Please help me find the answers to all the questions whoever answers all the question I will mark the brainlest.
Answers
Answer:
[tex]\textsf{a)} \quad \textsf{Recursive Rule}: \quad a_n=5n-2[/tex]
[tex]\textsf{Explicit Rule}: \quad \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]
b) 4998
c) explicit rule (see below for explanation)
d) see below
Step-by-step explanation:
An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Part aExplicit Formula
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termn is the number of the termd is the common differenceGiven sequence: 3, 8, 13, 18, 23, ...
To find the common difference, subtract one term from the next term.
Therefore:
a = 3d = 8 - 3 = 5Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:
[tex]\implies a_n=3+(n-1)5[/tex]
[tex]\implies a_n=3+5n-5[/tex]
[tex]\implies a_n=5n-2[/tex]
Recursive Formula
[tex]a_n=a_{n-1}+d \quad \textsf{for }n\geq 2[/tex]
where:
[tex]a_n[/tex] is the nth term[tex]a_{n-1}[/tex] is the term immediately before the nth termd is the common differenceWe already know the common difference our previous calculations.
Therefore:
[tex]\implies a_n=a_{n-1}+5[/tex]
When giving a recursive rule we also have to define the first term of the sequence, as it is not part of the formula. Therefore, the full recursive rule for the given sequence is:
[tex]\begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]
Part bTo find the 1000th term of the sequence, use the explicit rule and substitute n = 1000:
[tex]\implies a_{1000}=5(1000)-2[/tex]
[tex]\implies a_{1000}=5000-2[/tex]
[tex]\implies a_{1000}=4998[/tex]
Therefore, the 1000th term of the sequence is 4998.
Part cWe used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence without having to know any previous terms.
Part dThe disadvantage of a recursive rule when compared to an explicit rule is that we need to know the previous term to find the nth term, whereas the explicit rule doesn't need this information.
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Related Questions
Write the interval using interval notation to describe the set of values shown above.
Use "U" between the two intervals. Use "oo" (two lower case o's) for
∞.
Answers
The interval on the number line is (-∞, 2) U [3, ∞)
How to determine the interval?From the number line, we have the following inequalities
x < 2 and x ≥ 3
In inequalities, < and > are represented by brackets i.e. ( and )
While ≤ and ≥ are represented by square brackets i.e. [ and ]
So, we have:
x < 2 and x ≥ 3 = 2) and [3
The intervals must be closed and opened with infinity symbols.
So, we have:
x < 2 and x ≥ 3 = (-∞, 2) and [3, ∞)
Replace and with U
x < 2 and x ≥ 3 = (-∞, 2) U [3, ∞)
Hence, the interval on the number line is (-∞, 2) U [3, ∞)
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Pls help on algebra homework. Will mark brainliest!
Answers
Answer:
H)
Step-by-step explanation:
First, Length XY is 20 centimeters. Since YZ = 3/5 XY, [tex]\frac{3}5\times20=12[/tex]
YZ = 12 + 20 = 32 cm, hence H)
Hope you have a nice day! (Pls mark brainliest)
GIVING BRAINLIEST TO THE BEST ANSWER! Choose the proportion to use to solve side LM.
A. 9/13.5 = x/11
B. 9/11 = 13.5/x
C. 9/13.5 = x/21
D. 9/11 = x/21
(the / represents fractions)
Answers
The equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM
Similarity theorem of triangleIn order to find the measure of LM, we will take the ratio of the sides of the similar triangles.
Using the equation as shown
DF/EF = LK/LM
DF/LK = EF/LM
Substitute the measure of the sides
9/13.5 = 14/LM
Hence the equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM
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Rationalize 5+2√3 / 7+4√3
Answers
Answer:
Answer is in the 2nd attachment
Step-by-step explanation:
the first attachment is the work done.
The difference of two complementary angles is 48. Find the measures of the two angles.
The smaller angle is
Submit Question
and the larger angle is
B
Answers
The larger angle is 55 deg at the larger angle.
