Which unit would probably be used to measure how long a cell phone is?

Given the cost and demand functions:

we can find the revenue with the following expression:

then, the profit can be calculated with the difference between the revenue and C(x):

to find the max profit, we can find the derivative of P(x) and find its root to get the value of x that maximizes the function P(x):

therefore, the production level that results in the maximum profit is x = 1350.

Finally, to find the price, we can evaluate x = 1350 on p(x):

therefore, the price that the company should charge for each drill to maximize profit is $115

Question:

Solution:

The diagram of a triangle ABC, where C is the right angle is:

Now, by definition and according to the data of the problem, we get that:

that is:

now, to find the cos(B), first, we must find the missing side of the triangle. To do that, we can apply the Pythagorean theorem:

now, with respect to angle B, we obtain that:

So that, we can conclude that the correct answer is:

Answer:

9(x - 5)

Step-by-step explanation:

Just write the equation according to the sentence. It's THAT SIMPLE.

Answer:

d

Step-by-step explanation:

The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

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Answer:

B

Step-by-step explanation:

the lines cross at (-2,1)

Answer:

\( \bf \: y = 2 {x}^{2} - 6x - 8\)

It is equation of a parabolla.

It is to be noted that the graph of y = 2x * 2-6x-8 which when simplified is  y = -12x² - 12x. is attached accordingly.

The graph of y = -12x² - 12x is a downward-opening parabola.

It has a concave shape and its vertex is the highest point on the graph. The axis of symmetry is a vertical line passing through the vertex.

The graph may intersect or be tangent to the x-axis at two points, one point, or no points, depending on the discriminant.

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The club has to send 57 coupons to existing members.

Given,

The number of coupons sent out by a new club to boost sales for next year's membership = 152

They provide 3 times as many to potential members than to existing members

We have to find the number of coupons they send to existing members;

Here,

x be the number of coupons to existing members.

Then,

3x = 152

Now,

x = 152/3 = 50.66 ≈ 57

That is,

The club has to send 57 coupons to existing members.

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The equation that describes the simple harmonic motion of the particle is:

x = 7 * sin(2t + φ)

The equation that describes the simple harmonic motion of a particle moving uniformly around a circle can be represented as:

x = A * sin(ωt + φ)

In this equation:

x represents the displacement of the particle at time t.

A represents the amplitude of the motion.

ω represents the angular frequency or angular speed of the motion.

t represents time.

φ represents the phase constant.

In the given scenario, the particle is moving uniformly around a circle of radius 7 units, with an angular speed of 2 radians per second. In circular motion, the displacement can be represented by the arc length along the circumference of the circle.

Since the angular speed is 2 radians per second, the angular frequency (ω) is also 2 radians per second.

Since the particle is moving uniformly, the amplitude of the motion (A) is equal to the radius of the circle, which is 7 units.

The phase constant (φ) determines the initial position of the particle at t = 0.

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Answer:

B, C, D

Step-by-step explanation:

7x + 1 + 105 = 180

7x = 74

x = 74/7

4y + 14 + 7y + 1 = 180

11y = 165

y = 15

m<A = 4y + 14 = 4(15) + 14 = 74°

m<B = 7x + 1 = 7(74/7) + 1 = 75°

m<C = 7y + 1 = 7(15) + 1 = 106°

Answer: B, C, D

Answer:

\((x+8)^{2}\) =77

x= -8 +/- \(\sqrt\\ 77\)

From Khan Academy

Answer:

Step-by-step explanation:

Unit rate per fluid ounce = $0.15

Step-by-step explanation:

Given that:

Cost of one quart bottle of juice = $4.80

We know that:

One quart = 32 ounces

Unit rate is the rate in which two quantities are compared and one of them is one.

Unit rate =

Unit rate = $0.15 per fluid ounce

Hence,

Unit rate per fluid ounce = $0.15

Answer:

Wyatt bought 32 fluid ounces.

Step-by-step explanation:

If Wyatt bought a 1 quart bottle of juice, (which you would need to convert into fluid ounces) but every 0.1 quarts of juice would be 3.2 fluid ounces. And if 0.5 quarts of juice is 16 ounces we could do 16 + 16 (fluid ounces) and we would get 32 fluid ounces in total.

And that's how you get the answer! :)

Answer:

\(\{\sqrt b, -\sqrt b\}\)

Step-by-step explanation:

Given

\(a^2 - b = 0\)

Required

Determine the solution

Since b is  a perfect square, the equation can be expressed as:

\(a^2 - (\sqrt b)^2 = 0\)

Apply difference of two squares:

\((a - \sqrt b)(a + \sqrt b) = 0\)

Split:

\((a - \sqrt b)= 0 \ or\ (a + \sqrt b) = 0\)

Remove brackets:

\(a - \sqrt b= 0 \ or\ a + \sqrt b = 0\)

Make a the subject in both equations

\(a =\sqrt b \ or\ a =-\sqrt b\)

The solution can be represented as:

\(\{\sqrt b, -\sqrt b\}\)

To find the hypotenuse of a right triangle using trigonometry, we can utilize the Pythagorean theorem and the trigonometric ratios of sine, cosine, or tangent. Here's a step-by-step explanation:

1. Identify the right triangle: Ensure that the triangle has a right angle, which is a 90-degree angle.

2. Label the sides: Identify the two sides of the right triangle that are not the hypotenuse. These sides are typically referred to as the adjacent side and the opposite side.

