the ftoli (fundamental theorem of line integrals) says: (select all correct answers) group of answer choices none of these the work done by a gradient vector field is always zero. the work done by any vector field is independent of path. the line integral of a gradient vector field depends only on the initial and terminal points of the path. the work done by a gradient vector field is independent of path.

The required probability that the student will get 8 or fewer answers is 0.2475.

Binomial  distribution is a typical probability dissemination that models the likelihood of getting one of two results under a given number of boundaries. It sums up the quantity of preliminaries whenever every preliminary has a similar possibility accomplishing one explicit result.

By using binomial distribution for calculating the probability of getting 8 or less than 8 correct answer in the quiz.

Formula ; ⁿCₓ × pˣ × qⁿ⁻ˣ

We have, n = 20 p = 0.5, q = 1 - p = 1 - 0.5 = 0.5

Then,

P(x=0)=20C0*0.5^0*0.5^20=1/1048576

P(x=1)=20C1*0.5^1*0.5^19=5/262144

P(x=2)=20C2*0.5^2*0.5^18=95/524288

P(x=3)=20C3*0.5^3*0.5^17=285/262144

P(x=4)=20C4*0.5^4*0.5^16=4.621*10^-3

P(x=5)=20C5*0.5^5*0.5^15=969/65536

P(x=6)=20C6*0.5^6*0.5^14=0.03696

P(x=7)=20C7*0.5^7*0.5^13=4845/65536

P(x=8)=20C8*0.5^8*0.5^12=0.1201

Then, p(x≤8) = P(x=0)+.......+P(x=8) = 0.2475

Thus, required probability of answers ia 0.2475.

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If the slope is negative, the function is downward-sloping because y falls off as x rises. If the slope is zero, y remains constant—a horizontal line—and does not vary.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

Hence, If the slope is negative, the function is downward-sloping because y falls off as x rises. If the slope is zero, y remains constant—a horizontal line—and does not vary.

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The area of the triangle from the vertices is 27 square units

From the question, we have the following parameters that can be used in our computation:

$A\left(2,\ -2\right)$ , $B\left(4,\ -2\right)$ , and $C\left(6,\ -11\right)$ .

Represent the vertices properly

So, we have

A = (2, -2)

B = (4, -2)

C = (6, -11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |2 * (-2 + 11) + 4 * (-2 + 11) + 6 * (-2 + 2)|

Evaluate the sum of products

Area = 0.5 * |54|

Remove the absolute bracket

Area = 0.5 * 54

Evaluate

Area = 27

Hence, the area of ABC with vertices is 27 square units

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In linear equation, 1/5 min far will he travel in 1 hour .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6/8 = 3/4

1/5 min/hr *  1 hr = 1/5 min

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The standard height of the television is 12 inches.

What are ratios?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other.

The given ratio is 4:3. Let us take a variable 'x' such that 4x=16 and 3x=height.

We find x from 4x=16

x=4

Now putting the value of x in 3x, we get 12 inches.

Therefore, the height of the television is 12 inches.

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The standard height of the television is 12 inches.

The aspect ratio of a screen is the ratio of the width to the height. In the case of a television screen with a 4:3 aspect ratio, the width is 4 units and the height is 3 units.

If we let "h" represent the height of the television screen, we can set up the following equation:

4:3 = 16:h

To solve for "h", we can cross-multiply to get:

4h = 48

Dividing both sides by 4, we get:

h = 12

So the height of a television screen that is 16 inches wide and has a 4:3 aspect ratio is 12 inches.

what is aspect ratio?

The aspect ratio of a screen is the ratio of the width to the height of the viewable area of the screen. It is usually expressed as two numbers separated by a colon, such as 16:9 or 4:3.

Aspect ratios are used in a variety of applications, including television screens, computer monitors, and movie theaters. Different aspect ratios are used for different types of content, and some screens can be adjusted to display content in different aspect ratios.

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In linear equation, X = 200 millileters of each solution must joy use .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

              Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

X is the amount of the 20% saline solution

Y is the amount of the 40% saline solution

X + Y = 200

0.2X + 0.4Y = 0.20 * 200 = 40

Solving the first equation for Y and multiplying

the second equation by 10 to clear away the decimals

Y  = 200 - X

2x + 4y = 400

2x + 4(200 - x) = 400

2x + 800 - 4x = 400

0 = 400 - 2x - 800 + 4x

0 = 2x - 400

400 = 2x

x = 200

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Answer:

22

Step-by-step explanation:

we can set this up and make the unknown number X

32-x=10

Subtract 32 from both sides

32-x=10

-32.  -32

-x= -22

Divide both sides by -1

-x=-22

/-1.  /-1

x=22

Hopes this helps

Answer: The Commutative Law of Addition states that the order in which numbers are added does not affect the result. This means that for any two numbers a and b, we have a + b = b + a.

