Answer:
r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]
Step-by-step explanation:
V = πr²h ( isolate r² by dividing both sides by hπ )
[tex]\frac{V}{h\pi }[/tex] = r² ( take square root of both sides )
[tex]\sqrt{\frac{V}{h\pi } }[/tex] = r
Find values of x and y. Leave answer as a
fraction y-1 over x+1 = 3x over 2 = 5x+1 over 4x
Answer:
the solution to the system is x = 1 and y = 5/2.
Step-by-step explanation:
To find the values of x and y, we can simplify each equation in the system and then substitute the value of x into the other equation to find y.
Starting with the first equation:
y - 1 = 3x / 2
2 * (y - 1) = 3x
3x = 2y - 2
Next, we substitute the value of 3x/2 from the first equation into the second equation:
5x + 1 = 4x
x = 1
Finally, we can substitute the value of x = 1 into the first equation to find y:
y - 1 = 3 * 1 / 2
y - 1 = 3 / 2
y = 5 / 2
So the solution to the system is x = 1 and y = 5/2.
help?? class is almost over!!!
Answer:
the answer is 330000
Step-by-step explanation:
just do 22,000 divided by 4 and that 5, 500 so its 5,500 miles a month and then do 5,500 x 60= 330000
. in a warehouse of parts for a large mill, the request happens as poisson process and the average time between requests for parts is about 10 minutes. how can one compute the probabilities of following events using the perspective of: i) poisson distribution and ii) gamma distribution? (no need to evaluate the final number) (a) find the probability that in an hour there will be at least 10 requests for parts. (b) find the probability that the 10th request in the morning requires at least 2 hours of waiting time.
The probability that in an hour there will be at least 10 requests for parts is P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9) . The probability that the 10th request in the morning requires at least 2 hours of waiting time is P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) .
i) Poisson Distribution: The Poisson distribution can be used to model the number of requests for parts in a given time period, assuming that the average rate of requests is constant. The Poisson distribution with parameter λ is given by the following formula:
P(k requests in a time period) = (e^-λ * λ^k) / k! , where k is the number of requests, e is the mathematical constant approximately equal to 2.71828, and λ is the average rate of requests.
a) Using Poisson distribution, the probability that in an hour there will be at least 10 requests for parts is given by:
P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9)
b) To find the probability that the 10th request in the morning requires at least 2 hours of waiting time, we need to find the distribution of the time between requests. Since the requests are modeled as a Poisson process, the time between requests is modeled as an exponential distribution with parameter λ.
ii) Gamma Distribution: The gamma distribution is a continuous probability distribution that can be used to model the sum of k independent and identically distributed exponential random variables. In this case, the distribution of the time between requests is exponential, and the sum of 10 independent exponential random variables gives us the distribution of the time until the 10th request.
a) To find the probability that in an hour there will be at least 10 requests for parts using the gamma distribution, we need to first find the distribution of the number of requests in an hour.The sum of 10 independent exponential random variables with rate λ follows a gamma distribution with shape parameter k = 10 and scale parameter 1/λ.
Using the cumulative distribution function of the gamma distribution, the probability that in an hour there will be at least 10 requests for parts is given by:
P(number of requests ≥ 10) = 1 - P(number of requests < 10)
b) Using Gamma distribution, the probability that the 10th request in the morning requires at least 2 hours of waiting time is given by:
P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) , where the cumulative distribution function of the gamma distribution can be used to calculate the probability.
To learn more about poisson distribution click on,
https://brainly.com/question/15994281
#SPJ4
1. if you roll a pair of fair dice, what is the probability of: (a) getting a sum of 1? (b) getting a sum of 5? (c) getting a sum of 12?
The probability is 0, 1/9, and 1/36 for getting a sum of 1, the sum of 5, and the sum of 12 occurs.
Probability is something that is to happen or a chance that an event will occur.
