Answer:
a. Runner A ran at a constant rate throughout the race.
b. Runner B stopped running between 20 and 30 seconds.
c. Runner C started off slow and gradually increased speed until reaching their maximum speed, then gradually slowed down towards the end of the race.
d. Runner A won the race because they crossed the finish line first, at 40 seconds, which is before runners B and C.
Carrie drove 7 hours to a beach house for spring break. She spent the first hour averaging 30 miles per hour. After that, she spent the next 4 hours at an average speed of 65 miles per hour. She finished the last part of her drive averaging 52 miles per hour. Write a piecewise function to represent that total distance d (in miles) that carrie has traveled after t hours
the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.
To write a piecewise function to represent the total distance Carrie has traveled after t hours, we need to break down her journey into different parts and calculate the distance covered during each part.
Let's define the three different parts of her journey:
•Part 1: The first hour, during which she averaged 30 miles per hour
•Part 2: The next 4 hours, during which she averaged 65 miles per hour
•Part 3: The remaining 2 hours, during which she averaged 52 miles per hour
For Part 1, the distance covered can be calculated as:
d1 = 30t (where t is the time spent in the first hour, t ≤ 1)
For Part 2, the distance covered can be calculated as:
d2 = 260 + 65(t - 1) (where t is the time spent in the next 4 hours, 1 < t ≤ 5)
For Part 3, the distance covered can be calculated as:
d3 = 520 + 52(t - 5) (where t is the time spent in the remaining 2 hours, 5 < t ≤ 7)
Now, we can combine these three equations to form a piecewise function for the total distance traveled by Carrie:
d(t) = 30t, 0 ≤ t ≤ 1
d(t) = 260 + 65(t - 1), 1 < t ≤ 5
d(t) = 520 + 52(t - 5), 5 < t ≤ 7
Therefore, the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.
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the height of a parallelogram is 10 feet more than the length of the base. if the area of the parallelogram is 1200 square feet, find the length of the base and the height.
The length of the base of a parallelogram is 30 feet and the height is 40 feet.
Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.
We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.
Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.
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A small circle is centered inside of a larger circle. The large circle has a radius of 10 inches. The small circle has a radius of 3 inches.
Answer: 126in
Step-by-step explanation:
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5+10=24
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HELPPP
complete the problem by creating two binomials that represent that sides of the shape . Then multiply to get a quadratic equation . Draw a picture to help set up the problem . 6. Albert installs swimming pools . While the pools can come in different sizes, Albert only offers rectangular pools that are always twice as wide as they are long. He also puts a deck around the entire pool, and the deck is always 4ft wide on each side. Write an equation to represent the total area of the pool and deck.
The equation that represents the total area of the pool and deck is: A(x) = 2x² + 24x + 64.
Describe Binomial?In algebra, a binomial is a polynomial that consists of two terms connected by either an addition or a subtraction operator. A binomial can be written in the form (ax + b) or (ax - b), where "a" and "b" are constants and "x" is a variable.
Binomials are used in a variety of algebraic operations, such as factoring, expanding, and solving equations. They also appear in binomial probability distributions and binomial theorem.
Let's start by drawing a diagram to visualize the problem:
___________
| | 4 ft
| _________|_________
| | | |
| | | |
| | | | 2x
| | | |
| |_________|_________ |
| | 4 ft
|__________ |
2w
The rectangular pool is twice as wide as it is long, so we can let the length be x, and the width be 2x.
The deck around the pool is 4 feet wide on each side, so the total width of the pool and deck is (2x + 8), and the total length is (x + 8).
Therefore, the total area of the pool and deck can be represented as:
(2x + 8)(x + 8)
Expanding the expression, we get:
2x² + 24x + 64
So the equation that represents the total area of the pool and deck is:
A(x) = 2x² + 24x + 64
where A(x) is the area of the pool and deck, and x is the length of the pool.
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6x6x6x6x6x6x6 devided by 6x6x6x6x6x6 in indext form
The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.
In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:
(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:
6⁽⁷⁻⁶⁾ = 6¹ = 6.
Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.
