Two construction contracts are to be randomly assigned to one or more of three firms—I, II, and III. A firm may receive more than one contract. Each contract has a potential profit of $90,000.

a. Find the expected potential profit for firm I.

b. Find the expected potential profit for firms I and II together.

Answer:

i. 5(x + 0.2x) yards

ii. 6x yards

Step-by-step explanation:

Since the requested quilts are 20% larger than the normal pattern, then;

20% of x = 0.2 x

Thus,the yards of material to make each of the requested quilts increased by 0.2x yards.

So that;

To make one of the requested quilt, the yards required = x + 0.2x

For 5 requested quilts, the total yards required = 5(x + 0.2x)

Total yards of material for the requested quilts is 5(x + 0.2x).

Also,

5(x + 0.2x) = 5x + 5(0.2x)

                  = 5x + x

                  = 6x

Thus, the total yards required is 5(x + 0.2x) or 6x.

Answer:

234

Step-by-step explanation:

Answer:

x=10 and y=4

Im not sure if this is correct but I looked it up and it said it was right

Answer:

(if you're looking for intercepts then: x = 10, y = -4)

Step-by-step explanation:

\(\sf{2x - 5y = 20\)

\(\sf{Finding~x:\)

\(2x - 5y = 20\)

     \(+ 5y = + 5y\)

↪ 2x = 5y + 20

\(\frac{2x}{2} = \frac{5y}{2} + \frac{20}{2}\)

\(\sf{Finding~y:}\)

\(2x - 5y = 20\)

\(-2x~ = ~~~~-2x\)

↪ -5y = -2x + 20

\(\frac{-5y}{-5} = \frac{-2x}{-5} + \frac{20}{-5}\)

--------------------

Hope this helps!

The simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

As given in the question,

Given fraction :\(\frac{4^{11} }{4^{-8} }\)

Simplify the given fraction using the formula of exponents

\(\frac{x^{a} }{x^{b} } =x^{a-b}\)

The simplified form of the given fraction is given by :

\(\frac{4^{11} }{4^{-8} }\)

Substitute the value in the formula of exponent we get:

Here the value of x= 4 ,value of a=11 and value of b= -8

=(4¹¹ ⁻ ⁽⁻⁸⁾)

=(4¹¹ ⁺ ⁸)

=4¹⁹

Therefore, the simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

The complete question is:

Simplify the given fraction in simplified form: \(\frac{4^{11} }{4^{-8} }\).

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Answer:

Loss

Step-by-step explanation:

It would be a loss because you bought them for 30$ but could only sale them for 25$ meaning you lossed 5$.

This means the price you bought them for changed 16.667% decrease.

Hope it helps have a great day:)

The expression in the parentheses can be rewritten as a perfect square, which is then combined with the constant term on the right-hand side. The resulting equation is in the form of (x + p)² = q, where p and q are constants that can be used to solve for x.

In mathematics, an expression is a combination of numbers, variables, and mathematical symbols that represent a mathematical relationship or formula. Expressions can be simple or complex and can include operations such as addition, subtraction, multiplication, and division, as well as exponents, radicals, and functions.

Expressions are used to represent mathematical relationships and to perform mathematical calculations. For example, the expression "2x + 3" represents a linear.

In the given question,

After factoring the left-hand side of a quadratic equation when using the completing the square method, the next step is to add and subtract a constant term on the right-hand side that completes the square. This constant term is equal to half the coefficient of the x-term squared, or (b/2)², where b is the coefficient of the x-term in the original equation.

This step can be written as:

ax² + bx + c = 0

(ax²+ bx) + c = 0

a(x² + (b/a)x) + c = 0

a(x² + (b/a)x + (b/2a)² - (b/2a)²) + c = 0

a(x + b/2a)^² - (b²/4a) + c = 0

The expression in the parentheses can be rewritten as a perfect square, which is then combined with the constant term on the right-hand side. The resulting equation is in the form of (x + p)^2 = q, where p and q are constants that can be used to solve for x.

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Answer:

The value of \(r\) is 24 cm.

Option C. 24 cm

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the missing side.

Here is the formula for the Pythagorean theorem.

\(a^2+b^2=c^2\)

\(a\) and \(b\) are the legs of the triangle

\(c\) is the hypotenuse

In this example we are given the value of 1 leg and the hypotenuse.

Knowing 2 of the 3 sides, we can evaluate the missing leg.

Let \(a=r\)

We are given

\(b=10\\c=26\)

Inserting our values into the Pythagorean theorem gives us

\(r^2+10^2=26^2\)

Lets solve for \(r\).

\(r^2+10^2=26^2\)

Evaluate \(10^2\).

\(r^2+100=26^2\)

Evaluate \(26^2\).

