The cylindrical has a surface area of 414 square units due to its 9-unit radius and 14-unit height.
what is cylinder ?A cylinder is a three-dimensional geometric form made up of two circular bases that are parallel to one another and are joined by a curved lateral surface. It can be pictured as a solid item with a constant circular cross-section along its entire length. The measurements of a cylinder, such as the radius and height of the circular bases, affect its characteristics. The surface area, volume, and horizontal surface area of a cylinder are some of its typical characteristics. Mathematical formulas can be used to determine these properties.
given
The following algorithm determines a cylinder's surface area:
[tex]A = 2\pi r^2 + 2\pi rh[/tex]
where r is the cylinder's base's radius, h is the cylinder's height, and (pi) is a mathematical constant roughly equivalent to 3.14.
Inputting the numbers provided yields:
[tex]A = 2\pi (9)^2 + 2\pi (9)(14)\\[/tex]
A = 2π(81) + 2π(126)
A = 162π + 252π
A = 414π
The cylindrical has a surface area of 414 square units due to its 9-unit radius and 14-unit height.
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AGENT X IS IN DANGER
Question #1 (70 points)
- Create the matrix M and encode the message using the product of matrices A and M.
Question #2 (30 points)
The agents decided to make it harder to decode the message if intercepted by the enemies. The message
was initially encoded by a 2-letter circular shift to the right (Letter A was replaced with C, letter B was
replaced with D, etc.). The spaces remained zeros.
- Create the matrix M and encode the message using the product of matrices A and M.
Must show work.
The evaluation of the matrix multiplication can be presented as follows;
Question #1
The matrix M and A are;
[tex]M=\begin{bmatrix}1 &14 &24 &19 &14 &1&5 \\7 &20 &0 &0 &0 &14 &18\\5 &0 &9 &9 &4 &7 &0 \\\end{bmatrix}[/tex]
[tex]A = \begin{bmatrix} 1& 2 &3 \\3 & 1 & 2 \\ 2 & 3& 1 \\\end{bmatrix}[/tex]
The encoded message in matrix form is therefore;
[tex]A\times M=\begin{bmatrix}30 &54 &51 &46 &26 &50&41 \\20 &62 &90 &75 &50 &31&33 \\28 & 88 &57 &47 &32 &51&64 \\\end{bmatrix}[/tex]
The encoded message is; 30 20 28 54 62 88 51 90 57 46 75 47 26 50 31 51 41 33 64
Question #2
The matrices M and A × M are;
[tex]M=\begin{bmatrix}3 &16 &26 &21 &16 &3 &7\\9 & 22 & 0 &0 &0 &16&20 \\7 &0 &11 &11 &6 &9 &0\\\end{bmatrix}[/tex]
[tex]A\times M=\begin{bmatrix}42 &60 &59 &54 &34 &62&47 \\32 & 70 & 100 &85 &60 &43&41 \\40 & 98 & 63 &53 &38 &63 &74\\\end{bmatrix}[/tex]
The encoded message is; [tex]{}[/tex]42 32 40 60 70 98 59 100 63 54 85 53 34 60 38 62 43 63 47 41 74
What is the rule for matrix multiplication?The rule for matrix multiplication is that the number of columns in the first matrix should be the same as the number of rows in the second matrix
A m by n matrix can only multiply a n by p matrix to produce a m by p matrix
The matrix M for the message can be presented as follows;
The letters are replaced with the corresponding numbers to get;
[tex]{}[/tex]1 7 5 14 20 0 24 0 9 19 0 9 14 0 4 1 14 7 5 18 0
M = [tex]\begin{bmatrix}1 &14 &24 &19&14&1 &5 \\7 & 20 &0 &0 &0&14&18\\5 & 0& 9 & 9&4&7&0\\\end{bmatrix}[/tex]
The matrix A is presented as follows;
[tex]A=\begin{bmatrix}1 & 2 & 3 \\3 & 1 & 2 \\ 2& 3 &1 \\\end{bmatrix}[/tex]
Therefore;
[tex]A \times M = \begin{bmatrix}30 &54 &51 &46&26&50 &41 \\20 & 62 &90 &75 &50&31&33\\28 & 88& 57 & 47&32&51&64\\\end{bmatrix}[/tex]
The encoded message is therefore;
[tex]{}[/tex]30 20 28 54 62 88 51 90 57 46 75 47 26 50 32 50 31 51 41 33 64Question #2
The 2-letter circular shift indicates that the message becomes;
AGENT X IS IN DANGER
The above message becomes;
CIGPV Z KU KO FCOIGT
The numbers comes;
[tex]{}[/tex]3 9 7 16 22 0 26 0 11 21 0 11 15 0 6 3 15 9 7 20
The Matrix Mis therefore;
[tex]M = \begin{bmatrix}3 &16 &26 &21&16&3 &7 \\9 & 22 &0 &0 &0&16&20\\7 & 0& 11 & 11&6&9&0\\\end{bmatrix}[/tex]
The message becomes;
[tex]A \times M = \begin{bmatrix}42 &60 &59 &54&34&62 &47 \\32 & 70 &100 &85 &60&43&41\\40 & 98& 63 & 53&38&63&74\\\end{bmatrix}[/tex]
The encoded message is; [tex]{}[/tex] 42 32 40 60 70 98 59 100 63 54 85 53 34 60 38 62 43 63 47 41 74
The information in the attached file related to the question includes;
