There are two rectangular boxes, and their dimensions are as follows:
Dimensions of Box A
Length = 130 cm
Width = 104 cm
Height = 25 cm
Dimensions of Box B
Height = 52 cm
Length = 49 cm
Width = 65 cm
Dimensions of 5-litre paint cans
Radius = 9 cm
Height = 24 cm
Question 2.3.1 [6 marks] The packers argue that if they use Box A for packaging the paint cans, they will be able to pack more than two times the paint cans in Box B. Use calculations to prove if their argument is valid or not.​

So,

We see in Statement 3 that WY = WY.  This seems obvious, but it ensures that quantities don't change their values.  We call this property of something being equal to itself, the "reflexive property."

The correct answer is the third option.

Answer:

The answer is C.

Step-by-step explanation:

The theory of vertical angles, often known as the theorem of vertically opposite angles. According to the theorem, two opposed vertical angles created when two lines cross one other are always equal (congruent) to each other no matter what the circumstances are.

Answer:

(a) 280

(b)  £26

Step-by-step explanation:

(a) 20 workers eat 2 biscuits a day.

20 × 2 = 40

Since there are 7 days a week, multiply the 40 x 7 to find how many biscuits are eaten each week.

40 × 7 = 280

280 biscuits are eaten every week.

(b) Now, divide 280 (the number of biscuits eaten each week) by 14 (the number of biscuits in a packet) to find how many packets are eaten weekly.

280 ÷ 14 = 20

Now you have the number of packets eaten each week, so you can determine the price spent on biscuits. Multiply 20 packets by the price per packet, which is £1.30.

20 × 1.30 = 26

The office spends £26 on biscuits each week.

The definite integral of the function f(x) = \(x^4 - 3x^3 + 8x\) from an initial point to a final point can be evaluated. In this case, we need to find the integral of f(x) with respect to x over a certain interval.

First, we find the antiderivative of f(x) by integrating each term individually. The antiderivative of \(x^4\) is \((1/5)x^5\), the antiderivative of \(-3x^3\)is \((-3/4)x^4\), and the antiderivative of 8x is \(4x^2\).

Next, we evaluate the antiderivative at the upper and lower limits of integration and subtract the lower value from the upper value. Let's assume the initial point is a and the final point is b.

The definite integral of f(x) from a to b is:

\(\[\int_{a}^{b} (x^4 - 3x^3 + 8x) \, dx = \left[\frac{1}{5}x^5 - \frac{3}{4}x^4 + 4x^2\right] \bigg|_{a}^{b}\]\)

\(\[\int_{a}^{b} (x^4 - 3x^3 + 8x) \, dx = \left[\frac{1}{5}x^5 - \frac{3}{4}x^4 + 4x^2 \right] \Bigg|_{a}^{b} = \left(\frac{1}{5}b^5 - \frac{3}{4}b^4 + 4b^2 \right) - \left(\frac{1}{5}a^5 - \frac{3}{4}a^4 + 4a^2 \right)\]\)

In summary, the definite integral of the given function is \(\(\frac{1}{5}b^5 - \frac{3}{4}b^4 + 4b^2 - \frac{1}{5}a^5 + \frac{3}{4}a^4 - 4a^2\)\), where a and b represent the initial and final points of integration.

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The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena

In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.

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To convert rectangular coordinates (x,y) to polar coordinates (r,θ), use the following formula:  r = √(x^2 + y^2) and θ = arctan(y/x). Here, r is the distance from the origin to the point (x,y) and θ is the angle made by the line connecting the origin to the point (x,y) with the x-axis.

For example, if the rectangular coordinates are (3,4), the corresponding polar coordinates are (5, 53.13°). To obtain this, first calculate the distance r using the formula: r = √(3^2 + 4^2) = 5. Next, calculate the angle θ using the formula: θ = arctan(4/3) = 53.13°.

You can also convert from polar coordinates (r,θ) to rectangular coordinates (x,y) using the formulas: x = r*cos(θ) and y = r*sin(θ). Here, r is the distance from the origin to the point (x,y) and θ is the angle made by the line connecting the origin to the point (x,y) with the x-axis.

For example, if the polar coordinates are (5, 53.13°), the corresponding rectangular coordinates are (3,4). To obtain this, first calculate the x-coordinate x using the formula: x = 5*cos(53.13°) = 3. Next, calculate the y-coordinate y using the formula: y = 5*sin(53.13°) = 4.

In summary, to convert rectangular coordinates (x,y) to polar coordinates (r,θ), use the formula r = √(x^2 + y^2) and θ = arctan(y/x). To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), use the formulas x = r*cos(θ) and y = r*sin(θ). Rectangular coordinates to polar coordinates conversion Polar coordinates are the two-dimensional coordinate system that uses an angle (in radians) and the distance from the origin (in units) to describe the position of a point.

