Juan bought a basketball for 40% off. If
he paid $36 for the basketball, what was
the original price?
Answer:
$24
Step-by-step explanation:
since 40% is in 100% i did 100 - 40 which i got 60
then it says that he paid $36 so I subtracted 60 - 36 and I got $24 as the answer iihope this helps! :)
100 - 40 = 60
60 - 36 = 24
The original price when he paid $36 for the basketball should be considered as the $24.
Calculation of the original price:Since
Juan bought a basketball for 40% off And, If he paid $36 for the basketball.
So it be like
= 60% of $100 - $36
= $60 - $36
= $24
Hence, The original price when he paid $36 for the basketball should be considered as the $24.
Learn more about price here: https://brainly.com/question/24565996
What is the slope of this function. f(x)=-3x+5
Math COLL, help me plis
Using trigonometric functions, the value of cos O in simplest terms is 5/17.
What are trigonometric functions?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (CSC).So, we know that: cos α = Adjacent Side/Hypotenuse
We have,
adjacent side = 5hypotenuse = 17OM = 17 and ON =5As we know,
cos O = Adjacent Side/HypotenuseWe obtain:
cos O = ON/OMcos O = 5/17Therefore, using trigonometric functions, the value of cos O in simplest terms is 5/17.
To know more about trigonometric functions, visit:
https://brainly.com/question/1143565
#SPJ13
Suppose that we have two events, A and B, with P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.45. If needed, round your answer to three decimal digits.
Find P(A | B)
Find P(B | A
Are A and B independent? Why or why not?
The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.
To find P(A | B), we use the formula:
P(A | B) = P(A ∩ B) / P(B)
In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.
Plugging these values into the formula, we get
P(A | B) = 0.45 / 0.60 = 0.750.
To find P(B | A), we use the formula:
P(B | A) = P(A ∩ B) / P(A)
Here, P(A ∩ B) = 0.45 and P(A) = 0.50.
Substituting the values, we find
P(B | A) = 0.45 / 0.50 = 0.900.
A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.
To learn more about probability refer:
https://brainly.com/question/25839839
#SPJ11
After forming two right triangles, which right triangle theorem did you have to use twice to solve for side lengths that were not in the final equation? the tangent theorem the pythagorean theorem the right triangle theorem the cosine theorem.
Answer:
b
Step-by-step explanation:
no
Answer:
The answer is B. the Pythagorean theorem
Step-by-step explanation:
brainiest pls?
Answer these reflection
questions.
4
1. What does it mean for a
point to be a solution to a
system of equations?
2. When would you use the
substitution method instead
of the elimination method?
When a point is the solution of a system of equations, it means that all of the equations in the system are simultaneously satisfied by the values of the variables.
What is a linear equation?Use the substitution method to solve the system of equations when one of the variables in one of the equations can be easily isolated or solved for.
The system's remaining equations can then be modified to reflect the variable's expression, creating a new set of equations with one less variable. The system might be easier to manually solve as a result.
Learn more about equation:https://brainly.com/question/29538993
#SPJ1
A house was purchased in 2012 for $150,000 If the value of the home increases by 3% each year, what will the house be worth in the year 2015?
the letters that spell mississippi are each written on separate tiles lying facedown on a table. a tile is selected at random, the letter is recorded, and then the tile is placed facedown on the table. then the process repeats. what is the theoretical probability of choosing a tile with the letter p? responses 14 1 fourth 411 4 over 11 111 1 over 11 211
The theoretical probability of choosing a tile with the letter p is 1/8
The letter of the word MISSISSIPPI are written on separate tiles lying down on the table and tile is chosen at random and the the letter is noted and then the tile is lied again on the table.
Probability of the event is,
P(E) = Total favorable outcomes/Total possible outcomes.
Total possible outcomes in this case are 11 because there are a total of 11 letters.
The total favorable outcomes that the chosen letter is P is,
Total favorable outcomes = ¹¹C₁/(2!)(2!)(2!)
Total favorable outcomes = 11/8
Probability P that chosen number is P is,
P = (11/8)/11
P = 1/8
So, the probability that the chosen tile is with letter P is 1/8.
To know more about probability, visit,
https://brainly.com/question/24756209
#SPJ4
Using complete sentences explain which function as the greatest y-intercept.
The y-intercept of a function is the point where the graph of the function intersects with the y-axis. In other words, it is the value of the function when the input or x-value is equal to 0.
To determine which function has the greatest y-intercept, we need to evaluate each function at x=0 and compare their y-values. The function with the largest y-value at x=0 will have the greatest y-intercept.
For example, if we have two functions f(x) and g(x), we can evaluate them at x=0 as follows:
f(0) = 5
g(0) = 7
In this case, g(x) has the greatest y-intercept since its y-value at x=0 is larger than that of f(x). Therefore, we can say that the function g(x) has the greatest y-intercept.
In summary, to determine which function has the greatest y-intercept, we need to evaluate each function at x=0 and compare their y-values. The function with the largest y-value at x=0 will have the greatest y-intercept.
Visit here to learn more about y-intercept:
brainly.com/question/14180189
#SPJ11
genetically modified foods: according to a 2014 pew research survey, a majority of the american general public (57%) says that genetically modified (gm) foods are generally unsafe to eat. this month, in a survey of 500 randomly selected american adults, 60% say that gm foods are generally unsafe to eat. we test the hypothesis that the percentage who says that gm foods are generally unsafe to eat is greater than 57% this year. given this information, determine whether conditions are met for conducting a hypothesis test. which of the following statements are true? choose all that apply.
Statements that are true:
- The survey was conducted on a random sample of American adults.
- The sample size is large enough to conduct a hypothesis test.
- The sampling distribution can be assumed to be approximately normally distributed due to the large sample size.
To determine whether conditions are met for conducting a hypothesis test, we need to consider the following factors:
1. Random sampling: The survey should be based on a random sample of the population. In this case, the survey was conducted among 500 randomly selected American adults, which satisfies this condition.
2. Sample size: The sample size should be large enough to make the results more reliable. With 500 participants, the sample size is reasonably large.
3. Normality: The sampling distribution should be approximately normally distributed. Given the large sample size, we can apply the Central Limit Theorem, which states that the sampling distribution of the proportion will be approximately normally distributed.
Based on these conditions, we can conclude that it is appropriate to conduct a hypothesis test for the given situation.
Know more about hypothesis test here:
https://brainly.com/question/30588452
#SPJ11
If QP bisects ZDQL, m/DQP = 5x - 7, and m/PQL = 11 + 2x, determine
the measure of ZDQL.
m₂DQL =
When QP bisects DQL, then the angles DQP and angle PQL is 23°.
Given that,
In the picture we can see the diagram,
The QL line is there and the QD line.
QP line bisect the angles DQL
The angle DQP is 5x-7
The angle PQL is 11+2x
We have to find the x value and the angles DQP and PQL.
We know,
From the bisection we can say the angle are equal to each other
The angle DQP=The angle PQL
5x-7=11+2x
5x-2x=11+7
3x=18
x=18/3
x=6
Substitute x value in angles DQP and angle PQL.
The angle DQP=5x-7=5(6)-7=30-7=23°
The angle PQL=11+2x=11+2(6)=11+12=23°.
Therefore, the angles DQP and angle PQL is 23°.
To learn more about angle visit: https://brainly.com/question/28451077
#SPJ9
The Build-Your-Own-Sailboat booth that Althea visited gave her and hers friend the chance to make a sailboat model. Each boy chose a different quadrilateral for a sail. Althea chose a trapezoid, and her friend chose a parallelogram.
(a) Compose each shape into a rectangle to determine the area. The formula for area of a rectangle is A = lw . What is the area of each quadrilateral?
(b) Althea said that all quadrilaterals can be decomposed into triangles to find the area of the quadrilateral. Is this statement always true, sometimes true, or always false? Give two examples to support your answer.
A quadrilateral is a four sided figure. It is possible to decompose the quadrilaterals to give two triangles by taking apart the diagonal that runs across the figure
What is a quadrilateral?A quadrilateral is a four sided figure. The images are not shown here so we don't know what the dimensionof each figure is.
It is possible to decompose the quadrilaterals to give two triangles by taking apart the diagonal that runs across the figure and find the area of the two triangles in order to obtain the area of the orginal figure.
Learn more about quadrilateral: https://brainly.com/question/13805601
A baker needs 3/5 cup water for every 2/3 cup flour. Using this ratio, how much flour is needed for 1/3 cup water?
Answer:
10/27 cup of flourStep-by-step explanation:
Use the ratio below and solve for x:
3/5 : 1/3 = 2/3 : xx = 2/3*1/3 : 3/5x = 2/9 * 5/3x = 10/27Diameter measures from side to side
Radius measures from side to center.
For example, AE is the diameter and AH is the radius.
Here is a circle with center H and some line segments and curves joining points on the circle.
Identify examples of the following. Explain your reasoning.
The region's sector AHB is a circle's sector. This is due to the fact that it diameter is shaped like a slice of pizza and is bounded by two radii and an arc of the circle.
what is diameter?In geometry, the diameter of a circle is any linear fashion segment that has an endpoint mostly on circle and travels through its centre. Another way to put it is the tallest chord of a circle
The diameter of the circle is represented by the line segment AB. This is due to the fact that it runs through the centre H and connects two points on the circle.
The radius of the circle is represented by the line segment AH. This is because it connects the circle's centre H to a point A.
The chord is the line segment. The chord CD is a circle chord. This is due to the fact that it connects two points on a circle but does not pass through the centre.
Tangent to the circle: The line segment EF is tangent to the circle. This is due to the fact that it only intersects the circle at one point, G, and is perpendicular to the radius GH at that point.
ABG's curve is an arc of the circle. This is because it is part of the circle's circumference, connecting two points A and B.
The region's sector AHB is a circle's sector. This is due to the fact that it is shaped like a slice of pizza and is bounded by two radii and an arc of the circle.
To know more about diameter visit:
https://brainly.com/question/5501950
#SPJ1
How many sides does a regular polygon have when each side is 30 degrees
The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.
Let us consider 'n' be the number of sides of the regular polygon.
Let 'y' be the measure of each of the exterior angle of regular polygon.
y = 30 degrees
Measure of each of the exterior angle of regular polygon 'y'
= ( 360° ) / n
⇒ n = ( 360° / y )
Substitute the value we get,
⇒ n = ( 360° / 30° )
⇒ n = 12
Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.
Learn more about regular polygon here
brainly.com/question/12092158
#SPJ4
The above question is incomplete, the complete question is:
How many sides does a regular polygon have when each exterior angle measures 30 degrees?
Find the area of this circle. Use 3.14 for piπ.
Answer:
A =452.16 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 (12)^2
A =452.16 ft^2
Answer:
452.16ft^2
Step-by-step explanation:
So to answer this You need to use the formula A=πR^2
Step one is Figuring out what the equation is so A= (3.14)12^2Now what is 12 squared? The answer is 144ftStep three Multiply 144 by 3.14 since that is for PI to get 452.16ft^2suppose you have a class with 30 students — 10 freshmen, 12 sophomores, and 8 juniors. in how many ways can you put 6 freshmen, 4 sophomores and 8 juniors into a class of 18 students?
There are 103,950 ways to create a class of 18 students with 6 freshmen, 4 sophomores, and 8 juniors from the given pool of students.
To determine the number of ways you can put 6 freshmen, 4 sophomores, and 8 juniors into a class of 18 students, you will use the concept of combinations. Combinations are a mathematical technique for calculating the number of ways you can choose a specific number of items from a larger set without considering the order of those items.
In this case, you need to choose 6 freshmen out of 10, 4 sophomores out of 12, and 8 juniors out of 8. To do this, you will apply the combination formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of items in the set, and r is the number of items you want to choose.
For freshmen:
C(10, 6) = 10! / (6!(10 - 6)!) = 210
For sophomores:
C(12, 4) = 12! / (4!(12 - 4)!) = 495
For juniors:
C(8, 8) = 8! / (8!(8 - 8)!) = 1
Now, to find the total number of ways to create a class of 18 students, simply multiply the combinations for each group:
Total combinations = 210 (freshmen) × 495 (sophomores) × 1 (juniors) = 103,950
So, there are 103,950 ways to create a class of 18 students with 6 freshmen, 4 sophomores, and 8 juniors from the given pool of students.
