Phillip ordered 15 small bookcases with 3 shelves each and 13 large bookcases with 5 shelves each. How many total shelves did Phillip order?

The polar coordinates of the point (6, 6) are approximately (8.49, 0.79) in radians.

To convert the point (6, 6) from Cartesian to polar coordinates, we can use the formulas:

r = √(x² + y²)

θ = arctan(y/x)

Given that the point is (6, 6), we can substitute the values into the formulas to find the polar coordinates.

r = √(6² + 6²) = √(36 + 36) = √72 ≈ 8.49

θ = arctan(6/6) = arctan(1) = π/4 ≈ 0.79 (radians)

In polar coordinates, the value of r represents the distance from the origin (0, 0) to the point, and the value of θ represents the angle (measured in radians) between the positive x-axis and the line connecting the origin to the point. The angle θ is usually measured counterclockwise from the positive x-axis.

To learn more about Cartesian to polar coordinates click on,

https://brainly.com/question/29129911

#SPJ4

Complete question is:

Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.

(6,6)

Answer:

To draw a right triangle with a tangent ratio of 3/2 for one of the acute angles, we can choose any angle whose tangent is 3/2. Let's choose the angle θ.

We know that:

tangent ratio = opposite side / adjacent side

So, we can assign any value we want to the adjacent side, and then calculate the opposite side. Let's say the adjacent side is 2 units. Then, the opposite side would be:

opposite side = tangent ratio * adjacent side = (3/2) * 2 = 3

So, the sides of the triangle are:

adjacent side = 2

opposite side = 3

hypotenuse = √(2^2 + 3^2) = √13

We can now use trigonometry to find the measure of the other acute angle. The tangent of an angle is equal to the opposite side over the adjacent side, so we have:

tan(θ) = opposite side / adjacent side

tan(θ) = 3/2

Taking the inverse tangent of both sides, we get:

θ = tan^(-1)(3/2)

θ ≈ 56.3°

So, the other acute angle of the right triangle is approximately 56.3 degrees.

Answer: C  

Include the date on each page of notes

Step-by-step explanation:

I did the quiz

Answer:

  4) 16√3 in²

  5) 63 cm²

Step-by-step explanation:

The formula to use in these cases is ...

  A = (1/2)ab·sin(θ)

where a, b are the side lengths and θ is the angle between them.

It helps to know the trig functions of the "special" angles used here.

  sin(120°) = sin(60°) = (√3)/2

  cos(60°) = 1/2

  sin(135°) = cos(45°) = (√2)/2

__

4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...

  x = (8 in)cos(60°) = (8 in)(1/2) = 4 in

So, the bottom edge of the triangle is 12 in - 4 in = 8 in.

The area is ...

  A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²

__

5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...

  x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm

Then the base of the triangle is ...

  16√2 cm -9√2 cm = 7√2 cm

The area is then ...

  A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²

Answer:

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.

Step-by-step explanation:

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.

Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

To know more about  Engineers click here

brainly.com/question/30592664

#SPJ11

The percentage change in the bond's price using the duration concept is approximately 0.03645, or 3.645%.

To calculate the percentage change in the bond's price using the duration concept, we can use the following formula:

Percentage Change in Bond Price = - (Duration * Change in Yield)

Given:

Duration = 7.29 years

Change in Yield = -0.005 (50 basis points decrease)

Using the formula, we can calculate the percentage change in the bond's price:

Percentage Change in Bond Price = - (7.29 * (-0.005))

Percentage Change in Bond Price = 0.03645

Therefore, the percentage change in the bond's price using the duration concept is approximately 0.03645, or 3.645%.

learn more about percentage change on

https://brainly.com/question/14801224

#SPJ11

The solutions to the equation cos 2x = -cos x are x = π/3 + 2πn and x = π + 2πn, where n is any integer

To find the solution to the equation cos 2x = -cos x, we need to use the double angle formula for cosine. The double angle formula for cosine is:

cos 2x = 1 - 2sin^2x

We can substitute this into the original equation to get:

1 - 2sin^2x = -cos x

Next, we can rearrange the equation to isolate the sine term:

2sin^2x = 1 + cos x

Now, we can use the Pythagorean identity, which states that sin^2x + cos^2x = 1, to substitute for sin^2x:

2(1 - cos^2x) = 1 + cos x

Simplifying and rearranging gives us:

2cos^2x + cos x - 1 = 0

This is a quadratic equation in terms of cos x, so we can use the quadratic formula to find the solutions:

cos x = (-1 ± √(1^2 - 4(2)(-1))) / (2(2))

cos x = (-1 ± √9) / 4

cos x = (-1 ± 3) / 4

This gives us two possible solutions for cos x:

cos x = (-1 + 3) / 4 = 1/2

cos x = (-1 - 3) / 4 = -1

Therefore, the solutions to the equation cos 2x = -cos x are x = π/3 + 2πn and x = π + 2πn, where n is any integer.

To know more about double angle formula refer here:

https://brainly.com/question/30402422#

#SPJ11

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

Learn more about linear programming

brainly.com/question/30763902

#SPJ11

The stationary point of the function u(x, y) = x² + y² - 4xy + 1 is (0, 0).

To find the stationary points of the function u(x, y) = x² + y² - 4xy + 1, we need to find the values of x and y where the partial derivatives with respect to x and y are both equal to zero.

Let's start by finding the partial derivative of u with respect to x:

∂u/∂x = 2x - 4y.

Now, let's find the partial derivative of u with respect to y:

∂u/∂y = 2y - 4x.

To find the stationary points, we set both partial derivatives equal to zero:

2x - 4y = 0, and

2y - 4x = 0.

Simplifying these equations, we have:

x - 2y = 0, and

y - 2x = 0.

We can solve this system of equations using any method. Let's use the substitution method here.

From the first equation, we can express x in terms of y as x = 2y. Substituting this into the second equation, we have y - 2(2y) = 0. Simplifying, we get y - 4y = 0, which gives us -3y = 0. Therefore, y = 0.

Substituting this value of y back into x = 2y, we find x = 2(0) = 0.

Hence, the stationary point of the function u(x, y) = x² + y² - 4xy + 1 is (0, 0).

learn more about function here

https://brainly.com/question/30721594

#SPJ11

The given bounded region is the set

\(R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}\)

assuming the curves are \(y=x^4\) and \(x=y^4\implies y=x^{1/4}\) (since \(x>0\) in the first quadrant).

The coordinates of the centroid are \((\bar x, \bar y)\) where \(\bar x\) and \(\bar y\) are the average values of \(x\) and \(y\), respectively, over the region \(R\). These are given by the ratios

\(\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}\)

Compute the area of \(R\).

\(\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35\)

Integrate \(x\) and \(y\) over \(R\).

\(\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}\)

\(\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}\)

Then the centroid's coordinates are

\(\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463\)

\(\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}\)

Answer: c. det(PAP^-1) = det(A)

To show that det(PAP-1) = det(P)det(A)det(P^-1), we can use the following properties of determinants:

1. det(AB) = det(A)det(B) for any matrices A and B

2. det(A^-1) = 1/det(A) for any invertible matrix A

Starting with det(PAP^-1), we can apply property 1 to get:

det(PAP^-1) = det(P)det(A)det(P^-1)

Then, we can use property 2 to rewrite det(P^-1) as:

det(PAP^-1) = det(P)det(A)(1/det(P))

Simplifying this expression gives:

det(PAP^-1) = det(A)

Therefore, det(PAP^-1) = det(P)det(A)det(P^-1) is equivalent to det(PAP^-1) = det(A).

So, the correct answer is:

c. det(PAP^-1) = det(A)

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

Read more on probability:

https://brainly.com/question/251701

#SPJ1

Answer:

True

Step-by-step explanation:

All of them match up

A: √50x^2 and d: √72x^2 are like radicals.

Like radicals are square roots with the same coefficient outside the radical. For example, √50x^2 and √72x^2 can be simplified to √2 * √25x^2, which makes them like radicals. Simplifying the expressions helps to see if they are alike.

Expressions such as √32x and √18n cannot be simplified to have the same coefficient outside the radical and hence, they are not like radicals.

In conclusion, only √50x^2 and √72x^2 are like radicals after simplification.

You can learn more about like radicals at

https://brainly.com/question/3253643

#SPJ4

Answer:

A&D

Step-by-step explanation:

Got it right on edge

The cubed root of -512 is 8.  

Answer:

Step-by-step explanation:

x=8.6cm  x=7.9cm

15m

Answer:

The answer is x = 24.7

Step-by-step explanation:

Using the formula,

a/(sinA) = b/(sinB) = c/(sinC),

Here, we need to find x,

and for b = 15, the corresponding angle is 35 degrees,

and for x, the angle is 71 degrees, so,

\(x/sin(71) =15/sin(35)\\x = 15(sin(71)/sin(35)\\x = 24.7269\)

To one decimal place we get,

x = 24.7

The formula for the nth term of this arithmetic sequence having a first term of -2 and a common difference of 8 is aₙ = 8n - 10.

The formula for the nth term of an arithmetic sequence is:

aₙ = a₁ + (n - 1)d

where:

aₙ is the nth term of the sequence

a₁ is the first term of the sequence

d is the common difference

Plugging in the given values, we get:

aₙ = -2 + (n - 1)8

Simplifying this expression gives:

aₙ = -2 + 8n - 8

aₙ = 8n - 10

Therefore, the formula for the nth term of this arithmetic sequence is:

aₙ = 8n - 10

Learn more about arithmetic sequence here: brainly.com/question/6561461

#SPJ4

The expression 8(x+4) is a product between 8 and (x+4), which is a number (8) and a sum.

Then, it correspond to Option B: The product of a number and a sum.

Answer:

x+10=45

x+10-45=0

x-35=0

x=35

Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

Answer:

85$ was withdrawed.

Step-by-step explanation:

20 + 30 + 35 = 85 - 85 = 0

Answer:

Okays so Luke deposited $20.00, $15.00, and $35.00 so we can make the equation

$20.00 + $15.00 + $35.00 = $70.00

At the end of the month he withdrawaled all of his money which brought it back to $0.00. That means that Luke withdrawled $70.00 from his bank account!

I hope that this helps

The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

To learn more about interval visit: https://brainly.com/question/15050000

#SPJ4

Answer:

x = pm - pn

Step-by-step explanation:

m = n + \(\frac{x}{p}\)  Subtract n from both sides

m - n = n - n + \(\frac{x}{p}\)

m-n = \(\frac{x}{p}\)   Multiply both sides by p

p(m - n) = (\(\frac{p}{1}\)) \(\frac{x}{p}\)          \(\frac{p}{1}\) means the same as p

pm - pn = x             Distribute the p

x = pm - pn

Answer:

9 and 10

Step-by-step explanation:

The sqaure root of 85 is 9.21954445729.

9.21954445729 is greater than 9 but less than 10, meaning it falls in between them.

Answer:

x = 14.63

Step-by-step explanation:

The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.

The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.

Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.

To learn more about   conical surface click here: brainly.com/question/29129362

#SPJ11

Hello,

I hope you and your family are doing well!

To prove the statement "if x, y are integers then x^2-4y^2" by contradiction, we can start by assuming that x and y are integers and x^2-4y^2 is not true.

In other words, our assumption at the start of the proof would be that x and y are integers, but x^2-4y^2 is not true. From this assumption, we can then try to derive a contradiction, which means we can find a conclusion that contradicts our assumption. If we are successful in deriving a contradiction, then we can conclude that our assumption was incorrect and therefore the statement "if x, y are integers then x^2-4y^2" must be true.

Please consider giving this 5 stars and brainliest if you find it helpful.

Happy Holidays!

Answer:

-tan 20

Step-by-step explanation:

They have the same answer when typed in a calculator