Given:
[tex]a_n=a_{n-1}+3[/tex]
[tex]a_0=2[/tex]
To find:
The values [tex]a_1,a_2,a_3[/tex].
Solution:
We have,
[tex]a_n=a_{n-1}+3[/tex]
For [tex]n=1[/tex],
[tex]a_1=a_{1-1}+3[/tex]
[tex]a_1=a_{0}+3[/tex]
[tex]a_1=2+3[/tex]
[tex]a_1=5[/tex]
For [tex]n=2[/tex],
[tex]a_2=a_{2-1}+3[/tex]
[tex]a_2=a_{1}+3[/tex]
[tex]a_2=5+3[/tex]
[tex]a_2=8[/tex]
For [tex]n=3[/tex],
[tex]a_3=a_{3-1}+3[/tex]
[tex]a_3=a_{2}+3[/tex]
[tex]a_3=8+3[/tex]
[tex]a_3=11[/tex]
Therefore, [tex]a_1=5,a_2=8,a_3=11[/tex].
The value of [tex]\rm a_1=5[/tex], [tex]\rm a_2=8[/tex], and [tex]\rm a_3=11[/tex] and this can be determined by using the arithmetic operations and the given data.
Given :
Let {an} be a sequence that satisfies the recurrence relation [tex]\rm a_n=a_{n-1}+3[/tex] for n = 1, 2, 3,... and suppose that [tex]\rm a_0=2[/tex].
According to the given data, the recurrence relation is given below:
[tex]\rm a_n=a_{n-1}+3[/tex] --- (1)
Now, substitute the value of (n = 1) in the above expression.
[tex]\rm a_1=a_{1-1}+3[/tex]
[tex]\rm a_1=a_{0}+3[/tex] (put [tex]\rm a_0=2[/tex])
[tex]\rm a_1=2+3[/tex]
[tex]\rm a_1=5[/tex]
Now, substitute the value of (n = 2) in the expression (1).
[tex]\rm a_2=a_{2-1}+3[/tex]
[tex]\rm a_2=a_{1}+3[/tex] (put [tex]\rm a_1=5[/tex])
[tex]\rm a_2=5+3[/tex]
[tex]\rm a_2=8[/tex]
Now, substitute the value of (n = 3) in the expression (1).
[tex]\rm a_3=a_{3-1}+3[/tex]
[tex]\rm a_3=a_{2}+3[/tex] (put [tex]\rm a_2=8[/tex])
[tex]\rm a_3=8+3[/tex]
[tex]\rm a_3=11[/tex]
For more information, refer to the link given below:
https://brainly.com/question/10168678
What is 12+[2-(4*a2)]÷7+b
Answer:
86 - 4a^2 + 7b over 7
Step-by-step explanation:
Explain whether 13t−3t is equivalent to 3t−13t. Support your answer by evaluating the expressions for t=2.
Answer:
Not equivalentStep-by-step explanation:
13t - 3t = (13 - 3)t = 10t3t - 13t = (3 - 13)t = -10t10t ≠ -10tThey are not equivalent
When t = 2
13t - 3t = 13*2 - 3*2 = 26 - 6 = 203t - 13t = 3*2 - 13*2 = 6 - 26 = -20Answer:
They are not Equivalent.
Step-by-step explanation:
You can tell that they aren't by doing that equations.
13t-3t=10t
3t-13t=-10t
If you were to inert 2 into t's , spot, it still would not work.
13(2)-3(2), 26-6=20
3(2)-13(2), 6-26=-20
A bag contains 9 orange marbles and 36 green marbles. If a representative sample contains 2
orange marbles, then how many green marbles would you expect it to contain? Explain.
Because the ratio of orange marbles to green marbles is in the population, the expected number
of green marbles is times the number of orange marbles in the representative sample. There
should be green marbles.
Answer:
U can divide or multiply
Step-by-step explanation:
pls help asap!!!! and show work if you can!! :)
Answer:
vertex is y=x squared
axis of symmetry is x=-1
parabola= (-2,0) and (-3,2)
Step-by-step explanation:
follow steps
Answer:
As per graph we have
1. Vertex is:
(-1, -1)2. Axis of symmetry is a vertical line that passes through vertex:
x = -13. Roots, the x-intercepts:
(-2, 0), (0, 0)ZABD and ZDBC are supplementary angles.
