Given, X has a uniform distribution on the interval (-1,1]. We are to determine the incorrect statement among the following:
Statement 5: The variance of a uniform distribution is (b-a)^2/12. Here, a=-1 and b=1. Hence, Var(X) = (1-(-1))^2/12 = 1/3. This statement is correct .Therefore, the incorrect statement is P(X ≤ 0.5) = 0.5.
Statement 1: f(x) = 0.5 for -1 < x ≤ 1Statement 2: P(X ≤ 0.5) = 0.5Statement 3: P(X ≤ 1) = 1Statement 4: E[X] = 0Statement 5: Var(X) = 1/3Let's check each statement one by one:
Statement 1: The probability density function (PDF) of a uniform distribution is f(x) = 1/(b-a) for a < x ≤ b. Here, a=-1 and b=1. Hence, f(x) = 1/(1-(-1)) = 0.5 for -1 < x ≤ 1. This statement is correct.
Statement 2: The cumulative distribution function (CDF) of a uniform distribution is F(x) = (x-a)/(b-a) for a < x ≤ b. Here, a=-1 and b=1. Hence, [tex]P(X ≤ 0.5) = F(0.5) = (0.5-(-1))/(1-(-1)) = 0.75[/tex], which is not equal to 0.5. Therefore, this statement is incorrect.
Statement 3: P(X ≤ 1) = F(1) = (1-(-1))/(1-(-1)) = 1. This statement is correct.
Statement 4: The expected value of a uniform distribution is (a+b)/2. Here, a=-1 and b=1. Hence,[tex]E[X] = (-1+1)/2 = 0.[/tex] This statement is correct.
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Samuel bought four adult tickets to a movie for $48. Erica bought 3 adult tickets to a movie at a different theater. Erica paid $2.50 more than Samuel for each movie ticket she bought. How much did Erica spend on her movie ticket purchase?
Answer: £43.50
Step-by-step explanation:
each ticket from samuel is £12 if erica is spending £2.50 more per ticket that is £14.50 per ticket. £14.50 x 3 = £43.50
2x^3+15x^2+24x+k has 3 linear factors, two of which are identical. find k, and hence factorise the cubic
The value of k in the cubic equation is 2 and factorization of the equation is 2(x-1)^2(x+1)
What is the value of k?If 2x^3 + 15x^2 + 24x + k has three linear factors, then it must be in the form:
[tex]2x^3 + 15x^2 + 24x + k = a(x-b)(x-c)^2[/tex]
where a, b, and c are constants, and (x-c)^2 means that (x-c) is a repeated factor.
Expanding the right side, we get:
[tex]2x^3 + 15x^2 + 24x + k = a(x^3 - 2cx^2 + cx^2 - 2cx + c^2x - c^2)[/tex]
Simplifying, we get:
[tex]2x^3 + 15x^2 + 24x + k = ax^3 - 2acx^2 + ac^2x - 2acx + ac^2 + a(-c^2)\\2x^3 + 15x^2 + 24x + k = ax^3 + (-2ac + ac^2)x^2 + (-2ac + ac^2)x - ac^2[/tex]
Equating the coefficients of each power of x on both sides, we get:
[tex]a = 2\\-2ac + ac^2 = 15\\-2ac + ac^2 = 24\\-ac^2 = k\\\\[/tex]
From the second and third equations, we can see that -2ac + ac^2 = 15 and -2ac + ac^2 = 24. These equations are equivalent, so we can set them equal to each other:
[tex]-2ac + ac^2 = 15 = 24[/tex]
Simplifying, we get:
ac^2 - 2ac + 9 = 0
This is a quadratic equation in ac. Solving for ac using the quadratic formula, we get:
[tex]ac = [2 \± \sqrt(4 - 4(1)(9))] / 2[/tex]
[tex]ac = 1 \± \sqrt(-5)[/tex]
Since ac is the product of two real numbers (b and c), we know that the square root of -5 must cancel out. This is only possible if ac = 1 and c = -1. Therefore, b = -c = 1, and we can find k by setting ac^2 = -k:
[tex]1 = 2a\\15 = -2ac + ac^2 = -2a + a^2\\24 = -2ac + ac^2 = -2a + a^2\\-k = -ac^2 = 2(-1)^2 = 2\\[/tex]
Therefore, k = -2, and the factorization of 2x^3 + 15x^2 + 24x - 2 is:
2x^3 + 15x^2 + 24x - 2 = 2(x-1)^2(x+1)
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 3)
The required distance the ship traveled from its starting point to its destination is approximately 44.8 miles.
