
Let the weight of one duck be x and the weight of one duckling be y
ATQ, 3x+2y=32 and 4x+3y=44, solving for x and y we get, weight of one duck is 8kg and one duckling is 4kg. The weight of two ducks and one duckling is 20kg
According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.
a. True
b. False
Answer:
False
Step-by-step explanation:
Here, we want to check the validity of the given statement. The statement is false.
Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.
Please check attachment for diagrammatic representation of the empirical rule.
3. A medical devices company wants to know the number of MRI machines needed per day. A previous study found a standard deviation of four hours. How many MRI machines must the company study in order to have a margin of error of 0.5 hours when calculating a 90% confidence interval
Answer:
173 MRI machines
Step-by-step explanation:
Margin of error E = 0.5
Confidence interval 90% = 1-0.9 = 0.1
Standard deviation = 4 hours
Number of MRI machines needed per day n, = [(z alpha/2 * SD)/E]²
Z alpha/2 = 1.645 at alpha = 0.1
Inputting these values into n we have that
[(1.645*4)/0.5]²
= 13.16²
= 173.18 is approximately equal to 173
The company has to study 173 machines.
Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥8 300, α = 0.10
Sample statistics: x = 8000, s = 440, n = 24
A. What are the null and alternative hypotheses?
B. What is the value of the standardized test statistic?
C. What is the p-value?
D. Decide whether to reject or fail to reject the null hypothesis.
Answer:
A
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
B
[tex]t = -3.34[/tex]
C
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
D
reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 8300[/tex]
The sample mean is [tex]\ = x = 8000[/tex]
The standard deviation is [tex]s = 440[/tex]
The sample size is [tex]n = 24[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \ge 8300[/tex]
The alternative hypothesis is [tex]H_a : \mu < 8300[/tex]
The test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]
=> [tex]t = -3.34[/tex]
The p-value is obtained from the z -table ( reference calculator dot net ) , the value is
[tex]p-value = P(t< -3.34) = 0.00041889[/tex]
Looking at the values of [tex]p-value and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim
Answer:
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at least 64%, that is:
[tex]H_0: p \geq 0.64[/tex]
At the alternative hypothesis, we test if the proportion is of less than 64%, that is:
[tex]H_1: p < 0.64[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
64% is tested at the null hypothesis:
This means that [tex]\mu = 0.64, \sigma = \sqrt{0.64*0.36}[/tex]
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.
This means that [tex]n = 900, X = 0.61[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}[/tex]
[tex]z = -1.88[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.
Looking at the z-table, z = -1.88 has a p-value of 0.0301.
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
According to the Census Bureau, 3.34 people reside in the typical American household. A sample of 26 households in Arizona retirement communities showed the mean number of residents per household was 2.70 residents. The standard deviation of this sample was 1.17 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?
(a) State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)
H0: ? ?
H1: ? <
(b)
State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0 if t <
(c)
Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Value of the test statistic
(d)
Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons?
H0. Mean number of residents less than 3.34 persons.
Answer:
Step-by-step explanation:
Given that:
Mean = 3.34
sample size = 26
sample mean = 2.7
standard deviation = 1.17
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu \geq 3.34} \\ \\ \mathtt{H_1: \mu < 3.34}[/tex]
degree of freedom = n - 1
degree of freedom = 26 -1
degree of freedom = 25
level of significance = 0.10
Since the alternative hypothesis contains <, then the test is left tailed
[tex]\mathtt{t_{\alpha, df} = t_{0.10, 25}}[/tex]
[tex]\mathtt{t_{0.10, 25}}[/tex] = - 1.316
The rejection region therefore consist of all values smaller than - 1.316, therefore ; reject [tex]H_o[/tex] if t < -1.316
The test statistics can be computed as follows:
[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{2.7 - 3.34}{\dfrac{1.17}{\sqrt{26}}}[/tex]
[tex]t = \dfrac{-0.64}{\dfrac{1.17}{5.099}}[/tex]
t = - 2.789
Decision Rule: To reject the null hypothesis if the t test lies in the rejection region or less than the rejection region.
Conclusion: We reject the null hypothesis since t = (- 2.789) < -1.316. Then we conclude that the mean number of residents in the retirement community household is less than 3.34 persons.
The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point
of the preimage. Point D′ of the image coincides with point
of the preimage.
Answer:
Point C: G
Point D: F
Step-by-step explanation:
A hexagon has 6 sides.
360/6=60
Every 60°, it moves one section.
240/60=4.
So it moves 4 sections.
C would move 4 sections BACK (B, A, F, G)
D would also move 4 sections back (C, B, A, F)
Answer:
Point C is: E
point D is : F
Step-by-step explanation:
An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5 and 10.5 respectively. How long is the island ?
