Answer:
BRIAN DID NOT REACH HIS GOAL! Brian rode 5.52 miles!
Step-by-step explanation:
Answer:
he didn't reach his goal. he rode 5.52 miles
Step-by-step explanation:
The mean annual tuition and fees for a sample of 15 private colleges was with a standard deviation of . A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from 32,500 a) state the null and alternate hypotheses b) calculate the standard error c) calculate the test statistic d) find the p - value .
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500
Solution
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 32500
For the alternative hypothesis,
Ha: µ ≠ 32500
This is a two tailed test.
Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.
Since n = 15,
Degrees of freedom, df = n - 1 = 15 - 1 = 14
t = (x - µ)/(s/√n)
Where
x = sample mean = 35500
µ = population mean = 32500
s = samples standard deviation = 6500
t = (35500 - 32500)/(6500/√15) = 1.79
We would determine the p value using the t test calculator. It becomes
p = 0.095
Assuming alpha = 0.05
Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.
The height of the triangle is 10 cm. It is decreased by 25%. Calculate the new height.
Decreased height = 10 x [tex]\frac{100 - 25}{100}[/tex]
= 10 x [tex]\frac{75}{100}[/tex]
= [tex]\frac{750}{100}[/tex]
= 7.5 cm
Answer:
7.5 cm
Step-by-step explanation:
Decreased height = 25% of 10
[tex]=\frac{25}{100}*10\\\\=0.25*10\\=2.5[/tex]
New height = 10 - 2.5 = 7.5 cm
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340 found that 60% of the readers owned a laptop. State the null and alternative hypotheses. Answer
Answer:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Step-by-step explanation:
Information given
n=340 represent the random sample taken
[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.65[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v{/tex} represent the p value
Hypothesis to test
We want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65[/tex]
Alternative hypothesis:[tex]p \neq 0.65[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
24 1/2 is equal to what decimal
Answer:
24.5
Step-by-step explanation:
24 = 24
1/2 -->
convert to a decimal => 1 divided by 2
0.5
24+0.5 = 24.5
Hope this helps!
Can someone please help me??
Answer : The value of x is 4.1 cm.
Step-by-step explanation :
As we know that the perpendicular dropped from the center divides the chord into two equal parts.
That means,
AB = CB = [tex]\frac{15.6cm}{2}=7.8cm[/tex]
Now we have o calculate the value of x by using Pythagoras theorem.
Using Pythagoras theorem in ΔOBA :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](OA)^2=(OB)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side OB.
[tex](8.8)^2=(x)^2+(7.8)^2[/tex]
[tex]x=\sqrt{(8.8)^2-(7.8)^2}[/tex]
[tex]x=\sqrt{77.44-60.84}[/tex]
[tex]x=\sqrt{16.6}[/tex]
[tex]x=4.074\approx 4.1[/tex]
Therefore, the value of x is 4.1 cm.
Any help would be great
Answer:
-8 * 5 = -40
a⁵ * a = a⁶
b⁶ * b³ = b⁹
Answer is -40a⁶b⁹
A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have paid leave. In January 2012, a random survey of 1000 workers showed that 89% had paid leave. The resulting p-value is .0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people, who have paid leave from 2011 to January 2012. What type of error is possible in this situation?
Answer:
Is possible to make a Type I error, where we reject a true null hypothesis.
Step-by-step explanation:
We have a hypothesis test of a proportion. The claim is that the proportion of paid leave has significantly decrease from 2011 to january 2012. The P-value for this test is 0.0271 and the nunll hypothesis is rejected.
As the conclusion is to reject the null hypothesis, the only error that we may have comitted is rejecting a true null hypothesis.
The null hypothesis would have stated that there is no significant decrease in the proportion of paid leave.
This is a Type I error, where we reject a true null hypothesis.