How to use Pythagoras theorem to find distance?To solve this problem, we can use the Pythagorean theorem to find the distance the ship traveled from its starting point to its destination.
We can see that the ship traveled 35 miles east and 28 miles south, forming a right triangle. The distance from the starting point to the destination is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
[tex]$\begin{align*}\text{distance} &= \sqrt{35^2 + 28^2}\&= \sqrt{1225 + 784}\&= \sqrt{2009}\&\approx 44.8 \text{ miles}\end{align*}[/tex]
Therefore, the distance the ship traveled from its starting point to its destination is approximately 44.8 miles.
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A box contains 4 bags of sugar. The mass of each bag is 6 kilograms. What is the total mass of the box in grams?
240,000 grams
24,000 grams
2,400 grams
240 grams
Answer: 24000 g
Step-by-step explanation:
multiply together:
4 bags * 6 kg = 24 kg total
convert:
1 kg = 1000 g
24 kg * (1000 g / 1 kg) = 24000 g
To calculate the total mass of the box in grams, we need to first calculate the total mass of the 4 bags of sugar in kilograms, and then convert that to grams.
The mass of one bag of sugar is 6 kilograms.
The total mass of all 4 bags is:
4 bags x 6 kilograms/bag = 24 kilograms
To convert 24 kilograms to grams, we multiply by the conversion factor of 1000 grams/kilogram:
24 kilograms x 1000 grams/kilogram = 24,000 grams
Therefore, the total mass of the box, including all 4 bags of sugar, is 24,000 grams.
The correct answer is B) 24,000 grams.
A rectangular poster is to contain 450 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left wd right are to be inch. What should the dimensions of the poster be so that the least amount of poster is used_____ in (smaller value) _____ in (larger value)
The dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.
The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.A rectangular poster is given that is to contain 450 square inches of print. The margins at the top and bottom of the poster are 2 inches, and the margins on the left and right are 1 inch. Let us suppose the width of the poster is x in and the length of the poster is y in. Also, we need to find the least amount of poster used.Therefore, the dimensions of the poster be x in × y in. The printable area of the poster is given as 450 sq in. Hence, the area of the poster minus the area of the margins should be 450 sq in. Therefore,x × y = (x - 2) (y - 4) + 450x × y = xy - 2x - 4y + 8 + 450xy - xy - 2x + 4y = 8 + 450(y - 4)x = (450(y - 4) - 8) / (y - 1)x = (450y - 1808) / (y - 1)Now we need to calculate the dimensions of the rectangular poster. We need to find the value of x and y. Substituting the value of x in the first equation we get,y = (450 / (x - 2)) + 4We also know that x > 2 and y > 4. We need to minimize the amount of poster used. Hence we need to minimize x × y. The dimensions of the rectangular poster are 15 in × 32 in so that the least amount of poster is used.Therefore, the dimensions of the poster should be 15 in × 32 in so that the least amount of poster is used.
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A cat gave birth to 333 kittens who each had a different mass between 147147147 and 159\,\text{g}159g159, start text, g, end text. Then, the cat gave birth to a 4^{\text{th}}4 th 4, start superscript, start text, t, h, end text, end superscript kitten with a mass of 57\,\text{g}57g57, start text, g, end text.
The answer to the question is 334 kittens.
Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.
First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g
Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.
Therefore, the answer to the question is 334 kittens.
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Question In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. What normal distribution best approximates X? • Round to one decimal place if entering a decimal answer below.
The normal distribution that best approximates X is N(42, 21).
In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).
In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)
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Drag the correct equation for each graph into the blank spaces. Remember you should convert to slope intercept
form first!
In both cases, the slope (m) is the coefficient of the x-variable, and the y-intercept (b) is the constant. In the first equation, the slope (m) is 2, and the y-intercept (b) is -3. In the second equation, the slope (m) is 3, and the y-intercept (b) is 6.
