The probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.
To find the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur, we need to determine the individual probabilities of each event and then multiply them together since the events are independent.
Event A: The coin lands on heads
A fair coin has two equally likely outcomes, heads or tails. Since we are interested in the probability of heads, there is only one favorable outcome out of two possible outcomes.
P(A) = 1/2
Event B: The die is 5 or greater
A fair six-sided die has six equally likely outcomes, numbers 1 through 6. Out of these six outcomes, there are two favorable outcomes (5 and 6) for Event B.
P(B) = 2/6 = 1/3
To find the probability of both events occurring (A and B), we multiply the individual probabilities:
P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6
Therefore, the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.
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suppose we use two approaches to optimize the same problem: newton’s method and stochastic gradient descent. assume both algorithms eventually converge to the global minimizer. suppose we consider the total run time for the two algorithms (the number of iterations multiplied by
Comparing the total run time of Newton's method and SGD depends on the specific problem and the convergence properties of the algorithms. While Newton's method may converge faster per iteration, it can be more computationally expensive.
When comparing the total run time of Newton's method and stochastic gradient descent (SGD) for optimizing the same problem, we need to consider their convergence properties and computational efficiency.
Newton's method is a deterministic optimization algorithm that uses the second derivative (Hessian matrix) to find the minimum of a function. It usually converges faster than SGD, especially when the function is smooth and has well-behaved derivatives.
However, Newton's method can be computationally expensive for large-scale problems since it requires computing and inverting the Hessian matrix, which can be time-consuming and memory-intensive.
On the other hand, SGD is an iterative optimization algorithm commonly used in machine learning. It randomly selects a subset of training samples (mini-batch) at each iteration and updates the model parameters based on the gradient of the objective function.
SGD is particularly useful for large-scale problems as it only requires the calculation of the gradient, which can be done efficiently. However, SGD usually converges more slowly than Newton's method due to the noise introduced by the random sampling of the mini-batches.
If both algorithms eventually converge to the global minimizer, the total run time will depend on the specific problem and the convergence rates of the algorithms.
In general, Newton's method may require fewer iterations to converge but each iteration can be more computationally expensive.
On the other hand, SGD may require more iterations but each iteration is computationally cheaper. Therefore, the trade-off between the number of iterations and computational cost will determine the total run time.
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What is the difference between calculating the area and calculating the perimeter of a rectangle?
Answer:
For perimeter you add up the side lengths to get the perimeter but for area you multiply the length times width (L x W )to get area.
Step-by-step explanation:
is 1/2 • 2/3 greater than 2/3
Answer:
no, it is smaller
Step-by-step explanation:
1/2 * 2/3
We are multiplying 2/3 by a number smaller than 1
1/2 is smaller than 1
The number that we get out will be smaller than the number we started with
1/2 *2/3 < 2/3
Answer:
No
Step-by-step explanation:
No, half of (2/3) is SMALLER than (2/3).
2. Choose the correct expression.
√10
Answer: \(10^{1/2}\)
Is the following process correct? If not, which step is where the error occurs, justify your answer. Then rework the problem to find the correct answer.
We are given the following absolute value equation
\(|4x-1|=5x+37\)Let us solve the problem then we will compare it with the given solution.
\(\begin{gathered} |4x-1|=5x+37 \\ 4x-1=\pm(5x+37) \end{gathered}\)Now we will solve for the positive and negative sign separately
\(\begin{gathered} 4x-1=5x+37 \\ 4x-5x=37+1 \\ -x=38 \\ x=-38 \end{gathered}\)\(\begin{gathered} 4x-1=-5x-37 \\ 4x+5x=-37+1 \\ 9x=-36 \\ x=\frac{-36}{9} \\ x=-4 \end{gathered}\)Comparing it with the given solution, there is an error on the left-hand side step 2. (the sign of 38 should be positive but in the figure, it is shown negative)
Now let us substitute the obtained x values into the original absolute value equation and check if they satisfy the equation.
