a 6 ft man lifts a 100-lb weight from the floor to a height 1 ft above his head. how much work is done in lifting the weight?

Refer to the attached images.

Answer: 0.864

Step-by-step explanation:

0.6 x 0.8 x 1.8 = 0.864

The saving plan is an illustration of linear equations.

In his calculations, Jerome was faultless.

The equation is represented as;

Where:

x represents the number of months

The following procedures are used to identify Jerome's mistake (s)

Given

Addition property: Add -500 to both sides

Simplify

Division property: Divide both sides by 375

Simplify

Substitution: Substitute 3500 for y

Simplify

The steps above show that: He did not make any mistake

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Quadratic equation ax² + bx + c = 0 can be solved by factoring the equation using two methods :

a. Splitting the middle term of the equation.

b. Quadratic formula x = ( -b ±√b² -4ac )/2a.

As given in the question,

Standard quadratic equation is given by :

ax² + bx + c = 0

This can be factoring by using two methods:

a. Splitting the middle term of the equation.

b. Quadratic formula x = ( -b ±√b² -4ac )/2a.

Example : x² + 8x  - 9 =0

a. splitting middle term:

x² + 8x  - 9 =0

⇒ x² + 9x - x  - 9 =0

⇒ x( x + 9 ) - 1 ( x + 9 ) = 0

⇒ ( x - 1 ) ( x + 9 ) = 0

b. Quadratic formula:

here a = 1 , b = 8 , c = -9

x = ( -8 ± √8² - 4 (1 )(-9 ) )/ 2(1)

⇒ x = (-8 ± 10 ) / 2

⇒ x = 1 or x = -9

Therefore, the quadratic equation can be factoring by two methods :

a. Splitting the middle term of the equation.

b. Quadratic formula x = ( -b ±√b² -4ac )/2a.

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The correct value of "x" is equal to 4

Step-by-step solution:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Using Pythagoras's Theorem:-

[tex](Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}[/tex]

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

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

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

[tex](2x+1)(1) =3^{2}[/tex]

[tex](2x+1)(1) =9[/tex]

[tex](2x+1) =9\\2x=9-1\\2x=8\\x=4\\[/tex]

Therefore, the value of "x" is: x=4

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The line that intersects a circle at exactly one point and creates a right angle to the radius is called the Tangent .

What is Tangent ?

The tangent can be defined as a line that touches the circle at exactly one point .

The properties of tangent Lines are :

(i) The point where tangent line meets circle is called as the point of tangency.

(ii) The tangent line is perpendicular to the radius of circle, with which it intersects, that means , a right angle is created at the meeting point .

(iii) There is exactly one tangent  that can touch the circle at any given point .

Therefore , by the property of tangent to circle , we can say that , Tangent intersects a circle at exactly one point creates right angle to radius .

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Using linear regression to calculate the line of best fit is ŷ = 25.91429X + 553.13333

A line of best fit is a straight line that is used to describe the relationship between two variables in a scatter plot. The line of best fit is also known as the "trend line" or "regression line" and is used to make predictions about the values of one variable based on the values of the other variable.

Linear regression is a statistical method used to find the line of best fit for a set of data. Linear regression analysis is used to determine the linear relationship between two variables.

In the given data;

Sum of X = 21

Sum of Y = 3863

Mean X = 3.5

Mean Y = 643.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = 453.5

Regression Equation = ŷ = bX + a

b = SP/SSX = 453.5/17.5 = 25.91429

a = MY - bMX = 643.83 - (25.91*3.5) = 553.13333

ŷ = 25.91429X + 553.13333

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The value of x is 13.74 units.

Consider the following figure.

In this question we have been given a right triangle with the length of hypotenuse = 47 units.

From figure we can observe that the dotted line segments are parallel to the legs of right triangle.

So, the vertical side of right triangle = x units

And the angle opposite to side 'x' would be 17°  as they are the alternate angles formed by parallel lines and transversal.

