When dividing 878 by 31 a student finds a quotient of 28 with a remainder of 11 check the students work and use the check to find the error in the solution

Answer:

45

Step-by-step explanation:

If she spent $6.25 on earrings and 4 times that amount on a shirt. She take $39.50 to the mall originally.

The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

It is given that, Jan spent the entire day shopping. She brought $8.25 home. She spent $4 times that much on a blouse and $6.25 on earrings.\

We have to find the amount she take to the mall originally.

Suppose the total amount is x,

x=$8.25 + $6.25 + $6.25×4

x=25+14.5

x=39.50

Thus, if she spent $6.25 on earrings and 4 times that amount on a shirt. She take $39.50 to the mall originally.

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2x + 5 is the expression for the calculation double 2 then add 5.

The given statement is double 2 then add 5.

We have to make an expression using this statement.

We will separate the statement into two parts.

- Double 2

- Add 5

We need to assume a number and let that number be x.

So first we need to double that number as 2x and add 5.

We have,

2x + 5

Thus 2x + 5 is our expression.

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Alyssa can design her garage with dimensions that are factors of 240 square feet. Possible dimensions range from 1 ft x 240 ft to 15 ft x 16 ft, with more practical and reasonable options being dimensions that are narrower but still close to a square, such as 12 ft x 20 ft or 15 ft x 16 ft.

The question regarding Alyssa's garage design involves finding all the pairs of whole numbers that multiply to give an area of 240 square feet for a rectangular floor. To determine this, we must find the factors of 240 that can serve as potential lengths and widths of the garage.

Factors of 240 that represent possible lengths and widths (where the first number in each pair is the length and the second is the width) are:

However, choosing the dimensions that are reasonable for a garage floor requires considering practicality. Very long and narrow rectangles, such as 1 ft x 240 ft or 2 ft x 120 ft, are not practical for a garage. Usually, dimensions that are closer to square but still rectangular, like 12 ft x 20 ft or 15 ft x 16 ft, are more suitable and reasonable for a garage.

Area of a square = side²

Area of a rectangle = Length x Wide

The number of square brownies cut from the pan is 24 brownies.

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

Brownie dimensions:

Length = 18 inches

Wide = 12 inches

Area of a rectangle = Length x Wide

Area of the Brownie

= 18 x 12

= 216 square inches

The brownies are cut into squares:

Side = 3 inches

Area of the square brownies.

= 3 x 3

= 9 square inches

Now,

The number of squares with sides of 3 inches cut from the Brownie.

= Area of the brownies / Area of the square brownies

= 216 / 9

= 24

Thus,

The number of square brownies cut from the pan is 24 brownies.

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Final answer:

The question deals with an inequality representing that the product of an unknown number and 4 is at least -12, resulting in a solution where the number must be greater than or equal to -3.

Explanation:

The question 'The product of a number and 4 is at least -12' can be translated into the inequality 4x ≥ -12, where x represents the number. To solve this, divide both sides of the inequality by 4, which follows the multiplication rules for the sign. This gives us x ≥ -3. So, the number must be greater than or equal to -3.

This is consistent with the fact that when two negative numbers multiply, the answer is positive, and when a positive and a negative number multiply, the answer is negative.

The fish swam 28 feet down in the 32-foot deep lake.

To find out how many feet down the fish swam, we can multiply the depth of the lake by the fraction representing the proportion it swam.

The depth of the lake is given as 32 feet, and the fish swam 7/8 of this depth.

Multiplying 32 by 7/8:

32 * (7/8) = 224/8 = 28

Therefore, the fish swam 28 feet down in the 32-foot deep lake.

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Answer:

Elias is not correct. The new rectangle will be an enlargement because the scale factor is greater than 1. To be a reduction, the scale factor must be between 0 and 1.

Scale factor less than 1 gives the expanded form of the figure so Elias is wrong.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

If the dimension of any figure is 2 units by using scale factor 2/1 it will become 2 × scale factor ⇒ 2 × 2/1 = 4

Similarly,

Scale factor 8/3 creates all dimensions by a factor of 8/3 = 2.67 so all dimensions will be going to expand.

Hence "Scale factor less than 1 gives the expanded form of the figure so Elias is wrong".

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The product of 0.51 x 2.427 is 1.23777 will have five decimal places, therefore, Diego is correct

= 0.51 x 2.427 = 1.23777

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Answer:

Step-by-step explanation:

We can express the charge made by the companies as equations.

