Z = Y - X.We have the following probability distribution for X:X -1 0 1 P(X) 1/4 1/2 1/4Since Z is independent of X, its probability distribution is as follows:Z -1 0 1 P(Z) 1/4 1/2 1/4Thus, the distribution of Z is the same as the distribution of Y - X.
The marginal distribution of Y is given as follows: P(Y = 0) = P(X + Z = 0) = P(X = 0, Z = 0) + P(X = -1, Z = 1) = 1/4 + 1/4 = 1/2P(Y = 1) = P(X + Z = 1) = P(X = 0, Z = 1) + P(X = 1, Z = 0) = 1/4 + 1/4 = 1/2P(Y = 2) = P(X + Z = 2) = P(X = 1, Z = 1) = 1/4P(Y = 3) = P(X + Z = 3) = P(X = 2, Z = 1) = 1/4P(Y = 4) = P(X + Z = 4) = P(X = 2, Z = 2) = 1/4The marginal distribution of Y is as follows: Y 0 1 2 3 4 P(Y) 1/2 1/2 1/4 1/4 1/4So, the marginal distribution of Y is given by the table above. Also, Var(Y) = 7/4 which verifies the answer to part (6).
We are given that Y = X + Z for some random variable Z independent of X. Therefore, Z = Y - X.We have the following probability distribution for X:X -1 0 1 P(X) 1/4 1/2 1/4Since Z is independent of X, its probability distribution is as follows:Z -1 0 1 P(Z) 1/4 1/2 1/4Thus, the distribution of Z is the same as the distribution of Y - X.
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Factor the expression p^2q^2+pq-q^3-p^3 and then find its value for p=4 and q=-4
The value of the expression for p=4 and q=-4 is 240. To factor the expression [tex]p^2q^2+pq-q^3-p^3,[/tex] we can use the factoring by grouping method.
First, we can factor out a common factor of pq from the first two terms and a common factor of [tex]q^3[/tex] from the last two terms:
[tex]p^2q^2 + pq - q^3 - p^3[/tex]
[tex]= pq(pq + 1) - q^3 - p^3 + q^3[/tex]
[tex]= pq(pq + 1) - p^3[/tex]
Now, we can factor the expression [tex]-p^3[/tex] by using the difference of cubes formula:
[tex]= pq(pq + 1) - (p)(p^2)[/tex]
[tex]= pq(pq + 1 - p^2)[/tex]
So the fully factored form of the expression is [tex]pq(pq + 1 - p^2).[/tex]
To find the value of the expression for p=4 and q=-4, we can substitute these values into the factored form:
[tex]pq(pq + 1 - p^2)[/tex]
[tex]= (4)(-4)((4)(-4) + 1 - (4)^2)[/tex]
= (-16)(-15)
= 240
Therefore, the value of the expression for p=4 and q=-4 is 240.
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QUESTION 1 1.1 A list of numbers is given. -14 ; 36 ; 3 ; 2.13131.... ; 5 Choose from the given list (write your answer next to the space provided): 1.1.1 1.1.2 Irrational number 1.1.4 An even prime number 1.1.3 Recurring decimal An uneven square number 3,14234842...... ; 25; 2 1.1.5 A factor of 51 (1) (1) (1) (1)
By answering the presented question, we may conclude that 1.1.5: A inequality factor of 51 - 25 is a factor of 51 since 51 can be written as 25 x 2 + 1.
Describe inequality.An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.
1.1.1: Irrational number - 2.13131.... is a non-repeating, non-terminating decimal, which is a characteristic of irrational numbers.
1.1.2: Recurring decimal - None of the given numbers have a repeating decimal pattern, so this option is not applicable.
1.1.3: An uneven square number - None of the given numbers are perfect squares, so this option is not applicable.
1.1.4: An even prime number - The only even prime number is 2, which is not in the list. Therefore, this option is not applicable.
1.1.5: A factor of 51 - 25 is a factor of 51 since 51 can be written as 25 x 2 + 1.
