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9514 1404 393

Answer:

  10.49

Step-by-step explanation:

Since we know 110 = 10² +10, we can make a first approximation to the root as ...

  √10 ≈ 10 +10/21 . . . . . where 21 = 1 + 2×integer portion of root

This is a little outside the desired approximation accuracy, so we need to refine the estimate. There are a couple of simple ways to do this.

One of the best is to use the Babylonian method: average this value with the value obtained by dividing 110 by it.

  ((220/21) + (110/(220/21)))/2 = 110/21 +21/4 = 881/84 ≈ 10.49

An approximation of √110 accurate to hundredths is 10.49.

__

The other simple way to refine the root estimate is to carry the continued fraction approximation to one more level.

For n = s² +r, the first approximation is ...

  √n = s +r/(2s+1)

An iterated approximation is ...

  s + r/(s +(s +r/(2s+1)))

The adds 's' to the approximate root to make the new fraction denominator.

For this root, the refined approximation is ...

  √110 ≈ 10 + 10/(10 +(10 +10/21)) = 10 +10/(430/21) = 10 +21/43 ≈ 10.49

_____

Additional comment

Any square root can be represented as a repeating continued fraction.

  [tex]\displaystyle\sqrt{n}=\sqrt{s^2+r}\approx s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}[/tex]

If "f" represents the fractional part of the root, it can be refined by the iteration ...

  [tex]f'=\dfrac{r}{2s+f}[/tex]

__

The above continued fraction iteration adds 1+ good decimal places to the root with each iteration. The Babylonian method described above doubles the number of good decimal places with each iteration. It very quickly converges to a root limited only by the precision available in your calculator.

Answer:

30 minutes for $10.00

Step-by-step explanation:

30min=$10

60min=$20

90min=$30

210min(3.5 hours)=$30

120min(2hours)=$30

Answer:

50

Step-by-step explanation:

Answer:

-3x + 14

Step-by-step explanation:

Expand -3(x-5)

. -3 * x = -3x

. -3 * -5 = 15

So

. y+1 = -3x + 15

Subtract 1 from both sides so that y is the subject

. y = -3x + 14

Now you can juse replace y with f(x) since theyre basically the same thing

Answer:

Step-by-step explanation:

Hi sorry if I’m bugging just trying to help out by getting Them B bye

Answer: 15 inches

Step-by-step explanation:

15 × 1 ÷ 12 = 1.25 ft

1.25 ft = 1.25 × 12 = 15 in

Answer:

y = -6/7x - 10/7

Step-by-step explanation:

(-4,2) and (3,-4)

Slope: - 6/7

Take any point: (-4,2)

y-intercept: 2 - (- 6/7)(-4) = -10/7

Answer:

I Kinda Confused Man

Step-by-step explanation:

I Dont Even Know The Right Answer

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

1/4

1/2

3/5

7/8

11/4

13/4

11/2

The program is an illustration of loops.

Loops are used to perform iterative and repetitive operations.

The program where comments are used to explain each line is as follows:

public class MyProgram extends ConsoleProgram {

   public void run()     {

//This prompts the user for the number of times to repeat the message

       echo("Anybody home?", readInt("Times to repeat: "));

   }

    private void echo(String lineOne, String lineTwo, int numTimes)     {

//The following iteration is repeated numTimes times

       for (int i = 0; i < numTimes; i++){

//This prints lineOne

       System.out.println(lineOne);

//This prints lineTwo

       System.out.println(lineTwo);

       }

   }

}

Read more about similar programs at:

https://brainly.com/question/17972093

The annual percentage rate is the interest rate for payment for the car

loan.

The given parameters are;

The amount of loan Terry and Jim have = $26,004

The annual percentage rate (APR) on one loan = 3.1 %

The annual percentage rate (APR) on the other loan = 7 %

Total interest paid after one year = $1,481.25

Required:

The amount owed on each car

Solution:

Let X represent the loan, with 3.1% APR, we have;

The other loan with 7% APR = 26,004 - X

Therefore;

0.031·X + 0.07·(26,004 - X) = 1,481.25

0.031·X + 1,820.28 - 0.07·X = 1,481.25

1,820.28 - 1,481.25 = 0.07·X - 0.031·X = 0.039·X

339.03 = 0.039·X

Therefore;

Therefore;

The amount owed on the car with an APR of 7% ≈ 26,004 - 8693.08 =

17310.92.

Learn more here:

https://brainly.com/question/15400760

Using the probability concept, it is found that there is a [tex]\mathbf{\frac{1}{k}}[/tex] probability that “Relaxation Through Mathematics” is first to review.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

The probability is:

[tex]p = \frac{D}{T} = \frac{1}{k}[/tex]

A similar problem is given at https://brainly.com/question/24483829

Answer:

x=4y

Step-by-step explanation:

Solving for x means you need to get it in the form x=?.

1. let's isolate the variable.

-2x-7y=y-4x

Add 4x to both sides to isolate:

2x-7y=y

Add 7y to both sides to isolate the x term:

2x=8y

Now we divide both sides by 2 (as we are solving for x):

x=4y

Hope this helps!

Answer:

16 = y

Step-by-step explanation:

So you have the equation 6=-y+42+-2y

Find the y first

6=-y+42+-2y

add all y's together

6=-3y+42

subtract 42 on both sides

-48 = -13y

16 = y

------------------------------------------------

Now do the check:

Plug in 16 where ever it says y in the original equation

6= -(16) + 42 + -2(16)

open the brackets

6= -16+42-32

solve

6=26-32

6 = 6

Hope this helps

Answer:

73.5 pounds of dog food in 7 days

Step-by-step explanation:

10 1/2 x 7

10x 7 =70

1/2 x 7 = 3.5

70 + 3.5 =73.5 pounds of dog food in 7 days

Answer:

1 : 0.44.

Step-by-step explanation:

93 : 41

= (93/93) : (41/93)

= 1 : 0.44.

Answer:

Should be $368.94

Step-by-step explanation:

hope it helps

please mark brainliest

The total cost of 118.25 gallons of gas is $368.94. Therefore, option A is the correct answer.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Todd drives 2,365 miles in a month and the average is 20 miles per gallon

Now, number of gallons =2,365/20

= 118.25 gallons

So, total cost = 118.25×3.12

= $368.94

Therefore, the total cost of gas is $368.94.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

Answer:

ok so to do this you line them up like normal then always remember to make sure your decimal is in the right spot if you need more help there are many easy solutions online also if you need more help you can always send me a picture of the question or tell me it and it will make things a lot easier :)

Step-by-step explanation:

Answer:

$2.20/kg

Step-by-step explanation:

First, we must convert pounds to kilograms.

1 lb = 0.45 kg

If 1 lb costs $.99

then 0.45 kg costs $.99

0.45 kg = $.99

dividing both sides by 0.45

1 kg = .99 ÷ 0.45

1 kg = $2.20

Answer:

a. P(O) = ¹/₂ = 0.5

As a percentage, this is 50%

b. P(> 2) = ²/₃ = 0.666...

As a percentage, this is 66.6...%

c. P(< 7) = 1

As a percentage, this is 100%

d. P(prime) = ¹/₂ = 0.5

As a percentage, this is 50%

Step-by-step explanation:

a.

1, 3 and 5 are odd, 3 of the outcomes

2, 4 and 6 are even, 3 of the outcomes

So, 3 of the 6 possible outcomes are odd and 3 are even;

Thus, the probability of an odd roll is ³/₆ (and the same applies to even);

This can be simplified to ¹/₂

b.

3, 4, 5 and 6 are the outcomes > 2;

1 and 2 are the outcomes ≤ 2;

So, 4 of the 6 possible outcomes are > 2;

Thus, the probability of rolling < 2 is ⁴/₆;

This can be simplified to ²/₃

c.

All outcomes are less than 7 since they are 1, 2, 3, 4, 5 or 6;

This means the probability of rolling less than 7 is ⁶/₆, or simply 1

d.

Prime numbers: 2, 3, 5, 7 ...

The possible prime number outcomes are 2, 3 and 5;

3 of the 6 possible outcomes, therefore, are prime so the probability of rolling a prime is ³/₆ or ¹/₂

Answer:

Step-by-step explanation:

ASSUMING all family members purchased ride tickets

Let n be the number of family members

148 = 8 + n(16 + 12)

140 = 28n

n = 5

Answer:

y = -5/3 x + 40

Step-by-step explanation:

The general form is y = ax + b, where a is the slope and b is the y intercept.

So immediately you can see that b must be 40, since the line crosses the y axis at 40.

The slope can be calculated by finding two "nice" points on the line that are also grid lines.

How about (0,40) and (6, 30).

Then, calculate the slope by dividing the y difference by the x difference:

(30-40)/(6-0) = -10/6 = -5/3

So C must be the answer.

Answer:

w > -6

Step-by-step explanation:

divide each term n 2x > -12 by 2 then simplify

Based on the opening balance, the amounts deposited, and the amounts for checks, the balance in the account should be $517.

The deposits into the account will increase the balance whilst the checks will do the opposite.

The balance is therefore:

= Opening balance + Deposits - Checks

= 21 + 187 + 445 + 454 - 74 - 137 - 139 - 240

= 21 + 1,086 - 590

= $517

In conclusion, the balance will be $517.

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Answer:10 or someones else’s answer this not my best

Step-by-step explanation:

well, x-intercept means for a graphed funciton where the x-axis gets touched/intercepted, Check the picture below, when that occurs, y = 0, so if we want to know what "x" is at that point we can simply set y = 0 and solve for "x".

[tex]-3x-5y=12\implies \stackrel{\textit{setting y = 0}}{-3x-5(0) =12}\implies -3x-0=12 \\\\\\ -3x=12\implies x=\cfrac{12}{-3}\implies x = -4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{coordinates}}{(-4~~,~~0)}~\hfill[/tex]