A rappelling rope used for outdoor programs, rescue and industrial work, can safely support a weight "W" (in pounds) provided, where "d" is the rope's diameter (in inches). Determine the diameter of rope that would be needed to support a weight of at least 5,500 pounds.

The solution is Option D.

The sum of the arithmetic sequence is 5,490

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the sum of the arithmetic progression be represented as S

Now , the number of terms n = 60

Let the first term be a₁ = 3n , when n = 1

a₁ = 3

Now , the second term a₂ = 3n , when n = 2

a₂ = 6

So , the common difference of the arithmetic sequence d = second term - first term

d = 6 - 3

d = 3

Now , the sum of the first n terms of the sequence is

Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Substituting the values in the equation , we get

S₆₀ = ( 60/2 ) [ 2 ( 3 ) + ( 60 - 1 ) ( 3 ) ]

On simplifying the equation , we get

S₆₀ = 30 [ 6 + 59 ( 3 ) ]

S₆₀ = 30 [ 6 + 177 ]

S₆₀ = 30 ( 183 )

S₆₀ = 5490

Therefore , the value of S is 5,490

Hence , the sum of the arithmetic sequence is 5,490

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Answer:

Step-by-step explanation:

4+3=7,

4*7=28

28-3=25

Answer:

so the 2 questions i see are surveys so... you have to answer them with truth on your own self

Step-by-step explanation:

Answer:

hi i am the person that you are talking to with all the comments give him brainliest

Step-by-step explanation:

Answer:

Option 3 - This data set has no outliers.

Step-by-step explanation:

Given : The data {70, 67, 66, 65, 66, 78, 68, 71, 80, 78, 72}  

To find : Which statement is true about this data set?

Solution :

The statements is all about outlier.

So, we find the outlier of the data.

Step 1- Arranging the data from lowest to highest,

{65,66,66,67,68,70,71,72,78,78,80}  

Step 2 - Find the median of the data  

As the data is odd numbers so the median is  th term.

term.

6th term is 70 ⇒ Median =70

Step 3 - To find Upper quartile and lower quartile  

Lower quartile data set is the median of the upper terms from median

{65,66,66,67,68}

Median of the set is 66

∴    

Upper quartile data set is the median of the lower terms from median

{71,72,78,78,80}

Median of the set is 78  

∴    

Step 4 - To find the interquartile range.

Step 5 - To find the fences for the data set.  

The formula to find range is  

Substitute the values, we get

The range in which data lies is [48,96]

We have seen that all the data lie inside the range.

Therefore, This data set has no outliers.

Hence, Option 3 is correct.

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Answer:

4+4+1

Step-by-step explanation:

Answer:

4 + 4 + 1

Step-by-step explanation:

4 + 4 + 1 = 9

4 + 5 = 9

They both equal up to 9

Answer: 3/5 or 60% chance of not drawing red

Step-by-step explanation:

12 red

13 green

5 blue

30 total

30 - 12 = 18

so 18/30 or 3/5

Answer:

D. 225/4

Step-by-step explanation:

To complete the square (a technique that can be applied to many problems!), take half the coefficient of  x  and square the result.

The coefficient of  x  is 15.  Half of 15 is 15/2.  Square 15/2 to get 225/4.

Check:

[tex]x^2+15x+\frac{225}{4}=\left(x+\frac{15}{2}\right)\left(x+\frac{15}{2}\right)=\left(x+\frac{15}{2}\right)^2[/tex]

Answer:

255/4

Step-by-step explanation:

Answer:

$14

Step-by-step explanation:

The total amount, C charged by an electrician for h hours of work is ;

C= 7h+125

If the electrician spends 2 more hours on Sanchez job than Ronald, then the amount Mrs Sanchez paid more than Ronald can be obtained thus:

From the equation :

C= 7h+125

The slope relation with number of hours worked gives the change in amount paid for differebt work hours. Since the intercept is constant, we ignore its value in this exercise.

