How do I solve this problem??

The height and radius of the cup are 4.41 cm and 2.07 cm respectively

To minimize the amount of paper used, we need to minimize the surface area of the cup. Let h be the height and r be the radius of the cone. Then we have:
\(Volume of cone = \frac{1}{3}  πr^{2} h = 36 cm^{3}\)

Solving for h, we get:
\(h = \frac{108}{(πr^2)}\)

Now we can express the surface area of the cone as:
\(Surface area = πr^2+ πr\sqrt{r^{2}+h^{2}  }\)

Substituting the expression for h, we get:

\(Surface area = πr^2+πr \sqrt{(r^{2} +(\frac{108}{(πr^2)^{2}) } )}\)

To minimize this function, we take its derivative with respect to r and set it equal to zero:
\(\frac{d}{dx} (Surface area) =  \frac{2πr - 108r }{[(r^2+(\frac{108}{πr^2}))^{0.5}  }] - \frac{108π}{r^2 }  = 0\)

Simplifying, we get:
\(2r^3 - \frac{108^2}{π} = 0\)

Solving for r, we get:
\(r = (\frac{54}{π})^{\frac{1}{3} }\)

Substituting this value into the expression for h, we get:
\(h = \frac{108}{\frac{54}{π} ^{(\frac{2}{3}π )} }\)

Thus, the height and radius of the cup that will use the smallest amount of paper are:
height = 4.41 cm
radius = 2.07 cm (rounded to two decimal places)

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Answer:

The mean is the best measure of center because there are no outliers present.

Answer:

b or d

Step-by-step explanation:

igxgkztjsy,hfzfjzitzgmzfjztzutzjvahfzgkzjrJt

Answer:

A

Step-by-step explanation:

A mode is the value that appears most frequently in the data set because there is not more than one of any number the data set has no mode.

Here, we are required to determine the point where point H lie on the number line.

The point H is at point 2.5 on the number line.

The distance between point F and G on the number line is:

4 - (-2) = 6 numbers on the number line.

And since the ratio of FH to HG is 3:9

Therefore; FH/HG = (4 - x)/(x - (-2))

i.e 3/9 = (4 - x)/ (x +2).

By cross multiplication, 3x + 6 = 36 - 9x.

Therefore, 12x = 30

and, x = 2.5

Therefore, the point H is at point 2.5 on the number line.

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Answer:

2.5

Step-by-step explanation:

In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.

In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.

The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.

The values of all the variables associated with this basic feasible solution are:

x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.

Note that these values correspond to the entries in the tableau in the "BV" column.

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The missing tableau is in the image attached below

The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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Based on the calculations, the evaluation of the given mathematical expression is 44.5.

Given the following data:

To evaluate the given mathematical expression:

In this exercise, you're required to evaluate and solve the given mathematical expression by substituting the values of the variables as follows:

\(5 (8.4 - 2) + 10(1.25)\\\\5 (6.4 ) + 12.5\\\\32 + 12.5=44.5\)

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Answer:

Step-by-step explanation:

1. convert 2/7

2/7 = 6/21

2. convert 1/3

1/3 = 7/21

3. add 6/21 and 7/21

6/21 + 7/21 = 13/21

4. subtract 13/21 from 21/21

21/21 - 13/21 = 8/21

5. reduce

8/21 is already in the lowest form

Expand the mass of each:

Freight train: 9.98 x 10^6 = 9,980,000 kg

Aircraft carrier: 7.3x10^7 = 73,000,000 kg

Now subtract:

73,000,000 - 9,980,000 = 63,020,000 kg

Convert to scientific notation: 6.302 x 10^7 kg

Answer:

x° = 11°

Z FGI = 60°

Step-by-step explanation:

If GH bisects Z FGI

then Z FGH = Z HGI

or, (3x - 3)° = (4x - 14)°

or, 3x° - 4x° = - 14° + 3°

or, x° = 11°

Z FGI = 33° - 3° + 44° - 14°

= 60°

The interquartile range is a useful tool for measuring variability in a set of data because it overcomes the difficulty of the range being influenced too much by extreme values

The interquartile range is a measure of variability that is commonly used in statistics to describe the spread of a set of data. It is particularly useful because it overcomes the difficulty of the range being influenced too much by extreme values.

In mathematical terms, the interquartile range is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1).

The upper quartile represents the 75th percentile of the data and the lower quartile represents the 25th percentile of the data.

This means that 25% of the data falls below the lower quartile and 75% of the data falls above the upper quartile.