A point is described by its distance from the origin (radius) and the angle (in radians) that its position vector makes with the positive x-axis.Let (x, y) be any point in the rectangular coordinate system. Then, the polar coordinates of that point are (r, θ),

where:r = √(x2 + y2) is the distance from the origin to the point.(x,y) is the point in the rectangular coordinate system.θ = tan-1(y/x) is the angle in radians that the position vector of the point makes with the positive x-axis (assuming that x ≠ 0).

Note that the range of θ depends on the quadrant in which the point lies. If the point lies in quadrant I or IV, then θ is between 0 and π radians (i.e., 0 ≤ θ < π). If the point lies in quadrant II or III, then θ is between π and 2π radians (i.e., π ≤ θ < 2π).

To convert a point from rectangular coordinates to polar coordinates, we can follow these steps: Calculate the distance r from the origin to the point using the Pythagorean theorem = √(x2 + y2)Calculate the angle θ that the position vector of the point makes with the positive x-axis using the formula:θ = tan-1(y/x)

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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The relationship between the cost charged for the daily boarding of dogs

by the kennel is a directly proportional relationship.

The correct responses are;

1. The dog kennel charges $60 per day is; False

Correct statement; The dog kennel charges $30 per day

2. The equation y = 30·x can represent the graph; True

3. It costs $200 to board a dog for 7 days is; False

Correct statement; It costs $210 to board a dog for 7 days

4.The graph will contain the coordinate point (9, 270); True

Reasons:

Points on the graph of the given graph of the Cost to Number of days are;

(2, 60), (4, 120)

The slope of the graph is \(m = \dfrac{120 - 60}{4 - 2} = 30\)

Equation of the graph is therefore; y - 60 = 30·(x - 2)

Which gives;

y  = 30·x - 2×30 + 60 = 30·x

The equation of the graph is; y = 30·x

Therefore, the statement;

The cost of the dog kennel a day is given by the value of 'y', when x = 1, as

follows;

Cost per day, y = 30 × 1 = 30

The cost per day = $30 per day

Therefore;

The correct statement is; The dog kennel charges $30 per day

The amount it costs to board a dog for 7 days is y = $30×7 = $210

Therefore, the correct statement is; It costs $210 to board a dog for 7 days

Therefore, the statement; the graph will contain the coordinate point (9, 270) is; True

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Answer: The answer is 21360

Step-by-step explanation:

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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Answer:

Given expression is \(\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}\) = 2tan²A

We have to prove this identity.

\(\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}=\frac{(\text{cosecA+1})-(\text{cosecA-1})}{(\text{cosecA-1})(\text{cosecA+1})}\)

                              = \(\frac{(\text{cosecA}-\text{cosecA})+(1+1)}{cosec^2A-1}\)

                              = \(\frac{2}{cosec^{2}A-1}\)

                              = \(\frac{2}{cot^{2}A}\) [From the identity, (cosec²A - 1) = cot²A]

                              = 2tan²A [From the identity, cotA = \(\frac{1}{\text{tan}A}\)]

Hence the given equation is proved.

Answer:

3/5

Step-by-step explanation:

all you have to do is get the fraction to its lowest point and you get 3/5.

Remember: a^2 + b^2 = c^2

1

64 + 49 = 113

√113 = \(\sqrt{113}\)

2

100 - 25 = 75

square root of 75 = 5 \(\sqrt{3}\)

Step-by-step explanation:

7b+2b-5

=9b-5

Thank you

Answer: 9b - 5 is our answer

Step-by-step explanation:

7b - 5 + 2b

==> 7b - 5 + 2b ( we can order the terms in such a way, than we can add like terms)

==> 7b + 2b - 5  (combine like terms)

==> 9b - 5 is our answer

Hope this helped! Have a good day :D

Answer:

\(\pi = \)

236+453

The amount of cake which is eaten by Samuel is more than that eaten by Austin as Samuel ate half of the cake while Austin ate only one-third of the cake.

To calculate the quantity of the cake eaten by two people, the proportion of cake has to be calculated. Ratio and Proportion are the mathematical concepts which are used to represent the part of any matter with regard to the whole.

In the given problem, if we consider that the whole of cake is equal to 1 part, then part of Cake eaten by Samuel is equal to 3/6*1 = 1/2 part. Part of cake eaten by Austin = 2/6*1 = 1/3 part.

Since, 1/2 = 0.5 and 1/3 = 0.33, so we can say that 1/2 is greater then 1/3, therefore Samuel ate large amount of cake than Austin.