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Match the following terms with the descriptions. a. total purchase price b. unit pricing c. comparison shopping d. coupons e. rebates f. markdown g. markdown rate h. sale price 14. A technique that allows shoppers to compare prices 15. The total selling price plus the sales tax - 16. Discount 17. Regular selling price minus the markdown 18. Locating the best value for your money
a. Total purchase price: 15.The total selling price plus the sales tax.
b. Unit pricing: 18. Locating the best value for your money
c. Comparison shopping: 14. A technique that allows shoppers to compare prices
d. Coupons: 16. Discount
e. Rebates: 16. discount
f. Markdown: 17. regular selling price minus the markdown.
g. Markdown rate: 16. Discount
h. Sale price: 18. Locating the best value for your money
What is selling price?Selling price is the amount of money a customer pays for a product or service. It is the amount that a customer pays for the product or service after any discounts, taxes, or fees have been applied.
a. Total purchase price: The total selling price plus the sales tax. This amount is the total cost the customer pays for the good or service, including any taxes and fees.
b. Unit pricing: The cost per unit of a good or service. This allows shoppers to compare the cost of similar items and make an informed decision about which item offers the best value.
c. Comparison shopping: A technique that allows shoppers to compare prices, quality, and other factors when making a purchase.
d. Coupons: A form of discount that can be used when making a purchase. Coupons are often found in newspapers, magazines, or online and can be used to reduce the total purchase price.
e. Rebates: A form of discount where customers receive money back after making a purchase. Rebates are often found in the form of a check or a prepaid debit card.
f. Markdown: The regular selling price minus the markdown. The markdown is the amount that is discounted from the regular selling price.
g. Markdown rate: The percentage of the regular selling price that is discounted. This rate is used to calculate the amount of the markdown.
h. Sale price: The discounted price of a good or service. This is the amount the customer pays after any discounts or coupons have been applied.
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is the difference in years at the company between employees with a high school degree and those with an mba significant at the 95% confidence level? remember, differences are significant at the 95% confidence level when the p-value is less than .05.
To determine if the difference in years at the company between employees with a high school degree and those with an MBA is significant at the 95% confidence level, we can perform a hypothesis test for p-value.
We can run a hypothesis test to see if the difference in years spent at the organization between workers with a high school diploma and those with an MBA is significant at the 95% confidence level.
We must first specify our alternative hypothesis and null hypothesis. Our null hypothesis is that there is no discernible difference in the number of years that personnel with a high school diploma and those with an MBA have worked for the organization. Our alternate theory is that the two groups have significantly different average years of employment.
The probability of witnessing the data if the null hypothesis is correct can then be determined using a t-test. The null hypothesis can be rejected if the p-value is less than 0.05, and the difference in years spent at the company between workers with a high school diploma and those with an MBA is determined to be significant at the 95% level of confidence.
We can use a two-sample t-test to compare the means of the two groups if the data is normally distributed and the variances are identical.
If the t-test yields a p-value of less than 0.05, we can reject the null hypothesis and draw the conclusion that there is a significant difference in the number of years that employees with a high school diploma and those with an MBA have worked for the organisation. In contrast, if the p-value is higher than 0.05, we are unable to rule out the null hypothesis since there is insufficient data to support the existence of a significant difference.
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the atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by where is in years and corresponds to 1950. find and interpret the result. round to 2 decimal places as needed. answer: with unit
The atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by , where is in years and corresponds to 1950.
Substituting in gives , which means that the atmospheric carbon dioxide levels in parts per million (ppm) in the town is 386.50 in 2019.
This means that since 1950, the atmospheric carbon dioxide levels in parts per million (ppm) in the town have increased by 386.50.
This is a significant increase and reflects the growing levels of atmospheric carbon dioxide emissions globally due to human activity, leading to climate change.
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two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability at least one of them is spades
To find the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade, we can use the complement rule.
The complement of the event "at least one of the cards is a spade" is "neither of the cards is a spade."
The probability that the first card is not a spade is 39/52 since there are 39 non-spade cards out of a total of 52 cards. Once the first non-spade card has been drawn, there will be 51 cards remaining, of which 38 are non-spades. Thus, the probability that the second card is also not a spade is 38/51.To find the probability that neither of the two cards is a spade, we can multiply the probabilities of drawing a non-spade on the first card and a non-spade on the second card:
P(neither is spade) = (39/52) x (38/51) = 0.4498 (rounded to four decimal places)
The probability that at least one of the two cards is a spade is equal to 1 minus the probability that neither of the cards is a spade:P(at least one is spade) = 1 - P(neither is spade)
P(at least one is spade) = 1 - 0.4498
P(at least one is spade) = 0.5502 (rounded to four decimal places)
Therefore, the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade is 0.5502 or approximately 55.02%.