For two rolled dice, the total outcome is 6² = 36
Probability = Expected outcome/Total outcome
a) Pr of getting a sum of 1 = 0/36 = 0
we have a pair of dice, the least sum we can have is 2
b) The event that occurs a sum of 5 are (1, 4), (4, 1), (3, 2), (2, 3)
n(E) = 4
Pr of getting a sum of 5 = 4/36 = 1/9
c)The probability of getting a sum of 12 is (6, 6)
n(E) = 1
Pr of getting a sum of 12 = 1/36
Therefore, the probability that occurs a sum of 1, the sum of 5, and the sum of 12 are 0, 1/9, and 1/36 respectively.
To know more about Probability:
https://brainly.com/question/14319696
#SPJ4
Simon ran a 50 yard dash in 7.02 seconds and Tony ran a 200 yard dash into 24.19 seconds who run faster?
Answer: Tony
Step-by-step explanation: What I did is I took the 7.02 and multiplied it by 4 to make the 50 200 and I got 28.08 so since the time for Simon is larger than the time for Tony, tony went faster because it look him less time. Hope this helps!
Answer: Tony was faster
Step-by-step explanation: To find who ran faster we multiply Tony's time by 4. If it took Tony 7.02 seconds for 50 yards we can multiply that by for to find how long it would have taken him at that speed to run 200 yards.
7.02 x 4 = 28.08
Logan mows / lawns each week for 8 weeks. Eve mows 2 fewer lawns than Logan each week.
a. Write an expression that represents the number of lawns Eve mows in those 8 weeks.
b. Evaluate the expression from part (a) when /-3. Interpret the result.
c. Write an expression equivalent to the one from part (a) by using a tabular model.
d. If Logan mows 5 lawns each week, how many lawns does Eve mow in 8 weeks?
answer is c because i did math and got it right
The distance between points C(3, 3) and D(11, 9) on a directed line segment represents the steady growth of a tree over 16 years. What point represents the height of the tree after 10 years?
Point that represents height after 10 years is (10 , 8.25).
What is line?A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.
Given points
C(3, 3) and D(11, 9) are on a directed line segment that represents height of tree over 16 years.
Equation of the line segment
(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x ₋ x₁)
(y - 3) = [(9 - 3)/(11 - 3)](x - 3)
y - 3 = (6/8)(x - 3)
y - 3 = (3/4)x - 9/4
y = (3/4)x - 9/4 + 3
y = (3/4)x + 3/4
y is height, x is number of years
In 10 years,
= (3/4)10 + 3/4
y = 30/4 + 3/4
y = 33/4 = 8.25
Point is (10 , 8.25)
Hence, (10, 8.25) is point for height of tree after 10 years.
Learn more about line here:
https://brainly.com/question/30003330
#SPJ1
Plant A starts at a height 75 cm tall and grows at a rate of 10 cm per month. At the same time, Plant B starts at a height of 55 cm and grows at a rate of 12 cm per month. Use the variable t to represent the number of months. If the plants continue to grow at this rate, after how many months will the plants be the same height? What height will they be at that time?
The height of the plant A would be 95cm, while the height of the plant B would be 87 cm
How to solve for the heightWe can use an equation to represent the height of each plant as a function of time t:
Plant A: h_A = 75 + 10t
Plant B: h_B = 55 + 12t
We want to find the time t at which the two plants will be the same height, so we can set the two equations equal to each other:
75 + 10t = 55 + 12t
Solving for t, we get:
10t = 20
t = 2
So, after 2 months, the two plants will be the same height. To find the height at that time, we can substitute t = 2 into either equation:
h_A = 75 + 10t = 75 + 10 * 2 = 95
h_B = 55 + 12t = 55 + 12 * 2 = 87
So, after 2 months, the plants will both be 95 cm tall.
Read more on rate here:https://brainly.com/question/119866
#SPJ1
An outcome or collection of outcomes from a sample space is called?
An outcome or collection of outcomes from a sample space is called an event.
