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I have two fair dice each numbered 1 to 6. I am going to throw the two dice. What is
the probability that the sum of the numbers on the dice will be a square number?

The value of the following decimal floating-point number as a single precision floating point values following the ire std 754-1985111.125 is

1100    0001     0110     0100    0000     0000     0000    0000

= C1640000H

IEEE-754 representation for float (single-precision) type is as follows

Sign - 0

Exponent - 1 to 18

Mantissa - 9 to 31

So the exponent field is 8 bits and the mantissa is 23 bits (the precision is actually 24 bits due to the implicit 1 needed in the normalized representation; IEEE 754 also allows demoralized numbers close to 0, but this does not does not apply to the particular question).

Exponential fields also require signs to represent fractions. IEEE 754 does this by giving a bias - 127 for single precision, which means we just subtract 127 from the suggested value to get the actual value. So 0 becomes -127 and 255 (the maximum 8-bit value becomes 128.

Now, coming to the given question we need to represent -14.25 which equals -1110.01 in binary.

Converting to normalized form (only one to the left ) we get

-11101.01 =-1.11001 × 2³

Since we omit the implied  in IEEE-754 representation we get

Mantissa bits = 11001

Exponent bits = 11 + 0111111 = 10000010 (Adding bias Sign bit 1)

(since number is negative)

This will be 1 × 110000010 = 11001000000000

Grouping in 4 bits to convert ot Hexadecimal we get

1100    0001     0110     0100    0000     0000     0000    0000

= C1640000H

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The concept of Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different theorems and axioms.

The concept of Euclidean geometry as required to be discussed is basically introduced for flat surfaces or plane surfaces. The postulates of the Euclidean geometry are as follows!

1 : A straight line may be drawn from any one point to any other point.

2 :A terminated line can be produced indefinitely.

3 : A circle can be drawn with any centre and any radius.

4 : All right angles are equal to one another (Congruent).

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FALSE. Every random sample of the same size from a given population will not produce exactly the same confidence interval for μ.

The confidence interval is a statistical measure used to estimate the range of values within which a population parameter is likely to fall. The confidence interval is calculated based on the sample mean and standard deviation, as well as the level of confidence desired.

Suppose we take a random sample of size n from a population, and calculate the confidence interval for the population mean using this sample. The sample mean and the sample standard deviation will be used to estimate the true population mean and the population standard deviation, respectively. However, as the sample is random, each sample—despite being drawn from the same population—will have different values for the sample mean and standard deviation. Thus, different samples will produce different confidence intervals for the population mean.

Moreover, the size of the sample also affects the width of the confidence interval; larger samples tend to produce more precise estimates of the population mean, while smaller samples yield larger confidence intervals. Therefore, random samples of different sizes from a given population will also produce different confidence intervals.

In summary, the confidence interval is a statistical measure that provides a range of likely values for the population parameter, such as the population mean. While it can be calculated using any random sample from a population, different samples of the same size or different sizes will generally produce different confidence intervals.

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Answer:

Let x be the amount invested in Treasury bonds and y be the amount invested in mutual funds. Then we have the following constraints:

x + y ≤ 40 (total investment cannot exceed $40 million) x ≥ 5 (at least $5 million must be invested in Treasury bonds) y ≥ 15 (at least $15 million must be invested in mutual funds) 100x + 200y ≤ 7000 (total fees cannot exceed $7000)

The objective is to maximize the annual interest, which is given by:

0.06x + 0.08y

We can solve this problem using linear programming. The feasible region is a polygon with vertices at (5, 15), (5, 35), (30, 10), and (40, 0). We evaluate the objective function at each vertex:

At (5, 15): 0.06(5) + 0.08(15) = 1.2At (5, 35): 0.06(5) + 0.08(35) = 2.6At (30, 10): 0.06(30) + 0.08(10) = 2.8At (40, 0): 0.06(40) + 0.08(0) = 2.4

The maximum value of the objective function is 2.8, which occurs at (30, 10). Therefore, the amount that should be invested in Treasury bonds is $30 million and the amount that should be invested in mutual funds is $10 million.

