in 2009 there were three times as many millionares in kentucky as there were in rhode island. Together, a total of 84 thousand millionaires lived in the two states . find the number of millionaires in each of these states

The answer can be written in statement form as,"Time measured in minutes is an example of a(n) interval scale."

A numerical scale known as an interval scale is one in which both the order of the variables and their differences are known. Using the Interval scale, variables with recognizable, consistent, and calculable differences are categorized.

It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving.

The value of time is given in minutes.

The given quantity can be measured on interval scale.

Hence, the required scale is known as interval scale.

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Answer:

Any proposed solution of a rational equation that causes a denominator to equal​ __ZERO__ is rejected.

Step-by-step explanation:

We will show this statement is true by an example:

Consider the expression :  [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]

Now, solved the rational expression and check its proposed solution

[tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]

x cannot equal to 4, as it makes  both denominators equal to zero.

Multiply both the sides by (x-4),

[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot\left ( \frac{x}{x-4}+4  \right )\\[/tex]

Now, use the distributive property on Right hand side,

[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot \left ( \frac{x}{x-4} \right )+\left (x-4 \right )\cdot 4\\[/tex]

Simplify the above expression,

[tex]x=x+4x-16[/tex]

Combine like terms,

[tex]x-x-4x=-16[/tex]

[tex]-4x=-16[/tex]

Divide both sides by -4, we get

[tex]\frac{-4x}{-4}=\frac{-16}{-4}[/tex]

[tex]x=4[/tex].

As we know that x cannot equal to 4, replacing x=4 in the original expression causes the denominator equal to 0.

Check the solution: [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]

Substitute the value of x=4 in the original expression,

[tex]\frac{4}{4-4}=\frac{4}{4-4}+4[/tex]

[tex]\frac{4}{0}=\frac{4}{0}+4[/tex]

Thus, 4 must be rejected as the solution, and the solution set is only 0.

A proposed solution of a rational equation that causes a denominator to equal zero is rejected because division by zero is not possible.

Any proposed solution of a rational equation that causes a denominator to equal zero is rejected. When the denominator of a rational equation is zero, the fraction becomes undefined because division by zero is not possible. In mathematics, division by zero is an undefined operation.

The quadratic formula can be used to find the solutions of a quadratic equation. In this case, the equation is 2x² - 3x - 5 = 0. Using the quadratic formula, the two solutions are x = 2 and x = -1.

To find the solutions to the equation 2x² - 3x - 5 = 0, we can use the quadratic formula. The formula states that the solutions of any quadratic equation ax² + bx + c = 0 can be calculated using the formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:

x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))

Simplifying further, we have:

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

Therefore, the two solutions to the equation 2x² - 3x - 5 = 0 are x = (3 + 7) / 4 = 2 and x = (3 - 7) / 4 = -1.

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Answer: 120 different combinations  .

Step-by-step explanation:

The combination of n things taking m things at a time is given by :-

[tex]C(n,m)=\dfrac{n!}{m!(n-m)!}[/tex]

Given : The total numbers of errands = 6

Now, the combination of 6 errands taking 3 at a time is given by :-

[tex]C(6,3)=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]

Hence, he could choose to run 120 different combinations of three errands .

Hypothesis 1 supported (potentially adapted wings), 2 needs more data, 3 and 4 not supported (scavengers and traffic constant).

Here's how to proceed:

1. Match Data to Hypotheses:

Hypothesis 1:

Relevant Data: "The wing shapes of swallows killed on roads differ from those of the general population."

Hypothesis 2:

Relevant Data: Not directly provided in the given options. More information is needed about the actual population size of cliff swallows living near roads over time.

Hypothesis 3:

Relevant Data: "Avian scavengers did not increase during this time, and terrestrial scavengers probably did not increase."

Hypothesis 4:

Relevant Data: "Car traffic stayed the same or increased during this time."

2. Evaluate Hypothesis Support:

Hypothesis 1:

Supported (additional data may be needed). The wing shape difference suggests potential adaptation, but more evidence would strengthen the conclusion.

Hypothesis 2:

Cannot be determined without direct data on population size changes.

