Which is the best definition of an exterior angle of a triangle

A cylindrical tin boiler of volume 2000 cm³ is provided with a copper bottom and is open at the top.

Given that the cost of sheet copper is six times as expensive as sheet tin per square centimeter, we have to find the most economical dimensions (height and radius) for constructing the boiler.

In order to find the most economical dimensions, we have to minimize the cost of sheet material for a given volume of the boiler. Let r and h be the radius and height of the cylindrical boiler, respectively.

The surface area of the copper bottom of the cylindrical boiler is πr², and the surface area of the cylindrical side of the boiler is 2πrh.

The total surface area of the cylindrical boiler is πr² + 2πrh.

The volume of the cylindrical boiler is πr²h, which is equal to 2000 cm³.

The given cost ratio of sheet copper and sheet tin per square centimeter is 6:1.

The cost of the sheet material for the cylindrical boiler is directly proportional to the total surface area.

The cost of sheet copper per square centimeter is 6 times that of sheet tin. Therefore, the cost of sheet copper per unit surface area is 6 times that of sheet tin, which can be expressed as C = 6T. Where C and T denote the cost per unit surface area of copper and tin, respectively.

Let k be the constant of proportionality, then we have C = kπr² + 2kπrh and T = kπr² + 2kπrh / 6.

By substituting the value of C in the above equation, we get T = kπr² + 2kπrh / 36.

Using the volume constraint r²h = 2000/π, we can rewrite T as T = (2000k/πr) + 2kπr² / 36.

Now, differentiating T with respect to r and equating it to zero, we get:

r = 5h/3.

Substituting the value of r in the volume constraint equation, we get h³ = 2000π / 75.

Substituting the value of h in the expression of r, we get r = \(5/3 (2000/\pi  * 75)^1/3\).

The value of r is\((2000/π)^1/3 × (25/9)^1/3\).

The cost of copper sheet C = 6T can be written as C = \((5k/\pi )^1/3 × (2000/\pi )^2/3 * 25^1/3\).

Therefore, the most economical dimensions of the cylindrical boiler are r = 4.3914 cm and h = 17.2918 cm. The value of C at these dimensions is 6 × 26.722 = 160.332. The solution is verified as the volume of the boiler is πr²h = 2000 cm³. Hence, this solution is the minimum value of cost, and hence the answer is a minimum value. Solving algebraically methods of calculus, we get the most economical dimensions of the cylindrical boiler as r = 4.3914 cm and h = 17.2918 cm. Therefore, the value of the total surface area of the cylindrical boiler is 175.32 cm², and the cost of sheet copper is Rs. 160.332.

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Answer:

$9

Step-by-step explanation:

We know

They start at 10:15 and end at 11:45. It is 1 hour 30 minutes long.

1 hour 30 minutes = 90 minutes

The boat rental costs $1.50 for every 15 minutes.

How much will they pay?

We Take

90 divided by 15, then time 1.50 = $9

So, they pay $9

Answer:

Scott and Tom will pay a total of $9 for the boat rental.

Step-by-step explanation:

If Scott and Tom rent the boat between 10:15 and 11:45, then the total time they rented the boat is 1 hour and 30 minutes.

To convert 1 hour and 30 minutes to units of 15 minutes, we can divide the total number of minutes by 15:

⇒ 1 hour = 60 minutes

⇒ 1 hour and 30 minutes = 60 + 30 = 90 minutes

⇒ 90 minutes / 15 minutes = 6

Therefore, there are 6 units of 15 minutes in 1 hour and 30 minutes.

Given the cost for renting the boat is $1.50 per 15-minute interval, the total cost for renting the boat is:

⇒ 6 × $1.50 = $9

Therefore, Scott and Tom will pay $9 for the boat rental.

A random sample of approximately 1067 registered voters is needed to estimate the proportion of voters planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

To estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a

margin of error no greater than 0.03, we need to determine the sample size. We can use the following formula for

sample size calculation:

\(n = (Z^2 × p × (1-p)) / E^2\)
Where:
- n is the sample size
- Z is the Z-score (1.96 for 95% confidence)
- p is the estimated proportion of voters planning to vote for Chavez
- E is the margin of error (0.03 in this case)

Since we don't know the true proportion of voters planning to vote for Chavez, we can use the most conservative

estimate (p = 0.5) to ensure the required margin of error:

\(n = (1.96^2 × 0.5 × (1-0.5)) / 0.03^2\)
n = (3.8416 × 0.25) / 0.0009
n = 0.9604 / 0.0009
n ≈ 1067

Therefore, a random sample of approximately 1067 registered voters is needed to estimate the proportion of voters

planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

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The pH of the resulting solution, obtained by diluting 10 ml of the acidic solution to a final volume of 1000 ml, is 6.

The dilution equation states that the concentration of a solute remains constant when the volume of the solution changes.

Since the dilution factor is

1000 ml / 10 ml = 100

The concentration of H+ ions in the resulting solution is 1/100 times the concentration in the original solution.

The pH scale is logarithmic, meaning that each whole pH unit represents a tenfold change in the concentration of H+ ions.

