[tex] \rm\int_{0}^{2021} \frac{ \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x} + \cdots } } } }{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{x - \cdots} } } } } dx \\ [/tex]

The truth values of the composite propositions are listed below:

Case 7: T, Case 9: T, Case 11: F, Case 13: T, Case 15: F, Case 17: F

Propositions are constructions that contain itself a truth value. This exercise presents a proposition p is false and proposition q is true. Then, we proceed to find the truth value of each composite proposition, that is, a combination of propositions and operators.

Case 7

Case 9

Case 11

Case 13

Case 15

Case 17

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3y = -8x -27

Solution :

A line equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Given line: 3x - 8y = -7

-8y = -7 -3x

y=- (-7 -3x)/8

y= 7+3x/8

So, the slope (m1) = 3/8

Let’s consider the slope of the line perpendicular to the given line as m2

Then, m1 x m2 = -1

3/8 x m2 = -1

m2 = -8/3

Now,

The equation of the line perpendicular to the given line and passing through the point (-3, -3) will be

y – y1 = m (x – x1)

y – (-3) = -(8/3) (x – (-3))

y + 3 = (-8/3) (x +3)

3y + 3 = - 8x - 24

3y = -8x -24-3

3y = -8x -27

Thus, the equation of the required line is 3y = -8x -27

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The area of the shape with parallel sides is 35 unit² of trapezoid .

Describe the trapezoid shape?

A = (1/2) * (a + b)h

Where a, b is the length of the parallel sides and h is the height of the trapezoid.

Given that a = 8, b = 6 and h = 5, hence:

A = (1/2) * (8 + 6) * 5 = 35 unit²

The area of the shape with parallel sides is 35 unit².

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Answer:

(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)

Step-by-step explanation:

Answer:

(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)

[tex]p(x-1)[/tex] is a quadratic in the form

[tex]a(x-1)^2 + b(x-1) + c[/tex]

We want to write [tex]p(x-1)[/tex] instead in the form

[tex]a' x^2 + b' x + c[/tex]

To do this, simply expand the first form completely.

[tex]a(x-1)^2 + b(x-1) + c = a(x^2 - 2x + 1) + b(x-1) + c \\\\ ~~~~~~~~ = ax^2 + (-2a + b)x + (a - b + c)[/tex]

Then [tex]a'=a[/tex], [tex]b'=-2a+b[/tex], and [tex]c'=a-b+c[/tex].

Given

[tex]p(x-1) = 2(x-1)^2 + 3(x-1) + 4[/tex]

(so [tex]a=2[/tex], [tex]b=3[/tex], and [tex]c=4[/tex]) it follows that

[tex]a' = a = 2[/tex]

[tex]b' = -2a + b = -2^2 + 3 = -1[/tex]

[tex]c' = a - b + c = 2 - 3 + 4 = 3[/tex]

[tex]\implies p(x-1) = \boxed{2}\,x^2 - \boxed{1}\,x + \boxed{3}[/tex]

Given line A has a slope of m = -2/5, the slope of a line parallel to line A is m = -2/5

The slope of a line y = mx + c where

Is given by m = Δy/Δx where

Given a line y = mx + c where  

Also, given another line y' = m'x + c' where  

If y is parallel to y' then their slopes are equal. That is m = m'

Given that line A has a slope of m = -2/5, then by the condition above, the slope of a line paralllel to line A must also equal m.

So, the slope of a line parallel to line A is m = -2/5

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Answer:

3 1/6

Step-by-step explanation:

First, we turn 11/12 and 3/4 to have the same denominator  

3/4 x 3 is 9/12

11/12- 9/12 is 2/12

Now we add the extra 3 to 2/12 which is 3 2/12

3 2/12 can be simplified to 3 1/6

If she contracts to pay the loan in 18 months, Catherine would pay 209.66 in each month

The simple interest on purchase finance is determined as the cost of the items purchased multiplied by the annual interest of 20% and the period the month payments would last:

I=PRT

Where:

So we have:

I=2903*20%*1.5

I= 870.90

total payments=2903+ 870.90

total payments= 3,773.90

monthly payment=3,773.90/18

monthly payment= 209.66

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Correct answer is B. Fred Korematsu was arrested for Refusing to move to the detention center.

