Sofia is learning to knit. After her first three stitches, she had to undo the last two. Then she made three more stitches and again, had to undo the last two. If this pattern continues, how many stitches will Sofia have to make before she has six good stitches?

The cost of the two DVDs before the sales tax was added is  $21.60.

To find the cost of the two DVDs before sales tax, let's first calculate the total cost including tax and then backtrack to find the cost before tax.

Calculate Total Cost with Tax:

The total cost including tax is given by: Total Cost = Price + Tax

Calculate Tax Amount:

Tax = Price * Tax Rate

Given that the sales tax rate is 8 percent (0.08 in decimal form), the tax amount is: Tax = 0.08 * $21.60 = $1.728

Calculate Total Cost:

Total Cost = Price + Tax

Total Cost = $21.60 + $1.728 = $23.328

Find Cost of DVDs Before Tax:

Let the cost of the two DVDs before tax be represented by x.

Total Cost = Price of DVDs + Price of DVDs * Tax Rate

$23.328 = x + 0.08x

$23.328 = 1.08x

Solve for x:

Divide both sides by 1.08:

x = $23.328 / 1.08 = $21.60

So, the cost of the two DVDs before the sales tax was added is  $21.60.

Complete Question:

Anthony decided to buy two DVDs that we're not included in the deal. His price was $21.60. The sales tax is 8 percent. What was the cost of the two DVDs before the sales tax was added?

The cost for the larger room comes out to be $384. Option B) is the correct answer.

The cost of refinishing a wood floor in a room is related to the area of the floor. Since the ratio of the corresponding sides of the two rooms is 3:4, the ratio of their areas is the square of the ratio of the sides, being 9:16 (since 32 = 9 and 42 = 16). To find the cost to refinish the larger room, we can set up a proportion where $216 corresponds to an area with a 'weight' of 9, and x corresponds to an area with a 'weight' of 16.

Mathematically this can be represented as 216/9 = x/16. Solving for x, we calculate x = (216/9) imes 16 = 24 imes 16 = $384. Therefore, the cost to refinish the wood floor in the larger room would be $384, which corresponds to option B).

It cost to refinish wood floor in the larger room is $384. So option (b) is correct.

To solve this problem, we'll use the concept of ratios to find the cost of refinishing the wood floor in the larger room.

First, let's set up the ratio of the areas of the two rooms. Since the ratio of corresponding sides is 3:4, the ratio of their areas will be 3^2 : 4^2, which is 9:16.

Now, since the cost of refinishing the smaller room is $216, we need to find what portion of the total cost that represents. Since 9 parts represent $216, 1 part represents $216 ÷ 9 = $24.

Next, we'll find the total cost of refinishing the larger room. Since the larger room has 16 parts (as per the ratio), the total cost will be 16 parts × $24/part = $384.

So, the correct answer is B) $384.

Here's the detailed calculation:

Find the ratio of areas of the rooms: [tex]\(3^2 : 4^2 = 9 : 16\)[/tex]

Find the cost per part: (216 ÷ 9 = 24)

Find the total cost for the larger room: [tex]\(16 \times 24 = 384\)[/tex]

In 17.66 ounces of chips, 3180 calories are there.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, 1 oz of potato chips contains 180 calories.

∴ No. of ounces of chips that contains 3180 calories can be obtained if we divide total calories by calories in 1 oz which is,

= (3180/180).

= 17.66 ounces.

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Answer:  [tex]x+3y=-15[/tex]

Step-by-step explanation:

The equation of a line passes through (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Then, the equation of a line that passes through (-6,-3) (6,-7) will be :-

[tex](y-(-3))=\dfrac{-7-(-3)}{6-(-6)}(x-(-6))\\\\\Rightarrow y+3=\dfrac{-7+3}{6+6}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-4}{12}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-1}{3}(x+6)\\\\\Rightarrow\ 3(y+3)=-x-6\\\\\Rightarrow\ 3y+9=-x-6\\\\\Rightarrow\ x+3y=-15.[/tex]

Hence, the required equation is [tex]x+3y=-15[/tex].

Frank's current number of books, 'b', satisfies the inequality 2b ≤ 300, and hence, the maximum value for 'b' is 150.

1. Let's assume Frank currently owns 'b' books.

2. According to the given information, if Frank were to double the number of books he now owns, he would still have fewer books than Emily.

3. We know that Emily has 300 books. So, the inequality representing the given information is 2b ≤ 300.

4. To find the maximum value for 'b', we need to solve this inequality.

5. Dividing both sides of the inequality by 2, we get b ≤ 150.

6. This means Frank can own a maximum of 150 books in order to maintain a smaller collection than Emily's 300 books.

The detailed mathematical sentence representing this information is: Frank's current number of books, 'b', satisfies the inequality 2b ≤ 300, and hence, the maximum value for 'b' is 150.

Complete question:

Write a mathematical sentence that expresses the information given below. Use bas your variable name. If necessary: type < = to means or > = to mean . If you need to show multiplication, do not use the letter x. Use the asterisk (*) symbol instead, or simplify your answer. Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.

Answer:

1)

3 3/8=  (3/1) + (3/8)=

    = (3x8)/8 + (3/8)

    =(3x8 +3) / 8              putting both numbers with the same denominator

     =27/8

27 is the same as 3³      3x3x3= 27

8 is the same as 2³        2x2x2= 8

= 3³÷ 2³

2)

1 11/25= (1/1) + (11/25)

= (25/25) + (11/25)     putting both numbers with the same denominator

= (25+11)/25

=36/25

36 is the same as 6²     6x6=36

25 is the same as 5²     5x5=25

6²/5²

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Step-by-step explanation:

The density of copper bar is 9g/cm³

Given that :

Mass of copper bar = 216 g

Volume = 24 cm

Density of copper will be :

Recall :

Density = Mass / Volume

Density = 216 g / 24 cm³

Hence, Density of copper bar = 9 g/cm³

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The statement which correctly describes the relationship between graphs related as g(x)=f(x−7) is; Choice C {The graph of g(x) is the graph of f(x) translated 7 units right}

According to the question; g(x)=f(x−7).

However, In graphs: an increase on the x axis is depicted by a movement rightward on the number line.

Therefore, if the relation g(x)=f(x−7) holds;

The graph of g(x) is the graph of f(x) translated 7 units right.

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[tex]\(-ab^3 - ac = 38\)[/tex].

To evaluate the expression [tex]\(-ab^3 - ac\)[/tex] given a = -2, b = 3, and c = -8, we substitute the values into the expression:

[tex]-ab^3 - ac = -(-2)(3)^3 - (-2)(-8)\\= -(-2)(27) - (16)\\= 54 - 16 \\= 38[/tex]

The area of the base of a cube with a volume of 216 cm³ is 36 cm², obtained by first calculating the side length as the cube root of the volume and then squaring that length.

The volume of a cube is calculated by raising the length of one of its sides to the third power (Volume = s³), where s is the length of a side. Given that the volume of the gift box is 216 cm³, we can find the length of a side by taking the cube root of the volume. The cube root of 216 cm³ is 6 cm, which is the length of each side of the box.

Since the base of the cube is a square, the area of the base is simply the length of a side squared (Base Area = s²). Hence, the area of the base of the box is 6 cm × 6 cm, which equals 36 cm².