The annual interest earned is 0.06(30) + 0.08(10) = $2.8 million.

Step-by-step explanation:

Step-by-step explanation:

Set it up as a ratio:

14 is to (14 +6)   as   21 is to  ?

14/20 = 21/?

? = 21 * 20 / 14 = 30 units

Answer:

Perceptions of same-sex marriage: In June 2016, a CBS News poll asked a sample of adults worldwide whether it should be legal or not legal for same-sex couples to marry (reported at http://www.pollingreport.com). The opinions of adults worldwide were as follows: 58%, legal; 33%, not legal; and 9%, unsure/no answer.

What type of distribution is this? __________________________

Knowing that 1,280 adults were polled nationwide, how many Americans polled felt that same-sex couples should be allowed to legally marry? __________________________

Step-by-step explanation:

The distribution of opinions on the legality of same-sex marriage worldwide is not described in the prompt, so it is not possible to determine the type of distribution. However, it is possible to use the proportions provided to estimate the number of Americans who felt that same-sex couples should be allowed to legally marry.

If 58% of all adults worldwide believe that same-sex marriage should be legal, and 1,280 adults were polled nationwide, we can estimate the number of Americans who hold this opinion as:

0.58 x 1,280 = 742.4

Therefore, an estimated 742 Americans polled felt that same-sex couples should be allowed to legally marry.

Step-by-step explanation:

(a) Let the original price of each 6-day ski pass be x. Then, the sale price of each pass is 0.85x = 272. Solving for x, we have:

0.85x = 272

x = 320

Therefore, the original price of each 6-day ski pass was $320.

(b) Two 3-day ski passes cost 2 x £110 = £220. Converting to US dollars using the exchange rate, we have:

£220 x 1.70 = $374

Therefore, Andrew would save:

$374 - $272 = $102

by buying one 6-day ski pass in the sale rather than two 3-day ski passes.

If x is an integer, the least possible value of x is 4. So the option D is correct.

The triangle's third side should be less than the sum of the other two sides and more than the difference of the other two sides.

11 - 7.5 < x < 11 + 7.5

Simplify

3.5 < x < 18.5

So the value of the x is between 3.5 and 18.5.

From the option the value 4 and 5 lies between 3.5 and 18.5.

As we have to determine the least possible value of x, so the value of x should be 4. So the option D is correct.

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The complete question is:

The sides of a triangle have lengths 7.5, 11, and x. If x is an integer, what is the least possible value of x?

A. 1

B. 2

C. 3

D. 4

E. 5

The distance they ran is [tex]b * t1^2 * (d - 35) + 15 * t1 = 13t1.[/tex]

The length οf the line segment cοnnecting the twο sites is used tο measure distance between them. The shοrtest line segment between a pοint and a line will have a length equal tο the distance between them.

With the data abοve, we can create twο equatiοns using the fοrmula distance = speed x time:

Equatiοn 1: (d - 15) = b * t1

Equatiοn 2: (d - 35) = c * t1

Where t1 is the amοunt οf time it tοοk Anne tο cοmplete the race.

Carl cοvered a distance οf d - 22 after Bοris had dοne his 22 m οf running. The same fοrmula can be used tο create a different equatiοn:

Equatiοn 3: (d - 22) = c * t2

where t2 is the amοunt οf time it tοοk Bοris tο cοmplete the race.

Equatiοns 1 and 2 can be used tο find b and c in terms οf t1:

b = (d - 15) / t1

c = (d - 35) / t1

Substituting these equatiοns intο Equatiοn 3, we get:

(d - 22) = (d - 35) / t1 * t2

Simplifying, we get:

t1 * t2 = 13 / c

In the previοus equatiοn, we may substitute the fοrmulas fοr b and c in terms οf t1 tο οbtain:

t1 * t2 = 13t1 / (d - 35)

Simplifying, we get:

t2 = 13 / (d - 35)

Tο sοlve fοr b in terms οf t1, we can insert the fοllοwing fοrmula fοr t2 intο Equatiοn 1:

