As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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Roll a fair die three times. What is the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll?
The probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll when a fair die is rolled three times is 1/4.
Probability is the study of random events. It is a measure of the likelihood of an event occurring. Probability can be expressed as a decimal, a fraction, or a percentage. There are two types of probability - empirical probability and theoretical probability.
Empirical probability is calculated by conducting experiments or collecting data. It is calculated using the following formula:
Empirical probability = Number of favourable outcomes/Total number of outcomes
Theoretical probability is calculated using probability formulas. It is calculated using the following formula:
Theoretical probability = Number of favourable outcomes/Total number of possible outcomes
In the given problem, a fair die is rolled three times. We need to find the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll. There are 2 favourable outcomes for the first roll, 2 favourable outcomes for the second roll, and 2 favourable outcomes for the third roll.
Total number of outcomes = 6×6×6 = 216
Number of favourable outcomes = 2×2×2 = 8
Probability = Number of favourable outcomes/Total number of outcomes
Probability = 8/216
Probability = 1/27
Therefore, the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll when a fair die is rolled three times is 1/4.
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Move the manilla point as close to the circle as possible so that the blue arc almost disappears keep the manilla point on the circle
What previously learned theorem do these transformations reveal
A theorem which these transformations reveal include the following: theorem of intersecting secants.
What is the theorem of intersecting secants?In Mathematics and Geometry, the theorem of intersecting secants states that when two lines intersect outside a given circle, the measure of the angle formed by these intersecting lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, the value of any of the angle subtended by the intersecting lines can be calculated by using the following mathematical equation:
m∠a = One-half(y – x).
m∠a = ½(y – x).
Where:
x and y represent the angles formed by the intersecting lines.
Therefore, the theorem of intersecting secants describe these set of transformations.
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What is the value of x in the equation 1/4(4 + x) = 4/3
The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.
Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:
1/4(4 + x) = 4/3
4 * 1/4(4 + x) = 4 * 4/3
Simplifying:
4 + x = 16/3
Subtract 4 from both sides of the equation:
4 + x - 4 = 16/3 - 4
Simplifying:
x = 16/3 - 12/3
x = 4/3
A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.
Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.
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Find the surface area of the regular pyramid. Round your answer to two decimal places.
I think it’s to do with Pythagoras theorm
4. Assume that 4 years from now you will need $1,000. Your bank compounds interest
at an 8% annual rate. A. How much must you deposit 1 year from now to have a balance of $1,000 at
Year 4?
b. If you want to make equal payments at the end of Years 1 through 4 to
accumulate the $1,000, how large must each of the 4 payments be?
c. If your father were to offer either to make the payments calculated in part b
($221. 92) or to give you a lump sum of $750 one year from now, which would
you choose?
d. If you will have only $750 at the end of Year 1, what interest rate, compounded
annually, would you have to earn to have the necessary $1,000 at Year 4?
e. Suppose you can deposit only $186. 29 each at the end of Years 1 through 4, but
you still need $1,000 at the end of Year 4. What interest rate, with annual
A. deposit $735.03 one year from now. B. $210.48 for each of the four years. C. choose the lump sum of $750 from your father. D. Interest rate of 7.4% compounded annually. E. Interest rate of 12%.
a. To have a balance of $1,000 four years from now, you need to calculate the present value of this amount. Using the compound interest formula, we can calculate that you need to deposit $735.03 one year from now to have a balance of $1,000 four years from now.
b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, you can use the annuity formula to calculate the required payments. The formula gives us a payment of $210.48 for each of the four years.
c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 one year from now, you can compare the present value of both options. The present value of the four payments of $210.48 each, using an 8% annual interest rate, is $682.96. Therefore, you would choose the lump sum of $750 from your father.
d. If you have only $750 one year from now, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 7.4% compounded annually.
e. If you can only deposit $186.29 each at Years 1 through 4, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 12% compounded annually.
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Complete question:
Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.
a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?
b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?
c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?
d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now? 7.4%
e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?
Write a two column proof for the following statement. Given that the Bible is true, prove that you personally need the Gospel to be in relationship with God. Fo this proof, you will need to establish(using scripture) the following flow of logic: 1 the state of mankind without the Gospel. 2 the state of mankind's relationship with God as a result of #1. 3 the affect of the Gospel message has on mankind. 4 the affect on mankind's relationship with God as a result of #3.
It is important that our understanding and spreading of the gospel comes from the biblical text itself, and it is equal important that we continue to preach and defend the one true gospel. Jesus died and rose again for the forgiveness of our sins.
The word gospel occurs ninety-nine times in the NASB and ninety-two times in the NET Bible. In the Greek New Testament, the gospel is a translation of the Greek noun "good news" occurring 76 times and of the verb "to bring or announce good news" 54 times. Both words are derived from the noun angelos, "messenger". In classical Greek, euangelos is one who brings news of victory or other joyful political or personal news.
The gospel of the grace of God emphasizes that all aspects of salvation are based on grace, not on a merit system.The gospel of the Kingdom is the good news that God will establish His kingdom on earth through the two comings of the Lord Jesus Christ.The gospel of peace describes how this good news of salvation in Christ brings peace in all areas (peace with God, peace with God, peace with others, and peace in the world) through the Savior's victory.Learn more about Equally:
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At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answer:
Step-by-step explanation:
Let's use the variable "s" to represent the number of slices in each pizza.
The drama club bought 999 large pizzas, and each pizza had s slices. So, the total number of pizza slices is given by the product of 999 and s, which can be written as:
999s = 727272
To solve for s, we can divide both sides of the equation by 999:
s = 727272/999
Using a calculator, we can simplify this fraction to:
s ≈ 728.73
Therefore, each pizza has approximately 728 slices. Note that this is an unusual number of slices for a pizza, so it's possible that the problem is not intended to be taken literally, but rather as a math puzzle or word problem.
Answer:
Each pizza has 729 slices.
Step-by-step explanation:
question at a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. of the 210 people surveyed, 70 were adults and 140 were children. of the responses, 150 indicated the cone as the preferred method of eating ice cream. for those surveyed, there was no association between age and preferred method of eating ice cream. which of the following tables shows the distribution of responses? responses
Based on the information provided, the table that correctly displays the data is table III.
What conditions should be met for the table to correctly display the data?To begin, the table should show the total of people surveyed was 210 people.In the table, the total of adults should be 70 and the total of children should be 140.The table should show the results between those who preferred cones vs cups are distributed between adults and children rather than cup or cone being significantly preferred by a group.Note: The question is incomplete; below I attach the missing information:
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a
49⁰
Find the measure of a.
127⁰
72⁰
Answer:
112°
Step-by-step explanation:
Finding the unknown angle in a quadrilateral:
Sum of all angles of a quadrilateral = 360
a + 49 + 72 + 127 = 360
a + 248 = 360
a = 360 - 248
a = 112°
graph of 12x+6y=432 & 9x+3y=270
The line [tex]12x + 6y = 432[/tex] is represented by the red line, and the line equation [tex]9x + 3y = 270[/tex]is represented by the blue line. The point where these two lines intersect is (36,0).
What is equation?In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex]states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" [tex]x^2 + 2x - 3 = 0[/tex]," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.
To plot these lines on a graph, we first need to solve for y in terms of x for each equation.
can plot these lines
[tex]12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90[/tex]
[tex]|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300[/tex]
The line[tex]12x + 6y = 432[/tex]is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).
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& Management Sciences Assignment March 2 Jacob's Pet Shop is a small pet shop that stocks pet food and accessories and offers a local delivery service. The owner, Jacob, employs a shop manager-two shop assistants and a driver for deliveries. Jacob's Pet Shop PET SHOP Figure 1: Money, goods, services, and factors of production flow from Jacob's business into the econo 3.2.1. Discuss how money, goods and services and factors of production flow between Jacob's Pet Shop, consumers who buy pet food and accessorie from the business and the government. 3.2.2. Draw a diagram that shows all these flows. 3.3 List TWO features that a closed economy will prohibit. TOTAL MARKS [50] (2X-
Answer: 3.2.1. Money, goods, services, and factors of production flow between Jacob's Pet Shop, consumers, and the government as follows:
Money flows from consumers to Jacob's Pet Shop when they purchase pet food and accessories, and from Jacob's Pet Shop to the government in the form of taxes.
Goods and services flow from Jacob's Pet Shop to consumers when they purchase pet food and accessories, and from the government to Jacob's Pet Shop in the form of contracts or grants for the delivery service.
Factors of production flow from Jacob's Pet Shop to the economy in the form of employment opportunities for the shop manager, shop assistants, and driver, and from the economy to Jacob's Pet Shop in the form of raw materials and supplies for the business.
3.2.2. The diagram below illustrates the flow of money, goods and services, and factors of production between Jacob's Pet Shop, consumers, and the government:
+--------------------+
| |
| Consumers |
| |
+--------+-----------+
| Purchase pet food and accessories
+--------v-----------+
| |
| Jacob's Pet Shop |
| |
+-------+--------------+
| Sell pet food and accessories
|
+---------v-----------+
| |
| Government |
| |
+---------------------+
3.3. Two features that a closed economy will prohibit are:
International trade: A closed economy does not engage in trade with other countries. All economic activity is confined within the borders of the country.
Movement of capital: A closed economy does not allow the free movement of capital, such as investments or loans, in and out of the country. All capital transactions are restricted within the economy.
was this worth 5 points no way.
Step-by-step explanation:
Frannie has $120. She spends 30% of the money she has on a ticket to the theater. How much did Frannie pay for the theater ticket?
Answer:
36
Step-by-step explanation:
PxW=p
30x120=p
3600=p
x100%
$36=p
(overpriced ticket of you ask me lol)
Using the inverse transform method for discrete distribution, define a process for generating random variates from a binomial distribution with N 6 and p 0.4. (sixth decimal place.)
The another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
The process of generating random variates from a binomial distribution using the inverse transform method for discrete distribution is done as follows:Step 1: Determine the probability mass function (pmf) of the binomial distribution with parameters n and p. For example, for a binomial distribution with n = 6 and p = 0.4, the pmf is given by:P(X=k) = (6 choose k)(0.4)^k(1-0.4)^(6-k), where k=0,1,2,3,4,5,6Step 2: Calculate the cumulative distribution function (CDF) of the binomial distribution by summing the pmf up to each value of k. The CDF is given by:F(k) = P(X ≤ k) = ΣP(X=i) for i=0 to k, where k=0,1,2,3,4,5,6Step 3: Generate a uniform random variate, U, between 0 and 1. For example, U=0.23456.Step 4: Find the smallest value of k such that F(k) ≥ U. This value of k is the random variate X. For example, if U=0.23456, then F(0)=0.10737, F(1)=0.38223, and F(2)=0.74304. Since F(1) is the smallest value of F(k) that is greater than or equal to U, X=1. Therefore, a random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=1.To find another random variate from the same distribution, repeat steps 3 and 4. For example, U=0.987654, F(0)=0.10737, F(1)=0.38223, F(2)=0.74304, F(3)=0.91892, F(4)=0.98544, and F(5)=0.99856. Since F(3) is the smallest value of F(k) that is greater than or equal to U, X=3. Therefore, another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
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Write the equation of the line that passes through the points (- 9, - 9) and (- 8, 1) Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line
The point-slope form of the line equation that passes through the points (- 9, - 9) and (- 8, 1) is equals to the y= 10x + 81.
The standard equation of a line is, y = mx + b where m is the slope and b is the y-intercept. This is a very useful form of the linear equation when comparing lines. We have to determine the equation of the line that passes through the points (- 9, - 9) and (- 8, 1). First we determine the value of slope of line. The formula for slope of line that passing through the points (x₁,y₁),(x₂,y₂) is [tex]m = \frac{y_2 - y_1}{x_2- x_1} [/tex]
here, x₁ = -9, y₁ = -9 , x₂ = -8, y₂ = 1, so
[tex]m = \frac{1-(-9)}{-8-(-9)} = \frac{10}{1} = 10[/tex]
The point-slope form for line passing through points (x₁,y₁),(x₂,y₂) is y − y₁ = m(x − x₁)
=> y - (-9) = 10( x -(-9))
=> y + 9 = 10( x + 9)
=> y + 9 = 10x + 90
=> y = 10x + 81
Hence required equation is y = 10x + 81.