The interquartile range provides a better representation of the spread of the data because it eliminates the influence of extreme values.

These values, also known as outliers, can have a significant impact on the range and can make it appear as though the data is more spread out than it actually is.

By using the interquartile range, the outliers are excluded and a more accurate representation of the spread of the data is obtained.

Therefore, option (a) is correct.

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If the composite functions f(g(x)) and g(f(x)) both equal to x, then the function g is the Inverse function of f.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. 

Let us take the Example.

Suppose f(x)= x/4 and g(x)=4x.

Let x=1

then f(g(x))= f(g(1))=f(4)=1

and g(f(x))=g(f(1))=g(1/4)=1

Here, f(g(x))=g(f(x))=1

Therefore , we can say that f(g(x)) and g(f(x)) are inverse of each other.

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The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

42c

Step-by-step explanation:

The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

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Answer:

Today: Tuesday, 12th January 2021

21.16 PM

\( \tt 5x - 9 > 12\)

\( \tt 5x > 12 + 9\)

\( \tt 5x > 21\)

\( {\orange{\boxed{ \red{\tt x = \frac{21}{5} }}}}\)

The given relation 5x-9>12 represents inequality. the solution of inequality is x > ( 21 / 5).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequality, the relation is 5x-9>12. The solution to inequality be done as:-

5x - 9 > 12

5x > 12 + 9

5x > 21

x > 21 / 5

Therefore, the given relation 5x-9>12 represents inequality. the solution of inequality is x > ( 21 / 5).

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Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle , that is

3x + 2x + 6 + 6x - 3 ( simplify by collecting like terms )

= 11x + 3

Given the perimeter = 36 units , then

11x + 3 = 36 ( subtract 3 from both sides )

11x = 33 ( divide both sides by 11 )

x = 3

Then

base = 2x + 6 = 2(3) + 6 = 6 + 6 = 12 units

height = 3x = 3(3) = 9 units

hypotenuse = 6x - 3 = 6(3) - 3 = 18 - 3 = 15 units

Answer:

1134

Step-by-step explanation:

Table is a way to represent the data of the two or more variable.

The correct order for the ranks of the waves from the lowest energy wave to the highest energy wave of the given table is 1-4-3-2. Thus the option 1 is the correct option.

Table is a way to represent the data of the two or more variable.

To read the data from the table look for the value of one variable, and get the resultant value of other variable from the corresponding block.

Given information-

The first column labeled Wave has entries 1, 2, 3, 4.

The table given in the problem is,

First column                         Second column

  1                          This wave has 3 centimetre amplitude

  2                         The distance from the midpoint to the crest is 6 cm,

  3                         The distance from the midpoint to the trough is 12 cm,

  4                         This wave has a 4 centimetre amplitude.

The ranks of the waves from the lowest energy wave to the highest energy wave of the given table has to find out.

As the energy of a wave is related to the amplitude of the wave, as the how much amount of energy it is carrying with it.

The distance from the midpoint to the crest is called the amplitude.

Thus the more value of the amplitude gives the more energy.

Therefore,

Hence, the correct order for the ranks of the waves from the lowest energy wave to the highest energy wave of the given table is 1-4-3-2. Thus the option 1 is the correct option.

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Answer:

A

Step-by-step explanation:

Answer:

• (a)80 mg

• (c)f(t)=80(0.5)^t

• (d)0.625 mg

Explanation:

Part A

From the point (0, 80), we see that the person took 80 mg of the medicine at the start.

Part B

From the graph:

From points (0,80) and (2,20); and (2,20) and (4,5)

• After 2 hours, the amount of medicine has been reduced by a factor of 1/4.

Therefore, after 1 hour, the amount of medicine is reduced by a factor of 1/2.

The completed table is attached below:

Part C

An exponential function is written in the form:

Since the amount of medicine is halved every 1 hour:

The rate of decrease = 1/2

The starting amount, Ao = 80 mg

Therefore, an equation that defines f is:

Part D

After 7 hours, when t=7

After 7 hours, 0.625 mg of medicine remains in the person's body.

