a right triangle has a hypotenuse with a length of 10cm. one angle of the three in this triangle is 53.1 degrees. what is the length of the side opposite this angle?

Investment in automation cost = $8,750,000 when there

no further change in capacity.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Following are the informations of Cent:

Current automation = 7%

Capacity of next round = 1,100

New automation = 7 + 2 = 9

Investment in automation cost = Capacity * (4 * (New automation - previous automation)) * 1000

= 1,100 * (4 * (9 - 7)) * 1,000

= 1,100 * (4 * 2) * 1000

= 1,100 * 8 * 1,000

= $8,800,000.

Investment in automation cost = $8,800,000.

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The factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.

All related terms should be combined and moved to one side of the equation. Moving all of the components to one side of an equation while maintaining the x2 term positive is the first step in factoring an equation. The x2 terms, x terms, and constants (integer terms) must all be added to or subtracted from one another, and they must all be moved to one side of the equation so that nothing is left on the other. You may just write "0" on the other side of the equal sign if that side has no more words.

Given that the equation is 3x^2 + 2x -21 = 0

Using the method of expansion to solve the quadratic equation we have:

3x^2 + 2x -21 = 0

Multiply (a)(c) and find its prime factors:

(3)(21) = 63

Prime factors: 7, 9

Using the factors deduce the middle term:

3x^2 + 9x - 7x -21 = 0

Take the common in the first two and the last two terms:

3x(x + 3) -7(x+3) = 0

(3x - 7) (x + 3) = 0

Equate to 0:

(x + 3) = 0

x = -3

(3x - 7) = 0

x= 7/3

Hence, the factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.

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A line pae through the point (-2, -3) and (1, -9). Then the equation of the line is 2x + y + 7 = 0.

These are the specified parameters:

Passes through the points (-2, -3) and (1, -9).

With, x₁ = -2 and y₁ = -3

         x₂ = 1 and y₂ = -9

The equation of the line

[tex]\begin{aligned} \frac{y-y_1}{y_2-y_1} & = \frac{x-x_1}{x_2-x_1} \\ \frac{y-(-3)}{-9-(-3)} & = \frac{x-(-2)}{1-(-2)} \\ \frac{y+3}{-6} & = \frac{x+2}{3} \\ 3(y+3) & = -6(x+2)\\ 3y + 9 & = -6x - 12\\ 6x + 3y + 9 + 12 & = 0\\ 6x + 3y + 21& = 0\\ 2x + y + 7 & = 0\end{aligned}[/tex]

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The rating scale used by the restaurant is an example of an ordered categorical scale (c)

An ordered categorical scale is a type of categorical scale where the categories have a specific order or ranking. In this case, the categories "excellent," "very good," "good," and "poor" have a clear order from highest to lowest, indicating the level of customer satisfaction.

A binary/dummy scale, on the other hand, only has two categories, such as "yes" or "no."

An unordered categorical scale does not have a specific order or ranking, such as gender (male or female) or hair color (brown, black, blond, etc.).

A continuous scale, such as height or weight, has an infinite number of possible values and can be measured to any degree of precision.

So, the restaurant's questionnaire uses an ordered categorical scale to measure customer satisfaction.

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Answer:

The following linear equation represents the system:

x + y = 20 (speed of the riverboat and current in km/hr in the same direction)

x - y = 16 (speed of the riverboat relative to the current in km/hr in opposite directions)

Solving for x and y gives us:

x = 18 and y = 2 (speed of the riverboat and current in km/hr).

Step-by-step explanation:

If the value of a is 4 the equation will become true.

Two or more expressions with an Equal sign is called as Equation.

Let the number be a.

2× a = 8 ...(1)

We need to find the value of a such that the above equation is true.

Divide both sides of equation (1) by 2 .

a = 8/2

a = 4

Hence, if the value of a is 4 the equation will become true.

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The closed form for the matrix l−1 is the inverse matrix of l, which corresponds to an elementary transformation of type 1, which is a row transformation.

A closed form for the matrix L-1 is given by the following formula:

L-1 = (1/det(L)) * adj(L)

Where "det(L)" represents the determinant of the matrix L, and "adj(L)" is the adjugate matrix of L. The adjugate matrix of a matrix A is the transpose of its cofactor matrix, and is denoted as adj(A). The cofactor matrix of a matrix is the matrix of determinants of the minors of the matrix multiplied by alternating signs.

The elementary transformation of type 1 is row interchange. This means that two rows of the matrix are interchanged with each other. This transformation has the same effect when applied from the left as from the right, so when multiplying with L-1 from the left, it corresponds to a row interchange.

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The probability of exactly 2 packages being delivered to the correct houses is, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%.

The total number of ways to deliver the packages to the 4 houses is 4! = 24.

To find the number of ways that exactly 2 packages are delivered to the correct houses, we first choose which 2 houses will receive the correct packages, which can be done in 4 choose 2 = 6 ways.

Then, for each of the two remaining houses, we can choose which of the two remaining packages to deliver to that house in 2 ways. So, the total number of ways to deliver exactly 2 packages to the correct houses is    6×2×2 = 24.

the probability of exactly 2 packages being delivered to the correct

houses are, [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%

Therefore, the probability of exactly 2 packages being delivered to the correct houses is,  [tex]\frac{24}{24}[/tex] = [tex]\frac{1}{1}[/tex] or 100%.

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The greatest common factor of y²(2y - 1)  , 3(2y - 1) is 2y.

Given expressions,

y²(2y - 1)  , 3(2y - 1)

y²(2y - 1) = 2y³ - y

= 2 x y x y x y - y

3(2y - 1)

= 6y - 1

= 2 x 3 x y - 1

This way, you can find the elements that are shared by both terms.

2y(2y)(-y)(-3).

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The surface area of the whole solid will be 144 square inches.

The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.

The surface area will be calculated as:-

SA = SA of cuboid + SA of cube

SA = 6 x ( 11 x 2 ) + 6 x 2

SA = 132 + 12

SA = 144 square inches

Therefore, the surface area of the whole solid will be 144 square inches.

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Answer:

B; -2.5

Step-by-step explanation:

A is between the value -2 and -3. If we look at the options, there is only one value between -2 and -3, -2.5. So, A must represent -2.5, meaning that our answer is B.

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The system of equation (4) and (5) have no solution

From the question, we have the following parameters that can be used in our computation:

7(5x + 2) = 5x + 2

Divide both sides by 5x + 2

7 = 1

This equation is false, meaning there is no solution for y that satisfies both equations.

Here, we have

2y = 6

y = -15

Since these are two different equations with the same variable, y, we can use substitution to find a solution.

Starting with the second equation, y = -15, we can substitute this value into the first equation:

2y = 6

2(-15) = 6

-30 = 6

This equation is false, meaning there is no solution for y that satisfies both equations.

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Complete question

4. How many solutions will this equation have? 7(5x + 2) = 5x + 2

5. Solve the given system of equations 2y = 6 and y = -15

The value of x in the rhombus is -1

From the question, we have the following parameters that can be used in our computation:

The shape = rhombus

The diagonals of rhombus bisect each other at 90 degrees

So, we have

2x^2 - 25x + 3x^2 + 60 = 90

Evaluate the like terms

5x^2 - 25x - 30 = 0

Divide through by 5

x^2 - 5x - 6 = 0

So, we have

x^2 + x - 6x - 6 = 0

Factorize

(x + 1)(x - 6) = 0

This gives

x = -1 and x = 6

When x = 6, 2x^2 - 25x is negative

Hence, the value of x is -1

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The vector vec{a} = (1.5, -1) points into the second quadrant.

To determine this, we look at the signs of the components of the vector. Since the x-component is positive (1.5) and the y-component is negative (-1), the vector is in the quadrant with positive x-values and negative y-values, which is the second quadrant.

The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes. Roman numerals I (where the signs of the (x; y) coordinates are I (+; +), II (-; +), III (-;-), and IV (+;-) are frequently used to identify these.

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The equation 1.[tex]5^x[/tex] - x - 2 = 0 then the value of x be -1.44292524676275.

A line is an endlessly long object without breadth, depth, or curvature in geometry. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.

A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.

Let the equation [tex]$1.5^x-x-2=0$[/tex]

Lambert form: [tex]$1=-e^{-\ln (1.5) x}(-x-2)$[/tex]

The equation with [tex]$(-x-2) \ln (1.5)=u$[/tex] and [tex]$x=-\frac{u+2 \ln (1.5)}{\ln (1.5)}$[/tex][tex]$1=-e^{-\ln (1.5)\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)}\left(-\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)-2\right)$$[/tex]

Simplifying the above equation, we get

[tex]$1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$$[/tex]

[tex]$1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$[/tex] in Lambert form: [tex]$e^u u=-\frac{\ln (1.5)}{2.25}$[/tex]

Solve [tex]$e^u u=-\frac{\ln (1.5)}{2.25}: \quad u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$[/tex]

[tex]$$u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$$[/tex]

Substitute back [tex]$u=(-x-2) \ln (1.5)$[/tex], solve for x[tex]$(-x-2) \ln (1.5)=W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right): \quad x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$[/tex]

Therefore, the simplifying x, we get

[tex]$x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}, x=-\frac{W_0\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$[/tex]

Therefore, the value of x be x = -1.44292524676275.

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Answer:

[tex]14400i[/tex]

Step-by-step explanation:

(50 + 72i)^2 = 7200i - 2684

(50 - 72i)^2 = -7200i - 2684

= 7200i - 2684 - -7200i - 2684

= 7200i - 2684 + 7200i + 2684

= 14400i - 2684 + 2684

= [tex]14400i[/tex]

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2 }[/tex] - [tex]\frac{1}{4}[/tex]

[tex]\frac{2}{4}[/tex] - [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{1}{2}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{4}[/tex]

Answer:

Green: 5; White: 2; Blue: 3; Red: 2; Total: 12

A) 8/12

i) 5/12 and 3/11

ii) 10/12

Hope this helps!

Step-by-step explanation:

a) The probability that it is either green or a blue marble is 2/3

b) The probability that first draw will be a green and the second draw, a blue marble is 3/44

c) The probability that neither is a red marble is 15/22

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

A man has twelve identical marbles in his pockets consisting of five green, two white, three blue and two red

Now , the probability is

a)

The probability that it is either green or a blue marble is P(green or blue) = P(green) + P(blue)

P(green) + P(blue) = 5/12 + 3/12

P(green) + P(blue) = 8/12 = 2/3

Therefore , the probability is 2/3

b)

The probability that first draw will be a green and the second draw, a blue marble is P(green and blue) = P(green) x P(blue | green)

P(green) x P(blue | green) = (5/12) x (3/11)

P(green) x P(blue | green) = 15/132

c)

The probability that neither is a red marble is P(neither draw is red) = P(non-red on first draw) x P(non-red on second draw | non-red on first draw)

P ( neither red ) = ( 5/6 ) ( 9/11 )

P ( neither red ) = 15/22

Hence , the probability is solved

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It is an inferential technique that uses the data from a sample to draw inferences about a population.

Hypothesis testing is a type of statistical hypothesis that uses data from a sample to draw judgments about a population parameter or a population probability distribution.

First, an uncertain hypothesis is made about the parameter or distribution. This is named the null hypothesis and is denoted by [tex]H_{O}[/tex]. An alternative hypothesis (denoted [tex]H_{a}[/tex]), which is the opposite of the null hypothesis, is then described.

The hypothesis-testing process involves using sample data to decide whether or not [tex]H_{0}[/tex] can be rejected. If [tex]H_{O}[/tex] is rejected, the statistical determination is that the alternative hypothesis [tex]H_{a[/tex] is true.

Hence, the correct answer is c.

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--The given question is incorrect; the correct question is

"A hypothesis test is

a. a descriptive technique that allows researchers to describe a sample

b. a descriptive technique that allows researchers to describe a population

c. an inferential technique that uses the data from a sample to draw inferences about a population

d. an inferential technique that uses information about the population to make predictions about a sample"--

The function model for a bacteria culture that doubles in size every 8 hours is A(t) = 150*2^(t/8)

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Information about the problem:

The function that models the situation is the following:

A(t) = A(0)*2^(t/8)

A(t) = 150*2^(t/8)

Where A(0) is the culture start and t is the time passed.

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The rate of change of the radius when the radius is 2 is approximately 4 / (π³ * 2⁵).

         V = (1/6) * π³ * r⁶

         dV/dt = (1/6) * π³ * 6 * r⁵ * dr/dt

          dV/dt = 4

       4 = (1/6) * π³ * 6 * 2⁵ * dr/dt

       dr/dt = 4 / ((1/6) * π³ * 6 * 2⁵) = 4 / (π³ * 2⁵)

So the rate of change of the radius when the radius is 2 is approximately  with this one: dr/dt = 4 / (π³ * 2⁵).

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Answer:

  B.  1:484

Step-by-step explanation:

You want the scale of a 15-inch model that represents a 605-foot building.

The scale is the ratio of the model distance to the corresponding real-world distance. To express the scale as a ratio or fraction without units, the measures being compared must have the same units.

  scale = 15 in : 605 ft = 15 in : (605 ft · 12 in/ft) = 15 : 7260

  scale = 1 : 484

The ratio of heights is ...

  B.  1:484

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Step-by-step explanation:

What we have is...

[tex]4(-4.6+w) = 22.24[/tex]

What we'll first do is distribute the 4 into the -4.6 and w

-18.4+4w = 22.24

Next we add 18.4 to both sides to get rid of it on the right side

4W = 22.24+ 18.4

4W = 40.64

Last thing to get W alone, we will divide both sides by 4

W = 10.16

The monthly loan payment for the offer made by Juanita, given the cost of the car and the dealership, is A. 248.62

First, find the amount taken on loan :

= 15, 000 x ( 1 - 10 % down payment )

= $ 13, 500

The periodic rate is:

= 4 % / 12

= 1 / 3 %

The number of periods :

= 5 years x 12 months a year

= 60 months

The monthly payment is:

Present value of loan = Monthly Payment x Present value interest factor of annuity, 1 / 3 %, 60 months

13, 500 = 54.299068906557 x Monthly payment

Monthly payment = 13, 500 / 54.299068906557

= 248. 62

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The value of P (factor of 10) is, 1/4.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

There ae 4 cards to select.

Now, In all 4 cards the factor of 10 is, 2

Hence, The probability to be the factor of 10 is,

⇒ 1 / 4

Thus, The value of P (factor of 10) is, 1/4.

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The cubic polynomial with the given points is:

y = (1/4)*(x + 4)*(x - 2)*(x - 5)

Any polynomial of degree N with the zeros {a,b, c...} and a leading coefficient K can be written as:

y = k*(x - a)*(x - b)*...

Here we have the zeros: -4, 2, and 5, then we can write:

y = k*(x + 4)*(x - 2)*(x - 5)

And it also passes throuh the point (0, 10), then:

10 = k*(0 + 4)*(0 - 2)*(0 - 5)

10 = k*40

10/40 = k

1/4 = k

The polynomial is:

y = (1/4)*(x + 4)*(x - 2)*(x - 5)

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Answer:

The answer to the inequality is [tex]p\geq 4[/tex].

Step-by-step explanation:

Lets solve the inequality.

[tex]-2p\leq -8[/tex]

Divide both sides of the equation by -2.

There is an inequality rule that says when multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

First lets divide both sides by -2.

[tex]\frac{-2p}{2} \leq \frac{-8}{2}[/tex]

Simplify the left side by cancelling the common factor of −2.

[tex]p\leq \frac{-8}{2}[/tex]

Simplify the right side by dividing -8 by 2.

[tex]p\leq 4[/tex]

We need to flip the direction of the inequality sign.

[tex]p\geq 4[/tex]

The coins of each type are 346 nickels, 165 dimes and 173 quarters. when a newspaper carrier has $6.85 charge  by substitution method.

Let x = number of quarters

Then, x-4 = number of dimes and 5x = number of nickels

So, 0.05(5x) + 0.10(x-4) + 0.25x = 6.85

0.6x - 0.4 = 6.85

0.6x = 7.25

x = 12

There are 12 quarters, 8 dimes, and 60 nickels (or)

x = 8 + D(dimes)

D = Q -8

N(nickels) = 2Q

N + D + Q = 685

2Q + Q-8 + Q = 685

4Q = 685+ 8 = 693

Q = 693/4 = over 173

D= over 165

N= over 346

174+ 165 + 346 = 685

the answer is 346 nickels, 165 dimes and 174 quarters.

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Answer:It depends on the specific system of inequalities being considered. To determine if a point is a solution to a system of inequalities, you need to substitute the x and y coordinates of the point into each inequality and see if it is true for all of them. If it is true for all of the inequalities, then the point is a solution to the system.

give me a thanks and a 5 star pls!

Step-by-step explanation:

It depends on the specific system of inequalities being considered. To determine if a point is a solution to a system of inequalities, you need to substitute the x and y coordinates of the point into each inequality and see if it is true for all of them. If it is true for all of the inequalities, then the point is a solution to the system.