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in a regression analysis, the coefficient of determination measures goodness of fit. independence of variables. economic plausibility. independence of residuals.
The coefficient of determination measures goodness of fit.
The coefficient of determination, often referred to as R-squared, measures the goodness of fit in a regression analysis. It does not measure the independence of variables, economic plausibility, or independence of residuals.
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given the arithmetic sequence what is the domain for N?
The domain for n in the arithmetic sequence is the one in the first option:
all integers where n ≥1
What is the domain of N?We have a arithmetic sequence defined by the general formula:
aₙ = 4 - 3*(n - 1)
And we want to find the domain for the possible values of n that we can use in that formula.
Remember that the terms of a sequence are defined as:
a₁, a₂, a₃,...
So the values of n are positive whole numbers, in this case the first one is n = 1.
a₁ = 4 + 3*(1 - 1)
a₁ = 4
And then we can keep using any positive integer, then the correct option is:
all integers where n ≥1
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WILL GIVE BRIANLIST TO BEST ASNWWR
Richard buys a new car for $28,000. The car depreciates in value by 9% each year. Which of the following uses the variable y to represent the value of the car after t years in an exponential model to represent the situation?
y=28,000(1.09)
y=28,000(91)
y-28,000(-9)
y=28,000(0.09)
The variable y is used to represent the worth of the car after t years like an exponential model to reflect the scenario, and the third option, y=28,000(0.91)t, is the correct response.
The formula for the exponential model is what?A = A0(b)t/c is the formula for an exponential model, where A0 denotes the starting quantity of the thing being modeled. t stands for passing time. The quantity at time t is equal to A.
The exponentially decaying formula for an asset's value over time with such a consistent rate of depreciation is: y = a(1-r)t
Where:
Y is equal to the car's value after t years.
In this scenario, the car's original value is $28,000, and its rate of depreciation is 9%, or 0.09 in decimal notation.
t equals the amount of years
The exponential model can be expressed using the following formula: y = 28,000(1-0.09)t
By condensing the formula, we obtain the following result: y = 28,000(0.91)t
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Maggie is 15 years older than Bobby. How old is Bobby? 1) In 3 years, Maggie's age will be 50% greater than Bobby's age.
2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.
Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.
Maggie is 15 years older than Bobby. We have to determine Bobby's age.
Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.
1) In 3 years, Maggie's age will be 50% greater than Bobby's age.
The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.
According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.
So, (x + 15) + 3 = (1.5)(x + 3)
Simplifying the above equation, we get
x + 18 = 1.5x + 4
Now, we will solve for
x.x - 1.5x = -14-0.5x = -14x = 28
Therefore, Bobby is 28 years old now.
2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.
Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.
So, x + 25 = (x + 10) + 15x = 15
Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.
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Find the center and radius of a circle with the equation x^2 + y^2 = 20.
The given equation of the circle is:
[tex] \rm \: x^2 + y^2 = 20[/tex]
We can write this equation in standard form by completing the square:
[tex] \rm x^2 + y^2 = 20[/tex]
[tex] \rm x^2 + y^2 - 20 = 0[/tex]
[tex] \rm (x^2 - 2x + 1) + (y^2 - 20) = 1[/tex]
[tex] \rm (x - 1)^2 + y^2 = 21[/tex]
Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.
Thank you for the help!
Answer:
13 bags
Step-by-step explanation:
V = π(2^2)(1/2) = 2π = 6.28 cubic feet
6.28 ÷ .5 = 12.56
So Martin needs to buy at least 13 bags of sand.
. If your savings account has a %4.50 APR and you have $100 saved, what is the How
much money will earn by the end of the year? What is the equation you will use to figure
this out?
The required amount of money earned on the savings account by the end of the year is $4.50.
How to find the interest amount?To calculate the amount of money earned on a savings account with a given Annual Percentage Rate (APR), we can use the formula:
Interest = Principal x Rate x Time
where:
Principal is the initial amount of money in the account
Rate is the annual interest rate (as a decimal)
Time is the length of time the money is invested (in years)
In this case, the principal is $100, the rate is 4.50% per year (or 0.045 as a decimal), and the time is one year. Therefore, the interest earned can be calculated as:
Interest = $100 x 0.045 x 1
Interest = $4.50
So, the amount of money earned on the savings account by the end of the year is $4.50.
