3. Samantha is training to run a marathon. The first week she runs 4 km each day. The next week, she runs 7 km each day. During each successive week (each week following), each day she runs 3 km farther than she ran the days of the previous week. If she runs for five days each week, what total distance will Sara run in a 12-week training session?

Answers

Answer 1
1,230km


Week 1 = 5 x 4km = 20
Week 2 = 5 x 7km = 35
Week 3 = 5 x 10km = 50
Week 4 = 5 x 13km = 65
Week 5 = 5 x 16km = 80
Week 6 = 5 x 19km = 95
Week 7 = 5 x 22km = 110
Week 8 = 5 x 25km = 125
Week 9 = 5 x 28km = 140
Week 10 = 5 x 31km = 155
Week 11 = 5 x 34km = 170
Week 12 = 5 x 37km = 185

= 1230km
Answer 2

The total distance will Sara run in a 12-week training session is 1230 .

What is sum of terms in AP?

An arithmetic progression is a sequence of numbers or variables in which the difference between consecutive terms is the same. There can be an infinite number of terms in an AP.

The formula for finding the sum of first n terms of an AP given in the form of "a, a + d, a+2d, a+3d, ....., a+(n-1)d" is:

[tex]S _{n}[/tex]= [tex]\frac{n}{2}[/tex] [tex][2a + (n-1)d][/tex]

According to the question

Samantha is training to run a marathon.

She runs for five days each week

The first week she runs 4 km each day.  = 5 × 4 = 20

The second week, she runs 7 km each day. = 5 × 7 = 35

During each successive week , each day she runs 3 km farther than she ran the days of the previous week.

The third week, she runs 10 km each day. = 5 ×10 = 50

So on

Sara run in a 12-week training session

As this sequence is in AP  

First term (a) = 20

common difference (d) = 35 - 20

                                      = 15

Now,

Sum of 12 terms in AP

[tex]S _{n}[/tex]= [tex]\frac{n}{2}[/tex] × [2a + (n-1)d]

Substituting the values, a = 20, d = 15 and n = 12 in the above formula

[tex]S _{12}[/tex] = [tex]\frac{12}{2}[/tex] × [tex][2(20) + (12-1)15][/tex]

[tex]S _{12}[/tex] = [tex]6 [40 + (11)15}[/tex]

[tex]S _{12}[/tex] = [tex]6 [205][/tex]

[tex]S _{12}[/tex] = [tex]1,230[/tex]

Hence, the total distance will Sara run in a 12-week training session is 1230 .

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Related Questions

PLEASE HELP ME ITS TIMED!!

Answers

Answer:

x=10

Step-by-step explanation:

x^2 + 24^2 = 26^2

x^2 + 576 = 676

x^2 = 100

√x^2 = √100

x=10

Answer:

well,  we carry 2 of 2 of x so we know that 10 is in because of 6 +4  and 2+2=4  add them up so if im correct its 14 mark brainleist

Step-by-step explanation:

What is the value -5(-2)

Answers

Answer: 10

Step-by-step explanation: When multiplying integers,

if the signs are the same, the product is positive.

So a negative times a negative always equals a positive.

Therefore, -5(-2) is 10.

Answer:

10

Step-by-step explanation:

-5 x -2 = 10

On Tuesday, Bob brought home an oriental carpet on approval. The price in the store was 9900 Turkish Lira, but Bob was going to pay in dollars. On Tuesday, one dollar was worth 4.5 Turkish Lira. On Wednesday, the Turkish Lira was devalued such that one dollar was now worth 6.5 Turkish Lira. Feeling lucky by this change, Bob then bought the rug on Wednesday, paying the price of 9900 Turkish Lira with dollars at the new rate. To the nearest dollar, how much did he save due to the devaluation?

Answers

Answer:

Rounded to the nearest dollar, Bob saved $677 by buying the carpet on Wednesday.

Step-by-step explanation:

Since on Tuesday, Bob brought home an oriental carpet on approval and the price in the store was 9900 Turkish Lira, but Bob was going to pay in dollars and, on Tuesday, one dollar was worth 4.5 Turkish Lira but on Wednesday, the Turkish Lira was devalued such that one dollar was now worth 6.5 Turkish Lira, with which Bob then bought the rug on Wednesday, paying the price of 9900 Turkish Lira with dollars at the new rate, to determine to the nearest dollar, how much did he save due to the devaluation the following calculation must be performed:

(9,900 / 4.5) - (9,900 / 6.5) = X

2,200 - 1,523.07 = X

676.92 = X

So, rounded to the nearest dollar, Bob saved $ 677 by buying the carpet on Wednesday.

The number pattern shows a skip-counting rule. 5,20,35,50,65. Which number pattern follows the same rule?

