The number of the day is 936,165

Final answer:

The minimum cost combination of film production employees is 12 technical crew members and 24 support staff members, with a minimum feasible cost of $420,000.

Explanation:

To determine the combination of employees that will minimize the cost, let's set up variables for technical crew members (T) and support staff members (S).

The pay scales are $15,000 for each technical crew member (T) and $10,000 for each support staff member (S).

The objective is to minimize the cost C, where C = 15,000T + 10,000S.

From the constraints provided:

To minimize the cost while satisfying all constraints, we should aim to hire as few technical crew members as possible, given they are more expensive.

If T = 12 (the minimum), we can solve for S using T ≥ 0.5S, which gives us S ≥ 24.

However, S must be even due to the constraint T ≥ 0.5S and hence we can set S = 24 as a candidate solution, resulting in the minimum number of employees (12 + 24 = 36).

We also need to ensure that S ≤ 2T to satisfy the condition T ≥ 0.5S; with T = 12, the maximum S can be is 24.

The minimum feasible cost is determined by plugging T = 12 and S = 24 into the cost equation:

C = 15,000(12) + 10,000(24) = 180,000 + 240,000 = $420,000.

Jen: 1 2/3 = 5/3 *4 = 20/3 = 6 2/3 miles per hour

Max: 1 1/2 = 3/2 * 5 = 15/2 = 7 1/2 miles per hour

Max runs faster

Answer:

Max runs faster than Jen.

Average speed = 7.085 Miles per Hour

Step-by-step explanation:

Distance covered by Jen = [tex]1\frac{2}{3} = \frac{5}{3} \text{ miles}[/tex]

Time taken by Jen = [tex]\frac{1}{4}\text{ hours}[/tex]

Distance covered by Max = [tex]1\frac{1}{2} = \frac{3}{2} \text{ miles}[/tex]

Time taken by Jen = [tex]\frac{1}{5}\text{ hours}[/tex]

Formula:

[tex]Speed = \displaystyle\frac{Distance}{Time}[/tex]

Speed of Jen = [tex]\displaystyle\frac{\frac{5}{3} }{\frac{1}{4} } = \frac{20}{3} = 6.67 \text{ miles per hour}[/tex]

Speed of Max = [tex]\displaystyle\frac{\frac{3}{2} }{\frac{1}{5} } = \frac{15}{2} = 7.5 \text{ miles per hour}[/tex]

Hence, Max runs faster than Jen.

Average speed:

[tex]\displaystyle\frac{\text{Speed of Max + Speed of Jen}}{2} \\\\= \dsplaystyle\frac{6.67 + 7.5}{2} = 7.085\text{ Miles per Hour}[/tex]

Answer:

70

Step-by-step explanation:

10*7=70

To solve x/6 - x/7 = ab, find the common denominator, simplify, and then isolate x by multiplying both sides of the equation by the common denominator. The solution is x = 42ab. Always check your answer to ensure it satisfies the original equation.

To solve the equation x/6 - x/7 = ab, one must find a common denominator for the fractions. In this case, the common denominator is 42 because 6 and 7 are both factors of 42. By converting both fractions to have the denominator of 42, we have:(7x/42) - (6x/42) = ab

This simplifies to x/42 = ab, since 7x - 6x is x. Now, multiply both sides by 42 to get x = 42ab.

If we want to solve the equation for a variable other than x, such as y, we might need to return b to denominator status, which implies that we need to divide both sides by b if b represents a multiplication factor for y.

It's also important to confirm that our manipulations haven't altered the value of the equation, which can be done by checking the answer at the end to ensure it is reasonable and satisfies the original equation.

area of a square is S^2

2.6^2 = 6.76 square cm

The value of x is 1 after applying the property of the subtraction and division if the equation is 0.6x + 0.8 = 1.4.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The linear equation is:

0.6x + 0.8 = 1.4

Subtract 0.8 on both sides

0.6x = 1.4 - 0.8 (Subtraction property of the equality)

0.6x = 0.6

Divide by 0.6 into both sides

x = 1  (Division property of equality)

Thus, the value of x is 1 after applying the property of the subtraction and division if the equation is 0.6x + 0.8 = 1.4.

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m/18 = 15/12

m12 = 270

m = 270 /12 = 22.5

C. m = 22.5

Final answer:

The bookstore sold 107 notebooks at 38¢ each and 241 notebooks at 25¢ each. A system of equations was used to determine the number of each notebook sold.

