Raise the monomial to a power.
-4ax³ to the power of 3.
Answers
The question was hard to follow but I tried my best. Lmk what I can do if it is in incorrect format.
Have a nice day
Related Questions
Determine whether each of the following provides enough information to prove that △SQP ≅ △SQR. Select Yes or No for each statement.
Q is the midpoint of PR.
∠P ≅ ∠R
∠SQP is a right angle, ∠PSQ ≅ ∠RSQ
∠SQP is a right angle, m∠P = 33°, m∠RSQ = 57°
∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ
Answers
For each statement for triangle SQP and SQR, Q is the midpoint of PR: No, ∠P ≅ ∠R: No, ∠PSQ ≅ ∠RSQ: Yes, m∠P = 33°, m∠RSQ = 57°: No, ∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes.
What is triangle?
A triangle is a geometric shape that consists of three line segments connected end-to-end to form a closed shape. Triangles are one of the basic shapes studied in geometry and are used in a wide range of applications, from construction to computer graphics.
Here are the answers to whether each statement provides enough information to prove that △SQP ≅ △SQR:
Q is the midpoint of PR: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the angles or sides.
∠P ≅ ∠R: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.
∠SQP is a right angle, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-side (AAS) congruence criterion.
∠SQP is a right angle, m∠P = 33°, m∠RSQ = 57°: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.
∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-angle (AAA) congruence criterion.
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Simplify each expression.
Answers
steps :distribute ,-9 times 3 =-27 , -9 times 3x = -27x , now combine like terms :you have a 1 and a -27 ,1-27=-26,and you left with -27
2)D 11-49x
steps :distribute , positive 7 times 1= 7 and then positive 7 times negative 7x =-49, now combine like terms ,since you have a positive 4 combine it with positive 7 which is 11 and finally put it together with -49x which it would look like 11-49x
Chris and Hillary are remodeling their family room. They are deciding on the flooring, sofa and TV. How many possible combinations are shown in the tree diagram?
A. 10
B. 11
C. 12
D. 13
Answers
Answer:
its C ^^ makes more sense :D
Step-by-step explanation:
hope this helps
Write a sentence of the form “–––––––––––––– is a function of –––––––.”
Type your response in the space below.
Answers
"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.
It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.
In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.
Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.
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Point K is located at ( 1 , 2 ) on the following coordinate plane. A square that has a perimeter of 20 units will be drawn so that K is one vertex of the square. Which three ordered pairs could represent the location of another vertex of the square? Select the three correct answers.
Answers
Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).
To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.
One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.
Using the distance formula, we get:
\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 5
Simplifying and squaring both sides, we get:
(x-1)^2 + (y-2)^2 = 25
Expanding the left side and simplifying, we get:
\(x^{2}\) - 2x + \(y^{2}\) - 4y + 20 = 0
Completing the square for x and y, we get:
\((x-1)^{2}\) + \((y-1)^{2}\) = \(6^{2}\)
This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.
Using this method, we can find several possible locations of the other vertices of the square. Three of them are:
(7, 2), (-5, 2), (1, 8)
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What is the value of y?
Answers
Answer:
-1
Step-by-step explanation:
The table below shows the earnings, in thousands of dollars, for three different commissioned employees.
Employee #1
$2,000 + 3% on all sales
Employee #2
7% on all sales
Employee #3
5% on the first $40,000 + 8% on anything over $40,000
December
4.4
5.6
5.2
January
3.5
3.85
3.6
February
4.7
4.9
4.4
Which employee did not have the same dollar amount in sales for the month of February as the other two employees?
a.
Employee #1.
b.
Employee #2
c.
Employee #3
d.
They each had the same dollar amount in sales.
Answers
The employee who did not have the same dollar amount in sales for the month of February as the other two employees is (a) Employee 1.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Earnings of three employees in the month of February are :
Employee 1 = 4.7 = $4700
Employee 2 = 4.9 = $4900
Employee 3 = 4.4 = $4400
Earnings of employee 1 = $2,000 + 3% on all sales
Let the amount of all sales be x.
