Coal gas is produced at a gasworks. Pollutants in the gas are removed by scrubbers, which become less and less efficient as time goes on. The following measurements, made at the start of each month, show the rate at which pollutants are escaping (in tons/month) in the gas: Time (months) 0 1 2 3 4 5 6 Rate 5 7 9 14 22 31 40 A. Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first month. overestimate

Answer:

Step-by-step explanation:

Base perimeter: 5 x 2 x π = 10π

LA = 10π x 2 = 20π

Base area : 5^2π = 25π

SA = 25π x 2 + 20π = 70π

V : 25π x 2 = 50π

Answer:

D) -4 (with imaginary roots ±2i)

Step-by-step explanation:

Since you cannot take the square root of a negative number to produce a real result, the only option that has two imaginary roots is D) -4, where the two imaginary roots are 2i and -2i.

Answer:

360 mi^3

Step-by-step explanation:

The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values

solid  1

length = 11 - 4 = 7 mi

base area = length x width = 7 x 4 = 28 mi^2

V = base area x height = 28 x 6 = 168 mi^3

solid 2

base area = 8 x 4 = 32 mi^2

V = 32 x 6 = 192 mi^3

total volume: 168 + 192 = 360 mi^3

The volume of the figure is 360 mi³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a figure where two rectangular boxes are put on top of each other.

Volume of a rectangular prism = L × W × H

Here L is the length, W is the width and H is the height.

The dimensions of the rectangular prism are :

Larger one having L = 11 mi, W = 6 mi and H = 4 mi

Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.

Volume of the figure = volume of larger box + Volume of smaller box

                                  = (11 × 6 × 4) + (4 × 6 × 4)

                                  = 264 + 96

                                  = 360 mi³

Hence the volume of the figure is 360 mi³.

Learn more about Volume here :

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Answer:

140 Large sized drinks were sold last month

Step-by-step explanation:

Each large drink is sold at $3

Therefore, we divide the amount of money which is $420 by $3

  = $420 ÷ $3 = 140 Large sized drinks

Answer:

[tex]Height=\boxed{10\sqrt{2}} [/tex]

[tex] Area =\boxed{165\sqrt{2}} [/tex]

Step-by-step explanation:

By geometric mean theorem:

[tex] AC=\sqrt{25\times 8}[/tex]

[tex] AC=\sqrt{5^2 \times 2^2 \times 2}[/tex]

[tex] AC=5\times 2\sqrt{2}[/tex]

[tex] AC=10\sqrt{2}[/tex]

So,

[tex]Height=\boxed{10\sqrt{2}} [/tex]

[tex] Area = \frac{1}{2} \times base\times height [/tex]

[tex] \therefore Area = \frac{1}{2} \times (25+8)\times 10\sqrt{2} [/tex]

[tex] \therefore Area =33\times 5\sqrt{2} [/tex]

[tex] Area =\boxed{165\sqrt{2}} [/tex]

Answer:

1. wire is approx. 143.96 ft

2. pole is approx. 106.55 ft

Step-by-step explanation:

Mapping the information on the SOHCAHTOA picture below:

Φ = 46

wire = hypotenuse

adjacent side = 100

CAH is most suitable:

cos 46° = 100/wire => wire = 100/cos 46 ≈ 143.96

pole = opposite side + 3

TOA is most suitable:

tan 46° = (pole-3)/100 => pole = 3 + 100 * tan 46 ≈ 106.55

Answer:

20 Edges

Step-by-step explanation:

As this figure shows only 10 edges..so to meet the given condition (8 faces; 4 hexagons & 4 triangles) same figure is present at the back making total of 20 Edges.

Answer:

x-1/8y^2=0

Step-by-step explanation:

just took the test

Answer:

[tex]A=110.5\pi \ inches^2[/tex]

Step-by-step explanation:

Given that,

The slant height of a cone, l = 17 inches

The diameter of a cone, d = 13 inches

Radius, r = (D/2) = 6.5 inches

We need to find the lateral surface area of a cone. The formula for the lateral surface area of a cone is given by :

[tex]A=\pi rl[/tex]

Put all the values,

[tex]A=\pi \times 6.5\times 17\\\\A=110.5\pi \ inches^2[/tex]

So, the lateral surface area of the cone is equal to [tex]110.5\pi \ inches^2[/tex].

Answer:

B 110.5

Step-by-step explanation:

Answer:

1920 cm

Step-by-step explanation:

You multiply the values together. 8 times 20 times 12 is equal to 1920 cm.