We have to know which angles are called Complementary Angles...
if we add two angles and the total will be equal to 90 deg
let's say one angle is x and another angle is y
as they are complementary angles from the definition we can write the equation x + y = 90
one angle is 20 deg more than another one so from the above condition we write x = 20 + y
Substitute the value of x in the first eaquation we get, 20 + y + y = 90
Then, 20 + 2y = 90
subtracting 20 from both sides,
2y = 90-20 = 70
dividing both sides by 2,
2y/ 2 = 70 / 2
y = 35
So we got one angle is 35 deg
another angle is 35 + 20 = 55 deg.
Our answer is 55 deg the larger angle.
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how many solutions does y = x^2 + 7x - 11 have?
Answers
Answer:
infinite if you say that you have to find 2 or 3 solution so we can find by putting x value like 0 ,2,1 or also you can put y value
The breaking strengths of cables produced by a certain manufacturer have historically had a mean of pounds and a standard deviation of pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, , of the cables is now greater than pounds. To see if this is the case, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than pounds
Answers
No, we cannot claim that the population mean breaking strength of the newly- manufactured cables is greater than pounds.
Given mean=1900, standard deviation=65, sample size=150, sample mean=1902, level of significance=0.01.
The hypothesis are:
[tex]H_{0}:\\[/tex]μ=1900
[tex]H_{1}:[/tex]μ>1900
We have to use z test as the sample size is large and we know the population standard deviation.
z=(x-μ)/σ/[tex]\sqrt{n}[/tex]
z=(1902-1900)/65/[tex]\sqrt{150}[/tex]
z=0.38
finding the p value:
p value=P(Z>z)
=P(Z>0.38)
=1-P(Z<0.38)
from the z table we get;
P(Z<0.38)=0.6480
Therefore p value=1-0.6480
=0.3520
If the p value is less than 0.01 then we reject the [tex]H_{0}[/tex] otherwise we will reject the null hypothesis.
In this problem we also reject the null hypothesis.
Hence we cannot claim that the population mean breaking strength of the newly- manufactured cables is greater than pounds.
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Question is incomplete. It should includes:
mean=1900,
standard deviation=65,
sample size=150,
sample mean=1902,
level of significance=0.01.
Of the following points, name all that lie on the same horizontal line
(-5,7) (5,-7) (7,-5) (-7,5)
Answers
Answer:
(-5,7) (5,-7)
Step-by-step explanation:
When you are told to lable, show or name the points that lie on a horizontal line, it basically means that; when a line is drawn, it passes through the selected points without changing the direction when joined together (horizontally).
From the above problem, (-5,7) and (5,-7) lie in the same horizontal line.
For (7,-5) and (-7,5) lie in the same vertical line.
Thereforeour, the answer is (-5,7) (5,-7).
Write an equation for the graph below in terms of x
Answers
Explanation: Slope= rise/run = -1, the y-intercept is -3. Plug the numbers into the y=mx+b equation
ABC is a right angled triangle. If b=90 ac=96 c=30. What is ab?
Answers
Answer:
ab=48
Step-by-step explanation:
96/2=48
A property agent sells a house for $320 000, of which he receives a commission of 1.5 %.
Calculate the amount of commission the agent receives.
Answers
1. Annie and her friends are playing a game called Doubles. In the game, a player
rolls two number cubes at the same time. The outcome of each roll is the sum of the
two number cubes. Extra points are scored for rolling doubles the same number
on both number cubes.
-
Part A: Complete this table to show the sample space for each roll in the game. (6
points)
HELP ASAP WILL GIVE BRAINLIEST!!!!
Answers
The sample space is a combination of these two dice as we have shown in the attachment
Die A = {1,2,3,4,5,6}Die b = {1,2,3,4,5,6}What is sample space?This is the defined to be the set of all of the possible outcomes that can exist or be possible in a random experiment.
The question has two dice. These dice are made up of numbers from 1 to 6 each.
Die A = {1,2,3,4,5,6}
Die b = {1,2,3,4,5,6}
The sample space would be pairs of two of these two dices. The total number in the sample space would be 36.
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For the following exercises, find the x- and y-intercepts of the graphs of each function.
27. f(x) = −3| x − 2 | − 1
Answers
For the function f(x) = -3|x - 2| - 1, we have that:
The function has no x-intercepts.The y-intercept is of y = -7.What is the x-intercept of a function?The x-intercept of a function is the value of x when y = f(x) = 0, hence:
0 = -3|x - 2| - 1
-3|x - 2| = 1
|x - 2| = -1/3
The absolute value cannot be negative, hence the function has no x-intercepts.
