========================================================
Explanation:
We have this sequence
(2+1)+(2+1)+(2+1)...
Effectively, we're repeating "2+1" over and over.
We can see that
2+1 = 3(2+1)+(2+1) = 3+3 = 6(2+1)+(2+1)+(2+1) = 3+3+3 = 9Each time we add on another copy of (2+1), we're adding on 3
Dividing 26.2 over 3 gets us (26.2)/3 = 8.733 approximately
If we had 8 copies of (2+1) added together, then we would get
8*(2+1) = 8*3 = 24
This is 26.2-24 = 2.2 miles short of his goal.
He'll need to run 2 more miles, plus walk another 0.2 of a mile
----------------------------------------------------
In summary so far, Joey will run 8+1 = 9 sections (two miles each) and walk 8 sections that are 1 mile each. At the very end, he'll walk 0.2 miles to finish the race. Each running and walking section is alternated of course.
Since he runs 9 sections, each 2 miles, that accounts for 9*2 = 18 miles.
His running pace is 8 minutes per mile, so this means he has run for 8*18 = 144 minutes. This is just the running part and not the walking part.
Let A = 144 so we can use it later.
----------------------------------------------------
He walks 8 sections of 1 mile each. His walking pace is 16 minutes per mile. This must mean he spends 8*16 = 128 minutes on this walking portion.
Then for the last 0.2 mile section he walks, we can solve the proportion below
(1 mile)/(16 min) = (0.2 miles)/(x min)
1/16 = 0.2/x
1*x = 16*0.2
x = 3.2
He spends 3.2 minutes walking the remaining 0.2 of a mile at the end.
So his total walking time is 128+3.2 = 131.2 minutes.
Let B = 131.2
-----------------------------------------------------
To wrap things up, we'll add up the results of each of the previous two sections.
A = total running time = 144 min
B = total walking time = 131.2 min
C = total marathon time
C = A+B
C = 144+131.2
C = 275.2 minutes
This converts to 275 min, 12 sec.
This is also equivalent to 4 hrs, 35 min, 12 sec.
If 8 bags of chips cost 10.32;how much will you pay for 20 bags?
Answer:
$25.80
Step-by-step explanation:
First, let's find the cost of one bag of chip:
10.32/8 = 1.29
If one bag costs $1.29, simply multiply the number of bags (20) by 1.29
1.29 x 20 = 25.80
= $25.80
Answer:
25.80
Step-by-step explanation:
We can use a ratio to solve
8 bags 20 bags
------------- = ----------------
10.32 x dollars
Using cross products
8x = 10.32 * 20
8x =206.40
Divide each side by 8
8x/7 = 206.40/8
x =25.80
John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?
Question 17 and 18 plz show ALL STEPS and HELP ME ASAP
Answer:
17) 750/9 and 18) 364
Step-by-step explanation:
17. Summation of 75*(0.1)^i from i=0 to infinity, that is equal to 75*(Summation of (0.1)^i). Summation of (0.1)^I is a geometric series with a sum of 1/(0.9)=10/9. Hence the series have a sum equal to 75*(10/9)=750/9
18) It's a series with sum=1+3+9+27+81+243=364
The graph of the function f(x) = (x + 2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
Answer:
2nd option,
The function is negative for all read values of x where -6<x<-2
The function f(x) = (x + 2)(x + 6) is a quadratic function, and the function is negative for all real values of x where –6 < x < –2.
What are quadratic functions?Quadratic functions are functions that have an exponent or degree of 2
The function is given as:
f(x) = (x + 2)(x + 6)
From the graph of the function, the vertex is at (-4,-4) and the x-intercepts are at x = -6 and x = -2
Since the vertex is minimum, then the function is negative for all real values of x where –6 < x < –2.
Read more about x-intercepts at:
https://brainly.com/question/3951754
Multiply (2x-5)(x+3)
Answer:
2x^2+x-15
Step-by-step explanation:
foil
Answer:
2x^2 + x - 15
Step-by-step explanation:
using FOIL
(2x - 5)(x + 3)
[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]
[2x^2 + 6x - 5x - 15]
2x^2 + x - 15
find the range of the function f (x) = 2x + 5 for the domain 2,5,7
Answer:
The range is {9,15,19}
Step-by-step explanation:
f (x) = 2x + 5
Let x = 2
f (2) = 2*2 + 5 = 4+5 = 9
Let x = 5
f (5) = 2*5 + 5 = 10+5 = 15
Let x = 7
f (7) = 2*7 + 5=14+5 = 19
The domain is {2,5,7}
The range is {9,15,19}
Answer:
i think what you wrote is that the domain is 2 to 5.7.
so you plug in these two numbers inside the equation cause domain means the distance in the x axis so this is how it goes.
2(2) + 5 = 9
2(5.7) +5= 16.4
so the range is 9 to 16.4
hope that answers your question...
If you were to place $2,500 in a savings account that pays 3% interest
compounded continuously, how much money will you have after 5 years?
Assume you make no other deposits or withdrawals.
Answer:
$2904.59
Step by Step Explanation:
[tex] \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = what[/tex]
Answer I'll make and mark as brainlist.
Answer Fast.
Post on - 2 Aug 2021
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)
(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 3
You're looking for a solution of the form
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]
Differentiating twice yields
[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]
[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]
Substitute these series into the DE:
[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:
[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]
which indicates that the coefficients in the series solution are governed by the recurrence,
[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]
Use the recurrence to get the first few coefficients:
[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]
You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,
-7 = -7/0!
-7/2 = -7/2!
-7/6 = -7/3!
and so on, with only the coefficient in the n = 1 position being the odd one out. So we have
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]
which looks a lot like the power series expansion for -7eˣ.
Fortunately, we can rewrite the linear term as
3x = 10x - 7x = 10x - 7/1! x
and in doing so, we can condense this solution to
[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]
Just to confirm this solution is valid: we have
y = 10x - 7eˣ ==> y (0) = 0 - 7 = -7
y' = 10 - 7eˣ ==> y' (0) = 10 - 7 = 3
y'' = -7eˣ
and substituting into the DE gives
-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0
as required.
If Damien does a job in 21 hours less time than Caitlyn, and they can do the job together in 14 hours, how
long will it take each to do the job alone?
Answer: Damien = 7.5 hours and Caitlyn = 28.5 hours
Step-by-step explanation:
Damien = X -21
Caitlyn = X
2X - 21 = 14
2X = 14 + 21
X = (14+21)/2
X = 7.5
Which expression is equivalent to the given expression?
Answer:
a³b
Step-by-step explanation:
(ab²)³/b⁵
= a³b⁶/b⁵
= a³b
The sum of two consecutive even integers is 54. What are the two integers?
Answer:
26 and 2
Step-by-step explanation:
Given,
Sum of two even numbers = 54
let one number be x
another number be x +2
x + x +2 = 54
2x + 2 = 54
2x = 54 - 2
2x = 52
x = 52/2
x = 26
Therefore, the numbers are 26 and 26 + 2 = 28..
The absolute value inequality equation |2x – 1| > 3 will have what type of solution set?
Given:
The inequality is:
[tex]|2x-1|>3[/tex]
To find:
The solution set for the given inequality.
Solution:
We know that, if [tex]|x|>a[/tex], then [tex]x<-a[/tex] and [tex]x>a[/tex].
We have,
[tex]|2x-1|>3[/tex]
It can be written as:
[tex]2x-1<-3[/tex] or [tex]2x-1>3[/tex]
Case I:
[tex]2x-1<-3[/tex]
[tex]2x<-3+1[/tex]
[tex]2x<-2[/tex]
[tex]x<\dfrac{-2}{2}[/tex]
[tex]x<-1[/tex]
Case II:
[tex]2x-1>3[/tex]
[tex]2x>3+1[/tex]
[tex]2x>4[/tex]
[tex]x>\dfrac{4}{2}[/tex]
[tex]x>2[/tex]
The required solution for the given inequality is [tex]x<-1[/tex] or [tex]x>2[/tex]. The solution set in the interval notation is [tex](-\infty,-1)\cup (2,\infty)[/tex].
Therefore, the required solution set is [tex](-\infty,-1)\cup (2,\infty)[/tex].
Solve the equation by factoring: 5x^2 - x = 0
Answer:
Step-by-step explanation:
x = 0, 1/5
Find m<1.