Fred Korematsu is detained on May 30, 1942, in San Leandro, California, for defying President Franklin Roosevelt's contentious Executive Order 9066, which called for the internment of almost all Japanese Americans in the US following Japan's assault on Pearl Harbor.

Korematsu, who was 23 at the time, sued in federal court after being found guilty and being imprisoned in a Utah camp. The U.S. Supreme Court ultimately heard his case, and in 1944 it affirmed the government's argument that the detention was necessary due to "military necessity."

However, a federal court overturned Korematsu's sentence for escape internment in 1983, declaring that he had been the victim of a "grave injustice."

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The total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A total of 52 microphones are to be purchased. Each microphone costs $548.

Let x be the total purchase price

x = 52x548

x = $28496

Thus, the total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.

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Answer:

Step-by-step explanation:

x^2 - 14x = -48

x^2 +48 -14 x

x^2 - 14x - 48 = 0

a = 1

b = -14

c = 48

x=8, x=6

Answer:

20

Step-by-step explanation:

Answer:

x = r ,r is a whole number

y = 5(.5)^r

y=5(.5)

Step-by-step explanation:

The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].

Function:

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

For x=0 for  f(0)=(5)[tex](0.5^{0} )[/tex]=5

⇒ x=1 for  f(1)=(5)[tex](0.5^{1} )[/tex]=2.5

⇒ x=2 for  f(2)=(5)[tex](0.5^{2} )[/tex]=1.25

⇒ x=3 for  f(3)=(5)[tex](0.5^{3} )[/tex]= 0.625

Therefore,The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].

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1) The soccer team can make 48 pizzas using 12 one-pound packages of cheese.

2) The total cost Dan paid for the mulch was $87.50.

3) The number of acres that Mr. Hamilton will own after the planned purchase is 3¹³/₁₂.

The above values are determined using mathematical operations of addition, division, and multiplication.

For instance, Mr. Hamilton's land increased to 3¹³/₁₂ through the addition of 2¾ and 1¹/₃ acres.

The total cost that Dan paid for the mulch was a multiplication operation.

The number of pizzas the soccer team could make resulted from a division operation.

1) Quantity of cheese on each pizza = 1/4 lb

The total quantity of cheese = 12 lb

The number of pizzas to make = 48 (12/1/4) or (12/0.25)

2) The number of yards of mulch purchased = 3¹/₂ yards

Cost of mulch per yard = $25

The total cost for the mulch = $87.50 ($25 x 3¹/₂)

3) Measurement of land owned = 2¾ acres

The planned purchase of additional land = 1¹/₃

The total acres Mr. Hamilton will own = 3¹³/₁₂ (2¾ + 1¹/₃)

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Answer:

Step-by-step explanation:

8806

Answer:

1.296623028 grams

Step-by-step explanation:

your answer is 1.296623028 grams because you multiply the given number of moles which was 0.0564 by the molar mass to get the grams

Answer:

x equals plus or minus square root of 5 minus 2

Step-by-step explanation:

Let's solve your equation step-by-step.

x²+4x=1

Step 1: Subtract 1 from both sides.

x²+4x−1=1−1

x²+4x−1=0

For this equation: a=1, b=4, c=-1

1x²+4x+−1=0

Step 2: Use quadratic formula with a=1, b=4, c=-1.

[tex] \sf \: x = \frac{−b± \sqrt{ b {}^{2} −4ac}}{2a}[/tex]

[tex]\sf \: x = \frac{−(4)± \sqrt{4 {}^{2} −4(1)( - 1)}}{2(1)}[/tex]

[tex] \sf \: x = \frac{−4±√20}{2} [/tex]

x=−2+√5 or x=−2−√5

The total cost based on the equation illustrated as y= 10x is $230.

It should be noted that from the information, the equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost.

Therefore, it should be noted that the total cost when x is 23 will be illustrated thus:

y = 10x

y = 10 (23)

y = 230

Therefore, the total cost based on the equation illustrated as y= 10x is $230.

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The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost. Calculate the total cost when x is 23.

It should be noted that the multiplication of 2.102 × 12.62 is 25.39144.