Explanation:

Let's denote the number of notebooks sold at 25¢ each as [tex]x[/tex] and the number of notebooks sold at 38¢ each as [tex]y[/tex] .

We are given two pieces of information:

We can set up a system of two equations to represent this information:

[tex]x+ y = 348[/tex]                       (Equation 1)

[tex]0.25x + 0.38y = 100.91[/tex]      (Equation 2)

Now, we can solve this system of equations to find the values of x and y.

Multiply Equation 1 by 0.25 to make the coefficients of x in both equations the same:

[tex]0.25x + 0.25y = 87[/tex]             (Equation 3)

​Now, subtract Equation 3 from Equation 2 to eliminate [tex]x[/tex] :

[tex]( 0.25x + 0.38y ) - ( 0.25x +0.25 y) = 100.91 - 87[/tex]

[tex]0.13 y = 13.91[/tex]

[tex]y = 107[/tex]

Now that we have the value for  y, substitute it back into Equation 1 to find  x:

[tex]x + 107 = 348[/tex]

[tex]x = 241[/tex]

Hence , the solution is  x = 241 and y = 107, meaning 241 notebooks were sold at 25¢ each and 107 notebooks were sold at 38¢ each.

Answer:

The average speed of the runner is 7 miles per hour.

Step-by-step explanation:

Given:

Distance ran by [tex]2\frac{ 1}{3} miles[/tex]

Time taken  by the runner = 20 minutes.

To find:

The average speed of a runner=?

Solution:

Now, we know that ,

distance = speed x time

Then, [tex]2\frac{ 1}{3} miles[/tex] = average speed x 20 minutes  

=> average speed = [tex]\frac{(2 \frac{1}{3} miles)}{(20 minutes)}[/tex]

=> average speed = [tex](\frac{(2 x 3 + 1)}{3} miles)}{(20\times\frac{1}{60} hours)[/tex]

=> average speed=[tex]\frac{(\frac{(6+1)}{3})}{(\frac{20}{60})}[/tex]

=> average speed = [tex]\frac{ (\frac{7}{3})}{(\frac{1}{3})}[/tex]

=>average speed = [tex]\frac{7}{3}\times\frac{3}{1}[/tex]

=>average speed = 7

To find out how many miles Carlee rode, you need to divide the distance Brandon rode (58.5 miles) by 0.9 (representing 90%). The result is that Carlee rode 65 miles.

The problem requires you to determine the distance that Carlee biked based on the information provided. Given that Brandon rode his bike 90% of the distance Carlee did, and he rode 58.5 miles, to calculate the distance Carlee traveled, you would divide the distance Brandon rode by 0.9 (which represents 90%).

So, the calculation would be: 58.5 ÷ 0.9 = 65.

Therefore, Carlee must have biked 65 miles in total given the information provided.

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The term 'perfect trios' as a whole number is not a standard mathematical term, but it may refer to something like Pythagorean triples, which are sets of three positive integers that satisfy the equation a² + b² = c². Without additional context, the term remains unclear.

The term "perfect trios" is not a standard mathematical term, so it is a bit unclear what it refers to. It may be a term used in a specific textbook or class to refer to a certain type of number trio or to phenomena in physics or another field. However, in mathematics, we can talk about perfect numbers, which are positive integers that are equal to the sum of their proper divisors (excluding the number itself). Additionally, we may consider Pythagorean triples, which are sets of three positive integers a, b, and c, such that a² + b² = c². These are special cases of perfect squares and can be considered when discussing whole number trios in a mathematical sense.

Without more context, we can assume that 'perfect trios' might be an informal term for sets of three numbers that have some special property, such as those that make up a Pythagorean triple.

For example, the Pythagorean triple (3, 4, 5) is well-known because 3² + 4² = 5². Similarly, (5, 12, 13) is another Pythagorean triple as 5² + 12² = 13².

Answer:

Yes, she is correct.

Step-by-step explanation:

A real number that can be expressed as [tex]\frac{p}{q}[/tex],

Where,

p and q are integers,

Such that, q ≠ 0,

is called a rational number.

A terminating decimal is always a rational number,

Thus, 2.11 is a rational number,

Verification :

2.11 = [tex]\frac{211}{100}[/tex]

Where,    

Both 211 and 100 are integers,

Such that 100 ≠ 0.

The value 2.11 is a rational number and not a repeating decimal.

Given the number 2.11 ;

[tex]since \: 2.11 = \frac{211}{100} [/tex]

Then, we can conclude that 2.11 is a rational number

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