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When building a house, the number of days required to build is inversely proportional to with the number of workers. One house was built in 36 days by 27 workers. How many days would it take to build a similar house with 9 workers?
It would take 108 days to build a similar house with 9 workers.
What is variation ?
In mathematics, variation refers to the concept of how one variable or quantity changes in relation to another variable or quantity. It can refer to a number of different concepts, including direct variation, inverse variation, joint variation, and partial variation. Direct variation is when one variable increases proportionally with another variable, while inverse variation is when one variable decreases proportionally with another variable. Joint variation is when one variable depends on multiple other variables, while partial variation is when one variable depends on some, but not all, of the other variables.
According to the question:
We can use the formula for inverse variation, which states that if two quantities x and y are inversely proportional, their product is constant:
x * y = k
where k is the constant of proportionality.
In this case, let d be the number of days required to build the house, and w be the number of workers. Then we have:
d * w = k
We know that one house was built in 36 days by 27 workers, so we can use this information to find k:
36 * 27 = k
k = 972
Now we can use this value of k to find how many days it would take to build a similar house with 9 workers:
d * 9 = 972
d = 972/9
d = 108
Therefore, it would take 108 days to build a similar house with 9 workers.
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show that the matrices (1000), (0100), (0001) generate m2*2(f)
To show that the matrices (1000), (0100), and (0001) generate m2*2(f), we must show that any matrix in m2*2(f) can be written as a linear combination of these three matrices we can show A as a linear combination of the three matrices: A = a(1000) + b(0100) + c(0001)
A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Let A be any matrix in m2*2(f). Then A can be written in the form:
A = (a b)
(c d)
where a, b, c, and d are elements of the field f.
Now, we can write A as a linear combination of the three matrices:
A = a(1000) + b(0100) + c(0001)
So, the matrices (1000), (0100), and (0001) generate m2*2(f).
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the shelly group has leased new copier that costs $800 per month plus .25 for each copy. what is the total cost if shelly makes 6000 copies a month
If the new copier costs $800 per month plus $0.25 for each copy, then the total cost for 6000 copies a month is $2300.
The total cost of leasing a copier from the Shelly group depends on the number of copies made each month.
We have to find the cost for making 6000 copies a month,
The equation to represent the total cost is represented as :
⇒ Total cost = (Monthly lease cost) + (Cost per copy × Number of copies),
⇒ Monthly lease cost = $800
⇒ Cost per copy = $0.25
⇒ Number of copies = 6000,
Substituting the values,
We get,
⇒ Total cost = $800 + ($0.25×6000)
⇒ $800 + $1500
⇒ $2300
Therefore, the total monthly cost is $2300.
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SOLVE PLS! WILL GIVE BRAINLIST
-2x-9y=-25
-4x-9y=-23
What is the solution? and show all steps
Answer:
x = -1 and y = 3
Step-by-step explanation:
Let's solve your system by elimination.
−2x−9y=−25;−4x−9y=−23
Multiply the second equation by -1, then add the equations together.
(−2x−9y=−25)
−1(−4x−9y=−23)
Becomes:
−2x−9y=−25
4x+9y=23
Add these equations to eliminate y:
2x=−2
x = -1
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
−2x−9y=−25
Substitute−1forxin−2x−9y=−25:
(−2)(−1)−9y=−25
−9y+2=−25(Simplify both sides of the equation)
−9y+2+−2=−25+−2(Add -2 to both sides)
−9y=−27
y = 3
+
0
1
2
Which of these expressions or phrases can be used to represent the model?
Choose ALL the correct answers.
40 number of fourths in 1
40 number of fourths in 3
34
1
of 3
1
3
The expressions of the model are 3 ÷ 1/4, number of 4ths in 3
How to determine the expression of the modelFrom the question, we have the following parameters that can be used in our computation:
The model
On the model we have
Partions = 12
Sections = 4
Number = 3
This means that
1/4 of the partions = 3
So, we have
1/4 * 12 = 3
Rewrite as
3 /(1/4) = 12
Hence, the expression is 3 ÷ 1/4
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Find m∠DEF in the diagram.
Answer:
∠DEF = 31.8°
Step-by-step explanation:
∠DEF and the other angle (58.2°) are complementary.
Complementary angles add up to 90 degrees.So,
∠DEF + 58.2° = 90°
Subtract 58.2 from both sides∠DEF = 90° - 58.2°
∠DEF = 31.8°[tex]\rule[225]{225}{2}[/tex]
Answer:
m∠DEF = 31.8°
Step-by-step explanation:
We have two angles that form a right angle. I'm going to call the leading arrow of the bottom line "Point G". So angles DEF and FEG form a right angle, measuring a total of 90°
To find DEF, we subtract the known angle FEG from 90° because the two angles are complementary angles.
m∠DEF = 90° - 58.2°
m∠DEF = 31.8°
evaluate the sum \[ 22\binom{26}{0} 21\binom{26}{1} 20\binom{26}{2} \cdots (-3)\binom{26}{25} (-4)\binom{26}{26}. \] your answer formatting tips
sum_{k=2}^{26}\binom{26}{k}
To find out the value of the given expression, we will use the Vander monde's Identity which is as follows;\[\binom{m+n}{r} = \sum_{k=0}^r\binom{m}{k}\binom{n}{r-k}\]On comparing this with the given expression, we see that $m=n=26$, and $r=0, 1, 2, \cdots, 26$.Now we substitute these values in the given expression.\[\begin{aligned} 22\binom{26}{0} 21\binom{26}{1} 20\binom{26}{2} \cdots (-3)\binom{26}{25} (-4)\binom{26}{26} & = 22\binom{26}{26} - 21\binom{26}{25} + 20\binom{26}{24} - \cdots -3\binom{26}{3} + (-4)\binom{26}{2} \\ &= \binom{26}{26} - \left(\binom{26}{24} - \binom{26}{25}\right) + \left(\binom{26}{22} - \binom{26}{23}\right) - \cdots - \left(\binom{26}{4} - \binom{26}{3}\right) + \binom{26}{2} \\ &= \binom{26}{26} + \binom{26}{25} + \binom{26}{24} + \binom{26}{23} + \cdots + \binom{26}{4} + \binom{26}{3} + \binom{26}{2} \\ &= \sum_{k=2}^{26}\binom{26}{k} \end{aligned}\]Thus, we obtain $\sum_{k=2}^{26}\binom{26}{k}$ as the simplified value of the given expression.
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Sketch the net of the following figure on a sheet of paper. Write a short description about the net. Upload the net and
description.
A
The net of this figure would be a square with four equilateral triangles on each of its sides.
What would the net of this pyramid be like?To create the net of this figure we must analyze its sides and the joints of each of its faces. According to the above, we can conclude that this figure is made up of four equilateral triangular faces and a square at its base. To form the net of this figure, the most appropriate thing would be to start at the base and join the sides, in this case there would be four triangles, one on each side of the square. It is very important that the triangles are equilateral and have the same dimensions so that the pyramid can be formed correctly.
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The Hamilton path and Euler circuit are the same. The Hamilton circuit and Euler circuit are the same. The Hamilton circuit and Euler path are the same. The Hamilton path and Euler path are the same
None of the statements are true; Hamilton circuits/paths and Euler circuits/paths are different concepts.
A Hamilton path is a path that visits every vertex of a graph exactly once, while an Euler circuit is a circuit that passes through every edge of a graph exactly once.
A Hamilton circuit is a circuit that passes through every vertex of a graph exactly once, while an Euler path is a path that passes through every edge of a graph exactly once.
Therefore, Hamilton circuits and Euler circuits are different concepts, as are Hamilton paths and Euler paths.
To add further explanation:
A Hamilton path can exist in a graph that does not have a Hamilton circuit. For example, a path that visits all vertices of a cycle graph except for one vertex is a Hamilton path, but the graph does not have a Hamilton circuit.
An Euler circuit can exist in a graph that does not have a Hamilton circuit or Hamilton path. For example, a graph with multiple connected components can have Euler circuits in each component, but it may not have a Hamilton path or circuit.
