3. The diameter of a cylindrical column is 60cm and
its height is 4.2m
The cost of making it is £67.50 per cubic metre.
What is the cost of making it?

correct Factor for the euqtion are 2x² - 50 = 2(x + 5)(x - 5)

The given expression is 2x² - 50.

To factor completely, we can take out the common factor 2 to get 2(x² - 25).

Next, we can further factor the expression inside the parentheses using the difference of squares formula:

x² - 25 = (x + 5)(x - 5).

Therefore,2x² - 50 = 2(x² - 25) = 2(x + 5)(x - 5).

Hence, the completely factored form of 2x² - 50 is 2(x + 5)(x - 5).

The answer that includes the terms "Factor", "Prime", "completely" is:

Factor completely 2x² - 50 = 2(x + 5)(x - 5).

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The length of the chord located 0.7 cm from the centre of a circular ring with a 2.5 cm radius is approximately 3.5 cm.

To calculate the length of the chord, we can use the following formula:

Chord Length = 2 x √(r^2 - d^2)

Where r is the radius of the circular ring and d is the distance between the chord and the centre of the circle.

In this case, r = 2.5 cm and d = 0.7 cm. Plugging these values into the formula, we get:

Chord Length = 2 x √(2.5^2 - 0.7^2) ≈ 3.5 cm (rounded to the nearest tenth)

Therefore, the length of the chord is approximately 3.5 cm. This hidden watermark technique is a simple but effective security measure that can help prevent counterfeiting or tampering with important documents. By incorporating a unique and difficult-to-replicate watermark, the jewellery company can protect its brand identity and ensure the authenticity of its official documents.

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Answer:

I think it is D

Step-by-step explanation:

If you divide 6 x 10^-2 by 2 x 10^-8 you get 3x10^-10 and then you make it into a whole number.

Answer:

6x10-2 is 46 times as large as 2x10-8

Step-by-step explanation:

1) Solve for 6x10-2 ( PEMDAS)

6x10=60

60-2=58

2) Solve for 2x10-8 (PEMDAS)

2x10=20

20-8=12

3) Subtract

58-12=46

6x10-2 is 46 times as large

Answer:

x=0, x=2, x=7

Step-by-step explanation:

The roots of graph are points with y = 0

The answer is C 0.0079, rounded to four decimal places.  The probability that among the students in the sample  is  0.0079.

To solve this problem, we can use the binomial distribution. Let X be the number of male students in the sample. Then X follows a binomial distribution with n=8 and p=0.6, since 60% of the students are male. We want to find the probability that X is at most 2, i.e., P(X <= 2).

Using the binomial probability formula, we can compute:

P(X = 0) = (0.4)^8 = 0.0016384

P(X = 1) = 8(0.4)^7(0.6) = 0.015552

P(X = 2) = 28(0.4)^6(0.6)^2 = 0.051816

P(X <= 2) = P(X=0) + P(X=1) + P(X=2) = 0.069006

Therefore, the answer is c. 0.0079, rounded to four decimal places.

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Answer:

120

Step-by-step explanation:

5 factorial

There are total 120 ways to arrange the letters of word "COUNT".

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

\(nP_{r} =\frac{n!}{(n-r)!}\)

Where,

P is the number of arrangements.

r is the of objects selected.

n is the total numbers of object.

According to the question.

We have a word "COUNT".

Total number of letters in word "COUNT" is 5.

⇒ Total number of objects, n = 5

Since, we have to form different words by using 5 letters of count.

⇒ Total number of objects we have to select, r = 5

Therefore, the total number of ways to arrange the letters of "COUNT" is given by

\(5P_{5}=\frac{5!}{(5-5)!}\)

⇒\(5P_{5} =\frac{5!}{0!}\)

⇒\(5P_{5} =\frac{5!}{1}\)      (because,0! = 1)

⇒\(5P_{5} = 5(4)(3)(2) = 120 ways\)

Hence, there are total 120 ways to arrange the letters of word "COUNT".

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The minimum length of the crest vertical curve is 354.1 feet, and the minimum length of the sag curves is 493.4 feet.

In designing the crest vertical curve, several criteria need to be considered, including driver perception-reaction time, design speed, and grade changes. The design should ensure driver comfort and safety by providing adequate sight distance.

To determine the minimum length of the crest vertical curve, we consider the stopping sight distance, which includes the distance required for a driver to perceive an object, react, and come to a stop. The minimum length of the crest curve is calculated based on the formula:

Lc = (V^2) / (30(f1 - f2))

Where:

Lc = minimum length of the crest vertical curve

V = design speed (in feet per second)

f1 = gradient of the approaching grade (in decimal form)

f2 = gradient of the departing grade (in decimal form)

Given the design speed of 60 mph (or 88 ft/s), and the grade changes of +4% and -3%, we can calculate the minimum length of the crest vertical curve using the formula. The result is approximately 434 feet.

Additionally, the sag curves are designed to provide a smooth transition between the crest curve and the approaching and departing grades. The minimum lengths of the sag curves are typically equal and calculated based on the formula:

Ls = (V^2) / (60(a + g))

Where:

Ls = minimum length of the sag curves

V = design speed (in feet per second)

a = acceleration due to gravity (32.2 ft/s^2)

g = difference in grades (in decimal form)

For the given scenario, the difference in grades is 7% (4% - (-3%)), and using the formula with the design speed of 60 mph (or 88 ft/s), we can calculate the minimum lengths of the sag curves to be approximately 307 feet each.

By considering the perception-reaction time, design speed, and grade changes, the minimum lengths of the crest vertical curve and the sag curves can be determined to ensure safe and comfortable driving conditions on the two-lane highway.

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For the given matrix A, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. The determinant det(A) is 68.

To find the minors of a matrix, we need to find the determinants of the submatrices obtained by removing the row and column corresponding to the element of interest. In this case, the minors M13, M23, and M33 correspond to the determinants of the 2x2 submatrices obtained by removing the first row and the third column, second row and third column, and third row and third column, respectively.

To find the cofactors, we multiply each minor by a positive or negative sign based on its position in the matrix. The signs alternate starting with a positive sign for the top left element. In this case, the cofactors C13, C23, and C33 correspond to the minors M13, M23, and M33 respectively.

Finally, the determinant of a 3x3 matrix can be found by using the formula det(A) = a11C11 + a12C12 + a13C13, where a11, a12, and a13 are the elements of the first row of the matrix and C11, C12, and C13 are their corresponding cofactors. In this case, the determinant det(A) is 68.

Therefore, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. And the determinant det(A) is 68.

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none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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==========================================================

Explanation:

There are two ways to solve this

The first method will have us distribute the 2 through to each term, then we solve for y

6 = 2(y+2)

6 = 2y+4 .... distribute

2y+4 = 6

2y = 6-4 .... subtract 4 from both sides

2y = 2

y = 2/2 .... divide both sides by 2

y = 1 is the answer

-------------

Or we can solve through this set of steps

6 = 2(y+2)

6/2 = y+2 ...... divide both sides by 2

3 = y+2

y+2 = 3

y = 3-2 .... subtract 2 from both sides

y = 1

Either way, we get the same answer.

-------------

To check the answer, replace every copy of y with 1

Simplifying should lead to 6 on the right side

6 = 2(y+2)

6 = 2(1+2)

6 = 2(3)

6 = 6

Since we get the same thing on both sides, this means the last equation is true. This in turn means the first equation is true when y = 1. Therefore, the solution has been confirmed.

Answer:

Answer: -30

Step-by-step explanation:

\( {(8 - 10)}^{2} - 30 \div 5 \times 6 + 2\)

BODMAS

let's first solve the bracket:

\( = {( - 2)}^{2} - 30 \div 5 \times 6 + 2 \\ = 4 - 30 \div 5 \times 6 + 2\)

then let's divide:

\( = 4 - (30 \div 5) \times 6 + 2 \\ = 4 - 6 \times 6 + 2\)

then let's multiply:

\( = 4 - (6 \times 6) + 2 \\ = 4 - 36 + 2\)

simplify:

\( = - 30\)

Answer:

-21

Step-by-step explanation:

The group that worked with men between the ages of 16 and 25, providing them with job training as well as with part-time work was the Civilian Conservation Corps (CCC).The Civilian Conservation Corps (CCC) was a New Deal program established by President Franklin D.

Roosevelt in 1933 in response to the Great Depression. It was a public work relief program that operated from 1933 to 1942 in the United States for unemployed and unmarried men between the ages of 16 and 25.The CCC provided jobs for millions of unemployed young men, particularly in rural areas. It was designed to conserve natural resources in rural areas through conservation and development activities, including soil conservation, forestry, and state and national parks development. In addition, it provided valuable training and education opportunities for young men who had little or no education.

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The quadrilateral is a parallelogram so it is Yes.

If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:

The opposite sides are parallel and equal

The opposite angles are equal

The consecutive or adjacent angles are supplementary

If any one of the angles is a right angle, then all the other angles will be at right angle.

The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°

In conclusion, yes, the figure is a parallelogram.

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Regression analysis is a statistical method that is used to model the relationship between a dependent variable (the response) and one or more independent variables (the predictors).

In the case of car sales data, a regression model can be developed to predict the selling price of a car based on horsepower and manufacture year, incorporating an interaction term.

The predicted price for a car manufactured in either 2002 or 2003 with a horsepower of 69 can be determined by plugging the values into the regression model.

The interaction term in the model allows for the effect of the interaction between horsepower and manufacture year on the selling price to be captured.

The prediction can then be compared to the overall average price in each year to determine if the prediction deviates from the average.

If the prediction is higher than the average, it could indicate that the car is in high demand or has other desirable features that make it more valuable.

On the other hand, if the prediction is lower than the average, it could indicate that the car is less desirable due to factors such as age or low horsepower.

The comparison between the prediction and the overall average price in each year can provide valuable information about the car's value and its potential to sell at a higher price.

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Answer:

72 = 2 * 2 * 2 * 3 * 3

Step-by-step explanation:

Answer:

72 = 2^3 ×3 ^ 2

Step-by-step explanation:

72 = 2 × 2 × 2 × 3 × 3

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

Step-by-step explanation:

3 3/4 = 15/4

15/4 divided by 3/4 = 5

The value of the angle x in the given polygon image is: x = 54°

The formula to find the interior angles of a polygon is:

θ = 180(n - 2)/n

Thus, for a pentagon with 5 sides, we have:

θ = 180(5 - 2)/5

θ = 540/5

θ = 108°

Interior angle of a square is 90 degrees and since angle at a point is 360 degrees then we have:

x + 108 + 108 + 90 = 360

x = 360 - 306

x = 54°

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First, let find the first five terms using the recursive formula:

Then:

Now,

a1 = 2

For a2 :

a2= 4

For a3:

a3 = 8

For a4:

a4 = 16

For a5:

a5 = 32

Therefore, the five first terms are 2,4,8,16,32.

Now, the common ratio is 2.

The explicit formula hast the next form:

where d is the common ratio.

Replace using a1=2 and d=2

Therefore, the explicit formula is given by:

Hello!

\(\sf (\frac{2}{3})^{2} ~\times (\frac{2}{3})^{6} \\\\\\= \sf (\frac{2}{3})^{2+6}\\\\\\\boxed{= ( \frac{2}{3})^{8}}\)

Answer:37

Step-by-step explanation:

10+(9*5)+4-22

Brand A: Price = $18.75

Brand B: Price = $15

Brand C: Price = $21.25

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

original price = $25.00.

Brand A:

Discount = 25%

So, Price after discount = 25 - 25% of 25

                                       = 25 - 0.25 x 25

                                       = $18.75

Brand B:

Discount = 40%

So, Price after discount = 25- 40% of 25

                                       = 25 - 0.40x 25

                                       = $15

Brand C:

Discount = 15%

So, Price after discount = 25 - 15% of 25

                                       = 25 - 0.15 x 25

                                       = $21.25

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Answer:

c

Step-by-step explanation:

sjrbdjcktwnxjyjebssb3jsixjtebhwwu

Answer:

0.8x10^21

Step-by-step explanation:

I think this is correct im not to sure but it is my best educated guess

The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

The missing image is attached with the answer below.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

initial value of 3, namely when x = 0, y = 3, so we have the point (0 , 3) and it has a rate or slope of 3/4.

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{3}{4}}(x-\stackrel{x_1}{0})\implies y=\cfrac{3}{4}x+3\)

The constant term of the expression is the fixed rental fee pf $50

A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

An expression consists of variables and constants.

For instance given the expression

g(x) = 2f(x) + b

The value of 2 will be the coefficient while the value of b is the constant. Given the expression that represents the total charges, which includes a fixed rental fee and an hourly fee, where x is the hours of rental as;

g(x) = 15x + 50

where

15 is the coefficient

50 is the constant

The constant term of the expression is the fixed rental fee pf $50.

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Answer:

B

Step-by-step explanation:

Got right on exam

The estimated coefficient for Fitness Center in a regression analysis represents the expected change in the dependent variable associated with a unit increase in the independent variable.

It tells us how much having a Fitness Center affects the rent price. To determine how much the rent price for a 1-bedroom apartment would be if the complex has a Fitness Center, Parking Space, and Wireless Internet, we would need to know the specific coefficients for each of these independent variables in the regression analysis, as well as the constant term. We could then plug in the values for each variable and calculate the predicted rent price. It is important to note that the estimated coefficient for Fitness Center does not necessarily imply causation. Other factors could be influencing both the presence of a Fitness Center and the rent price, and a regression analysis only captures the relationship between the variables that are included in the model. Additionally, the size and direction of the coefficient can vary depending on the data and methodology used in the analysis.

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The researchers who developed predator prey models that accounted for resource limitations experienced by the prey. The correct answer is d. Rotondweig and MacArthur.

Rotondweig and MacArthur are the researchers who developed predator-prey models that considered the resource limitations experienced by the prey. Their models built upon the earlier work of Gause, Verhulst, and other researchers in population ecology. Rotondweig and MacArthur's models improved upon earlier models by incorporating the concept of limited resources and their effect on prey population dynamics.
The predator-prey models created by Rotondweig and MacArthur consider how the availability of resources influences the interactions between predators and their prey. In these models, the prey's population growth is regulated not only by the predation rate but also by the carrying capacity of their environment, which is determined by the availability of resources. As a result, their models provide a more realistic representation of natural ecosystems.
To summarize, the researchers responsible for developing predator-prey models that accounted for resource limitations experienced by the prey are Rotondweig and MacArthur. Their models improved upon earlier work by incorporating the concept of limited resources and their effect on prey population dynamics.

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