Two agents are to send a confidential message which is to be encoded using a 3 × 3 invertible matrix A that consists of natural number elements. The coding strategy consists of replacing each letter by the number representing the letter in the alphabet, after which the numbers representing the letters are placed in columns of 3 elements, completing the missing elements in the last column and blanks with zero in the matrix M. See above.
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could anyone help me out with this? thank you much in advance
Once we have this data, we can substitute the values into the formula to find the empirical probability that a person prefers apple pie given that they prefer whipped cream. Therefore, the missing probability is 1/12, and we know this because it is the value that makes the sum of all probabilities equal to 1.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. For example, if the probability of winning a coin toss is 1/2, this means that there is an equal chance of the coin landing heads or tails. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability approach. Another approach is empirical probability, where probabilities are calculated based on observed data or experiments. Lastly, subjective probability involves making an informed guess or estimate about the likelihood of an event occurring based on subjective factors such as experience, intuition, or expert opinion. Probability is a fundamental concept in statistics and is used in many application
Here,
1. The formula needed to calculate the empirical probability that a person prefers apple pie given that they prefer whipped cream is:
P(Apple Pie | Whipped Cream) = P(Apple Pie and Whipped Cream) / P(Whipped Cream)
where P(Apple Pie and Whipped Cream) is the probability that a person prefers both apple pie and whipped cream, and P(Whipped Cream) is the probability that a person prefers whipped cream.
This formula is used because it is a conditional probability, which is a measure of the probability of an event occurring given that another event has occurred. In this case, we want to find the probability that a person prefers apple pie given that they already prefer whipped cream.
To calculate P(Apple Pie and Whipped Cream), we would need to gather data on the number of people who prefer both apple pie and whipped cream. Similarly, to calculate P(Whipped Cream), we would need to gather data on the number of people who prefer whipped cream.
2. To find the missing probability, we need to use the fact that the sum of all probabilities in a probability distribution must be equal to 1. Therefore, we can set up an equation to solve for the missing probability:
1/6 + 1/3 + x + 5/12 = 1
Simplifying the equation by finding a common denominator gives:
2/12 + 4/12 + x + 5/12 = 1
Combining like terms gives:
11/12 + x = 1
Subtracting 11/12 from both sides gives:
x = 1 - 11/12
x = 1/12
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When two unequal forces act on an object, it causes the object to move.
These forces are called:
Answer:
resultant force
Step-by-step explanation:
the body will move to the direction where greater force is applied
valuate the
expression
12 - 3y
2
+
√²v=4] for y = 3.
2y -
The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
What are the ways to analyse an algebraic expression?When [tex]y = 3[/tex] is used, the value of the expression [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] has a value of [tex]-29/2[/tex] .
To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
If [tex]y = 3[/tex] , we can insert it into the expression & simplify as follows to evaluate [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for [tex]y = 3[/tex] .
[tex]12 - 3(3)^2 + (√4) / (2(3) - 2)[/tex] (y = 3 replacement)
[tex]12 - 27 + 2 / 4\s-15 + 1/2\s-29/2[/tex]
Therefore, The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
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A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
The cost to rent one shed of the rectangular prism shaped shed is $2772.
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
What is a prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.
