Different fuels produce different amounts of heat energy when burned. For example propane has a heat energy of 2,470 btu/ft^3 how much energy can propane tank with a volume of 43. 7 ft^3 produce

Answer:

x = 9.0

Step-by-step explanation:

sin E = CD/EC = CD/x

<=>     sin 50 = 6.9/x     <=> x = 6.9/sin 50 ≅ 9.0

The formula for the volume of an sphere of radius r is given as follows:

V = (2/3)πr³  

The radius as a function of the volume is obtained as follows:

r³ = 3V/2π

[tex]r = \sqrt[3]{\frac{3V}{2\pi}}[/tex]

Hence the radius of a sphere of volume 25 in³ is given as follows:

[tex]r = \sqrt[3]{\frac{25}{2\pi}}[/tex]

r = 2.29 in.

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[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-5}{h}~~,~~\underset{9}{k})}\qquad \stackrel{radius}{\underset{14}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-5) ~~ )^2 ~~ + ~~ ( ~~ y-9 ~~ )^2~~ = ~~14^2\implies (x+5)^2 + (y-9)^2=196[/tex]

Answer:

3/16

Step-by-step explanation:

hope it help

A minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.

Sample size refers to the number of observations or individuals included in a study or experiment. It is the number of subjects or units that are selected from a population to be studied. The sample size is an important consideration in statistical analysis, as it can affect the accuracy and generalizability of the results. A larger sample size generally leads to more precise estimates and stronger statistical power, but it can also be more costly and time-consuming to collect and analyze.

To calculate the minimum sample size required to maintain a margin of error of 0.05 or less with a 99% confidence level, we can use the formula:

n = (Z² * p * (1-p)) / E²

where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of the population that has a certain characteristic (we can use 0.5 for maximum variability), and E is the margin of error.

Plugging in the values, we get:

n = (2.576² * 0.5 * (1-0.5)) / 0.05²

n = 664.3

Rounding up to the nearest whole number, we get a minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.

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Answer:

First, we need to convert all the measurements to the same unit. Let's convert everything to inches, since the formula for the volume of a cylinder uses inches:

12 in = 12 in

14 in = 14 in

12 in = 12 in

4 in = 4 in

The object consists of a cylinder with a radius of 4 inches and a height of 12 inches, and a hemisphere with a radius of 4 inches. To find the volume of the object, we need to find the volume of the cylinder and the hemisphere, and then add them together.

Volume of the cylinder:

V_cyl = πr^2h

V_cyl = π(4 in)^2(12 in)

V_cyl = 192π in^3

Volume of the hemisphere:

The volume of a hemisphere is given by:

V_hemi = (2/3)πr^3

Since the radius is 4 inches, we have:

V_hemi = (2/3)π(4 in)^3

V_hemi = (2/3)π(64 in^3)

V_hemi = 128π/3 in^3

Total volume:

V_total = V_cyl + V_hemi

V_total = 192π in^3 + 128π/3 in^3

V_total = (576π + 128π)/3 in^3

V_total = 704π/3 in^3

Now we can substitute the value of π (3) to get the final answer:

V_total = 704π/3 in^3

V_total = 704(3)/3 in^3

V_total = 704 in^3

Therefore, the volume of the object is 704 cubic inches.

Answer:

Step-by-step explanation:

· Find the surface area of a cone with a slant height of 8 cm and a radius of 3 cm. SA = B + πrS = (πr2) + πrs = (π(32)) + π(3)(8) = 9π + 24π = 33πcm2 = 103.62cm2. Find the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.

The first step in finding the distance between vertex P and vertex V is find the length of diagonal between vertex P and vertex R.

option A.

To find the distance between vertex P and vertex V, we need to draw a diagonal line from vertex P to vertex V.

After drawing the diagonal line, we will notice that we have a new right angle triangle.

So since we know the height of the right triangle, we need to find the base of the right triangle first, which is equal to length of diagonal length PR or TV

So the correct answer will be "find the length of diagonal PR first.".

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Answer:

b)

Step-by-step explanation:

If x - 2 is a factor polynomial f(x), then the polynomial can be expressed as f(x) = (x - 2) g(x), where g(x) is another polynomial.

Using this information, we can check each statement to see which one does NOT have to be true:

A) f(2) = 0:

If x - 2 is a factor of f(x), then plugging in x = 2 gives f(2) = (2 - 2) g(2) = 0. This statement has to be true.

B) f(-2) = 0:

If x - 2 is a factor of f(x), then plugging in x = -2 gives f(-2) = (-2 - 2) g(-2) = -4 g(-2). This statement does NOT have to be true. For example, if g(-2) = 1/(-4), then f(-2) would not equal 0.

C) 2 is a root of f(x):

If x - 2 is a factor of f(x), then 2 is a root of f(x), meaning f(2) = 0. This statement has to be true.

D) 2 is a zero of f(x):

The term "zero" can be interpreted in different ways, but if it means the same as a root or a solution, then this statement is the same as statement C and has to be true.

Therefore, the statement that does NOT have to be true is B) f(-2) = 0.

The confidence interval in which you have the most confidence that it captures the population mean is the one with the highest level of confidence.