What is graph?Graph is a data structure that consists of nodes (vertices) and edges (connections between nodes). Graphs are used to represent networks, such as social networks, transportation networks, and communication networks. Graphs provide a way to visualize relationships between data points and can be used to discover patterns in data and make predictions. Graphs are a powerful tool in data science and can be used to analyze complex systems.
This is happening because the equations represent the linear relationships between the variables of the graphs. The first equation is in slope-intercept form, and can be used to calculate the y-value of a given x-value. The equation for the second graph is also in slope-intercept form, and can be used to calculate the y-value of a given x-value.
In both cases, the slope (m) is the coefficient of the x-variable, and the y-intercept (b) is the constant. In the first equation, the slope (m) is 2, and the y-intercept (b) is -3. In the second equation, the slope (m) is 3, and the y-intercept (b) is 6.
These equations represent the linear relationships between the variables of the graphs. The slope of the line is the rate of change between the x- and y-values, while the y-intercept is the starting point of the line. By using the equations, we can calculate the y-value of any given x-value on the graph, and thus accurately represent the linear relationships between the variables.
The diagram is given below.
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Complete questions as follows-
VAT is added at 15% for good and services in South Africa. What will be the selling price of a laptop that costs R4200 before VAT
The selling price of laptop after VAT (15 percent) is Rs 4830.
To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.
A number that is expressed as a fraction of hundred is what it is.
it is mostly used to compare and determine ratios and is represented by the symbol %.
We are given that:-
the selling price of laptop before VAT = Rs 4200VAT= 15%so the amount after VAT = 4200+4200*15%
= 4200+4200+0.15
= 4200+630= 4830.
therefore, the selling price of laptop after VAT is Rs 4830.
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assistants please --------> The members of a weight loss support group just collectively weighed in at 1,519 pounds, which is 2% lighter than their previous weight. How much did the group weigh last time?
Work Shown:
x = previous total weight
2% of x = 0.02x = amount of weight lost
x - 0.02x = 0.98x = current total weight
0.98x = 1519
x = 1519/0.98
x = 1550 pounds
Check:
2% of 1550 = 0.02*1550 = 31
The group collectively lost 31 pounds.
1550-31 = 1519
The answer is confirmed.
Note that 98% of 1550 = 0.98*1550 = 1519
how do i work this out i dont understand it
Answer:
37
Step-by-step explanation:
we know that:
C=?
c=17
b=26
a=14
using the law of cosine:
[tex]a^{2} +b^{2} -2ab Cosc=c^{2}[/tex]
[tex]14^{2} +26^{2} -2(14)(26)Cosc=17^{2} \\872-728Cosc=289\\-728Cosc=-583\\Cosc=\frac{-583}{-728} \\C=36.791\\C=37[/tex]
If John had 3 apples then Droped 2 then found 4 then gave one to his friend how many apples does he have now
Answer:
4 apples
Step-by-step explanation:
We know
John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.
How many apples does he have now?
3 - 2 + 4 - 1 = 4 apples
So, he has 4 apples now.
Answer:
4 apples
Step-by-step explanation:
We know that John had 3 apples
but then he had dropped 2 of them
he then found 4
then he gave 1 to his friend
3-2=1
1+4=5
5-1=4
The answer is 4
Hope this helps!
When solving the equation 3(x-2)=-12, what is a possible first step?
*
1)Distributing the 3 into each term of the parenthesis.
2)She could either divide by 3 or distribute 3 into the parenthesis
3)Adding 2 to each side of the equation
4) Subtracting 2 on each side of the equation
5) Dividing each side of the equation by 3
6)none of the answer choices tell what the first step could be.
Answer:
2)She could either divide by 3 or distribute 3 into the parenthesis
Under certain conditions, sound can travel 768 miles per hour. Under these conditions, Alan hears thunder 45 seconds after seeing lightening. His friend, Ryan hears thunder after seeing the same lightening in 30 seconds. What is the longest and the shortest possible distance that Alan and his friend are apart.
The shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles
What is distance?Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it has magnitude but no direction. Distance is usually measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement used.
What is sound?Sound is a type of physical energy that is produced by vibrating objects and travels through a medium, such as air, water, or solids, as a series of pressure waves. When an object vibrates, it creates a disturbance in the surrounding medium that causes molecules to move back and forth, creating areas of high and low pressure that propagate outward from the source of the sound.
