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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Consider the original parallelogram and the reduction.
A parallelogram with side lengths 18 centimeters and 45 centimeters. A second parallelogram with side lengths A and 5 centimeters.
Figures not drawn to scale.
What is the length of side A in the new parallelogram?
2 cm
9 cm
90 cm
162 cm
i believe it is a but someone pls confirm thx
I can confirm that it is A as I took the test and got 100%.
The length of side A in the new parallelogram will be [tex]2[/tex] cm.
What is Scale Factor ?Scale Factor is defined as the ratio of size of new image formed to the size of old image.
We have,
A parallelogram with side lengths [tex]18[/tex] centimeters and [tex]45[/tex] centimeters.
And,
A second parallelogram with side lengths [tex]A[/tex] and [tex]5[/tex] centimeters.
Now,
Scale Factor [tex]=\frac{size\ of\ new\ image}{size\ of\ old\ image}[/tex]
So,
Now, Comparing sides ,
We get,
Scale Factor [tex]=\frac{45}{5}=9[/tex]
i.e. the second parallelogram have Scale Factor of [tex]9[/tex].
So,
Other sides of both parallelograms will be of same Scale Factor.
i.e.
[tex]=\frac{18}{A} =9[/tex]
⇒
[tex]A=2[/tex] cm
Hence, we can say that the length of side A in the new parallelogram will be [tex]2[/tex] cm.
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a rectangular container, 12 cm long and 10 cm wide, is filled with water to a depth of 5 cm. find the volume of water in the container.
Plz i need help ASAP!!!!
Thank you!
Answer:
600 cm³
Step-by-step explanation:
12 x 10 = 120
120 x 5 = 600
what is 83,310.5 millimeters as centimeters? please answer 6th grade math
Answer:
8.3 centimeters
Step-by-step explanation:
Answer:
8331.05
Step-by-step explanation:
i hope this helps :)
What are some real-world scenarios for the Pythagorean theorem?
Answer:
There are loads, but for example you can find the diagonal from a lamppost the the end of its shadow if you know the height of the post and the length of the shadow.
Hope I helped x
Can anyone find d-bar (the d with the line over it) and explain it to me? For this problem five trials are done at eight am and then twelve am. The eight am trials are 98.4, 98.6, 97.8, 97.1, and 97.5. The 12am ones are 98.9, 99, 97.9, 96.6, and 97.7. The correct answer is -0.14 but I can't get that answer.
Answer:
d-bar= ∑d/n= -0.7/ 5= -0.14
Step-by-step explanation:
Eight am 12 am difference (8:00am- 12:00 am)= d
98.4 98.9 (98.4-98.9=) -0.5
98.6 99 (98.6-99=) -0.4
97.8 97.9 (97.8-97.9=) - 0.1
97.1 96.6 (97.1-96.6=)+0.5
97.5 97.7 (97.5-97.7=)-0.2
∑ -0.7
d= difference between 8 am and 12 am
First we subtract the 12.00 am times from 8:00 am times.
Then we add all the differences to get the total difference ∑d.
∑d= -0.7= total of the difference between two times.
n= number of observations=5
Putting the values in the formula would give the answer.
d-bar= d`= ∑d/n= -0.7/ 5= -0.14
Which is an equation for the line shown?
A) y = 3
B) x = 3
C) y=-3
D) x = -3
Answer:
The equation for the line shown is
C) y=-3
Is 499.50 great than or less than 499.05?
Answer:
greater
Step-by-step explanation:
Which layer of the Earth is the thickest?
a. crust
b. mantle
c. outer core
d. inner core
I will mark you the brainiest if you answer the question! <3
Answer:
The mantle
Step-by-step explanation:
The Earth can be divided into four main layers: the solid crust on the outside, the mantle, the outer core and the inner core. Out of them, the mantle is the thickest layer, while the crust is the thinnest layer
1+1
Please help this is worth 80% of my grade
Answer:
2
Step-by-step explanation:
Answer:
2.
Step-by-step explanation:
So you take your numbers, 1 and 1.
You add them together 1+1.
You have your answer, 2.
What value of x makes the equation − 1 3 x + 6 = − 6 + 2 3 x true?
Answer:
4
Step-by-step explanation:
soylindo del 1 al 10
Answer:
6.5
Step-by-step explanation:
Write the standard equation of a circle with center (-2, -1) and radius 2.
Answer:
(x+2)^2+(y+1)^2=4
Step-by-step explanation:
(x-h)^2+(y-k)^2=r^2 is the standard equation for a circle
Plug in point at (h,k) Negative points= positive in equation due to (x-h),(y-k) All equal to radius squared
Aiden and Haisem are going to eat the same amount of hamburgers and fries, but from different restaurants. Aiden goes to Burger King and spends $4.75. Each burger costs $1.25 and fries cost $0.50. Haisem spends $6.48 at McDonalods. Each burger costs $1.50 and fries cost $0.99. How many burgers and fries did Aiden and Haisem each buy?
Answer:
the burgers be 3 and fries be 2
Step-by-step explanation:
The computation is shown below:
Let us assume burgers be x
And, the fries be y
Now according to the questiojn
1.25x + 0.50y = $4.75
1.50x + 0.99y = $6.48
Now multiply by 1.2 in the first equation
1.50x + 0.6y = $5.70
1.50x + 0.99y = $6.48
-0.39y = -0.78
y = 2
Now put the value of y in any of the above equation
1.25x + 0.50(2) = $4.75
x = 3
Hence, the burgers be 3 and fries be 2
please help due pretty soon
Answer:
A
Step-by-step explanation:
just trust me I know what I'm talking about
will give brainliest: how do i solve this??
Answer:
Step-by-step explanation:
-y = -5x + 7
y = 5x - 7
perp.: -1/5
y - 2 = -1/5(x + 8)
y - 10/5 = -1/5x - 8/5
y = -1/5x + 2/5
Simplify the expression:
10 + 10j – 9
10+ 10 = 20j
20j- 9= 11
The answer is 11 or if in the quiz it is 11j
Hope this helps
1 1/2 - 2/5 ÷ 4 2/5 × 3/4
Answer:
1 19/44 (1.4318182)
Answer:
1 19/44
Step-by-step explanation:
Dots sells a total of 290 T-shirts ($2) and shorts ($4) . In April, total sales were $678. How many T-shirts and shorts did Dots sell?
Answer:
241 t-shirt and 49 short
Step-by-step explanation:
lets call shorts x and tshirts y
x+y=290 (first equation)
4x+2y=678 (second equation) { we multiply the price of short with the short so we can get the pieces sold and also with the t-shirt to get the pieces sold)
x=290-y
and substitute it with x in the second equation
4(290-y)+2y=678 then till u get to y=241 (the pieces sold)
290-241=49 (pieces sold)
so as proof 49+241=290 pieces sold
as proof also 4*49=196 price of all shorts sold
2*241=482 price of all t-shirts sold then add them together and u will get 196+482=678$
Taylor noticed that for the rectangle below she could multiply 2 times 3 to get its area of 6 square inches. How else could she find the area?
Answer:
Add 2+2+3+3
Step-by-step explanation:
Correct me if i'm wrong but that's my answer. I studied this 3 years ago.
Answer:
3 x 2 or 3 + 3
Given: Taylor noticed the rectangle she could multiply 2 times 3 to get its area of 6 square inches.
so, if we did 3 times 2 its 6 but if we did 3 + 3 it also 6 so therefore she could do 3 x 2 or 3 + 3 to find the area.
Step-by-step explanation:
A salesperson earns a base salary of $32,500 per year plus a commission of 8% on total sales. Her total sales for one year were $450,000. Find the salesperson's total pay for the year.
The salesperson's total pay for the year is $68500
How to determine the total pay?The given parameters are:
Base pay = $32,500
Commission = 8%
Total Sales = $450,000
The total pay is calculated as:
Total = Base pay + Commission * Total Sales
This gives
Total = $32,500 + 8% * $450,000
Evaluate
Total = $68500
Hence, the salesperson's total pay for the year is $68500
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What is the simplest form of 2(sqr rt) 3/ (sqr rt) 6??
Answer:
Option A will be your answer
Step-by-step explanation:
hope it's helpful...
These problems are so confusinggggggg
Answer:
C (both)
step by step explanation:
Answer:
C. Both (1, 11) and (-1, -5)Step-by-step explanation:
y = 8x + 3Substitute the values of (x, y)
(1, 11)
11 = 8*1 + 311 = 11yes(-1, -5)
-5 = 8(-1) + 3-5 = -8 + 3-5 = -5 yesBoth pairs are solutions
Correct choice is C
What is the value of the expression?
Answer:
6s2
= 6(2)2
= 12 × 12
= 144
: The value of the expression is equal to 144
Solve for the measure of c. Round decimals to the nearest tenth.
A. 3.7
B. 7
C. 8.8
D. 4.7
a coin is tossed and a dice is rolled. What is the probability of getting tails with rolling a 2?
Answer:
50% for the coin and 1/6 chance for the dice
What is the correct answer choice?
Answer:
G
Step-by-step explanation:
I need help on some of my math
Answer:
true
Step-by-step explanation:
i hope this helps :)
Assume the data below is exponential Determine the growth/decay factor. Estimate your answer to 3 places after the decimal.
15
16
У
90
74
Х
9514 1404 393
Answer:
37/45 ≈ 0.822
Step-by-step explanation:
The formula for an exponential relation is ...
y = a·b^x
This question is asking for the value of b. It can be found by substituting the given values of x and y, and taking the ratio of the resulting equations.
90 = a·b^15
74 = a·b^16
Dividing the second equation by the first, we have ...
74/90 = (a·b^16)/(a·b^15)
74/90 = b
The decay factor is 74/90 = 37/45 ≈ 0.822
Answer:
37/45=0.822 this is my answer
Find the area of the composite shape shown below:
6ft
9ft
3ft 4ft
Mrs. Baxter deposits $2000 in an account that earns 5% interest. How much is Mrs. Baxter's investment worth after 8 years
Answer:
2954.91088758
Step-by-step explanation:
exact answer