a reasonable estimate for 697 x 82 = 56,000. is this correct?

The art student decorating two gift boxes will cut full 78 pieces of paper from the roll that are 1/6 yard each, using a total of 2 1/6 yards of paper.

The art student is decorating two gift boxes using wallpaper that must be cut into 1/6 yard pieces. The student will use 1 1/3 yards of paper to decorate one box and 5/6 yard of paper to decorate the other box. To find out how many pieces of paper the student will cut, we first need to add the lengths of paper used for both boxes which gives us 2 1/6 yards.

To convert this total length into 1/6 yard pieces, we can divide the total length by the length of each piece. Therefore, 2 1/6 yards equals 13/6 yards. When we divide 13/6 by 1/6, we get 78. So, the student will cut 78 pieces for the gift boxes.

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Answer:

2.5 or 2.500

Step-by-step explanation:

Equivalent decimals are that decimal which is equal.

If we put zero on the right side of digit after decimal then it is said to be equivalent digits.

2.50 is called as 250 hundredth

2.5 is called as 25 tenth

2500 is called as 2500 thousandth

All 2.50, 2.5 and 2.500 are equal.

The two numbers that are equivalent to 2.50 are 2.5 and 2.50.

We have,

When we write a decimal number, the trailing zeros after the decimal point do not change the value of the number.

Thus, 2.5 and 2.50 represent the same value of 2.50.

The first decimal, 2.5, is the simplified or standard form of the number.

It is commonly used when the exact level of precision is not required or when rounding is involved.

In this case, 2.5 provides sufficient information about the number without the need for the trailing zero.

The second decimal, 2.50, includes the trailing zero.

This format is often used when a specific level of precision is desired or when the number is part of a larger set of numbers with consistent decimal places.

The trailing zero helps to maintain a consistent number of decimal places and can be useful in situations where exactness is important.

Thus,

Both 2.5 and 2.50 represent the same value of 2.50, with the second decimal including a trailing zero for added precision or formatting purposes.

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The student made mistake in step 2

The correct answer is an option (B)

"It is a mathematical statement which consists of equal symbol between two mathematical expressions."

"It is a value of the variable which makes equation true."

For given question,

We have been given an equation [tex]x^{2} +14x+45=0[/tex]

A student performed the following steps to find the solution to the equation [tex]x^{2} +14x+45=0[/tex]

Step1: factor the polynomial into (x+5) and (x+9)

Step2: x+5=0 and x-9=0

Step 3: x=-5 and x=9

Now we solve given equation.

[tex]\Rightarrow x^{2} +14x+45=0\\\\\Rightarrow x^{2} +9x+5x+45=0\\\\\Rightarrow x(x+9)+5(x+9)=0\\\\\Rightarrow (x+9)(x+5)=0\\\\\Rightarrow x+9=0~~and~~ x+5=0\\\\\Rightarrow x=-9~~and~~ x=-5[/tex]

We can observe that the student made mistake in step 2.

In stead of factor (x + 9), he wrote (x - 9)

Therefore, the student made mistake in step 2

the correct answer is an option (B)

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9/5 = 54/30

1/6 = 5/30

54/30 - 5/30 = 49/30 = 1 19/30

The difference is as follows:

  [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{49}{30}[/tex]

We are given two fractions and we are asked to find there difference.

The expression is as follows:

   [tex]\dfrac{9}{5}-\dfrac{1}{6}[/tex]

( since, the denominator of two fractions is different hence we take the least common multiple of the denominators.

i.e. lcm{5,6}=30 )

Now, we proceed as follows:

   [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{9\times 6-1\times 5}{30}[/tex]

i.e.

   [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{54-5}{30}[/tex]

i.e.

   [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{49}{30}[/tex]

The four-digit number that fits all the given conditions is 4710. It ends in 0 to be divisible by 5 and by 6, has a hundreds digit of 7, tens and ones digits that sum to 1, and has a total digit sum of 12, while being less than 5000.

Finding the Four-Digit Number

To find this four-digit number, we need to follow the given conditions closely:

The number is divisible by 5, which means the last digit must be either 0 or 5.