Volume of prism= BH
where B= area of base and H= height
B= 11*7 = 77 feet²
H= 12 feet
Volume= 77*12=924 cubic feet
Cost =$3 per cubic foot
Total cost= 3*924= $2772
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fill in the blank. Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in ______ different ways. (Give your answer as a whole number.)
Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.
To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.
The formula for finding the number of permutations is:
n! / (n-r)!
where n is the total number of objects and r is the number of objects we choose.
Using this formula, we can calculate the number of permutations as follows:
4! / (4-3)!
= 4! / 1!
= 4 x 3 x 2 x 1 / 1
= 24
Therefore, we can arrange the chosen 3 letters in 24 different ways.
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6TH GRADE MATH, SOMEONE PLS FIND THE SLOPE IN THIS EQUATION TY
Answer:
slope is -2
Step-by-step explanation:
100% correct :)
The slope is what is next to the x in y=mx+b
so if it was like this y=3x + 2
3 is the slope
hope that makes sense
PLEASE I NEED HELP, what is the equivalent of 7/tan b+7tan b
In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
Set A = 90 degrees and B = b degrees:
tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)
tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)
tan(90 + b) = -cot b
7/tan b + 7tan b
= 7/(tan b) + 7(tan(90 + b) - 1)
= 7/(tan b) + 7(-cot b - 1)
= (7 - 7tan b cot b)/sin b
The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
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Solve for x algebraically, given the domain.
4sin x+2=0, 0≤ x<2π
Answer:
x = [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }{6}[/tex] or x = 210°, 330°
Step-by-step explanation:
4sin(x) + 2 = 0
4sin(x) = -2
sin(x) = -1/2
x = [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }{6}[/tex]
In the diagram of right triangle ABC shown below, AB= 14 and AC = 9.
What is the measure of ZA, to the nearest degree?
1) 33
2) 40
3) 50
4) 57
The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a given a right angle triangle in the picture
It is required to find the measure of angle A
Applying cos ratio to find the measure of the angle A:
cosA = 9/14
cosA = 0.642
A = 49.99 ≈ 50 degree
Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
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solve the quadratic equation 9^2×-15×-6=0
The solutions to the quadratic function 9x² - 15x - 6 = 0 are given as follows:
x = -1/3 and x = 2.
How to solve the quadratic equation?The quadratic equation for this problem is defined as follows:
9x² - 15x - 6 = 0.
The coefficients of the function are given as follows:
a = 9, b = -15 and c = -6.
The discriminant of the function is obtained as follows:
D = b² - 4ac
D = (-15)² - 4 x 9 x (-6)
D = 441.
Then the solutions to the quadratic function are obtained as follows:
x = (-b - sqrt(D))/2a = (15 - sqrt(441))/18 = -1/3.x = (-b + sqrt(D))/2a = (15 + sqrt(441))/18 = 2.More can be learned about quadratic functions at https://brainly.com/question/1214333
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A parent donated 36 fruit cups and 24 bananas to fifth grade. The teacher wanted to make field trip snack bags with the donated food and wondered about the ways snacks could be packed. To be fair the teacher wants to make sure that all bags are exactly the same.
A) What is the greatest number of snack bags that the teacher can make, if each bag is identical? How do you know ?
B) What other numbers of snack bags could she make? How do you know?
2) Another parent also donated 24 bananas, so there are 48 bananas total. Now what is the greatest number of snack bags can that can be made?
3) The teacher realized that she miscounted and had only 30 fruit cups. How many snack bags can she make with 48 bananas and fruit cups?
4) What do the different numbers of snack bags that can be made have to do with the number of fruit cups and number of bananas?
If A =12 and 120% of A equal to 80% of B, then what is A+B
So,
120% is the same as 1.2 or 6/5. 80% is the same as 0.8 or 4/5.
We are given the value of a, which is 12.
6/5 of a, or 1.2 times a, is equal to 4/5 of b, or 4/5 times b.
[tex]\dfrac{6}{5} (12)=\dfrac{4}{5} b[/tex]
Simplify.
[tex]\dfrac{72}{5} =\dfrac{4}{5} b[/tex]
Multiply both sides by 5/4.
[tex]\dfrac{72}{4} \ \text{or} \ 18=b[/tex]
Therefore, the sum of a and b is 12 + 18 = 30.
please answer question i cannot do it
The value of the height of the trapezium is 10.3 cm.