It is also possible for a graph to have both a Hamilton circuit and an Euler circuit. In this case, the graph is said to be both Hamiltonian and Eulerian.
Overall, the concepts of Hamilton and Euler circuits and paths are important in graph theory and have applications in various fields such as computer science, physics, and biology.
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The complete question is:
Which of the following statements about Hamilton and Euler circuits/paths are true?
The Hamilton path and Euler circuit are the same.
The Hamilton circuit and Euler circuit are the same.
The Hamilton circuit and Euler path are the same.
The Hamilton path and Euler path are the same.
Select all that apply.
The area of a rectangular piece of land is represented by the polynomial 8x^2+40x+50. The length of the piece of land is equal to two times its width. What expressions represent the dimensions of the piece of land?
The dimensions of the rectangle are:
width = 2x + 5
length = 4x+ 10
How to get the length and the width?Here we know that the area of a rectangular piece of land is:
8x² + 40x + 50
Remember that for a rectangle of length L and width W, the area is:
A = L*W
So we can write:
L*W = 8x² + 40x + 50
We also know that the length is two times the width, so:
L = 2*W
Replacing that we get:
2*W*W = 8x² + 40x + 50
We an rewrite this as:
W² = (8x² + 40x + 50)/2
W² = 4x² + 20x + 25
Solving that for W we get:
W = √(4x² + 20x + 25)
W = √( 4x² + 2*2*5x + 5²)
W = √( (2x + 5)²)
W = 2x + 5
That expression represents the width, and the length is:
L = 2*(2x + 5) = 4x + 10
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Evaluate the expression for j= -1
Answer:
17
Step-by-step explanation:
Evaluating expressions by plugging in a value for a variable:
[tex]-18|j| -1[/tex]
Plug in -1
[tex]-18(-1)-1[/tex]
Multiply
[tex]18-1[/tex]
Subtract
[tex]17[/tex]
Richard has an account balance of -75 dollars. Which of the following equations accurately describes the size of Richard's debt?
Group of answer choices
-75=75 meaning that Richard has a debt of 75 dollars
Absolute value of |-75| = 75 meaning that Richard has a debt of 75 dollars
Absolute value of |-75|=-75 meaning that Richard has a debt of -75 dollars
Absolute value of |75|=-75 meaning that Richard has a debt of -75 dollars
The equation that describes the size of Richard's debt is absolute value of |-75| = 75 meaning that Richard has a debt of 75 dollars (second option)
What is the absolute size of Richard's debt?The account balance is a negative number. A negative number is a number that is less than 0. A negative number has a minus in front of it. An example of a negative number is -75.
If the account balance is negative, it means that Richard has overdrawn his account and he is in debt. He owes the bank money.
The sign that is used to represent absolute value in mathematics is I I. The absolute value of I-75I is 75.
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If a rock is thrown upward on the planet Mars with a velocity of 19 m/s, its height (in meters) after t seconds is given by H = 19t − 1.86t2.
(a) Find the velocity of the rock after one second. m/s
(b) Find the velocity of the rock when t = a. m/s
(c) When will the rock hit the surface? (Round your answer to one decimal place.) t = s
(d) With what velocity will the rock hit the surface? m/s
Answer:
Below
Step-by-step explanation:
A) The derivative of the position function is the velocity function
derivative = 19 - 3.72 t at t = 1 this = 15.28 m/s
B) unclear: 19 - 3.72a
C) H= 0 when at surface
0 = 19t - 1.86 t^2
Quadratic Formula shows t = 10.2 s
D ) it will come down at the same speed it went up (but opposite direction) = -19 m/s
A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f on [a, b]. If so, find all values c in [a, b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. f(x) = x2 – 1 x2 -4 on [0, 4] c= 2,-2 (Separate multiple answers by commas.)
