An observation that causes the values of the slope and the intercept in the line of best fit to be considerably different from what they would be if the observation were removed from the data set is said to be an outlier.
An outlier is an observation that is significantly different from other observations in a dataset. It is a data point that is located far away from the other data points, and it may have a disproportionate influence on the analysis and conclusions drawn from the data.
what is slope?
Slope is a measure of the steepness of a line. It is calculated as the change in the y-coordinate (vertical change) divided by the change in the x-coordinate (horizontal change) between two points on the line. The slope represents the rate at which the line is rising or falling.
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16.2-3. cars arrive at a tollbooth at a mean rate of five cars every ten minutes according to a poison process. find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll.
Therefore, the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll is approximately 0.038.
Since the arrival of cars at a tollbooth follows a Poisson process with a rate of 5 cars every 10 minutes, the time between arrivals of cars follows an exponential distribution with a mean of 2 minutes (10 minutes / 5 cars). Let X be the time between arrivals of cars. Then, X ~ Exp(1/2) since the mean of an exponential distribution is equal to the reciprocal of the rate.
To find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll, we need to find the probability that the sum of the waiting times for the first seven cars is less than 26.30 minutes and the waiting time for the eighth car is greater than the remaining time.
Let Y be the waiting time for the eighth car. Then, Y ~ Exp(1/2) since the waiting time for each car is independent and identically distributed. Therefore, the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll can be calculated as follows:
P(Y > 26.30 - T), where T is the sum of waiting times for the first seven cars.
Since the waiting times for each car are independent, the sum of the waiting times for the first seven cars follows a gamma distribution with parameters k = 7 and θ = 1/2. Therefore, we have:
T ~ Gamma(7, 1/2)
Now, we can calculate the desired probability as follows:
[tex]P(Y > 26.30 - T) = ∫∫\int\limits^a_b { (e^(-t/2) * (1/2)^{7})/6! } \, dx[/tex]
= 0.038
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Some members of a community garden in California want to plant an orchard to earn some extra income. After researching, they decided to plant avocado trees. Avocado saplings (baby trees) cost $20 each. It takes 3 years for avocado trees to reach maturity and bear fruit, but after they do, each tree will produce $125 worth of fruit. The community garden is made of 50 members and their goal is to sell $250 per capita each year.
Calculate the total number of trees that all the garden members will need in total in their orchard to meet the goal.
The total number of trees that all the garden members will need in total in their orchard to meet the goal is 40 trees.
To meet the goal of selling $250 per capita each year, the community garden will need to generate a total of:
[tex]$250 * 50 members[/tex] = [tex]$12,500 per year[/tex]
Each avocado tree costs $20 and produces $125 worth of fruit per year after maturity. Therefore, the net revenue per tree per year is:
$[tex]125[/tex]- $[tex]20[/tex] = $[tex]105[/tex]
Since it takes 3 years for a tree to mature, we can calculate the net revenue per tree over 3 years as:
$[tex]105[/tex] x [tex]3[/tex] = $[tex]315[/tex]
To meet the annual revenue goal of $12,500, the community garden will need to plant:
$[tex]12,500[/tex] / $315 per 3-year period = [tex]39.68[/tex] trees
Since we can't plant fractional trees, we need to round up to the nearest whole number. Therefore, the total number of trees that all the garden members will need in total in their orchard to meet the goal is: 40 trees
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for a bill totalling $5.65, the cashier received 25 coins consisting of nickels and quarters. how many nickels did the cashier receive?
Answer: 3 Nickles.
Step-by-step explanation:
22 quarters adds up to $5.50
The remaining 15c is accounted by the last 3 coins, which are nickles.
If Maira drives east from Atlanta to
Augusta in 2.5 hours. If her average
speed is 55 miles/hour, how far is
Augusta from Atlanta?
Answer:
137.5 miles
Step-by-step explanation:
To calculate the distance between Atlanta and Augusta, we can use the formula:
Distance = Speed x Time
We are given the speed and time, so we can substitute those values into the formula and solve for the distance.
Distance = 55 miles/hour x 2.5 hours
Distance = 137.5 miles
Therefore, Augusta is 137.5 miles away from Atlanta.
Answer: The answer is 147 miles per hour
Step-by-step explanation:
Each week you collect 20 cards. Your friend collects 12 cards each week. How many cards does your friend have if you have 240 cards?
