In the isosceles triangle, the size of angle, a is 50°
What is isosceles triangle?An isosceles triangle is a type of triangle which has two sides that are equal in length.
This type of triangle has two angles which are the same and the third angle is different from the other two. It also has three sides, with two sides being equal and the third side being different.
The base of the isosceles triangle is the side that has two equal sides, and the sides that are equal are called the legs. The angles that are equal are called the base angles. The point at which the two equal sides meet is called the vertex.
The angles of the isosceles triangle add up to 180 degrees. The base angles are the same, while the third angle is different and can be greater or smaller than the other two angles. This type of triangle is very symmetrical, as the two equal sides create a mirror image of the triangle.
Isosceles triangles are very useful in many areas, such as mathematics, engineering and architecture. In mathematics, isosceles triangles are used to solve problems involving angles, area, and perimeter.
In engineering, they are used in many structures such as bridges. In architecture, they are used to create aesthetically pleasing designs for buildings and monuments.
Given, one side of angle is 65°
For isosceles triangle two sides of angles are equal.
A triangle always have 180°
a + b + c = 180°
a = 180° - 65° - 65°
a = 50°
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help me white this for brainliested
Answer:
please take a better picture
Step-by-step explanation:
Marcus bought 4 packets of baseball cards and 4 packets of animals cards.Write an algebraic expression for the total number of cards Marcus bought.
Answer: How many cards are in a packet?
Step-by-step explanation:
subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. after 6 months, the numbers of respiratory tract infections each group had were compared.
Comparison of two randomly assigned groups is given by :
a. Given study is classified in experimental based.
b. Treatment group is represented by herb.
c. The independent variable is given by Placebo
d. The dependent variable represented by the Infection on respiratory tract .
e. Goal of the study is the comparison of two groups herb and the placebo.
Number of randomly assigned group = 2
One group is herb.
Second group is placebo.
a. Two different types of groups given so the study is experimental based.
b. Treatment group is represented by the group one herb.
c. Independent variable is represented by the group two placebo it does not dependent on herb treatment.
d. Dependent variable is represented by the infection on respiratory tract.
e. Goal of the study is given by the comparison of number of respiratory tract infection in each group.
Therefore, the answer of the following question based on the randomly assigned two groups is given by :
a. Study is experimental based.
b. Herb treatment.
c. Placebo represents the independent variable.
d. Infection represents the dependent variable.
e. Goal of the study is doing the comparison of two groups.
The above question is incomplete, the complete question is :
Subjects were randomly assigned to two groups. One group was given an herb and the other group a placebo. After 6 months the numbers of respiratory tract infections each group had were compared
a) Classify this study (circle the answer): experimental OR observational
b) Identify the treatment group:
c) Identify the independent variable_
d) Identify the dependent variable
e) What is the goal of this study?
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How to Use a Graphing Calculator to Solve a Word Problem Involving a Local Extremum of a Polynomial Function.
The graphing calculator was used to identify the coordinates of the local extremum point of the polynomial function. This allowed us to find the solution to the word problem by finding the x and y coordinates of the extremum point.
Using a Graphing Calculator to Find the Local Extremum of a Polynomial FunctionBegin by entering the polynomial function into your graphing calculator.Set the calculator to graph the function by pressing the appropriate keys.Observe the graph and locate any local extremum points.Using the calculator’s zoom feature to better view the graph, identify the x-coordinate of the local extremum point.Enter the x-coordinate of the local extremum point into your calculator and press the “Evaluate” key.The calculator will display the y-coordinate of the local extremum point. This is the solution to the word problem.Learn more about Graphing Calculator: https://brainly.com/question/28969437
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1 to 11 for 100 points (serious answers or report and 1 star)
Based on isosceles trapezoid base angle theorem the sides AD and BC demonstrated that corresponding parts are congruent.
What is isosceles trapezoid base angle theorem?It is a 2-dimensional geometry defined as a quadrilateral with four sides, two of which are parallel to each other.
