c(a + b)- d = f, for a

Using number sets, it is found that the set of dense numbers is composed by: rational and irrational numbers

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Numbers can be classified as:

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The form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).

To evaluate the polynomial [tex]y = x^3 - 5x^2 + 6x + 0.55[/tex]at x = 1.37 using 3-digit arithmetic with chopping, we substitute x = 1.37 into the expression:

[tex]y = (1.37)^3 - 5(1.37)^2 + 6(1.37) + 0.55[/tex]

Calculating each term;

[tex](1.37)^3[/tex]= 2.559

5[tex](1.37)^2[/tex]= 9.415

6(1.37) = 8.22

Substituting these values into the expression for y,

y = 2.559 - 9.415 + 8.22 + 0.55

y = 1.914

Now, let's move on to part (b).

We will express y as y = ((x - 5)x + 6)x + 0.55,

Now using 3-digit arithmetic with chopping.

Then, we substitute x = 1.37 into the expression:

y = ((1.37 - 5) 1.37 + 6) 1.37 + 0.55

Calculating each term separately:

(1.37 - 5) = -3.63

-3.63 x 1.37 = -4.98

-4.98 + 6 = 1.02

1.02 x 1.37 = 1.3974

Finally, adding 0.55:

y = 1.3974 + 0.55

y = 1.9474

Now, let's compare the percent relative round-off errors in both cases.

In part (a), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was also 1.914. Therefore, the percent relative round-off error is:

(1.914 - 1.914) / 1.914 x 100 = 0%

In part (b), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was 1.9474.

Therefore, the percent relative round-off error is:

(1.9474 - 1.914) / 1.914 x 100 ≈ 1.741%

Therefore, in this comparison, we can conclude that the form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).

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Answer:

0.437%

Step-by-step explanation:

given:

initial number =  71 M

final number = 102M

increase = final number - initial number

= 102 - 71

= 31 M

Percent increase

= increase / initial number x 100%

= (31 / 71) x 100%

= 0.437%

No. of valid passports in 2006 = 71M

No. of valid passports in 2011 = 102M

We have to find percentage increase in the number of passports[tex].[/tex]

[tex]\leadsto\sf\:\% Increase = \dfrac{N_2-N_1}{N_1}\times 100[/tex]

[tex]\leadsto\sf\:\% Increase = \dfrac{102M-71M}{71}\times 100[/tex]

[tex]\leadsto\sf\:\% Increase=\dfrac{31}{71}\times 100[/tex]

[tex]\leadsto\sf\:\% Increase=\dfrac{3100}{71}[/tex]

[tex]\leadsto\:\boxed{\bf{\blue{\% Increase=43.66\%}}}[/tex]

Hope it helps !

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Answer:

45 oz

Step-by-step explanation:

first you need to find the are of the yard. To do that you multiply the length by the width: 60x90=5400 feet

next you divide by 120: 5400/120=45

therefore, you need to buy 45 ounces of grass seed.

Answer:

1.4

Step-by-step explanation:

Sample size: 3

Lowest value: 2.89

Highest value: 4.29

Range: 1.4

formula for calculating the range:

Range = maximum(x_i) - minimum(x_i)

where x_i represents the set of values.

Answer:

259.85 K

Formula:

-13.3°C + 273.15 = 259.85K

Step by step solution:

To convert, just add 273.15 to the Celcius value to get the Kelvin value.

Hope this helps!

Answer:

86

Step-by-step explanation:

33+61=94

180-94=86

Answer:

7x+11 =  6y

(7x+11)/6 = y

7x/6= y-11

There are multiple answers for this

Step-by-step explanation:

Answer:

r = 5.56 mm

Step-by-step explanation:

vol of cone = 1/3 π r² h

where

vol = 180 mm³

h = r

find r

plugin values into the formula:

180 = 1/3 * π r³

r³ =  (180 * 3) / π

r = ∛171.9

r = 5.56 mm

Answer:

radius = 5.56 mm

Step-by-step explanation:

Answer:

Total amount earned = $500.25

Step-by-step explanation:

Given:

Wage per hour = $11.50

Time worked = 40 hours

Extra time worked = 7 hour

Wage paid per extra hour = $11.50 / 2 = $5.75

Find:

Total amount earned

Computation:

Total amount earned = [Wage per hour][Time worked] + [Extra time worked][Wage paid per extra hour]

Total amount earned = [11.50][40] + [7][5.75]

Total amount earned = [460] + [40.25]

Total amount earned = $500.25

[tex]4i[/tex]

[tex]i=\sqrt{-1}[/tex]

[tex]\sqrt{-16}=\sqrt{-1}*4[/tex]

[tex]\sqrt{-16}=i*4[/tex]

[tex]4i[/tex]

Hope this helps.

頑張って!

Answer:

As you can see, the difference between the reciprocal of [tex]x^2[/tex] and the inverse of   [tex]x^2[/tex] is that [tex]\frac{1}{x^2} =x^{-2}[/tex] and [tex]\sqrt{x} =x^{\frac{1}{2}[/tex].

Step-by-step explanation:

First lets find both the reciprocal of [tex]x^2[/tex] and the inverse of

Recall that the reciprocal of a value is where you take a fraction and swap the places of the terms. In the case of [tex]x^2[/tex], 1 is the denominator, so

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

To find the inverse of a function, you first need swap the locations of x and y in the equation

[tex]y=x^2\\\\x=y^2[/tex]

Now, you need to solve for y

[tex]y^2=x\\\\y=\sqrt{x}[/tex]

Now, lets rewrite each of these to better compare them

[tex]\frac{1}{x^2} =x^{-2}\\\\\sqrt{x} =x^{\frac{1}{2}[/tex]

As you can see, the difference between the reciprocal of [tex]x^2[/tex] and the inverse of

Answer:

one hundred forty-five thousand nine hundred seventy-three

hope this helps!

