The volume of a cylinder having height one and half of the radius is 12,936 m3 what minimum square cm of paper is needed to cover the curved surface area of the cylinder? The answer should be 1848m2. please solve my question.​

(a) The greatest common divisor of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) The greatest common divisor of \(x^2\)- 1 and 2\(x^7\) - 4x\(^5\) + 2 is 1.

(a) To find the greatest common divisor (GCD) of the polynomials, we can use polynomial long division.

Dividing \(x^3\) - 6x - 7 by \(x^4\), we get a remainder of \(x^3\) - 6x - 7.

Since the remainder is non-zero, the GCD of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) To find the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2, we can again use polynomial long division.

Dividing 2\(x^7\) - 4\(x^5\) + 2 by \(x^2\) - 1, we get a remainder of 2\(x^5\) + 2.

Since the remainder is non-zero, the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2 is 1.

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Answer:

253.5π

Step-by-step explanation:

Surface area of cylinder: 2πrh+2πr^2

Height: 13, Radius: 6.5

A = 2π6.5(13)+2π6.5^2

A = 169π + 84.5π

A = 253.5π

Hope THIS works if not ask a tutors

The unit which is used to measure the attribute under investigation is inches.

Given a histogram which shows the height of the adults in male.

Here in the X axis, the height in inches are marked starting from 66 to 74.

In the Y axis, the number of people who have a specified height is given.

Here we have to find the unit which is used to measure the attribute under investigation.

For that, first we have to find the attribute under investigation.

Here the point of graphing this is to find the height of the people.

So attribute under investigation is the height of the people.

So the unit is that of the unit used to measure the height.

Here the unit is inches.

Hence the unit used is inches.

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We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.

The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.

It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.

The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.

Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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The primitive function of the given function f(x) = -5/2 * x is F(x) = -5/4 * x² + C where C is the constant of integration. This means that F(x) is the antiderivative of f(x).

To find the antiderivative, integrate the given function with respect to x.

When we integrate the given function f(x) = -5/2 * x, we get;

∫f(x)dx = ∫-5/2 * x dx

= -5/2 ∫x dx

= -5/2 * x²/2 + C

The constant of integration C is an arbitrary constant and could take any real value.

Therefore, the antiderivative of f(x) is

F(x) = -5/4 * x² + C where C is a constant of integration.

The primitive function is usually the antiderivative of a function. The antiderivative of a function is its inverse operation of differentiation.

Therefore, to find the primitive function, we integrate the given function with respect to x.

In this case, the primitive function is given by F(x) = -5/4 * x² + C.

The primitive function of the given function f(x) = -5/2 * x is F(x) = -5/4 * x² + C where C is the constant of integration. This function is obtained by integrating f(x) with respect to x. The constant of integration C is an arbitrary constant and could take any real value.

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Scientific notation is built upon the idea of moving the decimal place to the left or right so many places.

A foundational background concept is that multiplying by 10 makes a number bigger and moves the decimal to the right.

For example: 3.4 x 10 = 34

The counterpart for that is that dividing by 10 makes a number smaller and moves the decimal to the left.

For example: 3.4 ÷ 10 = 0.34

So, when you see 3.4 x 10^5, this means you’re multiplying by 10 fives times, so that will move the decimal point five places to the right.

3.4 x 10^5 = 340 000

On the other hand, when you see a negative exponent on the 10, then that means you’re actually dividing by that many 10s and will move the decimal point that many places to the left. (to make the number smaller)

3.4 x 10^-5 = 0.000034

So, you need to first identify if you’ll make the number bigger or smaller (is the power of 10 postive or negative?) and then how many places the decimal point will need to move.

The graph shown in the figure is of the form

Where

Hence, the function that produce the graph shown is a absolute value

The commission the employee earns as a percentage of the total cost of the gym membership is 19%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this case, the gym keeps $42 and the employee who sold it gets $8.

The commission the employee earns as a percentage of the total cost of the gym membership will be:

= 8 / 42 × 100

= 19%

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He needs to add five over 12 of a cup.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The recipe says that he has to mix 32 grams of vanilla powder to the flour.

And, Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added two over three of a cup of vanilla powder to the flour.

Now,

Since, 1 cup of that particular vanilla powder has a mass of 128 grams.

Hence, 2/3 cup of that particular vanilla powder has a mass = 2/3 × 128    

                                                                                            = 256/3

And, The recipe says that he has to mix 32 grams of vanilla powder to the flour.

So, The amount of vanilla powder = 256/3 - 32

                                                    = 53 1/3 grams

Hence, The amount = 160/3 × 128

                                = 5/12

Thus,  He needs to add five over 12 of a cup.

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Answer:

8(2)+3(5)-10+4(2)

16+15 -10+8

=31-10+8

=21+8=29

Answer:

x² + 4 > 4x

x² - 4x + 4 > 0

(x - 2)² > 0 (true for all real x)

Note that the cost of wrapping both boxes will come to $1.11356. This is arrived at using simple arithmetic and the knowledge of the area of Right rectangular prisms.