Answer:

1) The cost function, f(x) = 10,000 + x × 50

2) The expression for the inverse of the cost function is y = x/50 - 200

3) The domain is 10,000, 10,050, 10,100, ... . x ∈ 10,000+(n - 1)×50

4) The range is the set of whole numbers, W. y ∈ W

Step-by-step explanation:

The given information are;

The base fee for the Grand Ballroom = $2,000

The fee per guest = $50

The limit of their budget for the Grand Ballroom = $10,000

1) The cost function, f(x), for the number of guests, x is given as follows;

f(x) = 10,000 + x × 50

2) The expression for the inverse of the cost function is given as follows;

Let f(x) = y, we have;

y = 10,000 + x × 50

Therefore;

y - 10,000 = x × 50

x = (y - 10,000)/(50)

Interchanging the variables a and y in the above equation, gives;

y = (x - 10,000)/(50) = x/50 - 200

The inverse of the function is therefore, y = x/50 - 200

3) The domain is the set of possible input values to x which is given as follows;

The value y in the situation of the inverse = The number of guests, which is the set of whole numbers

Therefore, the domain, consists of the following numbers;

10,000, 10,050, 10,100, ... , 10,000+(n - 1)×50

Where;

n = The set of real numbers

4) The range is the set of whole numbers, W.

The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1) is (x + 1)² + (y - 1)² = 16.

We know that, the center of a circle is (-1, 1).

We know that, the standard form for an equation of a circle is

(x - h)² + (y - k)² = r²

The (h, k) are co-ordinate of your Centre of circle, which in this case is (-1,1) and r is the radius of circle.

As we can see in the figure radius = 4units

From Centre (1,-2) to (1,-2)

Put these into the equation

(x + 1)² + (y - 1)² = 4²

(x + 1)² + (y - 1)² = 16

Therefore, option D is the correct answer.

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4466.44444444

40198

/

9

The function f(x) has at most one relative extremum on the interval 2 < x < 4, based on the behavior of its derivative f'(x) = sin(x^2 + 1). Therefore, the correct option is a. One.

To determine the number of relative extrema of the function f(x) on the interval 2 < x < 4, we need to analyze the behavior of its derivative f'(x).

We have that f'(x) = sin(x^2 + 1), we need to examine where the derivative changes its sign within the interval (2, 4) to identify the relative extrema.

Since the sine function oscillates between -1 and 1, we can observe that sin(x^2 + 1) will also oscillate between -1 and 1 as x^2 + 1 varies.

However, since the interval (2, 4) is relatively small, the value of x^2 + 1 will not vary significantly, and the sine function will not complete multiple oscillations within this interval.

Therefore, there will be at most one sign change for sin(x^2 + 1) within the interval (2, 4), indicating that f(x) may have at most one relative extremum within this interval.

Hence, the correct answer is: a. One.

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In mathematics, a constant rate of change is a rate of change that stays the same and does not change.

Therefore, The exponential function approaches zero as the input approaches negative infinity, and as x increases towards infinity, the value of e−3x approaches zero.

(a) The right end behavior of y = log6(x) as x approaches infinity is that y approaches negative infinity. This is because as x increases towards infinity, the value of log6(x) becomes larger and larger negative values. Explanation: The logarithm function approaches negative infinity as the input approaches zero, and as x increases towards infinity, the value of log6(x) approaches negative infinity.
(b) The right end behavior of y = e−3x as x approaches infinity is that y approaches 0. This is because as x increases towards infinity, the exponent -3x becomes larger and larger negative values, making the value of e−3x approach zero.  

Therefore, The exponential function approaches zero as the input approaches negative infinity, and as x increases towards infinity, the value of e−3x approaches zero.

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The probability that it rains at least one of the days is 40%.

Given data :

Let D1 = the event that it will rain on today

D2 = the event that it will rain on tomorrow.

P(D1) = 40% = 0.4

P(D2) = 40% = 0.4

The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N.

P(D1) + P(D2) / 2 = 0.4 + 0.4 = 0.8 / 2 = 0.4 = 40%

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.

Oh please help me i don't know how to do it

Answer:

A and D

Answer:

  y = 900(0.91^t)

Step-by-step explanation:

You want a function that describes the value of a $900 sound system that decreases in value by 9% per year.

When the amount of change is proportional to the amount, the amount is described by an exponential function:

  y = ab^x

where 'a' is the initial value, and 'b' is the "growth factor."

Here, the change is expressed as a "growth rate" of -9% per year. The growth factor is 1 added to the growth rate:

  b = 1 +(-9%) = 1 -0.09 = 0.91

The initial value is given as ...

  a = 900

So the function you want is ...

  y = 900(0.91^t)

__

Additional comment

The independent variable in this case is time, and the problem statement tells you to use 't' to represent it. The decay rate is given as a percentage per year, so the units of t will be years.