Answer:
d) 3
Step-by-step explanation:
1.5= 1 hour and 30 mins
+ 30 mins = 2 hours
.75 hours = 45 mins
+ 15 mins = 1 hour
2 hours + 1 hour = 3 hours
The solution is, d) 3 hours of activity do you have planned.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
given that, You have planned activities of 30 minutes, 15 minutes, 1.5 hours, and .75 hours.
now, we have,
1.5= 1 hour and 30 mins
with that add,
+ 30 mins = 2 hours
again, we know,
.75 hours = 45 mins
adding with that,
+ 15 mins = 1 hour
finally, adding we get,
2 hours + 1 hour = 3 hours
Hence, The solution is, d) 3 hours of activity do you have planned.
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Neeed Help ASAP Quick
Answer:
4; 7
Step-by-step explanation:
Small box = 25 and Large box = 50
small box = x and large box = x+3
25x+50(x+3)=450
25x+50x+150=450
75x=300
x=4
Large box = 4+3 = 7
Therefore, 4; 7
I hope this helped and have a good rest of your day!
If you are buying at item at a store for a price of $77, and there is a 7.5% tax added on
top, what would be the total amount due at the register, to the nearest cent?
Answer:
82.76
Step-by-step explanation:
77 x 7.5%=5.775
5.775 +77
The population of a small town in central Florida has shown a linear decline in the years 2002-2012. In 2002 the population was 34200 people. In 2012 it was 29300 people.
A) Write a linear equation expressing the population of the town, P , as a function of t , the number of years since 2002. Include the entire equation as your answer.
B) If the town is still experiencing a linear decline, what will the population be in 2015?
3kg of tomatoes cost $34.20 how much will 34 kg cost
Answer:
64.40$
Step-by-step explanation:
Answer:
3kg = $34.20
34kg= ?
x= (34 x $34.20)/3
x= 1162,80/3
x= $387,60
Factor completely, then place the answer in the proper location on the grid.
21a2-57a+ 30
Answer:
3 (7 a - 5) (a - 2)
Step-by-step explanation:
Factor the following:
21 a^2 - 57 a + 30
Factor 3 out of 21 a^2 - 57 a + 30:
3 (7 a^2 - 19 a + 10)
Factor the quadratic 7 a^2 - 19 a + 10. The coefficient of a^2 is 7 and the constant term is 10. The product of 7 and 10 is 70. The factors of 70 which sum to -19 are -5 and -14. So 7 a^2 - 19 a + 10 = 7 a^2 - 14 a - 5 a + 10 = a (7 a - 5) - 2 (7 a - 5):
3 a (7 a - 5) - 2 (7 a - 5)
Factor 7 a - 5 from a (7 a - 5) - 2 (7 a - 5):
Answer: 3 (7 a - 5) (a - 2)
at the audtions, 40 studens tried out for the school show choir, but only 12 will be chosen. How many different ways can the show choir be formed
Answer:D
Step-by-step explanation:
It’s a permutation
The product of a rational number
(Other than zero) and an irrational number is always irrational true or false
Answer:
I think it's true. hope this helps!!
8
17. Find the area of the shaded
portion of this figure, which
consists of a parallelogram
enclosing a right triangle
and a circle. Dimensions are
in feet. (Round off answer to
the nearest tenth of a foot.)
Answer:
37.4 ft^2
Step-by-step explanation:
The area of the parallelogram is given by ...
A = bh = (8 ft)(7 ft) = 56 ft^2
The area of the right triangle is given by ...
A = (1/2)bh = (1/2)(3 ft)(4 ft) = 6 ft^2
The area of the circle is given by ...
A = πr^2 = π(2 ft)^2 = 4π ft^2 ≈ 12.6 ft^2
__
The shaded area is the area of the parallelogram less the areas of the unshaded triangle and circle:
(56 ft^2) -(6 ft^2) -(12.6 ft^2) = 37.4 ft^2 . . . . shaded area
⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️
Answer:
a. [tex]f^-^1(x)=\frac{x}{4} +3[/tex]
b. [tex]f(-9)=-48[/tex]
c. [tex]f^-^1(-9)=\frac{3}{4}[/tex]
Step-by-step explanation:
In a, the -1 means inverse of f(x). To find the inverse, you rewrite the equation in terms of x and y. You replace the x with y and y with x. Then you solve for y.
[tex]f^-^1(x)=4x-12[/tex]
[tex]y=4x-12[/tex]
[tex]x=4y-12[/tex]
[tex]x+12=4y[/tex]
[tex]\frac{x}{4} +3=y[/tex]
[tex]f^-^1(x)=\frac{x}{4} +3[/tex]
In b, all you have to do is plug in -9 into f(x).