Answer:
154.10 Feets
Step-by-step explanation:
Given the following :
Height (h) of cliff = 320 feet
Angle of depression of near side = 16.5°
Angle of depression of far side = 10.5°
Using trigonometry :
We can obtain x and y as shown in the attached picture :
Tanθ = opposite / Adjacent
Adjacent = height of cliff = 320 Feets
For the near side :
Tanθ = opposite / Adjacent
Tan (16.5°) = x / 320
0.2962134 = x / 320
x = 0.2962134 * 320
x = 94.788318 Feets
For the far side :
Tanθ = opposite / Adjacent
Tan (10.5°) = x / 320
0.1853390 = x / 320
x = 0.1853390 * 320
x = 59.308494 Feets
Length of island = (59.308494 + 94.788318) feet
= 154.10 Feets
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
On an exam, the average score is 76 with a standard deviation of 6 points What is the probability that an individual chosen at random will have a score below 67 on this exam
Answer:
P [ X < 67 ] = 0,66,81 or 66,81 %
Step-by-step explanation:
We assume Normal Distribution N ( μ ; σ ) N ( 76 ; 6 )
z score for 67 is :
z(s) = ( X - μ ) /σ
z(s) = ( 67 - 76 ) / 6
z(s) = - 9 / 6
z(s) = - 1,5
with 1,5 we fnd n z-table area undr the curve α = 0,6681
Then P [ X < 67 ] = 0,66,81 or 66,81 %
The circumference of the circle shown below is 75 inches. Which expression
gives the length in inches of DE?
D
A.
. 75
72
O B.
360
75
O C.
361
. 75
O D.
360
75%
Answer:
B. 360 .75
Step-by-step explanation:
The circumference of the circle is represented by π * diameter of the circle. The circumference of the circle is its perimeter. The circumference is arc length of the circle. The perimeter is curve length around the figure of the circle. The circumference of the circle of 75 inches is represented by 75/360.
Answer: 72/360 multiply by 75
Step-by-step explanation:
i just did this question
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel
Answer:
the probability of no defects in 10 feet of steel = 0.1353
Step-by-step explanation:
GIven that:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.
Let consider β to be the average value for defecting
So;
β = 2
Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.
Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2
i.e
[tex]Y \sim P( \beta = 2)[/tex]
the probability mass function can be represented as follows:
[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]
where;
y = 0,1,2,3 ...
Hence, the probability of no defects in 10 feet of steel
y = 0
[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]
[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]
P(y =0) = 0.1353
Let the sample size of leg strengths to be 7 and the sample mean and sample standard deviation be 630 watts and 32 watts, respectively.
(a) Is there evidence that leg strength exceeds 600 watts at significance level 0.05? Find the P-value. There is_________ evidence that the leg strength exceeds 600 watts at ? = 0.05.
A. 0.001 < P-value < 0.005
B. 0.10 < P-value < 0.25
C. 0.010 < P-value < 0.025
D. 0.05 < P-value < 0.10
(b) Compute the power of the test if the true strength is 610 watts.
(c) What sample size would be required to detect a true mean of 610 watts if the power of the test should be at least 0.9? n=
Answer:
a. There is_sufficient evidence that the leg
C. 0.010 < P-value < 0.025
b. Power of test = 1- β=0.2066
c. So the sample size is 88
Step-by-step explanation:
We formulate the null and alternative hypotheses as
H0 : u1= u2 against Ha : u1 > u2 This is a right tailed test
Here n= 7 and significance level ∝= 0.005
Critical value for a right tailed test with 6 df is 1.9432
Sample Standard deviation = s= 32
Sample size= n= 7
Sample Mean =x`= 630
Degrees of freedom = df = n-1= 7-1= 6
The test statistic used here is
Z = x- x`/ s/√n
Z= 630-600 / 32 / √7
Z= 2.4797= 2.48
P- value = 0.0023890 > ∝ reject the null hypothesis.
so it lies between 0.010 < P-value < 0.025
b) Power of test if true strength is 610 watts.
For a right tailed test value of z is = ± 1.645
P (type II error) β= P (Z< Z∝-x- x`/ s/√n)
Z = x- x`/ s/√n
Z= 610-630 / 32 / √7
Z=0.826
P (type II error) β= P (Z< 1.645-0.826)
= P (Z> 0.818)
= 0.7933
Power of test = 1- β=0.2066
(c)
true mean = 610
hypothesis mean = 600
standard deviation= 32
power = β=0.9
Z∝= 1.645
Zβ= 1.282
Sample size needed
n=( (Z∝ +Zβ )*s/ SE)²
n= ((1.645+1.282) 32/ 10)²
Putting the values and solving we get 87.69
So the sample size is 88
Find the value of z.
