Find the length of ac , if ar=3x-12 and db=8x - 40

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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A) For the first question, we will use the first and second derivative criteria. First, we will compute the first and second derivatives of the given function:

Now, we set the first derivative equals to zero and solve for q:

Evaluating q=75 in the second derivative, we get a negative value since it is a constant, therefore there is a maximum for q=75.

B) We know the maximum is reached for q=75 therefore to find the maximum profit we evaluate the function at q=75:

The ship's speed during that time was approximately 22.2 kilometers per hour.

We have,

To calculate the ship's speed, we need to determine the distance traveled between 10 degrees north latitude and 12 degrees north latitude, and then divide it by the time taken.

The distance between two degrees of latitude is approximately 111 kilometers (or 69 miles).

Since the ship traveled from 10 degrees north latitude to 12 degrees north latitude, it covered a distance of:

Distance = (12 - 10) x 111 kilometers

Distance = 2 x 111 kilometers

Distance = 222 kilometers

Given that it took 10 hours to cover this distance, we can calculate the ship's speed as:

Speed = Distance / Time

Speed = 222 kilometers / 10 hours

Speed = 22.2 kilometers per hour

Therefore,

The ship's speed during that time was approximately 22.2 kilometers per hour.

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The simplified form of the 8b³c² + 4b³ c²  is (c) 12b³c².

The expression, 8b³c² + 4b³c², can be simplified by combining like terms. Both terms have the same variables, b³c², but with different coefficients. To simplify, we add the coefficients together: 8 + 4 = 12. Therefore, the simplified form of the expression is 12b³c².

This means that the sum of 8b³c² and 4b³c² is equal to 12b³c². The variables b and c are raised to the powers of 3 and 2, respectively, and they remain unchanged in the simplified form. The only change is the coefficient, which is 12.

Hence, the correct answer is c. 12b³c² By combining the terms and adding their coefficients, we have simplified the expression to its simplest form, representing the sum of the two terms.

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The cost of the rectangular deck is: $0.08 per square foot.

Area of rectangular shape = length × width

The deck is rectangular.

Thus:

Cost of the deck per square foot = area of rectangular deck/total cost of deck.

Area of rectangular deck = 8.25 × 12.5 = 103.125

Cost of the deck per square foot = 103.125/1,270 = 0.08

Therefore, the cost of the rectangular deck is: $0.08 per square foot.

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Answer:

mAngle1 + mAngle2 = 180°

Step-by-step explanation:

This is the answer hope it helps

if u had a picture i could give further details

Hope this helped

Answer:

What if I told you I guessed

Step-by-step explanation:

but submitted and got it correct

...

Answer:

0.857$ (Its really big in answer but This is the average result.

The REAL answer

0.857142857$

Answer:

5. find x= 32

6. find < C = 23

find c =

find a =

Sorry wish I could help more I need to learn more about this chapter in math.

Answer: 5:15:23 pm

Step-by-step explanation:

There are different time zones in the world due to the Earth's rotation as this results in different parts of the Earth receiving sunlight at different times.

GMT is used as a basis to find the times of other zones.

In this instance, EDT time is -4 that of GMT.

This means that EDT is 4 hours behind GMT.

Time in GMT is therefore:

=  1:15:23 + 4 hours

= 5:15:23 pm

Answer:

50%

Step-by-step explanation:

We are given this set of data: Age of professors in years

47, 44, 48, 43, 35, 65, 56, 37, 73,51

We can firstly rearrange the years properly in ascending order.

Hence we have:

35, 37, 43, 44, 48, 51, 53 56, 65, 73

The number of the professor given = 10 professors

The number of professors younger 50 years = 5

Therefore, the percentage of these professors who are younger than 50

Is:

5/10 × 100 = 50%

Therefore, 50% of the professors are younger than 50

The amount of garbage, G, produced by a city with a population, p, is given by the equation G(p) = 12p, where G is measured in tons per week and p is measured in thousands of people.

This equation represents a linear relationship where the amount of garbage produced is directly proportional to the population size.

The given equation, G(p) = 12p, relates the amount of garbage produced (G) to the population size (p) of a city. In this equation, G represents the amount of garbage produced and is measured in tons per week, while p represents the population size of the city and is measured in thousands of people.

The equation implies that for each unit increase in the population size (p), the amount of garbage produced (G) increases by a factor of 12. This indicates a direct proportionality between the population and the amount of garbage generated.

For example, if we have a city called Tola with a population of 45,000 (p = 45), we can calculate the amount of garbage produced per week using the equation G(p) = 12p:

G(45) = 12 * 45 = 540

So, Tola produces 540 tons of garbage per week.