Since the pH of the original solution is 4, which represents a concentration of 10^(-4) mol/L, the concentration of H+ ions in the resulting solution is 1

0^(-4) mol/L / 100 = 10^(-6) mol/L.

To calculate the pH of the resulting solution, we take the negative logarithm base 10 of the concentration:

pH_result = -log10(10^(-6))

= -(-6) (logarithm property)

= 6

Therefore, the pH of the resulting solution, obtained by diluting 10 ml of the acidic solution to a final volume of 1000 ml, is 6.

The dilution process has decreased the concentration of H+ ions, resulting in a less acidic solution with a higher pH value.

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Answer:

3.

Step-by-step explanation:

The mode is what number appears the most. Hope this helps!

Answer:

x-17/2

Step-by-step explanation:

here, we can set the number to x

the question is asking for 2(x-7)=3

let's solve this by distributing

2x-14=3

2x=17

x=17/2

Answer: 2 (x - 7) = 3

Use the distributive property: 2x - 14 = 3

2x - 14 = 3 + 14

2x = 17

2x/2 = 17/2

x = 8.5

Answer:

Cos P

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

To solve this problem, we can use the principle of inclusion-exclusion.
First, let's consider the total number of n digit ternary sequences. For each digit, we have 3 choices (0, 1, or 2), so the total number of n digit ternary sequences is 3^n.

Next, let's consider the number of n-digit ternary sequences in which no pair of consecutive digits are the same. To construct such a sequence, we can start with any digit (3 choices), and then for each subsequent digit, we must choose a different digit than the previous one (2 choices). Therefore, the number of n digit ternary sequences in which no pair of consecutive digits are the same is 3 x 2^(n-1).

Finally, to find the number of n digit ternary sequences in which at least one pair of consecutive digits are the same, we can use the principle of inclusion-exclusion. We want to subtract the number of n digit ternary sequences in which no pairs of consecutive digits are the same from the total number of n digit ternary sequences. However, if we simply subtract these two values, we will have double-counted the sequences in which there are two (or more) pairs of consecutive digits that are the same. So we need to add back in the number of sequences in which there are two (or more) pairs of consecutive digits that are the same, and so on.

The formula for the number of n digit ternary sequences in which at least one pair of consecutive digits are the same is:

3^n - 3 x 2^(n-1) + 3 x 2^(n-2) - 3 x 2^(n-3) + ... + (-1)^(n-1) x 3

So, for example, if n = 4, the number of n digit ternary sequences in which at least one pair of consecutive digits are the same is:

3^4 - 3 x 2^(4-1) + 3 x 2^(4-2) - 3 x 2^(4-3) = 81 - 24 + 12 - 6 = 63.

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Answer:

c

Step-by-step explanation:

atom is a particle of matter that uniquely defines a chemical element. An atom consists of a central nucleus that is surrounded by one or more negatively charged electrons. The nucleus is positively charged and contains one or more relatively heavy particles known as protons and neutrons.

Answer:

in △abc, the sides ab and ac are produced to ∠p and ∠q respectively. if the bisectors of ∠pbc and ∠qcb intersect at a point o. prove that ∠boc = 90 - ½ ∠a.

Answer:

11 degrees Fahrenheit

Step-by-step explanation:

-2 + 13 = 11

Answer:

11°F

Step-by-step explanation:

Answer: 6x+10

Step-by-step explanation:

honestly i looked it up hope it helps:)

Answer:

3

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The lateral area of the cylinder is given by the formula ...

  LA = 2πrh = πdh . . . . . . where h is the height, r is the radius, d is diameter

Here, the diameter is given as 8 mm, and the height is shown as 12 mm. Then the lateral area is ...

  LA = π(8 mm)(12 mm) = 96π mm² . . . . lateral area

__

The total surface area adds the areas of the circular bases to the lateral area:

  TSA = 2(πr²) +LA

  TSA = 2(π(4 mm)²) + 96π mm² = 128π mm² . . . . total surface area

__

We have provided two answers because you have asked two questions. Your text asks for the total area; the picture asks for lateral area.

A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is

Given n(sample size) = 84

Population mean(μ) = 180

Standard Deviation(σ) = 36

Standard error of the mean = σx-bar = σ/√n = 36/√84 = 36/9.165 = 3.927

Standardizing the sample mean we have

Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n

x-bar = 180

Z(x-bar=185 at point C) = (185 - 180)/3.927 = 5/3.927 = 1.273

Z(x-bar=181 at point D) = (181 - 180)/3.927 = 1/3.927 = 0.254

The area ABCD is the probability that the sample mean will lie between 181 and 185.

The shaded Area ABCD = (Area corresponding to Z = 2 or x-bar = 185) - (Area corresponding to Z = 1 or x-bar = 181)

Area corresponding to Z = 1.273 = 0.898

Area corresponding to Z = 0.254 = 0.598

The shaded Area ABCD = 0.898-0.598 = 0.300

Therefore the probability that the sample mean will lie between 181 and 185 is 0.300.