What is the y-intercept of a function?The x-intercept of a function is the value of y = f(x) when x = 0, hence:
f(0) = -3|0 - 2| - 1 = -6 - 1 = -7.
The y-intercept is of y = -7.
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I really need help asap! ty!
Answers
The length of AL in the triangle is 12cm.
How to calculate the value?From the information given, angle C = 90° and BAC is given as 2ABC.
In this case, the length of angle BC is given as 24cm. Therefore, the length of AL will be:
= 24/2
= 12..
Therefore, AL = 12cm
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CAN SOMEONE HELP ME
Triangle not drawn to scale
Given: measure of angle A = 15 degrees, b = 16, and
c = 18. What is the length of a to the nearest tenth?
Answers
Answer:
a ≈ 4.9
Step-by-step explanation:
using the Cosine Rule in Δ ABC
a² = b² + c² - (2bc cosA )
= 16² + 18² - (2 × 16 × 18 × cos15° )
= 256 + 324 - (576cos15° )
= 580 - 576cos15
= 23.6267 ( take square root of both sides )
a = [tex]\sqrt{23.6267}[/tex]
≈ 4.9 ( to the nearest tenth )
a triangle with base 14, sides 12 and 6, and height 5. what is the area of the triangle? a = one-half(14)(6) = 42 square units a = one-half(12)(5) = 30 square units a = one-half(14)(5) = 35 square units a = one-half(6)(5) = 15 square units
Answers
The triangle with base 14, sides 12 and 6, will have an area, a = (1/2)(14)(5) = 35 square units. Hence, the 3rd option is the correct choice.
The area of a plane figure is the space occupied within its boundary.
The area of a triangle is given as,
a = (1/2)(b)(h) sq. units, where a is the area of the triangle, b is its base, and h is its height.
In the question, we have been given a triangle with a base of 14, sides 12 and 6, and a height of 5.
We are asked to determine the area of this triangle.
To determine the area of the triangle, we will use the formula:
a = (1/2)(b)(h) sq. units, where a is the area of the triangle, b is its base, and h is its height.
Now, we are given that the base is 14 and the height is 5, thus substituting b = 14, and h = 5, in the above formula, we get:
a = (1/2)(14)(5) sq. units.
or, a = 35 sq. units.
Comparing this with the given options, we can choose the third option.
Thus, the triangle with base 14, sides 12 and 6, will have an area, a = (1/2)(14)(5) = 35 square units. Hence, the 3rd option is the correct choice.
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Select the correct answer.
Select the simplification that accurately explains the following statement.
3/7 = 73
O A.
100
B.
3
(71)² = 73.71.7371-1-1 = 78 = 7² = 7
(71)² = 78.73.7} = 7.73 = 3-1-7=1-7=7
3
C.
(7³)³ = 7³. 7³. 73 = 73 + } + ³ = 7³ = 7¹ = 7
D. (73)³ = 7³. 73. 73 = 7 · (++) = 7 ⋅ = 7 · 1 = 7
Answers
The simplification that represents ∛7=[tex]7^{1/3}[/tex] is [tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]
How to simplify an expression?The simplification that accurately explains the statement ∛7 = [tex]7^{1/3}[/tex] is as follows;
Therefore, the simplification is as follows
[tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]
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How many real solutions does this system of equations have? x² + y² = 25 and x-3y=15
Answers
[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]
[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]
[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]
[tex]10y {}^{2} + 90y + 200 = 0[/tex]
[tex]y {}^{2} + 9y + 20 = 0[/tex]
[tex](y + 4)(y + 5) = 0[/tex]
[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]
[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]
[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]
For the following exercises, determine whether the relation is a function.
1. {(a, b), (c, d), (e, d)}
Answers
Answer:
The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.
Step-by-step explanation:
A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.
It is required to determine whether the given relation is a function.
To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.
Step 1 of 1
The given relation is {(a, b),(c, d),(e, d)}.
The set of the first components of each ordered pair is called the domain.
From the relation, the domain is {a, c, e}.
The set of the second components of each ordered the range.
From the relation, the range is {b, d, d}.
The given relation is a function. But it is not a one-to-one function.