We can use the Commutative Law of Addition to rewrite the equation 177 + 563 = 740 as follows:

177 + 563 = 740

563 + 177 = 740

Both of these equations are equivalent to the original equation, because they represent the same mathematical statement.

Note that in the first equation, we simply reordered the terms of the original equation. In the second equation, we added the numbers in a different order, but the result is still the same.

The other equations you provided are not equivalent to the original equation and do not use the Commutative Law of Addition.

Answer:

R200

Step-by-step explanation:

R200

Answer:

Hope this helps good luck! :)

Step-by-step explanation:

[tex]2340=2l+2w\\l= w+410\\2340=2(w+410) +2w\\\\2340= 2w+820+2w\\1520=4w\\\\w=380\\\\l=380+410\\l= 790[/tex]

The measure of Angle JKL mJ = 159.4°, mK = 3.8°, and mL = 16.8°.

A ray is rotated about its endpoint, or vertex, to create an angle. The rotational difference between a ray's starting and ending positions is what is measured by an angle's degree.

If x = mJ, y = mK, and z = mL, then

Angle L exceeds Angle K by thirteen, hence z = y + 13 is the result (1)

Since angle J exceeds angle K by a factor of 7, x = 7(6y) = 42y (2)

X + Y + Z = 180 because the triangle's angles add up to 180°.

In place of (1) and (2) (3).

42y + y + (y + 13) = 180

44y + 13 = 180

44y = 167

y = 3.8°

x = 42y = 159.4°

z = y + 13 = 16.8°

The answer is that mJ = 159.4°, mK = 3.8°, and mL = 16.8°.

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Solution of x is  1± 5√2  for the given quadratic equation.

What is quadratic equation?

Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.

Main body;

11)

x² = 2x +48

The given is an quadratic equation:

solution of this can be found out using quadratic formula:

x =(-b ±[tex]\sqrt{b^{2} -4ac}[/tex])/2a

for this ,

x² -2x -48 = 0

a = 1

b= -2

c = -48

x =( 2±√ (4- 4*1*-48))/2

x = (2±√200)/2

x = 1± 5√2

Hence solution of x is  1± 5√2.

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Answer:

48 buckets of gravel

15 buckets of gravel

Step-by-step explanation:

Answer:

x^3-2x^2+6x+1

Step-by-step explanation:

x^3+2x-1-2x^2-4x+2

collect like terms

x^3-2x^2+2x+4x-1+2

x^3-2x^2+6x+1

The bare minimum required is $4500 to reserve 5 blocks totaling at least 34 rooms.

In mathematics, a relationship between two expressions or values that are not equal to each other is called "inequality".

Here,

The number of rooms Joe company needs is 50. Let the number of rooms needed be n, this can be represented by the inequality:

n ≥ 50

Joe has already reserved 16 rooms, therefore the number of additional rooms needed to be reserved = 50 - 16 = 34 rooms. At least 34 rooms have to be reserved, if B is the number of additional blocks that Joe reserves, the inequality is:

B ≥ 34

Each block contains 8 rooms therefore the minimum number of block (a) needed to be reserved = 34/8 = 4.25 = 5 to the next whole number. Therefore the minimum number of blocks needed is given as:

a ≥ 5

Since each block cost $900, let c represent the minimum amount of money needed, therefore the least amount of money needed is given as:

c = $900(5) = $4500

c ≥ $4500

The least amount of money needed is $4500 for booking 5 blocks that will reserve at least 34 rooms.

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Answer:

yes

Step-by-step explanation:

The answer to your question is yes. We have calculated all the numbers that 831 is evenly divisible by. The numbers that 831 is divisible by are 1, 3, 277, and 831.

Answer:

Statement 2 is a lie

Step-by-step explanation:

Statement 1 = TRUE

[tex]13^{2} * 13^{x} = 13^{6} \\13^{2+x} =13^{6}\\2 + x = 6\\x = 6 - 2\\x = 4[/tex]

x = 4 is True

Statement 3 = TRUE

[tex]5^{y} * 5^{6} =5^{12} \\5^{y+6} = 5^{12} \\y+6 = 12\\y=12 -6\\y =6[/tex]

y = 6 is True

Statement 2 =  LIE

[tex]m^{y} *m^{z} = m^{x} \\m^{6} *m^{z} = m^{4}\\m^{6+z} = m^{4}\\6 + z = 4\\z= 4-6\\z= -2[/tex]

z = -2 is Lie

Answer:

C) is 20

Step-by-step explanation:

3 inches x 5= 15

so we do the same with 4 minutes

4 minutes x 5= 20

15. commulative

16. distributive, distributing the 3 to the 'a' and 'b' within the parentheses.

17. distributive, distributing the w to the variables inside of the parentheses.

The required diameter of the dilated graphic is 8 inches.

Scale factor is the  ratio  of comparing sides on two comparative figures. In math, scale factor is utilized to decide how often bigger or more modest one item or figure is to another.

We have,

diameter of circular banner = 4 feet

scale factor = 1/6

Then, the diameter of circular sticker = 4(1/6) = 4/6 feet.

In inches, we know

1 foot = 12 inches

4/6 feet = 12(4/6) = 8 inches

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The interest rate would be 13%.

What is the simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.

To find the interest rate, we can use the formula for simple interest:

I = Prt

where I is the amount of interest earned, P is the principal (the initial amount of money deposited), r is the interest rate, and t is the time in years.

In this case, we know that I = $3,900, P = $10,000, and t = 3 years. We can use this information to solve for r:

I = Prt

$3,900 = $10,000r3

r = $3,900/($10,000*3)

r = 0.13 or 13%

Hence, the interest rate is 13%.

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Answer:

Step-by-step explanation: By using the verticle line test, because the line has passed more than one point, it is NOT A FUNCTION.

The line that goes through the point (2,-2) and is perpendicular to the line shown by y=2/5x +2 will have the slope intercept equation 5x+3y=6.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

Here,

Slope of the line given=2/5

Slope of the line perpendicular=-5/2

coordinates=(2,-2)

y=mx+b

-2=-5/2*2+b

b=3

y=-5/2x+3

3y=-5x+6

5x+3y=6

The equation in slope intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2 will be 5x+3y=6.

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For the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that the expression is,10of 0.9, and its simplification is obtained as 90.

We have to find out why Juliet is incorrect.

Juliet is incorrect because when any decimal value is multiplied by 10 the obtained value is increased by its one's place,

=10 × 0.9

=9

Thus, for the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.

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In particular, despite the language overlap, a glide reflection is not a reflection and a (ordinary) reflection is not a glide reflection.

There are many intriguing accounts of what occurs when you mix two of them together. Here are a few instances:

Each isometry may be classified as belonging to one of the five classes listed below.

The identity is the combination of two reflections along the same line.

Translation is the combination of two reflections in dissimilar but related directions. Rotation is the result of two reflections in non-parallel lines.

A gliding reflection is made up of a reflection over a line plus a translation along a non-perpendicular line (and not a reflection).

A reflection is made up of a translation along a perpendicular line and a reflection across a line (and not a glide reflection).

There are fascinating things to say about what occurs when you combine two isometries dependent on the types of the isometries that you combine, but it does not change the fact that the five types are all distinct from one another. I could go on, but I think you get the point now.

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While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no relationship between variables.

What is alternative hypothesis?

The alternative to your research topic is represented by the alternative hypothesis (Ha). It asserts that there is a population-wide impact.  

                                     Frequently, your study hypothesis and alternate hypothesis are the same. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

What is meant by a null hypothesis?

A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.

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By probability ,181753 are  ways are there to distribute the coupons so that at least one woman receives a coupon.

What does the math term "probability" mean?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                                        Statistics describes the examination of events subject to probability.

Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:

= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men

         = ( 20 10 ) - ( 15 10 ) = 184756 - 3003

          = 181753

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The complete question is -

10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.

(a) If the coupons are identical, how many ways are there to distribute the coupons so that at least one woman receives a coupon?

By probability ,181753 are  ways are there to distribute the coupons so that at least one woman receives a coupon.

What does the math term "probability" mean?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

Statistics describes the examination of events subject to probability.

Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:

= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men

        = ( 20 10 ) - ( 15 10 ) = 184756 - 3003

         = 181753

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Waterworks must produce more than 4 and fewer than 11 paddleboards.

What do you mean by polynomial?

A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and trinomial.

It is given that Waterworks is a company that manufactures and sells paddleboards. Its profit​ P, in hundreds of dollars​ earned, is a function of the number of paddleboards sold​ x, measured in thousands. Profit is modeled by the function ​

[tex]p(x) = -3x^{3}+45x^{2} -132x[/tex]

zeroes of the p(x) will show the quantity at which profit = 0 i.e. breakeven

Let p(x) = 0

[tex]-3x^{3} +45x^{2} -132x =0[/tex]

-3x ([tex]x^{2} -15x+44[/tex]) = 0

-3x ([tex]x^{2} -11x-4x+44[/tex] ) = 0

-3x (x(x-11) - 4(x-11)) = 0

-3x (x-11) (x-4) = 0

-3x = 0 or x-11 = 0 or x-4=0

x = 0,11,4

So,profit is obtained when 4<x<11.

Therefore,  Waterworks must produce more than 4 and fewer than 11 paddleboards.

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{5}}} \implies \cfrac{ -6 }{ -2 } \implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5})[/tex]

[tex]y-7=3x-15\implies y=3x-8\implies -3x+y=-8\implies {\Large \begin{array}{llll} 3x-y=8 \end{array}}[/tex]