We provided a trapezoid in which:
BA ≅ CD
It is necessary to demonstrate BD ≅ CD
We can demonstrate this by doing the following:
ABCD is a trapezoidal shape (given)
BA ≅ CD (given) (given)
ABCD is a trapezoid with isosceles angles (definition of isosceles trapezoid)
AD ≅ AD (by using reflexive property) (by using reflexive property)
Angle BAD is congruent to Angle CDA = 5) theorem of base angles
BAD angle CDA angle (base angle theorem)
BD ≅ CA (corresponding parts of congruent triangles are congruent) (corresponding parts of congruent triangles are congruent)
As a result, AD ≅ BC has demonstrated that corresponding parts of congruent triangles are congruent.
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an object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. the objects travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?
The acceleration of this object is equal to: d) 9.33 m/s^2.
How to calculate the acceleration of this object?In order to calculate the acceleration of the object, we would apply the second equation of motion. Mathematically, the second equation of motion is given by this mathematical expression:
S = ut + ½at²
Where:
S represents the distance travelled or covered.t represents the time.u represents the initial velocity.a represents the acceleration.At time, t = 1.00 seconds, the position is given by:
x₁ = 0 + 1/2(1²)a
x₁ = ¹/₂(a)
At time, t = 2.00 seconds, the position is given by:
x₂ = 0 + 1/2(2²)a
x₂ = 0 + 4a/2
x₂ = 2a
Therefore, the change in position is given by;
Change in position, Δx = x₂ - x₁
Change in position, Δx = 14
From the second equation of motion, the acceleration of this object is given by:
14 = 2a - 1/2(a)
14 = 3a/2
3a = 28
a = 9.33 m/s².
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Complete Question:
An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?
a) 5.20 m/s^2 b) 10.4 m/s^2 c) 8.67 m/s^2 d) 9.33 m/s^2 e) 12.1 m/s^2
The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by overbar(C)(x), is found by dividing C(x) by x. Find (x→9000) is under (lim)overbar(C)(x).
The average cost per tape is 10.
What is average cost?The average cost is the ratio of the total of cost of all the products to the total number of products. We can calculate the average cost by dividing the total cost by the total output quantity.
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. lim x →9000 C (x)
C (x) = 9000 + 9x
x
= 9000 + 9
x
Lim n→ 9000 C (x) = 9000 +9
9000
= 1 + 9
= 10
So, the average cost per tape is 10
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f(x) 2x + 7 and g(x) = 3x - 12, find f(g(-4))
Step-by-step explanation:
g(-4) = 3(-4)-12
= -24
f(g(-4)) = f(-24)
f(-24) = 2(-24)+7
= -41
i don't know it is true i'm just trying:)
Find the length of midsegment of the trapezoid.
MN=?
The length of midsegment of the trapezoid is MN = 66.5 units
How to find the length of midsegment of the trapezoid?
The midsegment of a trapezoid is a line segment that connects the midpoints of the legs of the trapezoid.
The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.
In this case, length of midsegment of the trapezoid will be:
MN = 1/2 × (76 + 57)
MN = 1/2 × (133)
MN = 66.5 units
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given three floating-point numbers x, y, and z, output x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). output each floating-point value with two digits after the decimal point, which can be achieved as follows: print(f'{your value1:.2f} {your value2:.2f} {your value3:.2f} {your value4:.2f}')
x to the power of z: 2.00^3.00 = 8.00
x to the power of (y to the power of z): 2.00^(4.00^3.00) = 2.00^64.00 = 4096.00
The absolute value of (x minus y): |2.00 - 4.00| = |-2.00| = 2.00
The square root of (x to the power of z): √(2.00^3.00) = √8.00 = 4.00
Given three floating-point numbers x, y, and z, the output would be x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). The formula for each output is as follows:
x to the power of z: x^z
x to the power of (y to the power of z): x^(y^z)
The absolute value of (x minus y): |x-y|
The square root of (x to the power of z): √(x^z)
For example, if x = 2.00, y = 4.00, and z = 3.00, then the output would be: 8.00 4096.00 2.00 4.00
The calculation for each output is as follows:
x to the power of z: 2.00^3.00 = 8.00
x to the power of (y to the power of z): 2.00^(4.00^3.00) = 2.00^64.00 = 4096.00
The absolute value of (x minus y): |2.00 - 4.00| = |-2.00| = 2.00
The square root of (x to the power of z): √(2.00^3.00) = √8.00 = 4.00
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2. The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s)
when f(x) = g(x)? Explain your answer
Answer: x= -3 and x= -1
Step-by-step explanation:
We can see from table that when x= -3, the f(x) have the same y with g(x). Also when x= -1, the f(x) have the same y with g(x).
