Solid metal support poles in the form of right cylinders are made out of metal with a density of 5.4 g/cm^3. This metal can be purchased for $0.71 per kilogram. Calculate the cost of a utility pole with a radius of 17.8 cm and a height of 700 cm. Round your answer to the nearest cent. (Note: the diagram is not drawn to scale)

Note that:

 a) 1 unit  of   agricultural production required to obtain 1 agricultural product.

b) 200,000 units of agricultural production are required to obtain 1 of agricultural product.

c) 22,727 units of agricultural production are required to obtain 50,000 units of energy.

d) we need 27,825 units of energy to produce 50,000 units of agricultural products.

a) According to the table, the coefficient of production for agriculture is 0.293, that is

0.293 units of agricultural production = a unit of agricultural product.

b) To obtain 200,000 units of agricultural products we say

0.293 x 200,000,=  58,600 units of agricultural production.

c) the coefficient of production for energy with respect to agriculture is 0.044,

that is ,

0.044 units of agricultural production = a unit of energy.

So

50,000 units of energy,=

0.044 by 50,000,

= 2,200 units of agricultural production.

d) To obtain 50,000 units of agricultural products

use the Leontief inverse of the input-output table, which is simply the inverse of the coefficient matrix.

      [ 3.4175  -0.2345  -0.5565 ]

       [-0.1894   4.8264  -0.2114 ]

       [-0.3074   0.1772   4.8324 ]

       [ (3.4175  x0) +   (-0.2345 x 0) + (-0.5565  x 50,000)  ]

       [ (-0.1894   x0) + (4.8264x 0) + (-0.2114  x50,000) ]

       [ (-0.3074   x0) + (0.1772  x0) + (4.8324  x50,000) ]

       [ -27,825 ]

       [ -10,570 ]

       [ 241,620 ]

Thus, we need 27,825 units of energy to produce 50,000 units of agricultural products.

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The possible values of x, given the number of bets are $54,999, $14,999, and -$1.

The expected winnings would be -$0.97.

The possible values of the net winning would be the amount you win at net if you win first prize, second prize, or nothing.

The possible values would therefore be:
$54,999, $14,999, and -$1.

These show that if you win the first or second prize, you will deduct the $ 1 you bet. And if you win nothing, you would have lost $ 1.

The expected winnings would be:

= ∑ ( Probability of event x Potential net win / loss)
= ( 1 / 3, 000, 000 x 54, 999 ) + ( 2 / 3, 000, 000 x 14, 999 ) + ( 2,999, 997 / 3, 000, 000 x - 1 )

= - $ 0.97

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Answer:

70%

Step-by-step explanation:

63 / (63+27)

63 / 90 = 0.7

Turn 0.7 into a fraction, 70 under 100

Then rewrite the fraction 70 under 100 to 70%

Since on average, 66% of the days in Seattle, Washington, are cloudy or rainy, a model that could be used to simulate this situation is an experimental probability model of about 2/3.

In this scenario and exercise, you are to required to describe a model that you could be used to simulate a situation in which 66% of the days in Seattle, Washington, are cloudy or rainy on an average.

In this context, we can reasonably infer and logically deduce that the most accurate and feasible model to use would be an experimental probability model of about 2/3;

66% = 66/100 = 33/50 ≈ 2/3.

In conclusion, you should select two (2) red marbles that each represent cloudy or rainy days and one (1) blue marble that represent non-cloudy or non-rainy days, and then pick one marble randomly. Repeat several times in order to determine experimental probability that a day would either be cloudy or rainy.

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Answer:

(x + 4)/x^2 - 8x)

Step-by-step explanation:

The four math sentences that have an answer of 2.4 are 1.2 + 1.2, 1.2 * 2, 3.6 - 1.2 and  4.8/2

From the question, we have the following parameters that can be used in our computation:

An answer of 2.4

Using a different operation in each sentence., we have the following math sentences

1.2 + 1.2

1.2 * 2

3.6 - 1.2

4.8/2

The solution to each of the above sentences is 2.4

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The amount of soil to fill the garden box is V = 1,134 inches³

Given data ,

Let the volume of the first rectangular box be V₁

Let the volume of the second rectangular box be V₂

where Volume of Rectangle = Length x Width x Height

So , V₁ = 21 x 7 x 2

V₁ = 294 inches³

And , V₂ = 12 x 10 x ( 7 )

V₂ = 120 x 7

V₂ = 840 inches³

And , the total soil in the garden box = V₁ + V₂

Amount of soil in garden box = 1,134 inches³

Hence , the volume is V = 1,134 inches³

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A) Maxine calculated the total mass of pH powder sold on day 1 by evaluating the algebraic expressions for small and large container sales.

B) If the variable s represents the number of containers sold, the value of the algebraic expression 0.75s represents the total mass of pH powder sold each day.

C) The algebraic expression to represent the mass (in kilograms) of powder sold in large containers daily is 1.25l.

D) The algebraic expression to show how Maxine calculated the total mass of pH powder sold on day 1 is 0.75s + 1.25l, which is evaluated to be 49.25 kg.

E). Using the algebraic expression, the total mass of powder sold on Day 2 and 3 is as follows:

An algebraic expression is a combination of of variables and constants, together with mathematical operands (addition, subtraction, division, and multiplication, etc.).

pH Plus Power Sales

Day       # of small containers    # of large containers    Total Mass

                    (0.75 kg)                            (1.25 kg)              (Kilograms)

Day 1               14                                       31                        49.25 kg

Day 2              19                                      42                        66.75 kg

Day 3             24                                      28                        53.00 kg

Let the number of small containers sold = s

Let the number of large containers sold = l

The mass of a small container = 0.75 kg

The mass of a large container = 1.25 kg

Total mass of small containers sold daily  = 0.75s

Total mass of large containers sold daily = 1.25l

Total mass of small and large containers sold daily = 0.75s + 1.25l

Day 1 = 0.75(14) + 1.25(31) = 49.25 kg

Day 2 = 0.75(19) + 1.25(42) = 66.75 kg

Day 3 = 0.75(24) + 1.25(28) = 53.00 kg

pH Plus Power Sales

Day       # of small containers    # of large containers    Total Mass

                    (0.75 kg)                            (1.25 kg)              (Kilograms)

Day 1               14                                       31                        49.25 kg

Day 2              19                                      42

Day 3             24                                      28

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Only afford a home with a market value of about $375,000, and she would require a down payment of $75,000 to do so.

First, we have to ascertain how much Kelly can comfortably afford to pay for her mortgage each month. Her income, expenses, and other financial commitments will determine this. Her monthly mortgage payment should not be more than 28% of her total monthly income, on average.

The loan is interest rate is the next thing we need to think about. Kelly will have a constant monthly payment for the duration of the loan thanks to a 30-year fixed rate loan at the current market rate of 4.25%.

With a 20% down payment and a loan with a 4.25% interest rate, we could be calculate the maximum purchase price to be roughly $375,000 using a mortgage calculator.

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Answer:

a)

[tex] log_{7}(3) - log_{7}(5) = log_{7}( \frac{3}{5} ) [/tex]

b)

[tex] log_{3}(11) + log_{3}(2) = log_{3}(22) [/tex]

c)

[tex] - 4 log_{8}(3) = log_{8}( {3}^{ - 4} ) = log_{8}( \frac{1}{ {3}^{4} } ) [/tex]

The angle in radians in simplest form is 7π/4 radians.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

By substituting the given parameters into the arc length formula, we have the following;

7π/2 = 2 × θ

θ = 7π/4 radians.

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The step that indicates the addition property of equality while solving the equation -1 - 6x = x - 15 is : (b) -1 - 6x + 15 = x - 15 + 15.

The "addition-property" of equality states that if we add the same quantity to both sides of an equation, the equation remains true.

In the equation -1 - 6x = x - 15, we need to isolate the variable term 'x'.

To isolate variable "x",  we are adding 15 to both sides of the equation, which is the addition property of equality. This step simplifies the equation and isolate the variable "x" on one side.

So, we get,  -1 - 6x + 15 = x - 15 + 15,

Therefore, the correct step indicating the "addition-property" is (b).

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The given question is incomplete, the complete, the complete question is

Which of the following steps indicates the addition property of equality while solving the equation -1 - 6x = x - 15?

(a) x = 14/2

(b) -1 - 6x + 15 = x - 15 + 15

(c) -1 - 6x = x - 15

(d) 23 - 6x - 24 = x - 15

The value of x is given as follows:

x = 13.1 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

We have that the important parameters are given as follows:

Hence the value of x is obtained as follows:

sin(57º) = 11/x

x = 11/sine of 57 degrees

x = 13.1 ft.

The triangle is given by the image presented at the end of the answer.

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The strategies that Alondra can use to complete the statement include:

When a decimal number is created by Alondra and possesses 4 or more in the tenths place, it will exceed 4.3, as stated to exemplify decimals including 4.31 or 4.32.

Similarly, if there are 3 units plus a greater number appended behind the second digit after the decimal point (hundredths place). Deriving an outcome extending further than 4.30 can occur for any value above that obtained from inputting the numbers 4 and 3 into their respective positions in a given sequence.

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Answer: f(x)=x-2

Step-by-step explanation:

Linear function means a straight line, so graph each one to find which is a straight line

The correct statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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The elevations of four locations.

Hence, the correct option is C.

Based on the elevation

Therefore, New Orleans has a lower elevation than Death Valley.

Hence, the correct option is C.

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Answer:

6 × 3 = 18

18 ÷ 2 = 9

Therefore, the expression 6 × 3 ÷ 2 simplifies to 9

Step-by-step explanation:

To simplify the expression, we follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right.There

are no parentheses or exponents,so we multiply 6 by 3 to give us 18.

Then we divide 18 by 2 to give us 9.

There for the Expression simplifies to 9.

HOPE IT HELPS.

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All the four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon are,

⇒ (1, 5) (2, 10) (3, 15) (4, 20)

Given that;

Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter.

Now,

Here are four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon:

⇒ (1, 5) (2, 10) (3, 15) (4, 20)

Hence, In each pair, the first number represents the side length of the pentagon, and the second number represents the perimeter of the pentagon.