For 2 more hours of work :

Additional amount = 7h ; h = 2

7h = 7 * 2 = 14

Hence, Mrs Sanchez pays $14 more.

Answer:

22

Step-by-step explanation:

First write an expression to represent the situation.

$1,300,000 ≤ $475,000 + $37,500a

This expression works because the least amount of money that can make to remain profitable is 1,300,000. They already have 475,000 of that and every a (number of ads sold) is $37,500

Using this equation, solve for a.

1300000 ≤ 475000 + 37500a

First, subtract 475000 from both sides.

825000 ≤ 37500a

Then divide both sides of the equation by 37500 to isolate a.

22 ≤ a

22 is less than or equal to a. So they must sell at least 22 ads to remain profitable.

Answer:

The first answer choice is correct

Step-by-step explanation:

Answer:

Area is 154 square meters

Step-by-step explanation:

Well lets think about this

If I take a rectangle and cut it into half diagonally I would get 2 triangles right?

So if I have 2 triangles of the same height and base I can make a rectangle

to find the area of a rectangle I do length times width

So lets take our scalene triangle and multiply our base with its width and then divide by 2

22*14 = 308

308/2 is 154

Answer:

I think 50 is 30% of 166.666667

Step-by-step explanation:

Answer:

III. m∠MEL = 90°, m∠ELM = 30°, and LM = 6 inches

Step-by-step explanation:

It´s lll Because to make a congruent shape one angle should be 90 and the longest side should be 6 inches. one angle should equal angle ELM.

So, by AAS criteria it would be congruent.

---------------------------

hope it helps...

have a great day!!

Answer:

III. m∠MEL = 90°, m∠ELM = 30°, and LM = 6 inches

Step-by-step explanation:

hope it helps you...

Answer:

4x - 3 = 37

+3         +3

4x = 40

Divide by 4 on both sides:

X = 10

Step-by-step explanation:

x=10

.......................

Answer:

1-m< +m<2 =180°

2-congruent

3-supplementary

4-m<1 + m<3 = 180°

5-m<2 + m<3 = 180°

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Answer:

2.27

Step-by-step explanation:

1.98+2.50+3.25 = 7.73 - 10.00 = 2.27

Answer:

$2.27

Step-by-step explanation:

Add the prices together

1.98 + 2.50 + 3.25 = 7.73

Susy owes the cashier $7.73 but payed with a $10 bill, so subtract

10 - 7.73 = 2.27

She should get back $2.27

Answer:

A

Step-by-step explanation:

hope this helps

-2x - 8 > 14

add 8 to 14 and get 22

-2x > 22

then divide 22 by -2 and get x < -11

Answer:

36.1

Step-by-step explanation:

53.9 + 36.1 = 90

Answer:

A.20 ft

Step-by-step explanation:

the shadow is double the height of the object.

Answer:

5x2 + 20x + 32 = 0 - 16977324

Step-by-step explanation:

Answer: B.) 19.6 feet.

Draw a right triangle ABC. AB will represent the ladder, with point A being on the ground and point B being against the building.

Label: AC=6 ft,  m<A=73° and <C is a right angle.

Use the trig mnemonic "SOHCAHTOA" to identify that BC/AC=tan<A. So BC, which is the height the ladder reaches, equals AC*tan<A=6*tan(73)=19.6 feet.

Step-by-step explanation:

Answer:

P

Step-by-step explanation:

The least absolute value is what number is closest to zero.

Answer: B

Step-by-step explanation:

Answer is B

The required method that is popular with the boys is going to school by walking.

A dual bar chart has been given, describing the method of going to school for boys and girls.

A bar chart displays the frequency counts of values for each level of a categorical or nominal variable.

Here,
According to the question,
Number of boys walk = 8,
Number of boys taking the bus = 2
Number of boys with car = 3
number of boys with cycle = 3
So the most popular method among the boys is given as by walk.

Thus, the required method that is popular with the boys is going to school by walking.

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