use the following long division. x squared 3 x 1 startlongdivisionsymbol 3 x superscript 4 baseline 7x cubed 2 x squared 13 x 5 endlongdivisionsymbol. minus 3 x superscript 4 baseline 9 x cubed 3 x squared to get a remainder of negative 2 x cubed minus x squared 13 x and a quotient of 3 x squared. the term 3x2 in the quotient is the result of dividing 3x4 by

On solving the provided question we got to know that - Thus, the temperature will be 14°C below zero at midnight.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The answer to the query is provided as,

Temperature at the start, or at midday, is 10°C.

Temperature change at a rate of 2°C per hour

Then,

[tex]Temperature at 1 PM = 10 + (-2) = 10 - 2 = 8[/tex] °C

[tex]Temperature at 2 PM = 8 + (-2) = 8 -2 = 6\\[/tex]°C

[tex]Temperature at 3 PM = 6 + (-2) = 6 - 2 = 4\\[/tex]°C

[tex]Temperature at 4 PM = 4 + (-2) = 4 - 2 = 2\\[/tex]°C

[tex]Temperature at 5 PM = 2 + (-2) = 2 - 2 = 0\\[/tex]°C

[tex]Temperature at 6 PM = 0 + (-2) = 0 -2 = -2\\[/tex]°C

[tex]Temperature at 7 PM = -2 + (-2) = -2 -2 = -4\\[/tex]°C

[tex]Temperature at 8 PM = -4 + (-2) = -4 – 2 = -6\\[/tex]°C

[tex]Temperature at 9 PM = -6 + (-2) = -6 – 2 = -8[/tex]°C

At nine o'clock at night, it will be eight degrees below zero.

Then,

the temperature at 12 AM, or midnight

Temperature change over 12 hours = -2°C divided by 12 equals - 24°C

Therefore, the temperature at midnight will be 10 + (-24)

= - 14°C

Thus, the temperature will be 14°C below zero at midnight.

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The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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The missing part of the triangle are x = 7.5 units, y = (7.5√3)/2 units, y = (7.5√3)/2 units, z = (15√3)/2 units, a = 3.75 units and b = 11.25 units

Given: c = a+b = 15, X = 30°, Z = 60°, C = 90° for the triangles

Using the sine rule

x/sin X = z/sin Z = c/sin C

x/sin X =  c/sin C

x/sin30 = 15/sin90

x/0.5 = 15/1

x = 0.5 × 15 = 7.5 units

Using trigonometrical ratio:

sin 60 = y/x

(√3)/2 = y/7.5

y = (7.5√3)/2 units

sin 30 = y/z

1/2 = (7.5√3)/2/z

z = [(7.5√3)/2] / (1/2)

z = (15√3)/2 units

cos 30 =  b/z

(√3)/2 = b/(15√3)/2

b = [(√3)/2] × [(15√3)/2]

b = 45/4 = 11.25 units

a+b = 15

11.25 + b = 15

a = 15 - 11.25

a = 3.75 units

b = 45/4 = 11.25 units

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The use of Fourier analysis in the chords of varying volumes is explained below .

What is Fourier Series ?

The Fourier Series can be defined as a expansion of a periodic function f(x) in terms of infinite sum of sine and cosine .

The Fourier Series make use of orthogonality relationship of sine and cosine function.

The process in which the Fourier Series analysis helps in determine the frequencies of any other particular chords at varying volumes is :

the Fourier series convert the time-domain input signal into a frequency-domain representation which is analyzed for the intensities of specific pitches.

and the relationship between the pitches at a particular given  time is then analyzed to find the chord that is being played.

Therefore , the process of Fourier series in music is explained above .

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Let f be a scalar field and F a vector field.

a) False-  can not take the curl of a scalar field.

b)True- it is a  vector fields.

c)True- it is a  scalar fields.

d)True- it is a vector fields.

e)False-  can not take grad of a vector field.

f)True- vector fields.

g)True- - scalar fields.

h)False-  can not take div of a scalar field.

i)True- - scalar fields.

j)False-  can not take div of a scalar field.

k)False-  can not cross product a vector with a scalar.

l)True- vector fields.

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When the polynomial (2x³+4x² - 9x -18) is divided by x+5, the quotient is 2x²-6+21 and the remainder is -123/(x+5).

Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

Here,

Dividend=(2x³+4x² - 9x -18)

Divisor=(x+5)

On dividing them using long division,

quotient=2x²-6+21

remainder=-123/(x+5)

The quotient is 2x²-6+21 and remainder is -123/(x+5) for the polynomial (2x³+4x² - 9x -18) when divided by x+5.

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Classifying the polynomial 5x³ + 4x − 2 by degree gives a degree of

An equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.

Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.

The degree refers to the highest exponents which is a positive integer

examining the function the degree is 3 and referred to as cubic

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The sum of money that will amount to 5,200 in 6 years at the same rate at which #1706 amounts to #3412 in 20 years is 4000.

The rate of simple interest for changing 1706 to 3412 in 20 years is this:

S.I = PRT/100

Since the principal amount doubled, we can call this a 100% increase.

Thus the rate in 20 years

= 100/20

=5%

Since the rate for the principal amount is 5%, we can apply the same in the second sentence which gives us:

5% × 6

= 30%

5200 = 130%X

X = 520,000/130

= 4,000

So, the sum of money that will amount to #5200 in 6 years at the same rate of interest (simple) as the initial figures is 4000.

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josh is 3 years older than 4 times kim's age. the sum of their ages is less than 43. inequality for the situation, then the oldest age kim could be.

4k + 3 < 43

k < 10

We are given that Josh is 3 years older than 4 times Kim's age. We can express this as 4k + 3, where k represents Kim's age. We are told that the sum of their ages is less than 43, so we can write this as an inequality: 4k + 3 < 43. To find the oldest age Kim could be, we can solve this inequality for k. To do this, we subtract 3 from both sides, giving us 4k < 40. Finally, we divide both sides by 4, giving us k < 10. Therefore, the oldest age Kim could be is 10.

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After solving the given equations the value obtained for x and y will be equal to 2 and 14 respectively.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The given equations are:

y = 9x - 4 and,

y = -2x + 18

Equate both equations,

9x - 4 = -2x + 18

9x + 2x = 18 + 4

11x = 22

x = 2

Substitute x = 2 in the first equation,

y = 9x - 4

y = 9(2) - 4

y = 14

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Answer:

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

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

The value obtained for new correlation will be 0.1

What is Correlation ?

Correlation is a term which is used in statistics. It is a statistical measure that indicates the range to which the two or more variables fluctuate together.

There are mainly two type of correlation that is positive correlation in which variables increase or decrease partially in negative correlation if one variable  is increases then other decreases

Given :

n = 15 pairs

r = 0.20

According to the Question , If each of the X values is multiplied by 2

The value obtained for new correlation will be  [tex]r = \frac{0.2}{2}[/tex] =  0.1

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Answer:

x < 4

Step-by-step explanation:

8 + 3x < 20 ( subtract 8 from both sides )

3x < 12 ( divide both sides by 3 )

x < 4

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{8 + 3x < 20}[/tex]

[tex]\mathsf{3x + 8 < 20}[/tex]

[tex]\text{Subtract by 8 to both sides}[/tex]

[tex]\mathsf{3x + 8 - 8 < 20 - 8}}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{3x < 20 - 8}[/tex]

[tex]\mathsf{3x < 12}[/tex]

[tex]\text{Divide 3 to both sides}[/tex]

[tex]\mathsf{\dfrac{3x}{3} < \dfrac{12}{3}}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x < \dfrac{12}{3}}[/tex]

[tex]\mathsf{x < 4}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x < 4}}}\huge\checkmark[/tex]

[tex]\rm{You\ have\ an\ O P E N\ circle\ shaded\ to\ the\ left\ }\large\checkmark[/tex]

[tex]\huge\text{Good luck on assignment \& enjoy your day!}[/tex]

We can compute Amy's monthly budget for each question using division operations, as follows:

1. Amy's monthly budget for textbooks and course supplies is $100.

2. Amy's monthly budget for rent, utilities, and food is $1,422.

3. Amy's monthly budget for personal and miscellaneous costs is $251.

4. Amy's total monthly budget is $1,825.

The total monthly budget is the total budget divided by the period (nine months).

Division operations can be used to determine the individual monthly budgets for each expense class by dividing the total cost by 9.

Textbooks and Course Supplies =         $900      $100

Rent, Utilities, and Food =                   $12,798   $1,422

Personal & Miscellaneous Expense = $2,259     $251

Transportation =                                      $468       $52

Total non-tuition expenses =             $16,425  $1,825 ($16,425/9)

The number of months for the year = 9 months

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Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.

a. The number is ⁴²P₅ = 42!/37!

                                    =42×41×40×39× 38 ×37!/37!

                                    =102080160 ways.

b. The number is ⁴²C₅ = 42!/ 5! × 37!

                               =42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!

                               = 850668 ways.

If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.

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Answer:Adım adım açıklama: cevap ekte kolay gelsin.

Step-by-step explanation:

To compare two fractions, we need to find a common denominator and then compare the fractions using the numerators. In this case, we can find a common denominator by finding the least common multiple (LCM) of 7 and 8. The LCM of 7 and 8 is 56.

