A propane tank with a volume of 43.7 ft³ can produce 107,639 BTUs of heat energy when burned.
Propane is a commonly used fuel for heating and cooking. It has a heat energy content of 2,470 BTUs per cubic foot (ft³). To calculate how much energy a propane tank with a volume of 43.7 ft³ can produce, we need to use a simple formula:
Energy = Volume x Energy Content
Plugging in the values we have:
Energy = 43.7 ft³ x 2,470 BTU/ft³
Energy = 107,639 BTUs
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the confidence interval in which you have the most confidence that it captures the population mean must be:
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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write an expression for the problem and evaluate the expression using the order of operations. bruce charged david and ricky $42 for parts and $12 per hour for labor to repair their motorcycle if he spent 3 hours repairing the bike how much money do david and ricky owe him?
The expression for the problem is:
Total cost = $42 + ($12/hour × 3 hours) × 2 people
How to write the expressionBruce 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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rosanne makes 112 liters of strawberry lemonade. she pours 14 of a liter of lemonade into a thermos to take to the park. her brother drinks 25 of the remaining lemonade. how much lemonade does rosanne's brother drink?write your answer as a whole number, fraction, or mixed number. simplify any fractions. liters
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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PLEASE HELP ME IM NOT GOOD AT MATH AND don’t understand!!
The total volume of the cylindrical can is given as follows:
C) 24.54 in³.
How to obtain the volume of a cylinder?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:
h = 5 in.r = 1.25 in.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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I need help with this. please
The only exponential growth equation is the third one:
y = 2*(4)^x
Which equation will produce a growth?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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a monkey types 10 letters on a computer. assume the keyboard contains only letters and that the monkey never repeats letters. what is the probability of seeing the word math in this string of 10 letters?
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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a freeway with two northbound lanes is shut down because of an accident. at the time of the accident, the traffic flow rate is 1200 vehicles per hour per lane and the flow remains at this level. the capacity of the freeway is 2200 vehicles per hour per lane when not impacted by an accident. the freeway is shut down completely for 20 minutes after the accident and then one lane is open for 20 minutes and finally both lanes are opened (40 minutes after the accident). what is the average delay per
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).
For each natural number , let ≔ {4, 4 + 1, … ,5}. Find ⋃[infinity] =1 and
⋂[infinity] =1 and prove your answers
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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a person swims 11 miles downriver in the same time they can swim 7 miles upriver. the speed of the current is 4 miles per hour. find the speed of the person in still water.
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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in order to maintain accuracy, political polling groups must maintain a certain degree of confidence with a small margin of error. fivethirtyeight is a polling company that wishes to survey a population of people, but maintain a margin of error of 0.05 or less with a 99% confidence level. what is the smallest number of consumers they should survey to guarantee this?
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.
What is the sample size?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.
According to the given informationTo 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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30
The number of tables needed is proportional to the number of
people who are attending a banquet. The table below shows the
relationship.
BANQUET TABLES
D 20
Number of Tables
5
15
25
Number of People Attending
60
180
300
A banquet for 192 people is being held. How many tables are
needed for this banquet?
A 8
B 12
C 16
D 20
[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]
Using Trig to find a side.
Solve for x. Round to the nearest tenth, if necessary.
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
suppose coach bennet selects one senior and one junior as the first two players. the coach then randomly selects the third player from either group. taylor and jamie are both juniors on the team. if taylor is selected as one of the first two players, what is the probability that jamie will be selected as the third player? type in the correct answer in the box. use numerals instead of words. if necessary, round your answer to the nearest tenth.
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%
How to find the probability of Jamie being selected?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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Find the volume of this object.
Use 3 for T.
Volume of a Cylinder
V= πr²h
12 in
14 in
12 in
V [?]cm
4 in
Enter
3
please help
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.
2. Allie plans to tile her living room but leave a square area in the upper right-hand corner
for carpet. The squares sides will half the length of the entire area. The entire area has a length
of 18' while the width will be 12'. How big is the tiled area?
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?
What is the measure of angle A in this triangle?
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°
Solve for s.
q+1+s=P
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.
Chester worked for 8hour each day for 5days.He earned P2190.00.How much did he earn per hour?
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
How do I round 9979.03 to the nearest gram?
Donna is sharing her snacks with her friends. She went to the store and spent $4 on chips, $2.75 on cookies, $3.37 on fruit snacks, and $11.55 on drinks. How much did she spend in all? How much change did she have left over from $25? Also, she shared ¼ of her bag of chips between her and her 2 friends. How much of the bag did each friend get?
Answer:
3/16
Step-by-step explanation:
hope it help
what is the probability that the larger of two continuous i.i.d. random variable will exceed the population median? stackage
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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Help me please….
it’s due tomorrow!!!
Help with algebra 2 homework
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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If x - 2 is a factor polynomial f(x), which of the following statements does NOT have to be true?
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.
I need this answer asap can someone help?
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.
What is the distance between vertex P and vertex V?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.
with a height of 17 inches a base of diagonal length PR or TVa hypotenuse of diagonal PVSo 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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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used. 6 one sixth 3 one third
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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1. Write the equation of a circle with a radius of 14 and the center at (-5, 9).
[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]
Miss Bailey went to the store and bought 8 packs of pencils and a binder that cost $12. He spent a total of $36. How much did each pencil pack cost?
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
A factory has 2 x 10^3 workers who make a total of 7 x 10^6 bikes each year. How many bikes does each worker make per year?
Answer:
7,000,000÷2000
= 3,500
Step-by-step explanation:
therefore, each worker makes 3500 bikes per year
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
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.