Answer:
a) 2400m on the 20th day for Charlie.
1) 728.41m of 20th day for Daniella.
Didn't find n, sorry.
Charlie ran 2400m on day 20 of his fitness program and Daniella ran 728m on day 20 of her fitness program.
It is given that Charlie and Daniella on day one both ran 500m on each subsequent day.
Charlie ran 100m more than the previous day.
Daniella increased her distance by 2% of the distance run on the previous day.
It is required to calculate how far Charlie and Daniella ran on day 20 and the value of n.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Charlie ran 500m on the first day:
[tex]\rm a_1 = 500[/tex]
[tex]\rm a_2 =600[/tex] ( because charlie ran 100m more than the previous day)
It is an arithmetic progression in which the difference between two consecutive terms:
d = 600 - 500 ⇒ 100
and [tex]\rm a_n = a+d(n-1)[/tex]
[tex]\rm a_2_0 = 500+100(20-1)\\\\\rm a_2_0 = 2400m[/tex]( ∵ n = 20 )
Daniella ran 500m on the first day:
[tex]\rm b_1 = 500[/tex]
[tex]\rm b_2 = 500+ 500\times2 \%[/tex] (because Daniella increased her distance by 2% of the distance run on the previous day)
We can write [tex]\rm n^t^h[/tex] terms:
[tex]\rm b_n= 500(1+2\%)^n^-^1[/tex]
[tex]\rm b_2_0= 500(1+2\%)^2^0^-^1[/tex]
[tex]\rm b_2_0= 500(1+0.02)^1^9\\\\\rm b_2_0 = 500\times 1.02^1^9\\\\\rm b_2_0 = 500\times1.456 \Rightarrow 728.40 \approx 728 m[/tex]
[tex]\rm b_n > a_n[/tex] (given in the question)
[tex]\rm500(1+2\%)^n^-^1 > 500+100(n-1) \ \ or \\\\\rm500(1+2\%)^n^-^1 > 100n+400[/tex]
The above expression is not true for all the values of 'n' ie. 'n' can not be determined.
Thus, Charlie ran 2400m on day 20 of his fitness program and Daniella ran 728m on day 20 of her fitness programme.
Learn more about the sequence here:
brainly.com/question/21961097
I have 4 groups . After I dived Ed them into groups there were 6 groups 0f 4 and 1 group of 3. How many students were in the class ? Show all your work.
Answer: 27 students
Step-by-step explanation: 6 x 4 = 24
24 + 3 = 27
Answer:
27 Students in the class
Step-by-step explanation:
First we have to find out how many people are in the 6 groups of 4. 6x4=24
And of course 1 group of 3 people. Add them together to get 27 people.
24+3=27
f(x)= -2x^3 +14x -8
g(x)= 2x+6
Answer:
F(2x+6)=-16x^3-144x^3-404x-356
Step-by-step explanation:
solve pls brainliest
Answer:
-3
Step-by-step explanation:
using pemdas, we first divide -18 by 6 to get -3. next, we subtract -3 from -6: -6-(-3)=-6+3=-3
Answer: -3
Step-by-step explanation:
For this, you want to use PEDMAS
This is Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction. The first step would be to divide -18/6. This will come out to -3
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=38(1.108)^x
what is the % increase
Is 6,702,512 divisible by 9?
To solve the given system by elimination, what is the first step to take? A) Rewrite each equation in standard form, ax + by = c. B) Multiply 2x + y + 1 = 0 by −3. C) Multiply 2x + y + 1 by −2. D) Combine the equations by adding like terms.
Answer:
option d
Step-by-step explanation:
Your should have attached the equation for answer to be explained
Graph the original function by indicating how the more basic function has ben shifted, reflected, stretched, or compressed
4x + y = 16
y = 0.5x -2
Answer:
x = 4, y = 0
Step-by-step explanation:
Help, please! You will be extremely smart if you answer this question, and if you do I will give brainliest. The test ends soon please help.
Answer:
B. y=6-1/3t
Step-by-step explanation:
If you graph this equation, it matches the given graph. Hope this helps :)
(03.02 MC) The figure shows the location of three points around a lake. The length of the lake, BC, is also shown. (The figure is not drawn to scale.) A 6 mi 2 mi 00 B С Which of the following choices is closest to the distance (in miles) between points A and B?
9514 1404 393
Answer:
(b) 5.66 mi
Step-by-step explanation:
You only need to eliminate the unreasonable answers to make the correct choice.
The hypotenuse of the right triangle is its longest side, so the unknown length must be less than 6. That eliminates the last two choices.
The unknown length cannot be less than the difference of the sides shown, so the unknown length must be more than 4. That eliminates the first choice.
The only reasonable choice is ...
