Answer:
8. Arithmetic Progression
9. [tex]f(9) = 300[/tex]
Step-by-step explanation:
Given
[tex]\{(1,55)\ (2, 45)\ (3, 35)\ (4, 25)\}[/tex]
Solving (8): Arithmetic or Geometric
We start by checking if it is arithmetic by checking for common difference (d).
[tex]d = y_2 - y_1 = y_3 - y_2 = y_4 - y_3[/tex]
This gives:
[tex]d = 45 - 55 = 35 - 45 = 25 - 35[/tex]
[tex]d = -10 = -10 = -10[/tex]
[tex]d=-10[/tex]
Because the common difference is equal, then it is an arithmetic progression
Solving (8):
[tex]f(n) = f(1) + f(n-1)[/tex]
To find f(9), we substitute 9 for n
[tex]f(9) = f(1) + f(9-1)[/tex]
[tex]f(9) = f(1) + f(8)[/tex]
We need to solve for f(8); substitute 8 for n
[tex]f(8) = f(1) + f(8 - 1)[/tex]
[tex]f(8) = f(1) + f(7)[/tex]
We need to solve for f(7); substitute 7 for n
[tex]f(7) = f(1) + f(7 - 1)[/tex]
[tex]f(7) = f(1) + f(6)[/tex]
We need to solve for f(6); substitute 6 for n
[tex]f(6) = f(1) + f(6 - 1)[/tex]
[tex]f(6) = f(1) + f(5)[/tex]
We need to solve for f(5); substitute 6 for n
[tex]f(5) = f(1) + f(5 - 1)[/tex]
[tex]f(5) = f(1) + f(4)[/tex]
From the function, f(4) = 25 and f(1) = 55.
So:
[tex]f(5)=55 + 25[/tex]
[tex]f(5)=80[/tex]
[tex]f(6) = f(1) + f(5)[/tex]
[tex]f(6) = 55 + 80[/tex]
[tex]f(6) = 135[/tex]
[tex]f(7) = f(1) + f(6)[/tex]
[tex]f(7) = 55 + 135[/tex]
[tex]f(7) = 190[/tex]
[tex]f(8) = f(1) + f(7)[/tex]
[tex]f(8) = 55 + 190[/tex]
[tex]f(8) = 245[/tex]
[tex]f(9) = f(1) + f(8)[/tex]
[tex]f(9) = 55 + 245[/tex]
[tex]f(9) = 300[/tex]
5. Viruses spread at an exponential rate. Write a model for a virus that starts with 1 person and increases by 400% every week. Write an exponential model in the form y=ab^x to represent this situation.
Answer:
y = 4^xStep-by-step explanation:
Initial number is 1 so a = 1
Weekly growth rate is 400% which is 4 times increase, therefore b = 4
So the function becomes:
y = 4^xSelect the equation in point-slope form for the line that passes through the point (1, –1) and has a slope of 4.
Is the answer
A. y + 1 = 4x – 1
B. y – 1 = 4x + 1
C. y – 1 = 4(x + 1)
D. y + 1 = 4(x – 1)
Answer:
I would say the best answer choice is B.
Helpppp meeee fassttt pleaseeee
Answer:
y = -1/3x + 3 2/3
Step-by-step explanation:
step 1. find the slope of the given line
y2-y1/x2-x1 2 - 4/ 3 + 3 = - 1 / 3
take the opposite of that and there is your slope
step 2. plug in the values to the following equation using the given point:
y - y1 = m ( x - x1 ) y - 4 = - 1/3 ( x + 1 )
step 3. solve for y
y-4 = -1/3(x+1)
-1/3(x) and -1/3(1) ----> y-4 = -1/3x-1/3
y-4+4 = -1/3x-1/3+4 ----> y = -1/3x + 3 2/3
hope this helps. if you need more help lmk in the comments. i am in algebra two so you can trust me. Happy holidays
Usha thinks that the area of the development will be greater than the total area of 50 football pitches.
Usha knows
• a football pitch is rectangular 100m by 50m
• 1 mile = 1600m.
Answer:
Usha is correct
Step-by-step explanation:
See attachment
Given
Dimension of the development
[tex]Height = \frac{1}{2}\ mile[/tex]
[tex]Base = \frac{1}{2}\ mile[/tex]
Dimension of a football field
[tex]Length = 100m[/tex]
[tex]Width = 50m[/tex]
First, we calculate the area of the development.
Because it is triangular in shape, the area is:
[tex]Area = \frac{1}{2} * Height * Base[/tex]
[tex]Area = \frac{1}{2} * \frac{1}{2}mile * \frac{1}{2}mile[/tex]
Convert mile to meter
[tex]Area = \frac{1}{2} * \frac{1}{2}* 1600m * \frac{1}{2} * 1600m[/tex]
[tex]Area = \frac{1}{2} * 800m * 800m[/tex]
[tex]Area = 400m * 800m[/tex]
[tex]Area = 320000m^2[/tex]
The area of 50 football pitch is then calculated as:
[tex]Area = 50 * Length * Width[/tex]
[tex]Area = 50 * 100m * 50m[/tex]
[tex]Area = 250000m^2[/tex]
By comparison:
[tex]320000 > 250000[/tex]
Hence, Usha's thought is correct
a boy has 10 cookies. and his brother has 2.5 times as many. how many does the brother have
Answer:
25
Step-by-step explanation:
What is the reason for each step in the solution of the inequality?