2000 + (3% x ) = 4700
2000 + 0.03x = 4700
0.03x = 2700
x = 90,000
Earnings of employee 2 = 7% on all sales
Let the amount of all sales be x.
0.07x = 4900
x = $70,000
Earnings of employee 3 = 5% on the first $40,000 + 8% on anything over $40,000
Let the amount of sales be 40,000 + x.
(0.05 × 40,000) + (0.08 x) = 4400
2000 + 0.08x = 4400
0.08x = 2400
x = $30,000
Amount of sales = $40,000 + $30,000 = $70,000
Hence employee 1 did not have the same amount as the other 2 in February.
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Write the SLOPE INTERCEPT form equation given the following information * 3 8) through: (2, 2), slope
Answers
We have the following two points given:
\((x_1=3,y_1=8)(x_2=2,y_2=2)\)And we want to find the SLOPE intercept form equation given by:
\(y=mx+b\)Where m represent the slope given by:
\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-8}{2-3}=6\)And we can find the intercept b using one of the two points given like this:
\(2=6(2)+b\rightarrow b=2-12=-10\)And then our equation would be given by:
\(y=6x-10\)please help me please please
Answers
Answer:
y=-1/2x-4
Step-by-step explanation:
divide other side by 2
y=-1/2x-8/2
y=-1/2x-4 this is slope-intercept form which is y=mx+b
Which statement defines Suppose that farmers grew an unexpectedly large number of tomatoes this year. How would this increase in production affect the price of tomatoes?the term markup?
Answers
Answer:
The price would go down as people would be more willing to buy cheaper potatoes and the producers would want to sell them for a lower price to get rid of them easy and fast.
Step-by-step explanation:
Hope this helps you :)
What is the value of ?
T
80°
25°
R
?
P
PLEASE
Answers
9514 1404 393
Answer:
105°
Step-by-step explanation:
The exterior angle marked "?" is equal to the sum of the remote interior angles:
? = 25° +80°
? = 105°
"HOT PIZZA" is offering a 20% discount on all its pizza
Ali orders a pizza for the reduced price of £5.60
What was the original price of the pizza?
Answers
Answer: the answer is 7
Step-by-step explanation:
first you divide the price by four then add a quarter to the original amount. gl
. Chad's pay rate for babysitting is y = 9x, where x is the number of hours he babysits, and y is the number of dollars he earns. Horatio's pay rate is shown in the graph below. Horatio's Babysitting Pay Rate. Which of the following statements is true? * HORATIO'S BABYSITTING PAY RATE 100 90 80 70 60 Dollars Earned (8.60) 50 40 30 20 10 (4, 30) 0 1 2 3 4 5 6 7 8 9 10 Hours A. Chad makes $1.00 more per hour than Horatio. O B. Chad makes $1.50 more per hour than Horatio. C. Chad makes $1.00 less per hour than Horatio. D. Chad makes $1.50 less per hour than Horatio.
Answers
Answer: Chad Makes $1.50 more
Step-by-step explanation:
You have to divide 30 from 4 to see Horatio’s hourly rate which is 7.5 and then you will see that 9 - 7.5 is 1.5. I hope this helped
The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:
4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1
11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5
7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4
8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2
5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3
7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2
5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2
8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7
5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6
10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6
7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3
9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2
8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Stems Leaves
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 (b) What is a typical, or representative, flow rate?
L/min
(c) Does the display appear to be highly concentrated or spread out?
highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out
(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?
Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.
(e) Would you describe any observation as being far from the rest of the data (an outlier)?
Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.
Answers
a ) Construction of stem and leaf display of the data is:
For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows
a stem-and-leaf display of the data.
Stems Leaves
2 28
3 1344567789
4 01356889
5 00001114455666789
6 0000122223344456667789999
7 00012233455555668
8 02233448
9 012233335666788
10 2344455688
11 2335999
12 17
13 9
14 36
15 0035
16 None
17 None
18 3
b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.
c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.
d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.
e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.
A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.