Bronson is ordering pizza at a restaurant, and the server tells him that he can have up to three toppings: spinach, bacon, and pepperoni. Since he cannot decide how many of the toppings he wants, he tells the server to surprise him. If the server randomly chooses which toppings to add, what is the probability that Bronson gets just spinach? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
The probability that Bronson gets just spinach is;
P = 1/7
or
P = 0.1429
Step-by-step explanation:
There are three possibilities;
- just one topping
- two topping
- three topping
For just one topping, the number of possible outcomes is;
N1 = 3C1 = 3!/(1!2!) = 3 possible outcomes
For two topping, the number of possible outcomes is;
N2 = 3C2 = 3!/(2!1!) = 3 possible outcomes
For three topping, the number of possible outcomes is;
N3 = 3C3 = 3!/3! = 1 possible outcomes
Total number of possible outcomes;
N = N1+N2+N3
N = 3+3+1 = 7
The probability that Bronson gets just spinach is;
Getting spinach is one out of seven possible outcomes, so;
P = 1/N = 1/7
P = 1/7 or 0.1429
from what area of the world is the earliest dated inscription with a symbol for zero?
Answer:
india
Step-by-step explanation:
what is the length of the line?
Answer:
root 61
Step-by-step explanation:
You can use the distance formula or draw a triangle with sides 5 and 6
Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.
Which value of y would make O P is parallel to L N?
16
24
32
36
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36
Answer:
D-36
Step-by-step explanation:
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4? P (number greater than 4) = StartFraction 1 over 6 EndFraction (50) P (number greater than 4) = StartFraction 2 over 6 EndFraction (50) P (number greater than 4) = StartFraction 3 over 6 EndFraction (50) P (number greater than 4) = StartFraction 4 over 6 EndFraction (50)
Answer:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
How do i work out the probability of rolling two sixes
Answer: p = 1/25
Step-by-step explanation:
Ok, you know that the probability of rolling a six is p = 1/5
now, if you want to have two sixes, then you have two events with a probability of 1/5.
And as you know the joint probability for two events is equal to the product of the probabilities, then the probability of rolling two sixes is:
p = (1/5)*(1/5) = 1/25.
A box contains 11 red chips and 4 blue chips. We perform the following two-step experiment: (1) First, a chip is selected at random from the box and is then removed from the box. (After this first step, there are 14 chips left in the box. ) (2) Then, a chip is selected at random from the box (that is, from the remaining 14 chips) . Let B 1 be the event that the chip removed from the box at the first step of the experi- ment is red. Let B 2 be the event that the chip removed from the box at the first step of the experiment is blue. Let A be the event that the chip selected from the box at the second step of the experiment is red.Find P(B1), P(B2), P(A), P(B1|A), and P(B2|A).
Answer:
P(B1) = (11/15)
P(B2) = (4/15)
P(A) = (11/15)
P(B1|A) = (5/7)
P(B2|A) = (2/7)
Step-by-step explanation:
There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.
B1 is the event that the chip removed from the box at the first step of the experiment is red.
B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.
Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
P(B1) = probability that the first chip selected is a red chip = (11/15)
P(B2) = probability that the first chip selected is a blue chip = (4/15)
P(A) = probability that the second chip selected is a red chip
P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/21) + (22/105) = (77/105) = (11/15)
P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip
The conditional probability, P(X|Y) is given mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
So, P(B1|A) = P(B1 n A) ÷ P(A)
P(B1 n A) = (11/15) × (10/14) = (11/21)
P(A) = (11/15)
P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)
P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip
P(B2|A) = P(B2 n A) ÷ P(A)
P(B2 n A) = (4/15) × (11/14) = (22/105)
P(A) = (11/15)
P(B2|A) = (22/105) ÷ (11/15) = (2/7)
Hope this Helps!!!
Frederick took out a 20-year loan for $70,000 at an APR of 2.2%, compounded monthly. Approximately how much would he save if he paid it off 9 years early?