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Write an equation to represent each relationship
This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.
However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]
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what is x−10=4 pls help me
Answer:
Step-by-step explanation: 14 = x
Answer:
The answer to your question would be 14
Step-by-step explanation:
Simple equation
14 - 10 = 4
I hope this helps and have a wonderful day!
Choose the equation that represents the line passing through the point (2, −5) with a slope of −3
The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).
To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:
y - (-5) = -3(x - 2)
Simplifying this expression, we get:
y + 5 = -3x + 6
y = -3x + 1
Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.
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Complete Question:
Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.
A.) y = −3x − 13
B.) y = −3x + 11
C.) y = −3x + 13
D.) y = −3x + 1
Answer:
The answer is y = -3x + 1
Find the missing dimension of the trapezoid. 8 in. h 12 in. A = 40 in. h=___in
Answer: h=4
Step-by-step explanation:
Find the area of a circle that has a radius of 7/2 centimeters. Use 22/7 as an approximation for π.
Answer: The answer is 38.5 cm^2
Step-by-step explanation:
Given:
Radius(r) = 7/2
Pie (π) = 22/7
We know that:
The area of Circle is = πr^2 = π * r * r
So, ans is = (22/7) * 7/2 * 7/2 = 38.5 cm^2
Answer:
A≈ 38.5cm^2
Step-by-step explanation:
Given:
The approximation of pi is 22/7 or 3.141592
The radius is 7/2 or 3.5
Work:
A=πr(2)=π·3.5(2)≈38.48451
now let's round it to 38.5cm^2
Gina is growing lettuce in a section of a garden. She represents this section with rectangle JKLM
The area of the rectangular section in the garden is Area = (x₂ - x₁) x (y₂ - y₁)
Now, let's look at the rectangular section of the garden represented by the coordinate plane. We are told that the section is represented by Rectangle JKLM. The four corners of this rectangle can be represented by their respective coordinates:
Point J: (x₁, y₁)
Point K: (x₂, y₁)
Point L: (x₂, y₂)
Point M: (x₁, y₂)
To find the area of this rectangle, we need to use the formula:
Area = length x width
The length of the rectangle is the distance between points J and K, which is given by:
Length = x₂ - x₁
The width of the rectangle is the distance between points J and M, which is given by:
Width = y₂ - y₁
Therefore, the area of the rectangle is:
Area = (x₂ - x₁) x (y₂ - y₁)
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Complete Question:
Gina is growing lettuce in a section of a garden. She represents this section with Rectangle JKLM. Each unit in the coordinate plane represents 1 foot.
What is the area of the section where lettuce grows?
Find the missing dimension of the triangle.
Area = 14 ft²
6 ft
b
b = ? ft
help pls I'll mark brainlisest
I NEED HELP! BRAINLIEST!
Answer: 40/7 or 5.7
Step-by-step explanation:
using angle bisector theorem we get,
x/5 = 8/7
Upon substituting our given values in above equation, we will get:
x/5 X 5 = 8/7 X 5
x = 40/7 or 5.7
Answer:
3.3
Step-by-step explanation:
Angle bisector theorem: In a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.
[tex]\dfrac{x}{8-x}=\dfrac{5}{7}[/tex]
Cross multiply,
x *7 = 5*(8 - x)
7x = 40 - 5x
7x + 5x = 40
12x = 40
[tex]x = \dfrac{40}{12}\\\\x = 3.3[/tex]
Who can help me? This is solving cube root equation help ?
Answer:
22: 2
23: -7
25: 6
26: 3
Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!
Step-by-step explanation:
For 22: 2 * 2 * 2 = 8, therefore, 2
For 23: -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).
For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6
For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.
Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!
the medians of a triangle intersect at the ___
Answer:
orthocentre
Step-by-step explanation:
this is the answer to your question
4. O -1 points 15 HW 080 Ask Your The sky Train from the terminal to the Cental car and long-term parking center is supposed to arrive every 6 minutes. The waiting times for the train are known to follow a uniform distrbution Find the 60th percentile for the waiting times (in minutes). Additional Qa Section 5.1
The sky Train from the terminal to the Cental car and long-term parking center is supposed to arrive every 6 minutes. The waiting times for the train are known to follow a uniform distribution. The 60th percentile of the waiting times is 3 minutes.