Consider the cosider the sine of angle 17°

sin(17°) = x/47

0.2924 × 47 = x

x =  13.74 units

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By calculating the value of given expression is -137/ 12 .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

Given ,

expression t + 14 = 2 7/12

t+14 = (2*12 + 7 ) / 12

So by sending 12 in LHS we get,

t+14 = 24+7  / 12

t+14 = 31/ 12

12 ( t+14) = 31

multiplying 12 on LHS

12 t  + 12*14 = 31

12t = 31-168

12 t = -137

t = -137 / 12

Hence, the value of given expression is -137/ 12 .

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$1897  she has in the account after 10 years.

Use the formula for calculating compound interest

Compound interest can be regarded as the addition of interest on the loan to the principal sum of the deposit.

where A(t) is the account balance, P0 is the principal, r is the yearly interest rate (in decimal form), n is the frequency of compounding interest, and t is the time (in years).

P=$1,100, r=0.037, n=1, and t=15 are all given to us.

Using a calculator to calculate the result after entering the variables into the formula, we discover

A(t)=P(1+rn)n⋅t=$1,100(1+0.0371)(15)(1)≈$1,897.03

So the final answer is $1,897

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The required factors of the given expression x³ - 6x² - x + 30 is  (x - 5)(x + 2)(x -3).  Option D is correct.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,

Gien expression,
=  x³ - 6x² - x + 30
= (x - 5)(x + 2)(x -3)

Thus, the required factors of the given expression x³ - 6x² - x + 30 is  (x - 5)(x + 2)(x -3).

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Note that where there's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 meters, then the statement that is TRUE is: "The correlation is most likely due to a lurking variable." (Option B).

A correlation does not imply causation, and a moderate positive correlation is not enough to establish a causal relationship between two variables.

It is possible that the correlation is due to an underlying factor (lurking variable) that affects both the length of the child's hair and the time it takes for the child to run 100 meters. To establish causality, other methods such as experimental design and statistical analysis are necessary.

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Answer:

Simple interest is calculated by multiplying the principal amount (the initial deposit) by the interest rate and the number of years.

The formula for simple interest is:

I = P * r * t

Where:

I = Interest

P = Principal (initial deposit)

r = Interest rate (expressed as a decimal)

t = Time (in years)

In this case, the principal amount is $500.00, the interest rate is 4.5%, and the time is one year.

The interest rate is expressed as a percentage, so we need to convert it to a decimal by dividing it by 100:

r = 4.5/100 = 0.045

Now we can plug in the values into the formula:

I = $500.00 * 0.045 * 1 = $22.50

So, Arisia earns $22.50 in interest per year.

The volume of a rectangular prism is lwh unit cube.

A rectangular prism can be defined as a 3-dimensional solid shape that has 6 faces, with its base as rectangles.

The volume of a rectangular prism is given by, the product of its dimensions.

Let us consider length, width and height of the rectangular prism be l, w, h respectively,

Then, the volume will be = length x width x height

= l x w x h

= lwh

And its unit will be unit cube because there are 3 dimensions in the prism which are being multiplied.

Hence, the volume of a rectangular prism is lwh unit cube.

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Answer:516 exams

Step-by-step explanation:

600 this year

84 more

subtract

equals 516

516 exams this year

Answer:

192.5 miles

Step-by-step explanation:

let h be number of hours Anne takes to drive to her friend's house

[tex](55mph)(h) = (35mph)(h+2)[/tex]

Both sides of this equation represent the miles to her friend's home. (speed * time = distance)

We add 2 to h on the right side because the way back takes 2 hours longer than the way to her friend's home.

Now we can solve.

[tex](55)(h) = (35)(h+2)\\55h = 35h+70\\20h = 70\\h = \frac{7}{2} = 3.5[/tex]

Now that we have how long the trip to her friend's house takes, we can solve for the distance to her friend's house by using either side of our equation. I will use the left side because it is simpler.

[tex](55)(h)\\(55)(3.5)\\\boxed{192.5}[/tex]

That is the answer

- Kan Academy Advance

y = -5x - 23, is the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3).

What is the slope intercept?

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3), we can use the point-slope form of a line which is y - y1 = m(x - x1), where m is the slope of the line, (x1,y1) is a point on the line.