For the given function, all values c in [a, b] guaranteed by the Mean Value Theorem Note is lies on the expression of 15x⁴ - 240x² - 256
To determine whether the Mean Value Theorem can be applied to f on [0, 4], we need to check whether f satisfies two conditions: 1) f must be continuous on [0, 4], and 2) f must be differentiable on (0, 4). The first condition ensures that the function has no jumps or breaks within the interval, while the second condition ensures that the function has a well-defined slope at each point in the interval.
Next, we need to check if f is differentiable on (0, 4). To do this, we need to take the derivative of f(x) and check whether it exists and is continuous on (0, 4).
f(x) = (x² – 1) / (x² -4) f'(x) = [(x² -4)(2x) - (x² -1)(2x)] / (x² -4)² f'(x) = -4x / (x² - 4)²
We can see that the derivative of f(x) exists and is continuous on (0, 4) except for x = ±2, where it has a vertical tangent. However, these points do not affect the differentiability of the function on (0, 4).
To find the values of c, we can use the formula for the Mean Value Theorem:
f'(c) = [f(4) - f(0)] / (4 - 0)
We already found the derivative of f(x) to be f'(x) = -4x / (x² - 4)². Using this and plugging in the endpoints of the interval [0, 4], we get:
f'(c) = [-15/16] / 4 f'(c) = -15/64
To solve for c, we need to find the value(s) of x that satisfy the equation f'(x) = -15/64. We can simplify this equation to get:
-4x / (x² - 4)² = -15/64 64x = 15(x² - 4)² 0 = 15x⁴ - 240x² - 256
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Please help i am having trouble with my homework in side lengths if a triangle can y’all please explain and answer the questions in the picture
BETHANY, PABLO, and TRENT are students who completed the task correctly.
Describe Triangles?A triangle is a three-sided polygon that is formed by three line segments that intersect at three points called vertices. Triangles can have different shapes, sizes, and angles, and are classified based on their side lengths and angles. Some of the properties of triangles include:
Types of triangles: Triangles can be classified based on their angles as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is equal to 90 degrees). They can also be classified based on their side lengths as scalene (all sides have different lengths), isosceles (two sides have the same length), or equilateral (all sides have the same length).
Sum of angles: The sum of the three angles in a triangle is always equal to 180 degrees. This property is known as the angle sum property of triangles.
Pythagorean theorem: In a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. This property is known as the Pythagorean theorem.
Congruence: Two triangles are said to be congruent if their corresponding sides and angles are equal. Congruent triangles have the same shape and size, but may be oriented differently.
Similarity: Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional. Similar triangles have the same shape, but may have different sizes.
Area: The area of a triangle is given by the formula A = (1/2)bh, where b is the length of the base and h is the height of the triangle. The height is the perpendicular distance from the base to the vertex opposite the base.
Inequality theorem: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side. This property is known as the triangle inequality theorem.
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Check each true statement, and only the true statements. The domain for all variables is the set of integers.
Group of answer choices
∀x ∃y (x+2y=1)
∃y ∀x (x+2y=1)
∃x ∀y (x+2y=1)
∀y ∃x (x+2y=1
The domain for all variables is the set of integers.The correct answer is: ∀y ∃x (x+2y=1).
This statement is true because for any integer value of y, there exists an integer value of x that satisfies the equation x+2y=1. For example, if y=0, then x=1; if y=1, then x=-1; if y=2, then x=-3, and so on.
The other statements are not true for all integer values of x and y. For example, ∀x ∃y (x+2y=1) is not true because there are integer values of x for which there is no integer value of y that satisfies the equation (e.g. if x=2, then y= -0.5, which is not an integer). Similarly, ∃y ∀x (x+2y=1) and ∃x ∀y (x+2y=1) are not true because there is no single integer value of y or x that satisfies the equation for all integer values of x or y, respectively.
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a wedge is cut from a circular tree whose diameter is 2 m by a horizontal cutting plane up to the vertical axis and another cutting plane which is inclined by 45 degrees from the previous plane. find the volume of the wedge.
The volume of the wedge is π/8 cubic meters.
To find the volume of the wedge, follow these steps:
1. First, find the radius of the tree by dividing the diameter by 2.
Since the diameter is 2 meters, the radius (r) is 1 meter.