Answer:

there are 6 outcomes

Step-by-step explanation:

there are only 6 spots, therefore it has to be 6

Answer:

The answer would be B  [tex]120ft^{3}[/tex]

Step-by-step explanation:

volume of triangular prism is 30 and volume of the cube is 90 :)

Answer:

The weight unit is 200 pounds per tire

Answer:

40

Step-by-step explanation:

24^2+32^2=c^2

square root of 1600 is 40

Answer:40

Step-by-step explanation:Because

a^2 + b^2=c^2

Answer:

how about no

Step-by-step explanation:

did anyone ask

Answer:

B

Step-by-step explanation:

s>t because s is on top of the scale and t is below the scale

Answer:

b.g(x)=[tex]x^{2}[/tex]+3

Step-by-step explanation:

If two graphs have the same shape and you only want to change one's y intercept, you just have to add or subtract the number at which you want the graph to intercept the y axis from the equation

Answer:

As can be seen, there has been a rise in the proportion of the population with HIV positive, from 7.5% to 9.94%.

Step-by-step explanation:

Given that a national organization sets out to investigate the change in prevalence of HIV since the last census in 2010, ya total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive, assuming that the data from the census indicated that the prevalence of HIV in the particular population was 7.5%, to determine if the proportion of the prevalence of HIV has changed (is equal to 7.5%) the following calculation should be performed:

4706 = 100

468 = X

468 x 100/4706 = X

46,800 / 4,706 = X

9.94 = X

Therefore, as can be seen, there has been a rise in the proportion of the population with HIV positive, from 7.5% to 9.94%.

Answer:

Option (4)

Step-by-step explanation:

From the table attached,

Ratio of spores in day 2 and day 1 = [tex]\frac{400}{200}[/tex]

                                                         = 2

Ratio of spores in day 3 and day 2 = [tex]\frac{800}{400}[/tex]

                                                          = 2

There is a common ratio of 2 in each successive to the previous term of the Mold spores.

Therefore, spores are growing exponentially.

Let the function representing exponential function is,

y = a(b)ˣ

Here, y = Number of spores after time 'x'

x = Number of days

a and b are the constants.

On day 1,

x = 1

y = 200

By substituting these values in the exponential function,

200 = a(b)¹

ab = 200 -------(1)

On day 2,

x = 2

y = 400

400 = a(b)² -------(2)

Divide equation 2 by equation 1,

[tex]\frac{400}{200}=\frac{ab^{2} }{ab}[/tex]

b = 2

By substituting the value of b in equation (1),

a(2) = 200

a = 100

Therefore, equation of the function will be,

y = 100(2)ˣ

Option (4) will be the answer.

Answer:

3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(10-4)/(7-5)

m=6/2

m=3

Answer:

A. 3

Step-by-step explanation:

I just did it on a calculator and got it correct

9514 1404 393

Answer:

  (b)  x +2y = 8

Step-by-step explanation:

The only offered line that includes the given point is ...

  x +2y = 8

__

We can check the other choices:

  x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)

  2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice

_____

Getting there from scratch

The standard form equation for a line can be written from ...

  (y2 -y1)x -(x2 -x1)y = constant

  (-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)

  -4x -8y = constant

For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.

  x +2y = constant

The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...

 x +2y = (2) +2(3) = constant = 8

The desired line has the equation ...

  x +2y = 8

Answer:

B on edge

Step-by-step explanation:

Answer:

H = independent variable

S = dependent variable

Step-by-step explanation:

number of hamburgers sold isnt affected by other factors

sales taken in depend on Hamburgers sold

Answer:

divide by avagadro number to get the amount of moles in the atoms you have

Answer:

x=8, 3

Step-by-step explanation:

24 has 8 factors: 1,2,3,4,6,8,12,24

8 and 3 make 11

If you factor it out, the equation is (x-8)(x-3)=0

to get 0, only one of the expressions has to equal 0

so x can have 2 different values

9514 1404 393

Answer:

  x = 30

Step-by-step explanation:

The sum of exterior angles of a convex polygon is 360°. Here, that means ...

  3x° +x° +2x° +2x° +4x° = 360°

  12x = 360

  x = 360/12 = 30

The value of x is 30.

Answer:

Sum of all angles = 360⁰

[tex] \to \sf \: 2x + 2x + x + 4x + 3x = 360[/tex]

[tex] \to \: 12x = 360[/tex]

[tex] \to \: x = \dfrac{360}{12} [/tex]

[tex] \sf \: x = 30[/tex]

Answer:

First question: LCL = 522, UCL = 1000.5

Second question: A sample size no smaller than 418 is needed.

Step-by-step explanation:

First question:

Lower bound:

0.36 of 1450. So

0.36*1450 = 522

Upper bound:

0.69 of 1450. So

0.69*1450 = 1000.5

LCL = 522, UCL = 1000.5

Second question:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The project manager believes that p will turn out to be approximately 0.11.

This means that [tex]\pi = 0.11[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The project manager wants to estimate the proportion to within 0.03

This means that the sample size needed is given by n, and n is found when M = 0.03. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.11*0.89}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.11*0.89}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.11*0.89}}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.11*0.89}}{0.03})^2[/tex]

[tex]n = 417.9[/tex]

Rounding up

A sample size no smaller than 418 is needed.

Answer:13+4(n-1)

Step-by-step explanation:

Answer:

$16 is correct answer

Hope it helps you