[tex]f(9)=4(9)-12[/tex]
[tex]f(9)=-48[/tex]
In c, you plug in -9 into inverse function f.
[tex]f^-^1(-9)=\frac{3}{4}[/tex]
The port of South Louisiana, located along miles of the Mississippi River between New Orleans and Baton Rouge, is the largest bulk cargo port in the world. The U.S. Army Corps of Engineers reports that the port handles a mean of million tons of cargo per week (USA Today, September). Assume that the number of tons of cargo handled per week is normally distributed with a standard deviation of million tons.
A. What is the probability that the port handles less than 5 million tons of cargo per week?
B. What is the probability that the port handles 3 or more million tons of cargo per week?
C. What is the probability that the port handles between 3 million and 4 million tons of cargo per week?
D. Assume that 85% of the time the port can handle the weekly cargo volume without extending operating hours. What is the number of tons of cargo per week that will require the port to extend its operating hours?
Answer:
(A) Probability that the port handles less than 5 million tons of cargo per week is 0.7291.
(B) Probability that the port handles 3 or more million tons of cargo per week is 0.9664.
(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is 0.2373.
(D) The number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.
Step-by-step explanation:
We are given that the port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge.
The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week with a standard deviation of 0.82 million tons.
Let X = Number of tons of cargo handled per week
SO, X ~ Normal([tex]\mu=4.5,\sigma^{2}=0.82^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 4.5 million tons
[tex]\sigma[/tex] = standard deviation = 0.82 million tons
(A) Probability that the port handles less than 5 million tons of cargo per week is given by = P(X < 5 million tons)
P(X < 5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{5-4.5}{0.82}[/tex] ) = P(Z < 0.61) = 0.7291
The above probability is calculated by looking at the value of x = 0.61 in the z table which has an area of 0.7291.
(B) Probability that the port handles 3 or more million tons of cargo per week is given by = P(X [tex]\geq[/tex] 3 million tons)
P(X [tex]\geq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\geq[/tex] -1.83) = P(Z [tex]\leq[/tex] 1.83)
= 0.9664
The above probability is calculated by looking at the value of x = 1.83 in the z table which has an area of 0.9664.
(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is given by = P(3 million tons < X < 4 million tons)
P(3 million tons < X < 4 million tons) = P(X < 4) - P(X [tex]\leq[/tex] 3)
P(X < 4) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{4-4.5}{0.82}[/tex] ) = P(Z < -0.61) = 1 - P(Z [tex]\leq[/tex] 0.61)
= 1 - 0.7291 = 0.2709
P(X [tex]\leq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\leq[/tex] -1.83) = 1 - P(Z < 1.83)
= 1 - 0.9664 = 0.0336
The above probability is calculated by looking at the value of x = 0.61 and x = 1.83 in the z table which has an area of 0.7291 and 0.9664 respectively.
Therefore, P(3 < X < 4) = 0.2709 - 0.0336 = 0.2373
(D) Now, it is given that 85% of the time the port can handle the weekly cargo volume without extending operating hours, that means;
P(X > x) = 0.85 {where x is the required no. of tons of cargo}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85
P(Z > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85
In the z table, the critical value of x which represents top 85% area is given as -1.036, that is;
[tex]\frac{x-4.5}{0.82} = -1.036[/tex]
[tex]{x-4.5} = -1.036\times 0.82[/tex]
x = 4.5 - 0.85 = 3.65 million tons
Hence, the number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.
Solve: 3(2d - 1) – 2d = 4(d– 2) + 5
The right answer is No solution.
Look at the attached picture
Hope it will help you
Could -free, automatic faucets actually be housing more bacteris than the old fashioned, manual kind The concern is that decreased water flow may increase the chance that bacteria grows, because the automatic faucets are not being thoroughly flushed through. It is known that 15% of cultures from older faucets in hospital patient care areas test positive for Legionella bacteria. A recent study at Johns Hopkins Hospital found Legionella bacteria growing in 10 of cultured water samples from 20 electronic faucets aIf the probability of Legionella bacteria growing in a faucet is 0.15, what is the prob ability that in a sample of 20 faucets. 10 or more have the bacteria growing (the Johns Hopkins study provide sufficient evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%? Explain.
Answer:
Not enough evidence to reject Null hypothesis
Step-by-step explanation:
Solution:-
- A comparative study for bacterial growth in manual and electronic faucets is made.
- It is observed that there is a higher growth in electronic faucets due to slower flow rates, i.e electronic faucets are not thoroughly flushed; hence, giving more resident time for the scaled bacteria to grow.