B. 5.66 miles
_____
If you like, you can calculate the distance using the Pythagorean theorem.
AB² + 2² = 6²
AB = √(36 -4) = √32 ≈ 5.66 . . . miles
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 7 fl oz per minute. How fast was the pipe leaking in gallons per hour? PLLLLLLLLLLLLZZZZZZZZZZZ
Answer:
It leaks 420 gallons per hour.
Step-by-step explanation:
7g/m
?/h
7/1 = x/60
(Cross Multiplication)
7 × 60 = x × 1
420 = x
It leaks 420 gallons per hour.
Answer:
3.28 gallons per hour
Step-by-step explanation:
Given that the pipe is leaking at a rate of 7 fluid ounce per minute, and that we need to determine the equivalent leaking rate in gallons per hour. It is important to establish the necessary conversion rates of fluid ounces (fl oz) to gallons (gal), and minutes to an hour.
Conversion rate for fluid ounces (fl oz) to 1 gallon (gal): 128 fl oz = 1 galConversion rate of minutes to hour: 60 minutes = 1 hour.Now that we have established the conversion rates, we can set up the following mathematical operations that will allow us to convert the leaking rate from fluid ounces per minute, to gallons per hour. We can express the conversion process in fraction form:
[tex](\frac{7 fl. oz.}{min})[/tex] × [tex](\frac{1 gal}{128 fl. oz.})[/tex] × [tex](\frac{60 min}{1 hr})[/tex]
Start by multiplying the first two fractions together:
[tex](\frac{7 fl. oz.}{min})[/tex] × [tex](\frac{1 gal}{128 fl. oz.})[/tex] = 0.546875 gallons per minute, or 0.546875 gal/min
Next, multiply 0.546875 gal/min by 60 min/hr. This cancels out the "minute" as a unit of measurement, leaving you with gal/hr.
[tex](\frac{0.546875 gal}{min})[/tex] × [tex](\frac{60 min}{1 hr})[/tex] = 3.28125 gallons per hour, or 3.28 gal/hr.
Therefore, the pipe is leaking at a rate of 3.28 gallons per hour.
Compute the total amount accumulated if you invested $3,000 for 6 years at 3% compounded
quarterly. Round your answer to the nearest cent and include '$' in your response.
Answer:
$3,582.16
Step-by-step explanation:
The Washington High key club is selling brownies and chocolate chip cookies to raise money. Their table only has room for 100 baked goods. Previous bake sells has taught them to plan to bake at most 30 brownies and at least 50 cookies. Write and graph a system of inequalities to represent the possible number of baked goods.
Step-by-step explanation:
Let x - brownies, y - cookies.
According to given w have following inequalities
Their table only has room for 100 baked goods:
x + y ≤ 100Plan to bake at most 30 brownies and at least 50 cookies:
x ≤ 30y ≥ 50See attached for the graphical solution
The solution is within the marked boundaries.
[2] A car is traveling at 55 MPH.
How long in minutes will it take, in minutes, to travel 33 miles?
Answer:
Step-by-step explanation:
So at 55 miles per hour you go 12 miles in a little over 13 minutes.
.
Hope this helps you to understand the problem and how to use the formula to solve it.
Distance = Speed * Time
.
You might be able to understand this by thinking, "If I go at 60 miles per hour for 2 hours,
how far do I travel?" The answer is:
.
Distance = 60 miles per hour* 2 hours = 120 miles
.
In the problem you are told that the distance to be covered is 12 miles. The speed is 55 miles
per hour. Put these into the equation and you get:
.
12 miles = 55 miles per hour * Time
.
You can then solve for the Time by dividing both sides of this equation by 55 to get:
.
12/55 = Time
.
So it takes 12/55 hours to go 12 miles. The fraction 12/55 converts to a decimal by dividing
55 into 12 to get 0.218181818 of an hour. Since an hour has 60 minutes, you can convert
the answer to minutes by multiplying 60 by 0.218181818 to get about 13.09 minutes.
Match the event with the most appropriate probability word: The roll of a normal fair dice will show a 7.
A. Certainly
B. Likely
C. Evens
D. Unlikely
E. Impossible
F. Other
Answer this, plz.
Answer:
Option 3
Evens
. . . . . .. . ..
H . E . L . P
this work is due tommorow, and i have absolutely no idea what the answer is. please help me if you can !
( don’t comment for points. )
Answer:
A) 25
B) 64
Step-by-step explanation:
Hope this helps :))
Step-by-step explanation:
x= 5
a) 5² = 5×5 =25
b) (5+3)² = 8²
= 8 × 8
= 64
Answer to what is CA
well, let's recall that A, B and C are medians of their segment, meaning each of those lines made by them are midsegments, Check the picture below.
