A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. A private contractor charges $75 per hour to develop a logo plus a $100 supply fee. Which equation can be solved to determine x, the number of hours after which the costs would be the same?

Answer:

Maximum area = 10000 square units.

Step-by-step explanation:

We are given the following information:

Rectangular perimeter of coral =  400 units.

Let length of the coral be x. Then,

Perimeter = 400 = 2(Length +Breadth)

[tex]400 = 2(x + Breadth)\\Breadth = 200 - x[/tex]

Thus, the area of rectangle is given by,

[tex]Area = Length\times Breadth = x\times (200-x) = 200x - x^2[/tex]

Thus, we have to maximize the function:

[tex]f(x) = 200x - x^2[/tex]

We will use double derivative test.

First we differentiate with respect to x.

[tex]\displaystyle\frac{d(f(x))}{dx} = \displaystyle\frac{d(200x - x^2)}{dx} = 200 - 2x[/tex]

Equating this to zero to obtain critical points,

[tex]200 - 2x = 0\\200 = 2x\\x = 100[/tex]

Now, again differentiating with respect to x.

[tex]\displaystyle\frac{d^2(f(x))}{dx^2} = -2 < 0[/tex]

Thus, by double derivative test, local maxima occurs for this function at x = 100

So, Length = x = 100 units

Breadth = 200 - x = 100 units

Maximum area = 10000 square units.

Final answer:

To determine the radius and height of the cylindrical tank with a given volume of 15.71 cubic meters, where height is 4 meters greater than the radius, we use the volume formula for a cylinder, resulting in a cubic equation that must be solved.

Explanation:

The question asks for the radius of the top and the height of a cylindrical tank with a volume of 15.71 cubic meters, where the height is 4 meters greater than the radius. The formula for the volume of a cylinder is V = πr²h, where V is volume, r is radius, and h is height. Since h = r + 4, we can write the equation in terms of r as V = πr²(r + 4).

To find the radius, we substitute the given volume, 15.71 m³, into the equation:

15.71 = πr²(r + 4)

This results in a cubic equation which we need to solve to find the value of r. After solving (which may require numerical methods or approximations due to the complexity of cubic equations), we find the value of the radius and can then determine the height by adding 4 meters to the radius.

Answer:

7 glasses

Step-by-step explanation:

Given: Jessica is filling glasses with water. Each glass holds [tex]\frac{3}{5}[/tex] cup of water. She pours [tex]4\frac{1}{5}[/tex] cups of water into the glasses.

To find: The number of glasses she fill with water.

Solution:

Each glass holds [tex]\frac{3}{5}[/tex] cup of water.

She pours [tex]4\frac{1}{5}[/tex] cups of water into the glasses.

To find the number of glasses she fill with water, we need to divide the total volume of water with the volume in each glass.

So, the number of glasses she fill with water can be calculated as

[tex]=\frac{4\frac{1}{5}}{\frac{3}{5}}[/tex]

[tex]= \frac{\frac{21}{5}}{\frac{3}{5} }[/tex]

[tex]=\frac{21}{5}\times\frac{5}{3}[/tex]

[tex]=\frac{21}{3}[/tex]

[tex]=7[/tex]

So, she can fill 7 such glasses with water.

The proportion in the population who will respond "no" is 0.25

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given:

Total people surveyed= 400

people say 'yes'= 300

people say 'no' = 100

Now, proportion in the population who will respond "no" is

= 100/400

=1/40

= 0.25

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In 1994, it will the price reach $5.00.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We are given with the equation as,

⇒ [tex]p(t) = 1.1 e^{0.047t}[/tex]

where p represents the price, t represents the time in years. price varies exponentially with time.

Now, If p is 5 dollars in the future,

Then, We can formulate;

5 =  [tex]1.1 e^{0.047t}[/tex]

ln 4.54 = 0.047 t

0.657 = 0.047 t

t = 13.97

t = 14 years

t = 14 years or year 1994.

Thus, In 1994, it will the price reach $5.00.

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The correct option is B. Side BC has a length of √10 units.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that Quadrilateral, ABCD is shown on the grid. Jonah finds the length of the sides of the quadrilateral before finding the perimeter.

The length of side BC will be calculated by using the distance formula:-

D = √ [ ( 3 - 2 )² + 4 - 1 )² ]

D = √ ( 1 + 9 )

D = √10

Therefore, the correct option is B. Side BC has a length of √10 units.

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Answer: n<7k+2p-4

Step-by-step explanation:

Answer:

sqrt15/3, sqrt 5, sqrt 25/5

Step-by-step explanation:

aye pex

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\boxed{\mathsf{2y(2y + 8)}}\\\\\large\text{DISTRIBUTE \boxed{\text{2y}} WITHIN the PARENTHESES}\\\\\large\boxed{\mathsf{= 2y(2y) + 2y(8)}}\\\\\large\boxed{\mathsf{= 4y^2+ 16y}}\\\\\large\text{You DON'T have any like terms so we cannot do anything to this}\\\large\text{equation.}\\\\\\\huge\boxed{\rm{Therefore, your\ answer \ is: \mathsf{4y^2 +16y}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]

Rate of interest (r) = 0.19% monthly

Step-by-step explanation:

Given: The total amount of money in a saving account after t years.