But keep in mind that this interval will be wider and less precise, so we must balance the level of confidence with the desired precision of your estimate.

The terms confidence interval, population mean, and level of confidence.
A confidence interval is a range of values that is likely to contain the population mean, which is the average value of a certain variable in the entire population.

The level of confidence, expressed as a percentage (e.g., 95%), represents the probability that the confidence interval captures the true population mean.
In general, the confidence interval with the highest level of confidence will give you the most certainty that it captures the population mean.

However, as the level of confidence increases, the width of the confidence interval also increases, making it less precise.

This means that while we have more confidence that the interval contains the population mean, you have less specific information about where the mean lies within that interval.

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If rosanne makes 112 liters of strawberry lemonade, she pours 14 of a liter of lemonade into a thermos to take to the park, rosanne's brother drink 25 liters of lemonade

To solve this problem, we can start by subtracting the 14 liters of lemonade that Rosanne poured into the thermos from the total 112 liters to get the amount of lemonade that remained:

112 - 14 = 98 liters

Next, we need to subtract the amount of lemonade that Rosanne's brother drank, which is 25 liters, from the remaining amount:

98 - 25 = 73 liters

Therefore, Rosanne's brother drank 25 liters of lemonade.

To check our answer, we can add the amount of lemonade in the thermos, the amount that Rosanne's brother drank, and the remaining amount to see if it adds up to the original 112 liters:

14 + 25 + 73 = 112

Since the sum is indeed equal to 112, we can be confident that our answer of 25 liters for the amount of lemonade that Rosanne's brother drank is correct.

In summary, to find the amount of lemonade that Rosanne's brother drank, we subtracted the amount that Rosanne poured into the thermos and the amount that her brother drank from the total amount of lemonade that Rosanne made. The answer is 25 liters.

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If Taylor is selected as one of the first two players out of ten players on the team, the probability of Jamie being selected as the third player is 4/9.

Using the multiplication rule of probability, the overall probability of both events happening is 8.9%

Assuming that there are only seniors and juniors on the team, the probability of Taylor being selected as one of the first two players is 2/10, since there are two juniors out of ten total players.

If Taylor is selected as one of the first two players, then there are nine players left, of which four are juniors, including Jamie.

Therefore, the probability of Jamie being selected as the third player, given that Taylor is already selected, is 4/9.

Using the multiplication rule of probability, the overall probability of both events happening is:

P(Taylor and Jamie) = P(Taylor) x P (Jamie | Taylor)

P(Taylor and Jamie) = 2/10 x 4/9

P(Taylor and Jamie) = 8/90

P(Taylor and Jamie) = 0.089 or 8.9% (rounded to the nearest tenth)

Therefore, the probability of Jamie being selected as the third player, given that Taylor is already selected as one of the first two players, is 8.9%.

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Answer:

The Answer is 40°

Step-by-step explanation:

Base angles of an isosceles triangle are equal

x+30=70

x=70-30

x=40°

so,

<C=70°

<A+<B+<C=180°

let <A be X

X+70+70=180°

X+140=180°

X=180-140

X=40°

X=2x-10

40°=2x-10

2x=40+10

2x=50°

divide both sides by 2

x=25°

Answer: miss bailey bought 8 for 3 dollars each  

Step-by-step explanation:

so if a binder cost 12 subtract that form the $36 and you are left with $24. divided it by 8 and are left with 3

[tex]\begin{array}{ccll} tables&persons\\ \cline{1-2} 15 & 180\\ x& 192 \end{array} \implies \cfrac{15}{x}~~=~~\cfrac{180}{192} \implies \cfrac{ 15 }{ x } ~~=~~ \cfrac{ 15 }{ 16 }\implies x=16[/tex]

The total volume of the cylindrical can is given as follows:

C) 24.54 in³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The parameters for this problem are given as follows:

Hence the volume of the cylinder is obtained as follows:

V = π x 1.25² x 5

V = 24.54 in³.

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Answer:

P54.75 per hour.

Step-by-step explanation:

If he earned 2190 pesos on working 8 hours each for 5 days then he earned 54.75

Equation: hours x days / earnings

Therefore, 8 hours x 5 days = 40

2190 / 40 = P54.75 / hour

The only possible elements that can appear in all the sets are 4 and 5. Since both 4 and 5 appear in each set, they must be in the intersection.

Based on the given set definition, we have:

A₁ = {4, 5}

A₂ = {4, 5, 6}

A₃ = {4, 5, 6, 7}

A₄ = {4, 5, 6, 7, 8}

and so on.

To find the union of all the sets, we need to find all the distinct elements that appear in at least one of the sets. We can do this by listing the elements in each set and removing duplicates:

⋃[infinity] =1 Aᵢ = {4, 5, 6, 7, 8, ...}

We can see that the union includes all the natural numbers greater than or equal to 4. We can prove this by showing that any natural number n greater than or equal to 4 is included in at least one of the sets. Indeed, for any such n, we can choose i = n - 3, which is a natural number since n is at least 4, and then we have n in Aᵢ.