(d - 15) = b * t1

(d - 15) = ((d - 35) / t1) * 13 / (d - 35) * t1

Simplifying, we get:

b = 13 / t1 - 2

Substituting this expressiοn fοr b intο Equatiοn 2, we get:

(d - 35) = c * t1

(d - 35) = ((d - 15) / t1 - 13 / t1 + 2) * t1

Simplifying, we get:

c = (d - 35) / t1 + 13 / t1 - 2

Nοw we can create anοther equatiοn using these expressiοns fοr b and c in terms οf t1:

d = (d - 15) + 15 = b * t1 + 15

d = (d - 22) + 22 = c * t2 + 22 = (d - 35) / t1 * 13 / (d - 35) + 22

When we equalize these twο expressiοns, we οbtain:

b * t1 + 15 = (d - 35) / t1 * 13 / (d - 35) + 22

Multiplying bοth sides by t1 * (d - 35), we get:

b * t1² * (d - 35) + 15 * t1 * (d - 35) = 13t1² + 22t1 * (d - 35)

Simplifying, we get:

b * t1² * (d - 35) + 15 * t1 = 13t1

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Yes, you can stop checking for factor pairs when you find a pair that repeats.

A factor pair is defined in mathematics as a set of two factors that, when multiplied together, produce a specific product. In other words, it is a set of two numbers that we multiply to get a product. For example, in the multiplication statement, 6 7 = 42, 6 and 7 is one of the factor pairs that gives us the product 42.

This is due to the fact that each number has a unique set of factors. When you find a factor pair that repeats, you know you've found all of the factors of that number. Any additional pairs you find will simply be a permutation of the same factors you've already discovered.

Consider the number 24 as an example. Its components are as follows:

1, 2, 3, 4, 6, 8, 12, 24

When looking for factor pairs, we begin with 1 and 24, then move on to 2 and 12, 3 and 8, and finally 4 and 6. We now have all of the factors of 24 because we discovered a pair (4, 6) that repeats the same factors as an earlier pair (6, 4).

As a result, once you find a pair of factors that repeats, you can be confident that you have discovered all of the factors of the number you are investigating.

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The intersection of two parallel lines; x = 10 metres.

Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.

The alternate interior angles are equal because of the parallel lines characteristic.

Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.

Setting these two angles equal to each other, we can get:

x+20 = 2x+10

Simplifying this equation, we get:

x = 10.

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The base of the triangle is decreasing at a rate of 36/19 cm/min when the altitude is 9.5 cm and the area is 94 sq cm.

We can differentiate composite functions using the chain rule in calculus. Any function that is created by fusing two or more other functions is referred to as a composite function. According to the chain rule, if y = f(g(x)), and f and g are both differentiable functions, then the derivative of y with respect to x is given by:

dy/dx = f'(g(x)) * g'(x)

Given that, the altitude is 9.5 cm and the area is 94 sq cm.

The area of the triangle is given as:

A = 1/2(b)(h)

Differentiating both sides with respect to time we have:

dA/dt = 1/2[(db/dt)(h) + b(dh/dt)

Now,

dA/dt = 2 and dh/dt = 2.

Substituting the values we have:

2 = (1/2) * (db/dt * 9.5 + b * 2)

4 = db/dt * 9.5 + 2b......(1)

Using the area of triangle we know that:

Area = (1/2) * b * h

94 = (1/2) * b * 9.5

b = 20

Substituting the value of b in equation 1 we have:

4 = db/dt * 9.5 + 40

db/dt = - 36/19 cm/min

Hence, the base of the triangle is decreasing at a rate of 36/19 cm/min when the altitude is 9.5 cm and the area is 94 sq cm.

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Answer:

Step-by-step explanation:

y2-y1/x2-x1

-7-(-19)/-2-1

12/-2

-6

The slope is -6

Therefore, each portion will be (1-x)/4 pounds.

Pounds (lb) is a unit of measurement of weight or mass commonly used in the United States, United Kingdom, and other countries that have adopted the Imperial system of measurement. One pound is equal to 0.453592 kilograms (kg). The symbol for pound is "lb", which comes from the Latin word libra. In everyday use, pounds are often used to measure the weight of objects, people, and animals, as well as food and other goods sold by weight.