What is the measure of x?
x = [?]°
DK
Х
AK
140°
B
>C
Angles are not drawn to scale.
Enter
Answer:
the answer would be 40
Step-by-step explanation:
supplementary angles are 180
180-140=40
x=40
a submarine was floating at a depth of 640m below the sea level. if it ascends 230 metres, what will be it's new position? express the position in terms of depth
Answer: It would be 410 meters below sea level.
→Pikachu I choose u←
simplfiy 3(4)^2 plzzz
Answer:
48
Step-by-step explanation:
Key
X
= -X
= 1 = -1
Which equation could represent the model?
Answer:
hey here the link it.ly/3dXyuz8
The square of a number decreased by ten times the number is negative nine.
Answer:
answers are 1 and 9
Step-by-step explanation:
x² - 10x = -9
x² - 10x + 9 = 0
(x - 9)(x - 1) = 0
x = 9, x = 1
Answer:
Replace key words with variables, numbers, and operations. “A number squared” is a power where the base is the variable and the exponent is 2. “Decreased by ten” means you must subtract 10 from the squared number.
Step-by-step explanation:
hope this helps
plzz help me i’ll give brainlest
Answer:
An octagonal prism has 10 faces.
Step-by-step explanation:
Please mark as brainliest!
A ratio of the number of boys to the number of girls in a choir is 5 to 4. There are 60 girls in the choir
HELP PLEASEE no links
Select all the shapes that do not have perpendicular sides.
A. Square
B. Equilateral triangle
C. Rectangle
D. Right triangle
E. Acute triangle
Answer:
B) equilateral triangle
E) acute triangle
Step-by-step explanation:
I really need help it’s due by 12:00
Answer:
what do you do
Step-by-step explanation:
would anoyone be willing to help
Sure, what do you need help with?
A credit card company decides to study the frequency with which its cardholders charge for items from a certain change of retail stores. The data values collected in the study appear to be normally distributed with a mean of 25 charged purchases and a standard distribution of 2 charged purchases. Out of the total number of cardholders about hw many would you expect are charging 27 or more in the study
Answer:
15.87% of the total number of cardholder would be expected to be charging 27 or more in the study.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 25 charged purchases and a standard distribution of 2
This means that [tex]\mu = 25, \sigma = 2[/tex]
Proportion above 27
1 subtracted by the pvalue of Z when X = 27. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27 - 25}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
Out of the total number of cardholders about how many would you expect are charging 27 or more in the study?
0.1587*100% = 15.87%
15.87% of the total number of cardholder would be expected to be charging 27 or more in the study.
which is the correct graph and solution for the following system of equations y=2x+3 y=-x-6
Answer:
last graph
Step-by-step explanation:
ZA and B are supplementary angles. If m A = (7x +3) and m ZB = (7x +23)", then find the measure of ZA.
Answer:
Angle A measures 80º.
Step-by-step explanation:
Supplementary angles:
Two angles are called supplementary when their measures add to 180º.
In this question:
Angle A measures 7x + 3
Angle B measures 7x + 23
Since they are supplementary:
[tex]A + B = 180[/tex]
[tex]7x + 3 + 7x + 23 = 180[/tex]
[tex]14x + 26 = 180[/tex]
[tex]14x = 154[/tex]
[tex]x = \frac{154}{14}[/tex]
[tex]x = 11[/tex]
Measure of Angle A:
Since x = 11
7*11 + 3 = 77 + 3 = 80º
Angle A measures 80º.
