By using sum of sequence the value of (3+6+9+...+57) is 570, which is option C).
What is sum of the sequence ?
The sum of a sequence is the total result of adding up all the numbers in the sequence. The method for finding the sum of a sequence depends on whether the sequence is arithmetic or geometric.
For an arithmetic sequence, in which each term is obtained by adding a fixed number (called the common difference) to the previous term, the sum of the first n terms can be found using the formula:
[tex]Sn = n/2(2a + (n-1)d)[/tex]
where a is the first term, d is the common difference, and n is the number of terms.
For a geometric sequence, in which each term is obtained by multiplying the previous term by a fixed number (called the common ratio), the sum of the first n terms can be found using the formula:
[tex]Sn = a(1-r^n) / (1-r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
According to the question:
We can notice that each number in the sequence 3, 6, 9, ..., 57 is 3 times the corresponding number in the sequence 1, 2, 3, ..., 19.
So, we can find the sum of the sequence 3, 6, 9, ..., 57 by finding the sum of the sequence 1, 2, 3, ..., 19 and then multiplying by 3.
The sum of the sequence 1, 2, 3, ..., 19 is:
1 + 2 + 3 + ... + 19 = (19/2)(1 + 19)/2 = 190
Multiplying by 3, we get:
3 + 6 + 9 + ... + 57 = 3(1 + 2 + 3 + ... + 19) = 3(190) = 570
Therefore, the value of (3+6+9+...+57) is 570, which is option C).
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(8) = 21 B. h(-3) = -1 C. h(13) = 18 D. h(2) = 16
We may conclude after answering the provided question that Option D is range ruled out because we lack sufficient information to calculate the value of h. (2).
What is range?The variable's range is calculated by taking its greatest observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or size of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before determining the region. Next, subtract (reduce) the lowest number from the greatest number. The solution includes the range of the list. The solution specifies the range of the list.
The following statement might be true for h:
A. h(8) = 21
We can see that h(x) has a range of 1 to 25, and h(8) = 19 falls inside that range. As a result, h(8) might equal 21 as long as it stays within the range of 1 to 25.
Option B is not practicable since h(x) has a domain of -3 x 11, and h(-3) is not in the domain.
Option C is ruled out since 13 is not in the domain of h. (x).
Option D is ruled out because we lack sufficient information to calculate the value of h. (2).
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The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 77 balcony tickets and 69 general admission floor tickets for Friday's show, for a total of $5,883 in receipts. For Saturday's show, 75 balcony tickets and 69 general admission floor tickets have been sold, equaling $5,775 in receipts. How much does each ticket cost?
The price of a general admission floor ticket is $25.
What is the system of equations?
A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.
Let's start by defining some variables:
Let b be the price of a balcony ticket
Let f be the price of a general admission floor ticket
We can set up a system of two equations based on the information given in the problem:
77b + 69f = 5,883 (equation 1 for Friday's show)
75b + 69f = 5,775 (equation 2 for Saturday's show)
We can use either substitution or elimination to solve for b and f. Let's use elimination by subtracting equation 2 from equation 1:
(77b + 69f) - (75b + 69f) = 5,883 - 5,775
2b = 108
b = 54
Now that we know the price of a balcony ticket is $54, we can substitute this value into either equation to solve for f. Let's use equation 1:
77(54) + 69f = 5,883
4,158 + 69f = 5,883
69f = 1,725
f = 25
Therefore, the price of a general admission floor ticket is $25.
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You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.
We would need to survey at least 600 randomly selected air passengers to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.
what is percentage?As a number out of 100, a percentage is a technique to express a fraction or a proportion. The sign "%" stands in for the word "percent," which is a contraction of "per hundred."
