Gabrielle's age is three times Mikhail's age. The sum of their ages is 32 . What is Mikhail's age?

I don't see in the problem what she is paid for over time but it is normally 1.5 times per hour

 so 40 hours at 25 = 1000

51-40 = 11 hours of over time

25 *1.5 = 37.50 per hour for over time

11 * 37.50 = 412.50

1000+412.50 = 1412.50 total

Answer:

In year 2012, 0.45 thousands dollars will bring the break even for the company.

Step-by-step explanation:

The table shows the annual profits of a county fair from 2008 to 2012.

We have to calculate the profit in 2012 to get the break even over the five year period.

Total profit in four years = profit in year (2008 + 2009) = 2.5 + 1.75 = 4.25 thousand dollars

Total loss in four years = loss in year (2010 + 2011) = 3.3 + 1.4 = 4.7 thousand dollars

Net profit or loss = Net profit - net loss = 4.25 - 4.7 = -0.45

There is a net loss of 0.45 thousand dollars.

If we get a profit of 0.45 thousand dollars in year 2012, we will be in the situation of no profit and no loss (break even).

Therefore, profit of 0.45 thousands of dollars is the answer.

The ratio of 34 days to 2 weeks is [tex]\(\frac{34}{2 \times 7}\)[/tex].

To find the ratio of 34 days to 2 weeks, we first need to convert 2 weeks into days, since there are 7 days in a week. Therefore, 2 weeks is equivalent to [tex]\(2 \times 7\)[/tex] days, which is 14 days.

Now, we can set up the ratio of 34 days to 14 days (2 weeks):

[tex]\[ \text{Ratio} = \frac{34 \text{ days}}{14 \text{ days}} \][/tex]

To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 34 and 14 is 2.

Dividing both by 2, we get:

[tex]\[ \text{Ratio} = \frac{34 \div 2}{14 \div 2} = \frac{17}{7} \][/tex]

So, the simplified ratio of 34 days to 2 weeks is [tex]\(17:7\) or \(\frac{17}{7}\)[/tex].

The required equation is y = 14x + 10 which is the number of cards in the collection and he will have 150 cards after 10 years

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

As per the question, we take the two points are (3,52) (7,108)

So slope = (108 - 52) / (7 - 3) = 56/4 = 14

y = mx + b

slope(m) = 14

Substitute the value of x = 3 and y = 52 in the equation

52 = 3(14) + b

52 = 42 + b

52 - 42 = b

10 = b

So the original amount of cards is 10

If x represents the number of years, while y is the total number of cards.

y = 14x + 10

He began with 10 cards and has added 14 cards every year thereafter.

So after 10 years

y = 14(10) + 10

y = 140 + 10

y = 150

Therefore, he will have 150 cards after 10 years

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Answer:

The answer is b=2A/h-a

The Golden Eagle, weighing 13.9 lbs, is approximately 4 times as heavy as the Red Tailed Hawk, which weighs 3.5 lbs.

To find out how many times as heavy the Golden Eagle is compared to the Red Tailed Hawk, we need to divide the weight of the Golden Eagle by the weight of the Red Tailed Hawk. The Golden Eagle weighs 13 9/10 lbs, which can be converted into an improper fraction as 139/10 or a decimal as 13.9 lbs. The Red Tailed Hawk weighs 3 1/2 lbs, which can be converted into an improper fraction as 7/2 or a decimal as 3.5 lbs.

To perform the division, we'll use the decimal form of the weights:

Dividing the Golden Eagle's weight by the Red Tailed Hawk's weight:

13.9 lbs ÷ 3.5 lbs = 3.9714 (approximately)

So, the Golden Eagle is approximately 4 times as heavy as the Red Tailed Hawk.

The equation 6|x| + 25 = 15 has no solution because it implies that |x| equals a negative number after simplification, and absolute values cannot be negative.

The equation 6|x| + 25 = 15 has no solution because the absolute value of x, denoted by |x|, represents the distance of x from zero on the number line, and as such, it can never be negative. When we solve the given equation, we isolate the absolute value on one side which gives us 6|x| = -10 after subtracting 25 from both sides. Dividing by 6, we obtain |x| = -10/6, which is a negative number. However, since an absolute value cannot equal a negative number, this indicates that there is no valid solution to the equation.

Answer:

2x^3 + 2x

Step-by-step explanation:

subtract the 2 x^4's

x^3 +x^3 = 2x^3

x +x = 2x

answer is 2x^3 + 2x

The difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]

Given the polynomials:

We are required to find their difference which can be solved as follows:

[tex](x^4 + x^3 + x^2 + x ) - ( x^4 - x^3 + x^2 - x)[/tex]

First, open the bracket by multiplying every term you have in [tex]( x^4 - x^3 + x^2 - x)[/tex] by -1:

[tex]x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x[/tex]

[tex]x^4 - x^4 + x^3 + x^3 + x^2 - x^2 + x + x\\\\\mathbf{2x^3 + 2x}[/tex]

Thus, the difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]

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The required fraction of the ice cream cones sold were either chocolate or vanilla is 5/6.

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

We have been given that of the ice cream cones sold yesterday at Percy's ice cream shop, 1/3 were chocolate and another 1/2 were vanilla.

We have to determine the fraction of the ice cream cones sold were either chocolate or vanilla

1/3 equals 2/6

According to the given question,

The fraction of either vanilla or chocolate will be:

⇒ 1/3 + 1/2

Change into a lowest common denominator,

⇒  2/6 + 3/6

Apply the addition operation to get

⇒  5/6

Therefore, the required fraction of either vanilla or chocolate is 5/6.

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