Answer:
$38,645.7208
Step-by-step explanation:
Given that
Principal = $70,000
Time = 20 years
Rate = 2.2%
The calculation of the amount of saving is shown below:-
[tex]=P(1+r)^t[/tex]
A = Future amount
P = Principal amount
[tex]r = \frac{APR}{12}[/tex]
[tex]r = \frac{0.022}{12}[/tex]
0.001833333
t = 20 years which is equals to 240 months
[tex]A=\$70,000\times (1+0.001833333)^{240}[/tex]
[tex]A=\$70,000\times 1.552081726[/tex]
= $108,645.7208
And, the loan amount for 20 years is $70,000
So,
He would save by paying off 9 years early is
= $108,645.7208 - $70,000
= $38,645.7208
Its $3644.67 since everyone couldn't find it solved it myself ;)
The sum of a number and twice the number is 24 what is the number?
Answer:
x = 8
Step-by-step explanation:
Step 1: Write out the expression
x + 2x = 24
Step 2: Combine like terms
3x = 24
Step 3: Isolate x
x = 8
And we have our final answer!
Answer:
X=8
Step-by-step explanation:
A newsletter publisher believes that less than 29% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
Step-by-step explanation:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a house in Midvale, UT for $ 172000 in 2004 in what year would the home be worth $ 249000 ?
Answer:
The home would be worth $249000 during the year of 2012.
Step-by-step explanation:
The price of the home in t years after 2004 can be modeled by the following equation:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the price of the house in 2004 and r is the growth rate.
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.
This means that [tex]r = 0.047[/tex]
$172000 in 2004
This means that [tex]P(0) = 172000[/tex]
What year would the home be worth $ 249000 ?
t years after 2004.
t is found when P(t) = 249000. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]249000 = 172000(1.047)^{t}[/tex]
[tex](1.047)^{t} = \frac{249000}{172000}[/tex]
[tex]\log{(1.047)^{t}} = \log{\frac{249000}{172000}}[/tex]
[tex]t\log(1.047) = \log{\frac{249000}{172000}}[/tex]
[tex]t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}[/tex]
[tex]t = 8.05[/tex]
2004 + 8.05 = 2012
The home would be worth $249000 during the year of 2012.
Before a researcher specified the relationship among variables he must have a (an): A: Inventory of variables B: Inventory of propositions C: Arrangement of propositions D: Schematic diagram
Answer:
Option B
Step-by-step explanation:
Before a researcher specifies the relationship among variables he must have an inventory of propositions/constructs which are mostly stated in a declarative form. These are then tested by examining the relationships between measurable variables of this constructs/propositions.
The percentage of households that include at least one frequent gamer is 58%. A gaming magazine is interested in studying this further to see how it impacts their magazine advertisements. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.02
Answer:
For a sample size of n = 609.
Step-by-step explanation:
Central limit theorem for proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
We have that p = 0.58.
We have to find n for which s = 0.02. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.02 = \sqrt{\frac{0.58*0.42}{n}}[/tex]
[tex]0.02\sqrt{n} = \sqrt{0.58*0.42}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.58*0.42}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{\sqrt{0.58*0.42}}{0.02})^{2}[/tex]
[tex]n = 609[/tex]
For a sample size of n = 609.
A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 22 is made, and it is found that they have a mean of 2045.0 millimeters with a standard deviation of 13.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
Step-by-step explanation:
Information given
[tex]\bar X=2045[/tex] represent the sample mean
[tex]s=13[/tex] represent the standard deviation
[tex]n=22[/tex] sample size
[tex]\mu_o =2058[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to cehck if the true mean for this case is equal to 2058 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2058[/tex]
Alternative hypothesis:[tex]\mu \neq 2058[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
Please help me with this math problem
Answer:
-1/4 is the slope and the y intercept is -4
Step-by-step explanation:
Solve for y
x +4y = -16
Subtract x
4y = -x-16
Divide by 4
4y/4 = -x/4 -16/4
y = -1/4 x -4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
-1/4 is the slope and the y intercept is -4
Please answer this correctly
Answer:
0
Step-by-step explanation:
The sorted data set is ...
