The correct answer for the given problem will be option C. The total depreciation value of the laptop.
What does the term "depreciation of value" means?The decline in worth or monetary value of an asset over time owing to different reasons such as wear and tear, obsolescence, or changes in market circumstances is referred to as depreciation in value. It is a typical accounting term that is used to distribute the cost of a physical or intangible asset throughout its useful life, indicating the loss of value over time.
The term '17m' in the given formula (856-17m) reflects the laptop's monthly depreciation value.
Depreciation is the gradual decline in the value of an asset. In this situation, the laptop's worth is declining by $17 every month. The variable'm' reflects the number of months since Pamela acquired the laptop. As a result, multiplying 17 by'm' yields the entire amount of depreciation that has happened on the laptop after'm' months.
As a result, the second word '17m' in the formula (856-17m) indicates the laptop's entire depreciation value after'm' months. The correct answer is Option C.
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Serena paid $194. 99 for a game system and then bought two equally-priced games. She spent a total of $284. 97. Part A
If p represents the price of one game, which equation represents the situation?
The condition that speaks to the circumstance is 194.99 + 2p = 284.97 where p represents the price of one game.
Let's begin by setting up the condition based on the data given.
Serena paid $194.99 for the amusement framework and two diversions that took a toll at the same cost, let's call it "p".
The whole sum that went through Serena was $284.97.
So able to set up the condition as:
194.99 + 2p = 284.97
The left-hand side of the condition represents the whole sum that went through the amusement framework and two diversions. The right-hand side speaks to the whole sum went through by Serena.
therefore, the equation that speaks to the circumstance is:
194.99 + 2p = 284.97 .
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about 4% of the population has a particular genetic mutation. 600 people are randomly selected.find the mean for the number of people with the genetic mutation in such groups of 600
The mean number of people with the genetic mutation in a randomly selected group of 600 people is 24.
Given that about 4% of the population has a particular genetic mutation, the probability that a randomly selected individual has the mutation is
P(mutation) = 0.04
The number of people with the mutation in a group of 600 individuals follows a binomial distribution, where the number of trials is 600 and the probability of success is 0.04.
The mean of a binomial distribution is given by the formula:
mean = n × p
where n is the number of trials and p is the probability of success.
Substituting the values, we get:
mean = 600 × 0.04
mean = 24
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customers arrive at a checkout counter in a department store according to a poisson distribution at an average of seven per hour. during a given hour, what are the probability that exactly five customers arrive?
If the customers arriving at "checkout-counter" in a department store follow a Poisson distribution, then probability of exactly 5 customers arriving in one hour is approximately 0.1277 or 12.77%.
The "Poisson-Distribution" is defined as a discrete probability distribution which represents the number of events occurring in a "fixed-interval" of time, given a known "average-rate" of occurrence.
In this case, the average-rate of customer arrivals is 7 customers per hour.
Let "average-rate" be "λ = 7",
We need to find the probability of exactly "5-customers" arriving in one hour, which means we need to calculate P(X = 5), where X follows a Poisson distribution with λ = 7.
The Poisson probability mass function (PMF) formula is:
⇒ P(X=x) = (λˣ × e⁻ˣ))/x!
where:
P(X=k) is the probability of X taking the value "x",
λ = average rate parameter. "e" = Euler's number,
"x" = number of events, "x!" = factorial of x,
Substituting the values of λ = 7, k = 5,
We get,
⇒ P(X=5) = (7⁵ × e⁻⁷)/5!,
⇒ P(X=5) ≈ 0.1277,
Therefore, the required probability of exactly 5 customers arriving in one hour is approximately 0.1277 or 12.77%.
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solve for x using soh cah toa I have tried figuring it out but it says its wrong
Answer:
13.416407865
Step-by-step explanation:
You wouldn't use soh cah toa
There is no angle given. Instead you should do 6²+12²=180
And then you would square root 180=13.416407865
Therefore the answer is 13.416407865
1. general junkfoods has collected data on the last 10,000 boxes of cereal they produced. a. what is the average weight of a box of their cereal? b. what is the standard deviation of the weight of their boxes of cereal? c. what are 1 sigma, 2 sigma and 3 sigma values for this data? d. draw a bell graph showing these sigma values (av 1sigma, av 2sigma, av 3sigma) and the usl and lsl.
