Please help me find the answers to all the questions whoever answers all the question I will mark the brainlest.

Please Help Me Find The Answers To All The Questions Whoever Answers All The Question I Will Mark The

Answers

Answer 1

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 a

Explicit 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 difference

Given sequence:  3, 8, 13, 18, 23, ...

To find the common difference, subtract one term from the next term.

Therefore:

a = 3d = 8 - 3 = 5

Substituting 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 difference

We 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 b

To 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 c

We 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 d

The 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

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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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

The answer for this is 320000 of the answer because I did the math

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 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

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.

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)

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.

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

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).

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]

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

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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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.

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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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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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]

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 )

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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. 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.


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)

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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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 triangle

In 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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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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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

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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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.

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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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 function

The 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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Write an equation for the graph below in terms of x

Answers

Answer: Y=-x-3
Explanation: Slope= rise/run = -1, the y-intercept is -3. Plug the numbers into the y=mx+b equation

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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i need help with this page Volume of a cone 27cm 13 cm Brad has the option of using three types of tables in his bagel shop: square tables with a side length of 39 inches rectangular tables 23 inches wide and 71 inches long round (circular) tables with a diameter of 48 inches. Which type of table has the largest area? Political leaders must have leading capacity rather than academic qualifications Find the area and the perimeter of the shaded regions below. Giveyour answer as a completely simplified exact value in terms of T (noapproximations). The figures below are based on semicircles orquarter circles and problems b), c), and d) are involving portions ofa square.Pls explain as best as you can i cant understand this stuff Which words provide clues as to what cultivated means? select all that apply. precision and deliberateness voice and accent great and celebrated pleasure and honor Ellen is currently twice as old as Maria, but in 6 years, Maria will be 2/3 as old as Ellen. How old is Ellen now? When it came to weapons, the Fourteen Points plan called for Aman: I spend a lot of time watching television every day. Muna: _________________________ Complete the equation of this circle:(x [?])+(y - [ ])=[ ] Angle B is a complement of angle A and the measurement of angle A = 65.2. Find the measurement of angle B A perspectve that there are (or ought to be) universal norms that unite people across the globe is ____________. [Hint: Diogenes the Cynic claimed to be this.] Think of possible advances around the corner and how the quality of life, disease prevention, or surgical correction will benefit patients of the future. Questions in the picture A buyer purchased a newly constructed house from a builder for use as a residence. The buyer did not perform an inspection of the house prior to the purchase. Neither the contract nor the deed contained any warranties as to the condition of the house. Six months later, during a heavy downpour, the basement flooded. Since that time, whenever there has been a substantial rain, there has been water in the basement. The source of the problem has been identified as several cracks in the foundation wall that surrounds the basement. An expert hired by the buyer has opined that the cracks formed due to settling after the home was built and could have been prevented by adherence to proper construction methods. The builder has repeatedly refused to address the problem. Just before the first anniversary of the purchase, the buyer filed suit against the builder for the defective foundation wall and the resulting damages. There are no applicable state statutes that address the issue. Who will prevail? Since 1948, Unverferth Manufacturing has manufactured innovative agricultural equipment. In 2003, the firm started developing a new 12-row strip-till subsoiler, which prepares 10-inch-wide seed beds spaced 40 inches apart, a width that is commonly used in cotton production. Before introducing the new tiller, Unverferth developed and tested almost three dozen product prototypes. Unverferth used the ____ approach to innovation. Drag each expression to show whether the expression is equivalent to 12x - 6,24x+12, or neither. A hockey puck with a mass of 160 g is sliding across an empty ice rink. The coefficient of friction between the hockey puck and the ice is 0. 51. The puck travels 47. 7 m before coasting to a stop. What was the initial velocity of the puck?. Which statement shows a major difference in George Washington's style of governing as president compared to Andrewlackson's style?O Washington worked toward compromise, and Jackson used presidential powers to impede congressional progress.ESave & EO Washington handled foreign affairs with political grace, and Jackson brokered treaties toward peaceful resolutions.O Washington restricted rights of Native Americans and immigrants, and Jackson supported the practice of slavery.O Washington squashed uprisings using military force, and Jackson supported federal rule over states' rights. Economic SurveyThe Economic Survey of India said that the government should refrain from raising exemption limits on income tax to facilitate natural growth of individual earnings and widen the taxpayers base, even as it also suggested increasing property tax.The Economic Survey 2015-16, tabled in Parliament on Friday, also called for a review and phasing out of the tax exemption raj that benefited the richer private sector and a reasonable taxation for better-off individuals. A cross-country comparison shows that India currently has the lowest number of taxpayers, it said, adding that nearly 85 per cent of the economy still remains outside the tax net.Just 5.5 per cent of earning individuals are in the tax net and the ratio should be raised to a desirable estimate of about 23 per cent, it said. Making a study of the data since Independence, the Survey said that the exemption thresholds have been raised much more rapidly than underlying income growth resulting in a widening of wedge between average income and threshold limit.One of the low hanging fruit would be to refrain from raising exemption thresholds for the personal income tax, allowing natural growth in income to increase the number of taxpayers. In some ways, this would be reform through inaction, the Survey said. It said that subsidies amounting to Rs. 1 lakh crore paid to well-off need to be scaled back. Also tax exemptions raj which often amount to redistribution toward the richer private sector will also need to be reviewed and phased out.Reasonable taxation of the better-off, regardless of where they got their income from industry, services, real estate or agriculture will also help build legitimacy, the Survey added. It also suggested that property taxation needs to be developed as sparse systematic data on property taxation shows how little attention has been given to this tax.Property taxes are especially desirable because they are progressive, buoyant and difficult to evade, since they are imposed on a non-mobile good which can be relatively easily identified, it said.Making a case for higher property tax rates, the Economic Survey said it would put sand in the wheels of property speculation.Smart cities require smart public finance and a sound property taxation regime is vital to Indias urban future, the Survey added.It said India has not fully translated its democratic vigour into commensurately strong fiscal capacity. In long run, if India is to stay on the line as its per capita income grows, it will need to build fiscal capacity.The Survey also said the governments spending priorities must include essential services that all citizens consume: public infrastructure, law and order, less pollution and congestion. It said the state should prioritise on reducing corruption and governments effort to improve transparency through transparent and efficient auctioning of public assets will help create legitimacy and over time strengthen fiscal capacity. The Survey said economic development in India lags political development.Independent India has averted famines, but chronic malnutrition is still a challenge. The Indian state can organise mega events, but routine safety for women has turned out to be more difficult to achieve. The Indian state responds effectively to floods and tsunamis but finds water and power metering more challenging, it added.Question 1 : What the case is all about? Provide the brief summary of the key issues discussed?Question 2: Do you really think that the Indias recent economic survey is against raising income tax exemption limits?Question 3: What has been said about property tax?