Given:
The first four terms of a sequence are:
8, 5, 2, -1
To find:
The function that defines the given sequence.
Solution:
We have,
8, 5, 2, -1
The differences between two consecutive terms are:
[tex]5-8=-3[/tex]
[tex]2-5=-3[/tex]
[tex]-1-2=-3[/tex]
The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.
The nth terms of an arithmetic sequence is:
[tex]f(n)=a+(n-1)d[/tex], for [tex]n\geq 1[/tex]
Where, a is the first term and d is the common difference.
Putting [tex]a=8,d=-3[/tex], we get
[tex]f(n)=8+(n-1)(-3)[/tex]
[tex]f(n)=8-3(n-1)[/tex]
[tex]f(n)=-3(n-1)+8[/tex], for [tex]n\geq 1[/tex]
Therefore, the correct option is A.
Can I have help :< Im stuck and confused
Answer:
B (the one upper right)
Step-by-step explanation:
1. X is at most, something, so x is = or <
2. X is at most 500 more than twice y ---> (2y + 500)
3. X ≤ 2y +500
4. Profits will be over 22500, so 22500 is less (<) than profit
5. Square of profits are 35 times x and 50 times y
6. P^2 = 35x + 50y
7. P = Square-root of (35x + 50y)
8. 22500 < Square-root of (35x + 50y)
Answer is (3) and (8), which is B
9.
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
A. (–2, 1); minimum
B. (–2, 1); maximum
C. (1, –2); minimum
D. (1, –2); maximum
Answer:
C. (1, –2); minimum
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The vertex is the turning point of the graph.
This is at (- 1, - 2)
The graph changes from decreasing to increasing at (- 1, - 2)
Hence is a minimum at (- 1, - 2)
A cylinder has a height of 5 feet. Its volume is 1,271.7 cubic feet. What is the radius of the cylinder?
Answer: [tex]9\ ft[/tex]
Step-by-step explanation:
Given
Height of the cylinder [tex]h=5\ ft[/tex]
Volume of the cylinder [tex]V=1271.7\ ft^3[/tex]
The volume of the cylinder is given by [tex]V=\pi r^2h[/tex]
Consider r be the radius of the circle
[tex]\Rightarrow 1271.7=\pi r^2\cdot 5\\\\\Rightarrow r^2=\dfrac{1271.7}{3.142\times 5}\\\\\Rightarrow r^2=80.948\\\Rightarrow r=8.99\approx 9\ ft[/tex]
Thus, the radius of the cylinder is [tex]9\ ft[/tex]
5w-8/3 =4w+2
Please solve with steps
Answer:
5w-8/3=4w+2
-8/3=-1w+2
-8=-1w+6
-14=-1w
14=w
Hope this helps, have a great day :)
What is the median of the following numbers?
10, 6, 4, 4, 6, 4, 1
Answer:
4
Step-by-step explanation:
4,7,2,x,2,9,6: the median is 5
Answer:
the median is 5
hope this helps
have a good day :)
Step-by-step explanation:
Ayaan does push-ups and sit-ups every morning. He does p push-ups and 2p + 5 sit-ups. Which statement describes the number of sit-ups Ayaan does every morning?
The number of sit-ups is 5 more than twice the number of push-ups he does.
The number of sit-ups is 5 more than half the number of push-ups he does.
The number of sit-ups is 5 fewer than twice the number of push-ups he does.
The number of sit-ups is 5 fewer than half the number of push-ups he does.
Answer:
A. The number of sit-ups is 5 more than twice the number of push-ups he does.
Step-by-step explanation:
Expressions:
p = push-ups done
2p + 5 situps = total situps
2p means that he does twice the amount of situps than he did as pushups.
+ 5 situps means that he does an extra 5 situps
Molly and her friends just dined at a restaurant and left a tip of $20.54, which was equal to exactly 30% of the total bill. What was the total bill in dollars? Round your answer to two decimal places.
Answer:
68.47
Step-by-step explanation:
30%=0.3
20.54/0.3=68.4666……
Which expression is equivalent to – 2x²y3 ( 4x2 + 3xy – 5y3)?
A. -8x4y3 - 6x3,4 + 10x2,6
B. _8x4 y3 - 6x2y3 + 10x2,9
OC. 2x4 y3 + x3y4 – 7x2,6
O D. 2x4y3 + x2y3 – 7x2y9
Quicklyyyy please
Answer:
A. -8x⁴y³ - 6x³y⁴ + 10x²y^6
Step-by-step explanation:
Given:
– 2x²y³ ( 4x² + 3xy – 5y³)
Open the parenthesis
= (– 2x²y³ * 4x²) + (– 2x²y³ * 3xy) - (– 2x²y³ * 5y³)
= -8x⁴y³ + (-6x³y⁴) - (- 10x²y6^6)
= -8x⁴y³ - 6x³y⁴ + 10x²y6^6
The correct answer is
A. -8x⁴y³ - 6x³y⁴ + 10x²y^6
Testing a robot. The robot is 17 inches tall and weighs 4 pounds. The employees of the company marked a grid on the floor and set the robot at (5,3). They programmed the robot to walk 2 yards east and 6 yards north each minute. What will
Answer:
After 7 steps, co-ordinate would be (35, 21) in the N-E direction
Step-by-step explanation:
Complete question
Testing a robot. The robot is 17 inches tall and weighs 4 pounds. The employees of the company marked a grid on the floor and set the robot at (5,3). They programmed the robot to walk 2 yards east and 6 yards north each minute. What will the co-ordinate after 7 steps
Solution
The grid on the floor is (5, 3)
5 is the X -co-ordinate and 3 is the y co-ordinate
Since the robot is walking in the north and east direction , it will be in the first co-ordinate only
After seven steps, in east direction, the co-ordinate would be 7 * 5 = 35
After seven steps, in north direction, the co-ordinate would be 7 * 3 = 21
So the co-ordinate would be (35, 21)
Hannah ordered a pizza. it was divided in 8 equal slices. Hannah ate two slices right away and another slice before bed. what friction of the pizza did she eat?
Answer:
3/8
Step-by-step explanation:
8 slices
she ate 2 and then another
3 in total
please someone help!!! i have no clue how to do this
Answer:
(5.84761111111)
Step-by-step explanation:
Length of an arc = 67/360 ×2×3.142×5
=Rationalize(5.84761111111)
Find the volume of the cone using 3.14 for pi. Please help asap i need it!
Answer:
29.32
Step-by-step explanation:
We are given the diameter on the bottom, so we can find the radius. Since a radius is half the diameter, the radius is 2mi. The formula for the volume of a cone is:
1/3 * pi * r^2 * h
We can substitute:
1/3 * pi * 2^2 * 7
29.32153
This rounds to about 29.32
Answer:
V = 117.23
Step-by-step explanation:
V = (1/3) pi x r^2 x h
Input.
V = (1/3) 3.14 x 4^2 x 7
V = (1/3) 3.14 x 16 x 7
V = (1/3) 3.14 x 112
V = (1/3) 351.68
V = 117.23
Note: Please disregard my answer as I used the incorrect radius. I needed to find the correct radius instead of using the diameter as it was.
A company rents bikes. The price, p, in dollars, to rent a bike for h hours can be found using the formula p (h)= 14 + 3h. What is the price to rent a bike for 2 hours?
$4 I got it right on a quiz
If the relation is given as p (h)= 14 + 3h. Then the price to rent a bike for 2 hours will be $20.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A company rents bikes.
The price (p) in dollars, to rent a bike for h hours can be found using the formula p (h)= 14 + 3h.
Then the price to rent a bike for 2 hours will be
p (h)= 14 + 3 x 2
p (h)= 14 + 6
p (h)= $20
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ2
different names were put into a hat. A name is chosen times and the name is chosen times. What is the experimental probability of the name being chosen? What is the theoretical probability of the name being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Answer:
the answer is 13/103
Step-by-step explanation:
Factor the following, I will give 5 stars and thanks.
Answer:
17) [tex]k=-5,-6[/tex]
18) [tex]x=6,4[/tex]
19) [tex]k=-2,-6[/tex]
20) [tex]v=6,-3[/tex]
Step-by-step explanation:
What is the value of a?
a+36°
a-27°
Answer:
hope this will help you more
Carlos bought a new skateboard for $99.46 and a helmet and pad for $73.49. How much did Carlos spend in all?