We can then rewrite both fractions using a denominator of 56:

-9/7 = -36/28

-11/8 = -44/28

Now we can compare the fractions using their numerators:

-36/28 < -44/28

Therefore, -9/7 is less than -11/8.

The Latin word "nomen" (which also appears in words like "nominate" and "nomenclature"), which meaning "name," is the root of the word "denominator." And that is essentially what the denominator of a fraction does: it "names" or specifies the kind of fraction that is specified by the numerator (the top part).

The numerator of a fraction, which determines how many parts are being taken into account, is equal to the number of equal parts that make up the total. You can think of a fraction as being composed of p parts, which is the numerator of an item, and q equal parts, which is the denominator.

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The area of the rhombus is 42 square units, and the correct answer is C.

A rhombus is one type of parallelogram and has 4 sides and 4 vertices.

Every side is equal in length and opposite angles are equal.

We have given that side of the rhombus is 7 units and height is 6 units.

To find the area of rhombus:

Remember that a rhombus is any quadrilateral that has four equal sides.

As a rhombus is also a parallelogram.

Formula to calculate area of rhombus using base and height;

Area of the rhombus = base x height

We have base = 7 units

And height = 6 units.

Substituting the values to the formula,

Area of the rhombus = 7 x 6

Area of the rhombus = 42 unit squared.

Therefore, the area is 42 square units.

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Therefore the answer to this question is the current price will  be $991.47

The amount of interest due each period is represented by an interest rate, which is expressed in relationship to the amount lent, deposited, or borrowed. How much money is lent or borrowed depends on the amount lent, the interest rate, the frequency of compounding, and the length of time that it is lent, deposited, or borrowed. much interest will be charged overall.

Here,

Given

n=6*2

i/y=7.5/2

pv=?

pmt=75/2

face value=1000

Annualized Interest Payment / Par Value of Bond * 100% =Coupon Rate

65/1000 * 100% =6.5%

and other coupon rate

75/1000*100%=7.5%

Therefore by calculating the given values we get the current price as $991.47

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Answer: No, i dont think so.

Step-by-step explanation:

AC = BC is not listed as given.

When she did all three activities on Tuesday, the number of days that Gina will do all three activities again on the same day is in 48 days.

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, denoted by lcm in arithmetic and number theory, is the smallest positive integer that is divisible by both a and b.

LCM is an abbreviation for "Least Common Multiple." The smallest multiple that two or more numbers have in common is defined as the least common multiple.

Since Gina runs every 8 days, cycles every 16 days, and jogs every 24 days. This will be:

Multiples of 8 = 8, 16, 24, 32, 40, 48

Multiples of 16 = 16, 32, 48

Multiples of 24 = 24, 48

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The number of items 125 they will sell if the price per item is $3.50. They will sell 125 items if the price is $3.50.

In the given question, a manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item.

If the relationship between the number of items sold i and the price per item p is a linear one then we have to find a formula that gives x in terms of p, x =

Now we have to use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.

Let’s find the slope using

m = {y(2)-y(1)}/{x(2)-x(1),

where

x(1) = 2.5      y(1)=275

x(2) = 2         y(2)=350

m = (350-275)/(2-2.5)

m = 75/(-0.5)

m = -150 is the slope

Point slope form to find the equation:

y - y1 = m(x-x1)

y - 275 = -150(x - 2.5)

y - 275 = -150x + 375

y = -150x + 275 + 375

y = -150x + 650,

But they want to have x = items sold and p = the price

So we have to write the equation where x is in terms of p

x = -150p + 650:

then use the formula to find the number of items they will sell if the price per item is $3.00.

x = -150(3.5) + 650

x = -525 + 650

x = 125 items sold when the price is $3.5

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a) The linear function for the 2005 estimate is given as follows: y = 30 + 5x.

b) The linear function for the 1990 estimate is given as follows: y = 53.75 + 2.25x.

c) They would be predicted to have the same cost in the year of 2013.

d) The 1990 prediction was closer, however it still had a large residual, hence neither was good enough.

The linear functions are defined in the slope-intercept format, given as follows:

y = mx + b.

In which:

Taking 2005 as the estimate, the function is given as follows:

y = 30 + 5x.

Taking 1990 as the estimate, the equation would be of:

y = 20 + 2.25x.

The estimate for 2005 would be of:

y = 20 + 2.25(15) = 53.75.

Hence the equation taking 2005 as the estimate would be of:

y = 53.75 + 2.25x.

The costs would be the same when:

30 + 5x = 53.75 + 2.25x.

2.75x = 23.75

x = 23.75/2.75

x = 8.63 -> + 2005 -> year of 2013.

