Melissa has started training for a race. The first time she trains, she bikes 5 miles. Each subsequent time she trains, she bikes 0.5 mile farther than she did the previous time.

A. Use summation notation to write an arithmetic series to represent the total distance Melissa has biked after she has trained n times.

B. Use the formula for a partial sum of the series you wrote in part a, above, to answer this question: What is the least number of times Melissa must bike for her total distance biked during training to exceed 60 miles? (3 points)

Answers

Answer 1

9514 1404 393

Answer:

  A. d = ∑[k=1,n] (4.5+0.5k)

  B. 9

Step-by-step explanation:

A) The series has first term 5 and common difference 0.5. The general term is given by ...

  an = a1 +d(n -1)

  an = 5 + 0.5(n -1) . . . . substitute numbers for this series

  an = 4.5 +0.5n . . . . . . simplify

The sum is the sum of these terms:

  [tex]\displaystyle \boxed{d_n=\sum_{k=1}^n(4.5+0.5k)}[/tex]

__

B) The sum of terms of an arithmetic series is the average of the first and last, multiplied by the number of terms. We want to solve for n to make the sum greater than 60.

  [tex]\displaystyle d_n=\frac{n}{2}(5 +4.5 +0.5n)\\\\\dfrac{n}{2}(9.5+0.5n)>60\\\\n(19+n)>240\qquad\text{multiply by 4}\\\\n^2+19n+9.5^2>240+9.5^2\qquad\text{complete the square}\\\\n+9.5>\sqrt{330.25}\qquad\text{square root}\\\\n>18.17-9.5=8.67\qquad\text{positive root, subtract 9.5}[/tex]

Melissa's total distance will first exceed 60 miles the 9th time she trains.

Answer 2

Answer:

 A. d = ∑[k=1,n] (4.5+0.5k)

 B. 9

Step-by-step explanation:

A) The series has first term 5 and common difference 0.5. The general term is given by ...

 an = a1 +d(n -1)

 an = 5 + 0.5(n -1) . . . . substitute numbers for this series

 an = 4.5 +0.5n . . . . . . simplify


Related Questions

Write the equation of the line in slope-intercept form

Slope= -7/4
Y-intercept= 5

Answers

Answer:

y = - [tex]\frac{7}{4}[/tex] x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{7}{4}[/tex] and c = 5 , then

y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line

Slope intercept form is y=Mx+b m=slope b= y-intercept. Your answer is Y=-7/4x+5

Find the area of the trapezoid

A. 44 Square units
B. 72 Square units
C. 88 Square units
D. 144 Square units

Answers

Answer:

Area = 13+9=22

22/2 = 11

11x 4 = 44 square units

pls answer correctly :)

Answers

I literally just did this its B

Find the circumference

Answers

12 times 3.14 = 37.68 CM
C=D x 3.14

Answer:

37.7 cm

Step-by-step explanation:

C = 2πr

diameter = 12cm

radius(r) = diameter ÷ 2radius(r) = 12 ÷ 2radius(r) = 6cmC = 2πr= 2 × 22/7 × 6Circumference = 37.7 cm

Antoinette Applied for a $6000 loan, which she will start paying back after the interest has accumulated. She had a initial offer for a simple annual interest rate of 6% for three years, but decided to consider other options. Which of the following options of all the crease the interest she pays the most?

F. $5500 loan, simple interest, annual rate of 6%, term of three years

G. $6000 loan, simple interest, annual rate of 5.75%, term of three years

H. $6000 loan, simple interest, annual rate of 6%, term of 2.8 years

J. $5500 loan, compound interest, annual rate of 6%, term of three years

Please Help

Answers


J. $5500 loan, compound interest, annual rate of 6%, term of three years

At a glass vase factory, 2 out of the last 20 vases produced were chipped. Considering this data, how many of the next 10 vases would you expect to be chipped?

Answers

2 out of 20 = 2/20 which reduces to 1/10 which means 1 out of every 10.

I would expect 1 out of the next 10 to be chipped.

Answer:

1

Step-by-step explanation:

A=144pi^2 ft. Find the radius

Answers

The radius is 12 because 12^2 equals 144

A right triangle has an area of 98 square inches. If the triangle is not an Isosceles triangle, what are the all possible lengths of the legs?