The diameter of a circle is 86 kilometers. What is the circle's area?
use 3.14 for pi or 22/7
Please help me lol
Answer:
5808.8km
Step-by-step explanation:
5. What does ARM stand for?
Answer:
Step-by-step explanation: ARM architecture
Find the 93rd term of the arithmetic sequence -11, -7, -3
Answer:
357
Step-by-step explanation:
hello :
note : the n th term of an arithmetic sequence is :
An =A1+(n-1)d ....a common difference is : d and A1 the first term
in this exercice : d = -3-(-7) =-7-(-11) = 4 A1 = -11
when : n =93 you have the 93rd term A93
so : A93 = -11 +(93-1)(4)
A93 = 357
Please i need help with this
Answer:
B.
Step-by-step explanation:
A study was conducted to compare the mean numbers of police emergency calls per 8-hour shift in two districts of a large city. Samples of 100 8-hour shifts were randomly selected from the police records for each of the two regions, and the number of emergency calls was recorded for each shift. The sample statistics are listed here:
Sample size region 1: 100
Sample size region 2: 100
Sample mean region 1: 2.4
Sample mean region 2: 3.1
Sample variance region 1: 1.44
Sample variance region 2: 2.64
Find a 90% confidence interval for the difference in the mean numbers of police emergency calls per shift between the two districts of the city. Interpret the interval.
Answer:
Step-by-step explanation:
EOC Review
Sue hits a ball from a height of 4 feet. The height of the ball above the ground is a function of the
horizontal distance the ball travels until it comes to rest on the ground. Consider
this complete graph of
the function.
Trajectory of Ball
80
60
Height of Ball (ft)
40
20
0
20 60 100 140 180
Horizontal Distance
the Ball Travels
Select all values that are in the domain of the function as shown in the graph.
DDDDD
D-5 feet
O feet
60 feet
200 feet
220 feet
Answer:
0ft and 60ft
Step-by-step explanation:
Given
The attached function
Required
Determine the valid values of the domain of the function
To do this, we simply consider the starting point and the end point of the trajectory on the x-axis (i.e. the horizontal distance).
From the attached graph, the horizontal distance starts from 0 and ends at 180.
This implies that the domain is: [tex]0 \le x \le 180[/tex]
From the options, the values that fall in this bracket are 0ft and 60ft
Scott paid 10.47 for a 6.08 - kg bag of dog food. A few weeks later, he paid 13.88 for a7.48 -kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.
Answer:
Scott paid $ 1.72 per kilo for the first bag, and $ 1.85 per kilo for the second bag, with which the best buy is the first bag.
Step-by-step explanation:
Since Scott paid 10.47 for a 6.08-kg bag of dog food, while a few weeks later, he paid 13.88 for a7.48-kg bag at a different store, to find the unit price for each bag, and then state which bag is the better buy based on the unit price, the following calculation must be performed:
10.47 / 6.08 = X
1.72 = X
13.88 / 7.48 = X
1.85 = X
Thus, Scott paid $ 1.72 per kilo for the first bag, and $ 1.85 per kilo for the second bag, with which the best buy is the first bag.
PLEASE HELP!!! WILL MARK BRAINLIEST PLUS EXTRA POINTS
To complete an observation the healthcare worker needs to think about the target of the observation To complete an observation, the healthcare worker needs to think about...
A) the target of the observation, such as the patient.
B) the nature of the observation or the focus, which can be a behavioral observation or an analysis of the information gathered.
C) the aim of the observation, such as the workup.
D) the focus of the observation, such as the patient's condition.
E) the focal point of the observation, such as the patient's previous medical records.
CHECK ALL THAT APPLY
Answer:
1,2, and 4
Step-by-step explanation:
I am stuck on these last four questions please help if possible.