If you have 240 cards and collect 20 cards per week, you have 96 cards after 8 weeks and your freind have 240 cards in 7.5 weeks.
First, we need to find the total number of cards collected per week by both you and your friend
Total cards collected per week = your cards + friend's cards
Total cards collected per week = 20 + 12
Total cards collected per week = 32
Now, we can find the number of weeks it would take for your friend to collect 240 cards
240 cards ÷ 32 cards per week = 7.5 weeks
Since we cannot have a fractional number of cards, we need to round up to the nearest whole number of weeks. Therefore, it would take your friend 8 weeks to collect 240 cards.
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random samples of size 400 are taken from an infinite population whose populalation proportion is 0.2. the mean and standard deviation of the sample proportion are
The mean of the sample proportion is 0.2, and the standard deviation of the sample proportion is approximately 0.02.
The mean and standard deviation of the sample proportion for random samples of size 400 taken from an infinite population with a population proportion of 0.2, we will use the formulas for the mean and standard deviation of sample proportions.
The mean of the sample proportion is equal to the population proportion (p):
μ_p = p
The standard deviation (σ_p) of the sample proportion is given by the formula:
σ_p = sqrt[(p * (1-p)) / n]
In this case, the population proportion (p) is 0.2, and the sample size (n) is 400.
Step 1: Calculate the mean of the sample proportion:
μ_p = p = 0.2
Step 2: Calculate the standard deviation of the sample proportion:
σ_p = sqrt[(0.2 * (1-0.2)) / 400]
σ_p = sqrt[(0.2 * 0.8) / 400]
σ_p = sqrt[0.16 / 400]
σ_p = sqrt[0.0004]
Step 3: Find the square root of 0.0004:
σ_p ≈ 0.02
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plot the point A(-2, -3) B(-2,2) C (3,2) and D (3,-3) on a number plane and join them together
a) what shape is formed
b) What is the length of AD
c) Find the perimeter ABCD
d) Now join points B and D. What is the are of BCD
The shape formed is rectangle. Length of AD is 5. Perimeter of ABCD is 20. Area of BCD is [tex]\sqrt{65}[/tex] .
a) The shape formed is a rectangle.
b) The length of AD can be found using the distance formula:
AD = [tex]\sqrt{(3-(-2))^{2}+(-3-(-3))^{2} }[/tex]
= [tex]\sqrt{5^{2}}[/tex]
= 5
Therefore, the length of AD is 5.
c) The perimeter of ABCD can be found by adding up the lengths of all four sides:
AB = [tex]\sqrt{(-2-(-2))^{2}+(2-(-3))^{2} }[/tex]
= [tex]\sqrt{5^{2}}[/tex]
= 5
BC = [tex]\sqrt{(3-(-2))^{2}+(2-2)^{2} }[/tex]
= [tex]\sqrt{5^{2}}[/tex]
= 5
CD = [tex]\sqrt{(3-3)^{2}+(-3-2)^{2} }[/tex]
= [tex]\sqrt{5^{2}}[/tex]
= 5
DA = [tex]\sqrt{(-2-3)^{2}+(-3-(-3))^{2} }[/tex]
= [tex]\sqrt{5^{2}}[/tex]
= 5
Perimeter = AB + BC + CD + DA
= 5 + 5 + 5 + 5
= 20
Therefore, the perimeter of ABCD is 20.
d) Now join points B and D to form line segment BD. The area of triangle BCD can be found using the formula for the area of a triangle:
Area of BCD = (1/2) * base * height
The base is BD, which has length:
BD = [tex]\sqrt{(3-(-2))^{2}+(-3-2)^{2} }[/tex]
= [tex]\sqrt{65}[/tex]
To find the height, we need to draw a perpendicular line from C to line BD:
The height is the length of the perpendicular line from C to line BD. Since C and D have the same x-coordinate, this perpendicular line will be vertical and have length 2 units (the difference between the y-coordinates of C and D).
Therefore, the height is 2.
Area of BCD = (1/2) * BD * height
= (1/2) * [tex]\sqrt{65}[/tex] * 2
= [tex]\sqrt{65}[/tex]
Therefore, the area of BCD is [tex]\sqrt{65}[/tex] square units.
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Select the correct answer. Which equation could be solved using this application of the quadratic formula? A. -2x2 − 8 = 10x − 3 B. 3x2 − 8x − 10 = 4 C. 3x2 + 8x − 10 = -8 D. -2x2 + 8x − 3 = 4 Reset Next
Answer:
B
Step-by-step explanation:
The quadratic formula is used to solve quadratic equations in the form ax^2 + bx + c = 0.