- It is known that 15% of cultures from older faucets were tested positive for the Legionella bacteria.
- A study at John Hopkins was conducted on a sample n = 20 electronic faucets with the probability of bacteria growing in a faucet is 0.15.
- We will conduct a hypothesis for at-least half proportion of electronic faucets have cultured bacteria.
- State the hypothesis for the proportion of electronic faucets culturing Legionella bacteria:
Null Hypothesis: P = 0.15
Alternate hypothesis: P > 0.15
- To determine the test statistics for the study conducted at John hopkins. We had a sample size of n = 20, and the probability for a bacteria to grow in a faucet is 0.15.
- Denote random variable, X: The number of electronic faucets culturing Legionella bacteria.
- Since, the probability for a bacteria to grow in a faucet is independent for each new faucet. We will assume the RV " X " to follow binomial distribution with probability of success 0.15:
X ~ Bin ( 20 , 0.15 )
- We are to determine that at-least half of the sample is subjected to the said bacteria. This is the probability of P ( X ≥ 10 ).
- The pmf for a binomially distributed random variable X is given below:
[tex]P ( X = r ) = n_C__r * ( p(success) )^r * ( p (fail) )^(^n^-^r^)[/tex]
Where,
p ( success ) = 0.15
p ( fail ) = 1 - p ( success ) = 1 - 0.15 = 0.85
- Use the pmf to determine the required test statistics:
[tex]P ( X \geq 10 ) = 1 - P ( X \leq 9 )\\\\P ( X \geq 10 ) = 1 - [ (0.85)^2^0 + 20*(0.15)*(0.85)^1^9 + 20_C_2 (0.15)^2*(0.85)^1^8 +\\\\ 20_C_3 (0.15)^3*(0.85)^1^7 + 20_C_4 (0.15)^4*(0.85)^1^6 + 20_C_5 (0.15)^5*(0.85)^1^5+\\\\ 20_C_6 (0.15)^6*(0.85)^1^4 + 20_C_7 (0.15)^7*(0.85)^1^3 + 20_C_8 (0.15)^8*(0.85)^1^2 + \\\\ 20_C_9 (0.15)^9*(0.85)^1^1\\\\\\P ( X \geq 10 ) = 1 - [ 0.03875 + 0.13679 + 0.22933 + 0.24282 + 0.18212 + 0.10284 + \\\\ 0.04537 + 0.01601 + 0.00459 + 0.00108 ]\\\\[/tex]
[tex]P ( X \geq 10 ) = 1 - [ 0.997 ] = 0.003[/tex]
- The probability that 10 or more electronic faucets is found to have Legionella bacteria growing is 0.003
- The test proportion of 10 and more electronic faucets have culturing bacteria is p = 0.003.
- Assuming normality of the population, the Z-statistics would be:
[tex]Z-test = \frac{ (p - P) \sqrt{n} }{\sqrt{P*(1 - P )} } \\\\Z-test = \frac{ (0.003 - 0.15) \sqrt{20} }{\sqrt{0.15*(0.85)} } \\\\Z-test = -1.84109[/tex]
- If we were to test the claim to 90% level of confidence:
significance level (α) = 1 - CI = 1 - 0.9 = 0.1
- The rejection region Z-critical is defined by a right-tail:
[tex]Z-critical \geq Z_\alpha \geq Z_0_._2\\\\Z-critical \geq 1.28[/tex]
- Compare the test statistics with the rejection criteria defined by the Z-critical:
Z-test < Z-critical
-1.84 < 1.28
Conclusion:
There is not enough evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%.
A $30 shirt is marked, "Get 1/3 off. What is the sale price of the shirt?
Answer:
$20 after the applied coupon
Step-by-step explanation:
The required sale price of the shirt after getting 1/3 off is $20.
What are percentages?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
A $30 shirt is marked, "Get 1/3 off.
The sale price of the shirt,
= 30 - 1 / 3×30
= 30 - 10
= $ 20
Thus, the required sale price of the shirt after getting 1/3 off is $20.
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Which expression is equivalent to 25a+5b-13
A couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child. However, if their first child is a boy, they will try again and have a second child. As it turns out, the probability of having a boy is slightly greater than having a girl. Here is the probability distribution for the number of boys the couple could have. Boys 0 boys 1 boy 2 boys 3 boys Probability 0.490 0.250 0.127 0.133
What is the expected number of boys the couple will have? (Recall: the expected value is the mean). 0.903 1.5 0.228
Answer:
0.903.
