The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3995 to rent trucks plus an additional fee of $225.75 for each ton of sugar. The second company charges $5500 to rent trucks plus an additional fee of $150.50 for each ton of sugar.

The answer is, the correct statement are , 1. The matrix B² is positive definite if A is positive definite. ,2. A square matrix and its transpose have the same set of eigenvectors. , 3. A real square matrix has only real eigenvalues. , 4. The dimension of the row space of a matrix A with rank 4 is 4. , 5. The dimension of the null space of matrix A is 4.

the correct statements from the options provided:

1. The matrix B² is positive definite if A is positive definite.
2. A square matrix and its transpose have the same set of eigenvectors.
3. A real square matrix has only real eigenvalues.
4. The dimension of the row space of a matrix A with rank 4 is 4.
5. The dimension of the null space of matrix A is 4.

Please note that the statements regarding the values of x, dx, v, r, Av, and trace are incomplete or incorrect, so I have not included them in my answer.

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A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ \(= \frac{360}{n}\)

θ  \(=\frac{360}{5} = 72\)

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

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The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

Answer:

\(\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}\)

Step-by-step explanation:

Fundamental Theorem of Calculus

\(\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

\(\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x\)

Rewrite 9 as 3²  and rewrite the 3/2 exponent as square root to the power of 3:

\(\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\)

Integration by substitution

\(\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}\)

\(\textsf{Let }x=3 \sin \theta\)

\(\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}\)

Find the derivative of x and rewrite it so that dx is on its own:

\(\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta\)

\(\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta\)

Substitute everything into the original integral:

\(\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}\)

Take out the constant:

\(\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta\)

\(\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}\)

\(\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta\)

\(\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}\)

\(\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}\)

\(\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}\)

\(\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}\)

\(\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:\)

\(\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}\)

\(\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:\)

\(\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}\)

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Answer:

Surface area of hemisphere = 150.72 meter²

Step-by-step explanation:

Given;

Diameter of hemisphere = 8 meter

Find:

Surface area of hemisphere

Computation:

Diameter of hemisphere = 8 meter

Radius of hemisphere = Diameter of hemisphere / 2

Radius of hemisphere = 8 / 2

Radius of hemisphere = 4 meter

Surface area of hemisphere = 3πr²

Surface area of hemisphere = 3(22/7)(4)²

Surface area of hemisphere = 3(22/7)(16)

Surface area of hemisphere = 3(3.14)(16)

Surface area of hemisphere = (9.42)(16)

Surface area of hemisphere = 150.72 meter²

please give brainliest

Answer:

The general equation of the cost of the billboard can be represented as follows:

y = 25 + 15x

In this equation:

"y" represents the cost of the billboard

"x" represents the number of days that your advertisement remains on the billboard

The fixed cost of $25 is added to the product of the daily cost of $15 and the number of days "x" that the advertisement is up.

Please note that this equation assumes a linear relationship between the number of days and the cost.

The formula to determine the angle subtended by an arc is:θ = (L/r), where θ is the angle in radians, L is the length of the arc, and r is the radius of the circle.

We are given a circle with a radius of 16 meters and an arc length of 4π meters. Therefore, we can plug in the values of L and r to obtain the angle in radians:

θ = (L/r) = (4π/16) = π/4 radians

We can convert radians to degrees using the formula:

π radians = 180 degrees

Therefore, we can convert the angle in radians to degrees as follows:

θ (in degrees) = (θ in radians) × (180/π) = (π/4) × (180/π) = 45 degrees

Hence, the angle subtended by an arc of length 4π meters on a circle of radius 16 meters is π/4 radians or 45 degrees.Conclusion:Thus, the angle, in radians, is π/4 and the angle, in degrees, is 45 degrees.

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Answer:

  y = x -6

Step-by-step explanation:

You can start with the slope-intercept form of the equation for a line:

  y = mx +b . . . . . . line with slope m and y-intercept b

and rearrange it to help you find the y-intercept:

  b = y - mx

For the given point and slope, the y-intercept is ...

  b = -8 -(1)(-2) = -8 +2 = -6

Then the equation for a line with slope m=1 and y-intercept b=-6 is ...

  y = x -6

Answer:

Step-by-step explanation:

x-intercept (x,0) , y intercept (0,y)

10: -3x-4y=12

x=0 , -3(0)-4y=12

-4y=12 , ⇒ y=12/-4 ⇒ y=-3

y=0 : -3x-4(0)=12

-3x=12 ⇒ x=12/-3 ⇒ x=-4

-9x+4y=-36

x=0 , 4y=-36 , y=-36/4 , y=-9  

y=0 , -9x=-36 , x=-36/-9 , x=4

5x-3y=-15

x=0 , -3y=-15 , y=-15/-3 , y=5

y=0 , 5x=-15 , x=-15/5 , x=-3

Answer:

78

Step-by-step explanation:

Let the two-digit number have the digits a and b.

It mentions that they add up to 15.

Then the possible numbers are :

=============================================================

Let's reverse the numbers :

69

78

=============================================================

Solution :

Hence, the number needed is 78

Step-by-step explanation:

no. 10y+x

no. formed by reversing the digits = 10x+ y

ATQ

EQ(1)= x+y=15

EQ (2)=10x+y+9=10y +x ( Digits are reversed)

9x-9y=-9

x-y=-1

x+y=15 ( given)

2x=14,x=7

and y=15–7=8

thus the number=78

Answer:

d

Step-by-step explanation:

The surface area of the cylinder is 603.19 square meters

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

Radius, r = 8 meters

Height, h = 4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 8 * (8 + 4)

Evaluate

Surface area = 603.19

Hence, the surface area is 603.19 square meters

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Answer:

The three straight paths intersect at different angles. In other words, the amountrequired to turn one path onto the other is different about each vertex. Thelargest angle is opposite the longest side, and the smallest angle is opposite theshortest side. If all three points of intersection look the same, the result is atriangle with three equal angles and three equal sides.

Step-by-step explanation:

The angle of intersection of AB, BC and AC when, they meet each other at three points, are 54.48°, 81.83° and 43.65°.

When the three sides of a triangle is known, then to find any angle, the law of cosine is used. It can be given as,

\(c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B\)

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

The three straight paths, AB, BC, and AC meet each other at three points, A, B, and C.

All the points of intersection of given angle A, B  and C keeps the different value as all the sides of the triangle is not equal.

The length of the angle C using the above formula,

\(5^2=4.24^2+6.08^2-2(4.24)(6.08)\cos (C)\\C=\cos^{-1}(0.581)\\C=54.48^o\)

Similarly, the measure of angle B,

\(6.08^2=5^2+4.24^2-2(5)(4.24)\cos (B)\\B=\cos^{-1}(0.142)\\B=81.83^o\)

The measure of angle A,

\(4.24^2=5^2+6.08^2-2(5)(6.08)\cos (A)\\A=\cos^{-1}(0.7235)\\A=43.65^o\)

The length of the side opposite to angle A is 4.24 units, side opposite to angle B is 6.08 units and side opposite to angle C is 5 units.

All the sides and angles of the triangle are different from each other. This triangle ABC is a scalene triangle.

When all the point of intersection of provided line intersect at a single point. Then all the points of intersection resemble one another.

Thus, the angle of intersection of AB, BC and AC when, they meet each other at three points, are 54.48°, 81.83° and 43.65°.

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Answer:

29

Step-by-step explanation: 5 + 2 [(48 - 40)/4+(2 x 5)]

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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Answer:

Step-by-step explanation:

Answer:

The truck is 315 inches long.

Step-by-step explanation:

180+75%=315.

Carne will have $2180, $2376.2 and $2590.058 after one, two and three years respectively.

The formula to be used for calculation for mount after given period of time is - A = \(P {(1 + r)}^{t} \) where A is amount, p is principal, r is rate of interest and t is time. Keep the values in formula to find amount after specified period of time.

Amount after one year -

A = 2000 × (1 + 9%)¹

A = 2000 × (100 + 9)/100

A = 20 × 109

A = 2180

Amount after two years -

A = 2000 × (1 + 9%)²

A = 2000 × ((100 + 9)/100)²

A = 2000 × 1.09²

A = 2376.2

Amount after three years -

A = 2000 × (1 + 9%)³

A = 2000 × ((100 + 9)/100)³

A = 2000 × 1.09³

A = 2590.058

Therefore, the amount after one, two and three years will be $2180, $2376.2 and $2590.058 respectively.