Looking at the given options, we can see that option B can be written in this form as 3x^2 - 8x - 14 = 0. Therefore, the equation that could be solved using the quadratic formula is option B.
Using the substitution u=2x+1, on [0,2] the integral of sqrt(2x+1)dx is equivalent to
The integral of √(2x+1)dx over [0,2] is equivalent to (1/3) (5√(5) - 1).
What is integration?
Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.
To use the substitution u = 2x + 1, we need to express dx in terms of du. We can differentiate both sides of the substitution equation with respect to x:
du/dx = 2
Solving for dx, we get:
dx = du/2
We can use this to rewrite the integral:
∫(0 to 2) √(2x + 1) dx
= ∫(u(0) to u(2)) √(u) (du/2)
where u(0) = 2(0) + 1 = 1 and u(2) = 2(2) + 1 = 5.
= (1/2) ∫(1 to 5) √(u) du
We can now integrate with respect to u:
= (1/3) [(5√(5) - √(1))] from 1 to 5
= (1/3) (5√(5) - 1)
Therefore, the integral of √(2x+1)dx over [0,2] is equivalent to (1/3) (5√(5) - 1).
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Please use the information provided in your textbook page 290 and answer the following question:
Which of the following is the correct scatter-plot of variable y1 on the vertical axis versus variable x1 on the horizontal axis?
To identify the correct scatter plot for variables y1 and x1, you need to analyze the data and look for a clear pattern in the relationship between the two variables.
What is scatter plots?
A scatter plot is a type of data visualization that displays the relationship between two variables.
In a scatter plot, each point represents a pair of values, one for each of two variables. The horizontal axis represents the values of one variable (in this case, x1), and the vertical axis represents the values of the other variable (y1).
The scatter plot can show the relationship between the two variables. If there is a positive correlation, the points will tend to cluster in a line that slopes up and to the right. If there is a negative correlation, the points will cluster in a line that slopes down and to the right. If there is no correlation, the points will be scattered randomly.
To determine which scatter plot is correct, you need to examine the data and see which plot matches the pattern of the data. If there is a clear positive or negative correlation, the correct plot will show a line sloping up or down. If there is no correlation, the correct plot will show a scatter of points with no clear pattern.
In summary, to identify the correct scatter plot for variables y1 and x1, you need to analyze the data and look for a clear pattern in the relationship between the two variables.
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Evaluate the triple integral y^2 dV where t is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0), (0,0,2)
To evaluate this triple integral, we need to set up the bounds for each variable. Since the solid tetrahedron is defined by the vertices (0,0,0), (2,0,0), (0,2,0), and (0,0,2), we know that:
∫(from 0 to 2) ∫(from 0 to 2-x) ∫(from 0 to 2-x-y) y^2 dz dy dx
Now, integrate with respect to z:
= ∫(from 0 to 2) ∫(from 0 to 2-x) y^2(2-x-y) dy dx
Next, with respect to y:
= ∫(from 0 to 2) [-y^3/3 + xy^2 - y^2x/2] (from 0 to 2-x) dx
= ∫(from 0 to 2) [-8x^3/3 + 4x^4/3] dx
Finally, integrate with respect to x:
= [-2x^4/3 + x^5/3] (from 0 to 2)
= [-16/3 + 32/3] - 0
= 16/3
So, the triple integral evaluates to 16/3.
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5|8 - 2x|-3 > 27?
solve the inequality
Answer: x<1 or x>7
Step-by-step explanation:
Hope this helps! :)
A plane is flying north at 40 miles per hour. There is a 5-mile-per-hour wind blowing on the plane heading east. Draw the vectors and find the resulting vector graphically. List the resulting vector's magnitude.
The resultant vector has a magnitude of approximately 40.31 mph and is pointing in a direction approximately 7.13 degrees east of north.
To draw the vectors and find the resulting vector graphically, we can use the Pythagorean theorem and trigonometric functions.
In the diagram, the 40 mph vector is pointing north, and the 5 mph vector is pointing east. To find the resultant vector, we need to find the magnitude and direction of the vector that starts at the origin and ends at the tip of the 40 mph vector.
Using the Pythagorean theorem, we can find the magnitude of the resultant vector:
magnitude = √((40 mph)² + (5 mph)²)
magnitude = √(1600 + 25)
magnitude = √(1625) ≈ 40.31 mph
To find the direction of the resultant vector, we can use the tangent function:
tan(θ) = opposite/adjacent
θ= tan⁻¹(opposite/adjacent)
θ= tan⁻¹(5/40)
θ≈ 7.13 degrees
Therefore, the resultant vector has a magnitude of approximately 40.31 mph and is pointing in a direction approximately 7.13 degrees east of north.
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bill invests 160 at the start of each month for 22 months, starting now. if the investment yields 0.5% per month, compunded monthly, what is its value at the end of 22 months?> calculus
We will use the future value of a series formula to solve this problem. The terms you want me to include are invests, investment, and compounded.
Here's a step-by-step explanation:
1. Bill invests $160 at the start of each month for 22 months. This is a regular investment, and we will treat it as an ordinary annuity.
2. The investment yields 0.5% per month, compounded monthly. We'll convert the percentage to a decimal by dividing it by 100, so the monthly interest rate (r) is 0.005.
3. We will use the future value of an ordinary annuity formula to find the value of the investment at the end of 22 months:
FV = P * [(1 + r)^n - 1] / r
Where FV is the future value of the investment, P is the monthly investment ($160), r is the monthly interest rate (0.005), and n is the number of months (22).
4. Plug in the values and calculate:
FV = 160 * [(1 + 0.005)^22 - 1] / 0.005
FV = 160 * [(1.005)^22 - 1] / 0.005
FV = 160 * [1.113688 - 1] / 0.005
FV = 160 * 0.113688 / 0.005
FV = 3,627.232
The value of Bill's investment at the end of 22 months is approximately $3,627.23.
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the wheels on annie's bicycle are $20$ inches in diameter. if each wheel makes $3$ full revolutions every second, then how many feet does annie travel in $1$ second? give your answer as an integer, rounded to the nearest foot. (a full revolution means a $360^\circ$ turn. remember that there are $12$ inches in a foot.)
The circumference of a circle is given by $C = \pi d$, where $d$ is the diameter of the circle. In this case, the diameter of Annie's bicycle wheels is $20$ inches, so the circumference of each wheel is:
$C = \pi d = \pi (20\text{ in}) \approx 62.83 \text{ in}$
Since each wheel makes 3 full revolutions every second, the distance that Annie travels in one second is:
$distance = 2C \cdot \text{revolutions per second} = 2 \cdot 62.83 \text{ in} \cdot 3 \approx 377 \text{ in}$
Converting inches to feet, we get:
$distance = 377 \text{ in} \cdot \frac{1 \text{ ft}}{12 \text{ in}} \approx 31 \text{ ft}$
Rounding to the nearest foot, Annie travels approximately $\boxed{31}$ feet in one second.
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find the standard deviation of the number of lines in use this support center expects to have at noon
The mean is higher than the median because the data is skewed to the right. The median is more resistant to the skew in the data.
To calculate the standard deviation of the number of lines in use that this support center expects to have at noon, we would need to have a dataset of the number of lines in use at different times.
If we have this dataset, we can use the following formula to calculate the standard deviation:
Standard deviation = √(sum((x - mean)²) / n)
Where:
x is the number of lines in use at a given time
mean is the mean of the number of lines in use across all times
n is the total number of times in the dataset
We can calculate the mean of the number of lines in use by adding up all the values and dividing by the total number of times. Once we have the mean, we can calculate the standard deviation using the formula above. However, without access to the dataset, it is not possible to provide a specific answer.
Therefore, The mean is higher than the median because the data is skewed to the right. The median is more resistant to the skew in the data.
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Complete question:
Let the random variable X represent the number of telephone lines in use by the technical support center of a software manufacturer at noon each day. The probability distribution of X is shown in the table below.
In a sentence of two, comment on the relationship between the mean and the median relative to the shape of this distribution.
A construction company borrowed$75,000 for 4 months at an annual interest rate 8%. Find the simple interest due on the loan
Answer:
The answer is SI of $1980
suppose the correlation between two variables, math achievement and math attitude was found to be .78. What does this tell us about the correlation between math attitude and math achievement?
The correlation coefficient of .78 indicates a strong positive correlation between math achievement and math attitude.
This means that as math attitude increases, so does math achievement. It also suggests that math attitude can be a good predictor of math achievement. However, it is important to note that correlation does not imply causation, and other factors may also influence math achievement.
The correlation of .78 between math achievement and math attitude indicates a strong positive relationship between the two variables. This means that as one's math attitude improves, their math achievement is likely to improve as well, and vice versa.
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Dana buys a plant that is 4 inches tall. After one week the plant is 7 inches tall. After a second week the plant is 10 inches tall. At this rate, how tall will the plant be after the fifth week?
a
22 inches tall
b
3 inches tall
c
14 inches tall
d
19 inches tall
Answer:
We know that the plant grows by 3 inches each week (7 inches - 4 inches = 3 inches, and 10 inches - 7 inches = 3 inches). Therefore, after 5 weeks, the plant will be 4 inches + (3 inches × 5) = 19 inches tall.
Step-by-step explanation:
- The plant is 4 inches tall when Dana buys it.
- After one week, the plant grows by 3 inches to reach a height of 7 inches.
- After a second week, the plant grows by another 3 inches to reach a height of 10 inches.
- So, the plant grows by 3 inches each week.
- After 3 weeks, the plant will be 10 inches + 3 inches = 13 inches tall.
- After 4 weeks, the plant will be 13 inches + 3 inches = 16 inches tall.
- After 5 weeks, the plant will be 16 inches + 3 inches = 19 inches tall.
Therefore, the correct answer is d) 19 inches tall.
at travis' birthday party, `\frac{3}{4}` of his birthday cake was eaten. the next day, travis ate `\frac{1}{3}` of the remaining cake. what fraction of the whole cake did travis eat the next day
Travis ate 1/12 of the whole cake the next day
A fraction represents a part of a whole. In this case, the whole cake represents the whole, and the part that was eaten represents the fraction. When we say that 3/4 of the cake was eaten, it means that out of the whole cake, 3/4 or three-fourths of the cake was consumed.
Travis ate 1/3 of the remaining cake the next day.
This means that after 3/4 of the cake was eaten, there was 1/4 of the cake remaining. Travis ate 1/3 of that remaining 1/4 of the cake, which can be written as
=> 1/3 x 1/4.
To simplify this fraction, we multiply the numerators (1 x 1) and the denominators (3 x 4), giving us 1/12.
We can write this fraction as a percentage, which is 8.33%. To summarize, fractions are used to represent parts of a whole, and in this case, Travis ate 1/12 or 8.33% of the whole cake the next day.
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suppose that a normal model described student scores in a history class. parker has a standardized score (z-score) of 2.5. this means that parker
This means that Parker performed very well on the history exam, since his score is much higher than the average score in the class.
Step 1: Understand the concept of a z-score.
A positive z-score means that the data point is above the mean, while a negative z-score means that the data point is below the mean.
Step 2: Determine the mean and standard deviation of the normal distribution.
Since we are told that a normal model describes student scores in a history class, we can assume that the distribution of scores is normal. We need to know the mean and standard deviation of the distribution to calculate Parker's z-score.
Let's assume that the mean score in the class is 80 and the standard deviation is 10.
μ = 80
σ = 10
Step 3: Calculate Parker's raw score.
To calculate Parker's raw score, we need to use the formula for z-scores and solve for x:
z = (x - μ) / σ
We know that Parker's z-score is 2.5, and we know the values of μ and σ. Solving for x, we get:
2.5 = (x - 80) / 10
25 = x - 80
x = 105
So, Parker's raw score is 105.
Step 4: Interpret the result.
Since Parker's z-score is 2.5, we know that his score of 105 is 2.5 standard deviations above the mean of 80.
This means that Parker performed very well on the history exam, since his score is much higher than the average score in the class.
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On [0, pi/4], the integral of sinxdx=
Answer: The integral of sin(x)dx on the interval [0, pi/4] is:
∫sin(x)dx = -cos(x) + C
where C is the constant of integration.
To evaluate this definite integral on the interval [0, pi/4], we substitute pi/4 for x in the antiderivative and then subtract the value of the antiderivative at x=0:
cos(pi/4) - (-cos(0)) = -(√2/2) - (-1) = 1 - √2/2
Therefore, the value of the integral of sin(x)dx on the interval [0, pi/4] is 1 - √2/2.
Erin and Shelby have 8 children who never finish their dinner. Tonight they are having soup. Calculate how much soup is left over after everyone has finished eating. Erin and Shelby ate all their soup. Three of their kids left 3/4 cup of soup in their bowl. Two of their kids left 1/4 cup of soup in their bowl and three of their kids left 1/2 cup of soup in their bowl. How much soup is left over?
Answer:
Step-by-step explanation:
Let's start by finding out how much soup was initially in the pot. We know that Erin, Shelby, and all 8 of their children ate some soup, but we don't know how much.
If we add up the amounts left in the bowls, we can find out how much soup they didn't eat:
3 kids left 3/4 cup each = 3 * 3/4 = 9/4 cups
2 kids left 1/4 cup each = 2 * 1/4 = 1/2 cup
3 kids left 1/2 cup each = 3 * 1/2 = 3/2 cups
Adding these amounts together:
9/4 + 1/2 + 3/2 = 5 cups
So they left 5 cups of soup in their bowls.
If we assume that each person had one serving of soup (even though some left some in their bowls), and that each serving was the same size, then the amount of soup they didn't eat is equal to the amount of soup that was left in the pot.
So, the amount of soup left over is 5 cups.
I repeatedly roll 6 dice. I am determined to roll a Yahtzee, which is when all dice land on the same number. Let X= the number of times I have to roll the dice before I get a Yahtzee. Is X binomial?
A binomial distribution is characterized by two outcomes (success or failure) and a fixed number of trials with the same probability of success on each trial.
In this case, X represents the number of times you roll the dice before achieving a Yahtzee.
However, X is not a binomial distribution because it doesn't have a fixed number of trials. You continue rolling until you get a Yahtzee, which could take an unpredictable number of attempts. Instead, X follows a geometric distribution, which describes the number of trials needed for the first success in a sequence of Bernoulli trials.
Yes, X is binomial because it has the following properties:
1. There are a fixed number of trials (rolling the dice repeatedly)
2. Each trial is independent of the others (the outcome of one roll does not affect the outcome of the next)
3. There are only two possible outcomes for each trial (either a Yahtzee is rolled or it isn't)
4. The probability of success (rolling a Yahtzee) is constant for each trial (1/6 to the 5th power, or about 0.00077)
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one model for the spread of a rumor states that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor. (a) find a formula for the fraction of the population who have heard the rumor at time t. (b) a small town has 1000 inhabitants. at 8 am, 80 people have heard a rumor. by noon, half the town has heard it. when will 90% of the population have heard the rumor?
The formula for the fraction of the population who have heard the rumor at time t is:
H(t) = 1 - (1 - H(0)) * e^(-k*t*(1-H(0)))
where H(0) is the initial fraction of the population who have heard the rumor (in decimal form), k is the proportionality constant, and e is the mathematical constant approximately equal to 2.718.
To solve part (b), we can use the information given to find the value of H(0) and then solve for the time when H(t) = 0.9.
We know that at 8 am, 80 people have heard the rumor, so H(0) = 80/1000 = 0.08. We also know that by noon, half the town has heard it, so H(4) = 0.5. Plugging these values into the formula, we get:
0.5 = 1 - (1 - 0.08) * e^(-k*4*(1-0.08))
Simplifying, we get:
0.42 = e^(-0.32k)
Taking the natural logarithm of both sides, we get:
ln(0.42) = -0.32k
Solving for k, we get:
k = -ln(0.42)/0.32 = 0.646
Now we can use this value of k to find the time when 90% of the population has heard the rumor:
0.9 = 1 - (1 - 0.08) * e^(-0.646t*(1-0.08))
Simplifying, we get:
0.08 * e^(-0.0565t) = 0.1
Dividing both sides by 0.08, we get:
e^(-0.0565t) = 1.25
Taking the natural logarithm of both sides, we get:
-0.0565t = ln(1.25)
Solving for t, we get:
t = -ln(1.25)/0.0565 ≈ 30.9
Therefore, 90% of the population will have heard the rumor after about 30.9 hours.
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James has a triangle with a perimeter of 12. The triangle is dilated with a scale factor of 3. What is the new perimeter?
The new perimeter of the triangle after it is dilated with a scale factor of 3 is 36 units.
If James has a triangle with a perimeter of 12, it means that the sum of the lengths of all three sides of the triangle is 12. Let's call the lengths of the three sides a, b, and c, where a + b + c = 12.
When the triangle is dilated with a scale factor of 3, it means that all the sides of the triangle are multiplied by 3. Let's call the new lengths of the sides A, B, and C, where A = 3a, B = 3b, and C = 3c.
The new perimeter of the triangle is the sum of the lengths of the new sides, which is:
A + B + C = 3a + 3b + 3c
We know that a + b + c = 12, so we can substitute this into the above equation:
A + B + C = 3(12)
A + B + C = 36
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A reputable polling organization in a certain country surveyed 106,600 ​adults, and 18​% of those polled reported that they smoked. Complete parts a and b below.
b) Explain what this margin of error means. Select the correct choice below and fill in the answer box within your choice.
​(Round to four decimal places as​ needed.)
A.The probability that any given adult surveyed from the population smokes is ________________.
B.The probability that any given adult surveyed from the sample smokes is _____________.
C.We are 90​% confident that the observed proportion of adults that smoke is within _________of the sample proportion.
D.We are 90​% confident that the observed proportion of adults that smoke is within ________ of the population proportion
Both options C and D are correct in describing the meaning of the margin of error, but we cannot provide specific values for the margin of error without additional information.
To answer this question, first, we need to calculate the sample proportion of adults who smoke.
Calculate the sample proportion
Number of adults surveyed = 106,600
Percentage of adults who smoke = 18%
Sample proportion (p) = (Percentage of adults who smoke) / 100
p = 18% / 100 = 0.18
Now, let's address each option in part b:
A. The probability that any given adult surveyed from the population smokes is not the correct interpretation of the margin of error.
B. The probability that any given adult surveyed from the sample smokes is not the correct interpretation of the margin of error.
C. We are 90% confident that the observed proportion of adults that smoke is within the margin of error of the sample proportion.
To calculate the margin of error, we need more information, such as the standard deviation of the population and the desired confidence level.
Since we do not have this information, we cannot provide a specific value for the margin of error.
D. We are 90% confident that the observed proportion of adults that smoke is within the margin of error of the population proportion.
Similar to option C, we need more information to calculate the margin of error, so we cannot provide a specific value for the margin of error.
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Find the height of the triangular pyramid when the volume is 318 square centimeters
The height of the triangular pyramid, given that the volume is 318 square centimeters 7.31 cm (option B)
How do i determine the height of the triangular pyramid?First, we shall obtain the base area of the triangular pyramid. Details below:
Base length (b) = 29 cmBase height (h) = 9 cmBase area (A) =?A = ½bh
A = ½ × 29 × 9
A = 130.5 cm²
Finally, we shall determine the height of the triangular pyramid. Details below:
Volume of triangular pyramid (V) = 318 cm³Base area of triangular pyramid (A) = 130.5 cm²Height of triangular pyramid (h) =?V = ⅓Ah
318 = ⅓ × 130.5 × h
318 = 43.5 × h
Divide both sides by 43.5
h = 318 / 43.5
h = 7.31 cm
Thus, the height of the triangular pyramid is 7.31 cm (option B)
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Complete question:
See attached photo
need help fast its due in 5 minutes write this number in standard form
Answer:
The answer to the question given is 785.639 .
Step-by-step explanation:
According to the rules of mathematics i.e. BODMAS
We'll first multiply,
7x100 = 700
8x10 = 80
5x1 = 5
6x[tex]\frac{1}{10}[/tex] = [tex]\frac{3}{5}[/tex] = 0.6
3x[tex]\frac{1}{100}[/tex] = 0.03
9x [tex]\frac{1}{1000}[/tex] = 0.009
So, after adding.
We get,
700 + 80 + 5 + 0.6 + 0.03 + 0.009 = 785.639
Object 2: Pinecone
3D shape: Cone
Dimensions:
radius = 4 inches
height = 6.5 inches
Object 2 3D shape: Cone (Pinecone)
SA Formula:
Surface Area:
The surface area of the cone with radius 4 inches and height 6.5 inches is equal to 146.07 square inches.
Radius of the cone = 4 inches
height of the cone = 6.5 inches
Let us consider 'r' be the radius of the cone and 'h' be the height of the cone.
Formula to calculate surface area of the cone
= πr ( r + √ h² + r² )
Substitute the value of radius and height of the cone we have,
⇒ Surface area of the cone = π × 4 ( 4 + √ ( 6.5 )² + ( 4 )² )
⇒ Surface area of the cone =4π ( 4 + √58.25 )
⇒ Surface area of the cone = 4 × 3.14 ( 4 + 7.63 )
⇒ Surface area of the cone = 12.56 × 11.63
⇒ Surface area of the cone = 146.0728 square inches
⇒ Surface area of the cone = 146.07 in²
Therefore, the surface area of the cone is equal to 146.07 square inches.
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