We know the slope of the line is -5 and the point is (-4,3), so we can substitute these values into the point-slope form to get:

y - 3 = -5(x + 4)

Simplifying this equation gives:

y = -5x - 23

Hence, y = -5x - 23, is the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3).

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The rational expression is

[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]

for x ∈ R - {1}

The ratio of two polynomials is a rational expression. If an expression is rational, it may be expressed in the form p/q, where p and q are polynomials.

When the numerator and denominator of an equation are both polynomials, the expression is said to be rational. The lowest form of the numerator and denominator is used to simplify rational formulas. An algebraic fraction is another name for a rational expression.

The value of a logical statement is diminished to its simplest form or lowest terms when it is simplified. Similar to how we simplify fractions, we can simplify a rational equation. In fractions, a rational number is said to be in its simplified form if its numerator and denominator share no factors other than 1. The only distinction is that when simplifying rational expressions, the same strategy also applies because the fraction contains polynomials.

The expression is

[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]

for x ∈ R - {1}

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There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.

A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.

Classification of triangles :-

There are two ways to classify triangles,

1) Based on the Angle :-

a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.

b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.

c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.

2) Based on the Sides :-

a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.

b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.

c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.

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Answer:

Step-by-step explanation:

the answer is 1163 :)

The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.

To determine the domain of a function, look at the equation defining the function and identify any restrictions on the input values. For example, if the function is a square root, the input (x) value can not be negative.

To determine the range of a function, you can use the equation of the function and test several input values to find the corresponding output values. You can also use the graph of the function to identify the range. If the function is continuous, you can use the graph to see the range of the function.

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The result of dividing 2x^3 + x^2 - 2x + 8 by x + 2 is:

Quotient: 2x^2 - 3x + 4

Remainder: 0

The given polynomial is 2x^3 + x^2 - 2x + 8.

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.

(x)(2x^2) = 2x^3

Thus, we multiply the divisor (x + 2) by 2x^2 which gives 2x^3 + 4x^2.

Now we subtract this from the polynomial which gives -3x^2 - 2x +8.

Next we multiply the divisor by -3x which gives -3x^2 - 6x. Again we subtract the same from the remaining polynomial -3x^2 - 2x +8 and get 4x + 8.

Repeating the same we multiply the divisor by 4 which gives 4x + 8. Subtracting the same from the remaining polynomial 4x + 8 we get the remainder 0.

Thus, the quotient is 2x^2 - 3x + 4.

The question is incomplete, the complete question is:

What is the result of dividing 2x^3 + x^2 - 2x + 8 by x+2?

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The length of arc COD is approximately 12.56 units.

To find the radius of the circle, we can use the area of sector COD and the angle COD.

We know that the area of a sector is (angle/360) * pi * r^2, and we know that the area of sector COD is 50.24 square units. We also know that the angle COD is 90 degrees.

So we can set up the following equation:

50.24 = (90/360) * 3.14 * r^2

Solving for r, we get:

r = sqrt(50.24 / (90/360) * 3.14) = sqrt(50.24 / (0.25 * 3.14)) = sqrt(50.24 / 0.785) = sqrt(64.28) = 8 (approximately)

So the radius of the circle is approximately 8 units.

To find the length of the arc, we can use the formula of arc length which is Arc Length = (Angle/360) * 2πr

So the length of the arc COD is (90/360) * 23.148 = 4*3.14 = 12.56 (approximately).

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The L angle is used for measuring the area of the rectangle.

A right angle is one that is 90 degrees in length. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, the L angle is used for measuring the area of the rectangle.

Complete question: What measurement is L angle used for?

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The equation for the horizontal asymptote of the function f is y=Lim x→∞ f(x).

In algebra and calculus, a horizontal asymptote is a horizontal line that the graph of a function approaches as the x-values or input values increase or decrease without bound.

The equation for the horizontal asymptote of a function f is:

Lim f(x) → ∞ = c

Where c is the horizontal asymptote.

Example:

f(x) = x2 + 3x + 2

Horizontal Asymptote:

Lim f(x) → ∞ = ∞

numeric value in equation

For example, if x = 5:

f(5) = 5^2 + 3*5 + 2 = 32

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