Use the Negative Area approach to depict the centroid of the section in Figure 2 beloW.
Use the reference ofigin O shown.
8cm
2cm
8cm
X
2cm
2cm
3cm
3cm
3cm
k
*
*
Figure 2
b) i. State any two (2) ways in which a structure may be deemed to lack Structural
Integrity.
(9 marks)
ii. Structural system refers to the load-resisting sub-system of a structure which transfers
loads through interconnected structural components or members. With the aid of
annotated sketches describe any two (2) of the basie types of structural systems.

Answer:

0.075 is a hundred times smaller than 7.5

Step-by-step explanation:

1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

An expression is combination of variables, numbers and operators.

The given expression is 3/4a + 8 - 1/4a - 2

Three by four times of a plus eight minus one by four times of a minus 2.

In the given expression a is a variable and plus and minus signs are the operators.

3/4a + 8 - 1/4a - 2

3/4a and  - 1/4a are the like terms

Add the like terms

3/4a   - 1/4a +8 - 2

2/4 a +6

1/2a+6

Hence, 1/2a+6 is the simplified form of the expression  3/4a + 8 - 1/4a - 2

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Equations 4 and 5 are not equivalent to any of the other equations.

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 equations that are equivalent are:

2 + x = 5

Negative 5 + x = negative 2

x + 1 = 4

Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.

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Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

Y = (1/x-3) has been moved 3 units to the right and up one unit. If it is moved to the right, it should look like this: (x-3). It should show up as (x+3) if it were moved to the left. If the result were moved ahead, the outcome would be (1/x-3).

The original function f is horizontally shifted into the new function g(x)=f(xh), where h is a constant. Given a function f. The graph will shift to the right in a positive h situation. If h is negative, the graph will slide to the left.

To move a function left in function notation, add within the function's argument: f(x + b) moves f(x) b units left. In the same way, shifting to the right moves f(x) b units to the right.

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Using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

The entire amount or sum of the two whole numbers is obtained by adding them.

The process of addition involves combining two or more numbers to determine their sum.

Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.

For instance, 7 + 7 equals 14.

So, we can get the total time using addition as follows:

= 0.6 + 2.4 + 5.2 + 1.4 + 1.8

= 11.4 hours

Therefore, using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

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To give Tara a lower price, coupon 2 should be applied first.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Tara has two store coupons.

Coupon 1 gives her $10 off on one item.

Coupon 2 gives her 10% off on one item.

Tara can use both coupons together on one item in the store and choose which coupon to apply first.

For an item that has an original price of x dollars,

let f be the function that models the discount price of the item using only coupon 1,

and let g be the function that models the discount price of the item using only coupon 2.

The price of each item in this store is more than $20.

Let the price is $50.

So applying coupon 1 and then coupan2,

we get,

(50 - 10) - ($50 - $10) x 0.10 = $36

Now, apply coupon 2 and then coupon 1,

we get,

$50 x 0.10 - $10 = $35

Therefore, she should apply coupon 2 and then coupon 1.

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The system of equations which has infinitely many solutions as required to be determined is; Choice D; 2x + y = 5 and 4x + 2y = 10.

By the standards of linear geometry, two equations have infinitely many solutions when their graphs coincide and in which case, they have the same slope and y-intercept.

Therefore, the system of equations which satisfy the said criterion is; 2x + y = 5 and 4x + 2y = 10.

Ultimately, the correct answer is; Choice D; 2x + y = 5 and 4x + 2y = 10.

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The summary of the given data is Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56  . So option C is correct.

The middle  number of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the median,  mode, and mean. The measures of central tendency are this trio of measurements.

Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)

Median = {(n+1)/2}th term (for odd)

Based on the given information,

we can see that the box plot shows the values of 44, 48, 50.5, 53, and 56.

These values represent the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum, respectively.