In the given question,
Let d be the distance between Alan and Ryan in miles. Then, the time it takes for sound to travel this distance is given by d/768. Therefore, we have:
d/768 = 45 - 30 = 15
Solving for d, we get:
d = 15 x 768 = 11520
So the distance between Alan and Ryan is 11520 miles.
If we take the lower bound of 750 miles per hour, we can calculate the minimum distance between Alan and Ryan as follows:
d/750 = 15
d = 15 x 750 = 11250
Therefore, the minimum distance between Alan and Ryan is 11250 miles.
If we take the upper bound of 800 miles per hour, we can calculate the maximum distance between Alan and Ryan as follows:
d/800 = 15
d = 15 x 800 = 12000
Therefore, the maximum distance between Alan and Ryan is 12000 miles.
Therefore, the shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles.
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7/19 as a percentage, round your answer to the nearest tenth of a percent
Answer: 36.8
Step-by-step explanation:
First convert 7/19 to a decimal.
7/19 = 0.368421...
Then to convert a decimal a percent by multiplying by 100
0.3684... x 100 = 36.8
PLEASE HELP ME
(Answer these four questions please)
3. The statement is true, the correlation coefficient is close to -1. 4. temperature for a city with a latitude of 48 is 43. 5. The statement is false. 6. cannot make a reasonable estimate
Describe Equation?Equations can be used to model real-world situations and solve problems in many fields, including science, engineering, finance, and more. They are an essential tool in mathematics and are used extensively in algebra, calculus, and other advanced branches of math.
Equations can involve various mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and others.
Question 3:
The statement is true. We can check this by calculating the correlation coefficient between the latitude and temperature data points, which should be close to -1. The calculated line of best fit is also consistent with the given data.
Question 4:
To estimate the temperature for a city with a latitude of 48, we can use the equation of the line of best fit:
y = -1.07x + 92.87
Substituting x = 48, we get:
y = -1.07(48) + 92.87
y = 42.79
Rounding to the nearest whole number, the estimated temperature for a city with a latitude of 48 is 43.
Question 5:
The statement is false. We can check this by calculating the correlation coefficient between the passengers and suitcases data points, which should be close to 1. The given line of best fit has a negative slope, which is inconsistent with the positive correlation between the variables.
Question 6:
To estimate the number of suitcases for a flight carrying 250 people, we can use the equation of the line of best fit:
y = -1.98x + 7.97
Substituting x = 250, we get:
y = -1.98(250) + 7.97
y = -485.03
However, it does not make sense for the number of suitcases to be negative. Therefore, we cannot make a reasonable estimate for the number of suitcases on a flight carrying 250 people using this line of best fit.
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Gastonia’s population of 15,000 in 2020 was expected to grow exponentially by 12% each DECADE for the rest of the century…
-------------------------------------------------
What will be the population in 2030?
ANSWER: people
-------------------------------------------------
What will be the population in 2040?
ANSWER: people
Answer: In 2030, the population will be 16,800 and in 2040 the population will be 18,816.
Step-by-step explanation: To find the population in 2030, we need to calculate one decade of growth from 2020 to 2030:
Population in 2030 = 15,000 x (1 + 0.12)^1 = 16,800
Therefore, the population in Gastonia is expected to be 16,800 in 2030.
To find the population in 2040, we need to calculate two decades of growth from 2020 to 2040:
Population in 2040 = 15,000 x (1 + 0.12)^2 = 18,816
Therefore, the population in Gastonia is expected to be 18,816 in 2040.
jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.
what is proportionality ?A mathematical relationship called proportionality asserts that two values are related in such a way that if one quantity rises or falls, the other quantity rises or falls by a fixed amount. The proportionality constant, also known as this constant factor, is typically represented by the letter "k".
given
The remaining 70% of Jerome's 1,040 songs are not country songs if only 30% of them are.
We can use the following calculation to get the proportion of non-country songs:
70% of 1,040 = 0.7 x 1,040 = 728
As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.
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What is −10y − 19 if y is 9?
Answer: -109
Step-by-step explanation:
Concept : First take note of what operations are in play and how they relate to y. In this case, -10 is being multiplied to y and then 19 is subtracted from the product of -10 and y.