For a general junk food has collected data on the last 10,000 boxes,
a) The average weight of a box of their cereal is "= Average ( A:10, A : 10010)."
b) The standard deviation of the weight of their boxes of cereal "= STD ( A:10, A : 10010)."
c)
We have a general junk food has collected data on the last 10,000 boxes of cereal they produced. We have no information about the data points related to 10000 boxes of cereal produced by general junkfoods. But we can use Excel function, Let the 10000 boxes values be lie in Excel sheet from row 10 to 10010.
a) the average weight of a box of their cereal is calculated by the following excel function, " = average ( range)"
that is ' = Average ( A:10, A : 10010)'
b) For standard deviations the weight of their boxes of cereal is calculated by the following excel function , "= STD ( A:10, A : 10010)."
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Complete question:
1. Using excel, answer the following questions. Write down the Excel formulas used at each step.1. General Junkfoods has collected data on the last 10,000 boxes of cereal they produced.a. What is the average weight of a box of their cereal
b. what is the standard deviation of the weight of their boxes of cereal? c. what are 1 sigma, 2 sigma and 3 sigma values for this data? d. draw a bell graph showing these sigma values (av 1sigma, av 2sigma, av 3sigma) and the usl and lsl.
Ant killer is a poison that is designed to attack an ant hill from the inside out. Ants take the bait inside and
feed it to the colony. The function A(t) = 45000 (. 271)* represents the population of an ant colony after
ant Kiler has been applied. A(t) represents the remaining population and t is time in days. After how many days will there be less than 250 ants remaining in the colony?
It will take approximately 29 days for the ant population to drop below 250.
What is natural logarithm means ?The logarithmic function to the base e is called the natural logarithmic function and it is denoted by loge.
f(x) = loge x
To find out how many days it will take for the ant population to drop below 250, we need to solve for the value of t in the equation:
A(t) = [tex]45000*(0.271)^t[/tex]< 250
We can start by simplifying the equation:
[tex]45000*(0.271)^t[/tex]< 250
[tex](0.271)^t[/tex] < 250/45000
[tex](0.271)^t[/tex]< 0.00555556
Next, we can take the natural logarithm of both sides to isolate t:
ln[[tex](0.271)^t][/tex] < ln(0.00555556)
t*ln(0.271) < ln(0.00555556)
t > ln(0.00555556) / ln(0.271)
t > 28.32
Therefore, it will take approximately 29 days for the ant population to drop below 250.
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HLEP me please with math
For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.
Explain about the scale factor:On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.
Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.
From the diagram:
coordinate of A = (1,1)
coordinate of A' = (5,5)
Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'
Same applies with the coordinates of B, C and D.
Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.
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The equation ( x + 6)^2 + ( y + 4) ^2 = 36 models the position and range of the source of a radio signal.
1. Where is the signal located?
2. What is the range of the signal? Only enter numerical values.
1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).
What is the range of the signal?2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).
To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.
In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.
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Please help solve this will give brainlyist
Segment CP is tangent to circle C at point B.
How to prove that the line is tangent to a circle?
Draw circle C with center at point A and radius AD = CD = DE.
Draw point P outside the circle C.
Draw segment AP and extend it to intersect the circle at point B.
Draw segment BD.
Draw segment CP.
Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.
Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).
Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).
Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.
Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.
Therefore, segment CP is tangent to circle C at point B.
Hence, the proof is complete.
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An isosceles triangle has an angle that measures 102°. What measures are possible for the other two angles? Choose all that apply.
Answer: 39°
Step-by-step explanation:
In an isosceles triangle, two sides are of equal length, and the angles opposite these equal sides are also equal. Let's call these two equal angles x. Given that one angle measures 102°, we can find the possible measures for the other two angles.
The sum of the interior angles of a triangle is always 180°. So, we have:
x + x + 102° = 180°
2x = 180° - 102°
2x = 78°
x = 39°
Therefore, the other two angles in the isosceles triangle are both 39°.
Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s correct.
Answer: spinner: yellow, die: 1
Step-by-step explanation:
We will look at the table given and select the answer option that correctly lines up with what we're looking for based on the given context, see attached.