I nee it done today
Answer:
Step-by-step explanation:
173
what is the result of subtracting the second equation from the first?
2x+7y=-8 - 2x-5y=-1
Answer:
12y = -7
Step-by-step explanation:
Need help ASAP and please don't be a scammer
Is this an enlargement or a reduction? How do you know?
Answer:
Reduction
Step-by-step explanation:
The resulting shape M'S'V' is smaller than the original shape MSV, so it is therefore classified as a reduction.
Find the value of:x^0+3
Answer:
4
Step-by-step explanation:
x^0 means 1. so 1+3=4
I need help immediately, you’ll receive brainlest if answered correctly!!!
Answer: 120
Step-by-step explanation:
Answer:
120°
Step-by-step explanation:
MORE MATH GENIUSES!!!!!!!!!!!!!!
Answer:
The friend caught the ball at 2 feet.
Step-by-step explanation:
1. False; the ball was not still in the air at 1 second the x-component of the vertex is 0.5.
2. False; the x-component of the vertex is 0.5
3. True; the ball was tossed at a height of 2 feet (when x=0, y=2), it is safe to assume the ball was caught at the same height.
4. False; when x = 0, y = 2.
Write in standard form: forty-seven hundredths
Answer:
0.47
Step-by-step explanation:
0.47
47 hundredths is equal to 0.47.
If this helps please mark as brainliest
Answer:
The standard form of forty-seven hundredths is 0.47.
Step-by-step explanation:
Have a nice day! :-)
TeamRocket3
hey! i’ll give brainliest please help
Answer:
B
Step-by-step explanation:
Four friends, Abe, Bob, Carl, and Darrel, are going to a fun park .They want to ride go-karts. The price to ride the go-karts is $2.15 for 5 minutes,$4.00 10 minutes ,or $6.75 for 15 minutes .Which price is the best deal?Explain why? math question
Answer:
Since in this option the minute is paid at $ 0.40, the best option is 10 minutes for $ 4.
Step-by-step explanation:
Since four friends, Abe, Bob, Carl, and Darrel, are going to a fun park, and they want to ride go-karts, and the price to ride the go-karts is $ 2.15 for 5 minutes, $ 4.00 for 10 minutes, or $ 6.75 for 15 minutes, to determine which price is the best deal, the following calculations must be performed:
2.15 / 5 = 0.43
4/10 = 0.40
6.75 / 15 = 0.45
Therefore, since in this option the minute is paid at $ 0.40, the best option is 10 minutes for $ 4.
6 $44 is shared between David, Jo and Mary in the ratio 2:3:5
How much does each receive?
Answer:
David=$8.8
Jo=$13.2
Mary=$22
Step-by-step explanation:
2+3+5=10
44/10=4.4
David=4.4x2=$8.8
Jo=4.4x3=$13.2
Mary=4.4x5=$22
8.8+13.2+22=44
Using the unit circle, determine the value of sin(-240°).
A) -1/2
B) √3/2
C) 1/2
D) -√3/2
Answer:
B. √3/2.
Step-by-step explanation:
If we follow the circle from (1,0) clockwise through 240 degrees we end up at 120 degrees.
sin(120)
= √3/2
Find the volume of each figure. Simplify your answers.
Please help ASAPPPP
thank you so much!!!!
Answer:
[tex]98.28\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is the width of the prism, and [tex]h[/tex] is the height of the prism.
Substituting given values, we get:
[tex]V=2.5\cdot 4.25\cdot 9.25=98.28125\approx \boxed{98.28\:\mathrm{ft^3}}[/tex]
Since "Simplify your answers" is very subjective, I've rounded to the nearest hundredth as that is reasonably universal, but you may need to adjust the rounding as desired.
Jada's test scores were 80, 80, 82, and 86. Find the MEAN.
Answer:
82
Step-by-step explanation:
80+80+82+86
328/4
82
Answer:
82
Step-by-step explanation:
mean-the average of numbers in a data set
[tex]mean=\frac{80+80+82+86}{4}[/tex]
[tex]mean=\frac{328}{4}[/tex]
[tex]mean=82[/tex]