Writing Exercises
428. Find a printed map and then write and solve an application problem similar to Example 8.79.
Answers
Answer:
Given a map of San Francisco, Las Vegas and Los Angeles on which triangles are drawn.
We find that the distance from Los Angeles to San Francisco is 351 miles.
Step-by-step explanation:
Given a map of San Francisco, Las Vegas and Los Angeles on which triangles are drawn.We need to find the distance from Los Angeles to San Francisco.Since, the triangles are same and hence similar triangles, the corresponding sides are proportional.In the proportion, we will make numerators as miles and denominators as inches and solve the equation.Step 1 of 2
In similar triangles, the corresponding sides are proportional.
We know that the distance between Los Angeles and Las Vegas is 270 miles and on the map it is 1 inches.
We need to form a proportion to find the distance between Los Angeles and San Francisco if on the map it is 1.3 inches.
Let the distance between Los Angeles and San Francisco be x .
[tex]\begin{aligned}&\frac{\text { miles }}{\text { inches }}=\frac{\text { miles }}{\text { inches }} \\&\frac{x \text { Miles }}{1.3 \text { inches }}=\frac{270 \text { Miles }}{\text { linch }} \\&\text { Multiplying both sides by } 1.3 \text { we get, } \\&x=270 \times 1.3 \text { Miles } \\&x=351 \text { Miles }\end{aligned}[/tex]
Step 2 of 2
To check if the answer is reasonable, we substitute it back in the formed proportion
[tex]\frac{x \text { Miles }}{\text { 1.3inches }}=\frac{270 \text { Miles }}{1 \text { inch }}$$[/tex]
We found x=351 Miles hence,
[tex]$$\begin{aligned}&\frac{351}{1.3}=\frac{270}{1} \\&270=270 \\&\text { Here, } L H S=\text { RHS }\end{aligned}$$[/tex]
Hence, our answer is correct.
Susan's calculator has a key that replaces the number displayed with its cube. If a² is displayed, how many times must Susan press the " cubing" key to display a number that is greater than 10^9?
Please explain it step-by-step! Also, I will give you a brainlist!!
Answers
If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.
How to determine a power by a "cubing" key
In accordance with the statement, Susan's calculator performs the following operation by pressing the "cubing" key:
x → x³
If we need to display a number that is greater than 10⁹, then we need to press the "cubing" key as many as needed. By algebra we have the following property for a power:
[tex](x^{m})^{n} = x^{m\cdot n}[/tex] (1)
Since we have a "cubing" key and we are supposed to make consecutive operation, we derive the following operation:
x → [tex]x^{3^{i}}[/tex], where i is the number of consecutive "cubing" operations.
If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.
Remark
The statement presents typing mistakes, correct form is shown below:
Susan's calculator has a key that replaces the number displayed with its cube. If a³, is displayed, how many time must Susan press the "cubing" key to display a number that is greater than 10⁹.
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Which graph shows y=3⌈x⌉+1?
Answers
The graph that shows y=3⌈x⌉ + 1 from the given options is the Third graph as shown attached.
Which graph shows the function best?The third graph shows the function and this can be tested as follows:
When x = 2, y = 7:
y = 3x + 1
= 3 x 3 + 1
= 7
When x = 3, y = 10:
y = 3 x 3 +1
= 10
When x = 1, y = 4
y = 3 x 1 + 1
= 4
This shows that the line on the third graph is well represented by the function, y=3⌈x⌉+1.
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Find the area in square centimeters of the composite, shape shown
below. Enter only a number as your answer.
A
11 cm
B
E
13 cm
18 cm
D
7 cm
C
Answers
The area of the composite shape is 136 square cm
Area of a composite functionThe area of the composite function is expressed as;
Area = area of triangle + area of rectangle
Area of the composite shape = (1/2* 4 * 5) + (7*18)
Area of the composite shape = 10 + 126
Area of the composite shape = 136 square cm
Hence the area of the composite shape is 136 square cm
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What if four girls want to share $9.60 equally? how much money will each girl get? complete the explanation. each girl will have how much money
Answers
Answer:
$2.40
Step-by-step explanation:
$9.60/4 = $2.40
Answer:
Step-by-step explanation:
[tex]\frac{9.60}{4} =$ 2.40[/tex]
One side of a triangle is 10 feet long, the second side is 20 feet long. What is the
range of possible values for the third side of the triangle? Why?