Similarly, we can calculate the amount of garbage produced per week for different population sizes using the same equation.


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Answer:

False.

Step-by-step explanation:

The RMS (Root Mean Square) value of a sine wave represents the equivalent DC voltage that would produce the same amount of power in a resistive load. However, the heat produced in a resistor is directly proportional to the square of the current passing through it (according to Joule's Law). In the case of an AC waveform, the current continuously changes direction, resulting in a time-varying power dissipation. Therefore, comparing the RMS value of an AC waveform to a DC voltage is not directly applicable in terms of heat produced in a resistor.

The length L and width W (with W≤L ) of the enclosure that is most economical to construct. L=10 W=20 the enclosure with dimensions L = 10 and W = 10 is the most economical to construct, as it has the minimum cost among the feasible options.

To find the enclosure that is most economical to construct given that L = 10 and W = 20, we need to minimize the cost function associated with constructing the enclosure.

Let's assume the cost function is given by C(L, W) = 2L + 5W, which represents the cost of constructing the enclosure based on its length and width.

To find the most economical enclosure, we can minimize the cost function C(L, W) subject to the constraint W ≤ L.

Since we are given L = 10, we need to find the width W that minimizes the cost function C(10, W) = 2(10) + 5W = 20 + 5W.

To minimize this function, we can take the derivative of C with respect to W and set it to zero:

dC/dW = 5

Setting this derivative equal to zero, we find that there is no critical point since the derivative is a constant.

However, since we have the constraint W ≤ L, we need to consider the endpoint W = L = 10 as a possible solution.

Calculating the cost at this endpoint:

C(10, 10) = 2(10) + 5(10) = 20 + 50 = 70

Therefore, the enclosure with L = 10 and W = 10 has a cost of 70.

In conclusion, the enclosure with dimensions L = 10 and W = 10 is the most economical to construct, as it has the minimum cost among the feasible options.

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Answer:

Step-by-step explanation:

slope 2 y intercept -1

Answer:

the mean and the standard deviation is 0.92 and 0.01808 respectively

Step-by-step explanation:

The computation of the mean and the standard deviation is shown below:

The mean is 0.92

And, the standard deviation is

= √0.92 × (1 - 0.92) ÷ √225

= √0.92 × 0.08 ÷ √225

= √0.0736 ÷ √225

= √3.27

= 0.01808

Hence, the mean and the standard deviation is 0.92 and 0.01808 respectively

Answer:

8,-1...............................

The probability that: either a or b occur

P(AUB)=0.9

This is further explained below.

Generally, In the fields of logic and probability, two occurrences are said to be mutually exclusive or discontinuous if it is impossible for both of them to take place at the same moment. One obvious illustration of this is the possible results of a single flip of a coin, which may produce either heads or tails, but not both at the same time.

Therefore,

P(AUB)=P(A)+P(B)

P(AUB)=0.7+0.2

P(AUB)=0.9

In conclusion,

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CQ

Suppose that a and b are mutually exclusive events for which p(a) = 0.2 and p(b) = 0.7. what is the probability that: either a or b occur7

Answer:

m∠C = 90°

Step-by-step explanation:

Triangle BDC is a right triangle with the measure of angle D = 90°

By applying Cosine rule in the given triangle,

Since, Cosine of any angle in a right triangle is a ratio of Its adjacent side and Hypotenuse (Opposite side of the right angle)

CosC = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

CosC = \(\frac{\text{DC}}{\text{BC}}\)

CosC = \(\frac{7}{8}\)

\(C=\text{Cos}^{-1}(\frac{7}{8})\)

C = 28.955

C = 29°

Therefore, m∠C = 29° will be the answer.

The function f(t) is: f(t) = 9(2/5) t^(5/2) - 19t + 8

To find f(t), we need to integrate the second derivative of f(t) with respect to t twice.

f''(t) = 9/sqrt(t)

Integrating once with respect to t:

f'(t) = 9(2/3) t^(3/2) + C1

where C1 is the constant of integration. We can use the initial condition f'(4) = 13 to find C1:

f'(4) = 9(2/3) 4^(3/2) + C1 = 13

C1 = 13 - 9(2/3) 4^(3/2)

C1 = -19

Integrating again with respect to t:

f(t) = 9(2/5) t^(5/2) - 19t + C2

where C2 is the constant of integration. We can use the initial condition f(4) = 27 to find C2:

f(4) = 9(2/5) 4^(5/2) - 19(4) + C2 = 27

C2 = 9(2/5) 4^(5/2) - 19(4) + 27

C2 = 8

f(t) = 9(2/5) t^(5/2) - 19t + 8

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The volume of the solid generated by revolving the region bounded by y = x² + 8 and y = x + 14 about the x-axis is 70π cubic units.