The area of a Right Rectangular Prism is given as:

A=2(wl+hl+hw)

Where:

l = length

w = width

h = height

For Box A

Length = 0.6

Width = 1

Height = 1.2

Thus, it's area = 2 [ (1*0.6) + (1*0.6) + (1.2 * 1)]

Area = 2(2.4)

Area of Box A = 4.8 Feet

Area of Box B computed using the above method =

A=2(wl+hl+hw)=

2·(1.6·0.5+1.6·0.5+1.6·1.6)

=8.32 feet

Since the cost of the wrapping costs $6.79 per 80feet

1 foot = 6.79/80

= $0.084875

Thus the cost of wrapping both boxes (since there won't be any overlap) is:

= 0.084875 (8.32 + 4.8)

= $1.11356

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Use at least 3 decimals in your calculations in this question. A group of economists would like to study the gender wage gap, In a random sample of 350 male workers, the mean hourhy wage was 14.2, and the standard deviation was 2.2. In an independent random sample of 250 female workers, the mean hocirly wage was 13.3, and the standard devlation Was 1.4. 1. The cconomists would like to test the null hypothesis that the mean hourly wage of male and female workers are the same, against the aiternative hypothesis that the mean wages are different. Use the reiection region approach to conduct the hypothesis test, at the 5% significance level. Be sure to include the sample statistic; its sampling distribution; and the reason why the sampling distritution is valid as part of your answer. 2. Calculate the 95% confidence interval for the difference between the popiation means that can be used to test the researchers nuill hypothesis (stated above) 3. Calculate the p-value. If the significance level had been 1% (instead of 58 ). What would the conclusion of the fipothesis test have bect?

Answer:

that is corresponding

The correct answer is b. Characteristic equation. the equation formed by equating the denominator of a transfer function to zero is known as the characteristic equation.

In control systems theory, the characteristic equation is formed by equating the denominator of a transfer function to zero. It plays a crucial role in the analysis and design of control systems.

The transfer function of a control system is represented as the ratio of the Laplace transform of the output to the Laplace transform of the input. The denominator of the transfer function represents the characteristic equation, which is obtained by setting the denominator polynomial equal to zero.

The characteristic equation is an algebraic equation that relates the input, output, and system dynamics. By solving the characteristic equation, we can determine the system's poles, which are the values of the complex variable(s) that make the denominator zero. The poles of the system are crucial in understanding the system's stability and behavior.

The characteristic equation helps in determining the stability of a control system. If all the poles of the characteristic equation have negative real parts, the system is stable. On the other hand, if any pole has a positive real part or lies on the imaginary axis, the system is unstable or marginally stable.

Moreover, the characteristic equation is used to calculate important system properties such as the natural frequency, damping ratio, and transient response. These properties provide insights into the system's performance and behavior.

In summary, it plays a fundamental role in control systems analysis and design, allowing us to determine system stability, transient response, and other important properties.

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the point on the surface where the tangent plane is horizontal is (-3, -4, 39).

To find the points on the surface where the tangent plane is horizontal, we need to find the critical points where the gradient of the surface function is equal to the zero vector.

The given surface is described by the equation: z = x² - 2xy - y² - 10x + 2y

To find the gradient, we need to compute the partial derivatives with respect to x and y:

∂z/∂x = 2x - 2y - 10

∂z/∂y = -2x - 2y + 2

Setting both partial derivatives equal to zero, we have:

2x - 2y - 10 = 0

-2x - 2y + 2 = 0

Solving these two equations simultaneously, we find:

x = -3

y = -4

Therefore, the critical point is (-3, -4).

To obtain the corresponding z-coordinate, we substitute these values back into the equation for z:

z = x² - 2xy - y² - 10x + 2y

 = (-3)² - 2(-3)(-4) - (-4)² - 10(-3) + 2(-4)

 = 9 + 24 - 16 + 30 - 8

 = 39

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Answer:

Step-by-step explanation:

solve the equation for x if 2 to the power x = 8​

2^x = 8

log(2x)=log(8)

x*log(2)=log(8)

x=((log(8))/((log(2))

x=3

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

check

2^3 = 8

2 * 2 * 2 = 8

8 = 8

the answer is good

The expected value of a gamble can be calculated by multiplying the probability of winning by the amount you could win and subtracting the probability of losing multiplied by the amount you could lose.

In this case, we are given that if a red card is drawn from a standard 52-card deck, you win $1200, and if a black card is drawn, you lose $1200.

First, let's determine the probability of drawing a red card from a standard 52-card deck. In a standard deck, there are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 spades and 13 clubs). So the probability of drawing a red card is 26/52, which simplifies to 1/2 or 0.5.

Next, let's calculate the probability of losing, which is the probability of drawing a black card. Similarly, the probability of drawing a black card is also 26/52 or 1/2.