To determine the sample size for the survey, we can use the following formula:
n = [tex](Z^2 * p * q) / E^2[/tex]
Where:
n is the required sample size
Z is the Z-value for the desired confidence level (in this case, Z = 1.645 for a 90% confidence level)
p is the estimated population proportion (we don't know this yet, so we will assume a conservative estimate of 0.5)
q is the complementary probability of p (q = 1 - p)
E is the maximum error or margin of error (in this case, E = 0.015)
Plugging in the values, we get:
n = ([tex]1.645^2[/tex] * 0.5 * 0.5) / [tex]0.015^2[/tex]
n = 599.27
Rounding up to the nearest whole number, we get a required sample size of 600.
Therefore, we would need to survey at least 600 randomly selected air passengers to be 90% confident that the sample percentage is within 1.5 percentage points of the true population percentage.
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Is 92 divisible of 3
Answer:No but it is 30.7
Step-by-step explanation:
Answer: No, 92 isn't divisible of 3.
Step-by-step explanation: We can see that the sum of the digits in this case is 11 and this number is not divisible by 3, which means that 92 is also not divisible by 3.
Students in Ms. Seiko's class recorded the number of books they read over the summer.
A line plot named
Manu looked at the line plot and concluded that "The number of books with the most dots is 12 books, so that is the greatest number of books read over the summer." Is Manu's conclusion correct? Explain.
A.
No, Manu's conclusion is not correct. He should look at the greatest data value on the number line that has any dots above it to find the greatest number of books read.
B.
No, Manu's conclusion is not correct. He should count the total number of dots to find the greatest number of books read.
C.
No, Manu's conclusion is not correct. He should multiply each data value by the number of dots above it and then sum these results to find the greatest number of books read.
Answer:
A.
Step-by-step explanation:
No, Manu's conclusion is not correct. He should look at the greatest data value on the number line that has any dots above it to find the greatest number of books read. The most dots represent the most frequent number of books read, but not necessarily the greatest number of books read.
how do you solve this?
Answer:
Step-by-step explanation:
A survey of customers at a local supermarket asks whether they found shopping at this market more pleasing than at a nearby store. Of the 3000 forms distributed to customers, 429 were filled in and 276 of these said that the experience was more pleasing. With 90% confidence, list and check the conditions, calculate the confidence interval to estimate the true proportion of customers that consider this market more pleasing than the other store, and write it in a complete sentence related to the scenario.
With 90% cοnfidence, we can say that the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre is between 0.601 and 0.685. In οther wοrds, we can be 90% cοnfident that the pοpulatiοn prοpοrtiοn οf custοmers whο prefer this market is within this range.
What is percentage?Percentage is a way οf expressing a number οr prοpοrtiοn as a fractiοn οf 100. It is represented by the symbοl "%".
Tο calculate the cοnfidence interval tο estimate the true prοpοrtiοn οf custοmers whο cοnsider this market mοre pleasing than the οther stοre with 90% cοnfidence, we need tο check the fοllοwing cοnditiοns:
In this scenariο, we can assume that the fοrms were distributed randοmly tο the custοmers, and the independence cοnditiοn is met because the respοnses οf οne custοmer dο nοt affect the respοnses οf anοther custοmer. Tο check the sample size cοnditiοn, we can calculate the expected number οf successes and failures in the sample:
Expected number of successes: n * p = 429 * (276/429) ≈ 277
Expected number of failures: n * (1 - p) = 429 * (1 - 276/429) ≈ 152
Both the expected number of successes and failures are greater than 10, so the sample size condition is met.
Now, we can calculate the confidence interval using the formula:
CI = p ± sqrt(p(1-p)/n)
where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level.
In this case, p = 276/429 ≈ 0.643, n = 429, and z = 1.645 (from a standard normal table for 90% confidence level).
Plugging in these values, we get:
CI = 0.643 ± 1.645sqrt(0.643(1-0.643)/429) ≈ (0.601, 0.685)
Therefore, with 90% confidence, we can say that the true proportion of customers who consider this market more pleasing than the other store is between 0.601 and 0.685. In other words, we can be 90% confident that the population proportion of customers who prefer this market is within this range.
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An angle measures 136.6° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the measure of the angle is 43.4 degrees, and the measure of its supplementary angle is 180 - 43.4 = 136.6 degrees.
