The correct form of the geometric sequence is:[tex]5, 35, 245, 1,715, ... = 5, 5 * 7, 5 * 7^2, 5 * 7^3, ...[/tex]
how to Identify the correct form of the geometric sequence.To identify the correct form of the geometric sequence 5, 35, 245, 1,715, ..., we can look for a common ratio between consecutive terms.
To find the common ratio, we divide any term by its preceding term. Let's take the second and first terms:
35 / 5 = 7
Now, let's check the third and second terms:
245 / 35 = 7
Similarly, for the fourth and third terms:
1,715 / 245 = 7
Since we obtained the same result (7) for all ratios, we can conclude that the common ratio of this geometric sequence is 7.
Now, let's express the general form of the sequence using the first term (a) and the common ratio (r):
a, ar, [tex]ar^2,[/tex] [tex]ar^3,[/tex] ...
Substituting the given values:
a = 5 (the first term)
r = 7 (the common ratio)
The correct form of the geometric sequence is:
[tex]5, 5 * 7, 5 * 7^2, 5 * 7^3[/tex], ...
Simplifying the terms, we get:
5, 35, 245, 1,715, ...
Therefore, the correct form of the geometric sequence is:
5, 35, 245, 1,715, ... = 5, 5 * 7, 5 * 7^2, 5 * 7^3, ...
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Need some help with geometry not very good at it.
Can I have some help please?
Answer:
your answer will be A. 12/24
Step-by-step explanation:
XZ=12+12=24
COSX=12/24
hope this helps you...
Please help! Answer and explanation please!
Answer:
12
Step-by-step explanation:
Since we can infer that those lines are the same length...
5x-15 = 3x+9
2x -15 = 9
2x = 24
x = 12
The table shows the cost of hiring a concrete mixer for up to 5 days.
1
2
Number of days
3
4
5
19
45
Cost in £
32
58 71
The cost of hiring the concrete mixer is made up
of a fixed charge and a daily charge.
(1)
(i) How much is the daily charge? £
(1)
(ii) How much is the fixed charge? £
Tota
Answer:
i. daily charge = £13
ii. fixed charge = £6
Step-by-step explanation:
Number of days (x) | Cost in £ (y)
1 | 19
2 | 32
3 | 45
4 | 58
5 | 71
Using the given table, we can represent this situation with an equation in slope-intercept form, y = mx + b, where,
m = slope = daily charge
b = y-intercept = fixed charge
✔️Thus, using the coordinates of any two given pairs, say (1, 19) and (2, 32):
Slope (m) = ∆y/∆x = (32 - 19)/(2 - 1) = 13/1
Slope (m) = 13
Therefore daily charge = £13
✔️To find y-intercept (b), substitute (x, y) = (1, 19) and m = 13 into y = mx + b.
Thus:
19 = (13)(1) + b
19 = 13 + b
b = 19 - 13
b = 6
Therefore, fixed charge = £6
✔️Substitute m = 13 and b = 6 into y = mx + b to represent the function given for the situation:
y = 13x + 6
9. A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.9, and the probability that it is received incorrectly (as a 1) is 0.1. When a 1 is sent, the probability that it is received correctly is 0.8, and the probability that it is received incorrectly (as a 0) is 0.2. (a) Find the probability that a 0 is received. (b) Use Bayes theorem to find the probability that a 0 was transmitted, given that a 0 was received.
Answer:
a) 0.6667 = 66.67% probability that a 0 is received.
b) 0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
(a) Find the probability that a 0 is received.
0.9 of 2/3(0 received when a 0 is sent).
0.2 of 1/3(0 received when a 1 is sent). So
[tex]p = \frac{0.9*2}{3} + \frac{0.2*1}{3} = 0.6667[/tex]
0.6667 = 66.67% probability that a 0 is received.
(b) Use Bayes theorem to find the probability that a 0 was transmitted, given that a 0 was received.
Event A: 0 received
Event B: 0 transmitted.
