40.8 gallons of paint among 8 containers

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:

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

0.059 seconds is equal to 59 milliseconds.

Unit conversion is the process of changing the measurement units of a quantity from one system to another. It is essential for comparing and working with measurements expressed in different units. Common examples include converting between metric and imperial units for length (e.g., meters to feet) or weight (e.g., kilograms to pounds).

Accurate unit conversion is crucial in fields like science, engineering, and international trade.Thus for the given case, 0.059 seconds is equal to 59 milliseconds.

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Answer:

mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.

Step-by-step explanation:

The planet Mars has two moons Phobos and Deimos.

Mass of Phobos = 10.8 × 10¹⁵ Kilograms

Mass of Deimos = 2 × 10¹⁵ Kilograms

So the difference in the masses of the moons

= 10.8 × 10¹⁵ - 2 × 10¹⁵

= (10.8 - 2) × 10¹⁵

= 8.8 × 10¹⁵ Kilograms

Therefore, mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.

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]

Final answer:

The division of the complex numbers (3 - i) by (1 + 5i) results in the standard form -1/13 - 8/13i, by multiplying both the numerator and denominator by the conjugate of the denominator. The correct answer is option D.

Explanation:

To divide the complex number 3 - i by 1 + 5i, we should multiply numerator and denominator by the conjugate of the denominator to get rid of the imaginary part in the denominator:

(3 - i) * (1 - 5i) = 3 - 15i - i + 5i2

Since i2 = -1, it simplifies to:

3 - 16i - 5 = -2 - 16i

(1 + 5i) * (1 - 5i) = 1 - 5i + 5i - 25i2

Similarly, it simplifies to:

1 + 25 = 26

(-2 - 16i) / 26 = -2/26 - 16i/26

Simplify the fractions:

-1/13 - 8/13i

The standard form of the result is -1/13 - 8/13i, which corresponds to option D.

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.

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

The side lengths of the rectangle are (x - 2) and (x + 5)

The area of a shape is the amount of space on the shape

The area of the rectangle is given as;

[tex]Area = x^2 + 3x - 10[/tex]

Expand the expression

[tex]Area = x^2 + 5x - 2x - 10[/tex]

Factorize the expression

[tex]Area = x(x + 5) - 2(x + 5)[/tex]

Factor out x + 5

[tex]Area = (x - 2)(x + 5)[/tex]

Hence, the side lengths of the rectangle are (x - 2) and (x + 5)

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The side lengths that model a rectangle with an area of x^2 + 3x – 10 are x + 5 and x – 2, obtained by factoring the quadratic expression.

To find the side lengths of a rectangle that model an area of x2 + 3x – 10 square units, we need to factor this quadratic expression. Factoring involves finding two binomials that when multiplied together, give the original quadratic expression. The factors of -10 that add up to 3 (the coefficient of the middle term) are 5 and -2. Therefore, the factored form of x2 + 3x – 10 is (x + 5)(x – 2), meaning the side lengths that can be used to model this rectangle are x + 5 and x – 2.

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.

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:

The Answer is 5 1/8

Step-by-step explanation:

The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

As per the given values,

A=4-3i, M= -4+i, S=i, and P=2

Put the above values into A - M + S - P as

4 - 3i - (-4 + i) + i - 2

⇒ 4 - 3i + 4 - i + i - 2

⇒ 4 - 2 + 4 - 3i

⇒ 6 + 3i

Hence "The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i".

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The value of |7.8| is 7.8 because the absolute value of a number is the non-negative value of that number without regard to its sign.

The student has asked what the value of |7.8| is. The absolute value, denoted by the vertical bars, refers to the distance of a number from zero on the number line without considering direction. Therefore, the absolute value of 7.8 is 7.8 itself, regardless of any negative sign. It's because the absolute value of a positive number is the number itself, and the absolute value of a negative number is the positive version of that number.

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.