Find the constant of proportionality for the table and write in the form y = kx.A) y = 9x

B) y = 10x

C) y = 90x

D) y = 1/10x

Please give an honest answer = )

Answers

Answer 1

Answer:

Answer:

B) y = 10x

Step-by-step explanation:

It should not be too hard for you to determine that every number on the bottom row is the same as the number on the top row with a zero appended.

Appending a zero to a number is the same as multiplying it by 10. For example, ...

... 90 = 10·9

... y = 10x

_____

In case that observation doesn't work out for you, you can always solve the given equation for k, then choose values from the table to fill in.

... y = kx

... k = y/x . . . . . divide by the coefficient of k, which is x

Fill in values from the table

... k = 20/2 = 10 . . . . . . from the second column

Now put this value where k is in the equation. After you do that, you know ...

... y = 10x

Answer 2

Answer:

slope = (30 - 20)/(3 - 2) = 10 /1 = 10

equation

y = 10x

Answer

B) y = 10x

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find the least number of sweets that can be packed into polythene bags which contain either 9or 15 or 20 or 24 sweets with none left over
Find the average of 72,95,100,85,and 88
You have a piggy bank containing a total of 106 coins in dimes and quarters. If the piggy bank contains $17.05, how many dimes are there in the piggy bank? There are how many dimes in the piggy bank.

This year, a small business had a total revenue of $81,900 . If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?

Answers

Answer:

total revenue was $65,000

Step-by-step explanation:

A small business had a total revenue this year = $81,900

This is 26% more than their total revenue the previous year.

Let the revenue of previous year be 'r'.

r + ( 26% of r ) = $81,900

r + ( 0.26r ) = 81,900

1.26r = 81,900

r = $(81,900)/(1.26)$

r = 65,000

Their total revenue was $65,000 the previous year.

$65000 was the total revenue for the previous year.
65000 x .26 = 16900
65000 + 16900 = 81,900

Select all that justify the following statement.2•1/2=1
commutative - addition
inverse - addition
associative - multiplication
symmetric
commutative - multiplication
associative - addition
inverse - multiplication

Answers

Answer:

G: Inverse multiplication

Step-by-step explanation:

Statement is 2•1/2=1

Now, what this means is that when we multiply a number by it's inverse form, the result will be 1.

This means that this statement denotes an inverse multiplication.

Thus, the last option is the correct answer

Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the letters of the word DANCER be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is . (b) How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit? (c) How many ways can the letters of the word DANCER be arranged in a row if the letters NCE must remain together (in order) as a unit?

Answers

Answer:

(a) 720 ways

(b) 120 ways

Step-by-step explanation:

Given

$Word = DANCER$

$n =6$ --- number of letters

Solving (a): Number of arrangements.

We have:

$n =6$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =6!$

This gives:

$Total =6*5*4*3*2*1$

$Total =720$

Solving (b): DA as a unit

DA as a unit implies that, we have:

[DA] N C E R

So, we have:

$n = 5$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =5!$

This gives:

$Total =5*4*3*2*1$

$Total =120$

Solving (c): NCE as a unit

NCE as a unit implies that, we have:

D A [NCE] R

So, we have:

$n = 4$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =4!$

This gives:

$Total =4*3*2*1$

$Total =24$

2. Anne needs to know how much of her back yard will be used by her newcircular pool. *
1 point
11 feet
What is the area of the pool? Use 3.14 for T.

Answers

Answer:

see below

Step-by-step explanation: 6 13 8 09

area = π r² is the equation to calculate the area of the pool r = radius

I don't no if the 1.11 ft is the diameter of the radius, so I will use the 1.11 ft as the diameter

diameter = 2×radius

diameter / 2 = radius

area = π (d/2)² = T (d/2)² d = diameter π = T

= 3.14(1.11 / 2)²

= 3.14 × (0.555)²

= 0.9677 ft² which seems like a small pool!

Find the product of (5.2 · 10^-6) and (8 · 10^3).A) 416 · 106-4
B) 4.16 · 10^-2
C) 41.6 · 10^-3
D) 0.416 · 10^-1

Answers

Answer: B) $4.16\cdot10^(-2)$

Step-by-step explanation:

The given product : $(5.2\cdot10^(-6))\cdot (8\cdot10^3)$

First open parenthesis :

$5.2\cdot10^(-6)\cdot 8\cdot10^3$

Write decimal values together and power of 10s together.

$5.2\cdot 8\cdot10^(-6)\cdot10^3$

Using Law of exponent : $a^m\cdot a^n= a^(m+n)$

The above expression becomes.

$41.6\cdot10^(-6+3)=41.6*10^(-3)$

In scientific notation, the decimal must be placed after one digit (from left).

$41.6*10^(-3)=4.16*10*10^(-3)\n\n=4.16\cdot10^(-3+1)\n\n=4.16\cdot10^(-2)$

Hence, the correct answer is B) $4.16\cdot10^(-2)$ .

$\displaystyle\n(5.2\cdot10^(-6))*(8\cdot10^3)=\n\n=\underbrace{5.2*8}_(41.6)*\underbrace{10^(-6)*10^(3)}_(10^(-6+3))=\n\n=41.6*10^(-6+3)=\boxed{\bf41.6*10^(-3)}\n\n\texttt{Correct answer:}~~\boxed{\bf C)}$

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Answers

Answer:

Iteration 1: $x_(2)=1.446$

Iteration 2: $x_(3)=1.337$

Step-by-step explanation:

Formula for Newton's method is,

$x_(n+1)=x_n-(f\left(x_n\right))/(f'\left(x_n\right))$

Given the initial guess as $x_(1)=1.6$ , therefore value of n = 1.

Also, $f\left(x\right)=x^(9)-9$ .

Differentiating with respect to x,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9-9\right)$

Applying difference rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9\right)-(d)/(dx)\left(9\right)$

Applying power rule and constant rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=\left(9x^(9-1)\right)-0$

$(d)/(dx)\left(f\left(x\right)\right)=9x^(8)$

Substituting the value,

$x_(1+1)=x_1-(f\left(x_1\right))/(f'\left(x_1\right))$

$x_(2)=1.6-(f\left(1.6\right))/(f'\left(1.6\right))$

Calculating the value of $f\left(1.6\right)$ and $f'\left(1.6\right)$

Calculating $f\left(1.6\right)$

$f\left(1.6\right)=\left(1.6\right)^(9)-9$

$f\left(1.6\right)=59.71947674$

Calculating $f'\left(1.6\right)$ ,

$f'\left(1.6\right)=9\left(1.6\right)^(8)$

$f'\left(1.6\right)=386.5470566$

Substituting the value,

$x_(2)=1.6-(59.71947674)/(386.5470566)$

$x_(2)=1.446$

Therefore value after second iteration is $x_(2)=1.446$

Now use $x_(2)=1.446$ as the next value to calculate second iteration. Here n = 2

Therefore,

$x_(2+1)=x_2-(f\left(x_2\right))/(f'\left(x_2\right))$

$x_(3)=1.446-(f\left(1.446\right))/(f'\left(1.446\right))$

Calculating the value of $f\left(1.446\right)$ and $f'\left(1.446\right)$

Calculating $f\left(1.446\right)$

$f\left(1.446\right)=\left(1.446\right)^(9)-9$

$f\left(1.446\right)=18.63851065$

Calculating $f'\left(1.446\right)$ ,

$f\left(1.446\right)=9\left(1.446\right)^(8)$

$f\left(1.446\right)=172.0239252$

Substituting the value,

$x_(3)=1.446-(18.63851065)/(172.0239252)$

$x_(3)=1.337$

Therefore value after second iteration is $x_(3)=1.337$

Final answer:

To calculate two iterations of Newton's Method, use the formula xn+1 = xn - f(xn)/f'(xn). Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, calculate f(xn) and f'(xn) at x1 and then use the formula to find x2 and x3.