Answers

Answer:

You keep adding 15.

Step-by-step explanation:

5+15=20

20+15=35

35+15=50

50+15=65

389 / 106
Round off to the nearest whole number ​​

Answers

Answer:

thi is the answer 3.66981132

Step-by-step explanation:

u just divided it

can someone help me with this and show me the steps if you don't mind

Answers

Answer:

(x+8)(x+5)

Step-by-step explanation:

Since we know x2 is equivalent to x times x we can automatically start by filling in the first two spaces with x. Then since we know that we're going to need two numbers that equal forty since it's part of the equation we can get two number that will also add up to 13x which is 8 and 5. We then get (x+8)(x+5). (Sorry lol this question is kind hard to explain over the computer.)

Which ordered pairs are solutions to the system of linear equations?
y = 2x + 1
2y - 4x = 2
O (0,1)
O (1,0)
O (2,3)
O (-1, - 1).
0 (0,0)
O (-1,3)

Answers

Answer:

answer is (0,1).........

A hemispherical tank is filled with water and has a diameter of 22 feet. If water
weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank,
to the nearest pound?

Answers

Answer:

just do the exam

Step-by-step explanation:

Answer:

173,949 lb

Step-by-step explanation:

Volume of a sphere:

[tex] V_{sphere} = \dfrac{4}{3}\pi r^3 [/tex]

A hemisphere is half of a sphere, so its volume is half of the volume of a sphere with the same diameter. Also, radius = diameter/2.

[tex] V_{hemisphere} = \dfrac{2}{3}\pi (\dfrac{d}{2})^3 [/tex]

[tex] V_{hemisphere} = \dfrac{2}{3} \times 3.14159 \times (\dfrac{22~ft}{2})^3 [/tex]

[tex] V_{hemisphere} = 2787.639~ft^3 [/tex]

Now we use the density of water to find the weight of the water contained in the tank.

weight = volume * density

weight = 2787.639 ft^3 * 62.4 lb/ft^3

weight = 173,949 lb

product of (7x + 2) and (5x − 11)?

Answers

Answer: -32x - 22

Step-by-step explanation:

Answer:

[tex]35x^{2}-67x-22[/tex]

Step-by-step explanation:

:)

The population of a school is 800 and is decreasing at a rate
of 2% per year; 4 years

Answers

Answer:

i think the answer is 738

AYO CAN YOU BE MY BAKA (HELP ME WITH MATH)

Answers

Answer:

Addition

Step-by-step explanation:

1) Add 275 to both sides.

[tex]800 + 275 = p[/tex]

2) Simplify 800 + 275 to 1075.

[tex]1075 = p[/tex]

3) Switch sides.

[tex]p = 1075[/tex]

We need to add in order to solve the equation.

so therefor, the answer is option G.

Answer:

Addition

Step-by-step explanation:

A rectangular piece of metal 12 cm long 18 cm wide and 10 cm high is melted and recast into 45 cylindrical plates,each of radius 1.2 cm.Find the thickness of each plate giving your answer correct to 2 decimal places?

Answers

Answer:

10.61 cm

Step-by-step explanation:

From the question,

The volume of the rectangular piece of metal = Volume of the 45 cylindrical plates.

Volume of a cuboid = 45×volume of a cylinder

lwh = 45×πr²h..................... Equation 1

Where l = length of the rectangular piece of metal, w = width of the rectangular piece of metal, h = height of the rectangular piece of metal, r = radius of the cylindrical plates, h = thickness of the cylindrical plates.

make h the subject of the equation

h = lwh/(45πr²).................... Equation 2

Given: l = 12 cm, w = 18 cm, h = 10 cm. r = 1.2 cm

Constant: π = 3.142.

Substitute these values into equation 2

h = (12×18×10)/(45×3.142×1.2²)

h = 2160/203.60

h = 10.61 cm.

The university of Toronto has about 91,000 student registered. If this number is rounded to the nearest thousandth, which of the following is a possible number of students? Answer ASAP please!

A. 92,392

B. 90,439

C. 91,142

D. 91,984

Answers

It would be C. 91,142

Find the surface area of a cube with sides = 9 inches. Think about finding area of 1 face and then multiplying by 6.

Answers

Answer:

Step-by-step explanation:

I need some help please it’s due in 20 minutes!

Answers

Answer:C

Step-by-step explanation:

I am not that sure.. but I think the answer is C.

please help i’ll give brainliest if you help thanks

Answers

Answer:

4b.