Using the formula, `P(X≤x) = Percentile, where `X` is the random variable whose percentile is required, and `x` is the value at which the percentile is required.
Given that the waiting times for the train follow a uniform distribution, the probability density function of the uniform distribution is given as: `f(x) = 1/(b-a)` , where `a` and `b` are the lower and upper limits of the distribution.
Now, it is given that the sky train is supposed to arrive every 6 minutes. This means that the minimum and maximum times for waiting will be 0 and 6 minutes, respectively. Hence, `a = 0` and `b = 6`.
Using the formula for the uniform distribution, we have `f(x) = 1/(6 - 0) = 1/6`. Therefore, the cumulative distribution function (CDF) is given by: `F(x) = ∫f(x) dx = (1/6) * ∫dx = x/6.
`Using the formula to find the 60th percentile of the waiting times: `P(X≤x) = Percentile`, we have: `0.6 = P(X≤x)`. Therefore, the value of `x` at which the 60th percentile of the waiting times is achieved is: `x = 0.6 * (b - a) + a = 0.6 * (6 - 0) + 0 = 3`. Thus, the 60th percentile of the waiting times is 3 minutes.
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how would i graph my question when the x and y intercept is (10,140) when the slope is -14
The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
What is point-slope form?When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).
The y value of the y-intercept point is denoted by the symbol b in the formula.
The general form of a linear equation is y-y1=m(x-x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
So, in the given situation:
The point-slope form is: y = mx + b
Then y is y and b is the x value and m is the slope.
Now, insert values as follows:
y = mx + b
140 = -14x + 10
Graph the equation as follows:
(Refer to the graph attached below)
Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
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what is $510,451 rounded to the nearest 1,000 dolllars?
Answer:
$510,000
Step-by-step explanation:
Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.
Remember, 4 or less, round down. 5 or more, round up.
Since the hundreds digit is 4, we do not need to round.
We only need to change the rest of the digits to 0.
So, our answer would be $510,000.
In an experiment, a fair four-sided die (its faces are labeled 0, 1, 2, 3) is thrown once. The outcome of the throw determines how many times a fair coin is to be flipped: if N is the number that results from throwing the die, we flip the coin N times. Let K be the total number of heads resulting from the coin flips. Suppose the die roll results in a 2. What form does the conditional distribution of distribution along with its parämeters calculated the probabilities in the table a) K have given that N-2? You don't need to calculate anything. Just state the b) Fill in this table for the joint PMF of N and K. Show your work for how you I k 0 2 3 c) Using the joint PMF, obtain the marginal for N. Show your work. d) Using the joint PMF, obtain the marginal for K. Show your work. e) What is the conditional PMF of N given K-2? i.e., what is pNk(njk-2)? Show your work f) Are N and K independent? Show work to support your answer
For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:
P(N=n,K=k) = P(N=n) * P(K=k)If this condition is not satisfied, then N and K are dependent.
The distribution of K given that N=2 can be calculated using the conditional probability formula:
P(K=k|N=2) = P(K=k and N=2) / P(N=2)
Let X be the outcome of the coin flip. Then the joint probability mass function of N and K can be expressed as:
P(N=n,K=k) = P(X=0) for n=0 and k=0
P(N=n,K=k) = P(X=1) for n=1 and k=0, 1
P(N=n,K=k) = P(X=2) for n=2 and k=0, 1, 2
P(N=n,K=k) = P(X=3) for n=3 and k=0, 1, 2
The marginal probability mass function of N can be obtained by summing over all possible values of K:
P(N=n) = P(N=n,K=0) + P(N=n,K=1) + P(N=n,K=2)
The marginal probability mass function of K can be obtained by summing over all possible values of N:
P(K=k) = P(N=0,K=k) + P(N=1,K=k) + P(N=2,K=k) + P(N=3,K=k)
The conditional probability mass function of N given that K=2 can be calculated using Bayes' theorem:
P(N=n|K=2) = P(K=2|N=n) * P(N=n) / P(K=2)
For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:
P(N=n,K=k) = P(N=n) * P(K=k)
If this condition is not satisfied, then N and K are dependent.
To learn more about joint probability, refer below:
https://brainly.com/question/29582649
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