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Complete question:
The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:
4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1
11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5
7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4
8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2
5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3
7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2
5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2
8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7
5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6
10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6
7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3
9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2
8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0
(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Stems Leaves
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
(b) What is a typical, or representative, flow rate?
L/min
(c) Does the display appear to be highly concentrated or spread out?
highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out
(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?
Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.
(e) Would you describe any observation as being far from the rest of the data (an outlier)?
Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.
Insert a rational number and an irrational number between √2 and √3
Answers
Answer:
1.5
π/2
Step-by-step explanation:
√2 ≈ 1.41
√3 ≈ 1.73
1.5 is a rational number (15/10) that is in between.
π/2 ≈ 1.57 is an irrational number that is in between.
In circle C, MGK = 38°, mKL = 56°, and mLH = 86°.KFigure not drawn to scaleWhat is the measure of angle LJH?m. All rights reserved.H
Answers
Answer: c
Step-by-step explanation: im smart
Triangle MAF has sides lengths 223, 258 , and 276. Find the measure of the largest angle. a) 68.72degrees b) 69.56degrees c)66.98degrees d) 70.45degrees
Answers
Answer:
Step-by-step explanation:
The largest angle will be opposite the longest side.
Use law of cosines
276² = 223² + 258² - 2(223)(258)cosθ
θ = 69.596009... = 69.60°
Which is closest to answer b)
Please help!
Find the value of x for which ABCD must be a parallelogram.
Answers
Answer:
x=5
Step-by-step explanation:
5x-8=2x+7
5x-2x=7+8
3x=15
X=15/3
x=5
Answer:
5
Step-by-step explanation:
cause
angle c and angle a are alternate angle and alternate angle are always equal so 5X-8=2x+7
5x-2x=7+8
3x=15
or x=5
What is the best name for the figure with the following coordinates?
(4, 1), (1, 1), (3,-2), and (0, -2)
A. rectangle
B. square
C. trapezoid
D. parallelogram
Please select the best answer from the choices provided
OA
OB
Answers
Answer: D. Parallelogram
Step-by-step explanation: Step 1. Input all the points on a graph, there's not really much to it, sorry if I didn't help but the answer is D
A consumer rights advocate wants to determine the lifetime of a certain type of tablet computer. She randomly selects a sample of 29 of these tablets, and calculates the mean and standard deviation to be
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
A consumer rights advocate wants to determine the lifetime of a certain type of tablet computer. She randomly selects a sample of 29 of these tablets, and calculates the mean and standard deviation to be x = 6.7 years and s = 2.3 years. Find a 95% confidence interval for the true mean lifetime (in years) of this type of tablet.
Solution:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 2.3
n = number of samples = 29
x = 6.7
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the t score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 29 - 1 = 28
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
t = 2.048
Margin of error = 2.048 × 2.3/√29
= 0.87
the lower limit of this confidence interval is
6.7 - 0.87 = 5.83
the upper limit of this confidence interval is
6.7 + 0.87 = 7.57
Therefore, we are 95% confident that true mean lifetime of a certain type of tablet computer lies between 5.83 years and 7.57 years
The wingspans of a common species of housefly are normally distributed with a mean of 5mm and a standard deviation of 0.5mm. Suppose that a biologist regularly collects random samples of 20 of these houseflies and calculates the sample mean wingspan from each sample.
What will be the shape of the sampling distribution of the sample mean wingspan?
Answers
Answer:
Approximately Normal
Step-by-step explanation:
Since the population is normally distributed, the sampling distribution of the sample mean will also be normally distributed, even when the sample size is small.
round 63,104,159,896 to the nearest hundred million
round 2,005,562,134 to the nearest hundred million
round 5,678,600,941 to the nearest hundred million
Answers
Answer:
The answer to each one is 1) 63,100,000,000
2) 2,000,000,000
3) 5,700,000,000
At the end of December, the Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. What is the Cookie Shop's profit at the end of January.
No Links Please
Answers
The Cookie Shop's profit at the end of January as a result of the 20% decrease was $12000.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let s represent the Cookie Shop's profit at the end of January. At the end of January, their profit had decreased by 20%:
Percentage decrease = 20% of 15000 = $3000
s = 15000 - 3000 = 12000
The Cookie Shop's profit at the end of January as a result of the 20% decrease was $12000.