It is also divisible by 6, which means the number must be divisible by both 2 and 3. Since the last digit is 0 or 5, to be divisible by 2, it must end in 0.

The sum of its digits is 12.

The hundreds digit is 7.

The sum of the hundreds, tens, and ones digits is 8, but since the hundreds digit is 7, the tens and ones must add up to 1.

The tens and ones digits must have a difference of 1.

Only one of its digits is divisible by 3, which must be the hundreds digit, 7.

It is less than 5000.

Considering all of the above, let's start by deciding the tens and ones digits. They must add to 1, and their difference must be 1. This means the tens digit is 1 and the ones digit is 0.

With a hundreds digit of 7, tens digit of 1, and ones digit of 0, the sum of the digits so far is 8. To make the total sum 12, the thousands digit must be 4.

The complete number following all these conditions is 4710.

As per linear equation, the value of 'c' equals 3/4.

A linear equation is an equation that contains one or multiple variable with the highest power of the variable is one.

Given, (3 - 5c) is 1 less than the value of (1 - c).

Therefore, (1 - c) - 1 = (3 - 5c)

⇒ - c = 3 - 5c

⇒ 4c = 3

⇒ c = 3/4

Hence, the value of 'c' is 3/4.

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Answer

So, you walked 6.5 miles from the lake back to your house, and the total distance you walked is 13 miles.

Step-by-step explanation:

To find the distance from the lake back to your house, we need to remember that the path is a straight line. Since you walked 2 miles from your house to the park and 4.5 miles from the park to the lake, the total distance you walked from your house to the lake is 2 + 4.5 = 6.5 miles.

Since you're returning home along the same straight path, the distance from the lake back to your house is also 6.5 miles.

To find the total distance you walked, you can add the distances for each leg of the journey. In this case, you walked 2 miles from your house to the park, 4.5 miles from the park to the lake, and 6.5 miles from the lake back to your house. Therefore, the total distance you walked is 2 + 4.5 + 6.5 = 13 miles.

The distance from the lake straight back to the house is 6.5 miles, the same as the total distance walked to reach the lake. As such, the total distance you walk is 13 miles.

To answer your question on distance calculation, first, we must understand that the distance from the lake directly back to your house is exactly the same as the distance you walked from your house to the park and then to the lake. This is because distance is the total amount of space between two points, regardless of the path taken. So, the

distance from the lake to your house is 2 miles (from your house to the park) plus 4.5 miles (from the park to the lake), for a total of 6.5 miles. Therefore, the total distance you walk is 2 miles to the park, 4.5 miles to the lake, and 6.5 miles back to your house, adding up to 13 miles altogether.

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You can go on a maximum of 5 rides with $16 after paying for the $5 admission at the amusement park, where each ride costs $2.

The amusement park charges $5 for admission and $2 for each ride. We can write an expression for the total cost as C = 5 + 2r, where C is the total cost and r is the number of rides. To find out how many rides you can go on with $16, we would set up the equation 16 = 5 + 2r.

Step-by-step solution:

Since you cannot go on half a ride, you could go on a maximum of 5 rides with your $16.

Dr. Hong prescribed the most medicine, and Dr. Evans prescribed the least medicine. This was determined by assuming Dr. Tannenbaum's prescription as a base and calculating the others accordingly.

To determine who prescribed the most and the least medicine, we need to perform a simple calculation based on the given information:

From these calculations:

Therefore, Dr. Hong prescribed the most medicine, and Dr. Evans prescribed the least medicine.

The perimeter of the rectangular football field, with a length of 110 yards and width of 55 yards, is calculated as 330 yards.

To calculate the perimeter of this rectangular football field, we need to add up the lengths of all four sides. Given that the width of the football field is 55 yards and the length is 110 yards, the formula to calculate the perimeter (P) of a rectangle is P = 2L + 2W where L is the length and W is the width.

Substituting the given numbers, we get P = 2(110) + 2(55) = 220 + 110 = 330 yards. Therefore, the perimeter of the football field is 330 yards.

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