The dimensions of the poster are 22 inches by 9 inches.
Let's solve for the dimensions of the rectangular poster. Let's assume the width of the poster is W inches.
Given that the length of the poster is 4 more inches than two times its width, we can write the equation:
Length = 2W + 4
We are also given that the area of the poster is 198 square inches, so we can write another equation:
Length * Width = 198
Now we have a system of two equations with two variables. We can solve this system of equations to find the values of Length and Width.
Substituting the value of Length from the first equation into the second equation, we get:
(2W + 4) * W = 198
Expanding the equation, we have:
2W^2 + 4W = 198
Rearranging the equation, we get a quadratic equation:
2W^2 + 4W - 198 = 0
We can simplify the equation by dividing all terms by 2:
W^2 + 2W - 99 = 0
Now, we can factorize this equation:
(W + 11)(W - 9) = 0
So, we have two possible values for W: W = -11 or W = 9.
Since the width cannot be negative, we discard W = -11.
Substituting W = 9 into the equation Length = 2W + 4, we find:
Length = 2(9) + 4 = 18 + 4 = 22
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Plz reply soon need help simplify
Answer:
2/7.
Step-by-step explanation:
Using order of operations (PEMDAS):
0.9 (3 / 2.25 - 1/8( 1 2/3 + 1/9)) - 4/7 / 0.8
= 0.9 (3 / 2.25 - 1/8( 5/3 + 1/9)) - 4/7 / 0.8
= 0.9 (3 / 2.25 - 1/8( 16/9) - 4/7 / 0.8
= 0.9 (3 / 2.25 - 2/9) - 4/7 / 0.8
= 0.9 (12/9 - 2/9) - 4/7 / 0.8
= 0.9 * 10/9 - 5/7
= 1 - 5/7
= 2/7.
Answer:
2/7 =0.2857
Step-by-step explanation:
0.9(300/225-1/8(1x3+2/3+1/9))-4/7/0.8
0.9(4/3-1/8(1x3+2/3+1/9))-4/7/0.8
0.9(4/3-1/8(3+2/3+1/9))-4/7/0.8
0.9(4/3-1/8(5/3+1/9))-4/7/0.8
0.9(4/3-1/8(15/9+1/9))-4/7/0.8
0.9(4/3-1/8x(15+1/9))-4/7/0.8
0.9(4/3-1/8x(16/9))-4/7/0.8
0.9(4/3-1x16/8x9))4/7/0.8
0.9(4.3-16/72)-4/7/0.8
0.9(4/3-2/9)-4/7/0.8
0.9(12/9-2/9)-4/7/0.8
0.9x(12-9/9)-4/7/0.8
0.9x(10/9)-4/7/0.8
9/10x(10/9)-4/7/0.8
1-4/7/0.8
1-4/7x0.8
1-4.56
1-40/56
1-5/7
7/7-5/7
7-5/7
2/7 = 0.2857
I had $13.00. My Mom gave $10.00. My Dad gave $30.00. My Aunt, My Uncle and grandma gave me $100.00. I had another $7.00. How much did I have?
Answer:
You have $160 in total :D
The total amount of money he had is $130 and this can be determined by using arithmetic operations.
Given :
I had $13.00.My Mom gave me $10.00. My Dad gave me $30.00. My Aunt, My Uncle, and grandma gave me $100.00. I had another $7.00.The following steps can be used to determine the total amount of money he had:
Step 1 - He had initially $13.
= 13
Step 2 - His mom gave him $10. Add 10 in the above expression.
= 13 + 10
= 23
Step 3 - His Aunt, Uncle, and Grandma gave him $100. So, add 100 in the above expression.
= 23 + 100
= 123
Step 4 - He also had $7. So, add 7 in the above expression.
= 123 + 7
= $130
The total amount of money he had is $130.
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the angle of elevation from a rowboat moored 75 feet from a cliff is 73.8 degrees.find the height of the cliff to the nearest foot.
The height of the cliff is approximately 269 feet.
We will be using the tangent function to find the height of the cliff.
Draw a right triangle with the rowboat at one corner, the cliff's base as the adjacent side, and the cliff's height as the opposite side.
The angle of elevation (73.8 degrees) is between the rowboat and the cliff's base.