The spinner must be on yellow and the die must be on 1 or 4, this leads us to the 3rd answer option;
spinner: yellow, die: 1
Choose the two data sets that have equal standard deviations.
Data set A: 40, 50, 60, 60, 70, 80
Data set B: 90, 95, 100, 105, 110
Data set C: 50, 55, 60, 65, 70
Data set D: 33, 54, 54, 60, 74
Find the two data sets that have the same standard deviation. Select all that apply.
Answer:
The two data sets that have equal standard deviations are:
Data set A: 40, 50, 60, 60, 70, 80
Data set C: 50, 55, 60, 65, 70
To see this, we can calculate the standard deviation for each data set using a formula or a calculator. Alternatively, we can observe that data sets A and C have similar ranges and distributions, which suggests that they may have similar standard deviations. In contrast, data sets B and D have different ranges and distributions, which suggests that their standard deviations may be different.
Find the radius of convergence, R, of the series. [infinity]
n = 2
(x + 8)n
8n ln(n)
The radius of convergence is 4.
To find the radius of convergence, R, of the collection, we can use the ratio test:
[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]
[tex]lim_n→∞ |(a_{(n+1})/[/tex]
[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]
For the series to converge, this limit need to be less than 1. therefore, we've:
[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]
For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:
|(x+8) / 4| < 1
Taking the absolute cost under consideration, we have cases:
Case 1: (x+8)/4 < 1
In this case, we have x < -4.
Case 2: (x+8)/4 > -1
In this case, we have x > -12.
Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):
R = min{8, 4} = 4
So, 4 is the radius of convergence.
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Can someone help me with this, please?
Learning Task 2: Try to solve the following problem. Use the block model
to help you. Write your answer in your notebook.
1) Ruben can paint square meters per hour. At the same rate, how
many square meters can he paint in an hour.
1
2 6
1
2 2
2) The lot has a length of meters and a width of meters. The
piece of lot per square unit is ₱ 850. 0. What is the total value of the lot?
Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.
Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour
Help with algebra 2 homework
The composite functions are given as follows:
[tex]f^{-1}(f(x)) = x[/tex][tex]f^{f^{-1}(x)} = x[/tex]How to define the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the function rule presented as follows:
(f ∘ g)(x) = f(g(x)).
For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).
The composite functions for this problem are given as follows:
[tex]f^{-1}(f(x)) = f^{-1}(0.5x^2 + 3) = \sqrt{2(0.5x^2 + 3) - 6} = \sqrt{x^2} = x[/tex][tex]f^{f^{-1}(x)} = f(\sqrt{2x - 6}) = 0.5(\sqrt{2x - 6})^2 + 3 = x - 3 + 3 = x[/tex]More can be learned about composite functions at https://brainly.com/question/10687170
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a circle of radius r has area a = πr2. if a random circle has radius that is uniformly dis- tributed on [0, θ]: what are the mean and variance of the area of the circle?
The variance of the area of the circle is [tex]\pi^2\theta^{4/45}[/tex].
The mean area of the circle is [tex]\pi\theta^{2/3}.[/tex]
Let X be the radius of the circle, uniformly distributed on [0, θ].
The probability density function of X is given by:
[tex]f(x) = 1/\theta, for 0 \leq x \leq θ[/tex]
= 0, otherwise
Let Y be the area of the circle. Then[tex]Y = \pi X^2.[/tex] We want to find the mean and variance of Y.
