Can anyone help, please?


-1.3 ≥ 2.9 -0.6r

Graph the solution

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'.

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.

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To determine the sales tax rate, divide the sales tax amount by the item's pre-tax cost and convert to a percentage, yielding a 7% sales tax rate for this scenario.

To find the sales tax rate, you need to divide the amount of sales tax by the cost before tax and then convert it to a percentage. For an item that cost $350 before tax and had a sales tax of $24.50:

Divide the sales tax ($24.50) by the cost before tax ($350): $24.50 \/ $350 = 0.07.

Convert the decimal to a percentage: 0.07 x 100 = 7%.

Therefore, the sales tax rate for the item is 7%.

The distance traveled by the taxi on trip is 4 miles.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Flat fee of a taxicab = $2.05

Fees per mile = $0.90

The total cost = $5.65

Distance traveled by the taxi on trip is

⇒ [tex]\frac{5.65-2.05}{0.90}[/tex]

⇒ [tex]\frac{3.60}{0.90}[/tex]

⇒ [tex]4[/tex]

Hence we can conclude that the distance traveled by the taxi on trip is   4 miles.

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

The height of woman who has a shoulder width of 18.5 inches is 74 inches

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 height of a woman who has a shoulder width of 18.5 inches be = A

Now , the equation will be

The height of the woman be = 64 inches

The shoulder width of the woman be = 16 inches

So , the equation will be

Let the height of a woman who has a shoulder width of 18.5 inches be = 18.5 x ( height of the woman be / shoulder width of the woman )

Substituting the values in the equation , we get

The height of a woman who has a shoulder width of 18.5 inches be A =
18.5 x ( 64 / 4 )

The height of a woman who has a shoulder width of 18.5 inches be A =

18.5 x 4

The height of a woman who has a shoulder width of 18.5 inches be A =

74 inches

Therefore , the value of A is 74 inches

Hence ,

The height of woman who has a shoulder width of 18.5 inches is 74 inches

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Final answer:

To find the candy consumption per person per month, divide the total consumption of candy by the population and then divide by 12 months. The calculation shows that each person consumes approximately 1.815 pounds of candy per month.

Explanation:

To calculate the amount of candy consumed per person per month, we first need to divide the total annual consumption by the population of the country. The total annual consumption is 6.6 billion pounds of candy, and the population is 303 million people. So, the annual consumption per person is:

(6.6 billion pounds) / (303 million people) = 21.78 pounds/person/year.

Now, to find the monthly consumption per person, we divide the annual consumption per person by 12 (months in a year):

(21.78 pounds/person/year) / (12 months/year) = 1.815 pounds/person/month.

Therefore, each person in the country consumes approximately 1.815 pounds of candy per month.

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.

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Answer:

The nearest hundred thousand of the provided number is 100,000.

Step-by-step explanation:

Consider the provided number 89, 659

According to place value.

Hundred Th.   Ten Th.   Thousands   hundreds   Tens   Ones

   100,000       10,000        1000             100           10         1

We need to round it to the nearest hundred thousand.

The provided number can be written as 089,659

The digit at the hundred thousand place is 0.

The rule of rounding a number is:

If 0, 1, 2, 3, or 4 follow the number, then no need to change the rounding digit.

If 5, 6, 7, 8, or 9 follow the number, then rounding digit rounds up by one number.

Here, the number at the ten thousands place is 8, so to round up the number increase the digit of hundred thousand place by 1.

The digit at the hundred thousand place is 0 so increase it by 1.

Thus, the number can be rounded to the nearest hundred thousand is shown as:

100,000

The nearest hundred thousand of the provided number is 100,000.

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

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.

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.