A random experiment's sample space is the collection of all conceivable results. A random experiment's related event is a subset of the sample space. Any outcome's probability is a number between 0 and 1.
Each consequence or set of outcomes in an experiment constitutes an event.
An outcome is a potential result of an experiment or trial in probability theory. Each experiment's possible results are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of experiment).
The sample space (also known as sample description space, possibility space, or outcome space) of an experiment or random trial is a collection of all potential outcomes or results of that experiment in probability theory.
For more questions on Event and Sample space
https://brainly.com/question/28044508
#SPJ4
Find the coordinates of X' with X(6,5) for a dilation centered at the origin with a scale factor of -2
On dilating the point X(6,5) with scale factor of -2, the value is obtained as X(-12,-10).
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
The coordinate point for X is given as X(6,5).
The dilation is centered at the origin (0,0).
The dilation scale factor is given as -2.
To find the value of X' use the formula -
X(a,b) → X[(a×(-2)) , (b×(-2))]→ X'
Substitute the values in expression -
X(6,5) → X[(6×(-2)) , (5×(-2))]
X(6,5) → X'(-12,-10)
Therefore, the coordinate point is X'(-12,-10).
To learn more about dilation from the given link
https://brainly.com/question/3457976
#SPJ1
To make a boxplot of a distribution, you must know A. the five-number summary. B. all of the individual observations. c. the mean and the standard deviation. D. None of the above
The required correct answer is A. the five-number summary.
What is box-plot of a distribution?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
According to question:The correct answer is A. the five-number summary. A boxplot is a graphical representation of the distribution of a set of data, and it provides information about the shape, spread, and skewness of the data. The five-number summary is used to construct a boxplot and includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value.
The boxplot uses these five values to display the range of the data and highlight any outliers or unusual observations. Knowing the five-number summary is sufficient to create a boxplot, while knowing all of the individual observations or the mean and standard deviation is not necessary.
Final answer: A. the five-number summary.
To know more about distribution visit
brainly.com/question/29062095
#SPJ4
A rectangle has vertices (e, g), (e, f), and (g, f). Find the fourth vertex.
The fourth vertex of the rectangle is given as follows:
(g,g).
How to obtain the fourth vertex of a rectangle?A rectangle is composed by two dimensions, which are given as follows:
Length.Height.A rectangle has four sides, meaning that two dimensions are equal, and the coordinates for this problem are given as follows:
x-coordinates of e and g.y-coordinates of g and f.The missing combination of one coordinate of x and one coordinate of y is given as follows:
(g,g).
More can be learned about rectangles at https://brainly.com/question/25292087
#SPJ1
¿Cuál es el número decimal equivalente a la fracción ?
Para encontrar el equivalente decimal de una fracción, divide el numerador por el denominador. Debido a que el número en el numerador es más pequeño que el número en el denominador, debe colocar el punto decimal después y agregar ceros.
Definición de números decimalesUn número decimal es un número formado por números enteros y fraccionarios, que al escribirse entre enteros y fracciones se separan por una coma, lo que se denomina punto decimal.
En números enteros, estamos familiarizados con los términos miles, centenas, decenas y unidades. Sin embargo, estos números aún pueden continuar con números más pequeños, a saber, décimas, centésimas, milésimas, etc.
En los números decimales, la parte cuyo valor es menor que el número de la unidad se coloca a la derecha de la coma, siempre que el número a la derecha del decimal sea un número de décimas, y cada número a la derecha sea una décima menor que el anterior.
Learn more about decimal at
https://brainly.com/question/109147
#SPJ1
Find the volume of the solid obtained by rotating the region bounded by the curves y=x2, x=5, and y=0about the x-axis
Answer:
Step-by-step explanation:
The volume of a solid obtained by rotating a two-dimensional region about an axis can be found using the method of cylindrical shells.
The region in question is bounded by the parabolic curve y = x^2, the vertical line x = 5, and the x-axis. We can find the volume of the solid obtained by rotating this region about the x-axis by adding up the volumes of an infinite number of infinitely thin cylindrical shells with radius equal to the distance from the axis to the boundary of the region at each y-value.
The formula for the volume of a cylindrical shell is given by V = 2 * pi * y * dV, where y is the distance from the x-axis to the boundary of the region at each y-value, and dV is the incremental volume at that y-value.
To find the volume, we need to find the incremental volume dV, and integrate the cylindrical shell formula over the region bounded by y = x^2 and x = 5. The incremental volume is given by dV = pi * (R^2 - r^2)dy, where R is the outer radius, r is the inner radius, and dy is the incremental change in y.
In this case, the outer radius R is equal to the value of x = 5 when y = x^2, and the inner radius is equal to zero. Thus, the incremental volume is given by: dV = pi * (5^2 - 0^2)dy = 25 * pi * dy.
The bounds of the integration are from 0 to 5^2 = 25. Integrating the cylindrical shell formula over this range, we find that the volume of the solid obtained by rotating the region bounded by y = x^2, x = 5, and y = 0 about the x-axis is:
V = 2 * pi * integral from 0 to 25 of (y * 25 * pi)dy = 2 * pi * (25^2 * 25 / 2) = 15625 * pi cubic units.
So, the volume of the solid is approximately 49,093 cubic units.
Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the
problem.
7) a=-11+7n
Find a
34
9) a = -7.1-2.1n
Find a
8) a = 65-100n
Find a
39
11
10) a= +-n
8 2
a23
The first five terms will be -4, 3, 10, 17 and 24.
The 34th term will be 227
How to calculate the APAn arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. The difference between consecutive terms in an arithmetic series is always the same and is known as the common difference d.
Based on the information, it should be noted that the AP is given as An = - 11 + 7b
First term = -11 + 7(1) = -4
Second term = -11 + 7(2) = 3
Third term = -11 + 7(3) = 10
Fourth term = -11 + 7(4) = 17
Fifth term = 24
The 34 term will be:
= -11 + 7(34)
= 227
Learn more about arithmetic progression on:
brainly.com/question/444245
#SPJ1
Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. An=-11+7b. Find a34
Rafael plays a trivia game with 2 rounds. In the first round, he earns 5 points for answering a question correctly and loses 3 points for answering a question incorrectly.
In the second round, he earns 10 points for answering a question correctly and loses 4 points for
answering a question incorrectly.
The equations below represent Rafael's
performance in each round.
5x-3y=22
10x-4y=46
Which condition must be true to make the pair of equations a system of equations?
(A) He answers a total of 15 questions correctly.
(B) He answers the same number of questions correctly as he answers incorrectly in each round.
(C) He answers twice as many questions correctly in the second round as he answers correctly in the first round.
(D) He answers the same number of questions correctly in both rounds and the same number of questions incorrectly in both rounds.
He answers the same number of questions correctly as he answers incorrectly in each round.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
For the pair of equations to be a system of equations, the number of questions answered correctly must equal the number of questions answered incorrectly in each round. Therefore, the equation 5x - 3y = 22 must have the same number of x and y variables, and the equation 10x - 4y = 46 must also have the same number of x and y variables. This is the only condition that must be true for the pair of equations to be a system of equations.
To know more about equation click-
https://brainly.com/question/26408808
#SPJ1
A contractor hired 18 workers to complete the construction of a road in 60 days. How many more workers should he hire to complete the construction work 15 days earlier?
Using proportions, if a contractor hired 18 workers to complete the construction of a road in 60 days, to complete the construction work 15 days earlier, the additional workers he should hire is 6.
How is the number of workers determined?We can use proportions to determine the number of workers needed to complete the work 15 days earlier, which is in 45 days.
Proportions are ratios equated to one another.
The number of workers needed to complete a road construction in 60 days = 18
If the contractor wants to complete the work 15 days earlier, he must complete it in 45 days (60 - 15).
The number of workers needed to complete the construction in 1 day = 1,080 (60 x 18)
The number of workers needed to complete the construction in 45 days = 24 (1,080/45)
The difference between completing the work in 60 days and 45 days = 6 workers (24 - 18).
Thus, proportionately, it will take 6 additional workers to complete the construction work 15 days earlier.
Learn more about proportions at https://brainly.com/question/1496357
#SPJ1
Find the 8th term of the geometric sequence 7, 28, 112, ...
Explanation:
a = 7 = first termr = 4 = common ratioThe common ratio is calculated by dividing each term by its previous one.
r = term2/term1 = 28/7 = 4r = term3/term2 = 112/28 = 4The nth term formula for this particular geometric sequence is:
[tex]a_n = a*r^{n-1}\\\\a_n = 7*4^{n-1}\\\\[/tex]
The last step is to plug n = 8 into that formula.
[tex]a_n = a*r^{n-1}\\\\a_n = 7*4^{n-1}\\\\a_8 = 7*4^{8-1}\\\\a_8 = 7*4^{7}\\\\a_8 = 7*16384\\\\a_8 = 114688\\\\[/tex]
The 8th term is 114688
Avoid using commas to separate out the digits. This is because commas are used to separate each term of the geometric sequence.
8th term of this geometric sequence is 114,688.
In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the 8th term, we need to know the common ratio and the first term. Given that the first term is 7 and the second term is 28, we can find the common ratio as follows:
r = 28/7 = 4
Now that we know the common ratio, we can find the 8th term by multiplying the first term by the common ratio raised to the power of 7:
a_8 = 7 * r^(8-1) = 7 * 4^7 = 7 * 16,384 = 114,688
Therefore, the 8th term of the sequence is 114,688.
Learn more about geometric sequence:
https://brainly.com/question/17282782
a tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate. find the number
The tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate, After 20 minutes, the amount of salt in the tank is still 50 grams.
In order To calculate the amount of salt in the tank after 20 minutes, we basically use the formula: Salt (in grams) = (Amount of salt in the tank x Time) / Total volume.So, after 20 minutes, the amount of salt in the tank is: (50 grams x 20 minutes) / 240 liters = 8.33 grams.
As we can see, both methods produce the same result, confirming that the amount of salt in the tank after 20 minutes is still 50 grams. since the rate of pumping in salt water is equal to the rate of pumping out salt water, so the total amount of salt remains the same.
To know more about pump refer to the link brainly.com/question/21864603
#SPJ4
A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate. find the number of grams of salt in the tank after 20 minutes
There are 16 flowers in a vase. Four flowers are daisies, 1 is rose, 3 are tulips and the rest are sunflowers. Suppose the probability of randomly choosing a flower is
. Which of the following flowers could it be?
The flower associated to the given probability is the sunflowers.
How to find the probability?We want to find the probability of randomly choosing a flower is:
Now, remember that the probability of randomly selecting a type of flower is equal to the quotient between the number of that type of flower and the total number of flowers.
Here we know that the probability is:
P = 0.5
We can rewrite that as:
P = 1/2
If we rewrite the denominator as 16, we will get:
P = 8/16
And we know that there are 8 sunflowers, then sunflower is the correct option.
Learn more about probabilities:
https://brainly.com/question/25870256
#SPJ1
The complete question is:
There are 16 flowers in a vase. Four flowers are daisies, 1 is rose, 3 are tulips and the rest are sunflowers. Suppose the probability of randomly choosing a flower is 0.5
Which of the following flowers could it be?
two percent of the circuit boards manufactured by a particular company are defective. if circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is a. .0167 b. .9833 c. 0.1829 d. 0.8171 e. the answer cannot be computed from the information given
If circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833. So, the correct option is b .
This is a geometric distribution problem, where we are trying to find the probability of the number of trials (inspections) until the first success (defective board). The probability of success (finding a defective board) on each trial is 0.02 and the probability of failure (not finding a defective board) on each trial is 0.98.