2. The angle of inclination of the second cutting plane is given as 45 degrees.
Since a full circle is 360 degrees, find the fraction of the circle that the wedge represents by dividing 45 by 360.
This gives us 45/360 = 1/8.
3. The volume of a cylinder can be calculated using the formula V = π[tex]r^2h,[/tex]
where r is the radius and h is the height.
In this case, the height of the wedge (h) is equal to the radius (r), which is 1 meter.
So, the volume of the whole cylinder (tree) would be V = π[tex](1^2)(1)[/tex]
= π cubic meters.
4. Now, multiply the volume of the whole cylinder by the fraction representing the wedge (1/8) to find the volume of the wedge: (1/8) × π = π/8 cubic meters.
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The fractions are: -2/3 , -3/4 , -2/6 , and -1/2
Answer:
-3/4, -2/3, -1/2, -2/6
Step-by-step explanation:
Making each fraction a percentage,
-2/3 x 100 = -66.67%
-3/4 x 100 = -75%
-2/6 x 100 = -33.33%
-1/2 x 100 = -50%
Arranging from least to greatest, -75%, -66.67%, -50%, -33.33%
Hence, -3/4, -2/3, -1/2, -2/6
Answer: -2/6 , -1/2 , -3/4 , -2/3
Step-by-step explanation:
Depending on the calculator, you can simplify the fractions into decimals. Or you can use your computer.
-2/6 = -0.3-1/2 = -0.5-3/4 = -0.75-2/3 = -0.067Correct me if this answer is wrong please! :)
41. Cancer Survivor Rates The 10-year survival rate for bladder cancer is approximately 50%. If 20 people who have bladder cancer are properly treated for the disease, what is the probability that: a. At least 1 will survive for 10 years? b. At least 10 will survive for 10 years? c. At least 15 will survive for 10 years?
The required probabilities are
a. At least 1 will survive for 10 years is 0.99902
b. At least 10 will survive for 10 years is 0.623
c. At least 15 will survive for 10 years is 0.008
Complement rule in Probability:The complement rule is a fundamental principle in probability theory that states that the probability of an event happening is equal to one minus the probability of the event not happening.
P(A') = 1 - P(A)
Here we have
The 10-year survival rate for bladder cancer is approximately 50%
The probability of one will survive for 10 years = 50% = 0.5
The probability of no one will survive for 10 years = 1- 0.5 = 0.5
To find the probability that at least 1 out of 20 people will survive for 10 years, use the complement rule,
The probability that no one will survive for 10 years is:
P(0 survivors) = (0.5)²⁰ = 0.00098
Therefore,
The probability that at least 1 person will survive for 10 years is:
P(at least 1 survivor) = 1 - P(0 survivors) = 1 - 0.00098 = 0.99902
b. To find the probability that at least 10 out of 20 people will survive for 10 years, use the binomial distribution formula:
=> P(X ≥ 10) = 1 - P(X < 10) = 1 - ∑(k = 0 to k = 9) (20, k) × (0.5)²⁰
Using a binomial distribution table or a calculator, we can find that:
=> P(X < 10) = 0.377
Hence, the probability that at least 10 people will survive for 10 years is:
P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.377 = 0.623
c. To find the probability that at least 15 out of 20 people will survive for 10 years, we can again use the binomial distribution formula:
P(X ≥ 15) = 1 - P(X < 15) = 1 - ∑(k= 0 to k = 14) (20 choose k) × (0.5)²⁰
Using a binomial distribution table or a calculator
=> P(X < 15) = 0.992
Hence, the probability that at least 15 people will survive for 10 years is:
=> P(X ≥ 15) = 1 - P(X < 15) = 1 - 0.992 = 0.008
Therefore,
The required probabilities are
a. At least 1 will survive for 10 years is 0.99902
b. At least 10 will survive for 10 years is 0.623
c. At least 15 will survive for 10 years is 0.008
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Rebecca bought one goldfish for $32. She spends the rest of her money on guppy fish. She starts with $80. Each guppy costs $6. Write an inequality for the number of guppies she can purchase. Then solve
Answer:6g+32<80
Step-by-step explanation:
Can anyone help with this question?