Mean of Y:
By the law of the unconscious statistician, the mean of Y is given by:
[tex]E(Y) = E(\pi X^2) = \pi E(X^2)[/tex]
[tex]E(X^2)[/tex] using the formula for the variance of X:
[tex]Var(X) = E(X^2) - [E(X)]^2[/tex]
Since X is uniformly distributed on [0, θ], we have:
[tex]E(X) = (0 + \theta)/2 = \theta/2[/tex]
[tex]Var(X) = [(\theta - 0)^2]/12 = \theta^{2/12}[/tex]
Solving for [tex]E(X^2)[/tex], we get:
[tex]E(X^2) = Var(X) + [E(X)]^2 = \theta^2/12 + (\theta/2)^2 = \theta^{2/3}[/tex]
Substituting this into the expression for E(Y), we get:
[tex]E(Y) = \pi E(X^2) = \pi (\theta ^{2/3}) = \pi \theta^{2/3}[/tex]
Variance of Y:
To find the variance of Y, we can use the formula for the variance of a function of a random variable:
[tex]Var(Y) = E(Y^2) - [E(Y)]^2[/tex]
We can find[tex]E(Y^2)[/tex] using the law of the unconscious statistician:
[tex]E(Y^2) = E[(\pi X^2)^2] = \pi^2E(X^4)[/tex]
To find [tex]E(X^4)[/tex], we can use the formula for the fourth moment of a uniform distribution:
[tex]E(X^4) = (\theta^4 + 2\theta^2)/5[/tex]
Substituting this into the expression for[tex]E(Y^2)[/tex], we get:
[tex]E(Y^2) = \pi^2E(X^4) = \pi^2[(\theta^4 + 2\theta^2)/5] = \pi^2\theta^{4/5} + 2\pi^2\theta^{2/5}[/tex]
Substituting this and the expression for E(Y) into the formula for the variance of Y, we get:
[tex]Var(Y) = E(Y^2) - [E(Y)]^2[/tex]
[tex]= \pi^2\theta^{4/5} + 2\pi^2\theta^{2/5} - (\pi\theta^2/3)^2[/tex]
[tex]= \pi^2\theta^4/45[/tex]
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An n-year loan involves payments of $800 at the end of each month. The interest rate is 12% convertible monthly. If the interest paid in the 45th monthly installment is $424.45, calculate the total amount of interest paid over the life of the loan.
The total amount of interest paid over the life of the loan is $1863.45.
The present value of the loan.
Since there are 12 months in a year, and the loan has n-years, there are 12n monthly payments.
Let's use the formula for the present value of an annuity due:
[tex]PV = PMT \times ((1 - (1 + r) ^(-n)) / r) \times (1 + r)[/tex]
PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.
Substituting the given values, we get:
[tex]PV = \$800 \times ((1 - (1 + 0.12/12) ^(-12n)) / (0.12/12)) \times (1 + 0.12/12)[/tex]
[tex]PV = \$800 \times ((1 - (1.01)^(-12n)) / 0.01) \times 1.01[/tex]
[tex]PV = \$800 \times ((1 - 1.01^(-12n)) / 0.01) \times 1.01[/tex]
[tex]PV = \$800 \times ((1 - 0.887^(-n)) / 0.01) \times 1.01[/tex]
The formula for the interest paid in any given month of an annuity due:
[tex]I = PV \times r \times (1 + r) ^(m - 1)[/tex]
I is the interest paid in the 45th month, PV is the present value of the loan, r is the monthly interest rate, and m is the month.
Substituting the given values for the 45th month, we get:
[tex]\$424.45 = PV \times 0.01 \times (1 + 0.01 )^(45 - 1)[/tex]
[tex]\$424.45 = PV \times 0.01 \times (1.01)^4^4[/tex]
[tex]PV = \$424.45 / (0.01 \times (1.01)^4^4)[/tex]
PV =[tex]\$75799.45[/tex]
Now that we know the present value of the loan, we can calculate the total amount of interest paid over the life of the loan.
Let's use the formula for the total interest paid in an annuity due:
[tex]Total interest = (PMT \times n \times (n + 1) / 2) - PV[/tex]
Substituting the given values, we get:
Total interest = [tex](\$800 \times 12n \times (12n + 1) / 2) - \$75799.45[/tex]
Total interest = [tex]\$9600n^2 + \$4800n - \$75799.45[/tex]
We can solve for n by using the fact that the interest paid in the 45th month is $424.45:
[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1 + 0.01)^(45 - 1)[/tex]
[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1.01)^4^4[/tex]
n = 4.5
Substituting n = 4.5 into the formula for total interest, we get:
Total interest =[tex]\$9600 \times (4.5)^2 + \$4800 \times 4.5 - \$75799.45[/tex]
Total interest = $1863.45
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If y varies directly with x and y=-16 when x=8, find y when x=2
Answer:
y=-4
Step-by-step explanation:
The answer is going to be -4 as when y=-16 x=8.
4.7. the time it takes a printer to print a job is an exponential random variable with the expectation of 12 seconds. you send a job to the printer at 10:00 am, and it appears to be third in line. what is the probability that your job will be ready before 10:01?