We are given the adjacent side (75 feet) and we need to find the opposite side (height of the cliff).
To do this, we will use the tangent function:
tan(angle) = opposite side / adjacent side
Plug in the given values:
tan(73.8) = height / 75
Solve for the height:
height = tan(73.8) * 75
Calculate the value:
height ≈ 269.4 feet
Round the height to the nearest foot:
height ≈ 269 feet.
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If laura bought 2.1 pounds of apples is the price per pound of apples greater than or less than $1? How can you tell?
Answer:
The price per pound of apples is greater than $1.
Step-by-step explanation:
Three coworkers decided to buy fruit to share at lunchtime. Antonii spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1? how can you tell?
To find the price of apples per pound, we need to divide the total amount paid by Laura ($2.88) with the total pounds of apples (2.1 pounds) bought.
Price of apples per pound = $2.88/2.1
price of apples per pound= $1.37142857
Since the price of apples per pound is $1.37, therefore, the price per pound of apples is greater than $1.
We can simply tell that the price per pound of apples is greater than $1 because 2.88 is greater than 2.1. So when we will divide 2.88 by 2.1, then we will get a number greater than 1.
(hope this helps can i plz have brainlist :D hehe)
The cost of one pound of apple is $1.37.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Laura spent $2.88 on apples.
If Laura bought 2.1 pounds of apples
Cost of 1 pound apple =2.88/2.1
= $1.37
1.37>1
Therefore, the cost of one pound of apple is $1.37.
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"Your question is incomplete, probably the complete question/missing part is:"
Three coworkers decided to buy fruit to share at lunch time. Antoni spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1 ? how can you tell?
how many different 7-digit license plates can be made if the first digit must not be a 0 and no digits may be repeated
There are 9 choices for the first digit (1-9), 9 choices for the second (0 and the remaining 8), and then 8, 7, 6, 5, and 4 choices for the subsequent digits. So, there are 9*9*8*7*6*5*4 = 326592 different 7-digit license plates.
To solve this problem, we will use the counting principle. The first digit cannot be 0, so there are 9 possible choices for the first digit (1-9). For the second digit, we can use 0 or any of the remaining 8 digits, making 9 choices. For the third digit, we have 8 choices left, as we cannot repeat any digit. Similarly, we have 7, 6, 5, and 4 choices for the next digits.
Using the counting principle, we multiply the number of choices for each digit:
9 (first digit) * 9 (second digit) * 8 * 7 * 6 * 5 * 4 = 326592
There are 326592 different 7-digit license plates that can be made under the given conditions.
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A man has to drive 40 more miles to a meeting in Indianapolis compared to Chicago,
which is 160 miles away. What is the percent increase in the number of miles to
Indianapolis?
Answer:
25% i believe
Step-by-step explanation:
40 is 1/4 (or 25%) of 160
PLSSSS HELP IF YOU TRULY KNOW THISSS
Answer:
The answer is 20%.
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
To write the decimal as a percent, we multiply it by 100
0.20 = 0.20 × 100 = 20%
Hence, 0.20 is the same as 20%.
a 24-centimeter by 119-centimeter piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. what size square should be cut from each corner to get a box with the maximum volume? enter the area of the square as an exact answer.
a) To get the maximum volume of the box, we should cut squares with side length of 5.66cm from each corner of the cardboard.
b) The area of each square is 31.96 square cm.
Let's denote the side length of the square that needs to be removed from each corner as "x"
The length of the cardboard box, after removing the squares from each corner, will be
L = 119cm - 2x
Similarly, the width of the cardboard box will be
W = 24cm - 2x
And the height of the cardboard box will be
H = x
To maximize the volume of the box, we need to find the value of "x" that maximizes the expression for the volume of the box, which is given by
V = LWH
Substituting the expressions for L, W, and H in terms of x, we get
V = (119cm - 2x)(24cm - 2x)(x)
Expanding this expression gives
V = 4x^3 - 286x^2 + 2856x
To find the value of "x" that maximizes this expression, we can take the derivative of V with respect to x and set it equal to zero
dV/dx = 12x^2 - 572x + 2856 = 0
Solving for x gives
x = (572 ± sqrt(572^2 - 4(12)(2856)))/(2(12))
x ≈ 5.66cm (ignoring the negative root)
Therefore, to get the maximum volume of the box, we should cut squares with side length of 5.66cm from each corner of the cardboard.
The area of each square is x^2 = 5.66^2 = 31.96 square cm.
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How much storage is needed to represent a simple graph with n vertices and m edges using
a) adjacency lists?
b) an adjacency matrix?
c) an incidence matrix?
The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:
a) Adjacency lists:
In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.
Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.
b) Adjacency matrix:
In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.
c) Incidence matrix:
In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.
Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.
In summary:
a) Adjacency lists: O(n + m)
b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs
c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs
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Round 3.46 to the nearest integer
Answer: 3.5 integers can be in decimals too. and any number counts as an integer except for 0
Answer:
3
Step-by-step explanation:
Find the number in the whole number place 3 and look one place to the right for the rounding digit on the right side of the decimal point 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5.
!!40 points and Brainliest if it’s correct!!ANSWER IT ONLY IF YOU KNOW THE ANSWER. IF YOU DONT KNOW DONT ANSWER IT. Make sure you explain please!
Which of the following shows the correct first step to solve x^2 - 16x = -21 by completing the square?
A)x^2 - 16x + 64 = -21
B) x^2 - 16x + 64 = -21 + 64
C) x^2 - 16x + 16 = -21 + 16
D) x^2 - 16x + 8 = -21 + 8
For using completing the square, first make sure that the coefficient of x² is 1, if it's not 1, then you need to make it 1, by dividing both sides of the equation by the coefficient whatever it is. So, jere the coefficient of x² is 1, so now we need to develop a whole square on both sides, for which,we will add the square of half of coefficient of x on both sides, so adding (-16/2)² = (-8)² = 64 on both sides, we will be having :
\({:\implies \quad \sf x^{2}-16x+64=-21+64}\)
Which suits the B) option
Hence, Option B) is correct
what mathematical shape is this?
Answer:
A quadrilateral.
Step-by-step explanation:
The shape has 4 sides, so it is a quadrilateral.
Answer:
dart
Step-by-step explanation:
Solve the triangle. What is the length 0 \( a= \) (Round to the neare) What is the measure \[ B=\circ \] (Round to the neare) What is the measure \[ C=0 \]
The length
�
a is approximately 0 units. The measure of angle
�
B is approximately 0 degrees. The measure of angle
�
C is approximately 180 degrees.
In a triangle, the sum of the measures of the three angles is always 180 degrees. Since angle
�
C is given as 0 degrees, the sum of angles
�
A and
�
B must be 180 degrees. We can set up the equation
�
+
�
=
180
A+B=180 and solve for angle
�
B.
Since angle
�
B is not given in the problem, we cannot determine its measure. The value of angle
�
B can be any number between 0 and 180 degrees. Therefore, we cannot provide an exact measure for angle
�
B without additional information.
Regarding the length
�
a, it is given as 0 units. A triangle with a side length of 0 units is degenerate and does not form a closed shape. In other words, it cannot exist as a triangle in a Euclidean plane. Therefore, we cannot provide a meaningful calculation or explanation for the length
�
a in this case.
In this scenario, the length
�
a is 0 units, angle
�
B can be any value between 0 and 180 degrees, and angle
�
C is 0 degrees. However, it is important to note that a triangle with a side length of 0 units is not a valid triangle in Euclidean geometry.
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A mathematical model is given below. Construct a Matlab & Simulink model to show the behavior of the value of x. dx d²x +3+4x+6=5cos (2t). dt² dt Hint: 2 Clock Gain 2t
The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.
To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:
1. Open Simulink in Matlab.
2. Drag and drop a Clock block from the Simulink Library Browser into the model.
3. Drag and drop a Gain block from the Simulink Library Browser into the model.
4. Double-click on the Gain block and set the Gain value to 2.
5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.
6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.
7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.
8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.
9. Run the simulation.
The Scope block will show the behavior of the value of x over time according to the given mathematical model.
In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.
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If you choose a line uniformly at random to wait in together, what is the probability that you and your friends are on time for the movie (treat your group as one person who will buy tickets for everyone)?
The probability that you and your friends are on time for the movie when choosing a line uniformly at random depends on the number of people in your group and the probability of each person being on time.
To calculate the probability that you and your friends are on time for the movie when choosing a line uniformly at random, we need to make some assumptions.