Step-by-step explanation:
Let x be the measure of the angle in degrees.
By definition, supplementary angles add up to 180 degrees, so the measure of the supplementary angle is 180 - x degrees.
According to the problem, the angle measures 136.6 degrees less than the supplementary angle, so we can write:
x = (180 - x) - 136.6
Simplifying the right-hand side, we get:
x = 43.4
Therefore, the measure of the angle is 43.4 degrees, and the measure of its supplementary angle is 180 - 43.4 = 136.6 degrees.
What is the volume of the cone in cubic feet?
hope you understood the answer
option A
Lesson 18.1 choosing a bank
There are many banks but nowadays SBI is the one of popular bank of World.So I choose SBI bank for explanation.
Details about SBI bank:
State Bank of India (SBI) is one of the largest and oldest banks in India. It was founded in 1806 as the Bank of Calcutta and later became the Imperial Bank of India in 1921. In 1955, the bank was nationalized and became the State Bank of India.
SBI is headquartered in Mumbai and has a widespread network of branches across India as well as in other countries. The bank offers a wide range of financial products and services such as savings and current accounts, loans, credit cards, investment options, insurance, and many more.
SBI is known for its advanced technology and customer-centric approach. The bank has implemented various digital initiatives to make banking easy and convenient for its customers. SBI's mobile app and internet banking portal are among the most popular digital channels used by customers.
Apart from traditional banking services, SBI has also been actively involved in various social initiatives such as promoting financial literacy, supporting education, healthcare, and environment conservation. The bank has also launched many welfare schemes for the benefit of its customers and society at large.
SBI is recognized as a global banking leader and has received many prestigious awards and accolades over the years. The bank has also been ranked among the top banks in the world by leading international publications.
Overall, SBI is a reliable and trustworthy bank that has played a significant role in shaping the Indian banking industry.
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Correct question is " Choose a name of a perticular bank and write about the bank."
thanks froggy for all the help i need more help
Answer:
∠KRL is 34°.
Hope this helps!
Step-by-step explanation:
∠KRL is a vertical angle to ∠QRP ( meaning they have the same angle ).
∠HM is a 180° angle and ∠PRM is a 90° angle which means ∠HRP is also a 90° angle. ∠HRQ plus ∠QRP is equal to 90°, ∠HRQ is 56° which means ∠QRP is 90° - 56° which is 34°. That means ∠KRL is also 34°.
If the home cost $64,000 and you put down 8,000 what percent did you put down
In conclusion you put down 12.5% of the total cost of the home.
How to solve and what is percentage?
To find the percentage you put down on the home, you need to divide the amount you put down (the down payment) by the total cost of the home, and then multiply by 100 to convert to a percentage.
The down payment was $8,000 and the total cost of the home was $64,000.
So the percentage you put down is:
($8,000 / $64,000) x 100% = 12.5%
Therefore, you put down 12.5% of the total cost of the home.
Percentage is a way of expressing a proportion or fraction as a portion of 100. It is denoted by the symbol %, and is often used to express a fraction of a quantity relative to the whole quantity.
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Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(-9,-5), (-6,1) and (5,8)
After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.
Perimeter = 32
To find the perimeter of a triangle whose vertices are specified points in the plane, we need to first calculate the lengths of the 3 sides of the triangle. To do this, we need to use the distance formula, which is the square root of (x2 - x1)^2 + (y2 - y1)^2. To calculate the first side, we need to calculate the distance between (-9,-5) and (-6,1), which is 7.14. For the second side, we need to calculate the distance between (-6,1) and (5,8), which is 11.18. For the last side, we need to calculate the distance between (5,8) and (-9,-5), which is 14.86. After calculating the lengths of all 3 sides, we need to add them together to get the perimeter, which is 32.
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WILL MARK AS BRAINLIST PLEASE HELP!!
Answer:
a = 125°
Step-by-step explanation:
Angle a and 55° together make up a straight angle (a straight line) that is 180°.
Write an equation.
a + 55° = 180°
subtract 55° from both sides.
a = 180°- 55°
a = 125°
The sum of the ages of david and marta is 60 years, and the difference is 16 years. if david is older than marta
Answer: 38 (David) 22 (Marta)
Step-by-step explanation: First you will do 60-16. Then you will divide 44 by 2. After that then you will do 22+16. Finally you will have 38 and 22. So 38 is David's age and 22 is Marta's age.
In a cross-country race, Duante took 8/9 as long as James to finish. Kofi took 7/8 as long as James to finish. Who took the longest to finish the race?
Using the LCM formula, it is deduced that James took the longest to finish the race.
What is LCM?
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers.
Let's assume that James took time "J" to finish the race. Then -
Duante took 8/9 of James' time, which is (8/9)J
Kofi took 7/8 of James' time, which is (7/8)J
To determine who took the longest to finish the race, we need to compare their times.
Let's start by comparing Duante and James -
Duante's time = (8/9)J
James' time = J
Since Duante took less time than James, we can conclude that James did not take the longest to finish the race.
Now let's compare Kofi and James -
Kofi's time = (7/8)J
James' time = J
To compare these times, we need to express them with a common denominator.
The least common multiple of 8 and 1 is 8, so we can rewrite James' time as (8/8)J:
Kofi's time = (7/8)J
James' time = (8/8)J
Now we can compare the times -
Kofi's time = (7/8)J < (8/8)J = James' time
Therefore, Kofi took the least time to finish the race, and James took the longest.
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How do I complete the table
Answer:
Plug in values
Step-by-step explanation:
solve for y, y=-3x+15
plug in x or y values on table to missing missing variable
ex.
y=-3(2)+15
y=9
3=-3x+15
-12=-3x
x=4
Neeed helpppp pleaseeee
Answer:
b. 840
Step-by-step explanation:
7!/3! is the same thing as saying (7*6*5*4*3*2*1)/(3*2*1). The 3*2*1 simplifies to 1 so the simplified expression is 7*6*5*4. If you compute that, you will get the answer is 840, b.
find the area of the figure helppp end of the quarter
Answer:
Step-by-step explanation:
if the front says 5ft+5ft so it equals 10ft
12ft+12ft it equals 24ft
the missing area looks alot like the 5ft+5ft so we measure it...
both sides of the back equals to 5ft each 5ft+5ft=10ft
so just put in the end of the quarter equals 10ft
and if he/she wants you to add it all together it all adds up to 44ft...
Two rectangular swimming pools are shown. The length of pool A is equal to the
width of Pool The width of Pool A is the length of Pool B. The perimeter of Pool B
is 120 feet. What is the perimeter of Pool A?
Perimeter of pool A is 90ft
Define perimeterPerimeter is a measurement of the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
For example, the perimeter of a rectangle can be calculated by adding up the length of all four sides of the rectangle. If a rectangle has a length of 6 units and a width of 4 units, its perimeter would be:
Perimeter = 2 x (length + width) = 2 x (6 + 4) = 20 units
To find: Perimeter of A
For Pool B;
Perimeter=120ft
Width=20ft and length=l
Hence, Perimeter of Pool B=2(l+w)
120=2(l+20)
60-20=l
l=40ft
Length of pool A=length of pool B=40
width of pool A=1/4width of pool B
1/4×20=width of pool B
width of pool B=5ft
Perimeter of pool A=2(l+w)
=2(40+5)
=2×45
=90ft
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The complete question is attached below;
Charlotte recorded the number of minutes she spent exercising in the past ten days:8,12,5,2,7,1,14,3,4,6 Find the median of the data.
Answer:
The median is 6.
If you need the mean, mode, range, minimum, maximum, count n, or sum they are
Mean- 6.6666666666667
Mode- 1,3,4,5,6,7,8,12,14
Min- 1
Max- 14
Count n- 9
Sum- 60
Answer:
5.5
Step-by-step explanation:
The median is the middle number in a sorted list of numbers.
Therefore, the first step to solving this problem is sorting this list of numbers from least to greatest:
1, 2, 3, 4, 5, 6, 7, 8, 12, 14
To find the middle number, start by crossing out a number from each side. In this case, the first two numbers to cross out are 1 and 14. 1 is the smallest number in the list and 14 is the greatest. Our list should then look like this:
2, 3, 4, 5, 6, 7, 8, 12
Now, cross out the next smallest and largest numbers of the list (2, 12):
3, 4, 5, 6, 7, 8
The next (3, 8):
4, 5, 6, 7
The next (4, 7):
5, 6
Now we are left with two numbers. When this happens, to figure out the middle number, we have to find the average of these last two remaining digits. The average can be found by adding these two digits and dividing that by the total number of digits you used to add.
In this case, we have 2 numbers left: 5 and 6
1. Add 5 and 6: 5+6=11
2. We used 2 numbers for the addition which means we have to divide 11 by 2: 11/2
= 5.5
Given the function f(x) = 72²+3x+3.
Find the average rate of change of f from z = -7 to z=6
Give your answer as an integer or reduced fraction.
I
Average rate of change:
the average rate οf change οf f frοm z = -7 tο z = 6 is 50/13 οr apprοximately 3.846 (rοunded tο three decimal places).
What is average?In mathematics, average refers tο a measure that represents the central οr typical value οf a set οf numbers. There are several types οf averages, including mean, median, and mοde.
The mean, alsο called the arithmetic mean, is the sum οf all the numbers in a set divided by the tοtal number οf values in the set. It is the mοst cοmmοnly used type οf average.
Tο find the average rate οf change οf f frοm z = -7 tο z = 6, we need tο calculate the change in f οver the change in z and then take the average.
First, we calculate f(6) and f(-7):
f(6) = 72² + 3(6) + 3
= 5184 + 18 + 3
= 5,191
f(-7) = 72² + 3(-7) + 3
= 5184 − 21 + 3
= 5,141
The change in f over the change in z is:
[tex]$\frac{5,191 - 5,141}{6 - (-7)} = \frac{50}{6 - (-7)} = \frac{50}{13}[/tex]
Therefore, the average rate of change of f from z = -7 to z = 6 is 50/13 or approximately 3.846 (rounded to three decimal places).
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The accurate scale drawing shows a car and a lamp post.
The car has a real width of 1.5 metres.
Find an estimate for the real height, in metres of the lamp post.
Answer:
Without any measurements, it is not possible to give a numerical estimate for the real height of the lamp post in metres. However, we can use the scale of the drawing to make an estimate.
Let's assume that the scale of the drawing is 1 centimetre (cm) represents 0.5 metres (m) in real life. This means that every 1 cm in the drawing represents 0.5 m in real life.
If we measure the height of the lamp post in the drawing and find that it is approximately 15 cm, we can estimate the real height of the lamp post as follows:
Real height of lamp post = (15 cm) x (0.5 m/1 cm) = 7.5 m
Therefore, using our estimated scale of the drawing, we can estimate that the real height of the lamp post is around 7.5 metres. However, this estimate is only as accurate as the assumptions we made about the scale of the drawing.
Step-by-step explanation:
Give one example of matrix of order 2 and 3 in which industrial
World problem is mentioned. Also solve them by using matrix
Inversion method.
It would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.
What is matrix ?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
Here is an example of a 2x3 matrix that represents a problem in industrial engineering:
Suppose a company produces two types of products, Product A and Product B, and they use three different machines to manufacture these products. The number of hours required to produce each unit of each product using each machine is given by the following matrix:
| 2 3 4 |
| 4 2 3 |
This matrix represents a system of linear equations that can be solved using matrix inversion to find the number of hours required to produce a given number of units of each product. For example, suppose the company needs to produce 100 units of Product A and 50 units of Product B. To find the number of hours required for each machine, we can set up the following system of equations:
2x + 3y + 4z = 100
4x + 2y + 3z = 50
where x, y, and z represent the number of hours required for each machine.