What is the area of a trapezium?The area of a trapezium is given by the formula:
Area = (1/2) x (sum of parallel sides) x (distance between the parallel sides)
The parallel sides of the trapezium are given as 18 cm and 13 cm
The area of the trapezium is given as 160 cm²
The height of the trapezium = h
The value of the height of the trapezium is calculated as follows;
160 = ¹/₂ (18 + 13) h
2 x 160 = (31)h
320 = 31h
h = 320 / 31
h = 10.3 cm
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I will mark you brainiest!
What is the measure of angle R?
A) 17 degrees
B) 25 degrees
C) 34 degrees
D) 65 degrees
Answer: D) Angle R is 65 degrees
Step-by-step explanation:
In the given figure, we have a right-angled triangle PQR.
Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,
∠QRP + ∠QPR + ∠PRQ = 180 degrees
Since ∠PRQ is a right angle (90 degrees), we have:
∠QRP + ∠QPR = 90 degrees
Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:
∠QRP + 25 = 90 degrees
Solving for ∠QRP, we get:
∠QRP = 90 - 25 = 65 degrees
Therefore, the measure of angle R is 65 degrees, which is option (D).
Answer:
Answer is D
Step-by-step explanation:
SPiDerMom is so hot bTw
can you solve this and convert in min at the end of the step
[tex] \frac{1}{30}(ln( \frac{15}{22}))t = [/tex]
The expression 1/30(ln(15/22))t = x when solved for t has a solution of t = -78.95x
Solving the expression for tGiven the following expression
1/30(ln(15/22))t =
The above expression cannot be solved for t
This is so because the expression is not an equation or inequality
To do this, we must equate the expression to a value (say x)
So, we have
1/30(ln(15/22))t = x
Multiply through by 30
This gives
ln(15/22)t = 30x
Evaluate the natural logarithm expression
This gives
-0.38t = 30x
Divide both sides by -0.38
So, we have
t = -78.95x
Hence, the solution for t is t = -78.95x
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Can someone help quick i have 6 questions left
Step-by-step explanation:
remember the trigonometric triangle inside a circle.
sine is the up/down leg, cosine is the left/right leg.
the Hypotenuse (baseline) of the right-angled triangle is the angle-defining radius of the circle.
this is the basic definition inside the norm-circle with radius = 1.
for any other size sine and cosine need to be multiplied by the actual radius for the actual triangle side lengths.
I think you need the answer in simplified fraction and square root notification (you cut that off), but I give you also the decimal result, just in case.
so,
78 = cos(30)×y
78 = (sqrt(3)/2) × y
y = 78 / (sqrt(3)/2) = 2×78/sqrt(3) = 156/sqrt(3) =
= 90.06664199...
x = sin(30) × y = 0.5 × 156/sqrt(3) = 78/sqrt(3) =
= 45.033321...
please help me with math quiz i’ll give you brainlist
Answer:
Answer: B. Symmetric.
Explanation:
In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.
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Since ∠1 ≅ ∠3 and ∠3 ≅ ∠7, then:
A) ∠6 ≅ ∠7
B) ∠7 ≅ ∠8
C) ∠1 ≅ ∠7
Answer:
C) ∠1 ≅ ∠7
Step-by-step explanation:
If ∠1 = ∠3, then ∠3 = ∠7, behind there is written ∠1 = ∠3, so it's A) ∠1 = ∠7.
Molly has 4 final test to study for. She wants to study an equal amount on each test. If she has 10 hours to study for all her finals, how much time should she study for each test. Record answer in hours and minutes.
Answer:
2.5 hours
Step-by-step explanation:
To find the number of hours for each test,
Divide the number of hours by the number of tests
10 divided by 4
2.5 hours for each test
2 Sasha believes her soccer team plays better at away games than at home games. Her team played 12 games at home and 12 games away. She recorded the wins over this season. Based on these results, what is the probability for home and away wins? Is she right about her team playing better away? Show your work. Place: Home Away
Frequency: 8 7
Probability of winning at home is 0.67, Probability of winning away is 0.58.
How to calculate the probabilitiesTo calculate the probability of home and away wins, we need to divide the number of wins by the total number of games played at home and away respectively.
Probability of winning at home = (Number of wins at home) / (Total number of games played at home)
= 8 / 12
= 0.67
Probability of winning away = (Number of wins away) / (Total number of games played away)
= 7 / 12
= 0.58
Based on these results, Sasha's team has a higher probability of winning at home (0.67) compared to away games (0.58).