Therefore, the five-number summary for this data is:

Min = 44,

Q1 = 48,

Median = 50.5,

Q3 = 53,

Max = 56

So the answer is: Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56

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The number of solutions to the trigonometric equation is; 1 solution which is x = 270°

The trigonometric equation is given as;

sin²x - 2sin x - 3 = 0

Now, factorizing this gives us;

(sin x - 3)(sin x + 1) = 0

Thus, we now have;

sin x - 3 = 0

sin x = 3

At this point, x has no real solution

For the second factor, we have;

sin x + 1 = 0

sin x = -1

x = sin⁻¹ -1

x = 270°

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Conclusions drawn from a sample of 50 monarch butterflies tagged from one location in California may not be entirely true for all monarch butterflies.

A sample is a subset of data drawn from a larger population by a researcher using a predetermined selection process. These components are referred to as sample points, sampling units, or observations.

The sample size is relatively small compared to the entire population of monarch butterflies. Additionally, the sample is only taken from one location, so the results may not be representative of the entire migration pattern.

The monarch butterfly is known to have a wide geographic range, migrating across North America, and covering a distance of thousands of miles during their annual migration. Thus, to make conclusions that apply to the entire population of monarch butterflies, a more comprehensive and representative sample size from various locations along their migration route would be needed.

In scientific research, it is essential to have a large and representative sample size to minimize the margin of error and to obtain accurate results. Therefore, a larger sample size and a more diverse geographical representation would provide a better understanding of the migration patterns of monarch butterflies.

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The radius of the circle is 7.8 cm.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Given that the area of a circle is 192 cm².

The area of a circle is πr², where r is the radius of the circle.

Assume that the radius of the circle is r.

Therefore,

πr² = 192

Divide both sides by π:

r² = 192/π

r² = 61.115

r = 7.817

r  ≈ 7.8 cm

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Answer: That’s easy… The answer is -13

Step-by-step explanation: -2 x 3 + -7 = ?

-2 x 3 = -6

-6 + -7 = -13

The supportive statement regarding the trapezoid based on the information is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

The non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The missing statement to support all other statements would be that m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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Answer:

284 + 28d

Step-by-step explanation:

Because she has 284 it is known

She plans to obtain 28/day

Therefor, it should be 248+28d

We would expect John to weigh approximately 216.4 pounds at the end of week 8.

To answer this question, we need to fit a regression model to the data to determine the relationship between the number of calories burned and John's weight. We can use linear regression to find the line of best fit that represents this relationship.

We can see that there is a negative relationship between the number of calories burned and John's weight, which is consistent with the statement that "the more someone exercises the less they will weigh." We can use linear regression to find the line of best fit that represents this relationship.

Using a linear regression model, we get the following equation:

Weight = 219.9 - 0.0007 * Exercise

We can use this equation to predict John's weight at the end of week 8 based on the number of calories he burned. Plugging in Exercise = 5000, we get:

Weight = 219.9 - 0.0007 * 5000

Weight = 216.4

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Answer:

The correct answer is:

e = 0.25 t + 1.75 .

Answer:

[tex]\frac{1}{22}[/tex]

Step-by-step explanation:

For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.

One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.

We have the fraction: [tex]\sqrt{x}-11[/tex], we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares. [tex](\sqrt{x}-11)(\sqrt{x}+11)=x-121[/tex] and we want to multiply the bottom by this amount as well, giving us the fraction:

[tex]\frac{x-121}{(x-121)(\sqrt{x}+11}[/tex]

Now we can cancel out the x-121 from the numerator and denominator, leaving us with:

[tex]\frac{1}{\sqrt{x}+11}[/tex]

and now we can directly plug in 121

[tex]\frac{1}{\sqrt{121}+11}=\frac{1}{11+11}=\frac{1}{22}[/tex]

The value of x for the given expression will be 22/3.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is triple x less by 10 is at least 12. The mathematical form of the expression can be written as below:-

3x - 10 = 12

3x = 10 + 12

3x = 22

x = 22 / 3

Hence, the value of x for the expression 3x - 10 = 12 is x = 22 / 3.

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Answer:

x=-13

Step-by-step explanation:

Since the two angles given are equivalent, you set up the equation as 7x+205=114.