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Having 1 as an exponent does nothing to the original number.

2/3^1 = 2/3

Best of Luck!

Answer:

\(\frac{2}{3}\)

Step-by-step explanation:

Anything to the power of 1 is itself.

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

If a number is to the power of 2, it multiplies itself and there are two 8 terms.

\(8^2=8*8\)

Thus, if a number is to the power of 1, it is just by itself.

\(8^1=8\)

We have that, when testing a certain type of truck tire on rough terrain, it is observed that 25% of the trucks fail to complete the test without blowout, the probability that of the next 15 trucks tested, at least one will not able to complete the test run without an explosion is 0.987

Given that when testing a certain type of truck tire on rough terrain, it is found that 25% of the trucks do not complete the test without blowout.So, the probability that a truck completes the test without a blowout is:

P (A complete truck test without blowout) = 1 - P (A complete truck test without an explosion) = 1 - 0.25 = 0.75

Now, we need to find the probability that of the next 15 trucks tested, at least one will not complete the test without an explosion. This can be found using the complement rule. The complement of the probability that at least one truck does not complete the test without a blowout is the probability that all 15 trucks complete the test without a blowout.

P(All 15 trucks complete the test without a blowout) = P(One truck completes the test without a blowout) x P(A second truck completes the test without a blowout) x ... x P(The fifteenth truck completes the test without a blowout) = 0.75 x 0.75 x ... x 0.75 (15 times)= 0.75^15= 0.013

But we need the probability that at least one truck fails to complete the test without a blowout, which is the complement of the above probability.

P(At least one truck does not complete the test without blowout) = 1 - P(All 15 trucks complete the test without blowout)= 1 - 0.013= 0.987

Therefore, the probability that of the next 15 trucks tested, at least one will not be able to complete the test run without an explosion is 0.987.

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Answer:

85 cm^2

Step-by-step explanation:

The surface area of a square pyramid is given by the formula:

Surface area = base area + 4 * (base edge length * slant height) / 2

In this case, the base area is 25 cm^2, because the side length of the base is 5 cm. The base edge length is also 5 cm, because it is a square pyramid. Plugging these values into the formula above, we get:

Surface area = 25 cm^2 + 4 * (5 cm * 6 cm) / 2

= 25 cm^2 + 60 cm^2

= 85 cm^2

So the surface area of the square pyramid is 85 cm^2.

both containers have the same surface area and neither has a smaller surface area than the other.

Container 1:

Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2

Total surface area of 4 balls = 12,370.48 mm^2

Container 2:

Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2

Total surface area of 4 balls = 12,370.48 mm^2

Both containers have the same surface area.

To calculate the surface area of the two containers, I first calculated the surface area of one ball by using the formula π x (diameter/2)^2. I then multiplied this by 4 to get the total surface area of 4 balls. I repeated this process for both containers and found that both containers had the same surface area of 12,370.48 mm^2. both containers have the same surface area and neither has a smaller surface area than the other.

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Answer:

24 cubic inches.

Step-by-step explanation:

\(2a \times a^{2} +a^{3} \\2a^{3} +a^{3}\)

\(3a^3\\3(2)^3\\3 \times 8\)

Answer:

7.5 mL

Step-by-step explanation:

If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.

Answer:

0.0018

Step-by-step explanation:

Answer:

168/169

Step-by-step explanation:

169 if you round 168.68 to 169

Answer:

y=-3x+2 y=-x-4

Step-by-step explanation:

We can use parametrization. By substituting y/x = t, we can express the equation in terms of t. We then integrate to find the area under the curve.

Let's substitute y/x = t into the equation x³ + y³ = 3xy:

(x³) + (tx)³ = 3(x)(xt)

x³ + t³x³ = 3t(x²)

x³(1 + t³) = 3t(x²)

Simplifying, we have:

x = (3t)/(1 + t³)

Now we can express the area as an integral:

A = ∫[0 to ∞] (x) dx

A = ∫[0 to ∞] [(3t)/(1 + t³)] dt

To evaluate this integral, we can use a substitution u = 1 + t³, du = 3t² dt:

A = ∫[(u-1)/u²] du

A = ∫[(1/u) - (1/u²)] du

A = ln(u) + (1/u) + C

Replacing u with 1 + t³ and applying the limits of integration, we have:

A = ln(1 + t³) + (1/(1 + t³)) |[0 to ∞]

Evaluating the expression at the limits, the area of region D is given by:

A = ln(∞) + (1/∞) - [ln(1) + (1/1)]

A = ∞ - 0 - (0 + 1)

A = ∞ - 1

Therefore, the area of region D is infinite.

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Answer:

80

Step-by-step explanation:

Answer:

(x-1.3)^2 + (y+3.5)^2 = 37

In general, (x-c)^2 + (y-k)^2 = r^2 where (c,k) is the center and r is the radius.

So if the circle with radius 5 has center (3,-4) then it's equation is:

(x-3)^2 + (y+4)^2 = 25

Notice that the second term is (y+4)^2 because the y-coordinate is -4 and y-(-4) = y+4