Therefore, her belief that her team plays better away is not supported by the data.
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If z=x+y ;where x varies p Square and y varies 1/p, find the equation connecting z and p . If z=5 when p=2 ,and z=6 when p=4 find z when p=6
The equation connecting z and p is:
z = x + (1/p)
To find z when p = 6, we can use the values of x and y when p = 2 and p = 4 to calculate the corresponding value of z when p = 6.
When p = 2, x = 4 and y = 1, so z = 5
When p = 4, x = 16 and y = 0.25, so z = 16.25
Therefore, when p = 6, x = 36 and y = 0.167, so z = 36.167
alexia lunch at a restaurant costs $34.00, without tax. She leaves the waiter a tip of 12% of the cost of the lunch, without tax. What is the total cost of the lunch, including the tip?
Answer:
$38.08
Step-by-step explanation:
12% of 34.00 as an equation would be [tex]34*0.12[/tex], [tex]34*0.12=4.08[/tex] so we add 4.08 to the total of the lunch already. [tex]34.00+4.08=38.08[/tex]. So the answer is $38.08. Hope this helps :)
In which three statements below will the number 8 correctly fill
in the blank?
the correct options are A), B), and E).
why it is and what is Gallon?
A) 2 quarts = 8 cups
B) 8 cm = 80mm
E) 96 inches = 8 feet
The number 8 cannot correctly fill in the blank for statements C and D.
C) 1 gallon = 16 cups, so 4 gallons = 64 cups, not 8 cups.
D) 1 hour = 60 minutes, so 96 minutes = 1 hour and 36 minutes, not 8 hours.
Therefore, the correct answers are A), B), and E).
A gallon is a unit of measurement for volume commonly used in the United States and some other countries. There are two different sizes of gallons: the US gallon and the imperial gallon.
The US gallon is defined as exactly 3.785411784 liters, and is used for measuring liquids such as gasoline, milk, and other beverages.
The imperial gallon, which is used in the United Kingdom and some other countries, is defined as exactly 4.54609 liters.
In both cases, a gallon is typically divided into smaller units such as quarts, pints, and fluid ounces for measuring smaller amounts of liquid.
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For a standard normal distribution, find:
P(-2.11 < z < -0.85)
Answer:
Step-by-step explanation:
Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.
P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)
Using the table, we find:
P(z < -0.85) = 0.1977
P(z < -2.11) = 0.0174
Therefore,
P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803
So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.
6 TH GRADE MATH , WHAT IS THE SLOPE? TY
Answer:
Step-by-step explanation:
The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.
The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.
That is what Slope is.
Answer:
Step-by-step explanation:
Slope :( 1,1)
You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)
A fair coin is tossed five times. Explain why the probability of getting exactly three heads is 0.3125.
The value of the probability is 0.3125 and this is proved by the calulations below
How to explain the value of the probabilityThe probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.
The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.
There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.
For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.
Therefore, the probability of getting exactly 3 heads is:
Probability = 10 * (1/32)
Probability = 10/32
Probability = 0.3125.
Hence, the value of the probability is 0.3125.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The rate at which the water level is rising in the pyramid is 5 cm/s when the water level is 3 cm.
What is a pyramid?A pyramid is a three-dimensional object with triangle faces that meet at a shared vertex and a base that is a polygon. The perpendicular distance between a pyramid's base and apex determines the structure's height. The base form of a pyramid can be used to categorise them. A square pyramid, for instance, has a square base, a triangle-shaped pyramid, a triangle-shaped base, and so on. From the ancient Egyptian pyramids to the contemporary pyramids found in cities all over the world, pyramids have been employed in architecture and art for thousands of years.
Given that, sides of length 3 cm and the height is 5cm.
The volume of a pyramid is given by:
V = (1/3) * A * h
where A is the area of the base.
The base of the pyramid is a square thus,
Area = (3)(3) = 9 sq. cm.
Substitute the value of A and h in volume:
V = (1/3) * 9 * 5 = 15
Now, water is being filled at a constant rate of 45 cubic cm per second.
The rising level can thus be calculated as:
r - 45/9 = 5 cm/s
Hence, the rate at which the water level is rising is 5 cm/s when the water level is 3 cm.
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Find the missing side in each triangle using any method.
AC has a length of ____ units. DE has a length of ____ units.