0.6667 = 66.67% probability that a 0 is received, which means that [tex]P(A) = 0.6667[/tex]
A zero is transmitted two-thirds of time, which means that [tex]P(B) = 0.6667[/tex]
When a 0 is sent, the probability that it is received correctly is 0.9, which means that [tex]P(B|A) = 0.9[/tex]
So
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.6667*0.9}{0.6667} = 0.9[/tex]
0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.
I’m pretty sure the answer is a ?
okok so this isnt a question but as i was scrolling through brainly and suddenly the lights went off and everybody was in the living room, the door was closed and it wasnt a electricity problem somrwiefnau help im nervous i don know what to do
Cart 1 (500 g) moves to the right at 0.40 m/s. Cart 2 (250g) moves to the left at 0.50 m/s. a. If the carts stick after the collision, what will be their velocity?
Answer:
after the collision cart 1 will stop and cart 2 will keep moving will 0.1.m/s after stop.
algebra 2
Can you help me pls
Answer:
ln25 = 3.219
ln50 = 3.912
ln22.3 = 3.105
lne^3 = 3lne = 3
ln0.45 = -0.799
Step-by-step explanation:
Calculator
the square root of 125 is closest to what whole number? *
Answer:
11
Step-by-step explanation:
the square root of 125 is 11.18033989 so when you round it you get 11
Which statement best describes the point (2,-5)
A.5 units to the left and 2 units up from the origin
B. 5 units to the right and 2 units up from the origin
C. 2 units from the left and 5 units down from the origin
D. 2 units to the right and 5 units down from the origin
HELPPPPPP!!!!!!!
Select the correct answer from each drop-down menu.
A cylinder has a diameter of 10 units.
Its radius is
units. If its height is twice its radius, its height is
units. Its volume is about
cubic units
Answer:
1st blank: 5
2nd blank: 10
3rd blank: 785
Step-by-step explanation:
the radius of a circle or the base/top of a cylinder is measured from the center to the side of the face, where as the diameter is measured from side to side through the middle, so the diameter will always be twice the radius of the same circle, meaning if the diameter is 10 units, then the radius will be half that, 5 units, then all we do is double the radius like the question says to get the height (NOTE this is NOT part of any formula for finding any dimensions for any shape and is specific to this question) then all we do to find the volume is use the formula below
V = (pi) (r^2) h
plug the radius or 'r' in as well as height or 'h' in the equation and solve
PLEASE NOTE: the question is asking for an APROXAMATE so your answer should be close to one of the drop down options by about >1 integer, but will not be exact
Plz help me! Plz it’s due today,!
Answer: I think it is D
Step-by-step explanation:
in volume you multiply all the numbers(LxWxH)
hope this helps
please help this is due today
Answer:
A and D
Step-by-step explanation:
A) x = 3
B) x = 0
C) x = ⅓
D = x = 3
Answer:
A and D
Step-by-step explanation:
The three angles of triangle are in
the ratio 2:3:5. Calculate the size of
the smallest angle.
A. 90°
B.549
C.36
D. 30°
E. 20°
AN
D
♡
Answer:
E I think
..........hope this helps
PLEASE PLEASE HELP!! A ferris wheel with a radius of 38 feet rotates at a rate of 8 revolutions per minute. The height above the ground of the carriage labeled C below is a function of time, t, in minutes
Please help me quick
Answer: 20 inches
Step-by-step explanation:
using pythagorean theorem according to which hypotebous ^2=altitude ^2+base^2
c^2=a^2+b^2
c^=(12)^2+(16)^2
c^2=144+256
c^2=400
c=20
How many solutions does the system of equations have?
a. no solution
b. one solution x=0, y=5
c. One solution x=1, y=4
d. Infinitely many solutions
Answer:
one solution at x=1,y=4 point
Two trains on opposite tracks leave the same station at the same
time. One train travels at an average speed of 80 kilometers per
hour and the other travels at an average speed of 70 kilometers
per hour. How long after they leave the station will they be 50
km apart?