Now, we can calculate the expected value using the formula:
Expected value = (probability of winning * amount won) - (probability of losing * amount lost)

Expected value = (0.5 * $1200) - (0.5 * $1200)
Expected value = $600 - $600
Expected value = $0

Therefore, the expected value of the gamble is $0. This means that, on average, you neither win nor lose money in the long run by playing this gamble.

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Answer:

1.AAS

2.ASA

AND THE OTHERS

Answer:

x = 10

Step-by-step explanation:

Since the ray AE is an angle bisector, it means that it cuts the angle 50 / 50, or perfectly in half.

This means that angle BAE and angle EAC are actually congruent

∠BAE = ∠EAC

\(x + 30 = 3x - 10\)

Get rid of x on one side. Since you are solving for x, use the more simple x

This becomes this ⇅

\(30 = 2x + 10\)

Subtract 10 from both sides

20 = 2x

20 divided by two

2x divided by two

x = 10

Answer: To solve the equation 2X = X + 5, we can start by isolating X on one side of the equation by subtracting X from both sides:

2X - X = X + 5 - X

X = 5

Therefore, X = 5 is the solution of the equation 2X = X + 5.

Step-by-step explanation:

The solution for x in the equation 2x = x + 5 is obtained by isolating the variable x, leading to the answer x = 5.

To solve for x in the equation 2x = x + 5, you need to isolate x. Start by subtracting x from both sides of the equation to get 2x - x = x + 5 - x which simplifies to x = 5.

The procedure used here is a standard method in algebra known as isolating the variable. This means the objective is to get the variable (x in this case) alone on one side of the equation.

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Answer:

Step-by-step explanation:

Writing Algebraic Expressions

Writing Algebraic Expressions

Group workProblem: Ms. Jensen likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.

Solution: Let g represent the number of groups in Ms. Jensen's class.

Then 2 · g, or 2g can represent "g groups of 2 students".

In the problem above, the variable g represents the number of groups in Ms. Jensen's class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number can vary (change). Let's look at an example in which we use a variable.

Example 1: Write each phrase as a mathematical expression.

Phrase Expression

the sum of nine and eight 9 + 8

the sum of nine and a number x 9 + x

The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.

Example 2: Write each phrase as an algebraic expression.

Phrase Expression

nine increased by a number x 9 + x

fourteen decreased by a number p 14 - p

seven less than a number t t - 7

the product of 9 and a number n 9 · n   or   9n

thirty-two divided by a number y 32 ÷ y   or    

In Example 2, each algebraic expression consisted of one number, one operation and one variable. Let's look at an example in which the expression consists of more than one number and/or operation.

Example 3: Write each phrase as an algebraic expression using the variable n.

Phrase Expression

five more than twice a number 2n + 5

the product of a number and 6 6n

seven divided by twice a number 7 ÷ 2n   or    

three times a number decreased by 11 3n - 11

bonusExample 4: A small company has $1000 to distribute to its employees as a bonus. How much money will each employee get?

Solution: Let e represent the number of employees in the company. The amount of money each employee will get is represented by the following algebraic expression:

electricianExample 5: An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day.

Solution: Let x represent the number of hours the electrician works in one day. The electrician's earnings can be represented by the following algebraic expression:

Solution: 45x - 20

Answer: 400 meters per minute.

Formula to find average speed: total time / total distance

Total time taken is 2+4+1+3 which is 10 minutes.

Total distance traveled is 4 kilometers.

(Unitary method)

In 10 minutes Marco runs 4 kilometers.

In 1 minute Marco will run 4/10 (0.4)kilometers.

Now to convert 0.4 kilometers to meters,multiply it by 1000.

0.4 * 1000 is 400 meters

so the final answer is he will run 400 meters in 1 minute.

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

Let's first define the terms and state the Secant-Tangent Segment Theorem.

1. Equation: A mathematical statement that shows the equality of two expressions.

2. Secant: A line that intersects a circle at two points.

3. Tangent: A line that touches a circle at only one point, without crossing it.

Secant-Tangent Segment Theorem: If a secant and a tangent are drawn from a point outside a circle, the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

Let's represent the given lengths as follows:
- Length of tangent segment = a
- Length of secant segment (inside the circle) = 12
- Length of the external part of the secant segment (outside the circle) = x

According to the Secant-Tangent Segment Theorem, the equation is:
(a)(a) = (12)(x + 12)

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

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The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:

Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly

Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$

Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter

Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}

Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09

Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

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The transformation of the graph f(x) = x² to the graph g(x) = -3(x+5)² + 12 involves a horizontal shift, a vertical stretch, and a vertical translation.

The graphs of f(x) = x² and g(x) = -3(x+5)² + 12 are the parabola.

The transformation of the graph is following as:

Firstly, the parabola has been shifted horizontally by 5 units to the left, which is reflected in the expression (x+5)².

Secondly, the parabola has been stretched vertically by a factor of -3, which is reflected in the coefficient in front of (x+5)².

Finally, the parabola has been raised up to 12 units. This means that the vertex of the parabola has been shifted upwards from the origin to the point (−5,12).

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.