\(r^2+100=676\)

Subtract \(100\) from both sides of the equation.

\(r^2=576\)

Take the square root of both sides to eliminate the exponent.

\(r=\sqrt{576}\)

\(r=24\)

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\((5^{4} *\frac{1}{b^{10} }) ^{-6}\)

\((\frac{5^{4} }{b^{10} } )^{-6}\)

\(\frac{b^{60} }{5^{24} }\)

Answer:

No

Step-by-step explanation:

-2 divided by 1 is -2 while -1 divided by - 2 is -0.5

Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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Answer:

the answer is 4.62*4=18.48

Step-by-step explanation:

the 4.62 is the cost for bus and food added up.

the cost for bus and food for four days is 18.48

The triple integral in spherical coordinates for an arbitrary continuous function f(x, y, z) over the given solid with limits ρ: 1 to 6, θ: unspecified, and φ: 0 to 2π, is ∫∫∫ f(ρ, θ, φ) ρ² sinθ dρ dθ dφ.

In spherical coordinates, we represent points in 3D space using three coordinates: ρ (rho), θ (theta), and φ (phi).

To set up the triple integral of an arbitrary continuous function f(x, y, z) in spherical coordinates over the given solid, we follow these steps:

Identify the limits of integration for each coordinate:

The radial coordinate, ρ (rho), represents the distance from the origin to the point in space. In this case, the solid is defined by a and b, where a = 1 and b = 6. Thus, the limits for ρ are from 1 to 6.

The azimuthal angle, φ (phi), represents the angle between the positive x-axis and the projection of the point onto the xy-plane. It ranges from 0 to 2π, covering a full revolution.

The polar angle, θ (theta), represents the angle between the positive z-axis and the line segment connecting the origin to the point. The limits for θ depend on the boundaries or description of the solid. Without that information, we cannot determine the specific limits for θ.

Express the volume element in spherical coordinates:

The volume element in spherical coordinates is given by ρ² sinθ dρ dθ dφ. It represents an infinitesimally small volume element in the solid.

Set up the triple integral:

The triple integral over the solid is then expressed as:

∫∫∫ f(ρ, θ, φ) ρ² sinθ dρ dθ dφ.

Evaluate the triple integral:

Once the limits of integration for each coordinate are determined based on the solid's boundaries, the triple integral can be evaluated by iteratively integrating over each coordinate, starting from the innermost integral.

It is important to note that without specific information about the boundaries or description of the solid, we cannot determine the limits for θ and provide a complete evaluation of the triple integral.

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Answer:

entrance fee: $8

cost of each ride: $3

the answer of your question is angle 3

Symmetrical balance, also known as bilateral symmetry, is a type of balance in which two halves are mirror images of each other. This type of balance can be found in both visual art and in nature.

In visual art, symmetrical balance is achieved when similar shapes, colors, lines, and textures are repeated on either side of a vertical axis. This creates an even distribution of visual elements and creates a sense of harmony and equilibrium. In nature, symmetrical balance is created when there is a symmetrical arrangement of organs and features in plants and animals.

Symmetrical balance is often used to create a sense of order and balance in visual works of art, as well as to emphasize the balance of nature in landscapes. It can also be used to convey a sense of unity and tranquility, as the repetition of similar elements creates an overall feeling of calmness and symmetry. Symmetrical balance is an important element in many types of artwork, and it is used in all kinds of visual art, including paintings, photographs, sculptures, and more.

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Answer: 4.5 hours

Step-by-step explanation: i used cross multiplication.

2.5/x=60,000/108,000

60,000x=270,000

divide 270,000 by 60,000

x=4.5

An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that the amount of time it takes a water pump to empty a tank varies directly with the capacity of the tank. Therefore, the relationship can be written as,

V ∝ T

V = kT

Substituting the volume and time in the equation,

60,000 gallons = 2.5 hours × k

Solving the equation for k,

k = 60,000 gallons / 2.5 hours

k = 24,000 gallons per hour

Now, the equation for the relationship can be written as,

V = 24,000 gallons per hour × T

Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,

V = 24,000 gallons per hour × T

108,000 gallons = 24,000 gallons per hour × T

108,000 gallons / 24,000 gallons per hour = T

T = 4.5 hours

Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

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The slope of the line passing through any two of the points is the same, the points are collinear & the line that fits the given points is y = 3x + 2.

The given points are (0, 2), (1, 5), (2, 8).

To determine whether the points are collinear,

we can find the slope of the line passing through any two of the points and then check if the slope is the same for all the pairs of points.

Let's take (0, 2) and (1, 5) to find the slope of the line passing through them:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

                = (5 - 2) / (1 - 0)

                 = 3 / 1

                 = 3Now

Let's take (1, 5) and (2, 8) to find the slope of the line passing through them:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

               = (8 - 5) / (2 - 1)

                = 3 / 1

                = 3

Since the slope of the line passing through any two of the points is the same, the points are collinear.

To find the line y = c₀ + c₁x that fits the points,

we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

We can use any of the points and the slope found above.

Let's use (0, 2):

y - 2 = 3(x - 0)

y - 2 = 3x + 0

      y = 3x + 2

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The number of outstanding shares that BBQ Corp. will have post-split, given the number of outstanding shares is, 4, 050, 000 shares

A stock split refers to when the number of outstanding shares that a company has, are divided into a certain number of shares which is based on the split ratio.

For a 3:1 stock split ratio, the number of outstanding shares will be split into three shares each.

BBQ Corp. has 1. 35 million shares so post - split, they will have:

= Outstanding shares x  3

= 1, 350, 000 x  3

= 4, 050, 000 shares

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The answer to the question above is C which is equal to (=) is the symbol that represents the answer to the inflation gap π3−π1.

The correct option is-C

It is important to know that Inflation gap refers to the difference between actual inflation and target inflation. Inflation gaps are also associated with inflation targeting. Inflation targeting is a monetary policy where a central bank tries to keep inflation within a particular range by adjusting interest rates. If inflation is too high, the central bank will increase interest rates to cool off the economy and prevent prices from rising too quickly.

Inflation gaps are also associated with inflation targeting. Inflation targeting is a monetary policy where a central bank tries to keep inflation within a particular range by adjusting interest rates. If inflation is too high, the central bank will increase interest rates to cool off the economy and prevent prices from rising too quickly. If inflation is too low, the central bank will lower interest rates to encourage borrowing and spending, which will stimulate the economy and boost prices. According to the question, the inflation gap π3−π1 is 0.

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Answer:

x^2+(4-1)x-4=0

x^2+4x-x-4=0

x(x+4)-1(x+4)=0

(x-1)(x+4)=0

either (x-1)=0                                   Or,(x+4)=0

x-1=0

x=0+1

x=1

x+4=0

x=0-4

x=-4

therefore x=-4,1

Step-by-step explanation:

The required solutions for x are x₁= 1 and x₁= -4, and we can write them from least to greatest as -4, 1.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To solve for x in the quadratic equation x² + 3x - 4 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation (ax² + bx + c = 0).

In this case, a = 1, b = 3, and c = -4, so we have:

x = (-3 ± √(3² - 4(1)(-4))) / 2(1)

x = (-3 ± √(25)) / 2

x = (-3 ± 5) / 2

x₁ = (-3 + 5) / 2 = 1

x₂ = (-3 - 5) / 2 = -4

Therefore, the solutions for x are x₁= 1 and x₁= -4, and we can write them from least to greatest as -4, 1.

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Answer:

Step-by-step explanation:

\(\frac{3 +NZ}{3}\) = \(\frac{5+5}{5}\)  ⇒  NZ = 3

XZ = 6 × 2 = 12

The length of NZ = 3 units.

The length of XZ = 12 units

A line that runs perpendicular to one side of a triangle and crosses the other two sides equally splits the two sides.

Step 1: Consider side NY, NZ, YM, MX

By the theorem,

\(\frac{YN}{NZ}=\frac{YM}{MX}\)

\(\frac{3}{NZ}=\frac{5}{5}\)

\(NZ=3\) units

Step 2: Consider sides YM, YX, NM, ZX

\(\frac{YM}{YX} =\frac{NM}{ZX}\)

\(\frac{5}{10} =\frac{6}{ZX}\)

\(ZX = 12\) units.

Therefore, the values for the sides are NZ = 3 units and XZ = 12 units.

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Using the exponential growth formula, the population in 2005 was 161 million.

The equation f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value.

Growth factor = (159/154) for the eleven-year period between 1990 and 2001.

The population growth might thus be described by the exponential equation

p(t) = 154(159/154)^(t/11), where t is the number of years since 1990.

The model forecasts a population of... p(15) = 154(159/154)^(15/11)

= 160.86 = 161 million

In 2005, there were about 161 million people living there.

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Correct Question:

A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.

Answer:

Y, Z , X

Step-by-step explanation:

angle y will give the smallest size, angle x will give the largest side

Answer:

1000

Step-by-step explanation:

To solve this you divide 10/0.01 and you get 1000.

Hope it helps!

The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.

The total number of ways to assign six employees to six desks is 6! (6 factorial), which equals 720. Now we need to find the number of ways that the married couple will not have adjacent desks.

First, we can treat the married couple as one entity, which means we have 5 entities to assign to 6 desks. There are 6 possible ways to choose the position of the married couple in the row. For each of these positions, we can then assign the other 4 entities to the remaining 4 desks in 4! ways.

Therefore, the total number of ways to assign employees to desks without the married couple having adjacent desks is 6 x 4! = 144.

The probability of this happening is the number of favorable outcomes (144) divided by the total number of possible outcomes (720), which is 144/720 = 1/5.



The probability that the married couple will not have adjacent desks when six new employees are randomly assigned to six desks that are lined up in a row is 1/5.

We calculated this probability by first treating the married couple as one entity and then finding the number of ways to assign the remaining entities to the desks without the married couple being adjacent to each other. The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.

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line e is parallel to line m because angle 1 + angle 2 = 180°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Represent the adjascent angle to angle 2 by x and adjascent angle to angle 1 by y

therefore ;

2 = y ( corresponding angles are equal)

1 = x ( corresponding angles are equal)

angle 1+y = 180 ( angle on a straight line)

angle 2 + x = 180

<1= 180-y

<2 = 180 -x

and both equations

< 1 +<2 = 180

therefore since < 1 +<2 = 180, then line e is parallel to line m

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Answer:

Multiply 7/6 by 3/3

Step-by-step explanation:

Multiplying 7/6 by 3/3 will give you a result of 21/18.

Hope this helps!

21/18 has a common denominator of 3, which makes it 7/6

21÷3=7

18÷3=6

Answer:

-12 and -6

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

ABCD is a parallelogram.

Angle B and Angle C are adjacent (successive) angles.

Adjacent angles of a parallelogram are supplementary.

Therefore,

\((5x) \degree + (2x + 12) \degree = 180 \degree \\ \\ (5x + 2x + 12) \degree = 180 \degree \\ \\ (7x+ 12) \degree = 180 \degree \\ \\7x+ 12 = 180 \\ \\7x = 180 - 12 \\ \\ 7x = 168 \\ \\ x = \frac{168}{7} \\ \\ x = 24\)

\(\boxed{\pink{\sf\leadsto Value \ of \ x \ is \ 24^{\circ}}}\)

\(\boxed{\pink{\sf\leadsto Value \ of \ \angle C \ is \ 60^{\circ}}}\)

\(\boxed{\pink{\sf\leadsto Value \ of \ \angle D \ is \ 120^{\circ}}}\)

A parallelogram is given to us . in which m ∠ B = 5x and m ∠C = 2x + 12 ° . And we need to find x .

Figure :-

\(\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\thicklines\put(0,0){\line(1,0){5}} \put(5,0){\line(1,2){2}}\put(7,4){\line( - 1,0){5}}\put(2,4){\line( - 1, - 2){2}}\put(0,-0.4){$\bf A$}\put(5,-0.4){$\bf b$}\put(6.5,4.3){$\bf c$}\put(2,4.3){$\bf d$}\qbezier(4.4,0)( 4.5, 0.8)(5.22,0.54)\put(4,0.4){$\bf 5x$}\put(4.7,3.3){$\bf 2x + 12$}\end{picture}\)

Q. no. 1 ) Find the value of x.

Here we can clearly see that ∠DCB and ∠ABC are co - interior angles . And we know that the sum of co interior angles is 180° .

\(\tt:\implies \angle DCB + \angle ABC = 180^{\circ} \\\\\tt:\implies (2x + 12)^{\circ} + 5x^{\circ}=180^{\circ} \\\\\tt:\implies 7x = (180 - 12 )^{\circ} \\\\\tt:\implies 7x = 168^{\circ} \\\\\tt:\implies x =\dfrac{168^{\circ}}{7} \\\\\underline{\boxed{\red{\tt\longmapsto x = 24^{\circ}}}}\)

\(\rule{200}2\)

Q. no. 2 ) Determine the measure of < C .

Here we can see that <C = 2x + 12 ° . So ,

\(\tt:\implies \angle C = 2x + 12^{\circ} \\\\\tt:\implies \angle C = 2\times 24^{\circ} + 12^{\circ} \\\\\tt:\implies \angle C = 48^{\circ} + 12^{\circ} \\\\\underline{\boxed{\red{\tt\longmapsto \angle C = 60^{\circ}}}}\)

\(\rule{200}2\)

Q. no. 3 ) Determine the measure of < D .How you determined the answer .

Here we can clearly see that ∠D and ∠C are co - interior angles . And we know that the sum of co interior angles is 180° .

\(\tt:\implies \angle C + \angle D = 180^{\circ} \\\\\tt:\implies 60^{\circ} + \angle D = 180^{\circ}\\\\\tt:\implies \angle D = 180^{\circ} - 60^{\circ} \\\\\underline{\boxed{\red{\tt\longmapsto \angle D = 120^{\circ}}}}\)