[tex]A=1000(1.023)^t[/tex]

Formula:

[tex]A=P(1+r)^t[/tex]

Now we compare this formula with with given model.

P=1000

Rate of interest annually (r) = 0.023

Time = t

We need to change into monthly interest

New rate will divide by 12

New time will multiply by 12

[tex]r=\frac{0.023}{12}=0.0019[/tex]

[tex]t=12\times t =12t[/tex]

Function for monthly rate

[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]

Rate of interest (r) = 0.19% monthly

[tex]\text{Thus, Function Monthly interest rate: }A=1000(1+\frac{0.023}{12})^{12t}\text{ and Monthly Interest rate }= 0.19\%[/tex]

Your answer is B..........

When the mean, median, and mode are not located at the same point, the distribution is skewed, either to the left (negatively skewed) or to the right (positively skewed).

When the mean, median, and mode are not in the same place, the distribution is known to be skewed. If the mean is less than the median, which is often less than the mode, the distribution is skewed to the left (or negatively skewed). Conversely, if the mode is less than the median, which is less than the mean, the distribution is skewed to the right (or positively skewed). Skewness indicates that the data is not symmetrically distributed and reflects the direction of the tail where the values trail off more.

In symmetrical distributions, the mean, median, and mode are all located at the same point, typically at the center of the distribution. However, when the values are not symmetrical, it indicates a skew. For example, in a data set with the values 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, the distribution is not symmetrical since it is skewed to the left, with a higher frequency of higher values.

Thus, understanding the relationship among the mean, median, and mode helps in recognizing the type of distribution and in making inferences about the data set.

Answer:

C: 1   -2

   2  -10

   3   -18

   4   -26

Step-by-step explanation:

how because its me i'm always right

The probability of rolling either a 5 or a 6 using a six-sided die is 1/3.

Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.

Now it is given that a six-sided die is rolled.

Total Number of outcomes = 6

To get either a 5 or a 6

So, Possible number of outcomes = 2

Since ,

Probability = Possible number of outcomes / Total Number of outcomes

⇒ Probability of rolling either a 5 or a 6 = 2/6

or, Probability of rolling either a 5 or a 6 = 1/3

Thus, the probability of rolling either a 5 or a 6 using a six-sided die is 1/3.

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Answer:

D

Step-by-step explanation:

A pair of adjacent angles being supplementary, a pair of opposite angles congruent and a pair of opposite sides congruent, and one pair of opposite sides being both parallel and congruent are not sufficient conditions on their own to prove that a quadrilateral is a parallelogram.

Among the given statements concerning the characteristics that are sufficient to prove a quadrilateral is a parallelogram, the following are NOT sufficient on their own:

A pair of adjacent angles are supplementary (statement II).

A pair of opposite angles congruent and a pair of opposite sides congruent (statement IV).

One pair of opposite sides are both parallel and congruent (statement VII).

While having a pair of adjacent angles that are supplementary is common in parallelograms, it alone does not guarantee that a quadrilateral is a parallelogram, as many quadrilateral types can have supplementary adjacent angles. Similarly, having just one pair of opposite angles and one pair of opposite sides congruent doesn't necessarily make a quadrilateral a parallelogram, as these characteristics could describe a kite or other quadrilaterals as well. The condition of one pair of opposite sides being both parallel and congruent, although a property of parallelograms, is not by itself a conclusive proof, as there may need to be additional information to rule out other shapes like rectangles.

Correct Answer: B. II, VI, and VII only

Answer:

121,854

Step-by-step explanation:

Initial population of the town A= 39194

rate growth of population R= 6.9%= 0.069

we need to find the population after n = 17 years

we can find that easily using growth rate formula

A= P(1+R/100)^n

A= 39194(1+0.069)^17

= 121,854

therefore population at the end of 17 years= 121,854

The earnings of Jill Hartman for the week is A = $1,305

Given data ,

To calculate Jill's earnings for the first week, we need to determine the amount of sales in excess of $6,500 and then calculate her additional earnings based on that amount.

Sales in excess of $6,500 = Total sales - $6,500 = $25,000 - $6,500 = $18,500

Now we can calculate Jill's additional earnings based on the sales in excess of $6,500:

Additional earnings = 3% of sales in excess of $6,500 = 0.03 * $18,500

Additional earnings = $555

Finally, we can calculate Jill's total earnings for the first week by adding her base salary to her additional earnings:

Total earnings = Base salary + Additional earnings = $750 + $555

Total earnings = $1,305

Hence , Jill's earnings for the first week, with sales of $25,000, are $1,305

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The value of (goh)(3) is 26.

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

given:

g(x) = 2x , h(x) = x²+4

Now,

(goh)(3)

=g(h(3))

=g(9+4)

=g(13)

=2*13

=26

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