Given by the question.

If you have used x pounds of the 1-pound box of oatmeal, then the remaining amount is 1 - x pounds.

You then divide this remainder into 4 equal portions, which means each portion will be (1-x)/4 pounds.

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Answer:

According to the scale, 1 inch on the drawing represents 1.5 feet in real life. So, to find the actual length of the door, we need to multiply the length on the drawing by the scale factor:

4 inches x 1.5 feet/inch = 6 feet

Similarly, to find the actual width of the door, we need to multiply the width on the drawing by the scale factor:

7 inches x 1.5 feet/inch = 10.5 feet

Therefore, the actual measurements of the door are 6 feet by 10.5 feet.

Answer:

w = 1

Step-by-step explanation:

If we read the problem, we are given the instructional steps to solve this problem. Lets do it anyway without any help.

[tex]11w+3=14[/tex]

We, subtract 3 on both sides (3 - 3, 14 - 3)

[tex]11w=11[/tex]

Divide by 11w (11w/11w, 11/11w)

[tex]w=1[/tex]

The correct option b) [tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.

The graph οf a relatiοn is said tο reflect a functiοn if a vertical line drawn anywhere οn the graph οnly intersects the graph οnce. In the event when a vertical line can graph is nοt a representatiοn οf a functiοn if there are mοre than twο pοints οn it.

The graphs coordinate is at (-3, 3)

Lets put the value in all the given function to find the correct function

a. [tex]\rm y = \sqrt{x - 3} + 3[/tex]

Using (-3, 3) as x and y

[tex]\rm 3 = \sqrt{(-3) - 3} + 3[/tex]

[tex]\rm 3 = \sqrt{9} + 3[/tex]

[tex]\rm 3 \neq 3 + 3[/tex]

[tex]\rm y = \sqrt{x - 3} + 3[/tex] is not a function of graph.

b. [tex]\rm y = \sqrt{x+ 3} + 3[/tex]

Using (-3, 3) as x and y

[tex]\rm 3 = \sqrt{-3+ 3} + 3[/tex]

[tex]\rm 3 = \sqrt{0} + 3[/tex]

[tex]\rm 3 = 0 + 3[/tex]

[tex]\rm 3 = 3[/tex]

[tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.

The other two options are no the functions as cube root is used and the value of x wont satisfy there.

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A vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the null space. The orthogonal vector is :

A = [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]

The orthogonal complement of the subspace V contains any vector perpendicular to V. This orthogonal subspace is denoted V⊥. (pronounced "V perp").

By this definition, null space is the orthogonal complement of row space. Every x perpendicular to the line satisfies Ax = 0 and lies in null space.

vice versa. If v is orthogonal to null space, it must be in row space. Otherwise, we can add this v as an extra row of the matrix without changing its null space. The rice space will become larger, breaking the rule of r+(n−r) = n.

The column space extent of A. These two vectors are the basis of col(A) , but they are not normalized.

In this case, the columns of A are already orthonormal, so you don't need to use the Gram-Schmidt procedure. To normalize a vector and then divide it by its norm:

                   [tex]\left[\begin{array}{ccc}1&2&1\\2&4&3\\3&6&4\end{array}\right][/tex]

and the vector after orthogonal process is:

                  [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]

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R(x) = 47x denotes the total revenue function, and C(x) = 100 + 30x + 0.1x2 is the total cost function.

(a) P(100) = -200

(b) MP(x) = 47 - (30 + 0.2x)

(c) MP(100) = -3

(d) P(101) - P(100) = -0.2

(a) P(100) represents the profit made when x=100 units are sold. It can be calculated as follows:

P(x) = R(x) - C(x)

P(100) = R(100) - C(100)

P(100) = [tex]47(100) - (100 + 30(100) + 0.1(100)^2)[/tex]

P(100) = 4700 - 4000 - 100

P(100) = -200

(b) The marginal profit function MP represents the rate of change of profit with respect to the number of units sold. It can be calculated as follows:

MP(x) = R'(x) - C'(x)

MP(x) = 47 - (30 + 0.2x)

(c) MP(100) represents the marginal profit at x=100 units. It can be calculated by substituting x=100 into the marginal profit function:

MP(100) = 47 - (30 + 0.2(100))

MP(100) = 47 - 50

MP(100) = -3

Profit will drop by |MP(100)| dollars at x = 100, according to MP(100).