Steps:
Plug 9 in for y (parentheses just mean multiply):
-10(9)-19
Simplify using correct order of operations:
-90-19
-109
Hope this helps :)
Suppose that 6 out of the 19 doctors in a small hospital are General Practitioners, 5 out of the 19 are under the age of 40 , and 2 are both General Practitioners and under the age of 40. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 40
The probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 from a small hospital is 9/19, given 6 out of 19 are General Practitioners, 5 out of 19 are under 40, and 2 are both.
To find the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40, we need to add the probabilities of these two events and subtract the probability of selecting a doctor who is both a General Practitioner and under the age of 40, since we don't want to count that case twice:
P(General Practitioner or under 40) = P(General Practitioner) + P(Under 40) - P(General Practitioner and under 40)
we know 6 out of 19 doctors are General Practitioners, 5 out of 19 doctors are under the age of 40, 2 doctors are both General Practitioners and under the age of 40.
Therefore:
P(General Practitioner) = 6/19
P(Under 40) = 5/19
P(General Practitioner and under 40) = 2/19
Substituting these values into the formula:
P(General Practitioner or under 40) = 6/19 + 5/19 - 2/19
= 9/19
Therefore, the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 40 is 9/19.
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use a direct proof to show that every odd integer is the difference of two squares. [hint: find the difference of the squares of k 1 and k where k is a positive integer.]
Yes, every odd integer can be written as the difference of two squares.
To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.
To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.
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what is t he chance that a randomly selected indivudal found to have a positive result actuall yhas the disease
The chance that a randomly selected individual found to have a positive result actually has the disease is called the Positive Predictive Value (PPV). What is the chance that a randomly selected individual found to have a positive result actually has the disease?
The probability that a randomly chosen individual with a positive test result really has the disease is referred to as the Positive Predictive Value (PPV). It reflects how well the test can detect disease in those who have it. In statistics, the PPV is calculated as follows:
PPV = True Positives / (True Positives + False Positives) x 100
In addition, the PPV is influenced by a variety of factors, including the disease's prevalence, the sensitivity and specificity of the test, and the prevalence of the disease in the population.
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What is 999999999999999999292929292929923798341038701384710348710387017+74569273469287465294875629837469523746539287465927346592873654987264982768
Answer: 8377828766289
Step-by-step explanation:
Answer:
The sum is:
74569273469287465294875629837469523746539287465927346592873654987264982768
999999999999999999292929292929923798341038701384710348710387017
= 74569273469287465294875629837469523746539287465927346592873655087264969785
The function g is continuous on the interval [a, b] and is differentiable on (a, b). Suppose that g(x) = 0 for 4 distinct values of x in (a, b). What is the minimum number, k, of z in (a, b) such that g'(z) = 0?
We have to find the minimum number, k, of z in (a, b) such that g'(z) = 0. The function g is continuous on the interval [a, b] and is differentiable on (a, b). Suppose that g(x) = 0 for 4 distinct values of x in (a, b).
Let x1, x2, x3, and x4 be the four distinct values of x such that g(x) = 0.Now consider the following cases:Case 1: All four x1, x2, x3, x4 are local extrema of g(x).If this is the case, then g′(x1)=g′(x2)=g′(x3)=g′(x4)=0. Therefore, the minimum number, k, of z in (a, b) such that g′(z) = 0 is 4.Case 2:
There are less than four local extrema of g(x).In this case, by Rolle's Theorem, there exists at least one point z in (a, b) such that g′(z)=0. Since there are less than four local extrema of g(x), this point z is not equal to any of x1, x2, x3, and x4. Therefore, the minimum number, k, of z in (a, b) such that g′(z) = 0 is 1.In conclusion, the minimum number, k, of z in (a, b) such that g′(z) = 0 is either 1 or 4 depending on whether there are less than four local extrema of g(x) or all four x1, x2, x3, and x4 are local extrema of g(x).
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Which of the following Boolean expressions are equivalent to the expression num ≥ 15 ?Select two answers.(A) (num > 15) AND (num = 15)(B) (num > 15) OR (num = 15)(C) NOT (num < 15)(D) NOT (num < 16)
Boolean expressions that are equivalent to the expression num ≥ 15 are (B) (num > 15) OR (num = 15) and (D) NOT (num < 16).
In Boolean algebra, a Boolean expression is an algebraic expression made up of Boolean variables and logical operations. Boolean logic deals with logical variables and has only two values: 1 or 0 or TRUE or FALSE. Boolean expressions evaluate to a Boolean value of either 0 or 1 or TRUE or FALSE.(A) (num > 15) AND (num = 15) - this expression is not equivalent to num ≥ 15 because (num > 15) is false for all values of num that are less than or equal to 15.
However, num ≥ 15 is true for all values of num that are greater than or equal to 15.(C) NOT (num < 15) - this expression is not equivalent to num ≥ 15 because NOT (num < 15) is true for all values of num that are greater than or equal to 15. However, num ≥ 15 is true for all values of num that are greater than or equal to 15.(B) (num > 15) OR (num = 15) - this expression is equivalent to num ≥ 15 because if num is greater than 15, then (num > 15) is true and (num = 15) is false. However, if num is equal to 15, then (num > 15) is false and (num = 15) is true.
In either case, (num > 15) OR (num = 15) is true, which means that num ≥ 15 is true.(D) NOT (num < 16) - this expression is equivalent to num ≥ 15 because if num is less than 16, then (num < 16) is true and NOT (num < 16) is false. However, if num is greater than or equal to 16, then (num < 16) is false and NOT (num < 16) is true. In either case, NOT (num < 16) is true, which means that num ≥ 15 is true.
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80% off of the sale price $90 what is the original price
Answer: So that means the answer is $112.5
Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.
YES THIS IS RIGHT!!!!
write subtraction problem as an addition problem problem she writes what is -3+ -4 how can how can you use a number right now -3+ -4 as a subtraction problem
the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".
How to solve and what is subtraction?
To write the subtraction problem "-3 - 4" as an addition problem using negative numbers, we can rewrite it as follows:
-3 - 4 = -3 + (-4)
So, the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".
Subtraction is a fundamental arithmetic operation used to find the difference between two values or quantities. It involves taking away a certain amount from a starting value, resulting in a lower value.
The starting value is called the minuend, the amount being subtracted is called the subtrahend, and the result is called the difference. Subtraction is commonly used in everyday life, such as in calculating change when making a purchase or determining how much time has elapsed between two events. It is also an important concept in more advanced mathematical topics such as algebra and calculus.
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a display shelf in a retail shop will showcase the stores handmade artisan soaps. the length of the shelf given to each bar of soap will be uniformly distributed with a mean of 3 inches and a standard deviation of 0.5 inch. for 50 bars of soap what is the probability the length of the display will exceed 154 inches?
The probability the length of the display will exceed 154 inches is 0.1292
What is the probability?The probability that the length of the display shelf given to each bar of soap will exceed 154 inches when there are 50 bars of soap is 0.0062 or 0.62%. This is because the mean is 3 inches and the standard deviation is 0.5 inches, which means that the length of the display will have a normal distribution.
We can calculate this probability by using the following formula:
P(x > 154) = P (x > 154 - 50 × 3/√(50×0.5)) = P(Z > 1.13) = 1 - P(Z < 1.13) = 1 - 0.870 = 0.1292
The probability the length of the display will exceed 154 inches is 0.1292.
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Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.
Answer:
Step-by-step explanation:
The coordinates of the endpoints of PQ are P( – 12,7) and Q( – 4, – 9). Point R is on PQ and divides it such that PR:QR is 3:5
The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.
Using the distance formula, we have:
d(P,Q) = √((x2-x1)² + (y2-y1)²)
= √((-4-(-12))² + (-9-7)²)
= √(8² + (-16)²)
= √(320)
= 8 √(5)
Since PR:QR is 3:5, we can set up the following equation:
d(P,R)/d(R,Q) = 3/5
Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.
Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)
Using the distance formula again, we can find the distance between P and R:
d(P,R) = (3/8) d(P,Q)
= (3/8) (8 √(5))
= 3 √(5)
Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:
d(R,Q) = (5/3) d(P,R)
= (5/3) (3 √(5))
= 5 √(5)
Finally, we can use the midpoint formula to find the coordinates of R:
x = (-12 + (3/8) (8))/2 = -8
y = (7 + (-1))/2 = 3
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Complete Question:
The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?