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Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for π, and do not round your answers.
Area=?
Circumference=?
Answers
Answer:
\(Area = 153.938040026m^2\)
\(Circumference= 43.9822971503m\)
Step-by-step explanation:
Area
\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)
Circumference
\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)
In a lab a substance was cooled b 6 degrees each hour for 42 hours what was the total change it in temperature
Answers
9514 1404 393
Answer:
total cooling was 252 degrees
Step-by-step explanation:
quantity = rate × time
The total temperature change is ...
(-6°/h)(42 h) = -252°
The total change in temperature was a cooling of 252 degrees.
The nth term of an AP is given by 2n +9 find the first term
Answers
For a certain brand of tomato seeds, the seed package claims that it takes 87 days after planting for the tomato plants to produce fruit. Sarah, a botanist, wanted to know whether the mean number of days for the plants to produce fruit where she lives is different from 87 days. She planted 40 seeds and recorded the number of days for each plant to produce fruit. With all conditions for inference met, the hypothesis test was conducted at the significance level a = 0.05, and the test resulted in a p-value of 0.0752. ?
Which of the following is a correct conclusion?
A. Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.
B. Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
C. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.
D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
E. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is equal to 87 days.
Answers
Answer:
D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
Step-by-step explanation:
The population mean, μ is given as 87
This population value is used to state the Null hypothesis ;
H0 : μ = 87
The alternative hypothesis is the opposite of the Null ; and hence, claims that the mean is different from the population mean, μ ≠ 87
H1: μ ≠ 87
The Decison level :
When Pvalue < α ; We reject the Null otherwise we fail to reject the null
The given p and α value :
P-value = 0.0752
α = 0.05
0.075 > 0.05 ; Hence ;
Pvalue > α ; We fail to reject the Null
We can thus conclude that there is not enough evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
Someone please help I will give BRAINLIST I’m exhausted
Answers
Answer:
4x - 4
Step-by-step explanation:
Add up all common numbers and then subtract from the total amount.
Hope it helps :))
The following 5 questions are based on this information: An economist claims that average weekly food expenditure of households in City 1 is more than that of households in City 2. She surveys 35 households in City 1 and obtains an average weekly food expenditure of $164. A sample of 30 households in City 2 yields an average weekly expenditure of $159. Historical data reveals that the population standard deviation for City 1 and City 2 are $12.50 and $9.25, respectively.
Required:
At the 5% significance level, is the economist claim supported by the data?
Answers
Answer:
>> Null hypothesis; H0: μ1 - μ2 ≥ 0
Null hypothesis; Ha: μ1 - μ2 < 0
>> z = 1.85
>> p-value = 0.03
>> there is evidence sufficient to reject the claim that average weekly food expenditure of households in City 1 is more than that of households in City 2.
The economist claim is not supported by data.
Step-by-step explanation:
We are given;
Sample mean of city 1; x1¯ = 164
Sample mean of city 2; x2¯ = 159
Sample size of city 1; n1 = 35
Sample size of city 2; n2 = 30
Standard deviation of city 1; σ1 = 12.5
Standard deviation of city 2; σ2 = 9.25
Let's define the hypotheses;
Null hypothesis; H0: μ1 - μ2 ≥ 0
Null hypothesis; Ha: μ1 - μ2 < 0
Test statistic which is the z-score Formula between 2 mean is;
z = ((x1¯ - x2¯) - 0)/√((σ1)²/n1) + ((σ2)²/n2))
z = (164 - 159 - 0)/√((12.5²/35) + (9.25²/30))
z = 5/2.705
z = 1.85
From online p-value from z-score calculator attached, using z = 1.85, one tailed, significance value of 0.05, we have;
p-value = 0.03
The p-value is less than the significance value, and so we will reject the null hypothesis and conclude that there is evidence sufficient to reject the claim that average weekly food expenditure of households in City 1 is more than that of households in City 2.
What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.
Answers
\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108\)