(d) P(101) - P(100) represents the additional profit made when the 101st unit is sold compared to when the 100th unit is sold. It can be calculated as follows:

P(101) - P(100) = R(101) - C(101) - R(100) + C(100)

P(101) - P(100) =[tex]47(101) - (100 + 30(101) + 0.1(101)^2) - 47(100) + (100 + 30(100) + 0.1(100)^2)[/tex]

P(101) - P(100) = 47 - 30 - 0.2(101) - 47 + 30 + 0.1(100)

P(101) - P(100) = -0.2

The sale of the 101st unit will increase profit by $0.20.

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Preparation of a Corrected set of Financial Statements :

Income Statements :

PARTY WAGON .INC

INCOME STATEMENT

FOR THE YEAR ENDED DECEMBER 31

CURRENT YEAR

Party Revenue Earned

156,000

Total Revenue

156,000

Expenses :

Insurance Expenses

2,160

Office Rent Expense

14,400

Supplies Expense

1,440

Salary Expense

90,000

Repair and Maintainence expense

2,400

Travel Expense

7,200

Miscellaneous Expense

4,320

Interest Expense

5,280

Depreciation - Van

9,600

Depreciation -Music and Equipment

8,400

Total Expenses

145,200

Income Before Income Tax

10,800

Less : Income Tax Expense

2,400

Net Income

8,400

Jack included balance sheet accounts in the income statement, therefore the corrected income statement consisting of revenue and expenses accounts is provided above.

Statement of Retained Earnings :

Retained Earnings (As per adjusted trial balance)  18,000

Add : Net Income  8,400

Less : Dividends  (1,200)

Retained Earnings Dec 31, Current Year  25,200

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Answer:

B is correct

Step-by-step explanation:

If it is spun twice then the probability of it landing on 2 and then an odd number is:

Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)

1/49 * 4

4/49

a) The probability that a randomly selected subprime mortgage in the state during November 2008 was neither in foreclosure nor repossessed is 0.50.

b) The probability that a randomly selected subprime mortgage in the state during November 2008 was not current is 0.32.

Probability describes the chance or likelihood that an expected outcome or event does or does not occur.

Probability is the quotient of the expected outcome over the total number of possible outcomes or events.

Probabilities can be stated in ratios (fractions, decimals, or percentages).

Mortgage Status

                  Current    Past Due    In Foreclosure    Repossessed    Total

Number     156,330      58,310              8,550                5,590       228,780

The number of subprime mortgage neither in foreclosure nor repossessed = 114,640 (156,330 + 58,310)

The probability that a subprime mortgage in the state was neither in foreclosure nor repossessed = 0.50 (114,640/228,780).

The number of subprime mortgage that was not current = 72,450 (58,310 + 8,550 + 5,590) or (228,780 - 156,330)

The probability that a subprime mortgage in the state was not current = 0.32 (72,450/228,780).

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The marginal profit at the following expenditures for $8000 is 0 for $6000 is 8 for $12,000 is -16 and for $20,000 is -48.

When one more unit is produced and sold, a company or individual will make a profit known as marginal profit. The additional expense or profit made while manufacturing the next unit is referred to be marginal. Whereas marginal cost is the additional expense for manufacturing one extra unit, marginal product is the additional income received.