To solve this system of equations using matrix inversion, we can first write the system in matrix form:
| 2 3 4 | | x | | 100 |
| 4 2 3 | * | y | = | 50 |
| 0 0 0 | | z | | 0 |
Next, we need to find the inverse of the coefficient matrix:
| 2 3 4 |^-1 = 1/10 | -6 12 -3 |
| 4 2 3 | | 9 -6 4 |
| 0 0 0 | | 0 0 0 |
Finally, we can solve for x, y, and z by multiplying both sides of the equation by the inverse of the coefficient matrix:
| x | | -6 12 -3 | | 100 | | 90 |
| y | = | 9 -6 4 | * | 50 | = | 20 |
| z | | 0 0 0 | | 0 | | 0 |
Therefore, it would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.
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a box being pushed at a force of 125 newtons
is this a vector or a scalar quantity? and why?
Answer:
force is a vector quantity because we can't add it using simple algebra
it's direction dependent
however in this case
specific direction is not given
though it's mentioned it is pushed
so
force is a vector quantity
What is the value of the expression below when w=4
Answer:2(3)
Step-by-step explanation: 3w-3w+8
2with a power 3
Answer:
= 44
Step-by-step explanation:
3w² - 3w + 8
When
w = 4
Then:
3*4² - 3*4 + 8
= 3*16 - 12 + 8
= 48 - 12 + 8
= 48 + 8 - 12
= 56 - 12
= 44
Find an equation for the line perpendicular to 4x + 36y= 288 and goes through
the point (10,8).
Write your answer in the form y = mx + b.
The equation of the line perpendicular to 4x + 36y = 288 and passing through the point (10, 8) is: y = 9x - 98
Calculating the equation of the perpendicular lineTo find the equation of the line perpendicular to 4x + 36y = 288, we need to first find the slope of the given line.
We can rewrite the equation in slope-intercept form y = mx + b by solving for y:
4x + 36y = 288
36y = -4x + 288
y = (-1/9)x + 8
Therefore, the slope of the given line is -1/9
The slope of a line perpendicular to this line is the negative reciprocal of the slope of the given line.
So, the slope of the line we want to find is:
m = -1 / (-1/9) = 9
The equation is then calculated as
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Plugging in the values, we get:
y - 8 = 9(x - 10)
Simplifying, we get:
y = 9x - 98
Therefore, the equation of the line perpendicular is: y = 9x - 98
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a 3.75 kg stone hanging from a rope
vector or scalar? and why?
The object represented by a 3..75 kg stone is scalar object
How to determine if the object is scalar or vectorThe quantity "3.75 kg" is a scalar because it is a single value that only has magnitude, and it does not have a direction associated with it.
On the other hand, the force of gravity acting on the stone and the tension force of the rope holding the stone up are vector quantities because they have both magnitude and direction.
It is important to note that the stone itself does not have a direction associated with it, but the forces acting on it do have direction.
Therefore, when describing the motion of the stone, both scalar and vector quantities are involved.
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Determine the length of FE.
18
20
21
26
Using the concept of similar triangles, the length of FE is: 26
How to find the length of similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.
Using the concept of similar triangles and trigonometric ratios, we can apply that to the given diagram and say that:
tan E = 4/8 = 1/2
tan E = DF/FE
Thus:
1/2 = 13/(FH + HE)
1/2 = 13/(FH + 8)
FH = 18
FE = FH + HE
FE = 18 + 8
FE = 26
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If A = 68 kilometers and B =51 kilometers, what is c? If necessary, round to the nearest tenth.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{68}\\ o=\stackrel{opposite}{51} \end{cases} \\\\\\ c=\sqrt{ 68^2 + 51^2}\implies c=\sqrt{ 4624 + 2601 } \implies c=\sqrt{ 7225 } \implies c=85[/tex]