It should be noted that multiplication simply means the product of a number. It should be noted that this contains the number a specified number of times.

Therefore, it should be noted that the value of 2.012 multiplied by 12.62 will be illustrated thus:

= 2.102 × 12.62

= 25.39144

In conclusion, it should be noted that the multiplication of 2.102 × 12.62 is 25.39144.

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Answer:

-9

Step-by-step explanation:

[tex]z^{-1}(-2)=k \implies z(k)=-2 \\ \\ k=-9 \implies z^{-1}(-2)=-9[/tex]

a) There is 2.54 quarts in the resulting mixture (b) The percentage of the resulting mixture is  50.8% antifreeze.

Percentage is defined as parts per hundred. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.

a) 18% of 3 quarts antifreeze contains (18/100) × 3 quarts of antifreeze.

amount of antifreeze = 0 .18 × 3 = 0.54 quarts

Now to this solution 2 quarts of antifreeze is added.

Therefore total amount of antifreeze in the resulting mixture = 2 + 0.54 = 2.54 quarts.

b) Total amount of the resulting mixture = 2 + 3 = 5 quarts

amount of antifreeze in the mixture = 2.54 quarts

Percentage antifreeze in the mixture = (2.54 / 5) × 100 % = 50.8 % .

Therefore there is 2.54 quarts of antifreeze in the mixture and its percentage is  50.8% of the total mixture.

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Step-by-step explanation:

1. 10.58

2. 15.87

3. 20.37

4 25.88

5. 8.89

6. 2.24

7. 9.95

8. 4.80

The geometric probability which represents the chances of having the waste material hit the car as described in the task content is; 3/20,000.

It follows from the task content that the probability which is to be evaluated is the chance of having the waste material hit the car.

First, since the dimension of the parking lot is; 500 by 800 feet. It follows that;

Area of parking lot = 500 × 800 = 400,000.

Also, since the dimension of the rectangular car is approximately 6 by 10. It follows that;

Area occupied by car = 6 ×10 = 60.

Consequently, the chances of the waste material hitting the car is the ratio of desired outcome to the possible outcome and hence is;

P = 60/400,000

P = 3/20,000.

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Answer: 8 – (2 + 1) × (5 – 3) = 2

Step-by-step explanation:

8 – 2 + 1 × 5 – 3 = 2

8 – 2 + 1 × 5 – 3 = 2      ==> notice there is an '8-' in the equation, Let's solve for the difference between 8 and 2.

8 – (2 + 1 × 5 – 3)+(2 + 1 × 5 – 3) = 2 + (2 + 1 × 5 – 3)

8=2 + (2 + 1 × 5 – 3)

8-2=2-2+(2 + 1 × 5 – 3)

6=2 + 1 × 5 – 3   ==> 6 is a multiple of 2 and 3. Let's see how we can convert 2 + 1 × 5 – 3 into the product of 2 and 3

6=(2 + 1) × (5 – 3)

6=3 × 2

6=6√  ==> since this is right, let's substitute the parentheses to the original equation

8 – 2 + 1 × 5 – 3 = 2    ==> 8 – (2 + 1) × (5 – 3) = 2

The absolute and relative errors are 0. 8 and 0. 01 respectively.

Absolute error can be defined as the difference between the inferred or measured value and the actual value of a given quantity.

The formula for absolute error is expressed as;

Absolute error = | VA - VE |

Where;

Substitute the values into the formula

Absolute error = | 60. 8 - 60. 0|

Find the difference

Absolute error = | 0. 8|

Absolute error = 0. 8

Relative error = Absolute error/ actual value

Relative error = 0. 8/ 60. 0

Relative error = 0. 01

Thus, the absolute and relative errors are 0. 8 and 0. 01 respectively.

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Answer:

c) S : {30}

Step-by-step explanation:

a) S : {17}

→ 17 - 3 > 15

→ 14 < 15

So, it is not suitable.

b) S : {18}

→ 18 - 3 > 15

→ 15 = 15

So, it is not suitable.

c) S : {30}

→ 30 - 3 > 15

→ 27 > 15

So, it is correct answer.

d) S : {15}

→ 15 - 3 > 15

→ 12 < 15

So, it is not suitable.