7x+205=114

7x=114-205

7x=-91

7x/7=-91/7

x=-13

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Two pairs of separate sides are parallel in a quadrilateral with a single arrow once per pair of opposite sides.

A quadrilateral has four straight sides and is a two-dimensional form. Parallelograms, isosceles triangles, rectangles, kites, rectangles, and rhombuses are a few examples of quadrilaterals.

Option (c) illustrates a trapezoid in which one set of opposing sides has arrows indicating how they are parallel to one another. Alternative (d) has both couples of opposing sides indicated with arrows, indicating that all side are parallel, while options (a) and (b) don't even have any linear opposite sides.

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Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².

A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.

According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.

Given that the total surface area of one cylinder is:

2πrh + 2πr²,

The total surface area of two drums will therefore be:

(2πrh + 2πr²) * 2

⇒ 4πrh + 4hr²

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In order to infuse 0.5 grams of magnesium sulfate, 6.25ml must be administered in 1 hour.

A magnesium salt with the counterion sulfate is known as magnesium sulfate. It functions as a medication called, anaesthetic, tocolytic, anti-arrhythmia, analgesic, fertilizer, anticonvulsant, cardiovascular medication, analgesic, and all of the above. Drug is used to treat constipation temporarily.

Additionally, it is employed as a soaking solution to treat minor sprains, bruises, muscular aches, joint stiffness, and fatigued feet. A cleanse and soaking solution, this medication Magnesium sulfate, also known as Bath, is a natural compound used for a variety of therapeutic and physiological benefits.

xml = 0.5*50     (cross multiplication)

               4

So xml = 6.25ml

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When a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

If Victoria signed up for a gym membership 21 weeks after Monica and we let a represent the number of weeks Victoria has been a member and b represent the number of weeks Monica has been a member, then we have a = b + 21.

Substituting a = 9, we get:

9 = b + 21

Solving for b, we subtract 21 from both sides:

b = 9 - 21

b = -12

Therefore, when a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.

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The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.

In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.

The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:

z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])

where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).

In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:

z - 7 = (-3)(x - 5) + (7)(y - 4)

Simplifying this equation, we get:

z = -3x + 7y + 8

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The shape of the newly cut cross section is option A. A rectangle, 5 inches by 6 inches.

Rectangle is a two dimensional shape or figure which consists of four sides and four angles and all the angles are right angles.

Opposite sides are equal.

It is clearly seen that the red line is passing along the length of the  block.

So the new cross section cannot have the dimension 15 inches in any part.

And the width and height is not getting cut.

So the dimension will be 5 inches by 6 inches.

A square has all the sides equal.

Since both the dimensions are not equal it is a rectangle and not a square.

Hence the new cross section is A. A rectangle, 5 inches by 6 inches.

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The complete question is as follows and the image for the block is attached below :

Landis cuts a foam block along the red line. When he looks at the newly

exposed face, what is the shape of the cross-section?

A. A rectangle, 5 inches by 6 inches

B. A rectangle, 15 inches by 6 inches

C. A rectangle 5 inches by 15 inches

D. A square, 5 inches by 5 inches

In the image of the trapezoid the value of angle C is 82 degrees

A trapezoid is a quadrilateral with one pair of parallel sides.

Opposite angles of a trapezoid are angles that are located across from each other, with a side of the trapezoid between them.

In a trapezoid, opposite angles are always congruent, meaning they have the same measure. This is a result of the fact that a trapezoid is a parallelogram, which means that its opposite sides are parallel and equal in length.

When opposite sides of a parallelogram are parallel, it follows that opposite angles are congruent.

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A circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent.

What is the division?

Division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into equal parts or determining how many times one quantity is contained within another.

If you add all of the numbers together you get 500, but you need to make it 100 percent so you divide the total number by five. to know what percent out of 100 you need to divide all of the variables by 5.

85 ÷ 5 = 17

240 ÷ 5 = 48

125 ÷ 5 = 25

50 ÷ 5 = 10

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Answer:

BBBBBBBBB

Step-by-step explanation: