Nathan brought a pair of boots for $80 and 1 shirt for $20. the sales tax is 5%. how much did Nathan pay for all the items including tax ?

The product of the dimensions of the box is 240.

What is mean by Cuboid?

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

Given that;

The dimensions of the cubes boxes are 4 by 5 by 6.

Now,

Since, The dimensions of a box that will hold twice as many cubes as a box.

And, The volume of the box = 4 x 5 x 6

                                            = 120

So, The volume of the  box that will hold twice as many cubes as a box;

= 2 x 120

= 240

And, We are not sure the exact dimensions of the box.

Thus, The product of the dimensions of the box is 240.

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To solve the equation 0.5p = p + 5, subtract p from both sides and divide both sides by -0.5.

To solve the equation 0.5p = p + 5, we can start by simplifying both sides. Let's subtract p from both sides: 0.5p - p = 5. Combining like terms, we get -0.5p = 5. Now we can divide both sides by -0.5 to isolate p: p = 5 / -0.5. Dividing 5 by -0.5 gives us p = -10. Therefore, the solution to the equation is p = -10.

Repeated reasoning is a strategy used in mathematics to find multiplication facts by recognizing patterns and making generalizations. It involves using known facts to find other facts and making connections between different problems.

Repeated reasoning is a strategy used in mathematics to find multiplication facts. It involves recognizing patterns and using them to make generalizations about multiplication. When using repeated reasoning, you can start with a known fact, such as 2 x 3 = 6, and then apply that knowledge to find other facts. For example, you can use the fact that 2 x 3 = 6 to find 2 x 4 by adding another group of 2, resulting in 6 + 2 = 8.

Another example of using repeated reasoning is the commutative property of multiplication. This property states that the order of the factors does not change the product. So, if you know that 3 x 4 = 12, you can use repeated reasoning to determine that 4 x 3 = 12 as well.

By using repeated reasoning, you can build upon your knowledge of multiplication facts and make connections between different problems, which helps in understanding multiplication concepts more deeply.

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Answer:

1.2

Step-by-step explanation:

The x in each point is 3 so we can leave that alone.

Then we subtract.

2.6 - 1.4 = 1.2

The distance between the points (3, 2.6) and (3, 1.4) will be 1.2 units.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x – h)² + (y – k)²

Point A is at (3, 2.6) and point B is at (3, 1.4) on a coordinate grid.

(x, y) ⇒ (3, 2.6)

(h, k) ⇒ (3, 1.4)

Then the distance between the points (3, 2.6) and (3, 1.4) will be

D² = (3 - 3)² + (2.6 - 1.4)²

D² = 0 + 1.2²

D = 1.2 units

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Final answer:

Norah and Janice share £300 in a 9:1 ratio. Norah receives £270 while Janice gets £30, after dividing the total amount into 10 parts and then allocating the shares according to the ratio.

Explanation:

To calculate the share of the money Norah and Janice will each receive from £300 in the ratio of 9:1, we need to find out how many parts we divide the total sum into, and then allocate the appropriate amount to each based on the ratio.

Firstly, the total number of parts is 9 (for Norah) + 1 (for Janice) = 10 parts.

Next, we calculate the value of each part by dividing the total sum of £300 by 10: £300 / 10 = £30 per part.

Now, to find Norah’s share, we multiply 9 (her part of the ratio) by the value of one part: 9 * £30 = £270.

Janice’s share is simply one part, so it's £30: 1 * £30 = £30.

Therefore, Norah will receive £270 and Janice will receive £30.

Answer:$19

Step-by-step explanation: 152 ÷ 8 = 19

So one shirt cost $19.

The domain of the function y = 1725 - 75x, representing money left in a lunch account, is between 0 and 20 weeks. The range is the amount of money, from $225 to $1725.

The equation y = 1725 - 75x represents the amount of money left in a lunch account after x weeks. If we consider the function f(x) for 0 ≤ x ≤ 20. The domain of this function, which is the set of allowable values for x, is from 0 to 20, inclusive. This means that x can take on any real number value between 0 and 20. For the range, we calculate the minimum and maximum values of y using the equation, which are y when x = 0 and y when x = 20 respectively. For x = 0, y = 1725 and for x = 20, y = 1725 - 75(20) = 1725 - 1500 = 225. So the range of y is from 225 to 1725 dollars.

                                 b

Step-by-step explanation:

The number 30 tens is equivalent to three hundred.

In the decimal system, there are ten units in a group called a "ten." Likewise, there are ten tens in a group called a "hundred."

Therefore, one hundred is equal to ten tens.

Since we know that one hundred is equal to ten tens, calculate how many hundreds are equivalent to 30 tens.

Divide 30 by 10 to find out how many groups of ten are present:

= 30 tens ÷ 10

= 3

Therefore, 30 tens are equal to 3 hundreds.

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Final answer:

To solve the expression 5 ∙ 23, we multiply 5 by 23, which gives us the answer 115.

Explanation:

The student has asked to find the value of 5 multiplied by 23. In mathematics, when we see an expression like 5 ∙ 23 without any parentheses, it simply means we need to multiply the number 5 by 23 to get the answer. Let's perform this calculation step by step:

First, we write down the number we need to multiply, which is 5.

Next, we write down the number by which we are multiplying, which is 23.

Now we multiply these two numbers: 5 * 23 = 115.

The answer to the expression 5 ∙ 23 is 115.

The value of [tex]\(5 \cdot 2^3\)[/tex] is 40.

To find [tex]\(5 \cdot 2^3\)[/tex], adhere to the order of operations. The expression involves exponentiation before multiplication.

First, compute the exponent: [tex]\(2^3\)[/tex] equals [tex]\(2 \times 2 \times 2\)[/tex], resulting in 8.

Then, multiply this value by 5, yielding [tex]\(5 \times 8\)[/tex], which simplifies to 40.

The process follows the principles of the order of operations (PEMDAS/BODMAS), ensuring accurate computation.

Thus, [tex]\(5 \cdot 2^3\)[/tex] equals 40.

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