A. 25.25
B. 76.25
C. 51
D. 129
Answer:
25.25
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
The angle formed by the two chords is (180 -x)
We need to find x first
x = 1/2 (54+204)
x = 129
The angle formed by the two chords is (180 -129) = 51
51 = 1/2 ( z+3z+1)
Multiply by 2
102 = 4z+1
101 = 4x
Divide by 4
101/4 = z
25.25 =z
Use a calculator to find
the mean of the data.
{217, 253, 214, 247,
217, 253, 232, 246,
223, 227, 229, 247,
206, 241, 239, 223,
222, 216, 252, 209,
236, 256}
A. 230.811
B. 231.045
C. 232.045
D. 232.811
Answer:
232.045
Step-by-step explanation:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
5105 / 22 = 232.045454545
Bob decided to give up a full-time salary of $45000 a year to go to school for 4 years. The total cost of going to school will not include the loss of income because he has saved money and has grants/scholarships to support living cost during this time. But the cost of going to school will be $2,858 per semester, plus $391 per semester for books. If he wants to recover his investment in 6 years or less what is the minimum salary he would need to earn upon earning his degree.
Answer:
Step-by-step explanation:
Semester Costs = 8*2858 = 22864
Books / semester= 8 * 391 = 3128
Total 25992
If he wants to repay all this in six years the answer would be
45000 + 25992/6 = 45000 + 4332 = 49332
Answer:
49332
Step-by-step explanation:
If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?
We have
M(X) = (X + 5)/(X - 1)
N(X) = X - 3
So,
M(N(X)) = [(X - 3) + 5]/[(X - 3) - 1]
M(N(X)) = [X + 2]/[X - 4]The M(N(X)) domain will be:
D = {X / X ≠ 4}
4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be
H(X) = 1/(X - 4)
An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).
Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
PLEASE HELP Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes betweenh
$250 and $300.
Answer: 0.0215 .
Step-by-step explanation:
Let X denotes the weekly wages at a certain factory .
It is normally distributed , such that
[tex]X\sim N(\mu=400,\ \sigma= 50)[/tex]
Then, the probability that a worker selected at random makes between
$250 and $300:
[tex]P(250<X<300)=P(\dfrac{250-400}{50}<\dfrac{x-\mu}{\sigma}<\dfrac{300-400}{50})\\\\=P(\dfrac{-150}{50}<z<\dfrac{-100}{50})\ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(-3<z<-2)\\\\=P(z<-2)-P(z<-3)\\\\=1-P(z<2)-(1-P(z<3))\\\\=P(z<3)-P(z<2)\\\\=0.9987-0.9772\\\\=0.0215[/tex]
Hence,the required probability = 0.0215 .
Mr Osei has a rectangular field measured 85m long and 25m wide. How long is the distance around the field?
Answer:
220m
Step-by-step explanation:
l=85m
b=25m
perimeter=2(l+b)
2(85+25)
2(110)
=220m
perimeter is 220m
Answer:
Distance around the field is 220mStep-by-step explanation:
The distance around the field means the perimeter of the field
Since the field is rectangular
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
From the question
l = 85m
w = 25m
Perimeter = 2(85) + 2(25)
Perimeter = 170 + 50
The final answer is
Perimeter = 220m
Hope this helps you
13.
а/8 = $1.25
Can someone help explain
Answer:
a= $10.00
Step-by-step explanation:
It's very simple. Move /8 to the other side of the equation. It should give you $1.25 x 8. Solve the multiplication and you should get $10.00.
If I didn't make my explanation clear enough, please comment. I sometimes don't even explain myself very well.
Answer:
a = 10
Step-by-step explanation:
a/8 = 1.25
multiply both sides by 8 to isolate a.
(8)(a/8) = 1.25(8)
which gives you
a = 1.25(8)
which simplifies to
a = 10
Snoopy has a spoon that measures out 2(3)/(4) cups of sugar with every scoop. Snoopy takes 5(1)/(3) scoops with this spoon. How many cups of sugar does Snoopy scoop out?
33/64 cups of sugar does snoopy scoop out.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
The amount of sugar needed = 2 3/4 cups
Amount of sugar per scoop = 5 1/3 cups/scoop
So, number of cups of sugar scoops
= cups of sugar needed/ cups of sugar per scoop
=11/4 /16/3
=11/4 *3/16
=33/64
Hence, 33/64 cups of sugar does snoopy scoop out.
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U = { z | z is an integer and − 1 ≤ z < 2 }
Answer:
(-1,0,1,2)
Step-by-step explanation:
in listing the values of z it will now be (z:z= -1,0,1,2)
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80What is the factorization of the polynomial below? 9x^2+12x+4
Answer:
(3x+2)^2
Step-by-step explanation:
Polar coordinates: which is not the same?
Answer:
The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.
Step-by-step explanation:
Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.
Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.
Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)
We know that :
7.518 - 1.236 = 6.282 = ( About ) 2π
5.047 + 1.236 = 6.283 = ( About ) 2π
1.236 + 1.906 = 3.142 = ( About ) 2π
Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).