The surface area of the pyramid is 44.2 square inches, which is closest to option (C) 44.2.
Surface area calculation.
To solve the problem, we can start by using the formula for the area of an equilateral triangle to find the length of one side of the base. Let s be the length of one side of the base, then we have:
Area of the base = (sqrt(3)/4) * s^2 = 13
Solving for s, we get:
s^2 = (4 * 13) / sqrt(3)
s = 8.0
Therefore, the perimeter of the base is 3 * s = 24 inches
Next, we can use the formula for the surface area of a pyramid to find the surface area of the entire pyramid. Let B be the area of the base, then we have:
Surface area = B + (1/2) * P * h
where P is the perimeter of the base and h is the height of the pyramid.
Substituting the given values, we get:
Surface area = 13 + (1/2) * 4.8 * 13
Surface area = 13 + 31.2
Surface area = 44.2 square inches
Therefore, the surface area of the pyramid is 44.2 square inches, which is closest to option (C) 44.2.
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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:
how many positive integers less than 100 are neither multiples of 2 nor multiples of 3 ? 30 31 32 33 34
Positive integers less than 100 that are neither multiples of 2 nor multiples of 3 are 33. Option (d)
How to count the number of integers that are not multiples of 2 or 3?To solve this problem, we can use the principle of inclusion-exclusion.
There are a total of 99 positive integers less than 100 (from 1 to 99, inclusive).
We want to count the number of integers that are not multiples of 2 or 3.
The number of integers that are multiples of 2 is 49 (from 2 to 98, inclusive, with a common difference of 2).
The number of integers that are multiples of 3 is 33 (from 3 to 99, inclusive, with a common difference of 3).
However, we have double-counted the integers that are multiples of both 2 and 3 (i.e., multiples of 6). There are 16 such integers (from 6 to 96, inclusive, with a common difference of 6).
Therefore, the number of integers that are not multiples of 2 or 3 is:
99 - (49 + 33 - 16) = 83
So there are 83 positive integers less than 100 that are neither multiples of 2 nor multiples of 3.
Therefore, the answer is (d) 33.
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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.
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:
Need help ASAP
there are 600 poetry books at the library.Of the poetry books,8 1/2% are for children.How many poetry books at the library are for children
The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.
What is number?Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.
8 1/2% is equal to 0.04.
To calculate the number of poetry books for children, multiply 0.04 by 600.
0.04 x 600 = 24
To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.
In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.
To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.
Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.
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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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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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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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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:
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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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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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:
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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23. What is the solution set of the equation
x²-3x - 10 = 0
(1) {5,-2}
(2){-5,-2}
(3) { 5,2}
(4) {-5,2}
Answer:
Step-by-step explanation:
x²-3x - 10 = 0
x² -5x + 2x - 10 = 0
(x² -5x)+ (2x - 10) = 0
x(x - 5) +2(x - 5) = 0
(x + 2) (x - 5) = 0
x +2 = 0
x = -2
OR
x -5 = 0
x = 5
hence ans is, (1) {5,-2}
PLEASE HELP!! ITS TIMED! WILL GIVE BRAINIEST TO THE FIRST CORRECT ANSWER!
Elijah bought earrings to give to his mother for her birthday. The earrings are in a case
shaped like a rectangular prism that is 2 inches long, 1½ inches wide, and 1 inches tall. He
doesn't want his mother to guess what the gift is, so he put the case in a larger, cube-shaped
gift box. The gift box is 4 inches along each edge.
What is the volume of the extra space left in the gift?
Answer:
The answer is 59 ½
Step-by-step explanation:
4×4×4-2×1 ½×1 ½
= 64 - 2× 3/2 × 3/2
= 64 - 9/2
= 128/2 - 9/2
= 119/2
= 59 ½ in3
Hope this helped :)
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.
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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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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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]
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
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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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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On Wednesday, it rained 2 1/2 inches. This was 3/4 of an inch more than how much it rained the week before. What was the rainfall amount the week before?
Therefore , the solution of the given problem of fraction comes out to be the previous week's rainfall total was 7/4 inches.
A fraction is what?Any combination of sections of the same size can be used to represent the whole. Quantity is described as "a portion" under a particular measurement in Standard English. 8, 3/4. Fractions are included in wholes. These act as the ratio divisor, which is a pair of integers in mathematical words. Here are a couple of examples showing how to change straightforward halves into entire numbers.
Here,
Let's refer to the amount of rain that fell the previous week as x inches.
The information provided indicates that it rained 2 1/2 inches on Wednesday, which is 3/4 of an inch more than the quantity that fell the previous week. This knowledge can be expressed as an equation:
=> 2 1/2 = x + 3/4
=> 2 1/2 - 3/4 = x
=> 2 1/2 = 5/2
=> 3/4 = 3/4
=> 5/2 - 3/4 = x
In this instance, 2 and 4 have a common denominator of 4, which is 4. So, using 4 as the common denominator, we can rewrite the fractions as follows:
=> 5/2 - 3/4 = x
=> (5/2) × (2/2) - 3/4 = x
=> 10/4 - 3/4 = x
=> 7/4 = x
Therefore, the previous week's rainfall total was 7/4 inches.
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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
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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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
When comparing the data from the two locations, the measure of center that should be used to determine which location typically has the cooler temperature is the median.
In Sunny Town, the histogram shows that the shaded bars are skewed to the right, indicating that the distribution is positively skewed. This means that there are a few high temperatures that pull the mean towards the higher end.
However, the median, which represents the middle value when the data is arranged in ascending order, is less affected by extreme values and is a better measure of the center for skewed distributions.In Desert Landing, the histogram shows a symmetric distribution, with the shaded bars evenly distributed around the center.
In this case, both the mean and median can be considered reliable measures of the center.Therefore, to determine which location typically has the cooler temperature, we should use the median.
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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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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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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°.
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