Answer:
20 minutes( 0.3333 hours) after they leave the station will they be 50 km apart, if the Two trains on opposite tracks leave the same station at the same time.
Step-by-step explanation:
One train travels at an average speed of 80 km/hr and the other travels at an average speed of 70 km/hr.
someone please help me answer this!!
Answer:
0.55x10= 5.50
Step-by-step explanation:
For each value of u , determine whether it is a solution to 23=4u-1 .
Answer:
6
Step-by-step explanation:
Transposition
23+1=4u
24=4u
Divide both side by 4
u=6
Games at the carnival cost $3 each. The prizes awarded to winner cost $145.65. How many games must be played to make at least $50?
Answer:About 17 games
Step-by-step explanation:
$50 divided by $3 is about 17 games
How are the acute angles of the right triangle below related? Please don’t answer me with a link
Answer:
An acute angle is an angle whose measure is less than 90∘. That is, in a pair of intersecting non-perpendicular lines, the smaller of the angles are acute. A right angle is an angle whose measure is equal to 90∘. That is the measure of the angles of perpendicular lines.
Step-by-step explanation:
Can someone please help i would really appreciate it
Answer:
[0, -7, 1]
[0, 3, 4]
Select all the statements that are true
Answer:
Options 2, 4 and 6 are True.
Step-by-step explanation:
Triangle MNO is dilated by a scale factor of [tex]\frac{3}{2}[/tex] centered at M(0, 6).
Rule to be followed to dilate the vertices of the given triangle,
(x, y) → (kx, ky)
Here, k = scale factor
By this rule vertices of the new triangle M'N'O' will be,
M(0, 6) → M'(0, 6) [Coordinates of M' will remain same as M because center of dilation is point M]
N(-4, -4) → N'(-6, -6)
O(6, -2) → O'(9, -3)
Option 1
M'N' is shorter than MN
Distance between M and N = [tex]\sqrt{(0+4)^2+(6+4)^2}[/tex]
= 10.77
Distance between M' and N' = [tex]\sqrt{(0+6)^2+(6+6)^2}[/tex]
= 13.42
Therefore M'N' > MN
Therefore, Option A is False.
Option 2
ON is shorter than O'N'
True.
Option 3
OM is longer than O'M'
False
Option 4
ON is parallel to O'N'
Since OM and MN are dilated with the same scale factor, O'N' will be parallel to ON.
True.
Option 5
OM is parallel than O'M'
Since, O'M' is the dilated form of OM,
Therefore, all the points (O, M and M') will be in a straight line.
False
Option 6
M'N' coincide with MN
True.
Therefore, Options 2, 4 and 6 are True.
This graph is the parent function of quadratic functions
True or false
If Tyesha only wants to eat 115 calories of the Italian Ice, how many ounces is she allowed to eat?
Answer:
Answered!!
Step-by-step explanation:
If Tyesha only wants to eat 115 calories of the Italian Ice, how many ounces is she allowed to eat? In this case she is only allowed to eat 10 ounces
Mike did so well with his bike sale, he's going to Discount his helmets 15% off. If the Sale Price is $23.80, find the ORIGINAL PRICE of a helmet.
Answer:
$3.57
Step-by-step explanation:
Multiply $23.80 by %15
Change %15 to a decimal by multiplying it by 100.
0.15 x $23.80= $3.57
A group of volunteers has been collecting toys to deliver to a local charity. Over the last 3 days, the volunteers have collected 324 toys. What has been their collection rate, in toys per day?
A.
110 toys per day
B.
105 toys per day
C.
107 toys per day
D.
108 toys per day
Answer:
D 108
Step-by-step explanation:
324/3=108
Answer: 108 toys per day
Step-by-step explanation: 324/3
Calculate the value of the expression. 4+2 (17 – 12)
Answer:
14
Step-by-step explanation:
4+34-24 (distribute)
Which graph could represent a function f(x) = log(x + b) where b < 0?
Answer:
I think that the answer would be B .
Hope it helps . ♡