The difference between marginal cost and marginal product is known as marginal profit (also known as marginal revenue). Managers can utilise margin analysis to help them decide whether to increase output, reduce production, or halt production completely, a decision known as the shutdown point.

we have,

P(x)= 1000+32x - 2x²

Formula for derivative of function:

[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Finding the derivative,

P(x+h) = 1000 + 32(x+h) - 2(x+h)²

P(x+h) = -2x² -4xh - 2h² + 32x + 32h + 1000

P(x+h) - P(x) = h(-4x - 2h + 32)

P'(x) = -4x + 32

Finding derivatives for given values of x is,

P'(8) = -4(8) + 32 = 0

P'(6) = -4(6) + 32 = 8

P'(12) = -4(12) + 32 = -16

P'(20) = -4(20) + 32 = -48

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Complete question:

The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x)= 1000+32x - 2x². Find the marginal profit at the following expenditures.

a. $8000

b. $6000

c. $12,000

d. $20,000

After answering the provided question, we can conclude that slant height  of pyramid  [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The edges of the base form triangle faces known as sides, which connect to the top.

            /\

          /    \

        /         \

      /______\

         5

         |

         |

         |

         |

         |

         2

The square pyramid in the diagram above has a two-unit-long square base and four five-unit-high triangular faces. The Pythagorean theorem can be used to calculate the slant height of each triangular face:

slant height [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

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Answer:

No.

Step-by-step explanation:

Given two triangles on a coordinate plane, you can check whether they are congruent by using the distance formula to find the lengths of their sides. If three pairs of sides are congruent, then the triangles are congruent by the above theorem.

Over here, they aren't congruent by the SSS.

By analyzing the relationship between the distance traveled and the time taken from the given graph, we determined that the cruising speed of the airplane is 567 units of distance per 1 unit of time.

To find the cruising speed of the airplane, we can analyze the given graph and observe the relationship between the distance traveled and the time taken.

Looking at the data points provided, we see that the distance traveled is directly proportional to the time taken. This means that for every unit increase in time, there is a corresponding increase in the distance traveled.

Let's consider the first two data points: (1,567) and (2,1134). The time difference between these two points is 2 - 1 = 1, and the distance traveled difference is 1134 - 567 = 567.

Since the distance traveled is directly proportional to time, we can conclude that the speed of the airplane is equal to the distance traveled divided by the time taken. In this case, the speed would be 567 units of distance per 1 unit of time.

Now, let's calculate the cruising speed using the other data points as well:

(2,1134) - (1,567) = 1134 - 567 = 567 units of distance per 1 unit of time

(3,1701) - (2,1134) = 1701 - 1134 = 567 units of distance per 1 unit of time

(4,2268) - (3,1701) = 2268 - 1701 = 567 units of distance per 1 unit of time

(5,2268) - (4,2268) = 2268 - 2268 = 0 units of distance per 1 unit of time

We can see that for each time interval, the distance traveled is always 567 units. Therefore, we can conclude that the cruising speed of the airplane is 567 units of distance per 1 unit of time.

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The volume of the frustum of the pyramid is 4530 cubic units.

To find the volume of a frustum of a pyramid, we can use the formula

V = (1/3)h(A1 + A2 + sqrt(A1A2))

Where

V is the volume of the frustum.

h is the height of the frustum.

A1 is the area of the base of the frustum.

A2 is the area of the top of the frustum.

In this case, the frustum has a square base of side 27 and a square top of side 15. Therefore, we have

A1 = 27^2 = 729

A2 = 15^2 = 225

h = 10

Now we can plug these values into the formula

V = (1/3)10(729 + 225 + sqrt(729*225))

V = (1/3)10(954 + sqrt(164025))

V = (1/3)10(954 + 405)

V = (1/3)10(1359)

V = 4530 cubic units

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Answer:

Step-by-step explanation:

We can factor out a common factor of -4x from the equation:

y = -4x(x² + 4x - 21)

To factor the quadratic expression in the parentheses, we need to find two numbers that multiply to -21 and add to 4. These numbers are 7 and -3:

y = -4x(x + 7)(x - 3)

To check our work, we can multiply the three factors:

y = -4x(x + 7)(x - 3) = -4x(x² + 4x - 21) = -4x³ - 16x² + 84x

So the factored form is y = -4x(x + 7)(x - 3), and the check shows that we have factored the equation correctly.