700 + 16 < -5(4 – 5x)
Match the reason with the correct step in the inequality.
The price of a pair of sunglasses was reduced from $55 to $33. By what
percentage was the price of the sunglasses reduced?
Answer:
166.6% (put a little line over the LAST 6.)
Step-by-step explanation:
Convert the fraction to a decimal, then multiply by 100.
Answer:
60%
Step-by-step explanation:
33×100=3300÷55=60
60%×55=33
Can I get him with all the questions please?
Answer:
[tex]14.16\\15. a) 14[/tex]
Step-by-step explanation:
[tex]14. We\ are\ given\ that,\\The\ assumed\ number\ x\ is\ 4\ more\ than\ 12\\Hence,\\x=4+12\\x=16\\Lets\ see\ that\ x=16\ as\ a\ solution,\ matches\ with\ the\ other\ information\ provided.\\We\ are\ also\ given\ that,\\x<20, 16\ is\ less\ than\ 20\ too.\\x>13, 16\ is\ greater\ than\ 13\ too.\\x<17, 16\ is\ less\ than\ 17\ too.\\As\ all\ the\ conditions\ are\ satisfied,\ x=16\ as\ a\ solution\ is\ verified.\\[/tex]
[tex]15. a)\\Let\ the\ assumed\ no.\ be\ y\\Here,\ we\ are\ given\ the\ following\ information\ about\ y:\\y>10,\\y<20\\y>12\\y<15\\Hence,\\The\ number\ y\ lies\ in\ between\ 12-15.\\Hence,\\y\ could\ either\ be\ 13,14.\ But\ the\ phrase\ 'Of\ the\ numbers\ are\ left\\ I\ am\ the\ greater\ number', tells\ us\ that,\ y\ is\ the\ greater\ no.\ among\ 13\ and\ 14.\\Hence\ as\ 14>13,\\y=14[/tex]
Michelle had 600 fish to feed the dolphins in a zoo. Each dolphins ate the same number of fish. There are 9 dolphins in all. How many fish did Michelle have left?
Answer:
each dolphins eat 600÷9=66.67
Uhm ian askin fo a lot buh ,,, uh someone add me on Rblx , XxColdTyXx is da user
Answer:
Mk! I will when I get my account back!
Step-by-step explanation:
Marta's pet snake is 10 inches shorter than three times the length of Dilbert's pet snake. If both their snakes laid together end to end measure 110 inches, how long is Marta's snake? Which equation would NOT solve this problem?
x + 3x - 10 = 110
3x - 10 = 110
4x - 10 = 110
x + 3x = 120
1. Find the 8th term of the following linear sequences.
i) 2,4,6,8,...
ii) -7,-4,-1.2- iii)0,-1/2,-1,-1 1/2
iv) 12,5,-2. v) 8,14, 20,...
vi) 63,58, 53, ...
We know the formula,
t =n =ar
n−1
Here n=8
Common ratio =−2 and first term =a=−6
t =8
=(−6)×(−2)
8−1
t =8
Use this formula
=(−6)×(−2)
7 t= 8
=768
The Table Shows The Number Of Rows Of Bricks A Worker Can Lay In Different Numbers Of Hours
Number Of Hours.
4
6
8
10
Number Of Rows
12
18
24
30
How Many Bricks Can The Worker Lay Each Hour?
A 2
B 3
C 6
D 9
Easy algebra 1 please help
9514 1404 393
Answer:
(H) y = 1/3x + 5
Step-by-step explanation:
When x=0, y=5, so you know G is not a possibility.
Y increases at a lower rate than x does. For example, between the first two table entries, x goes up by 6, but y goes up by 2. The only choice with a rate of change less than 1 is ...
(H) y = 1/3x + 5
How do you find the mean and standard deviation?
Six ninth-grade students and six 12th-grade students were asked: How many movies have you seen this month? Here are their responses.
Ninth-grade students: 5,1, 2, 5, 3,8
12th-grade students: 4,2,0, 2, 3, 1
a. By hand, calculate the mean, variance, and standard deviation of each of these data sets. Which is more spread out, the ninth-grade or 12th-grade data set?
b. Make a graph of both data sets. Which of these data sets appears more spread out? Does your answer agree with your conclusion in part (a)?
Answer:
Following are the solution to the given point:
Step-by-step explanation:
Grade of students:
Grade of student:
In point a:
Grade of [tex]9^{th}[/tex] students:
[tex]\to n= 6\\\\\to Mean = \frac{ \sum x_i}{n} \\\\[/tex]
[tex]= \frac{ 5+1+2+5+2+8}{6}\\\\ = \frac{24}{6}\\\\ = 4[/tex]
[tex]\to Variance\\\\\sigma^2 = \frac{\sum(x_i -\bar{x})^2}{n-1}[/tex]
[tex]=\frac{1}{5}(10)\\\\=2[/tex]
[tex]\to Standard \ deviation ( \sigma) :\\\\= \sqrt{\sigma^2}\\\\= \sqrt{2}\\\\= 1.141[/tex]
Since the Grade of [tex]9^{th}[/tex] student's variance is higher than [tex]12^{th}[/tex]grade,
In point b:
Please find the attached file.