Step-by-step explanation:

PLEASE HELP WILL GIVE BRAINLIEST TO THE CORRECT ANSWER!! Which of the following could be factored by grouping?
a: ab+ad-ac+ae
b: ac+ad+bc-bd
c: ac+ad+bc+bd
d ab+cd-ab+cd

Answers

Answer:

B

Step-by-step explanation:

Please make  me branlist

Factoring ac + ad + bc + bd by grouping gives (a + b)(c + d)

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Factorization by grouping means grouping the terms with common factors before factoring.

Given the equation:

ac + ad + bc + bd

Factorizing by grouping:

= a(c + d) + b(c + d)

= (a + b)(c + d)

Factoring ac + ad + bc + bd by grouping gives (a + b)(c + d)

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Factor the expressions.
9. ​3x + 2410.

10. 9c - 63

solve both and number the answers

Answers

Answer:

[tex]3x + 2410 \\ x = 2410 - 3 \\ x =2407 \\ \\ \\ 9c - 63 \\ 9(c - 7) [/tex]

Nathan is going to invest in an account paying an interest rate of 4.8% compounded continuously. How much would Nathan need to invest, to the nearest ten dollars, for the value of the account to reach $1,310 in 13 years?

Answers

Answer:

700

Step-by-step explanation:

Answer:

$712

Step-by-step explanation:

A x (1 + 4,8%)¹³ = 1310

=> A = 1310 : (1 + 4,8%)¹³ = 712,1551532

If 2 inches on a map represents 100 miles, how much does 3.5 inches
represents on the same map? *

Answers

Answer:

175 miles

Step-by-step explanation:

3.5 has 2 miles in it so it has 100 then it has another 1 to make It 3 and half of 2 is ahh it's hard to explain but there's the anwser

Help me answer this please

Answers

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

do you guys know the answer to this problem?

Answers

I think -5, sorry if I’m wrong.

How to Simplify (7^6)^2

Answers

Answer:

Well, since your question is asking how to simplify and not the actual answer itself, all we have to do is first simplify 7^6=117,649. Now we just take that number and make it 117,649^2. I hope im correct with the way i set up the equation even though the number is absurdly large

Step-by-step explanation:

Answer: (7⁶)² = 7¹²

Step-by-step explanation:

All you have to do is multiply the exponents here and keep the 7. So, your final answer is 7¹².

Hope this helps, and don't forget to mark me brainliest! Have a wonderful day!

—-PLEASE HELP QUESTION IS IN THE PICTURE-



is this wrong?

Answers

looks good I can't see anything wrong

help plz im so stuck

Answers

Answer: yes

Step-by-step explanation:

Lines A and B parallel lines cut by the transversal c. If the measure of angle 5 is 123, what is the measure of angle 1?


Will mark b if correct:)

Answers

123. angle 1 would be the same as angle 5, seeing as the lines are parallel. 5&1 are both on top on lines A & B AND on the same side of transversal

There are 80 students in a 8th grade, 20% are boys. How many boys are in 8th
grade?

Answers

Answer:

16 boys

Step-by-step explanation:

Lets go with easy example:

20% of 100 students means 20 students: what is done there

We converted 20% to 20/100 so

[tex]\frac{20}{100}*100=20[/tex]

Lets do the same with 80 students as well

[tex]\frac{20}{100}*80=16[/tex]

Answer:

16

Step-by-step explanation:

[tex]\frac{20}{100} x \frac{x}{80} =16[/tex]

or do

80 x 0.20=16

both works

Use the table. What inference can you make by comparing the measures of variability? Use the drop-down menus to explain your answer.

Finish Times of 30 Runners
in the 100-meter Dash
Mean MAD
Last Year 16.2s 1.2
This Year 14.7s 1.9
The is greater for this year’s 100-meter dash, which suggests that all 30 students equally.

Answers

Answer:

The first one is mean absolute deviation and the second one is did not improve

Step-by-step explanation:

I took the test

The MAD is greater for this year’s 100-meter dash, which suggests that all 30 students did not improve equally.

What is Mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The given table is:

                  Mean     MAD

Last Year    16.2 s     1.2

This Year    14.7 s      1.9

Looking at this table we can see that this year, the meantime is smaller than the one from last year, so the runners are faster on average.

The mean absolute deviation is bigger, but the change in the mean is bigger.

difference of the mean   16.2 - 14.7 = 1.5

difference of the MAD  1.9 - 1.2 = 0.7

This means that the average speed of the runners increased since last year,

and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike as last year.

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Are these ratios equivalent?
6 men to 7 women
12 men to 14 women ​

Answers

Answer:

Yes 6 times 2 is 12 and 7 times 2 is 14

Answer:

6:7=12:14

12:14=6:7

:-)))

what is the slope of the equation y=2/3x-4

Answers

Answer:

2/3

Step-by-step explanation:

y=mx+b

y=2/3x-4

m=slope

b=y intercept

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