Let's assume that there are only two lines to choose from, and that the probability of being on time for the movie is the same for both lines. Also, let's assume that your group consists of n people.
The probability that all n people in your group are on time for the movie is p^n, where p is the probability of one person being on time. This assumes that each person's arrival time is independent of the others.
Now, let's consider the probability that at least one person in your group is late. This can happen in several ways:
- One person is late: p*(1-p)^(n-1)
- Two people are late: p^2*(1-p)^(n-2)
- Three people are late: p^3*(1-p)^(n-3)
- ...
- All n people are late: (1-p)^n
The probability of at least one person being late is the sum of these probabilities:
P(at least one person is late) = p*(1-p)^(n-1) + p^2*(1-p)^(n-2) + ... + (1-p)^n
Therefore, the probability that everyone in your group is on time for the movie when choosing a line uniformly at random is:
P(everyone is on time) = 1 - P(at least one person is late)
We can use this formula to calculate the exact probability for any given value of n and p.
It can be calculated using the formula P(everyone is on time) = 1 - P(at least one person is late), where P(at least one person is late) is the sum of the probabilities of each possible number of people being late.
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The perimeter of the rectangle below is 65 inches.
a. What is the value of x?
b. What are the dimensions of the rectangle?
Answer:
A :-) Given -
perimeter = 65 inches
Side ‘a’ = 2x
Side ‘b’ = 3 1 by 4x + 1
Solution -
Perimeter = 65
= a + b = 65
= 2x + 3 1 by 4x + 1 = 65
( 3 1 by 4 = 4 x 3 + 1 = 12 + 1 by 4
= 13 by 4 )
= 2x + 13 by 4x + 1 = 65
= 2x + 13 by 4x = 65 - 1
= 2x + 13 by 4x = 64
= 15 by 4 x = 64
= x = 64 x 4 by 15
= x = 256 by 15
= x = 17.06
.:. The value of x = 17.06.
How do we convert decimal numbers into binary numbers 2483?.
Answer:
Places in binary coding
1 - 2 - 4 - 8 - 16 - 32 - 64 - 128 - 256 - 512 - 1024 - 2048
2483 - 2048 = 435 there is 1 in the 2048 position
435 - 256 = 179 there is 1 in the 256 position
179 - 128 = 51 there is 1 in the 128 position
51 - 32 = 19 there is 1 in the 32 position
19 - 16 = 3 there is 1 in the 16 position
3 - 2 = 1 there is 1 in the 2 position
1 - 1 = 0 there is 1 in the 1 position
10011011 0011 would be the binary result
Check:
2048 + 0 + 0 + 256 + 128 + 0 + 32 + 16 + 0 + 0 + 2 + 1 = 2483
Help sorry here’s. A pic
so the sign is made up a rectangular 17x8 piece, and then we cut out a whole with a radius of 2.2 cm, so if we put it on the sidewalk, the sign will end up looking like the one in the picture below.
so if we just get the whole area of the rectangle and then subtract the area of the circle, in effect making a hole in it, what's leftover is their difference.
\(\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(17)(8)}~~ - ~~\stackrel{circle}{\pi (2.2)^2}} \implies 136-4.84\pi ~~ \approx ~~ \text{\LARGE 121}~cm^2\)
Select all the correct answers.
Which expressions are equivalent to log4 (²) ?
Answer:
A: -1 + 2 log4^x
C: log4 (1/4) + log4 x^2
Step-by-step explanation:
Apply logarithm properties:
log4 (1/4x^2) = log4 (1/4) + log4 x^2
Evaluate: log4 (1/4)
log4 (1/4) = -1
Substitute the value back:
-1 + lg4 x^2
Apply logarithm properties:
-1 + 2 log4 ^x
Draw a conclusion:
The expressions equivalent to: log4 (1/4x^2) are:
Answer Choices: A, and C
A= -1 + 2 log4^x
C= log4 (1/4) + log4 x^2
Hope this helps!
An election ballot asks voters to select five city commissioners from a group of nineteen candidates. In how many ways can this be done?
Answer:
Hello! I Have the Correct Answer to This Question, 8,568 ways
Hope This Helps!
Explination:
C(18, 5) = 18!/((18 - 5)! 5!)