Answer:

Coplanar points

Step-by-step explanation:

Coplanar points are three or more points that lie in the same plane.

Answer: true or yes

A number minus 6 is few then 8

Step-by-step explanation:

if you do 6-5=1 or 6-3=3 so true or yes ????

hoped this helped?????????

Answer:

First one: x= -1/2

Second one: x= 1/4

Answer:

6=8x

Step-by-step explanation:

Answer:

6+8x

Step-by-step explanation

We are going to make sure we can do this as best as possible. We need to make sure that the words that you are reading are making sense.

Sum can be taken out because its just 6. We do not know what adds to 6, it could be 1 +5,  2+4, 3+3, -3 and 9, WE DO NOT KNOW. So don't put extra information into the expression, when it is not given.

The and would be an addition to something, because when we are speaking and say the word AND, we want to add to that sentence. So, and is the plus sign.

6+

Then product is multiplication. So 8 times x.

Put it all together and you get the expression:

6+8x

I really hoped that helped you!

Hey there! I'm happy to help!

Let's call our number n.

The word sum means to add.

Therefore....

n+5

Have a wonderful day! :D

Answer:

C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]

Step-by-step explanation:

First of all, let us learn about the formula to find Focus and Directrix from the standard equation of a parabola.

Standard form of a parabola is given as:

[tex](x - h)^2 = 4p (y - k)[/tex]

where the focus is [tex](h, k + p)[/tex] and

the directrix is [tex]y = k - p[/tex]

Now, we are given the equation of parabola as:

[tex]y= \dfrac{1}2 (x+2)^2 - 3[/tex]

Let us try to convert it to standard form:

[tex]\Rightarrow y+3= \dfrac{1}2 (x+2)^2 \\\Rightarrow 2(y+3)= (x+2)^2 \\\Rightarrow (x+2)^2 = 2(y+3)\\\Rightarrow (x+2)^2 = 4\times \frac{1}{2}(y+3)[/tex]

Comparing the above with standard equation of parabola [tex](x - h)^2 = 4p (y - k)[/tex]:

[tex]h = -2, p = \frac{1}{2}, k = -3[/tex]

So, Focus is at [tex](h, k + p)[/tex]

[tex]k + p = -3+\frac{1}{2} = -2\frac{1}{2}[/tex]

Focus is at [tex](-2, -1\frac{1}2)[/tex].

Equation of directrix:

[tex]y = k - p=-3-\frac{1}{2}\\\Rightarrow y = -3\frac{1}{2}[/tex]

Also, please refer to the attached image for the diagram of given parabola, focus and directrix.

So, the answer is:

C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]

Answer:

2700

Step-by-step explanation:

One hour is 300 sheets. We need to find 9 hours,

so 300*9= 2700

Answer:

84.64.

Step-by-step explanation:

(-9.2)^2

= (9.2)^2

= 84.64.

Answer:

[tex]=\left(-\frac{19}{2},\:-2\right)[/tex]

Step-by-step explanation:

[tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-10,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(-9,\:-9\right)\\\\=\left(\frac{-9-10}{2},\:\frac{-9+5}{2}\right)\\\\Simplify \\=\left(-\frac{19}{2},\:-2\right)[/tex]

The value of antiderivative F will be;

⇒ F = 4x - 3 arc tan x - 7 + 3π/4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = 4 - 3 (1 + x²)⁻¹

Now,

Since, The function is,

⇒ f (x) = 4 - 3 (1 + x²)⁻¹

Hence, The antiderivative F of f (x) is,

⇒ F = ∫ (4 - 3 (1 + x²)⁻¹ ) dx

⇒ F = ∫ 4 dx - 3 ∫ (1 + x²)⁻¹ dx

⇒ F = 4x - 3 arc tan x + c

Where, c is constant of integration.

Here, The antiderivative of f (x) is satisfy F(1) = - 3,

So, Substitute x = 1, F = - 3

⇒ F = 4x - 3 arc tan x + c

⇒ - 3 = 4×1 - 3 arctan (1) + c

⇒ - 3 = 4 - 3π/4 + c

⇒ - 3 - 4 + 3π/4 = c

⇒ c = - 7 + 3π/4

Thus, The antiderivative F of f (x) is,

⇒ F = 4x - 3 arc tan x - 7 + 3π/4

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Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{19 \: inches}}}}}[/tex]

Step-by-step explanation:

Let the width be 'w'.

Length of a rectangle ( l ) = 5 + w

Perimeter of a rectangle = 66 inches

First, finding the width of a rectangle

[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}[/tex]

[tex] \dashrightarrow{ \sf{66 = 2(5 + w + w)}}[/tex]

[tex] \dashrightarrow{ \sf{66 = 2(5 + 2w)}}[/tex]

[tex] \dashrightarrow{ \sf{66 = 10 + 4w}}[/tex]

[tex] \dashrightarrow{ \sf{10 + 4w = 66}}[/tex]

[tex] \dashrightarrow{ \sf{4w = 66 - 10}}[/tex]

[tex] \dashrightarrow{ \sf{4w = 56}}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{4w}{4} = \frac{56}{4} }}[/tex]

[tex] \dashrightarrow{ \sf{w = 14 \: inches}}[/tex]

Width of a rectangle ( w ) = 14 inches

Now, Substituting / Replacing the value of w in order to find the length of rectangle

[tex] \sf{length = 5 + w}[/tex]

[tex] \dashrightarrow{ \sf{length = 5 + 14}}[/tex]

[tex] \dashrightarrow{ \sf{19 \: inches}}[/tex]

Length of a rectangle = 19 inches

Hope I helped!!

Best regards! :D

Answer:

zx

Step-by-step explanation: