Prove that 1=2 with well arranged steps and justify each step

The rate of inflation from last year to this year is calculated by finding the 'change in CPI' which is then divided by the 'old CPI' and multiplied by 100 to convert it into percentage. The change in CPI is the new CPI minus the old CPI. By following the steps, we find that the rate of inflation is 10%.

To calculate the rate of inflation, we first need to determine the 'change in CPI', which will then be divided by the 'old CPI'. The formula is:

(New CPI - Old CPI) / Old CPI x 100%

The 'change in CPI' is the new CPI (this year's CPI) minus the old CPI (last year's CPI). This will be:

121 (this year's CPI) - 110 (last year's CPI) = 11

Now, we'll divide 'change in CPI' by old CPI, which is:

11 (change in CPI) / 110 (old CPI) = 0.1

To convert the value into percentage, we should multiply it by 100:

0.1 x 100 = 10

So, this year's rate of inflation is 10%.

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Answer: 2 and 4/5

Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.

[tex]\sqrt[5]{14}[/tex] = 2 with a remainder of 4

Therefore, 14/5 can be written as the mixed number 2 and 4/5.

The fraction 14/5 written as a mixed fraction is equivalent to 2 4/5

Given the expression below:

14/5

Since 5 can go in 14 twice, the whole number of the mixed fraction will be 2.

Given the remainder as 4, the numerator will be 4 and the denominator will be the same that is 5 as shown below:

14/5 = 2 4/5

Hence the fraction 14/5 written as a mixed fraction is equivalent to 2 4/5

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Final answer:

The Long family spent $38.62 for school supplies and $215.78 for new school clothes. To find the total amount spent, add the cost of school supplies and new school clothes. To calculate the sales tax, multiply the total amount spent by the sales tax rate.

Explanation:

To find the total amount spent, we need to add the cost of school supplies and new school clothes. The Long family spent $38.62 on school supplies and $215.78 on new school clothes, so the total amount spent is $38.62 + $215.78 = $254.40. Now, to calculate the sales tax, we need to find the percentage of the total amount spent. Let's assume the sales tax rate is 8%. To find the sales tax amount, we multiply the total amount spent by the sales tax rate as a decimal: $254.40 x 0.08 = $20.35.

The two base numbers can be represented as x and y. Setting them equal in the equation x * y = 2(x + y) allows you to solve for them. One solution is x = 2 and y = 2.

This problem can be solved using basic algebra. Let's assume the two base numbers be x and y. Since the product of the two base numbers (x * y) is twice as large as the sum of those numbers (x + y), we can create the following equation: x * y = 2(x + y).

To solve for x and y, you may set x and y to different numbers and check if they satisfy the equation. One solution is x = 2 and y = 2, since 2*2 = 2(2+2). Similarly, other pairs of numbers may also satisfy this equation based on the specific constraints of Frederick's number puzzle.

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To solve the number puzzle, we need to find two base numbers whose product is exactly twice as large as their sum. By rearranging the terms and factoring, we can find the base numbers that satisfy the equation. An example solution is provided with a = 3 and b = 6.

To solve the number puzzle, we need to find two base numbers whose product is exactly twice as large as their sum. Let's represent the base numbers as 'a' and 'b'. According to the information given, we have the equation:

ab = 2(a + b).

We can simplify the equation by rearranging the terms and factoring: ab - 2a - 2b = 0. Using a technique called 'completing the square', we can rewrite the equation as (a - 2)(b - 2) = 4.

From here, we can choose different values for 'a' and 'b' that satisfy the equation, such as a = 3 and b = 6. Therefore, the base numbers for the number puzzle are 3 and 6.

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Answer: One card is 0.005 inches thick.

Step-by-step explanation:

Since we have given that

Number of cards in a stack = 150

Thickness of the stack = [tex]\dfrac{3}{4}\ inches[/tex]

So, Thickness of each card is calculated by "Unitary method":

Thickness of 150 cards  = [tex]\dfrac{3}{4}\ inches[/tex]

Thickness of 1 card is given by

[tex]\dfrac{3}{4\times 150}\\\\=\dfrac{1}{4\times 50}\\\\=\dfrac{1}{200}\\\\=0.005\ inches[/tex]

Hence, One card is 0.005 inches thick.

For the round trip of 930 miles each way, you will need to purchase about 62 gallons of gas, given a car's gas mileage of 30 miles per gallon.

To calculate the gallons of gas needed for the round trip, follow these steps:

Calculate the total distance for the round trip.

The round trip distance is twice the one-way distance.

Round trip distance = 2 * 930 miles = 1860 miles.

Find the number of gallons required for the round trip.

Divide the total distance by the car's gas mileage (miles per gallon).

Gallons required = Round trip distance / Gas mileage

Gallons required = 1860 miles / 30 miles per gallon

Perform the division.

Gallons required = 62 gallons.

Round the answer.

Since you cannot purchase a fraction of a gallon, round the answer to the nearest gallon.

You will need to purchase approximately 62 gallons of gas for the round trip.

So, to make the trip to see your friends and return home, you will need to purchase about 62 gallons of gas.

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Answer:

16 2/3

Step-by-step explanation:

The bicyclist's average speed was 16.67 miles per hour

The student asks about the average speed of a bicyclist who traveled for 1.5 hours and covered 25 miles. The average speed can be found using the formula v = d/t, which suggests speed (v) equals distance (d) divided by time (t). To solve for the bicyclist's average speed, we'll insert the given values into the formula.

Here's the step-by-step calculation:

Identify the given variables: d = 25 miles and t = 1.5 hours.

Substitute the values into the formula: v = 25 miles / 1.5 hours.

Calculate the quotient to find the average speed: v = 16.67 miles per hour (rounded to two decimal places).

Therefore, to find the bicyclist's average speed, divide the distance traveled, 25 miles, by the time spent, 1.5 hours, which yields an average speed of 16.67 miles per hour.

The set of counting numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...} is called the set of natural numbers. The natural numbers begin at 1 and go on indefinitely.

Three examples of natural numbers are below.

642,000

440

81

Answer:

The Answer is 5 1/8

Step-by-step explanation:

The solution to the inequality -1.3 ≥ 2.9 -0.6r, is r ≤ 7. This is represented on a graph by placing a closed circle on 7 and drawing a line to the left, to represent all numbers less than 7.

To solve this inequality, -1.3 ≥ 2.9 -0.6r, first, we isolate the variable r (which represents solving for 'r'). Start by subtracting 2.9 from both sides of the inequality.

This gives us -4.2 ≥ -0.6r. Then divide both sides by -0.6. However, remember when dividing or multiplying an inequality by a negative number, the direction of the inequality changes. So, it becomes r ≤ 7.

When graphing this inequality, you will place a closed circle at 7 (showing that point is included) and draw a line to the left from 7, extending to infinity (since all numbers less than 7 satisfy the inequality).

The graph represents the mathematical solution to the inequality.

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Answer:

I am pretty sure this is either a Linear Equation or called a Contradiction

An equation that is not true for any values of the variable is called a false or inconsistent equation.

An equation that is not true for any values of the variable is called a false equation or an inconsistent equation. This means that the equation has no solution that satisfies the given equation. For example, if we have the equation x + 3 = x + 5, subtracting x from both sides gives us 3 = 5, which is not true for any value of x.

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Answer:

Value of 5×198 is:

990

Step-by-step explanation:

We have to find the value of  5 x 198 with the help of distributive property that includes multiplication and subtraction

Distributive property says that if a,band c are three numbers

then,  a(b-c)= ab-ac

5 x 198= 5(200-2)

           = 5×200 - 5×2

           = 1000-10

           = 990

Hence, Value of 5×198 is:

990

Answer:  The correct option is (C) [tex]\dfrac{1}{4}.[/tex]

Step-by-step explanation:  We are given to find the common ratio for the following geometric sequence :

64,   16,   4,   1,   .   .    .

We know that

if a(n) represents the n-th term of a geometric series, then the common ratio is given by

[tex]r=\dfrac{a(n+1)}{a(n)},~~~n=0,~1,~2,~~.~~.~~.[/tex]

For the given geometric sequence, we have

a(1) = 64,  a(2) = 16,  a(3) = 4,  a(4) = 1,  .  .  .

So, the common ratio r will be given by

[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.[/tex]

We have

[tex]\dfrac{a(2)}{a(1)}=\dfrac{16}{64}=\dfrac{1}{4},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{4}{16}=\dfrac{1}{4},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{1}{4},~~\cdots[/tex]

Thus, the required common ratio for the given geometric sequence is [tex]\dfrac{1}{4}.[/tex]

Option (C) is CORRECT.

To make A the subject in the equation w = 3(2a + b) - 4, the rearranged equation is: a = (w + 4 - 3b) / 6.

To rearrange the equation w = 3(2a + b) - 4 to make A the subject, we need to isolate A on one side of the equation. Here's how we can do it step by step:

Step 1: Distribute the 3 to the terms inside the parentheses:

w = 6a + 3b - 4.

Step 2: Move the 3b and -4 terms to the other side of the equation:

w + 4 = 6a + 3b.

Step 3: Rearrange the terms to isolate a:

6a = w + 4 - 3b.

Step 4: Divide both sides of the equation by 6 to solve for a:

a = (w + 4 - 3b) / 6.

Now, a is the subject of the equation. We have successfully rearranged the equation to express a in terms of w and b.

The probable question maybe:

rearrange w=3(2a+b)-4 to make A the subject in the equation.

The rearranged equation solving for [tex]\( a \)[/tex] is : [tex]\[ a = \frac{{w + 4}}{6} - \frac{{b}}{2} \][/tex]

This equation expresses [tex]\( a \)[/tex] as a function of [tex]\( w \)[/tex] and [tex]\( b \)[/tex], where [tex]\( w \)[/tex] is multiplied by [tex]\( \frac{1}{6} \) and \( b \)[/tex] is subtracted and then divided by [tex]\( 2 \)[/tex]. This equation can be used to calculate the value of [tex]\( a \)[/tex] given [tex]\( w \) and \( b \).[/tex]

To rearrange the equation [tex]\( w = 3(2a + b) - 4 \)[/tex] to solve for [tex]\( a \)[/tex], the first step is to isolate the term containing [tex]\( a \)[/tex] on one side of the equation.

1. Start by distributing the [tex]\( 3 \)[/tex] on the right side:

[tex]\[ w = 6a + 3b - 4 \][/tex]

2. Next, move the constants to the other side of the equation by adding [tex]\( 4 \)[/tex] to both sides:

[tex]\[ w + 4 = 6a + 3b \][/tex]

3. Now, to isolate [tex]\( a \)[/tex], divide both sides by [tex]\( 6 \):[/tex]

[tex]\[ \frac{{w + 4}}{6} = a + \frac{{3b}}{6} \][/tex]

4. Simplify:

[tex]\[ \frac{{w + 4}}{6} = a + \frac{{b}}{2} \][/tex]

5. To solve for [tex]\( a \)[/tex], subtract [tex]\( \frac{{b}}{2} \)[/tex] from both sides:

[tex]\[ \frac{{w + 4}}{6} - \frac{{b}}{2} = a \][/tex]

So, the rearranged equation solving for [tex]\( a \)[/tex] is:

[tex]\[ a = \frac{{w + 4}}{6} - \frac{{b}}{2} \][/tex]

To convert the distance from the Earth to the Moon from miles to feet, multiply 250,000 miles by the number of feet in a mile, which is 5,280. This calculation yields a result of approximately 1.32 billion feet.

The distance from the Earth to the Moon is given as 250,000 miles. To convert this distance from miles to feet, we use the fact that there are 5,280 feet in a mile. Thus, we multiply the distance in miles by the number of feet per mile.

To find the distance in feet, perform the following calculation:

Multiply the distance in miles by the number of feet per mile: 250,000 miles × 5,280 feet/mile.

This equals 1,320,000,000 feet.

Therefore, the Moon is approximately 1.32 billion feet away from Earth.