Subtract: 23.87 - 1.12 Answers: A) 12.67 B) 13.75 C) 22.75 D) 24.99

f(1)=72 f(n)=f(n−1)+9 Find an explicit formula for f(n)

myrzilka [38]

$a_{n}$ = 9n + 63

generate the first few terms using the recursive equation

f(1) = 72

f(2) = 72 + 9 = 81

f(3) = 81 + 9 = 90

f(4) = 90 + 9 = 99

the sequence is 72, 81, 90, 99, .....

This is an arithmetic sequence whose n th term formula is

$a_{n}$ = $a_{1}$ + (n - 1 )d

where $a_{1}$ is the first term and d the common difference

d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and $a_{1}$ = 72

$a_{n}$ = 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula

8 0

3 years ago

Peter is buying office supplies he is able to buy three packages of paper in for staplers for $40 or he is able to buy five pack

Damm [24]

Answer:

Cost of package of paper = 4$

Cost of stapler = 7$

Explanation:

Consider the cost of package of paper = x and that of stapler = y.

Now, we are given that cost of 3 paper packages and 4 staplers = 40$

Hence we get, 3x + 4y = 40 as 1st equation.

we are also given, cost of 5 paper packages and 6 staplers = 62$

Hence, the second equation is 5x + 6y = 62

Now, solving the two equations by method of elimination, we first equate coefficients of any one variable say x by multiplying 1st equation by 5 and second by 3 we get ->

15x + 20y = 200

15x + 18y= 186

Subtracting the two we get y = 7 and substituting this value of y in first equation we get x = 4

which gives the required cost of one paper package = x = 4$

and one stapler = y = 7$

7 0

3 years ago

Please help! An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain

Eduardwww [97]

draw a perpendicular line from the directrix passing through the focus, this will be the line of symmetry. The vertex(h, k) will be located on the line half way between the focus and directrix. The distance from the focus to the vertex is called the focal length, call it a. The then equation is (x - h)^2 = 4a(y - k) the equation can be manipulated to y = 1/4a(x - h)^2 + k hope it helps

8 0

3 years ago

Read 2 more answers

The resting heart rate of 60 patients is shown in the frequency table below.

Murrr4er [49]

The standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.

<h3>How to determine the standard deviation of the data set?</h3>

The dataset is given as:

Heart Rate Frequency

60 1

65 3

70 4

75 12

80 8

85 15

90 9

95 5

100 3

Calculate the mean using

Mean = Sum/Count

So, we have

Mean = (60 * 1 + 65 * 3 + 70 * 4 + 75 * 12 + 80 * 8 + 85 * 15 + 90 * 9 + 95 * 5 + 100 * 3)/(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3)

Evaluate

Mean = 82.25

The standard deviation is

$\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f -1}}$

So, we have:

SD = √[1 * (60 - 82.25)^2 + 3 * (65 - 82.25)^2 + 4 * (70 - 82.25)^2 + 12 * (75 - 82.25)^2 + 8 * (80 - 82.25)^2 + 15 * (85 - 82.25)^2 + 9 * (90 - 82.25)^2 + 5 * (95 - 82.25)^2 + 3 * (100 - 82.25)^2)]/[(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3 - 1)]

This gives

SD = √85.9533898305

Evaluate

SD = 9.27

Hence. the standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.

Read more about standard deviation at:

brainly.com/question/4079902

#SPJ1

5 0

1 year ago

a wrestler is weighing in for their match this evening. their normal weight is 168 pounds, but that weight can vary by as much a

Natalija [7]

Introduction

Wrestling is a wonderful activity with many advantages for the student-athlete. It is a sport that is highly

competitive, exciting and satisfying. It is a sport that provides for individual and team competition. It is -

and should be - fun. Unfortunately, the practice of losing weight by not eating, restricting fluid intake and

over-exercising reduces the sport's fun. This information is presented to help clear up misconceptions

regarding wrestling and weight loss. I also hope to give some guidance to those who desire to manage

their weight properly in preparation for and during the wrestling season.

History and Stigma

For too long, the wrestling community has unthinkingly accepted the myth that to be a good wrestler, you

must cut weight. The generally accepted thinking is something like this: if your natural weight is 135

pounds, you may be a good wrestler at 135 pounds. But if you wrestle at 130 pounds, you'll be a better

wrestler. And if you can make it down to 125, you'll be a state champion. No facts support that widely held

view, yet wrestlers and parents subscribe to that faulty reasoning. Looking further back, many remember

the days that losing excessive weight was a specific practice and expectation among wrestlers. It was

supposed to teach sacrifice, commitment, and the idea of “No Pain, No Gain.”

Regardless of the current attitude of the majority of the wrestling community, the stigma that an unhealthy

loss of weight is a requirement of wrestling among outside observers sticks. The Virginia High School

League has followed national guidelines to establish rules that encourage healthy weight management

among wrestlers.

Current Regulations

Preseason weight certification is accomplished with three steps. The first is determining each wrestler’s

body fat percentage using skin fold calipers. Next, the wrestler completes a hydration test, to insure

against a dehydrated weight measurement, and the wrestler weighs in. The third step is the calculation of

the wrestler’s minimum wrestling weight based on 7% body fat for males and 12% for females. The

wrestler may not wrestle at a weight class below his minimum weight during the season. The wrestler is

also restricted from losing more then 1.5% body weight loss per week (official weigh-ins at certification,

matches, and tournaments are used for this calculation). A one-pound per month growth allowance is

provided to allow for the natural growth of this age group. The VHSL advises, and we have instituted,

daily weigh-ins before and after practice to monitor weight-loss and dehydration.

Additionally, the National Federation of State High School Associations has adopted several other rules to

guide coaches and wrestlers while managing their weight. Wrestlers are discouraged from wrestling at a

weight class more then one weight class above their certified weight.

5 0

3 years ago