The plot above shows that the student of the ninth grade is spread more widely, as the student from 0-8 to 12 is from 0-4.
I really need the answer ASAP
100pts!!!PLZ answer my question for God's sake PLZ
3×2-2×y+c
hope that helps you
Answer:
lick a my suck a my
Step-by-step explanation:it is 3×2-2×y+c
Josh wants to add a model of a tree house to his model railroad layout how big should the tree be if the actual tree is 315 inches and the scale is 1:90
Answer:
3.5 inches on the scaled model
Step-by-step explanation:
So using the ratio, 1:90 I thought of two ways to solve this
1) Proportion
2) Equation
Using the proportion method
1:90=x:315
Now cross multiply
315=90x
Now solve and you’ll get 3.5
Equation is just
315/90=X?
Just solve and you’ll also get 3.5
...............................................................................................
Answer:
ummmmmmmmmmmmm ok but nice
Step-by-step explanation:
Please help ill give brainliest
Answer:
1- true
2- dairy
3- false
what is the greatest common factor of 24 40 and 56
The common factors for 24,40,56 24 , 40 , 56 are −8,−4,−2,−1,1,2,4,8 - 8 , - 4 , - 2 , - 1 , 1 , 2 , 4 , 8 .
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
24 divided by 3 = 8
40 divided by 5 = 8
56 divided by 7 = 8
GCF is basically the greatest common factor. Mostly the greatest number factor of these multiples.
A particle starts to move from rest in a straight line with an acceleration which increases with constant time rate from 1 ft./sec^{2} to 4 ft./sec^{2} in one second. prove that the particle will move a distance of 1 ft. in this second.
The particle's acceleration a increases at a constant rate, so that its average rate of change is equal to its instantaneous rate of change, which is equal to
(4 ft/s² - 1 ft/s²) / (1 s) = 3 ft/s³
The particles starts with acceleration a (0) = 1 ft/s², so we can determine its acceleration at time t by the fundamental theorem of calculus:
a(t) = a (0) + ∫₀ᵗ (3 ft/s³) du
a(t) = 1 ft/s² + (3 ft/s³) t
It also starts from rest, so with initial velocity v (0) = 0. Integrating again gives us the velocity function,
v(t) = v (0) + ∫₀ᵗ a(u) du
v(t) = ∫₀ᵗ (1 ft/s² + (3 ft/s³) u) du
v(t) = (1 ft/s²) t + 1/2 (3 ft/s³) t ²
Taking the particle's initial position to be x (0) = 0, compute the integral again to determine the distance it travels in 1 s:
x(t) = x (0) + ∫₀ᵗ v(u) du
x(t) = ∫₀ᵗ ((1 ft/s²) u + 1/2 (3 ft/s³) u ²) du
x(t) = 1/2 (1 ft/s²) t ² + 1/6 (3 ft/s³) t ³
→ x (1 s) = 1/2 (1 ft/s²) (1 s)² + 1/6 (3 ft/s³) (1 s)³ = 1 ft
write an equation in point slope form of the line that passes through the point (0,1) and has a slope if -3/2
Step-by-step explanation:
y - 1 = -3
x - 0 2
2y - 2 = -3x
2y = -3x + 2
A store is having a sale in which the cost of any item is 35% off.
Can the expression be used to find the cost, x, of an item?
Select Yes or No. Please look at your picture.
Answer:
1. no
2. yes
3. no
4. yes
Step-by-step explanation:
only the second and last expression works. If x is the final cost, and it is 35% off, then you are subtracting 0.35xor keeping 0.65x
please give thanks by clicking heart button! :)
GIVIVNG AWAY ALL MY POINTS FOR THIS QUESTION PLS ANSWER
Answer:
50 miles
Step-by-step explanation:
50 because 1 inch is 20 miles. There is two and a half inches.
Assume that when adults with smartphones are randomly​ selected, 63​% use them in meetings or classes. If adult smartphone users are randomly​ selected, find the probability that exactly of them use their smartphones in meetings or classes.
Answer:
Solved using binomial, probability = 5.7%
Step-by-step explanation:
Number of people (N) = 7
Probability of success (using phone) = 63% = 0.63
So, probability of failure (not using phone) = 1 - 0.63 = 37
Number of success (r) = 2
N c r . P^r . Q^n-r
7 c 2 (0.63)^2 (0.37)^5
= 21 (0.3969) (0.0069)
= 0.057
Easy Unit Rate. Help quick!
Answer:
vuguvcfhhhhhhhhcgyy
Find the value of x
Will give brainliest
4 ones + blank = 1 ten
Answer:
6 ONES
Step-by-step explanation:
Answer:
6 ones
Step-by-step explanation: