use deductive reasoning to show that the following procedure always produces the number 8. procedure: pick a number. add 5 to the number and multiply the sum by 3. subtract 7 and then decrease this difference by the triple of the original number.

The line integral can be evaluated using Green's Theorem.

Green's Theorem states that for a simply connected region D with continuous partial derivatives, the line integral of the curl of a vector field around a closed path C is equal to the double integral of the curl over the region enclosed by C.

In this case, the curl of the vector field (4xy, 2x^2 - 3xy) is (3, -4), so the line integral is equal to the double integral of (3, -4) over the region enclosed by the circle x^2 + y^2 = 1.

The double integral can be calculated using polar coordinates, and the result is (-π/2, π/2) = π.

Therefore, the line integral ∫ 4xy dx + 2x^2 - 3xy dy, where C is the arc of the circle x^2 + y^2 = 1, from (1, 0) to (0, 1) in the counterclockwise direction, is equal to π.

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The amount of money each student will pay, excluding taxes and tip,  $23.534

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

The receipt is for lunch for five students. Each student will pay 1/5 of the bill

The amount of money each student will pay = ?

⇒  1/5x117.67

⇒   23.534

Therefore, the amount each student will pay, $23.534

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Answer:

Engineer: 9.5 hr

Assistant: 4.5 hr

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Given the engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour, and a customer received a bill for $425 for a certain job:

Given the assistant worked 5 hours less than the engineer:

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases}40x+10y=425\\ \quad \qquad \;\;\;y=x-5\end{cases}[/tex]

Substitute the second equation into the first equation to eliminate y:

[tex]40x+10(x-5)=425[/tex]

Solve the equation for x to find the number of hours the engineer worked:

[tex]\begin{aligned}40x+10(x-5)&=425\\40x+10x-50&=425\\50x-50&=425\\50x&=475\\x&=9.5\end{aligned}[/tex]

Therefore, the engineer worked 9.5 hours.

Substitute the found value of x into the second equation and solve for y to find the number of hours the assistant worked:

[tex]\begin{aligned}y&=x-5\\y&=9.5-5\\y&=4.5\end{aligned}[/tex]

Therefore, the assistant worked 4.5 hours.

The value of [tex]$$45 \sqrt{7930.45}$$[/tex] be 4007.38833.

When multiplied by itself, a square root value equals the original value. There are four ways to calculate the square root: prime factorization, repeated subtraction, long division, and the estimation approach.

Using the square root function, you can convert rational numbers into algebraic numbers (which are a subset of rational numbers). The Euclidean norm (and distance) and generalizations like Hilbert spaces both depend on the square root of a nonnegative number.

Squares are the results of multiplying an integer by itself. Alternatively, the square root of an integer is a value that, when multiplied by itself, returns the original value.

Let the equation be [tex]$$45 \sqrt{7930.45}$$[/tex]

[tex]$$\begin{aligned}& \sqrt{7930.45}=89.05307 \ldots \\& =45 \cdot 89.05307 \ldots\end{aligned}$$[/tex]

= 4007.38833

Therefore, the value of [tex]$$45 \sqrt{7930.45}$$[/tex] be 4007.38833.

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The value of  be 4007.38833.

Let the equation be

= 4007.38833

Therefore, the value of  be  4007.38833.

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Answer: 34 on both?

Step-by-step explanation:

The rental cost for each movie and each video game is $ 1 and $8 respectively.

We have 2 variables (cost of movie and cost of video game) and we need 2 equations to find them. Let's say the cost of movies is M and the cost of video games is V. In the first month, Lashonda rented 5 movies (5M) and 3 video games (3V) for $29.

5M + 3V = 29 (equation 1)

The next month, he rented 7 movies and 9 games for $73.

7M + 9V = 73 (equation 2)

Let's isolate one of the variables. I choose to isolate M in equation 2:

M = (73-9V)/7

Now, substitute our new equation 2 into equation 1.

5*(73 - 9V) + 3V = 29

365 - 45V + 3V = 29

365-29 = 45V - 3V

336 = 42V

V = $8

Now, substitute the value of V into one of our earlier equations to find M.

M = $1

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The reasoning represent by the both of the students for congruent of vertical angle are correct but the reasoning of student 1 is more suitable and cleared than student 2.

The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees.

In this, ∠1 and ∠2 are adjacent angle so the sum of the measure of these two angles are 180°

∠1 + ∠2 = 180 ⇒ ∠1 = 180 -∠2

like this ∠2 and ∠3 are adjacent angle so the sum of the measure of these two angles are 180°

∠2 + ∠3 = 180 ⇒ ∠3 = 180 -∠2

from the above equation;

∠1 = ∠3

or, we can say that the vertically opposite angles are equal in measure.

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Answer:

84%

Step-by-step explanation:

21/25*100%

21*4

84%

Answer:

52

Step-by-step explanation:

2*(4*3+2*3+4*2) = 52

Step-by-step explanation:

The volume of the right rectangular prism can be determined by finding the product of its length, width, and height in cubic units.

The sampling methods here that are not examples of simple random sampling are;

A) Select the first 10 people from a list of members.

B) Ask 10 members in the gym on a Monday morning

E) Select every 20th person from a list of members until she has 10 .

F) Ask all members of the gym

A subset of a certain population chosen at random is referred to as a simple random sample. You'll see that each person in the population has an exact equal probability of getting chosen using this sampling technique.

Simple random sampling is significant because it eliminates all prejudice because each member has an equal probability of being chosen. As a result, it will provide a good illustration of the topic of our investigation.

A) Choose the top 10 individuals from a list of members; this is not a straightforward random sampling because the selection is targeted rather than random.

B) This is not random because it is particular to one day of the week—a Monday morning—and we have no idea who might show up on other days.

C) Pick 10 people at random from a list using a random number generator; this is known as basic random sampling.

D) Without looking, choose the names of 10 members at random from a box; this method is random since each member has an equal chance of being chosen.

E) Choose 10 members at a time from a list of members; this is not a random process because not all members have an equal probability of getting chosen.

F) Consult with every gym patron; this is not a random pick.

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There are no real solutions for this system of equations.

[tex](1)2x - 8y = 11\\ \\(2)x - 4y = 6[/tex]

For this solutions, we're going to solve equation (2) for variable "x".

[tex]x - 4y = 6[/tex]

Add "4y" on both sides of the equation.

[tex]x - 4y+4y = 6+4y \\ \\x=6+4y[/tex]

Calculated value: [tex]x=6+4y[/tex]

Equation to substitute in: [tex](1)2x - 8y = 11[/tex]

Substitution:

[tex]2(x) - 8y = 11\\ \\2(6+4y) - 8y = 11[/tex]

Simplify.

[tex]2(6+4y) - 8y = 11\\ \\(2)(6)+(2)(4y)-8y=11\\ \\12+8y-8y=11\\ \\12=11[/tex]

We obtained a false statement (12=11) which means that there's either no solution, or an infinite amount of solutions.

To see what's the exact case, try to make the coefficients of the equations be the same by multiplying one of the equation by a constant.

In this case, we could multiply all elements of equation (2) by number "2" in order to make the variables have the same coefficients as equation 1:

[tex]2(x - 4y = 6)\\ \\2x-8y=12[/tex]

Comparing the result to the other equation:

[tex]2x - 8y = 11\\ \\2x - 8y = 12[/tex]

There are no real solutions for this equations system, since the variables have the same coefficients and the contant terms are different (11 and 12).

Important note. If after multiplying the equation by a constant we had obtained the exact same equation, then we would've concluded that there where infinite solutions for the equations system.

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Answer:

511 million km²

Step-by-Step Explanation:

Let the total surface area of the Earth be x.

Water covers 70.7% of the total surface area of the Earth, i.e.,

70.7% of x = 3.61 x 10⁸ km²

or, 70.7x /100 = 3.61 x 10⁸ km²

or, 707x/1000 = 3.61 x 10⁸ km²

or, 707x = 3.61 x 10⁸ x 1000km²

or, 707x = 3.61 × 10^11 km²

or, x = 0.0051 × 10^11 km²

or, x = 5.1 × 10⁸ km² = 511 million km²

Hope it helps.