The charge made by the Company A starts at 35 cents, and cost 3 additional cents per minute. We can write this as:

[tex]charge_A(t)= 35 \ c + 3 \ \frac{c}{min} * t[/tex]

where t is the length of the call in minutes. For the company B the charge starts at 45 cents, and cost 2 additional cents per minute. This is:

[tex]charge_B(t)= 45 \ c + 2 \ \frac{c}{min} * t[/tex].

Now. At what length t' the cost of the phone call is the same? We can write the condition as:

[tex]charge_A(t')= charge_B(t')[/tex]

this means:

[tex]35 \ c + 3 \ \frac{c}{min} * t'= 45 \ c + 2 \ \frac{c}{min} * t'[/tex]

doing a little work...

[tex]35 \ c + 3 \ \frac{c}{min} * t' - 35 \ c = 45 \ c + 2 \ \frac{c}{min} * t' - 35 \ c[/tex]

[tex]3 \ \frac{c}{min} * t'= 10 \ c + 2 \ \frac{c}{min} * t'[/tex]

[tex]3 \ \frac{c}{min} * t' - 2 \ \frac{c}{min} * t'= 10 \ c[/tex]

[tex] 1 \ \frac{c}{min} * t'= 10 \ c[/tex]

[tex] \frac{1 \ \frac{c}{min} * t'}{1 \ \frac{c}{min}}= \frac{10 \ c}{1 \ \frac{c}{min}}[/tex]

[tex] t'= 10 min [/tex]

And this is the length of time we are looking for.

Answer:

Some

Step-by-step explanation:

Term and expression are two different concepts in mathematics. When numbers, symbols and operators are combined at one place to express or show some value, it is called expression. For example;

4y-3 or 3-1

It is an expression.

Where the term can be stated or defined as a single or smallest identity. Any number or variable or combination of them can be stated as term.

For example, if we take above expression 4y-3

4y-3, we can say that 4y is one term and 3 is second term.

Now the point to be noted here is, if you separately take 4y, it can be expressed as expression as well, because 4y is expressing value of something which is in accordance with the definition of expression.

1. Identity Property of Multiplication: [tex]\(1 \times (a+3) = a+3\)[/tex]

2. Associative Property of Multiplication: [tex]\((ab) c = c (ab)\)[/tex]

3. Associative Property of Multiplication: [tex]\(m (nr) = (mn) r\)[/tex]

4. Associative Property of Addition: [tex]\(2p + (3q+2) = (2p +3q) + 2\)[/tex]

5. Zero Property of Multiplication: [tex]\(2t \times 0 = 0\)[/tex]

6. Identity Property of Addition: [tex]\(0+ 2s = 2s\)[/tex]

1. Identity Property of Multiplication: [tex]\(1 \times (a+3) = a+3\)[/tex]

  - The identity property of multiplication states that any number multiplied by 1 equals the number itself.

2. Associative Property of Multiplication: [tex]\((ab) c = c (ab)\)[/tex]

  - The associative property of multiplication states that the grouping of factors does not affect the result of multiplication.

3. Associative Property of Multiplication: [tex]\(m (nr) = (mn) r\)[/tex]

  - Similar to statement 2, this demonstrates the associative property of multiplication.

4. Associative Property of Addition: [tex]\(2p + (3q+2) = (2p +3q) + 2\)[/tex]

  - The associative property of addition states that the grouping of terms does not affect the result of addition.

5. Zero Property of Multiplication: [tex]\(2t \times 0 = 0\)[/tex]

  - The zero property of multiplication states that any number multiplied by 0 equals 0.

6. Identity Property of Addition: [tex]\(0+ 2s = 2s\)[/tex]

  - The identity property of addition states that adding 0 to any number does not change the value of the number itself.

Complete question:

Name the property shown by each statement

1. 1 * (a+3) = a+3

2. (ab) c = c (ab)

3. m (nr) = (mn) r

4. 2p + (3q+2) = (2p +3q) + 2

5. 2t * 0 = 0

6. 0+ 2s = 2s

Cindy's shortcut will not work because;

She made a mistake by not multiplying the 2 tens by 3 .

Now, for 24; 2 is the tens digit and 4 is the units digit.

This means according to partial products, we can rewrite 24 as; (2 × 10) + (4 × 1)

Now, to multiply 3 by (2 × 10) + (4 × 1) gives the expression;

3[(2  × 10) + (4 × 1)]

3(2  × 10) + 3(4 × 1)

This corresponds with the solution i got which is 3(4 × 1) = 12.

Now, the second part of the solution is; 3(2  × 10) = 60

But she just used 2 tens which is (2 × 10) = 20.

This means she failed to multiply 2 tens by 3 and that was her mistake.

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