The formula for the probability of exactly k trials until the first success is given by:
P(X = k) = (1 - p)^(k-1) * p
where p is the probability of success and k is the number of trials.
Plugging in p = 0.02 and k = 10, we get:
P(X = 10) = (1 - 0.02)^(10-1) * 0.02 = 0.9833
So the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833.
To learn more about probability click on,
https://brainly.com/question/12523885
#SPJ4
Example #2.
Find the perimeter of the trapezoid.
The perimeter of the trapezoid is 50 cm.
What is a trapezoid?A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
Given the trapezoid,
let us consider ABCD be the trapezoid,
so given angle B = 90°
AB = 12 cm, AD = 10 cm, and BC = 15 cm
let us draw a perpendicular from D on BC parallel to AB
which forms the right triangle DEC
from the Pythagorean theorem, from the figure attached in the image.
DC² = DE² + EC²
DC² = 12² + 5²
DC² = 144 +25
DC² = 169
DC = 13 cm
perimeter is the sum of all sides,
P = AB + BC + AD + DC
P = 12 + 15 + 10 + 13
P = 50 cm
Hence perimeter is 50 cm.
Learn more about trapezoids;
https://brainly.com/question/8643562
#SPJ1
what is the decimal value of the following binary number? 10011101
The following binary number has the value of 157 in decimal form.
How can a binary number be converted to a decimal?Step 1: Compose the binary number in writing. 10011101
Multiplying each binary digit by the corresponding power of two in step two:
1x27 + 0x26 + 0x25 + 1x24 + 1x23 + 1x22 + 0x21 + 1x20
Solve the powers in Step 3:
1x128+0x64+0x32+1x16+8+4+0x2+1x1=128+0 + 0 + 0 + 16+8+4+0 + 0 + 1
Step 4: Add the figures listed above:
128 + 0 + 0 + 16 + 8 + 4 + 0 + 1 = 157.
What does the binary number system mean?A binary number is a number that is expressed in the binary system or base 2 numeral system, according to digital technology and mathematics. It talks about numerical values.by the two distinct digits 1 (one) and 0 (zero). The base-2 system is the positional notation that uses 2 as the radix.
Define decimal.A number that has been divided into a whole and a fraction is called a decimal. To express the numerical value of entirely and partially entire quantities between integers, decimal numbers are used.
To know more about binary number visit:
https://brainly.com/question/8649831
#SPJ4
what is the most appropriate measure of spread for this data, and why? group of answer choices standard deviation, because the boxplot is skewed to the right. standard deviation, because the boxplot is bell-shaped. iqr, because the boxplot is skewed to the right. iqr, because the boxplot is bell-shaped.
The most appropriate measure of spread for this data is standard deviation, because the boxplot is skewed to the right.
The most appropriate measure of spread for this data is standard deviation. The data is represented by a boxplot, which is a graphical representation of the data that shows the median, quartiles, and range of the data. In this case, the boxplot is skewed to the right, meaning that the data is not normally distributed. When the data is not normally distributed, the standard deviation is the best measure of spread to use. Standard deviation measures the spread of data by calculating the distance between each data point and the mean, and then taking the average of these distances. This allows us to accurately measure the spread of data that is not normally distributed. Therefore, standard deviation is the most appropriate measure of spread for this data.
Learn more about standard deviation here
https://brainly.com/question/20553308
#SPJ4
a candle is lit and burns until it is burned out, and the length of the candle decreases at a constant rate of 1.2 inches per hour. after 3 hours since the candle was lit, it is 10.5 inches long. what is the original length of the candle? show all your work.
The length of the candle was 13.5 inches before it was lit.
Let the length of candle in the beginning be c.
Constant rate of change in length of candle= 1.2 inches per hour
Since rate of change is constant so the length of candle can be represented by a linear function [Linear function has constant rate of change.]
Linear function : f(x)= mx+c , where x= independent variable.
m= constant rate of change and c= initial value of function.