Step-by-step explanation:
Okay, from the question we are given the following information or data or parameters:
''couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child"
Additionally, from the question we are given that; ''However, if their first child is a boy, they will try again and have a second child".
Also, the probability distribution is given as Boys 0, boys 1 , boy 2, boys 3 boys with Probability 0.490, 0.250, 0.127, 0.133 respectively.
That is, we now have:
Number of boys × probability.
Boys 0 = 0 × 0.490 = 0.
Boys 1 = 1 × 0.250 = 0.250.
Boys 2 = 2 × 0.127 = 0.254.
Boys 3 = 3 × 0.133 = 0.399.
The addition of the products for each Number of boys × probability gives us the expected value. That is to say;
0 + 0.250 + 0.254 + 0.399 = 0.903 = mean.
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Data
Center = (2, -16)
A (2, -13)
P (-1, -16)
Equation
(x - h)² + (y - k)² = r² or
(x₁ - h)² + (y₁ - k)² = (x₂ - h)² + (y₂ - k)²
Substitution
(2 - 2)² + (-13 + 16)² = (-1 - 2)² + (-16 + 16)²
The signs in my equation and the one in the options are different but the results are the same
Find the area underneath the normal distribution between these two Z-Scores.
Z = 1.21 and Z = 0.01
Answer:
03829
Step-by-step explanation:
A suitable calculator is useful for this.
the perimeter of this quarter circle with radius, r= 23mm.
Give your answer rounded to 1 DP.
Answer:
82.1
Step-by-step explanation:
So the circumference of the whole circle is 46π.
A quarter of that is 11.5π.
11.5π ≈ 36.1283155163
Simplify that to 1 decimal point: 36.1
Then you add 46 to that.
36.1 + 46 = 82.1
What is the following quotient?
StartFraction 2 Over StartRoot 13 EndRoot + StartRoot 11 EndRoot EndFraction
StartRoot 13 EndRoot minus 2 StartRoot 11 EndRoot
StartFraction StartRoot 13 EndRoot + StartRoot 11 EndRoot Over 6 EndFraction
StartFraction StartRoot 13 EndRoot + STartRoot 11 EndRoot Over 12 EndFraction
StartRoot 13 EndRoot minus StartRoot 11 EndRoot
Answer: on edge i got D, sq rt 13-sq rt 11
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
edge
Please help with this!
Answer:
166 quarters, 40 dimes
Step-by-step explanation:
x - quarters
y - dimes
x + y = 206
0.25x + 0.10y = 45.50
y = 206 - x
0.25x + 0.10(206 - x) = 45.50
0.25x + 20.6 - 0.10x = 45.50
0.15x = 45.50 - 20.6
0.15 x = 24.9
x = 24.9/ 0.15 = 166 quarters
y =206 - 166 = 40 dimes
Check:
0.25*166+ 0.10*40 = 45.50
45.50 = 45.50
A number is randomly selected from 10 to 20. X is the event of selecting
a number divisible by 3. Y is the event of selecting a prime number.
a) Draw a Venn diagram to represent the information.
b) Are events X and Y mutually exclusive? Explain.
c) Find P(X) and P(Y).
Answer:
not sure
Step-by-step explanation:
can someone explain?
State who is correct and explain why
Answer:
12.4+3√7 is irrational
Step-by-step explanation:
12.4 is a rational number
3√7 is an irrational number
The sum of a rational number and an irrational number is irrational.
So, 12.4+3√7 is irrational
The area of the figure below is 9 ft. What is the
height of the triangle?
Answer:
4 ft
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
9 = 1/2 (4.5)h
9 =2.25 h
Divide each side by 2.25
9/2.25 = 2.25h/2.25
4 =h
Answer:
Hieght=4
hope it helps u...
Step-by-step explanation:
Find the equation of the line. Write the equation of the line in standard form.
Vertical line; through (-4,-8).
Answer:
x = -4
Step-by-step explanation:
The equation of a vertical line in standard form is ...
x = constant
In order for this line to go through the point with x-coordinate -4, the constant must be -4:
x = -4
1/2 cup serving provides 180 calories and 6 grams. How many calories and grams of fiber are in 1/3 cup serving
Answer:
1/3 cup Serving will provide 120 calories and 4 grams of fibre
Step-by-step explanation: one gram = 7.716 calories
1/2 cup serving provides 180 calories and 6 grams.
One cup serving with you provide 360 calories and 12 grams
So
1/3 cup Serving will provide 360/3 calories and 12/3 grams
1/3 cup Serving will provide 120 calories and 4 grams of fibre
I need some assistance on this
Answer:
1650
Step-by-step explanation:
The shape is a pyramid on top of a prism.