Answers
The range for the length of the third side is it must be greater than 10 feet and less than 30 feet.
What is the condition for the sides of triangles?The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.
The length of the third side had to be greater than the difference between the two given sides and less than the sum of the two given sides.
(20 – 10) < S <(20+ 10) ; 10< S < 30
Therefore, the range for the length of the third side is it must be greater than 10 feet and less than 30 feet.
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Enter the correct answer in the box.
What is the inverse of function f?
f(x)=-7x-4
Answers
Answer:
The inverse is -1/7(x+4)
Step-by-step explanation:
We have the function
y = -7x-4
To find the inverse, exchange x and y
x = -7y -4
Solve for y
Add 4 to each side
x+4 = -7y -4+4
x+4 = -7y
Divide each side by -7
-1/7(x+4) = -7y/-7
-1/7(x+4) = y
The inverse is -1/7(x+4)
. If x is an even integer, which of the following cannot be an odd integer?
A) x+1
B) x/2
C) x/3
D) 2x+1
Answers
Answer:
x/3
Step-by-step explanation:
x+1 will always be an odd integer, since x is an even integer because the pattern of integers is odd, even, odd, even, odd... and so on, in intervals of 1.
x/2 will sometimes be an odd integer. Because x/2 will always be an integer, since x is an even integer, meaning it is divisible by 2. So by definition any integer, even or odd, multiplied by 2 will give you an even integer. For example 3*2 = 6, 5*2 =10, 7*2=14. These are all even integers, and when you divide by 2, you'll get an odd integer
So let's look at x/3. 1*3 = 3, 3*3 = 9, 5*3 = 15, 7*3 = 21. See how it always results in another odd integer? Well this is because you essentially have (odd + odd + odd), the odd+odd will result in an even, which is explained in the previous question, but then adding another odd number to an even number, will result in an odd. This means that any time you multiply an odd integer by 3, you will always get an odd result, meaning no even integer can be divided by 3 to get an odd integer.
which is the secondary use of data from the 2000 census classification system to identify disparities in mentalhealthcare
Answers
The secondary use of data from the 2000 census classification system to identify disparities in mental healthcare.
What is the 2000 census classification system?The 2000 Census classification system helps our communities choose where to build everything from homes to hospitals to schools and shops. It also reveals who we are as a country and where we are headed. It aids in the government's decision-making about the allocation of cash and assistance to cities and states.
The government-wide 2000 Standard Occupation Classification (SOC) system served as the foundation for the 2000 Census classification system, while the 1980 SOC was used for the 1990 Census.
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mrs chapagain borrowed rs 9900 from a bank at the rate of 8% per annum. how much amount should she pay at the end of 2 years
Answers
Answer:
If compounding = rs 11547.36
If not compounding = rs 11484
The area of a rectangular pool is (x 2 + 17x + 72) square meters. There is a 3-meter-wide concrete
walkway around the pool. Write expressions to represent the dimensions of the outside border of the
walkway. (Lesson 8.1)
Answers
Step-by-step explanation:
the area is
(x² + 17x + 72) m²
it is the result of the usual
length × width
calculation.
length = x + g
width = x + h
length × width = x² + gx + hx + ab = x² + (g+h)x + gh =
= x² + 17x + 72
g + h = 17
gh = 72
just by looking at it that gives us 9 and 8 as g and h.
FYI - formally to calculate them we can say
g = 17 - h
(17 - h)h = 72
17h - h² = 72
h² - 17h + 72 = 0
the solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = h
a = 1
b = -17
c = 72
h = (17 ± sqrt(17² - 4×1×72))/(2×1) =
= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2
h1 = (17 + 1)/2 = 18/2 = 9
h2 = (17 - 1)/2 = 16/2 = 8
as we can see
g = 17 - h
if we say h = 9, then g = 8.
if we say h = 8, then g = 9.
so, these are our solutions.
we simply pick that length is longer than width, so, g = 9, h = 8.
the area including the walkway is then
(length + 3)(width + 3) =
= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²
and the dimensions incl. the walkway are
length = x + 9 + 3 = x + 12
width = x + 8 + 3 = x + 11