3. Choose the appropriate trigonometric ratio: Depending on the information you have, select the appropriate trigonometric ratio that relates the sides you know.

- If you have the adjacent side and the hypotenuse, use cosine: cosθ = adjacent/hypotenuse.

- If you have the opposite side and the hypotenuse, use sine: sinθ = opposite/hypotenuse.

- If you have the opposite side and the adjacent side, use tangent: tanθ = opposite/adjacent.

4. Substitute the known values: Plug in the values you have into the trigonometric equation and solve for the unknown side (hypotenuse).

5. Apply the Pythagorean theorem: If you don't have the hypotenuse directly but know the lengths of both the adjacent and opposite sides, you can use the Pythagorean theorem, which states that the sum of the squares of the two legs (adjacent and opposite sides) is equal to the square of the hypotenuse. The formula is a² + b² = c², where c represents the hypotenuse.

6. Simplify and calculate: After substituting the known values into the equation, simplify and solve for the hypotenuse.

By following these steps and applying the appropriate trigonometric ratio or the Pythagorean theorem, you can find the length of the hypotenuse in a right triangle using trigonometry.

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The triangles with the given side lengths are classified as follows:

The ordered side lengths of the triangles are given as follows:

a, b and c.

Considering these side lengths, the triangles are classified as follows:

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Answer:

A. don't know if this helps but with plotting but (x, y) the x always comes first

Answer:

A

Step-by-step explanation:

A. Derek decorates 5 cookies every 10 mins

Answer:

\(5 \sqrt{5 \: } is \: \: the \: \: answer \: \: of \: \: this \: \: question\)

Answer:

so basically, you want to solve the fraction. Remember with exponents, if the base is the same (in this case it is), you can ADD the exponents. 2/3 + -1/4 = 8/12-3/12 = 5/12

5 = a

12 = b

HOPE THIS HELPS!!!

(a) To be a probability density function, f(x) must satisfy two conditions: f(x) ≥ 0 for all x. The total area under the curve of f(x) must be equal to 1.

We have:\(f(x) = c/(1 + x^2)\)

For f(x) to be non-negative, we need c > 0. To find the value of c such that the total area under the density function of f(x) is equal to 1, we integrate f(x) from −∞ to +∞ and set the result equal to 1:

∫(−∞ to +∞) f(x) dx = ∫(−∞ to +∞) c/(1 + x^2) dx = cπ = 1

Therefore, c = 1/π, and f(x) = 1/(π(1 + x^2)) is a probability density function.

(b) We want to find \(P(−9 < X < 9) for X ~ f(x) = 1/(π(1 + x^2))\)

Using the cumulative distribution function (CDF), we have:

\(F(x) = P(X ≤ x) = ∫(−∞ to x) f(t) dt = ∫(−∞ to x) 1/(π(1 + t^2)) dt\)

\(= (1/π) tan^−1(x) + (1/2)\)

So, using the CDF, we have:

\(P(−9 < X < 9) = F(9) − F(−9) =\) \([tan^−1(9)/π + 1/2] − [tan^−1(−9)/π + 1/2]\)

=\([tan^−1(9) − tan^−1(−9)]/π\)

=\((1/π) tan^−1(9/−1)\)

= 0.499 (rounded to three decimal places)

Therefore, P\((−9 < X < 9) ≈ 0.499.\)

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Answer:

8.56

Step-by-step explanation:

d=2

r=d/2

r=1

area of the circle=πr², but we also have to subtract the square from it

a=π2²

a= 12.56

now the area of the square is 2*2

the area of the shape 12.56-(2*3)

the area of the shape is 8.56

Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

\(S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23\)

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

it raised 6

Step-by-step explanation:

Step-by-step explanation:

the line passes through (6, 2) and (10, -1),

the slope =

(-1-2)/(10-6) = -3/4

the equation :

y-2 = -3/4(x -6)

Answer:

y = 1.5

Step-by-step explanation:

Given x is inversely proportional to \(\sqrt{1+x}\) , then the equation relating them is

y = \(\frac{k}{\sqrt{1+x} }\) ← k is the constant of proportion

To find k use the condition when x = 8, y = 2

2 = \(\frac{k}{\sqrt{1+8} }\) = \(\frac{k}{\sqrt{9} }\) = \(\frac{k}{3}\) ( multiply both sides by 3 )

6 = k

y = \(\frac{6}{\sqrt{1+x} }\) ← equation of proportion

When x = 15 , then

y = \(\frac{6}{\sqrt{1+15} }\) = \(\frac{6}{\sqrt{16} }\) = \(\frac{6}{4}\) = \(\frac{3}{2}\) = 1.5

i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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Answer:

\(\frac{8}{32}\)

Step-by-step explanation:

2×4=8

Caron are a total of 8 slices.

8×4=32

There were 32 slices between all 4 pizzas.