1 2 3 3 5 7 8 9
The median is the average of the middle two numbers: (3+5)/2 = 4.
Replacing one of the 3s with a 1 makes the data set be ...
1 1 2 3 5 7 8 9
The average of the middle two numbers is (3+5)/2 = 4.
The median increases by 4 - 4 = 0.
segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?
1/2
2
3
4
Answer:
the answer is 3
Step-by-step explanation:
i took the test
It is known that 4% of children carry a certain virus, but a leading health researcher suspects that the percentage is actually higher. Which of the following provides the most convincing evidence to support the researcher's suspicion?
A. Out of 5,000 randomly chosen children, 210 children carry the virus.
B. Out of 60 randomly chosen children, 3 children carry the virus.
C. Out of 5,000 randomly chosen children, 250 children carry the virus.
D. Out of 20 randomly chosen children, 1 child carries the virus.
Answer:
(C)Out of 5,000 randomly chosen children, 250 children carry the virus.
Step-by-step explanation:
[tex]\text{Option A}: \dfrac{210}{5000}=0.042=4.2\% \\\text{Option B}: \dfrac{3}{60}=0.05=5\% \\\text{Option C}: \dfrac{250}{5000}=0.05=5\% \\\text{Option D}: \dfrac{1}{20}=0.05=5\%[/tex]
The higher the research sample, the more credible the results. In options A and C, the research sample was 5000. However, since the relative frequency of children carrying the virus is 5% in both, we take the result with a higher number of positives.
Option C is the correct option.
Please answer this correctly
Description:
As we that that 3 of the students voted for counting .
4 Students voted for sorting
6 Students voted for shapes
7 Students voted for addition
Answer:
Counting - 3%
Sorting - 4%
Shapes- 6%
Addition- 7%
Please mark brainliest
Hope this helps.
Answer:
Counting: 15%
Sorting: 20%
Shapes: 30%
Addition: 35%
Step-by-step explanation:
Counting: [tex]\frac{3}{3+4+6+7} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Sorting: [tex]\frac{4}{3+4+6+7} =\frac{4}{20} =\frac{20}{100} =[/tex] 20%
Shapes: [tex]\frac{6}{3+4+6+7} =\frac{6}{20} =\frac{30}{100} =[/tex] 30%
Addition: [tex]\frac{7}{3+4+6+7} =\frac{7}{20} =\frac{35}{100} =[/tex]35%
The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 900 voters in the town and found that 60% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is above 56%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
Test statistic z = 2.3839.
P-value = 0.0086.
At a signficance level of 0.05, there is enough evidence to support the claim that the percentage of residents who favor construction is above 56%.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the percentage of residents who favor construction is above 56%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.56\\\\H_a:\pi>0.56[/tex]
The significance level is 0.05.
The sample has a size n=900.
The sample proportion is p=0.6.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.56*0.44}{900}}\\\\\\ \sigma_p=\sqrt{0.000274}=0.017[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.56-0.5/900}{0.017}=\dfrac{0.039}{0.017}=2.3839[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.3839)=0.0086[/tex]
As the P-value (0.0086) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the percentage of residents who favor construction is above 56%.
Does the graph represent a function. Explain
Answer:
Yes
Step-by-step explanation:
functions include parabolas so yes!
Solve 2cos3x=0.9.
Pls help me with this trigonometric equations with multiple angles.
Answer:
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
Step-by-step explanation:
Given: [tex]2 cos(3x)=0.9[/tex]
To find: solutions of the given equation
Solution:
Triangle is a polygon that has three sides, three angles and three vertices.
Trigonometry explains relationship between the sides and the angles of the triangle.
Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]
[tex]2 cos(3x)=0.9[/tex]
Divide both sides by 2
[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]
[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]
So,
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]