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ANSWER:

24 mm

EXPLANATION:

Given:

To find:

The length of the missing leg

Let x represent the length of the missing leg

We can go ahead and solve for x using the Pythagorean theorem as sen below;

So the length of the missing leg is 24 mm

Answer:

Step-by-step explanation:

A composition of transformations is a combination of two or more transformations, each performed on the previous image. A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines)

Answer:

A. Amplitude: 1; midline: y = 1

Answer:

A. Amplitude: 1; midline: y = 1

Step-by-step explanation:

i took the test

To solve the given equations using Laplace transforms, we will apply the Laplace transform to both sides of the equations and use the initial values to find the inverse Laplace transforms.

Applying the Laplace transform to both sides of the equation, we get the transformed equation:

s²Y(s) - sy(0) - y'(0) - 9(sY(s) - y(0)) + 3Y(s) = (s/(s²-9)) - 1

Substituting the initial values y(0) = -1 and y'(0) = 4, we can simplify the equation as follows:

(s² - 9)Y(s) + 8s - 9 = (s/(s²-9)) - 1

Simplifying further, we have:

(s² - 8s - 18)Y(s) = (s-1)/(s²-9)

Dividing both sides by (s² - 8s - 18), we obtain the expression for Y(s):

Y(s) = (s-1)/[(s-3)(s+3)(s-6)]

Now, we can use partial fraction decomposition and inverse Laplace transform to find the solution y(t) in the time domain.

Applying the Laplace transform to both sides of the equation, we get the transformed equation:

s²X(s) - sx(0) - x'(0) + 4(sX(s) - x(0)) + 3X(s) = 1/s - e^(-6s)

Substituting the initial values x(0) = 0 and x'(0) = 0, we can simplify the equation as follows:

(s² + 4s + 3)X(s) = 1/s - e^(-6s)

Dividing both sides by (s² + 4s + 3), we obtain the expression for X(s):

X(s) = [1 - e^(-6s)]/[(s+1)(s+3)]

Now, we can use inverse Laplace transform to find the solution x(t) in the time domain. By applying the inverse Laplace transform to the expressions of Y(s) and X(s), we can obtain the solutions y(t) and x(t) respectively for equations 7.1 and 7.2.

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The solution to 1 1/2 - 3 is -1 1/2 or -1.5. we need to first convert 1 1/2 to an improper fraction

To find the solution, which is 3/2. Then, we can rewrite the subtraction expression as 3/2 - 6/2. Simplifying this expression, we get -3/2, which can also be written as -1 1/2 or -1.5. To place a point on the answer, we can mark the number line at -1.5.

It is important to remember to convert mixed numbers to improper fractions before performing operations.

In this case, we could not subtract 3 from 1 1/2 directly without converting it to an improper fraction. Additionally, we can represent the solution on a number line to visualize where it falls in relation to other numbers.

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A 95% confidence interval compared to a 90% interval, tends to result in a wider confidence interval because of a higher level of confidence requires a larger interval to account for the increased certainty.

Based on the given information, there seems to be some inconsistency in the provided data. The number of respondents is mentioned as 2000 in one part and 1500 in another part. To provide an accurate analysis, it's important to have consistent and accurate data.

However, I can still explain the concept of confidence intervals and their widths based on general understanding.

A confidence interval is a range of values calculated from sample data that is likely to contain the true population parameter with a certain level of confidence. The width of a confidence interval depends on two main factors: the sample size and the desired level of confidence.

In general, a larger sample size tends to result in a narrower confidence interval. This is because larger sample sizes provide more precise estimates of the population parameter, reducing the uncertainty and thus narrowing the interval.

Without the specific sample data and the stated confidence levels, it is difficult to determine which confidence interval (specified by the given percentages) would be wider or why. Additionally, the inconsistency in the provided information further hinders a specific analysis.

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Answer:

1892.7 ml

Hope this helps!

The general solution to the given differential equation y'' + 9y = sin^4x can be expressed as y(x) = Asin(3x) + Bcos(3x) - (1/192)*(3x + sin(6x)), where A and B are arbitrary constants.

Explanation:

To find the general solution, we can start by considering the homogeneous equation y'' + 9y = 0, which has the characteristic equation r^2 + 9 = 0. Solving this equation, we get the roots r = 3i and -3i. Therefore, the homogeneous solution is y_h(x) = Asin(3x) + Bcos(3x), where A and B are constants.

Next, we need to find a particular solution to the non-homogeneous equation y'' + 9y = sin^4x. Since the right-hand side contains a trigonometric function, we can use the method of undetermined coefficients and assume a particular solution of the form y_p(x) = C*(3x + sin(6x)), where C is a constant to be determined.

Taking the derivatives and substituting into the differential equation, we find that C = -1/192. Therefore, the particular solution is y_p(x) = -(1/192)*(3x + sin(6x)).

Finally, the general solution is obtained by combining the homogeneous and particular solutions: y(x) = y_h(x) + y_p(x) = Asin(3x) + Bcos(3x) - (1/192)*(3x + sin(6x)), where A and B are arbitrary constants.

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