For x = -4:
\(\begin{gathered} |4(-4)-1|=5(-4)+37 \\ |-16-1|=-20+37 \\ |-17|=17 \\ 17=17 \end{gathered}\)Hence, x = -4 is a valid solution.
For x = -38:
\(\begin{gathered} |4(-38)-1|=5(-38)+37 \\ |-152-1|=-190+37 \\ |-153|=-153 \\ 153\ne-153 \end{gathered}\)Hence, x = -38 is not a valid solution.
The above is an example of an extraneous solution.
An extraneous solution is a solution that we get during the process of solving an equation but it is not really the solution meaning that it does not satisfy the equation!
Therefore, x = -4 is the only solution to the given equation.
Identify the slope type of the following graph.
A. negative
B. Zero
C. Undefined
D. Positive
Answer:
Negative
Step-by-step explanation:
If it is tilted in that sort of way it is negative, vice versa if it was titled the other way then it would be positive.
If it were to be un-defined/infinite then it would be parallel to the y axis
If it were to be 0 then a line would be parallel to the x axis.
Answer:
A negative
Step-by-step explanation:
Can someone please tell me the answer! THANK YOU
Answer: approximately 24 square units in the shaded areas
Step-by-step explanation:
The area of the entire dark circles will be for each πr², then divided by 2 to get the area of the semicircles created on the sides of the triangles:
16π + 9π = 25π Half that times value for pi
≈ 39.2699 is the area of the dark semicircles. Round to 39.27
Now the fun! Find the area of the parts subtracted by the light semicircle:
The area of the entire circle is 25π or about 78.54. The triangle is half of an inscribed rectangle, 6×8, so 48. Subtracted from the circle leaves about 30.54 in the four slices between the arcs of the circumference and the perimeter of the rectangle. We are concerned with only half of the slices, so we will subtract 15.27
Area of the dark semicircles minus the area of the light slices will leave the area of the shaded crescents:
39.27 - 15.27 = 24 square units . Voila!The radius of a cylinder is 4 inches and the height is 5 inches. Which statements are correct? Check all that apply.The area of the two bases is 16π in2.The area of the two bases is 32π in2.The lateral area is 40π in2.The lateral area is 72π in2.The total surface area is 72π in2.The Correct Answer is: 2,3,5
The radius of a cylinder is 4 inches and the height is 5 inches. The surface area is equal to the sum of the areas of all the faces of a solid.
A cylinder has two circular bases, and each circular base has an area of πr² square units, where r is the radius of the base. The lateral area of a cylinder is the area of the cylinder's curved surface, which is the height of the cylinder multiplied by the cylinder's base perimeter. It is given by the formula: 2πrh. The surface area of the cylinder is obtained by summing the lateral area and two times the area of the base. Hence, we have:
Surface area = 2πrh + 2πr²
Let us calculate the area of the two bases by plugging the given values into the formula.
Area of one base = πr²= π (4)²= 16π square inches
Therefore, the area of the two bases is 2 × 16π = 32π square inches. Thus, statement 2 is correct
Lateral area of a cylinderLateral area = 2πrh= 2 × π × 4 × 5= 40π square inches.
Thus, statement 3 is correct.
The total surface area of the cylinderTotal surface area = Lateral area + 2 × Area of base= 2πrh + 2 × πr²= 2πr(h + r)= 2π × 4(5 + 4)= 72π square inches.
Therefore, statement 5 is correct.
Therefore, the following statements are correct:Statement 2: The area of the two bases is 32π square inches.Statement 3: The lateral area is 40π square inches.Statement 5: The total surface area is 72π square inches are true.Therefore, the correct statements are 2, 3, and 5.
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Δ WILL GIVE BRAINLIEST Δ
Write down 2-3 quotes to show gratitude to teachers to give an extra boost of energy and joy to the teachers and staff during this hard times.
Answer:
1. the best teacher
teach from the heart ❤️
not from the book
2. a good education can change anyone.
a good teacher can change everything.
3.teaching is a work of a Heart
write 14/3 as a decimal.if necessary,use a bar to include which digit pr group of digits repeats.
To convert a fraction to a decimal, we simply divide.
Shown below:
This is never ending decimal with the "6" repeating.
Thus, we can put a bar over "6".
So,
\(\frac{14}{3}=4.\bar{6}\)A stainless steel patio heater is a square pyramid. The length of one side of the base is 20.8 The slant height of the pyramid is 89.6 What is the height of the pyramid?
The square pyramid is having a height of 89 units.
What is a Pyramid?A pyramid is a three-dimensional shape. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid.
As per the given data:
length of the base (\(a\)) = 20.8 units
slant height of the pyramid (\(s\)) = 89.6 units
Height of the pyramid (\(H\)) = \(\sqrt{s^2 - (\frac{a}{2})^2}\)
= \(\sqrt{(89.6)^2 - (\frac{20.8}{2})^2}\)
= \(\sqrt{(89.6)^2 - (\frac{20.8}{2})^2}\)
= \(\sqrt{(89.6)^2 - (10.4)^2}\)
= \(\sqrt{(8028.16) - (108.16)}\)
= \(\sqrt{7920}\)
= \(89\) units
The height of the square pyramid is 89 units.
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Practice questions for a textbook are marked with difficulty levels of easy, Intermediate, and difficult. 30 of the 149 practice questions are rated as intermediate, approximately what percentage of the questions are intermediate level?
The percent of questions that are intermediate is approximately %
(Round to the nearest whole percent as needed.)
X
3
VE
The required percentage of the 30 intermediate-level questions is 20%.
Given that,
Practice questions for a textbook are marked with difficulty levels of easy, Intermediate, and difficult. 30 of the 149 practice questions are rated as intermediate, approximately what percentage of the questions are intermediate level is to be determined.
the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
the required percentage of the intermediate difficult question,
= 30 / 149 * 100
≈ 0.20 * 100
≈ 20%
Thus, the required percentage of the 30 intermediate level question is 20%.
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Solve:
The width of a rectangle is 12 cm less than the length. The perimeter is 156 cm. Find the width and length.
Answer:
Length = 45width = 33Step-by-step explanation:
Formula for perimeter of a rectangle = 2l +2w
where L= length ,w= width /breadth
Now;
with the question the length and width is unknown but the width is 12cm less than the length so;
width =( L -12cm )
Also the length is not given so remains L
Using the formula
2l + 2w
= 2l + 2( l- 12cm )
This must be equated to the perimeter
So;
2l + 2(l- 12cm ) = 156
2l + 2l -24cm = 156
4l = 156 +24
4l = 180
l = 45cm
therefore the length is 45cm
The width can be gotten by using the guideline provided which is, (L -12cm)
placing L which is already known
= (45-12)
= 33cm
therefore the width is 33cm
I need help with problem.
Answer:
The measure of DC is 20ft.
Step-by-step explanation:
Because the problem states that BA=AC, AD becomes the bisector of angle BAC. This means that BD and DC must be the same length.
If P(A) = 0.7 P(B) = 0.6 and A and B are independent event, find P(A and B)
Answer:
0.42
Step-by-step explanation:
multiply .6 by .7
ASAP! Which of the following scatter plots has/have a non-linear line of best fit?
Answer:
IV
Step-by-step explanation:
dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe. how much sugar, in cups, did dominik use for both recipes?
Dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe.
To find out how much sugar Dominik used in total for both recipes, we need to add the amounts of sugar he used in each recipe.
7/8 cup + 3/4 cup
To add these two fractions, we need to find a common denominator. In this case, the smallest common denominator is 8, which is the same as the denominator of the first fraction.
7/8 cup + 3/4 cup = (7/8) cup + (6/8) cup
Now we can add the two numerators
(7/8) cup + (6/8) cup = 13/8 cup
Hence, Dominik used 13/8 cups of sugar for both recipes combined.
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Savannah is making pots and plates to sell at a local art fair. Each pot weighs 2 pounds and each plate weighs 1 pound. Savannah cannot carry more than 50 pounds to the fair. She only has enough clay to make 40 plates. In addition, she only has enough clay to make 24 pots. She will make $12 profit on every plate and $25 for every pot that she sells. How many pots and how many plates should Savannah make to maximize her profit?
Answer:
24 pots 2 plates
Step-by-step explanation:
Answer:
24 pots and 2 plates
Step-by-step explanation:
Jump to level 1 Dijkstra's shortest path algorithm is run on the graph, starting at vertex E. Each row in the table below represents one iteration of the while loop in Dijkstra's algorithm. When a vertex is dequeued, 0 or more adjacent vertices' distances are updated. Complete the table. Enter updated vertices as A, B, C or "none" if no adjacent vertices are updated. 8 D Iteration Vertex dequeued Adjacent vertices updated 1 Ex: C Ex: A, B, C or none 2 3 4 5 B - 4 2 5 A 7 E
The Dijkstra's shortest path algorithm is a technique that is used to determine the shortest path between two nodes in a graph.
In this algorithm, we start at a particular vertex, and we explore the adjacent vertices to find the shortest path. This algorithm works by maintaining a table that contains information about the vertices and their respective distances from the starting vertex.
Here, the starting vertex is E.
Each row in the table below represents one iteration of the while loop in Dijkstra's algorithm.
Iteration Vertex dequeued Adjacent vertices updated
1 E CA, B
2 C B, A
3 B None
4 A None
5 B None
Here's the explanation of the above table:
Iteration 1:
Vertex dequeued: E
Adjacent vertices updated: C, A, B
Explanation: The algorithm starts at vertex E. The distances of the adjacent vertices are updated in the table. The vertices C, A, and B are updated with their respective distances.
Iteration 2:
Vertex dequeued: C
Adjacent vertices updated: B
Explanation: The algorithm dequeues vertex C, and updates the distance of its adjacent vertex B.
Iteration 3:
Vertex dequeued: B
Adjacent vertices updated: None
Explanation: The algorithm dequeues vertex B, but there are no adjacent vertices to update their distances.
Iteration 4:
Vertex dequeued: A
Adjacent vertices updated: None
Explanation: The algorithm dequeues vertex A, but there are no adjacent vertices to update their distances.
Iteration 5:
Vertex dequeued: B
Adjacent vertices updated: None
Explanation: The algorithm dequeues vertex B again, but there are no adjacent vertices to update their distances.
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Katy has kidney stones that need to be broken down and removed. Which healthcare professional would be primarily in charge of the procedure?
an endourologist
a surgical technician
a cytoscopic nurse
a urologic oncologist
Answer:
an endourologist
Step-by-step explanation:
just took the review
Answer:
a
Step-by-step explanation:
HELP!!! =∆=
Applying the Pythagorean theorem, solve this triangle.
Answer:
c = sqrt(106)
Step-by-step explanation:
Since this is aright triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 9^2 = c^2
25 +81 = c^2
106 = c^2
Taking the square root of each side
sqrt(106) = sqrt(c^2)
c = sqrt(106)
What is the appropriate description for a chain-style franchise? a.A franchisee makes or sells a franchisor's product under their own business name or organization. b. A franchisee sells a franchisor's product in a specific geographic area. c. A franchisee produces and sells a franchisor's product using the franchisor's name.
C. A chain-style franchise is a type of franchise where the franchisee produces and sells a franchisor's product using the franchisor's name.
The franchisee operates under the franchisor's established system and business model, including marketing strategies, training programs, and support services. This type of franchise is also known as a product distribution franchise because the franchisee distributes the franchisor's product to customers within a specified territory.
In a chain-style franchise, the franchisor maintains control over the quality and consistency of the product, while the franchisee is responsible for the day-to-day operations of the business. Examples of chain-style franchises include fast-food restaurants, gas stations, and retail stores.
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2.10 volume ratios
Two Similar solids have a scale
factor of 8:11 what is the ratio of thier volumes,
expressed in lowest terms?
Answer:
512 : 1331Step-by-step explanation:
The volume is the product of three dimensions, so the ratio of volumes is the cube of the scale factor:
k = 8/11k³ = (8/11)³ = 512 / 1331Which overlapping triangles are congruent by ASA?
B.
3
Select one:
O a.
AABE , ADEA
O b. AADC AEDA
O c.
AABE & ACDA
O d.
AADC AEBC
ya
Answer:
D. ADC EBC
Step-by-step explanation:
cb & cd have that little line showing they're the same
Jims backpack weighs 3 kg when filled how many pounds is this approximately?
Answer:
6.6
Step-by-step explanation:
1 kilogram to pounds is 2.2 lbs
therefore, 3kg= 2.2× 3 lbs= 6.6 lbs
Answer:
approximately 6.6 lb
Step-by-step explanation:
1 kg equals approximately 2.2 lb.
Therefore (multiplying both sides by 3) we get
3 kg equals approximately 6.6 lb
how many ternary strings (digits 0, 1, or 2) are there with exactly 5 0s, 5 1s and 5 2s?
A ternary string is a string composed of characters 0, 1, and 2. The number of ternary strings that contain exactly n characters, each of which is one of three types, is 3^n.Exactly 5 0s, 5 1s, and 5 2s are required for the ternary string, which means that the total number of characters is 15.
Each of these characters can be one of three types (0, 1, or 2). As a result, the total number of possible strings is 3^15. This is equivalent to 14,348,907. We arrived at this conclusion by computing 3 to the fifteenth power.Explanation:When constructing a sequence of three symbols, the first symbol has three alternatives, the second symbol has three alternatives, and so on. There are n choices for each of the n characters, resulting in a total of 3^n possible sequences.Example 1:Let's assume we have to create 5-character sequences with three symbols: a, b, and c. There are 3*3*3*3*3 = 243 possible sequences since there are three choices for each symbol.Example 2:Let's assume we have to construct a 10-character sequence using three symbols: 0, 1, and 2. There are 3*3*3*3*3*3*3*3*3*3 = 59,049, a total of 59,049 possible 10-character sequences. We can perform the same calculation for 15-character strings using the same logic.
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7 out of a group of 10 people are men. What percentage are men?
Answer:
70%
Step by step explanation:
linear equation with a slope of -3/5 and a y-intercept of 4
Answer:
y = -3/5x + 4
Explanation:
Slope intercept form: y = mx + b
m = slope
b = y-int
~ fill in the formula ~
y = (slope)x + y-intercept
y = (-3/5)x + 4
Final equation: y = -3/5x + 4
Suppose you are given two ordered pairs A and B. Explain how to write the equation of a line parallel to AB through a given point.
Answer: To write the equation of a line parallel to AB through a given point, we need to follow these steps:
Find the slope of the line AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Let the coordinates of points A and B be (x1, y1) and (x2, y2) respectively. Then, the slope of the line AB is:
m = (y2 - y1)/(x2 - x1)
Since we want to find the equation of a line parallel to AB, the slope of this line will also be equal to m.
Let the given point be (x0, y0). Using the point-slope form of the equation of a line, we can write the equation of the line passing through (x0, y0) with slope m as:
y - y0 = m(x - x0)
Substituting the value of m found in step 1, we get:
y - y0 = (y2 - y1)/(x2 - x1) * (x - x0)
This is the equation of the line parallel to AB passing through the point (x0, y0).
Note that we assume that the line passing through A and B exists and is not vertical. If the line is vertical, then its slope is undefined, and we cannot find the equation of a parallel line using this method. In that case, we need to use a different method to find the equation of the line.
Step-by-step explanation:
I got a score of 3374 on Just Dance. My friend got a score of 5500. How much did my friend beat me by?
Answer:
Your friend beat you by 2126 points.
Explanation:
5500 - 3374 = 2126