If you have any query, feel free to ask .

Answer:

511 million km²

Step-by-step explanation:

Let x be the approximate total surface area of the Earth.

Given water covers 70.7%, or about 3.61 × 10⁸ km², set up an equivalent ratio of percent (in decimal form) to area:

[tex]\implies 0.707:3.61 \times 10^8=1:x[/tex]

Solve for x:

[tex]\implies\dfrac{0.707}{3.61 \times 10^8}=\dfrac{1}{x}[/tex]

[tex]\implies0.707x=3.61 \times 10^8[/tex]

[tex]\implies x=\dfrac{3.61 \times 10^8}{0.707}[/tex]

[tex]\implies x=\dfrac{3.61 }{0.707}\times 10^8[/tex]

[tex]\implies x=5.10608203...\times 10^8[/tex]

One million has 6 zeros and can be written in scientific notation as:

Therefore, to write x in millions as x × 10⁶, subtract 2 from the exponent and move the decimal point to the right by 2 places:

[tex]\implies x=510.608203...\times 10^6[/tex]

Therefore, the approximate surface area of the Earth is 510.608203... million km², which is 511 million km² to the nearest million.

Answer:

55 boxes

Step-by-step explanation:

The linear equation provided is: [tex]y=78x+8840[/tex] and since we want to check if we can carry 60 boxes, we just need to weight by substituting in "60" as x and then comparing that to the limit of 13200 pounds.

[tex]y = 78(60)+8840\\\\y=4680+8840\\\\y=13,520[/tex]

This of course is over the limit of 13200 pounds but we can set up an inequality and solve for "x"

[tex]78x+8840 < 13200[/tex]

From here we subtract 8840 from both sides

[tex]78x < 4,360[/tex]

Now divide both sides by 78

[tex]x < 55.89[/tex]

now of course we can't have 55.89 boxes, so we want to round down as we can't have 56 boxes as that would go over the limit, but we can have 55 boxes.

Triangle HGI and RPQ are similar triangle. Any options that do not match with the condition of similarity given below would be the required incorrect options.

Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.

Here,
Triangle HGI and RPQ
GH/RQ = GI /PQ = HI/RP
∠H = ∠R
∠G = ∠Q
∠I = ∠P

Triangle HGI and RPQ are similar triangle

Thus, Triangle HGI and RPQ are similar triangle. Any options that do not match with the condition of similarity given below would be the required incorrect options.

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P(z > -5.233): Not the usual approximation, but the exact binomial computation is used for the computation of the the probability of correctly tossed 63 or more.

For the stated question:

In 63 out of 100 trials inside a blind ESP test, the person accurately determines whether a coin will land on its head or tail.

Thus, P(z > -5.233) is the  normal approximation.

Not the usual approximation, but the exact binomial computation is used for the computation of the the probability of correctly tossed 63 or more.

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The Number line 1 :  -45 - 20 + 5

Number line 2 : -45 + 35 - 15

Number line 3 :-45 + 10 + 5

Number line 4:-45 + 30 - 20

A number line is a depiction of a graded straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. How a number is utilized depends on the issue it is associated with, such as when graphing a point

Number lines offer a method for mentally adding and subtracting. It's simple to see them as a type of support system for those in need, but this is untrue. They are crucial because they encourage effective mental arithmetic techniques, according to research.

The Number line 1 :

-45 to -60 so the jump is -15 = -45 - 20 + 5

Number line 2 :

-45 to -25 so the jump is +20 = -45 + 35 - 15

Number line 3 :

-45 to -30 so the jump is +15 = -45 + 10 + 5

Number line 4:

-45 to -35so the jump is +10 = -45 + 30 - 20

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The function table for the given domain should be completed as follows;

x           2         3       4         5        6

f(x)        10        5       2         1        2

In order to use the given quadratic function to complete the table, we would have to substitute each of the values of x (domain or x-values) into the quadratic function and then evaluate as follows;

When the value of domain x = 2, the quadratic function is given by;

f(x) = (x - 5)² + 1

f(2) = (2 - 5)² + 1

f(2) = (-3)² + 1 = 10

When the value of domain x = 2, the quadratic function is given by;

f(x) = (x - 5)² + 1

f(3) = (3 - 5)² + 1

f(3) = (-2)² + 1 = 5

When the value of domain x = 4, the quadratic function is given by;

f(x) = (x - 5)² + 1

f(4) = (4 - 5)² + 1

f(4) = (-1)² + 1 = 2

When the value of domain x = 5, the quadratic function is given by;

f(x) = (x - 5)² + 1

f(5) = (5 - 5)² + 1

f(5) = (0)² + 1 = 1

When the value of domain x = 6, the quadratic function is given by;

f(x) = (x - 5)² + 1

f(6) = (6 - 5)² + 1

f(6) = (1)² + 1 = 2

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Answer: C. 40%

Step-by-step explanation:

To convert a fraction to a percentage, we multiply it by 100. So 2/5 can be written as (2/5) * 100 = 40%.

2/5= .40

To convert into a percentage move the decimal point two places to the left.

2/5= 40% (C)

Answer:

2x=9-4y

Step-by-step explanation:

5x+9y=18+x+y

5x-x=18+y-9y

4x=18-8y

2x=9-4y

Answer: Option a:   y = 4 + 6x

Step-by-step explanation:

We can simplify the expression as follows:

(x2z)1/4/x-1/2z1/2 = (x2z)1/4 * (x1/2z-1/2)

Using the property of exponents: (a^b)^c = a^(bc)

x2z = x^(2 * 1) * z^(1 * 1) = x^2 * z

x1/2z-1/2 = x^(1/2 * 1) * z^(-1/2 * 1) = x^(1/2) * z^(-1/2)

Substituting back into the expression:

(x^2 * z)^(1/4) * (x^(1/2) * z^(-1/2))

= x^ (2 * 1/4) * z^(1 * 1/4) * x^(1/2) * z^(-1/2) = x^(1/2) * z^(1/4) * x^(1/2) * z^(-1/2)

Combining like terms:

x^(1/2) * z^(1/4) * x^(1/2) * z^(-1/2) = x^(1/2 + 1/2) * z^(1/4 - 1/2) = x^1 * z^(-1/4) = x * z^(-1/4)

So, the simplified expression is x * z^(-1/4) with positive exponents.

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The number of marbles of each color is 2/3.

Tessa puts 50 marbles in a bag. The number of marbles of each color is shown in the table below.

The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are connected, but probability determines what the odds are. Probability is required before calculating the likelihood of an occurrence.

P(blue)=10 / 3 = 50 /15, meaning there are 15 blue marbles.

P(yellow)= 2 / 1 = 50 / 25 meaning that there are 25 yellow marbles.

10 black marbles are present.

P(black)=50 /10 = 5 and P(white)= 0

15 / 20 = 2/3.

The number of marbles of each color is 2/3.

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Answer:

- 81, 243

Step-by-step explanation:

to obtain a term in a geometric sequence, multiply the previous term by the common ratio r

here r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-9}{3}[/tex] = - 3

then

27 × - 3 = - 81

- 81 × - 3 = 243

the next two terms are - 81 and 243

The value of x is 5 and the value of y is 6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are y=2x-4 and y=x+1. The two equations can be solved as below,

y=2x-4 and y=x+1, Equate both the equations and solve for the value of x,

2x-4 =x+1

2x - x = 4 + 1

x =5

y=x+1

y = 5 + 1 = 6

Hence, the value of x is 5 and the value of y is 6.

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i thinkAnswer:152

Step-by-step explanation:

Answer:

4?

Step-by-step explanation:

(143-35)/3^3

108/27

4

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

[tex]\mathsf{\dfrac{143 - 35}{3^3}}[/tex]

[tex]\mathsf{= \dfrac{108}{3^3}}[/tex]

[tex]\mathsf{= \dfrac{108}{3 \times 3 \times 3}}[/tex]

[tex]\mathsf{= \dfrac{108}{9 \times3}}[/tex]

[tex]\mathsf{= \dfrac{108}{27}}[/tex]

[tex]\mathsf{= 4}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{4}}\huge\checkmark[/tex]

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

The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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Answer:

Step-by-step explanation:

THIS SOLUTION IS x=15