The weight of outlet boxes is proportional to the volume of boxes involved. if 400 boxes weigh 120 pounds, how much would 500 boxes weigh?

600 can be written as [tex]\(2^3 \times 3^1 \times 5^2\)[/tex], where 2, 3, and 5 are prime numbers.

To express 600 as the product of prime numbers, we'll use prime factorization.

Prime factorization involves breaking down a number into its prime factors.

Here's how we can do it:

**Start with the smallest prime number, 2:**

  [tex]\( 600 \div 2 = 300 \)[/tex]

  [tex]\( 300 \div 2 = 150 \)[/tex]

  [tex]\( 150 \div 2 = 75 \)[/tex]

**Next, continue with the next smallest prime number, 3:**

  [tex]\( 75 \div 3 = 25 \)[/tex]

  [tex]\( 25 \div 5 = 5 \)[/tex]

**Now, we can't divide further by smaller prime numbers, so we try dividing by the next smallest prime, 5:**

  [tex]\( 5 \)[/tex] is already a prime number.

**There are no more prime factors to consider, so we stop.**

Now, let's write down the prime factors we obtained:

[tex]\[ 600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 \][/tex]

So, [tex]\( a = 2 \), \( b = 2 \), \( c = 3 \), and \( d = 5 \).[/tex]

Therefore, we can write:

[tex]\[ 600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 \][/tex]

Thus, [tex]\( 600 \)[/tex] can be written as [tex]\( 2^3 \times 3^1 \times 5^2 \)[/tex], where [tex]\( 2, 3, \) and \( 5 \)[/tex] are all prime numbers.

Final answer:

The function g(x), being different for rational and irrational numbers, is nowhere continuous on the set of real numbers because it cannot satisfy the condition for continuity at any point.

Explanation:

We are asked to determine for what values of x the function g(x) is continuous. The function is defined to be 0 if x is rational, and 4x if x is irrational, over the set of real numbers. First, let's understand a key concept: for a function to be continuous at a point, the limit of the function as it approaches the point from either direction must be equal to the function's value at that point. In the case of g(x), the function takes the value of 0 for all rational numbers, but instantly changes to 4x for irrational numbers which are densely populated around every rational number.

Since the value of g(x) for rationals (0) is different from the nearby values for irrationals (which would be non-zero and depend on x), g(x) does not have a limit that equals its value at rational points and thus cannot be continuous at any rational number. Moreover, at irrational values of x, we cannot have continuity either, as any neighborhood around an irrational number contains rational numbers where g(x) would suddenly jump to 0, disrupting the limit process once again.

Therefore, the function g(x) is nowhere continuous on the set of real numbers since it cannot satisfy the condition for continuity at any point. Hence, the correct answer to the given question is 'none of these'.

Answer:

Option A : [tex]\frac{log(x+2)}{log(4)}[/tex]

Step-by-step explanation:

Write the expression when the change of base formula is applied to log4(x+2

Given [tex]log_4(x+2)[/tex]

USe change of base formula

[tex]log_b(a)= \frac{log(a)}{log(b)}[/tex]

WE apply change of base formula for the given log

the base of log becomes the denominator .

Numerator becomes the x+2

[tex]log_4(x+2)= \frac{log(x+2)}{log(4)}[/tex]

option A is the correct answer

A because you are multiplying 3/4 by 1/2, you make the product smaller than 3/4

B beacue any number multiplied by one remains that number, since you are multiplying 3/4 by 1 it will remaim 3/4

C because the number multiplied by 3/4 is larger than 1 ( 3/2 = 1 1/2) the product will be larger than 3/4

The number of pounds of coffee used is 30 pounds.

Given data:

Let x be the number of pounds of type A coffee used.

Since the blend uses three times as many pounds of type B coffee as type A, the number of pounds of type B coffee used is 3x.

The cost of type A coffee is $4.50 per pound, so the cost of x pounds of type A coffee is 4.50x dollars.

The cost of type B coffee is $5.50 per pound, so the cost of 3x pounds of type B coffee is 5.50 * 3x = 16.50x dollars.

The total cost of the blend is $634.50, so the equation is:

4.50x + 16.50x = 634.50

Combine like terms:

21x = 634.50

On solving for x:

x = 634.50 / 21

x = 30

Hence, 30 pounds of type A coffee were used in the blend.

To learn more about equations, refer:

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Answer:

[tex]3ax+3b^2-3c+2[/tex]

Step-by-step explanation:

We have been given an expression [tex]3(ax+b^2-c)+2[/tex]. We are asked to remove the parenthesis and combine like terms for our given expression.

Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:

[tex]3*ax+3*b^2-3*c+2[/tex]

[tex]3ax+3b^2-3c+2[/tex]

We can see that our given expression don't have like terms, therefore, our expression would be [tex]3ax+3b^2-3c+2[/tex].

Answer:

The equation is:  x + 20 = 44

The area of the rectangle is 24 inches.

Step-by-step explanation:

The total area of the shape is 44 square inches.

The area of the triangle is 20 square inches.

We need to find the area of the rectangle.

Total area = Area of the triangle + Area of the rectangle.

Let "x" be the area of the rectangle.

So the equation is

44 = 20 + x

This can be written as x + 20 = 44

Now let's find the value fo x.

Subtract 20 from both sides, we get

x + 20 - 20 = 44 - 20

x = 24 square inches.

Therefore, the area of the rectangle is 24 inches.

(450-210)/4+50=110

 hope this helps

597 is a greater value than 579.

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Rounding some number to a specific value is making its value simpler mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We have to find How are the numbers 579 and 597 different to each other.

As we can see that the last two digit of the numbers 79 and 97 are flipped.

We know that 97 is greater than 79.

Therefore, 597 is a greater value than 579.

Learn more about a number pattern:

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I just had the same question on a test and the answer was 90 MPH. Hope this helps somebody!