Store ABC sells 8 lbs. of oranges for $6.00. Store XYZ sells 14 lbs. or oranges for $11.20. Which store is less expensive, and by how much per pound?
1. ABC is less expensive by $.50 per pound
2. XYZ is less expensive by $.50 per pound
3. ABC is less expensive by $.05 per pound
4. XYZ is less expensive by $.05 per pound

Chad bought 8 dozens of note pads, which totals 96 note pads. When he divides these into 6 boxes, each box will contain 16 note pads.

To solve the problem of dividing 8 dozen note pads equally into 6 boxes, we first need to know the total number of note pads Chad has. As one dozen is equal to 12 objects, Chad has 8 x 12 = 96 note pads. Then, we divide this total by the number of boxes to find out how many note pads go into each box.

So, 96 note pads / 6 boxes = 16 note pads per box.

To find the new coordinates of point F after translating it 4 units left and 3 units up, we adjust its x-coordinate by subtracting 4 and its y-coordinate by adding 3, resulting in the new coordinates (2, 11).

The student is asking about a translation of a geometric figure in the coordinate plane. The coordinates of point F are initially (6,8). A translation of 4 units left and 3 units up would change these coordinates. To translate 4 units left, we subtract 4 from the x-coordinate, and to translate 3 units up, we add 3 to the y-coordinate.

Therefore, the new coordinates of point F after the translation would be:

F' = (6 - 4, 8 + 3) = (2, 11).

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The distributive property of multiplication over addition can be used when you multiply a number by a sum. The distributive property lets you multiply a sum by multiplying each addend separately and then add the products:

[tex] a\cdot (b+c)=a\cdot b+a\cdot c. [/tex]

The distributive property of multiplication over subtraction can be used when you multiply a number by a difference. The property states that the product of a number and the difference of two other numbers is equal to the difference of the products:

[tex] a\cdot (b-c)=a\cdot b-a\cdot c. [/tex]

Therefore, you can see what sign is in the brackets, if sign is "+", then you have to add, if sign is "-", then you have to subtract.

The addition or subtraction in the distribution property depends on the sign between the two real numbers in the expression.

Further explanation:

The distributive property states that if a number [tex]a[/tex] is multiplied with the sum of the two numbers [tex]b[/tex] and [tex]c[/tex] then the result is same as if the numbers are multiplied separately.

[tex]\fbox{\begin\\\ \math a(b+c)=(a\cdot b)+(a\cdot c)\\\end{minispace}}[/tex]          ....(1)

The distributive property states that if a number [tex]a[/tex] is multiplied with the difference of the two numbers [tex]b[/tex] and [tex]c[/tex] then the result is same as if the numbers are multiplied separately.

[tex]\fbox{\begin\\\ \math a(b-c)=(a\cdot b)-(a\cdot c)\\\end{minispace}}[/tex]             ....(2)

For example: Consider [tex]5[/tex] as [tex]a[/tex], [tex]6[/tex] as [tex]b[/tex] and [tex]2[/tex] as [tex]c[/tex].

Substitute [tex]5[/tex] for [tex]a[/tex], [tex]6[/tex] for [tex]b[/tex] and [tex]2[/tex] as [tex]c[/tex] in the equation (1) as follows:

[tex]\begin{aligned}5(6+2)&=(5\cdot 6)+(5\cdot 2)\\5\cdot 8&=30+10\\40&=40\end{aligned}[/tex]  

Now, substitute [tex]5[/tex] for [tex]a[/tex], [tex]6[/tex] for [tex]b[/tex] and [tex]2[/tex] as [tex]c[/tex] in the equation (2) as follows,

[tex]\begin{aligned}5(6-2)&=(5\cdot 6)-(5\cdot 2)\\5\cdot 4&=30-10\\20&=20\end{aligned}[/tex]

Therefore, the addition or subtraction in the distributive property is based on the sign between the two real numbers. If the sign between the real number is positive then the numbers are added and if the sign between the real number is negative then the numbers are subtracted.

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Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Real numbers

Keywords: Distributive property, a(b+c)=ab+ac, a(b-c)=ab-ac, real numbers, positive value, negative value, multiply, add, sum, difference.

The cost of 4.5 pounds of peanut is $9.45.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Cost of 3 pounds peanuts = $6.30

So, Cost of 1 pounds = 6.30/ 3

                                   = $2.10

Then, Cost of 4.5 pounds

= 4.5 x 2.10

= $9.45

Hence, cost of 4.5 pounds of peanut is $9.45.

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By subtracting the weight difference of 24.8 pounds from the Springer Spaniel's weight of 48.5 pounds, we determine that the Cocker Spaniel weighs 23.7 pounds.

The question involves basic arithmetic, specifically subtraction, to solve for the weight of the Cocker Spaniel.

First, we need to start with the weight of the Springer Spaniel, which is given as 48.5 pounds. The Cocker Spaniel weighs 24.8 pounds less than the Springer Spaniel.

To find the weight of the Cocker Spaniel, we simply subtract:

48.5 pounds (Springer Spaniel's weight) - 24.8 pounds (difference in weight) = 23.7 pounds (Cocker Spaniel's weight)

Therefore, the Cocker Spaniel weighs 23.7 pounds.