C(18, 5) = 18!/(13! 5!)
C(18, 5) = 14*15*16*17*18/(2*3*4*5)
C(18, 5) = 8,568 ways
Brainliest?
i need the perimeter of this two asap!!
u will get the brainlezt for the best answer
Answer:
a. 44 cm b. 126 cm
Step-by-step explanation:
a. it is semi circle
perimeter is πd
22/7*14
44 cm
b. it is equilateral triangle
so perimeter is side* 3
42 *3 = 126cm
Answer:
(a) 44 cm (b) 214 cmStep-by-step explanation:
(a)
The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.
The length of a circle is L₀ = πd, where d is the diameter.
Therefore:
\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)
(b)
A full circle it is 360°, so the circle sector of 60° is \(\frac{60^o}{360^o}=\frac16\) of the circle. So the arc of 60° is ¹/₆ of the full circle length.
The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).
Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.
The length of a circle is L₀ = 2πr, where r is a radius.
Therefore:
\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)
2. A plane flew out of Las Vegas on a 1,515-mile flight to Chicago. When the plane was 723 miles
away from Chicago, the plane experienced a technical problem and the pilot had to divert to
the closest available airport, which was 42 miles away from the plane's current location. When
the plane landed, it was 701 miles away from Chicago. How many degrees did the pilot turn to
divert to the closest airport?
it is not possible to use a relational operator and math operators in the same expression.
It is possible to use a relational operator and math operators in the same expression.
In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.
For example, consider the following expression:
`if (2 * 3) > (4 + 1)`
In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:
`if (6) > (5)`
Then, the relational operator (>) is evaluated, and the expression becomes:
`if True`
The expression is true because 6 is greater than 5.
It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.
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The quality control manager of at Long John Silver's restaurant wants to analyze the length of time that a car spends at the drive-thru window waiting for an order. It is determined that the mean time spent at the window is 59.3 seconds with a standard deviation of 13.1 seconds. The distribution of time at the window is skewed right. The quality control manager wishes to use a new delivery system designed to get cars through the drive-thru system faster. A random sample of 40 cars results in a sample mean time spent at the window of 56.8 seconds. What is the probability of obtaining a sample mean of 56.8 seconds or less, assuming that the population mean is 59.3 seconds
Answer:
0.11314
Step-by-step explanation:
The Long John Silver's restaurant parameters are;
The mean time spent at the window, μ = 59.3
The standard deviation, σ = 13.1
The time distribution is skewed right
The number of cars in the sample, n = 40 cars
The mean time spent at the window with the delivery system, \(\overline x\) = 56.8 seconds
The Z-value for a mean time of 56.8 seconds is given as follows;
\(Z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}\)
Therefore, we get;
\(Z=\dfrac{56.8-59.3 }{\dfrac{13.1 }{\sqrt{40}}} \approx -1.20697620617\)
Therefore, the z-value ≈ -1.21
From the normal probability table, we have;
P(\(\overline X\) ≤ 56.8) = P(Z < -1.21) = 0.11314
The probability of obtaining a sample mean of 56.8 second or less, assuming that the population mean is 59.3 seconds P(\(\overline X\) ≤ 56.8) = 0.11314.
What is the equation of the blue line?
Answer:
y=4x-3
Step-by-step explanation:
Positive integers (counting numbers) which have more than two factors are called composite numbers or simply composites. They are not prime but they do have factors which are prime. For example, here are some prime factorisations: 20 = 2 × 2 × 5, 21 = 3 × 7, 22 = 2 × 11. Thus the greatest prime factors (GPFs) of 20, 21, 22 are 5, 7, 11 respec- tively. The list of GPFs of successive composites is called a GPF sequence. For example, the sequence of GPFs for the composites from 40 to 49 is 5, 7, 11, 5, 23, 3, 7. Note that 41, 43, and 47 are prime and do not contribute to the sequence of GPFs. a Find the sequence of GPFs for the composites from 60 to 65. b Explain why successive composites that give the sequence of GPFs 41, 19, 79 must all have at least four digits. c Find the smallest successive composites that give the sequence of GPFs 17, 73, 2, 19. d Find the largest composite less than 1000 with a GPF of 3 and prove that it is the largest.
