Question#2: a wise man once said 300 reduced by 4 times my age is 32 what is his age

Answer:

Sales tax for the refrigerator is $31.53.

Step-by-step explanation:

The price of a refrigerator = $525.50

Sales tax rate = 6%

Sales tax on the price of refrigerator = 6% × 525.50

                                                             = [tex]\frac{6}{100}[/tex] × 525

                                                             = 0.06 × 525.50

                                                             = $31.53

Sales tax for the refrigerator is $31.53.

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.

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.

The problem is solved by setting up a ratio of green lights to white lights. Given 30 green lights, and knowing the ratio is 6 green lights for every 4 white lights (or 3:2), we find that there are 20 white lights.

The problem can be solved by setting up a ratio. We know that for every 6 green lights, there are 4 white lights. Therefore the ratio of green lights to white lights is 6:4, or simplified to 3:2. Given that there are 30 green lights on the string, we can set up the equation (3/2 = 30/x), where x represents the number of white lights. Solving for x (multiplying both sides by 2 and then dividing both sides by 3) gives us x = 20. Therefore, there are 20 white lights on the string.

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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.

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.

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.

The area of rectangular shelf with length 5 feet and width 3 feet is 15 feet².

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of rectangular shelf = 5 feet

The width of rectangular shelf = 3 feet

We know that;

Area of rectangle = Length × Width

So, We get;

The area of rectangular shelf = 5 × 3

                                             = 15 feet²

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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.

The result of the expression 18(26) using the distributive property is 468

Given the product of integers 18(26), we are to write it using the distributive property.

Given 3 integers A, B and C

A(B+C) = AB + AC

This shows that the variable A was distributed over A and B

Applying this in the given question;

18(26) = 18 (20 + 6)

18(26) = 18 (20) + 18(6)

18(26)  = 360 +  108

18(26)  = 468

Hence the result of the expression 18(26) using the distributive property is 468

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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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