What does x equal???
here is ur answer seeee now
what is the y intercept
x y
34 -52
51 -65
68 -78
Answer:
y- intercept = - 26
Step-by-step explanation:
to find the y- intercept, obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (34, - 52) and (x₂, y₂ ) = (68, - 78) ← 2 ordered pairs from the table
m = [tex]\frac{-78-(-52)}{68-34}[/tex] = [tex]\frac{-78+52}{34}[/tex] = [tex]\frac{-26}{34}[/tex] = - [tex]\frac{13}{17}[/tex] , then
y = - [tex]\frac{13}{17}[/tex] x + c
to find c substitute any of the ordered pairs into the equation and solve for c
using (51, - 65 ) , then
- 65 = - [tex]\frac{13}{17}[/tex] (51) + c = - 39 + c ( add 39 to both sides )
- 26 = c
then y- intercept = - 26
review the select balance sheet and income statement for apple, inc. (found in the 10-k). for the account assigned to you (see below on assignments), identify assertions that you think are relevant for the assigned accounts.
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Account Assigned: Trade and other receivables
The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.
Existence assertion means that the receivables must exist and they must be recorded in the books of Apple Inc. Rights and obligations assertion means that the receivables must be legally enforceable, and Apple Inc. must have the right to receive the payment from its customers. Completeness assertion means that all the receivables must be recorded in the books of Apple Inc. Valuation assertion means that the receivables must be recorded in Apple Inc.’s financial statements at the correct amount. Valuation can be measured by calculating the amount of receivables as a percentage of total revenue. For example, if the total revenue is $100 million and the total receivables are $20 million, then the receivables are 20% of total revenue.
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Please help me, I need this.
Answer:
Slope = 4/3
Step-by-step explanation:
The coordinates are,
→ x1 = 6, y1 = 0
→ x2 = 0, y2 = -8
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-8 - 0)/(0 - 6)
→ m = (-8)/(-6)
→ m = 8/6
→ [ m = 4/3 ]
Hence, the slope is 4/3.
Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant.
Coordinates Quadrant
P( , -5/7) IV
The missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant is √(2/7) or √(2/7)
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. If a point P lies on the unit circle, then the distance from the origin to P is 1.
We can use the distance formula to find out the missing coordinate of P.
The distance formula: [tex]d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where (x1, y1) is origin and (x2, y2) is the point P.
Given in the problem that P is in Quadrant IV, then the (x, y)-coordinate is negative.
So we can use the given information and the distance formula to find out the missing coordinate.
[tex]d = \sqrt((x2 - 0)^2 + (y2 - 0)^2) = 1[/tex]
x2 = -5/7, y2 = -5/7
[tex]d = \sqrt((-5/7 - 0)^2 + (-5/7 - 0)^2) = \sqrt((-5/7)^2 + (-5/7)^2) = \sqrt(25/49 + 25/49) = \sqrt(50/49) = \sqrt(2/7) = 1[/tex]
Therefore, the missing x coordinate of P is √(2/7) or √(2/7)
P = (-5/7,√(2/7))
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−3/5×8/6= helpplease
Answer:
-4/5 OR -0.8
Step-by-step explanation:
This problem is very simple but it can be broken down
First we do -3 times 8 and get -24
Then we do 5 times 6 and get 30
We put the first answer over the second which equals
-24/30
This can then be simplified further if we divide both sides by 6
-4/5 as a fraction
-0.8 as a decimal
-80% as a percent
three girls shared a piece of land. One got x/3y of the land. Another got x/6y of the land. What fraction of the land will the third girl get.
The third girl will recieve a land area equals to the fraction (2y-x)/2y.
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
The fractions are x/3y, x/6y and z(say)
so sum of all the fraction must be 1 so
x/3y + x/6y + z = 1
⇒z = (2y-x)/2y
The third girl recieve a land area equals to (2y-x)/2y.
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dont ignore please :( i need help
Answer:5
Step-by-step explanation:
Please help me with this!!
Answer:
0.084
Step-by-step explanation:
Decimal form:[tex]\sf Thousandth = \dfrac{1}{1000}\\\\\\[/tex]
[tex]\sf Eighty \ four \ thousandth = 84 * \dfrac{1}{1000}=\dfrac{84}{1000}\\[/tex]
= 0.084
In a certain bag, the ratio of red to green to blue marbles is 1:2:3 . There are 5 red marbles. How many blue marbles are there?
Explanation
The ratio 1:2:3 refers to the idea we could have: 1 red, 2 green, 3 blue. The order of the colors is important. Follow the order mentioned in the 1st sentence of the instructions. That order being red:green:blue.
Then the instructions mention that there are actually 5 red (instead of 1 red). This means we multiply each part of the ratio by 5
1*5 = 5 red2*5 = 10 green3*5 = 15 blueThe ratio 1:2:3 scales up to 5:10:15
We see that there are 15 blue marbles
find the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2. (source: hmmt)
The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.
The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2 can be calculated using the following formula:
Range = Maximum Value - Minimum Value
The expression inside the parentheses can be simplified to 3cos2a cos4a + 3sin2a sin4a and the expression inside the exponential can be simplified to tan2a (1 / cos2a - sin2a). This gives us the expression
Range = 3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)
To calculate the maximum and minimum values, we can use derivatives to find the critical points of the expression. Taking the first derivative with respect to a, we get
d/da (3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)) = 0
Solving this equation gives us the critical points of a = ±7t/6. Using these values, we can calculate the maximum and minimum values of the expression.
Maximum Value = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6)
Minimum Value = 3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6)
Finally, using the formula for the range, we can calculate the range of the expression to be
Range = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6) - (3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6))
This expression gives us the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.
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What is the following difference?? PLSS help
The simplified expression is ab∛ 3ab².
The correct option is (C).
What are Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])
Now, factorizing the terms as
192ab² = 2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b
81 [tex]a^4b^5[/tex] = 3 x 3 x 3 x 3 x a x a x a x a x b x b x b x b x b
So, 2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])
= 2ab (∛2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b) -5(∛3 x 3 x 3 x 3 x a x a x a x
a x b x b x b x b x b)
= 2ab ( 2 x 2 ∛ 3 x a x b x b) -5( 3 x a x b ∛3 x a x b x b )
= 8ab ∛ 3ab² - 15ab∛ 3ab²
= -7ab ∛ 3ab²
Hence, the simplified expression is ab∛ 3ab².
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What is the inverse of function f? f(x) = √x + 7
The inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
What is inverse of function?A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.
Given that the equation of the function is:
f(x) = √x + 7
Covert the given function into an equation:
y = √x + 7
Interchange the variables in the equation:
x = √y + 7
Isolate the value of y.
Subtract, 7 from both sides of the equation:
x - 7 = √y + 7 - 7
x - 7 = √y
Take square on both sides of the equation:
(x-7)² = (√y)²
(x-7)² = y
Replace, y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) = (x-7)^2[/tex]
Hence, the inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].
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help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2
All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.
What do you meant by rational expression ?[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$[/tex]
[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$[/tex]
Simplify
[tex]$\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$[/tex]
[tex]$\frac{x-2}{7}=\frac{x-2}{7}$[/tex]
Seven times both sides
[tex]$\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$[/tex]
Simplify
[tex]$x-2=x-2$[/tex]
There is equality between the two sides.