The volume of the solid generated by revolving the given region about the x-axis can be determined using the method of cylindrical shells.

The region is bounded by the graphs of y = x² + 8 and y = x + 14, with x ranging from -2 to 6. The formula for finding the volume of such a solid is given by

V = ∫[a to b] 2πx(f(x) - g(x)) dx,

where f(x) represents the upper function and g(x) represents the lower function.

Substituting the given functions into the formula, we have V = ∫[-2 to 6] 2πx[(x² + 8) - (x + 14)] dx. Simplifying further, we get V = ∫[-2 to 6] 2πx(x² - x - 6) dx. Integrating this expression, we have V = 2π ∫[-2 to 6] (x³/3 - x²/2 - 6x) dx.

Evaluating the integral, we obtain V = 2π[(x⁴/12 - x³/6 - 3x²)][-2 to 6]. Simplifying the expression within the brackets, we have V = 2π[(6⁴/12 - 6³/6 - 3(6²)) - ((-2)⁴/12 - (-2)³/6 - 3(-2)²)].

Calculating further, we find V = 2π[(72 - 48 - 108) - (2/3 + 4/3 - 12)] = 2π[(84/3 - 14/3)] = 70π cubic units.

Therefore, the volume of the solid generated by rotating the given region about the x-axis is 70π cubic units.

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Answer:

He should have said that his small brother had 100 small building bricks, but lost 5 in total now.

Answer:

1/2 divided by 5

Step-by-step explanation:

Answer:

The first answer

Step-by-step explanation:

B or D are completely correct.

Personally, I'd do D, but I know people would would rather do B.  Both help you get to your solution.

the answer is b

after that you  need to

- simplify

- multiply by -1

- simplfy again

-divide both sides by two

- simplfy

- add 4 to both sides

- divide both sides by 5

and you should get

x>2! followthe steps in order

dm me or smth if this is not the answer that you wanted!

ly,

dannie :)

Answer:

$1.19 per quart

Step-by-step explanation:

one gallon = 4 quarts

$4.76/4 = $1.19 per quart

A. The variable is qualitative because it is a numerical measure is correct answer.

Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. for instance: Eye color (variables include: blue, green, brown, hazel).

In statistics, qualitative variables are given nominal scales since they cannot be ordered on a numerical scale. Qualitative variables are exactly what the word "nominal" means: names. No ordering is either conceivable or inferred on a nominal scale (except for alphabetical ordering like New York, Washington, West Virginia or Chelsea, Edinburgh, London). In other words, data are classified according to a category on the nominal scale.

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To find \((f+g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\) together. Let's start by writing down the given functions:

The sum of the functions \(f(x) = 4x^2 + 3x - 2\) and \(g(x) = 6x^3 - 3x^2 - 4\) is \((f+g)(x) = 6x^3 + x^2 + 3x - 6\). This resulting function is a cubic polynomial with coefficients that reflect the combined terms of the original functions.

\(f(x) = 4x^2 + 3x - 2\)

\(g(x) = 6x^3 - 3x^2 - 4\)

Now, let's add them together:

\((f+g)(x) = f(x) + g(x)\)

\(= (4x^2 + 3x - 2) + (6x^3 - 3x^2 - 4)\)

To simplify the expression, we combine like terms:

\((f+g)(x) = 6x^3 + 4x^2 - 3x^2 + 3x - 2 - 4\)

\(= 6x^3 + (4x^2 - 3x^2) + 3x + (-2 - 4)\)

\(= 6x^3 + x^2 + 3x - 6\)

So, the sum of the functions \(f(x) = 4x^2 + 3x - 2\) and \(g(x) = 6x^3 - 3x^2 - 4\) is \((f+g)(x) = 6x^3 + x^2 + 3x - 6\).

In other words, the resulting function (f+g)(x) is a cubic polynomial with the highest degree term of \(6x^3.\) The other terms in the polynomial are \(x^2\), 3x, and a constant term of -6.

It's important to note that this sum is valid for all values of x within the domain of the original functions f(x) and g(x), unless otherwise specified. Therefore, \((f+g)(x) = 6x^3 + x^2 + 3x - 6\) is the expression representing the sum of the functions f(x) and g(x).

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