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with k being all the numbers from one to 100, whats x3+y3+z3=k?
X = -80538738812075974, Y = 80435758145817515,
and Z = 12602123297335631 are the values of x,y,z of whole numbers.
What in mathematics is a whole number?
Complete numbers the sum of all natural numbers plus zero. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.
Natural numbers with a starting value of 1 and higher are considered whole numbers. Let's examine a few instances of entire numbers. The alphabet "W" stands for the collection of whole numbers. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}
x3+y3+z3=k, with k being all the numbers from one to 100
X = -80538738812075974,
Y = 80435758145817515,
and Z = 12602123297335631
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PLEASEEE HELP I NEED THIS ASAPPP
Answer:
perimeter=42
Area=90
Step-by-step explanation:
find the length of DEFG:
perimeter=a=b+a+b
28=10+b+10+b
28=20+2b
8=2b
4=b
finding the scale factor:
15/10=3/2
to find the perimeter of WXYZ:
the missing side:
=4x3/2
=6
perimeter=a+b+a+b
perimeter=15+6+15+6
perimeter=42
Area of WXYZ:
Area=bh
Area=15x6
Area=90
PLEASE HELP ME!
i have no clue what to do
Answer:
Step-by-step explanation:
you are going to give more info ?????
the nutty professor sells cashews for $7.70 per pound and brazil nuts for $4.80 per pound. how much of each type should be used to make a 27 pound mixture that sells for $6.41 per pound?
The amount that each type would be 11.87 lbs of cashews and 15.13 lbs of brazil nuts
1. First, find the total cost of 27 lbs of the mixture: 27 lbs x $6.41/lb = $171.07.
2. Next, find the cost of cashews and brazil nuts in the mixture. Cashews cost $7.70/lb and brazil nuts cost $4.80/lb.
3. Subtract the cost of the brazil nuts from the total cost of the mixture: $171.07 - (27 lbs x $4.80/lb) = $105.27.
4. Divide the cost of the cashews ($105.27) by the cost of one pound of cashews ($7.70): $105.27/$7.70 = 13.66 lbs.
5. Subtract the number of pounds of cashews (13.66) from the total pounds of the mixture (27) to find the number of pounds of brazil nuts: 27 - 13.66 = 15.13 lbs.
6. Therefore, the mixture should contain 11.87 lbs of cashews and 15.13 lbs of brazil nuts.
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how to calculate the product of two random variable that follows normal distribution with mean 0 and variance 1
To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula
Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]
Given that two random variables follow a normal distribution with mean 0 and variance 1.
Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)
Now, The expected value of the product of two random variables is given by;
E[XY] = E[X]E[Y] + Cov(X,Y)
Where E[X] and E[Y] are the means of the two random variables X and Y respectively.
Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;
Cov(X,Y) = E[XY] - E[X]E[Y]
Now, E[X] = E[Y] = 0 as both have a mean of 0.
Cov(X, Y) = E[XY] - E[X]E[Y]
⇒ E[XY] = the expected value of the product of X and Y.
As X and Y are independent, their covariance will be zero, which implies;
Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]
Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.
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the diameters of ball bearings are distributed normally. the mean diameter is 58 millimeters and the standard deviation is 6 millimeters. find the probability that the diameter of a selected bearing is greater than 52 millimeters. round your answer to four decimal places.
The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:
P(x > 52) = 1 - P(x ≤ 52)
P(x ≤ 52) = (52 - 58) / 6 = -1
P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.
Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.
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HELP PLEASE … Assuming the input of energy continues for another 2.5 seconds, where will the particle be?
A) cannot be determined
B) positive maximum
C) negative maximum
D) equilibrium
Answer:
To determine the position of a particle given the input of energy, we need to know the type of energy input and the initial position and velocity of the particle. Without this information, we cannot determine the position of the particle after 2.5 seconds.
Therefore, the answer is A) cannot be determined.
Step-by-step explanation:
ABOVE
I need help on this ! Please
Answer: Infinitely many solutions
Step-by-step explanation:
On the graph I have attached, you can see the two lines overlap each other. This means the linear equations have an infinite amount of solutions.
Mrs Smith walks a half a mile a day after work. She works five days a week. How many yards will she have walked for the week by Friday morning?
The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.
One week has seven days in total.
Mrs. Smith walks half a mile each day after work, she walks a total of
0.5 miles/ day × 7 days/ week = 3.5 miles/ week
Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.
Therefore,
0.5 miles/ day × 4 days = 2 miles
To convert miles to yards, we can use the fact that there are 1760 yards in one mile:
2 miles/week × 1760 yards/mile = 3520 yards/week
Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.
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A shipping company is packing a box with one cubic centimeters blocks. The box is 14 centimeters long. 12 centimeters wide and 16 centimeters high. How many one cubic centimeter blocks will fill the box ?
The shipping company will need 2,688 one cubic centimeter blocks to fill the box.
The volume of the box can be calculated as:
Volume = length x width x height
Volume = 14 cm x 12 cm x 16 cm
Volume = 2,688 cubic cm
Since each block is also one cubic cm in volume, we can simply divide the total volume of the box by the volume of one block to find the number of blocks needed to fill the box:
Number of blocks = Volume of box / Volume of one block
Number of blocks = 2,688 cubic cm / 1 cubic cm
Number of blocks = 2,688
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17- 20: In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%."17. What is the population of interest?18. What is the sample being used?19. What is the population parameter of interest, and what is the correct notation for this parameter? What is the relevant statistic?20. Find an interval estimate for the parameter of interest. Interpret it in terms of dissatisfaction in the quality of education students receive. Use two decimal places in your answer.
17. The population of interest is U.S. adults (age 18 and over).
18. The sample being used is 1,012 randomly selected U.S. adults (age 18 and over).
19. The population parameter of interest is the percentage of U.S. adults (age 18 and over) who are dissatisfied with the quality of education students receive in kindergarten through grade 12. The correct notation for this parameter is p and the relevant statistic is 53%.
20. The interval estimate for the parameter of interest is 49% - 57%, which indicates that between 49% and 57% of U.S. adults (age 18 and over) are dissatisfied with the quality of education students receive in kindergarten through grade 12.
The radius of a circle is 8 meters. What is the circle's circumference?
Use 3.14 for л.
Answer:
circumference=50.24
Step-by-step explanation:
c=2x3.14xr
c=2x3.14x(8)
c=50.24
is this A.less then
b.equal too
c.more then
Answer:
A. Less than
Step-by-step explanation:
Keilantra and Samantha work at a dry cleaners ironing shirts. Keilantra can iron 30 shirts per hour, and Samantha can iron 15 shirts per hour. Keilantra and Samantha worked a combined 11 hours and ironed 240 shirts. Graphically solve a system of equations in order to determine the number of hours Keilantra worked, x, and the number hours Samantha worked, y.
Answer: Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours
Step-by-step explanation:
We will use the variables x and y the question provides. We know the time worked by each person added together will equal the combined total time. We can write an equation to show this using addition.
x + y = 11 hours
Next, we know that Keilantra ironed 30 per hour, Samantha ironed 15 per hour and that they ironed 240 shirts. We can write another equation to represent this using addition and multiplication.
30x + 15y = 240
Next, we will graph these two equations. See attached. The solution is the point of intersection written as (x, y). This is (5, 6) meaning that Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours.
Environment An accident at an oil drilling platform is causing a circular oil slick. The slick is 0.08 foot thick, and when the radius of the slick is 150 feet, the radius is increasing at the rate of 0.5 foot per minute. At what rate (in cubic feet per minute) is oil flowing from the site of the accident?
The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.
To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.
We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".
The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.
Differentiating both sides with respect to time, we get:
dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)
We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.
Substituting these values into the formula, we get:
dV/dt = 2π(150)(0.5) + π(150)^2(0)
dV/dt = 47123.74 cubic feet per minute
Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.
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