Let x = Number of hours after the candle was lit.
Put m= 1.2 , x= 3 and f(x)= 10.5 , we get
c= 13.5
Hence, the length of the candle was 13.5 inches before it was lit.
learn more about of candle here
https://brainly.com/question/14735040
#SPJ4
A rectangular room is 5 meters longer than it is wide, and it’s perimeter is 26 meters. Find the dimension of the room
Answer:
length=9
width=4m
Step-by-step explanation:
Let the width of the rectangle be, x and the length be, x+5
perimeter=2(L+W)
26 m=2(x+5+x)
26=2x+10+2
26-10=4x
16=4x
x=
length=9m
width=4m
What is the EXACT (not approximate, so your answer should include pi) area of the shaded region? Be sure to include units in your answer.
The area of the shaded region of the semicircle is 108π mm²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a semicircle with a diameter of 24 mm, a circle is fitted in it, we need to find the measurement of the area which is shaded.
The diameter of the smaller circle = radius of semicircle.
Therefore,
Radius of smaller circle = 24/4 = 6 mm
To find the area of shaded region, we will subtract the area of the smaller circle from the area of semicircle.
Area of a circle = π × radius² {area of semicircle is just half of it}
Area of shaded region = π × 12² - π × 6²
= π(144-36)
= 108π
Hence, the area of the shaded region of the semicircle is 108π mm²
Learn more about areas, click;
https://brainly.com/question/27683633
#SPJ1
prove that there is a positive integer that equals the sum of the positive integers not exceeding it. is your proof constructive or nonconstructive? proof by cases
The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10
The proof of this statement is constructive, as it will provide a way to explicitly construct a positive integer which is equal to the sum of the positive integers not exceeding it.
To prove this, we will use the following formula:
Let n = the positive integer
Let S = the sum of the positive integers not exceeding n
n = 1 + 2 + ... +n-1 + n
S = 1 + 2 + ... +n-1
Therefore, n = S + n
For example, let n = 5. The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10. Therefore, 5 = 10 + 5, which is true. This proves that for any positive integer, n, it is equal to the sum of the positive integers not exceeding it.
Learn more about positive integers here:
https://brainly.com/question/28165413
#SPJ4
what is the volume of 113
The sphere has a volume of 113 cubic units, the sphere's radius is 2.99 units.
What is meant by Volume?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume is measured in cubic units.
the sphere's diameter.
Having said that,
The sphere's volume is equal to[tex]4/3 \pi r^3.[/tex]
The volume is already known.
[tex]113 = 4/3 (3.14) r^3[/tex]
339 = 4 (3.14) r³
339/4 = 3.14 r³
84.75 = 3.14 r³
84.75/3.14 = r³
26.99 = r³
r = ∛26.99
r = 2.99
Consequently, the sphere's radius is 2.99 units.
To learn more about volume from given link
https://brainly.com/question/463363
#SPJ1
Complete question -
Consider a sphere whose volume is 113 cubic units what will be the radius of the mirror?
if a car is traveling at 85 mph, how fast is the car traveling in feet per second? round to 2 decimal places.
The speed of the car travelled after converting 85 meter per hour into feet per second is equal to ( 0.08 feet per seconds )(round to 2 decimal places)
Speed of the car in meter per hour is equal to 85 mph.
Conversion of unit meter per hour in feet per second is :
1 meter = 3.28084 feet
1 hour = 60 minutes
= 3600 seconds
85 mph = ( 85 × 3.28084 feet ) / ( 3600 seconds )
⇒ 85 mph = ( 278. 8714 feet ) / ( 3600 seconds )
⇒ 85 mph = ( 0.07746 feet per seconds )
⇒ 85 mph = ( 0.08 feet per seconds )( round to 2 decimal places )
Therefore, the car travelled in feet per seconds is equal to ( 0.08 feet per seconds ).
Learn more about travelled here
brainly.com/question/29055485
#SPJ4