The estimates for 2011(6 years after 2005) are given as follows:

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Answer:

Step-by-step explanation:

A gate-array logic circuit for the equation x² + 3xy - 14 = output could be designed as follows:

First, we need to calculate x² and 3xy. This can be done using AND, OR, XOR, and NOT gates.

Next, we need to add the two values obtained in step 1 using a full-adder circuit.

Finally, we need to subtract 14 from the sum obtained in step 2. This can be done using a subtractor circuit, which is essentially a full-adder circuit with an additional input for the subtrahend (in this case, 14).

Here is a schematic of the gate-array logic circuit:

   _______________

  |               |

X--| AND/OR/XOR/NOT |---x²

Y--| AND/OR/XOR/NOT |---3xy

  |_______________|

             |

          ______

         |      |

      x²--| Full |---(x² + 3xy)

      3xy--| Adder|

         |______|

             |

          ______

         |      |

 (x² + 3xy)--| Sub |---output

         14--| tract|

         |______|

Note that this is just one possible way to design the circuit, and there may be other ways to achieve the same result.

The Z-value posted in part(c) for a confidence level of 74% is 1.150

The Confidence level in statistics denotes the likelihood that an estimate of the location of a statistical parameter (such as an arithmetic mean) in a sample survey will also hold true for the population.

Confidence levels must be determined before conducting a survey since they affect the poll's margin of error and necessary coverage. 90, 95, and 99% confidence intervals are widely employed in surveys.

A calculated statistic that was based on a sample would also be true for the entire population, within the established confidence level, with a 95% likelihood, if the confidence level were set at 95%.

Every confidence level has different z-value

In the question, We have to write the Z-value of 74% which is 1.15

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Answer:

40

Step-by-step explanation:

let x = # of Qs on the test

0.85x = 34

x = 34/0.85 = 40

Answer:

The Venn diagram below shows information

about the number of items in sets A and B.[asy]

label("A",(0,75));

label("B",(100,75));

label("C",(50,0));

label("D",(0,45));

label("E",(100,45));

draw(Circle((50,60), 40));

draw(Circle((50,30), 40));

draw(Circle((20,60), 20));

draw(Circle((80,60), 20));

[/asy]To find P(A'|B), we can use the formula:P(A'|B) = P(A' and B) / P(B)We can find P(A' and B) by looking at the Venn diagram. It is the number of items in the intersection of sets A' and B, which is represented by the region labeled "D" in the Venn diagram. This region contains 10 items.To find P(B), we can look at the Venn diagram and add up the number of items in both sets B and the intersection of A and B. This is represented by the regions labeled "D" and "E" in the Venn diagram, and contains a total of 20 items.Plugging these values into the formula above, we get:P(A'|B) = (10 items) / (20 items) = 1/2So, the probability that an item chosen at random belongs to A' given that it belongs to B is 1/2. This fraction is already in its simplest form.

Step-by-step explanation:

The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

A wall is to be worked to encase a rectangular area of 260 square feet. The wall along three sides is to be made of material that costs 3 bucks for every foot, and the material for the fourth side costs 15 bucks for each foot.

LW = 260

L = 260 / W

Then the minimum cost is given as,

y = 3L + 3W + 3L + 15W

y = 18W + 6L

y = 18W + 6(260 / W)

y = 18W + 1560 / W

Differentiate with respect to W and put it zero, then we have

y' = 0

18 - 1560/W² = 0

W² = 1560 / 18

W = 86.67 feet

Then the length is given as,

L = 260 / 86.67

L = 3 feet

The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.

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A person who watches 14 hours of TV can do 21.1 sit-ups.

The regression equation is used to predict or estimate the value of the response (or dependant) variables based on an understanding of the explanatory (or predictor) variables.

A regression equation has the following general form:

y = ax + b

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The regression equation showing the relationship between the number of sit-ups a person can accomplish (y) and the number of hours of TV viewed each day (x) is:

y = -1.284x + 39.108

Compute the number of sit-ups a person who watches 14 hours of TV can do as follows:

y = -1.284(14) + 39.108

y = -17.976 + 39.108

y = 21.132 ≈ 21.1

Thus, a person who watches 14 hours of TV can do 21.1 sit-ups.

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The correlation between Exam 1 scores and Exam 2 scores is r = .6

The standard mistake of the relapse is the typical distance that the noticed qualities tumble from the relapse line. For this situation, the noticed qualities fall a normal of 4.89 units from the relapse line. Variance is a proportion of how information focuses varies from the mean. As indicated by Layman, a difference is a proportion of how far a bunch of information (numbers) is fanned out from their mean (normal) esteem. Fluctuation means to track down the normal distinction of deviation from real worth. Hence, the correlation between Exam 1 scores and Exam 2 scores is r = .6

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