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Using Euler integration, the next values of x and y can be determined as follows:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Euler integration is a numerical method used to approximate solutions to differential equations. It is based on the concept of dividing the interval into small steps and using the derivative at each step to calculate the next value. In this case, we are given the current values of x=2, y=8, and y'=9, with a step size of delta_X=5.

To determine the next values of x and y, we use the following formulas:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Substituting the given values into the formulas, we have:

x_next = 2 + 5 = 7

y_next = 8 + 5 * 9 = 53

Therefore, the updated values of x and y using Euler integration are x=7 and y=53.

It's important to note that Euler integration provides an approximate solution and the accuracy depends on the chosen step size. Smaller step sizes generally lead to more accurate results. Other numerical methods, such as Runge-Kutta methods, may provide more accurate approximations.

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Thus, the wind speed at 80 meters is approximately 8.74 m/s when the wind speed at 60 meters is 8 m/s and the shear exponent is 1/7.

In order to find the wind speed at 80 meters, we need to use the shear exponent. The industry standard for the shear exponent is 1/7, which means that the wind speed will decrease by a factor of 1/7 for every meter increase in height.

To calculate the wind speed at 80 meters, we can use the following formula:

Wind speed at 80m = Wind speed at 60m * (80/60)^(1/7)

Plugging in the given values, we get:

Wind speed at 80m = 8 * (80/60)^(1/7)
Wind speed at 80m = 8 * 1.092
Wind speed at 80m = 8.74 m/s

Therefore, the wind speed at 80 meters is approximately 8.74 m/s when the wind speed at 60 meters is 8 m/s and the shear exponent is 1/7.

It's important to note that the shear exponent can vary depending on the atmospheric conditions, terrain, and other factors. So, this calculation provides an estimate based on the given standard.

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Hope this helps, have a nice day!!

The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

We know that the phone numbers of a small town either begin with 373 or 377. We are required to find out the number of phone numbers that are available. To solve this question, we need to count the number of phone numbers that are available for each prefix.

The prefix 373 can have numbers ranging from 3730000 to 3739999. Similarly, the prefix 377 can have numbers ranging from 3770000 to 3779999.

Therefore, the total number of phone numbers that are available is the sum of the phone numbers available for each prefix.

Total number of phone numbers = Number of phone numbers available for prefix 373 + Number of phone numbers available for prefix 377

Total number of phone numbers = 10000 + 10000

Total number of phone numbers = 20000

Therefore, The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

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1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer:

110°F

Explanation:

The temperature on the thermometer is taken at the point where the red ends as highlighted in the diagram below:

At this point, the value is 110.

Therefore, the temperature shown on the thermometer is 110°F.

Answer: 804.25 yards3

Step-by-step explanation: : Explanation We have height (H) = 4 yards Diameter = 4x4 = 16, Radius (r) = 16/2 = 8, volume and cylinder V = nr2h. V= 3.14 x 8x8x4, V= 804.25 yards 3

Answer:

pls give more detail

Step-by-step explanation:

Answer:

Programmed

Step-by-step explanation:

Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.

Answer: 23 kg

Step-by-step explanation:

Let's begin by using algebra to solve the problem.

Let x be the number of kilograms of salmon the fish-shop owner bought at the market.

We know that the total cost of the salmon was $400, so we can write:

400 = x * c

where c is the cost per kilogram of salmon.

We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.

The total revenue from the sale of the fish was $540, so we can write:

540 = (x - 2) * (c + 10)

Now we can use these two equations to solve for x.

First, we can use the first equation to solve for c:

c = 400 / x

Then we can substitute this expression for c into the second equation:

540 = (x - 2) * (400/x + 10)

Simplifying this equation:

540 = 4000/x + 10x - 20 - 80/x

Multiplying both sides by x:

540x = 4000 + 10x^2 - 20x - 80

10x^2 - 20x - 4600 = 0

Dividing both sides by 10:

x^2 - 2x - 460 = 0

We can solve for x using the quadratic formula:

x = [2 ± sqrt(4 + 4*460)] / 2

x = [2 ± 44] / 2

Discarding the negative solution, we get:

x = (2 + 44) / 2

x = 23

Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.