Answer:
a=180 b=180 and 914 c=180
Step-by-step explanation:
simple
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Alex wants to fence in an area for a dog park. He has plotted three sides of the fenced area at the points E (1, 5), F (3, 5), and G (6, 1). He has 16 units of fencing. Where could Alex place point H so that he does not have to buy more fencing?
(0, 1)
(0, −2)
(1, 1)
(1, −2)
Answer: That would be C
Step-by-step explanation: Let H's coordinates be (x, y).
We obtain using the distance formula,
EF is equal to ( 3 - 1)2 + (5 - 5)2 = ( 4 + 0) = 2 units.
FG = (9 + 16) = 5 units (i.e., 6 - 3)2 + (1 - 5)2).
→ GH = √{(x - 6)² + (y - 1)²}
→ HE = √{(x - 1)² + (y - 5)²}
since,
16 units = EF + FG + GH + HE
→ 2 + 5 + √{(x - 6)² + (y - 1)²} + √{(x - 1)² + (y - 5)²} = 16
9 units are equal to (x - 6)2 + (y - 1)2 + (x - 1)2 + (y - 5)2.
utilizing the options available to us now,
A) (0, 1) (0, 1)
→ √(36) + √(1 + 25) = 6 + √26 ≠ 9 units.
B) (0, - 2) (0, - 2)
→ √(36 + 9) + √(1 + 49) = √45 + √50 ≠ 9 units .
C) (1 , 1) (1 , 1)
→ √(25 + 0) + √(0 + 16) = 5 + 4 = 9 = 9 units .
Alex should then position Point H at (1, 1).
Answer: C, (1,1)
Step-by-step explanation: If you plot the three points given in the equation, you can then see that (1,1) is closest to the remaining points. Because it is the closest, the perimeter is shorter and Alex would not have to buy more fencing.: :)
y = x - 4 y = 6x - 10
The solution to the system of equations y = x - 4 and y = 6x - 10 is (6/5, -14/5).
This question is incomplete, the complete question is;
What is the solution to the system of equation; y = x - 4, y = 6x - 10.
What is the solution to the given system of equation?Given the system of equation in the question:
We have two equations:
y = x - 4 ---(1)
y = 6x - 10 ---(2)
To find the solution, we need to solve for x and y that satisfy both equations.
Substituting equation (1) into equation (2) to eliminate y, we get:
x - 4 = 6x - 10
Simplifying the equation by combining like terms, we get:
5x = 6
x = 6/5
Substituting the value of x into equation (1) to find y, we get:
y = (6/5) - 4
y = -14/5
Therefore, the solution to the system of equations is x = 6/5 and y = -14/5).
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The values of x and y in the equations are: x = 6/5 and y = -2.8
What is simultaneous equation?Simultaneous equations are sets of two or more algebraic equations that share common variables and are solved at the same time (that is, simultaneously)
The given equations are
y = x - 4 .....................1
y = 6x - 10 .................2
Using substitution method, put y= x-4 in equation 2
x-4 = 6x - 10
x-6x = -10 +4
Simplifying the expression to find y we have
-5x = -6
Dividing by the coefficient of x to get
x = 6/5
Recall that y = x - 4
Therefore y = 6/5 -4
Therefore the value of y = -2.8
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Find the intersection of the planes x+(y-1)+z=0 and -x+(y+1)-z=0
The intersection of the given planes is $$(x,y,z) = (1,-y,-y)$$
The given planes are: $x+(y-1)+z=0$ and $-x+(y+1)-z=0$.We have to find the intersection of these two planes.Intersection of two planes can be found as follows:
First, convert the planes into parametric equations.$x+(y-1)+z=0$$\Rightarrow x = -y+1-z$$\Rightarrow (x,y,z) = (-y+1-z,y,z)$$(-x+(y+1)-z=0$$$$\Rightarrow x = y+1+z$$$$\Rightarrow (x,y,z) = (y+1+z,y,z)$So, we have,$$(x,y,z) = (-y+1-z,y,z) = (y+1+z,y,z)$$
This gives two equations,$$-y+1-z=y+1+z$$$$\Rightarrow -2y=2z$$$$\Rightarrow z=-y$$$$$$$$y+1+z=y$$$$\Rightarrow z=-1$$$$$$$$x = -y+1-z$$$$= -y+1-(-y)$$$$= 1$$
So, the intersection of the given planes is $$(x,y,z) = (1,-y,-y)$$
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In Exercises 19–22, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 1 h 4 1 h -3 19. 20. 6 8 4 6 [-1 :] 3 21. 1 -4 3 -2 h 8 22. 2 -3 -6 9 h 5
Answer: For the matrix to be the augmented matrix of a consistent linear system, the rows of the matrix must satisfy some equations, if there is a row with zero in the leftmost column and non-zero in any other column, the system will not be consistent.