-Solving equations with variables on both sides
Answer:
Step-by-step explanation:
9). -2.2(4 - 1.9x) = 3.3(0.2x - 0.8)
-8.8 + 2.2(1.9x) = 0.66x - 2.64
-8.8 + 4.18x = 0.66x - 2.64
4.18x - 0.66x = 8.8 - 2.64
3.52x = 6.16
x = 1.75
10). 3.2(1 + 2.6x) = 2.4(x - 3.6)
3.2 + 8.32x = 2.4x - 8.64
8.32x - 2.4x = -3.2 - 8.64
5.92x = -11.84
x = 2
11). 4.6(2x - 5.5) = 3.9 + 0.8(1 + 5.5x)
9.2x - 25.3 = 3.9 + 0.8 + 4.4x
9.2x - 25.3 = 4.7 + 4.4x
9.2x - 4.4x = 25.3 + 4.7
4.8x = 30
x = 6.25
12). 0.2(3x + 2.5) - 4.9 = 3.8 - 2.2(x - 5.5)
0.6x + 0.5 - 4.9 = 3.8 - 2.2x + 12.10
0.6x - 4.4 = -2.2x + 15.90
0.6x + 2.2x = 15.90 + 4.4
2.8x = 20.30
x = 7.25
A person had a rectangular-shaped garden with sides of lengths 16 feet and 9 feet. The garden was changed into a square design with the same areas as the original rectangular-shaped garden. How many dlfewt in length are each of the sides of the new square-shaped garden?
Answer:
144
Step-by-step explanation:
16x9
The side length of the square garden would be 12 ft.
What is a expression? What is a mathematical equation? What is the volume of a cube and a prism?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. The volume of a cube is - [V] = a x a x a- where [a] is side length of cube.
The volume of a prism is - [V] = [h] × [w] × [L]- where [h] is prism height, [w] is its width, and [L] is its length.
We have a person who had a rectangular-shaped garden with sides of lengths 16 feet and 9 feet.
The garden was changed into a square design with the same area as the original rectangular-shaped garden. Assume the side length to be [x] ft. Then, you can write -
x² = 16 x 9
x² = 144
x = 12
Therefore, the side length of the square garden would be 12 ft.
To solve more questions on area and volumes, visit the link below -brainly.com/question/29424737
#SPJ2
The circumference of the base of a
5
-foot-high cylinder is
46
inches. What is the volume of the cylinder?
Answer:
V≈33238.05
Step-by-step explanation:
The circumference of the cylinder base is
= ( 2 )*(pi)*( r ) cm where r = radius of the circular base.
That is ( 2 )(pi)( r ) = ( 44 )cm or
( radius ) = [ (44/((2)(pi)) ] = ( 7.0064 )cm.
I have approximated ( pi ) as ( 3.14 ) for this calculation.
The area of the cylindrical base is ( pi )*( radius )^2
Therefore area of the base
= ( 3.14 )*( 7.0064 )^2 =( 154.1415 )cm squared.
Volume of Cylinder
Volume = Atea of the base multiplied by cylinder height or
= ( 154.1415 ) * ( 7 )
= ( 1079.0 ) cubic centimeters approximately with some slight loss inaccuracy due to rounding of pi.
Lateral Surface Area
The lateral surface area = circumference of the cylindrical base multiplied by the height of the cylinder.
= ( 44 )*( 7 ) = ( 308 ) cm squared
Inherent Assumption
It is assumed that the thickness of the cylinder material is small and the cylinder doesn't overlap the area of the base. If it did, the lateral surface area calculated here might be understated slightly.
Which chocolate chip cookies have the greater spread in the number of chips per cookie?
Regular
or
Reduced Fat
Step-by-step explanation:
18
Answer:
Reduced fat had the greater spread.
Step-by-step explanation:
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if it satisfies the given conditions. The person holding ticket 47 wins one of the prizes.
Answer:
The total number of ways the person holding ticket 47 wins one of the prizes = 941,094
Step-by-step explanation:
Given - One hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti).
To find - How many ways are there to award the prizes if it satisfies the given conditions. The person holding ticket 47 wins one of the prizes.
Proof -
The order of selection is important because 1st selection is grand prize , 2nd selection is second prize and so on . So , we use permutation for this question
Now,
As The person holding ticket 47 wins one of the prizes and other 3 prizes are also given to the remaining 99 persons who got chosen
So,
The number of ways = 1* ⁹⁹P₃
= [tex]\frac{99!}{(99-3)!}[/tex]
= [tex]\frac{99!}{96!}[/tex]
= [tex]\frac{99*98*97*96!}{96}[/tex]
= 99*98*97
= 941,094
∴ we get
Total number of ways the person holding ticket 47 wins one of the prizes = 941,094