The largest composite less than 1000 with a GPF of 3 is 996. To prove that it is the largest, we can note that any larger multiple of 3 would either be a prime or have a larger prime factor than 3.
a) To determine the sequence of GPFs for the composites from 60 to 65, we can list the prime factors of each number and take the largest:
- 60 = 2 x 2 x 3 x 5, so the GPF is 5
- 61 is prime
- 62 = 2 x 31, so the GPF is 31
- 63 = 3 x 3 x 7, so the GPF is 7
- 64 = 2 x 2 x 2 x 2 x 2 x 2, so the GPF is 2
- 65 = 5 x 13, so the GPF is 13
Therefore, the sequence of GPFs for the composites from 60 to 65 is 5, prime, 31, 7, 2, 13.
b) The given sequence of GPFs is 41, 19, 79. All of these numbers are prime, so any successive composites that would give this sequence of GPFs would have to be divisible by each of these primes. The product of 41, 19, and 79 is 62,999, which is a four-digit number. Therefore, any composite that would give the sequence of GPFs 41, 19, 79 would have to have at least four digits.
c) To find the smallest composites that give the sequence of GPFs 17, 73, 2, 19, we can start with 17 x 73 x 2 x 19 = 45634, which is a five-digit number. The next composite with these GPFs would be obtained by adding the product of these primes to 45634. This gives 3215678, which is a seven-digit number. Therefore, the smallest successive composites that give the sequence of GPFs 17, 73, 2, 19 are 45634 and 3215678.
d) To find the largest composite less than 1000 with a GPF of 3, we can list the multiples of 3 less than 1000 and eliminate the primes by inspection:
- 3 x 1 = 3
- 3 x 2 = 6
- 3 x 3 = 9 (prime)
- 3 x 4 = 12
- 3 x 5 = 15
- 3 x 6 = 18
- 3 x 7 = 21 (prime)
- 3 x 332 = 996
- 3 x 333 = 999 (prime)
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WILL GIVE BRAINLIST!! please show all work
What is the arc length of an arc with a central angle of 11r/6 radians in a circle with a radius of 18cm? Round to the nearest whole number
\(\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{11\pi }{6}\\[1em] r=18 \end{cases}\implies s=18\cdot \cfrac{11\pi }{6}\implies s=33\pi \implies s\approx 104~cm\)
Write in plain English what is going on in the proof- explaining the Statements and the Reasons- and state what theorem is being used to conclude the two triangles are congruent.
Stumped on this due to being absent, could use some help
The congruence theorem used to justify the congruence of triangles ABC and DEF is given as follows:
Angle-Side-Angle Theorem (ASA Theorem).
What is the Angle-Side-Angle Theorem?The Angle-Side-Angle theorem justifies the congruence of two triangles when two equivalent angles on two congruent triangles, along with the length between these two sides, have the same measure.
For the triangles ABC and DEF in this problem, we have that:
Equivalent Angles B and E are equal. (Angle).Equivalent Lengths BC and EF are equal (Side).Equivalent Angles C and F are equal (Angle).These 3 statements in the problem form the proof of the congruence of triangles ABC and DEF by the ASA theorem.
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Please help with this question... Which expression is equivalent to x^3/2?
Answer: D
Step-by-step explanation:
Answer:
Solve (x+2/x-3);(x-2/x-3) Equating the equation to zero and taking out (x-3) as common denominator (x+2)(x-2)/ (x-3)2 Solving using the identities we get => (x2– 4)/(x2 -6x + 9)= 0 => (x2– 4)=(x2-6x + 9) => -4= -6x +9 => -4 -9= -6x => -13= -6x => 13=6x => x= 13/ 6
Please solve this question
For a given block code (n, k), how many possible valid code vectors can we find?
The number of possible valid code vectors in a given block code (n, k) is 2^k.
In a block code, (n, k) represents the number of bits in a code vector and the number of information bits, respectively. The remaining (n-k) bits are used for error detection or correction.
Each information bit can take on two possible values, 0 or 1. Therefore, for k information bits, we have 2^k possible combinations or code vectors. This is because each bit can be independently set to either 0 or 1, resulting in a total of 2 possibilities for each bit.
Hence, the number of possible valid code vectors in the given block code (n, k) is 2^k. This represents the total number of distinct code vectors that can be constructed using the available information bits.
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