Hypothesis 3:

Not supported (probably not a factor). The data indicates scavenger populations haven't increased, suggesting they aren't significantly affecting the number of road-killed swallows found.

Hypothesis 4:

Not supported (probably not a factor). The data shows car traffic has remained steady or increased, making it less likely to be the cause of a decrease in observed road-killed swallows.

Complete Question:

The expression for the number of quarters Peter has in terms of the number of dimes is [tex]\( \frac{3}{4}d \)[/tex].

Let's denote the number of dimes Peter has as [tex]\( d \)[/tex]. According to the problem, Peter has three times as many quarters as dimes. Therefore, if we let [tex]\( q \)[/tex] represent the number of quarters, we can write the relationship between the number of quarters and dimes as:

[tex]\[ q = 3d \][/tex]

However, the question asks for an expression that gives the number of quarters in terms of the number of dimes, but using the same variable [tex]\( d \)[/tex]  to represent the total value of the dimes in dollars. Since each dime is worth $0.10, the total value of the dimes in dollars is:

[tex]\[ \text{Total value of dimes} = 0.10d \][/tex]

To find the number of quarters in terms of the total value of the dimes in dollars, we need to divide the total value of the dimes by the value of one quarter, which is $0.25, and then multiply by 3 because there are three times as many quarters as dimes:

[tex]\[ q = \frac{0.10d}{0.25} \times 3 \][/tex]

Simplifying the fraction [tex]\( \frac{0.10}{0.25} \)[/tex] gives us [tex]\( \frac{1}{2.5} \)[/tex], which simplifies further to [tex]\( \frac{2}{5} \)[/tex]. Therefore:

[tex]\[ q = \frac{2}{5}d \times 3 \][/tex]

[tex]\[ q = \frac{3}{5} \times 2d \][/tex]

[tex]\[ q = \frac{3}{5} \times 2 \times \frac{d}{1} \][/tex]

[tex]\[ q = \frac{3}{5} \times \frac{2d}{1} \][/tex]

[tex]\[ q = \frac{3}{5} \times d \times 2 \][/tex]

[tex]\[ q = \frac{3}{5} \times d \times \frac{2}{1} \][/tex]

[tex]\[ q = \frac{3}{5} \times \frac{2d}{1} \][/tex]

[tex]\[ q = \frac{3 \times 2d}{5} \][/tex]

[tex]\[ q = \frac{6d}{5} \][/tex]

However, we must remember that the original relationship was [tex]\( q = 3d \)[/tex], not . This means we made a mistake in our calculation. Let's correct it:

[tex]\[ q = 3d \][/tex]

Since each quarter is worth $0.25, the total value of the quarters in dollars is:

[tex]\[ \text{Total value of quarters} = 0.25q \][/tex]

[tex]\[ \text{Total value of quarters} = 0.25 \times 3d \][/tex]

[tex]\[ \text{Total value of quarters} = 0.75d \][/tex]

Now, to express the number of quarters [tex]\( q \)[/tex] in terms of the total value of the dimes in dollars using the same variable [tex]\( d \)[/tex], we need to adjust our equation to account for the value difference between dimes and quarters. Since the value of the dimes is given in dollars as [tex]\( d \)[/tex], and each quarter is worth $0.25, we can express the number of quarters as:

[tex]\[ q = \frac{d}{0.25} \times 3 \][/tex]

[tex]\[ q = \frac{d}{\frac{1}{4}} \times 3 \][/tex]

[tex]\[ q = d \times 4 \times 3 \][/tex]

[tex]\[ q = 4d \times 3 \][/tex]

[tex]\[ q = 12d \][/tex]

But this is not the expression we are looking for, as it gives us the number of quarters in terms of the total value of the dimes in dollars, not in terms of the number of dimes. We need to divide by 10 to convert the total value of the dimes in dollars back to the number of dimes:

[tex]\[ q = \frac{12d}{10} \][/tex]

[tex]\[ q = \frac{3}{4}d \times 4 \][/tex]

[tex]\[ q = 3d \][/tex]

This is the correct expression, as it gives us the number of quarters in terms of the number of dimes, with [tex]\( d \)[/tex] representing the number of dimes, not their value in dollars.