Answer:

a. 992 stickers

b. 2 stickers

c. 4 stickers

Step-by-step explanation:

Let Lindsay has x stickers,

∵ Menon has 4 times as many stickers as Lindsay,

So, the number of stickers Menon has = 4x,

Thus, the total stickers = x + 4x = 5x

According to the question,

5x = 1240

⇒ x = 248,

a. Thus, the number of stickers Menon has = 4x = 4(248) = 992,

b. If Menon fills some pages in album such that each page contains 6 stickers,

Then the number of such pages = [tex]\frac{\text{stickers contained by Menon}}{6}[/tex]

[tex]=\frac{992}{6}[/tex]

= 165 pages and 2 stickers,

Thus, 2 stickers are left over.

c. ∵ Every page contains 6 stickers,

I.e. he needs 4 more stickers for one more page.

There are 53 rolls of wrapping paper.

To solve for the number of rolls of wrapping paper that Shya has, we can set up a system of linear equations based on the information provided:

Let R be the number of rolls of wrapping paper.

Let P be the number of packages.

From the question, we have two equations:

R + P = 125 (the total number of rolls and packages)

3.50R + 2.25P = 347.50 (the total cost of rolls and packages)

To find the value of R, we will solve this system using the substitution or elimination method.

First, let's use the substitution method by expressing P in terms of R from the first equation:

P = 125 - R

Now substituting this expression into the second equation gives us:

3.50R + 2.25(125 - R) = 347.50
3.50R + 281.25 - 2.25R = 347.50
1.25R = 347.50 - 281.25
1.25R = 66.25
R = 66.25 / 1.25
R = 53

Therefore, there are 53 rolls of wrapping paper.

Simon bought a $48 table on sale. The price of the table can be estumated by $50.

The sale propose 30% off, then an estimate for the discount can be calculated using proportion:

$50 -- 100%,

$x -- 30%

that is mathematically

[tex]\dfrac{\$50}{\$x}=\dfrac{100\%}{30\%}.[/tex]

Find x:

[tex]\$x=\dfrac{\$50\cdot 30\%}{100\%}=0.3\cdot \$50.[/tex]

Answer: correct choice is B

Answer:

b. [tex]0.3\cdot(50)[/tex]

Step-by-step explanation:

We have been given that Simon bought a $48 table on sale at 30% off. We are asked to choose the correct option that gives an estimate for the discount .

Since 48 is very closer to 50, so to find an estimated amount of discount we need to find 30% of 50.

[tex]\text{Estimated amount of discount}=30\%\text{ of }50[/tex]

[tex]\text{Estimated amount of discount}=\frac{30}{100}\cdot(50)[/tex]

[tex]\text{Estimated amount of discount}=0.3\cdot(50)[/tex]

Therefore, an estimate for the discount is [tex]0.3\cdot(50)[/tex] and option 'b' is the correct choice.

Answer: 22 feet per second

Step-by-step explanation:

Hi, the question asks for the speed rate in feet per second.

Since 1 minute = 60 seconds, 4 minutes x 60 = 240 seconds.

So, he ran 5,280 feet in 240 seconds.

To calculate the speed rate in feet per second we simply have to divide the distance (5280) by the time (240):

5280 feet / 240 sec = 22 feet per second

Feel free to ask for more if needed or if you did not understand something.

Answer:

Option (b) is correct.

The monthly bill if we uses 50 additional minutes this month is $ 55

Step-by-step explanation:

Given: Your new cell phone plan charges $50 per month for 400 minutes of talk time. The plan charges $0.10 for each additional minute you talk.

We have to find the monthly bill if we uses 50 additional minutes this month.

Consider the given plan.

cell phone plan charges $50 per month for 400 minutes of talk time. The plan charges $0.10 for each additional minute you talk.

Let the monthly charge be y and x be the number of additional minutes.

So, the equation becomes,

y = 50 + 0.10(x)

For, The given month the additional minutes are 50.

so, y = 50 + 0.10(50) = 55

Therefore, The monthly bill if we uses 50 additional minutes this month is $ 55

The value of the expression s is 12 1/4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the given expression be s + 1/4 = 12 1/2

On Simplifying the equation , we get

s + 1/4 = 12 1/2

Now ,

1/4 = 0.25

1/2 = 0.5

So , Subtracting 1/4 on both sides , we get

s = 12 1/2 - 1/4

s = 12.5 - 0.25

s = 12.25

And ,

Substituting the value of 1/4 from the expression , we get

s = 12 1/4

Hence , the value of the expression s is 12 1/4

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Final answer:

The height of the computer monitor with a 15-inch diagonal and 13-inch width, using the Pythagorean theorem, is approximately 7.5 inches.

Explanation:

To find the height of the computer monitor when given the diagonal length and the width, we can use the Pythagorean theorem.

The diagonal, width, and height of the monitor form a right-angled triangle, where the diagonal is the hypotenuse.

The formula is c² = a² + b², where c is the diagonal (hypotenuse), a is the width, and b is the height we want to find.

Let's plug in the values we have: 15² = 13² + b².

Simplifying, we get 225 = 169 + b². Subtract 169 from both sides to get b² = 56. Take the square root of both sides to find the height, which gives us b ≈ 7.5 inches.

Hence, the height of the screen would be approximately 7.5 inches when rounded to the nearest tenth.