Answers

Answer:

The possible length of the triangle =

1) (1inches, 196inches)

2) (2incheq, 98inches)

3) (4inches , 49 inches)

4) (7 inches , 28 inches)

Step-by-step explanation:

We are told the above Triangle is not an Isosceles Triangle

Hence, we assume it is a right angle triangle

The area of a triangle is = 1/2 × Base × Height

= let us represent Base and Height = x

Hence:

1/2 × x × x = 98

x² /2 = 98

Cross Multiply

x² = 98 × 2

x² = 196

Step 2

We find the factors of 196

1× 196 = 196 (1, 196)

2 × 98 = 196 (2, 98)

4 ×49 = 196 (4, 49)

7 × 28 = 196 (7, 28)

Therefore, all the possible length of the triangle =

1) (1inches, 196inches)

2) (2incheq, 98inches)

3) (4inches , 49 inches)

4) (7 inches , 28 inches)

Hello! I need a bit of help with this problem.

Answers

Answer:

I'm pretty sure it's 15 for orange and 30 for blue

A box contains 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles. 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles. Which color marble is most likely to be picked?

Answers

Answer:

A red marble

Step-by-step explanation:

First, add all of the possible combinations of marbles that can be picked from the box ( 2 + 2 + 3 + 5 = 12 ). Next, write down the amount of each marble ( 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles). Then, find the marble that appears most in the box. (red marble). Finally, not only have you found that the red marble is most likely to be picked, you also know the probability of picking a red marble, (5/12).

Answer: red

Step-by-step explanation:

Which of the following is equivalent to
601/2

Answers

Answer:

B

Step-by-step explanation:

mixed number: 300 1/2 (reduced or equivalent)

decimal: 300.5 (reduced or equivalent)

percentage: 30,050% (reduced or equivalent)

Give me brainllest

Answer:

300.5 or 300[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Just divide.

find the measure of each angle

Answers

Answer:

Step-by-step explanation:

m∠ 1  =  180 - 117

m∠ 1  = 63

m∠2 = the same as m∠ 1

m∠2 = 63

m∠3 is also the same b/c of the same length of the "legs" of the triangle

m∠3 = 63

Need help on this one last question

Answers

Answer:

available

Step-by-step explanation:

if its available if available comment

Sarah had 25 candies. Sarah gave 2/5 of the candies to her sister. Of the amount left, she gave 2/3 to her friend. How many candies does Sarah have left for herself?

Answers

3 left for herself (:

Answer:

5 candies left for herself

Step-by-step explanation:

please help

if your gonna scam just leave i really need help

Answers

Answer:

x = 23

Step-by-step explanation:

The measures of the angles in a triangle add up to equal 180

That being said we can create an equation to solve for x

180 = 2x + 3x + 1 + 3x - 5

Now we solve for x using basic algebra

step 1 combine like terms

2x + 3x + 3x = 8x

1 - 5 = -4

now we have 180 = 8x - 4

step 2 add 4 to each side

-4 + 4 cancels out

180 + 4 = 184

now we have 184 = 8x

step 3 divide each side by 8

8x/8=x

184/8=23

we're left with x = 23

Write the quotient as a mixed number. 99 ÷ 5 = 19 R4
PLEASE HELP :(

Answers

Answer:

19 4/5

Step-by-step explanation:

99 = 5*19 + 499/5 = 19 + 4/599/5 = 19 4/5

Answer:

Solution given

99/5=19 4/5 is your quotient in mixed number.

Girrls and boys plsss i need help like frl:)

Answers

D- Most babysit because it pays more per-hour.

The reason this is the correct answer is because the question said which is NOT a valid response. This one is not because it didnt tell you how much they get paid per-hour so its incorrect.

Hope this helps!

Have a great day!

- Hailey

What is the median of the data set? History Test Scores 5 0 8 6 5 6 8 9 7 0 3 5 8 8 0 6 7 7 7 9 0 1 3 5 6 8 9 9 5 0 = 50 points

Answers

Answer:

The median is 6

Step-by-step explanation:


I need Help please!!

Answers

I think it’s A because the s is between P&Q and S&C if it’s wrong I’m sorry!

The ages of six boys are given as 12years 3 months,18years 10months,18years 8months,13years 4months,17years 11month and 15years respectively, what is their average age?

Answers

7 yrs old


12+0.25+18+0.83+13+0.333+17+0.916+15=77.326
77.326/11=7.029 which rounds to 7

evaluate 5^28·5^-32·5^-4
A. 17,920
B. 0.017920
C. 0.000256
D. 0.00000256

Answers

Answer:

D 0.00000256

Step-by-step explanation:

[tex]5^{28} *5^{-32}*5^{-4}=5^{28-32-4}=5^{-8}=\frac{1}{5^{8}} =0.00000256[/tex]

Answer:

B. 0.000256

Step-by-step explanation:

5^28 . 5^- 32 . 5^ -4

= 5^( 28 - 32 - 4 )

= 5^( 28 - 36 )

= 5^- 8

= 1 / 5^8

= 1 / 390625

= 0.000256

PLS ACTUALLY HELP ME , I WILL MARK BRAINLIEST

Answers

Answer: 15/8

Step-by-step explanation:

15/8 idrk the tangent tho

Look at the inequality.
3y > 27
Which set of values for y will make this inequality true?
A. 4,5,8
B. 5, 7,9
C9, 12, 14
D. 11, 13, 22

Answers

Answer:

D) 11,13,22

Step-by-step explanation:

If 3y>27, then y>9. Therefore, D is the correct answer (C is not correct BTW because 9 isn't included in the inequality).

Find the perimeter of the figure to the nearest hundredth.
12 in.
5 in.
5 in.
9 in.
perimeter: about
in.

Answers

Answer:

50.28 inches

Step-by-step explanation:

From the Image, we can find the length of the arc of the semi-circle by dividing the circumference of the resulting circle by 2

Radius= 9in

C= 2πr

C=2*3.142*9

C=2*3.142*9

C= 56.556 inches

Hence the length of the arc is

=56.556/2

=28.278 inches

The perimeter of the shape

=28.278+5+12+5

=50.28 inches

Answer:

its actualy 50.26, but follow what the guy before me did.

Step-by-step explanation:

 

One customer paid $12 for 14 postcards and 5 large envelopes. Another customer paid $24.80 for 10 postcards and 15 large envelopes. What was the cost in dollars of each large envelope?

Answers

Answer:

$1.42

Step-by-step explanation:

Since, The first customer paid $12 for 14 postcards and 5 large envelopes.

That is, 14 x + 5 y = 12        ------ (1)

And, The second customer paid $24.80 for 10 postcards and 15 large envelopes.

That is, 10 x + 15 y = 24.80  -------(2)

3 × equation (1),

We get, 42 x + 15 y = 36 ---------(3)

Equation (3) - Equation (2)

32 x = 11.20

⇒ x = 11.20/32

⇒ x = 0.35

By putting the value of x in equation (1),

We get, 14 × 0.35 + 5 y = 12

⇒ 4.9 + 5 y = 12

⇒ 5 y = 7.1

⇒ y = 1.42

Thus, the cost of one postcard = $ 0.35

And, the cost of each large envelope = $ 1.42

Help ME DUE in 10 mins WILL GIVE BRAINIEST IF HELP!!! SHOULD BE EASY FOR SOME

Answers

Answer:

-9n - 3

Step-by-step explanation:

Angel está adaptando un espacio para hacer actividades recreativas en casa y quiere rodear el borde con plantas, cuántos metros mide el borde si la ecuacion para calcularlo es 2a+2b, donde a representa el ancho y b el largo del espacio, a=1 metro y b=2 metros

Answers

Answer:

El borde mide 6 metros.

Step-by-step explanation:

Sabemos que la ecuación para el borde está dada por:

borde = 2*a + 2*b

Si sabemos que:

a = 1 metro

y  

b = 2 metros

podemos simplemente remplazar esos valores en la ecuación para el borde, asi obtendremos:

(es decir, donde hay una "a" en la ecuación, escribimos "1 metro", y end donde hay una "b" en la ecuación, escribimos "2 metros", luego resolvemos)

borde = 2*(1 metro) + 2*(2 metros) = 2 metros + 4 metros =  6 metros.

Podemos concluir que el borde mide 6 metros.

Idil has a smart phone data plan that costs $25 per month that includes 10 GB of
data, but will charge an extra $20 per GB over the included amount. How much
would Idil have to pay in a month where she used 4 GB over the limit? How much
would Idil have to pay in a month where she used went over by x GB?

Answers

If you times 4 by 20 you would get 160 then you add the 25 per month and then you would get 185

A rectangular garden has an area of 84 square feet and a length of 7 feet. What is the width of the garden?

Answers

Answer:

12 ft

Step-by-step explanation:

Given data

Area= 84 ft^2

Length= 7ft

The expression for the area is

Area= L*W

substitute

84=7*W

W= 84/7

W= 12ft

Hence the width is 12 ft

Answer:12ft

Step-by-step explanation:

an athlete did one round around a circle of radius 42m.what is the total distance covered by him

Answers

Answer:

2 * pi * 42 meters

Step-by-step explanation:

One round means a parameter of the circle

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