So to determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system, we will use this idea to write equations:
1. h + 4 = 0 and 1h - 3 = 0 Solving for h gives h = -4 and h = 3/1 respectively, therefore the value of h such that the matrix is the augmented matrix of a consistent linear system are -4 and 3/1.
2. -1h + 3 = 0 Solving for h gives h = 3/1, therefore the value of h such that the matrix is the augmented matrix of a consistent linear system is 3/1.
3. 1h - 4 = 0, 3 - 2h + 8 = 0 Solving for h gives h = 4/1 and h = 11/(-2) respectively, therefore the value of h such that the matrix is the augmented matrix of a consistent linear system are 4 and -5.5. 4. 2h - 3 = 0, -6h + 9 = 0, and 5 - h = 0
Solving for h gives h = 3/2, h = 3/(-6), and h = 5 respectively, therefore the value of h such that the matrix is the augmented matrix of a consistent linear system are 3/2 and -0.5.
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Give one explanation on what could have led to the difference in the number of water tank deliveries on construction site in the 2 month period
Difference in water tank deliveries on a construction site in a 2-month period could be due to various factors, such as weather changes, project size, worker numbers, water sources, and equipment malfunctions.
One possible explanation for the difference in the number of water tank deliveries on a construction site in a 2 month period could be a change in the weather conditions, which could have affected the water needs for construction purposes. For example, if the weather was drier and hotter in one month, more water may have been needed to compensate for evaporation and to keep the site hydrated.
Other possible reasons for the difference in the number of water tank deliveries on a construction site in a 2 month period could include changes in the size or scope of the project, shifts in the number of workers on the site, or variations in the availability or quality of local water sources. Additionally, factors such as equipment malfunctions or supply chain disruptions could also impact the frequency of water tank deliveries.
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A right rectangular prism is 2.75 in by 4 in by 16.5 in. what is the total surface area of the prism? 244.75 in2 222.75 in2 122.375 in2 112.75 in2
If the right rectangular prism is 2.75in by 4in by 16.5in, then the total surface area of the prism is (a) 244.75 in².
We know that the total surface area of a right rectangular prism is given by the formula ⇒ 2lw + 2lh + 2wh
Where ⇒ l, w, and h are length, width, and height of rectangular prism, respectively.
The dimensions of the rectangular prism is 2.75in by 4in by 16.5in,
Substituting the values of length , width and height , we get:
⇒ 2×2.75×4 + 2×2.75×16.5 + 2×4×16.5,
⇒ 22 + 90.75 + 132
⇒ 244.75
Therefore, the total surface area of the prism is 244.75 in²,the correct option is (a).
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The given question is incomplete, the complete question is
A right rectangular prism is 2.75 in by 4 in by 16.5 in. What is the total surface area of the prism?
(a) 244.75 in²
(b) 222.75 in²
(c) 122.375 in²
(d) 112.75 in²
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
The values of x that satisfy the equation are x = 13 and x = 1. The values x = -29 and x = 42 do not satisfy the equation.