To find the intersection of all the sets, we need to find the elements that appear in all the sets. We can do this by listing the elements in each set and finding the common elements:

⋂[infinity] =1 Aᵢ = {4, 5}

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Answer:

s = p - q - 1

Step-by-step explanation:

q + 1 + s = p  Subtract q and 1 from both sides

q -q +1 - 1 + s = p - q -1

s = p - q - 1

Helping in the name of Jesus.

vehicle?

The average delay per vehicle would be 20 minutes. This is calculated by taking the total time the freeway was shut down (40 minutes) and dividing it by the total number of vehicles that would have been on the freeway during that time (2400 vehicles).

The expression for the problem is:

Total cost = $42 + ($12/hour × 3 hours) × 2 people

Bruce charged David and Ricky a fixed fee of $42 for parts plus an hourly rate of $12 for labor. He spent 3 hours repairing the motorcycle. Since there are two people (David and Ricky), we need to multiply the hourly rate by the number of hours worked (3) and then multiply that by 2. Finally, we add the fixed fee for the parts to get the total cost.

To evaluate the expression using the order of operations, we need to perform the multiplication first and then the addition. So, we have:

Total cost = $42 + ($12/hour × 3 hours) × 2 people

= $42 + ($36) × 2

= $42 + $72

= $114

Therefore, David and Ricky owe Bruce a total of $114 for the motorcycle repair.

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The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive.

The i.i.d means two random variable where there is an equal chance that one will be greater then the other.

So, it means there is 50% chances for both of them to be greater then the median.

The probability that the greater of the two random variables will surpass the population median is just 0.5 because both events are mutually exclusive. This conclusion is valid as long as the variable are given to be continuous and i.i.d.

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The scale factor used for the dilation of the triangle ABC to A'B'C' is 3.

To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's start by finding the length of side AB in both triangles.

Length of AB in the original triangle ABC:

AB = √[(3-(-3))² + (3-(-3))²]

= √[6² + 6²]

= 6√(2)

Length of A'B' in the dilated triangle A'B'C':

A'B' = √[(9-(-9))²+(9-(-9))²]

= √[18² + 18²]

= 18√(2)

Now we can find the scale factor by dividing the length of A'B' by the length of AB:

scale factor = A'B'/AB

= (18√(2))/(6√(2))

= 3

Therefore, the scale factor used is 3. The dilation has enlarged the triangle by a factor of 3.

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The only exponential growth equation is the third one:

y = 2*(4)^x

A general exponential equation is:

y = A*(b)^x

if 0 < b < 1, then it is a decay.

if 1 < b, then it is a growth.

So any equation where the base, b, is larger than 1, represents a growth.

Then the correct option is the third one:

y = 2*(4)^x

All the other options are decays.

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The probability of seeing the word "math" in a 10-letter string typed by a monkey is 0.0024 (or 0.24%).

To calculate this probability, we first need to determine the total number of possible 10-letter strings that the monkey can type. Since the monkey never repeats letters, the number of possible 10-letter strings is given by the permutation formula:

10P10 = 10!/(10-10)! = 3,628,800

Next, we need to determine the number of 10-letter strings that contain the word "math". We can do this by fixing the position of the "m" and the "a", and then allowing the monkey to freely choose the remaining 6 letters. The number of ways to do this is given by:

8P6 = 8!/(8-6)! = 56

Finally, we divide the number of 10-letter strings containing "math" by the total number of possible 10-letter strings to obtain the probability:

56/3,628,800 = 0.000024 = 0.0024 (or 0.24%)

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Answer:

7,000,000÷2000

= 3,500

Step-by-step explanation:

therefore, each worker makes 3500 bikes per year

The speed of the person in still water is 18 miles per hour

Let's call the speed of the person in still water "x".

When the person swims downriver, they are swimming with the current, so their effective speed is the sum of their swimming speed and the speed of the current, which is "x + 4".

When the person swims upriver, they are swimming against the current, so their effective speed is the difference between their swimming speed and the speed of the current, which is "x - 4".

We know that the person covers 11 miles downriver in the same amount of time it takes them to cover 7 miles upriver. This means that the two distances are equal in terms of time:

[tex]11 / (x + 4) = 7 / (x - 4)[/tex]

To solve for x, we can cross-multiply and simplify:

[tex]11(x - 4) = 7(x + 4)[/tex]

[tex]11x - 44 = 7x + 28[/tex]

[tex]4x = 72[/tex]

[tex]x = 18[/tex]

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The solution is :; 1256.63  tiles would be needed.

We have,

the question is not quite clear but I assume that it is asking how many tiles of length 70cm is required in order to pave the circular area.

Given,

radius(r) = 14m= 1400cm

Area of the circle= πr²= π×1400²

                                    = 6157521.6 cm²

length of square tile(l)= 70cm

area of square= l²= 70×70= 4900cm²

now,

number of tiles required= area of circle ÷ area of tile

= 6157521.6 ÷ 4900

= 1256.63 tiles

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complete question:

A circular room of radius 14 m is to be covered by a square carpet. What will be the maximum area the carpet can cover? If the same area is to be paved with square tiles with a side length of 70 cm, then how many tiles would be needed?