The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.
We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.
The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.
Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.
The probability that the first job is finished before 10:01 is given by:
P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935
Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:
P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693
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Determine the density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm3.
The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.
What do you mean by the density of an object?Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.
Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:
Density = Mass/Volume
Substituting the given values, we get:
Density = 6 grams/12 cm³
Density = 0.5 grams/cm³
Therefore, the density of the sample is 0.5 grams/cm³.
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if I have an 84% which is a B but get a 65 which is a D whats my grade now?
Answer: C
Step-by-step explanation:
I need this answer asap can someone help?
The volume of the solid is 4,503.22 in³.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes
The volume of a solid with a hollow cylinder can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
Assuming the dimensions in the figure are in inches, the outer cylinder has a height of 17 inches and a radius of 9 inches, so its volume is:
[tex]V_{outer} = \pi * r^2 * h[/tex]
= π × 9² × 17 ≈ 4,842.51 in³
The inner cylinder has a height of 12 inches and a radius of 3 inches, so its volume is:
[tex]V_{inner} = \pi * r^2 * h[/tex] = π × 3² × 12 ≈ 339.29 in³
To find the volume of the solid, we need to subtract the volume of the inner cylinder from the volume of the outer cylinder:
[tex]V_{solid }= V_{outer} - V_{inner}[/tex]
≈ 4,842.51 - 339.29 ≈ 4,503.22 in³
Hence, the volume of the solid is 4,503.22 in³.
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345.5 - 131.75 (explain how to get that answer)
Answer: 213.75
Step-by-step explanation:
Add a zero to the hundredths place of 345.5 making it 345.50, then subtract as you would normally.
Use the medians to compare the lengths of the alligators from the two swamps
Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.
To compare the lengths of the alligators from two different swamps using medians, we need to collect data on the lengths of alligators from each swamp. Then we can calculate the median length of alligators in each swamp and compare them.
Let's say we have collected the following data on the lengths of alligators from Swamp A and Swamp B:
Swamp A: 4 feet, 5 feet, 6 feet, 7 feet, 8 feet
Swamp B: 3 feet, 5 feet, 6 feet, 7 feet, 9 feet
To find the median length of alligators in Swamp A, we need to arrange the lengths in order from smallest to largest: 4, 5, 6, 7, 8. The middle value is 6, so the median length of alligators in Swamp A is 6 feet.
To find the median length of alligators in Swamp B, we also need to arrange the lengths in order from smallest to largest: 3, 5, 6, 7, 9. The middle value is also 6, so the median length of alligators in Swamp B is also 6 feet.
Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length. However, it is important to note that this comparison is based only on the median length and not on the full distribution of alligator lengths, so it is possible that there are other differences between the two populations of alligators that are not captured by this comparison.
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Suppose you had a bag that contained 100 Skittles! How many red Skittles would it need to have in order for you to have the same ratio of that color?, Show your work and explain your reasoning
Answer: Let's say we want to find out how many red Skittles we need to add to the bag to have the same ratio of red Skittles as in the original bag.
Suppose the original bag contains x red Skittles. Then, the ratio of red Skittles to the total number of Skittles in the bag is x/100.
Let's say we add y red Skittles to the bag, so the total number of red Skittles in the bag becomes x + y. The total number of Skittles in the bag becomes 100 + y, since we only added red Skittles.
For the ratio of red Skittles to be the same as in the original bag, we need:
(x + y) / (100 + y) = x / 100
Cross-multiplying, we get:
100(x + y) = x(100 + y)
Simplifying and rearranging, we get:
y = 100x / (100 - x)
So, we need to add 100x / (100 - x) red Skittles to the bag to have the same ratio of red Skittles as in the original bag. For example, if the original bag has 20 red Skittles, we need to add:
y = 100(20) / (100 - 20) = 25
So, we need to add 25 red Skittles to the bag to have the same ratio of red Skittles as in the original bag.
Step-by-step explanation:
An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 6269 fur seal pups were
tagged in early August. In late August, a sample of 1100 pups was observed, and 221 of these were found to have been previously
tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.
The estimated total number of fur seal pups in Rookery A is.
(Round to the nearest whole number.)