33°
47°
42°
28°
Answer:
<1 = 33
Step-by-step explanation:
The sum of the angle of a triangle is 180
31+116+x = 180
x+147=180
x = 180-147
x = 33
[tex]f(x)=e^{3x} .sinx[/tex] . tính [tex]d^{2} f(0)[/tex]
Answer:
6
Step-by-step explanation:
đạo hàm cấp 2 của f(x) rồi thế 0 vào
Graph x^2/49+y+1^2/4=1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Perhaps you want a graph of ...
x^2/49 +(y +1)^2/4 = 1
This is an ellipse centered at (x, y) = (0, -1) with a major axis in the x-direction of 14, and a minor axis in the y-direction of 4.
The LARGEST angle has a measure of ______degrees
Answer:
90 i think
Step-by-step explanation:
A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?
which of the following portions are true
A. 20/48 = 40/90
B. 25/40 = 48/80
C. 18/48 = 27/72
D. 12/15 = 21/25
slope of (30, 600) (75, 1050)
Answer:
y2-y1/x2-x1
y2: 1050
y1:600
x2:75
x1:30
1050-600=450
75-30=45
450/45=10
slope is 10
Answer:
let:
A(30, 600)=(x1,y1)
B((75, 1050)=(x2,y2)
now,
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{1050 - 600}{75 - 30} [/tex]
[tex] = \frac{450}{ 45} [/tex]
[tex] = \frac{10}{1} [/tex]
Find the surface area of a cube that has side length of 3.5 inches
Answer:
73.5
Step-by-step explanation:
which one of these points lies on the line described by the equation below y - 5 = 6 ( x - 7 )
Answer:
the answer would be (7,5)
3. Find F(3).
F(x)=-x^3+4x^2-2x
Answer:
To Find F(3) you just have to replace x=3 so:
F(3)= -3^3 + 4×3^2 -2×3 = -27 +4×9 - 6 = -33 + 36 = 3
What is the slope? Please Help
Answer:
-1
Step-by-step explanation:
Pick two points on the line
(0,2) and (2,0)
Using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 0-2)/(2-0)
= -2/2
= -1
Answer:
-1
Step-by-step explanation:
Use two points on the line to find the slope, using rise over run.
We can use the points (0, 2) and (2, 0).
From the first point to the other, the y value decreases by 2 and the x value increases by 2.
Use rise (change in y value) over run (change in x value):
-2 / 2
= -1
So, the slope is -1.
The figure below is a net for a right rectangular prism. Its surface area is 104 ft2 and
the area of some of the faces are filled in below. Find the area of the missing faces,
and the missing dimension.
Answer:
12+12+10+10=44
104-44=60
60÷2=30
30 is the surface area of A
30÷6=5
5 is a missing dimention
help whats the volume of this
Answer:
93.6
Step-by-step explanation:
The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.
in the given circle the radius is 9 cm what is its diameter?
Answer:
18
Step-by-step explanation:
The diameter is equal to twice the length of the radius
So if the radius is 9 then the diameter is 9 * 2 = 18
Based on what we have learned, how can we ensure that we choose a sample of students that is representative of all 8:00 AM classes that take place on a given morning
Sampling technique is a way of selecting a sample from a given population. The best way to get a sample of students that represents all 8:00 AM classes is by using a stratified sampling technique.
From the complete question, we can summarize the given data as follows:
[tex]Buildings = 3[/tex] ----3 buildings in the college
[tex]Lecture\ Halls =2[/tex] ---- 2 lecture halls in each building
[tex]Capacity = 100[/tex] --- 100 students in each lecture hall
Because the students' lecture halls are not in the same building, the best way to get a sample is as follows:
Divide the students into groups (In this case, the students will be grouped by the buildings of their lecture halls)The number of students in each building is:
[tex]Students = Capacity \times Lecture\ Halls[/tex]
[tex]Students = 100 \times 2[/tex]
[tex]Students = 200[/tex]
There are 200 students in each building
Then select at random an equal proportion of student from each building (say 30 students in each building)The above method is referred to as a stratified sampling technique because the population of the students are divided into groups, before being randomly selected.
Read more about sampling techniques at:
https://brainly.com/question/9612230
Plz help me find x and y on the triangle big thanks
Answer:
This is a 30-60-90 right triangle.
The ratio of sides:
a : b : c = 1 : √3 : 2Compare with the given values:
a = 3√3, b = y, c = xy = 3√3*√3 = 9x = 2*3√3 = 6√3