Volume of a pyramid is V = ⅓ Ah, where A is the area of the base and h is the height of the pyramid.
Volume of a prism is V = Ah, where A is the area of the base and h is the height of the prism.
The base of both shapes is a right triangle. The area is:
A = ½ bh
A = ½ (22) (10)
A = 110
The height of the prism is 6. The height of the pyramid is 33 − 6 = 27. The total volume is:
V = (110) (6) + ⅓ (110) (27)
V = 1650
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Yes, because the product of their slopes are -1. Rest explanation in the attached file. Hope it helps :)
Answer:
AB(y = ax + b) contains A(2, 1) and B(3, 4)
=> 2a + b = 1
3a + b =4
=> a = 3, b= -5 => Slope AB = a = 3
CD (y = cx + d) contains C(-2, -1) and D(1, -2)
=> -2c + d = -1
c + d = -2
=> c = -1/3, d = -5/3 => Slope CD = c =-1/3
If AB is perpendicular to CD, then Slope's AB x Slope's CD = -1
Check:
a x c = 3 x (-1/3) = -1
=> AB is perpendicular to CD
=> Option B is correct.
Hope this helps!
:)
What is the price per square inch of the better buy: A large pizza with an 18 inch diameter for $20, or a medium pizza with a 14 inch diameter for $14?
Answer:
The large pizza has the lower cost per square inch, so it is the better buy.
Step-by-step explanation:
A pizza has the format of a circle.
The area of a circle with radius r is given by the following equation:
[tex]A = \pi r^{2}[/tex]
A large pizza with an 18 inch diameter for $20
The radius is half the diameter, so [tex]r = 9[/tex].
In square inches, the area is:
[tex]A = \pi*9^{2} = 81\pi = 254.47[/tex]
254.47 square inches cost $20. So the price per square inch is 20/254.47 = 0.0786.
Medium pizza with a 14 inch diameter for $14:
Radius is 7. So
[tex]A = \pi*7^{2} = 49\pi = 153.938[/tex]
153.938 square inches cost $14. So the price per square inch is 14/153.938 = 0.0909.
The large pizza has the lower cost per square inch, so it is the better buy.
To study the effectiveness of a certain adult reading program, researchers will select a random sample of adults who are eligible for the program. The selected adults will be given a pretest before beginning the program and a posttest after completing the program. The difference in the number of correct answers on the pretest and the number of correct answers on the posttest will be recorded for each adult in the sample. Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results?a) A one-sample z-interval for a population proportion.b) A one-sample t-interval for a sample mean difference.c) A matched-pairs t-interval for a population mean difference.d) A matched-pairs t-interval for a sample mean difference.e) A two-sample t-interval for a difference between means.
Answer:
c) A matched-pairs t-interval for a population mean difference
Step-by-step explanation:
Matched-Pairs t-Test. A matched-pairs t-test is used to test whether there is a significant mean difference between two sets of paired data.
A matched pair t test is used for comparison between means of two sets of paired data.
Thus, Option C: A matched-pairs t-interval for a population mean difference. is correct choice.
Given that:The selected sample of people will have to give pretest and then training and then post-test and the difference in the scores is recorded.
The researches want to identify the resultant difference so as to identify the effectiveness of the program.
Explanation:For such type of cases, we use matched pair t test.
A matched pair t test is used to see if there is significant difference between means of two sets of paired data.
By paired data, we mean the data in both set which is paired.
Since the person is same who gives pre and post test after training, thus the data is paired.
Also since the difference is to be analyzed to check the significance of the reading program, thus matched pair t test is perfect fit here.
Thus, option C: A matched pairs t-interval for a population mean difference is correct option.
Learn more about t-tests here:
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Is 144m,165m,219m a right triangle
Answer:
Yes
Step-by-step explanation:
For a triangle to be rights angled.
It should follow Pythagoras theorem.
Pythagoras theorem states that if sides containing right angle is a and b
then is given by
hypotenuse = [tex]\sqrt{a^2+b^2}[/tex]
As hypotenuse is always the greatest side
Out of the given sides 144m,165m,219m
219 can only be hypotenuse
Thus side containing right angle will be 144m and 165m .
Lets plug these value in formula of Pythagoras theorem
[tex]hypotenuse = \sqrt{144^2 + 165^2} \\hypotenuse = \sqrt{20,736 + 27,225} \\hypotenuse = \sqrt{47961} \\hypotenuse = 219\\[/tex]
As we can see that hypotenuse calculated by us is same as given in problem.
Thus the given triangle is right angled.