Answer: We can use a proportion to estimate the total number of fur seal pups in Rookery A. Let x be the total number of fur seal pups in Rookery A. Then we have:
6269/x = 221/1100
Cross-multiplying, we get:
221x = 6269 * 1100
Dividing both sides by 221, we get:
x = 6269 * 1100 / 221
Simplifying, we get:
x = 31,245.25
Rounding to the nearest whole number, we get:
x ≈ 31,245
Therefore, the estimated total number of fur seal pups in Rookery A is 31,245.
Step-by-step explanation:
Use the graph to write a linear function that relates y to x
PLEASE HELP
Answer:
[tex]y = \frac{1}{3} x + 3[/tex]
Step-by-step explanation:
Start at the point (-3, 2). Go up 1 unit, then right 3 units, to the point (0, 3). The slope of the line is 1/3, and the y-intercept is 3, so we have
[tex] y = \frac{1}{3} x + 3[/tex]
Pierre received a parking ticket with an original fee of $22. Each month that he failed to make payment, fees of $7 were added. By the time he paid the ticket, his bill was $36. What was the ratio of fees to the cost of the ticket?
Answer: 7:11
Step-by-step explanation:
Use Euler's method with the given step size to estimate y(1. 4) where y(x) is the solution of the initial-value problem
y′=x−xy,y(1)=0
1. Estimate y(1. 4) with a step size h=0. 2ℎ=0. 2.
Answer: y(1. 4)≈
2. Estimate y(1. 4) with a step size h=0. 1ℎ=0. 1.
Answer: y(1. 4)≈
Euler's method with step size [tex]$h = 0.2$[/tex], we estimate [tex]$y(1.4) \approx 0.32$[/tex].
Euler's method with step size[tex]$h = 0.1$[/tex], we estimate [tex]$y(1.4) \approx 0.343$[/tex].
Euler's method to approximate the solution of the initial-value problem:
[tex]y \prime =x - xy,y(1)=0[/tex]
with step size [tex]$h = 0.2$[/tex]and [tex]$h =0.1[/tex]
Euler's method with step size [tex]$h = 0.2$[/tex], we have:
[tex]x_0 &= 1 \y_0 &= 0 \x_1 &= 1 + h = 1.2 \y_1 &= y_0 + hf(x_0, y_0) = 0 + 0.2(1-1\cdot 0) = 0.2 \x_2 &= 1.2 + h = 1.4 \y_2 &= y_1 + hf(x_1, y_1) = 0.2 + 0.2(1.2 - 1.2\cdot 0.2) = 0.32 \[/tex]
Euler's method with step size [tex]$h = 0.2$[/tex], we estimate.
[tex]$y(1.4) \approx 0.32$[/tex].
Euler's method with step size[tex]$h = 0.1$[/tex], we have:
[tex]x_0 &= 1[/tex]
[tex]y_0 &= 0[/tex]
[tex]x_1 &= 1 + h = 1.1[/tex]
[tex]y_1 &= y_0 + hf(x_0, y_0) = 0 + 0.1(1-1\cdot 0) = 0.1[/tex]
[tex]x_2 &= 1.1 + h = 1.2[/tex]
[tex]y_2 &= y_1 + hf(x_1, y_1) = 0.1 + 0.1(1.1 - 1.1\cdot 0.1) = 0.19[/tex]
[tex]x_3 &= 1.2 + h = 1.3[/tex]
[tex]y_3 &= y_2 + hf(x_2, y_2) = 0.19 + 0.1(1.2 - 1.2\cdot 0.19) = 0.266[/tex]
[tex]x_4 &= 1.3 + h = 1.4[/tex]
[tex]y_4 &= y_3 + hf(x_3, y_3) = 0.266 + 0.1(1.3 - 1.3\cdot 0.266) = 0.343 \\end {align}[/tex]
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Dos numeros enteros consecutivos en lenguaje algebraico
Two consecutive integers in algebraic language would be 7 and 8
How is this so?
Let's call the first integer "X" then the next consecutive integer would be "x+1".
so if the sum of the two integers is 15, we can write the following expression.
x + (x+1) = 15
Solving for x we get
2x + 1 = 15
2x =14
x = 7
Hence, the two consecutive integers in this case are 7 and 8.
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Translation:
Two consecutive integers in algebraic language