For every x Verify Solutions, true
Search for ill-defined (singularity) points: [tex]$x=-6$[/tex]
Because -6, the equation is undefined.
[tex]x \neq -6[/tex]
Therefore the correct answer is option C ) All real numbers except -6 .
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Find the answer for "X"
Answer:
(x, y) = (2, 5)
Step-by-step explanation:
You want to solve the system of equations ...
y = 2x +1x = 12 -2ySolutionSubstituting for y, we have ...
x = 12 -2(2x +1)
x = 12 -4x -2 . . . . . eliminate parentheses
5x = 10 . . . . . . add 4x
x = 2 . . . . . . divide by 5
Then the value of y is ...
y = 2(2) +1 = 5
The solution is ...
x = 2y = 5<95141404393>
Hannah makes 5 out of 8 attempted free-throws! What is the average waiting time for Hannah to make her first basket, and what is the probability that she will make a basket on or before her last attempt within her average waiting time?
The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.
Given;
Hannah makes 5 out of 8 attempted free-throws
Now,
The average waiting time of hannah to make her first basket=5/8
The probability of hannah making basket at her last attempt=1/8
The probability of hannah making basket before her last attempt= 2/8
Therefore, the probabilty will be 1/8 and 2/8.
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Consider a pool of six I/O buffers. Assume that any buffer is just as likely to be available or occupied as any other. Compute the probabilities associated with the following events:
A = At least two but no more than five buffers occupied.
B = At least three but no more than five buffers occupied.
C = All buffers available or an even number of buffers occupied.
D = At least one of the events A, B, and C occurs.
The associated probabilities are A = At least two but no more than five buffers occupied.
There are a total of 2^6 = 64 possible outcomes when rolling 6 dice.
To find the probability of event A, we need to find the number of outcomes where at least two but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where two, three, four, or five buffers are occupied and subtracting the probabilities where six or zero buffers are occupied.
The probability of two buffers being occupied is (6 choose 2)(1/64) = 15/64
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)(1/64) = 6/64
So the probability of event A is (15/64) + (20/64) + (15/64) + (6/64) = 56/64.
B = At least three but no more than five buffers occupied.
To find the probability of event B, we need to find the number of outcomes where at least three but no more than five buffers are occupied.
This can be done by summing the probabilities of each individual outcome where three, four, or five buffers are occupied and subtracting the probability where six buffers are occupied.
The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64
The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64
The probability of five buffers being occupied is (6 choose 5)*(1/64) = 6/64
So the probability of event B is (20/64) + (15/64
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HELP MATH THIGNY PLSSS
Answer:
Step-by-step explanation:
Your slope would be -1/4 because it is rise over run meaning your y-axis over your x-axis. I am not sure exactly what your question is needing but I hope that helps in some way.
Let us choose some number t and consider a point A(2t+3,24t+1).Prove that all such points make a line.What is the slope and the y intercept of this line?
The parametric vector represents a line, whose slope and intercept are 12 and - 35, respectively.
How to analyze and interpret parametric functions
Parametric functions are multi-dimensional functions in terms of a variable t that is a real number. In this problem we find a parametric function with coordinates, that is, a vector of the form (x, y) = (f(t), g(x)) and we are supossed to determine the rectangular form of such function, that is, a function of the form:
y = f(x)
The rectangular form of the function is a line if and only if the resulting expression is of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableFirst, write the components of the parametric functions:
x = 2 · t + 3
y = 24 · t + 1
Second, clear variable t in each parametric expression:
t = (x - 3) / 2
t = (y - 1) / 24
Third, eliminate parameter t by transitive property:
(x - 3) / 2 = (y - 1) / 24
Fourth, obtain the equation of the line:
24 · (x - 3) = 2 · (y - 1)
24 · x - 72 = 2 · y - 2
24 · x - 70 = 2 · y
y = 12 · x - 35
Fifth, determine the slope and intercept of the equation of the line:
m = 12, b = - 35
To learn more on parametric functions: https://brainly.com/question/23725782
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