And,  If you add 1 to the side length in each pair, you'll see that the perimeter increases by 5, just as Fernando learned in math class.

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Answer:

poor photo quality.

Step-by-step explanation:

The equation r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8 to rectangular form is (x - 1)² + y² = 9

From the question, we have the following parameters that can be used in our computation:

r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8

The above equation is in its polar form, where

r² = x² + y²

cos(θ) = x/r

sin(θ) = y/r

Rearrange the terms in r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8

So, we have

r²cos²(θ)  + r²sin²(θ) - 2rcos(θ) = 8

Factorize

r²(cos²(θ)  + sin²(θ)) - 2rcos(θ) = 8

In trigonometry

cos²(θ)  + sin²(θ) = 1

So, we have

r² - 2rcos(θ) = 8

Recall that

r² = x² + y²

cos(θ) = x/r

So, we have

x² + y² - 2r * x/r = 8

Evaluate

x² + y² - 2x = 8

Rearrange

x²  - 2x + y² = 8

Express as perfect squares

(x - 1)² + y² = 8 + 1

So, we have

(x - 1)² + y² = 9

Hence, the equation to rectangular form is (x - 1)² + y² = 9

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The formula for the inverse function h⁻¹(P) is:

The population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is approximately 17.5 days.

To find the inverse function h⁻¹(P), we need to solve the equation P = h(t) for t in terms of P.

Starting with P = h(t) = [tex]100/1+4e^-^0^.^0^5^t[/tex]

we can first multiply both sides by [tex]1+4e^-^0^.^0^5^t[/tex] to get:

[tex]P(1+4e^-^0^.^0^5^t) = 100[/tex]

t = -20ln(4/(P-100)+1)

Therefore, the formula for the inverse function h⁻¹(P) is:

h⁻¹(P) = -20ln(4/(P-100)+1)

(b) To find h⁻¹(90)

we substitute P = 90 into the formula for h^-1(P):

h⁻¹(90) = -20ln(4/(90-100)+1)

= 17.5

This means that if the population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is  17.5 days.

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When the y-value starts to decrease and the x-value remains constant over time, Y decreases and X increases to a consistent slope.

A consistent slope represents a constant rate of change between two variables, typically represented by the ratio of the change in y to the change in x.

When the y-value starts to decrease and the x-value remains the same over time, the consistent slope represents a negative correlation between y and x.

This means that as the value of y decreases, the value of x remains the same or may increase, depending on the context of the problem.

Therefore, the answer is option B: Y decreases and X increases.

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Step-by-step explanation:

Exponetial (compounding ) growth

  New Price = original price ( 1 + .10)^n      n is months  .10 is 10% per month

                     = $  110 ( 1.10)^3 = $ 146 . 41   three months later

A type of association that is seen between the age and height of the children include the following: C. positive linear association.

In Mathematics and Statistics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values (age) and y-values (height) because they both increase simultaneously.

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Using the sine ratio, the value of p in the right triangle, in simplest form is: p = 4.

To find the value of p, we have to determine what formula to use. We would apply the sine ratio, which is:

sin ∅ = opposite side / hypotenuse.

From the right triangle in the diagram, we have:

sin 30 = p / 8

p = sin 30 * 8

Note: sin 30 = 1/2

Therefore, we have:

p = 1/2 * 8

p = 4

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The picture for reduction and enlargement is attached

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying. while that of decrease is reduction.

The drawing of the the reduction is a square of side 8 units. The scale factor given is 1/2 hence we have the dimensions are as follows

preimage: 8 units x 8 units

image: 4 units x 4 units

The drawing of the the enlargement is a circle of radius 2 units. The scale factor given is 2, hence we have the dimensions are as follows

preimage: radius = 2 units

image: radius = 4 units

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The fraction in factored form is determined as  (x - 8)(x + 10) / (x - 10)(x + 8).

The quotient of the division is calculated as follows;

( x² - 3x - 40 )/ (x² + 8x - 20) ÷ (x² + 13x + 40)/(x² + 12x + 20)

Factorize each of the expressions;

x² - 3x - 40

= x² + 5x - 8x - 40

= x(x + 5) - 8(x + 5)

= (x + 5)(x - 8)

x² + 8x - 20

= x² + 2x - 10x - 20

= x(x + 2) - 10(x + 2)

= (x + 2)(x - 10)

x² + 13x + 40

=  x² + 5x + 8x + 40

= x(x + 5) + 8(x + 5)

= (x + 5)(x + 8)

x² + 12x + 20

=  x² + 2x + 10x + 20

= x(x + 2) + 10(x + 2)

= (x + 2)(x + 10)

The fraction in factored form is written as;

(x + 5)(x - 8)/(x + 2)(x - 10) ÷ (x + 5)(x + 8)/(x + 2)(x + 10)

(x + 5)(x - 8)/(x + 2)(x - 10)  x  (x + 2)(x + 10)/(x + 5)(x + 8)

= (x - 8)(x + 10) / (x - 10)(x + 8)

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Answer:

[tex] \frac{4}{5} [/tex]