[tex]CA = \cfrac{SR}{2}\implies 2CA=SR\implies 2(3x-1)=5x+4 \implies 6x-2=5x+4 \\\\\\ x-2=4\implies x =6~\hfill \stackrel{~\hfill CA}{3(6)-1\implies 17}[/tex]
perform the operation and simplify
Answer:
[tex] \frac{x + 4}{3x(x + 1)} \\ [/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{2} + 10x + 24 }{3 {x}^{2} + 3x} \div (x + 6) \\ \frac{ {x}^{2} + 4x + 6x + 24}{ 3x(x + 1)} \times \frac{1}{(x + 6)} \\ \frac{x( x+ 4) + 6(x + 4)}{3x(x + 1)} \times \frac{1}{(x + 6)} \\ \frac{(x + 4)(x + 6)}{3x(x + 1)} \times \frac{1}{(x + 6)} \\ \frac{(x + 4)}{3x(x + 1)} \\ [/tex]
Answer: the finished equation is (x+4)/3x*(x+1), so fill in one in the green square
Step-by-step explanation: it worked for me, the explanation is very long, but I would recommend using tiger algebra for a very detailed step by-step explanation, hope I could be a help
Will be giving brainliest! Have a good day and you’ll get through it !
Answer:
ok you to !!!!!!!!! good night!!
Step-by-step explanation:
George read 72% of a book. If he reads 270 pages how many pages are there in the book?
Answer:
375 pages
Step-by-step explanation:
270 = 72%
=> 270/72 = 72/72
=> 3.75 = 1%
=> Number of Book pages = 375
Hoped this helped.
One number is six less than a second number. Twice the first is 12 more than 6 times the second. Find the numbers.
The value of the first number is
The value of the second number is
Answer:
Step-by-step explanation:
Let x be the first number
Let y be the second number
x = y - 6
2x = 12 + 6y
2(y - 6) = 12 + 6y
2y - 12 = 12 + 6y
-4y = 24
y = -6
x = -6 - 6 = -12
True or False: This table describes a linear function
Answer:True
Step-by-step explanation:
There is a constant rate of change. For x, it'd be +1. For y, it'd be +3.
Vote brainliest please!
Answer:
true
Step-by-step explanation:
This is because the slope is y= 3x, you can prove that by plugging in the x values, and if they equal the y then that slope is right.
Find the measure of the angle ACD in the given figure???
Answer:
∠ACD = 33.5°
Step-by-step explanation:
The arc length will be twice ∠ ABD,
∠ABD will equal ∠ACD because they subtend the same arc length.
3x + 7 = 2(2x - 6.5)
3x + 7 = 4x - 13
x = 20
∠ABD = (2(20) - 6.5) = 33.5
Please answer! Only if correct, please.
Answer:
f(-4) = -6
g(2) = -14
Step-by-step explanation:
To evaluate a function we must plug in the values of x. So for:
f(x) = 2x+2
we have:
f(-4) = 2(-4)+2
then we simplify:
f(-4) = -8+2
so f(-4) = -6
Now the same steps are taken for g(x) in which the answer would be -14.
HELPPP LAST ATTEMPT!!
(3/4x-1) - (1/3x+4) what is the difference
Answer:
[tex]\huge\boxed{\dfrac{5}{12}x-5}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{3}{4}x-1\right)-\left(\dfrac{1}{3}x+4\right)=\dfrac{3}{4}x-1-\dfrac{1}{3}x-4=\left(\dfrac{3}{4}x-\dfrac{1}{3}x\right)+(-1-4)\\\\=\left(\dfrac{3\cdot3}{4\cdot3}x-\dfrac{1\cdot4}{3\cdot4}x\right)+(-5)=\left(\dfrac{9}{12}x-\dfrac{4}{12}x\right)-5=\dfrac{9-4}{12}x-5\\\\=\dfrac{5}{12}x-5[/tex]
Jen has 93 beads ana has 46 red beads and 29 blue beads.How many more beads does Ana need to have 93 beads Also?
Answer: 18
Step-by-step explanation: 93 - (46 + 29) = 18
5. Aaron sold 126 boxes of cookies. This is 14 more than twice the
number of boxes his sister, Victoria, sold. How many boxes of
cookies did Victoria sell?
Answer:
56 boxes
Step-by-step explanation:
1. First subtract 14 from 126 to get 112 boxes
2. Now divide 112 by 2 to get Victoria's total of 56
The quotient of a number p and 3 is 24
Answer:
p= 8
Step-by-step explanation:
because 8 x 3 is 24
hope this helps!❄︎
no link no bot fast right please is it inch or inch 2
Answer:
its just inch
Step-by-step explanation:
you would multiply the 3 and the other three and you would get 9