Learn more about sophomores here:
https://brainly.com/question/29331924
#SPJ11
Which pair of angles must be supplementary? 50 POINTS!!! 2 lines intersect to form right angles. Another line goes through the lines diagonally to form 6 angles. From top left, clockwise, the angles are 2 (90 degrees), 1, 6, 5 (90 degrees), 4, 3. Angle 1 and Angle 6 Angle 2 and Angle 5 Angle 5 and Angle 4 Angle 6 and Angle 2
Answer:
1,6
Step-by-step explanation:
i just did the test on edge
Answer:
angle 6,2
Step-by-step explanation:
supplementary angles means that the sum of all the angle eqaul 180 degrees, so 6,2 would equal 180 degrees
And i got it correct on e d gu n i t y 2020
Find the slope of the line. pleaseee
Answer:
0
Step-by-step explanation:
The slope is the change in y divided by the corresponding change in x:
∆y/∆x = (54.99 -54.99)/(7 -6) = 0/1 = 0
The slope of the line is zero.
please help asap for the area. i got homework to submit in 5 minutes
Answer:
area = 228 m^2
Step-by-step explanation:
here's your solution
=> length = 20 m. , width = 12 m
=> Area of rectangle = length*width
=> Area of rectangle = 12*20
=> Area of rectangle = 240 m^2
now we need to find area of traingle
=> base = 4 m. , height = 6 m
=> area of traingle = 1/2*base*height
=> area of traingle = 1/2*4*6
=> area of traingle = 12 m^2
=> now , area of figure = 240 m^2 - 12 m^2
=> 228 m^2
hope it helps
Answer:
p= 66.32 m
a= 228 m squared
Step-by-step explanation:
The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x – 72.5| = 4. What are the minimum and maximum temperatures in the house?
Answer:
Minimum temperature is 68.5 ° and maximum temperature is 76.5 °
Step-by-step explanation:
Given :
|x – 72.5| = 4.
When the Temperature of x is minimum So the Minimum temperature is
\(|x - 72.5| = 4\\it\ can \ be \ written \ as \\72.5-x=4\\-x=4-72.5\\x=68.5\)
When the Temperature of x is maximum So the Maximum Temperature is
\(|x -72.5| = 4\\x-72.5=\ 4\\x=72.5+4\\x=76.5\)
Therefore The minimum temperature is 68.5 ° and the maximum temperature is 76.5 °
Answer:
b
Step-by-step explanation:
becasue I did and and check with teacher
Find the surface area of the prism.
Therefore, the surface area of the prism is 453.5 square meters.
What is surface area?Surface area is the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces, surfaces, or sides of the object. Surface area is measured in square units, such as square inches, square feet, or square meters, depending on the units used to measure the object's dimensions. Surface area is an important concept in geometry and is used in many real-world applications, such as calculating the amount of paint needed to cover a surface or the amount of material required to build a structure.
Here,
To find the surface area of the prism, we need to find the area of all six faces and then add them together. The prism has two congruent rectangular faces (front and back) and four trapezoidal faces (top, bottom, left, and right).
The area of the rectangular faces is:
20 m × 4 m = 80 m² (each face)
The area of the trapezoidal faces can be found using the formula for the area of a trapezoid:
Area = (a + b) × h / 2
where a and b are the lengths of the parallel sides, h is the height, and the slanting height is used to calculate the height.
For the top and bottom faces, the parallel sides are 5 m and 20 m, and the height is 4.47 m. So, the area of each face is:
(5 m + 20 m) × 4.47 m / 2 = 56.75 m² (each face)
For the left and right faces, the parallel sides are 4 m and 5 m, and the height is 20 m. So, the area of each face is:
(4 m + 5 m) × 20 m / 2 = 90 m² (each face)
Now, we can add up the areas of all six faces to get the total surface area:
Total surface area = 2 × 80 m² + 2 × 56.75 m² + 2 × 90 m²
Total surface area = 160 m² + 113.5 m² + 180 m²
Total surface area = 453.5 m²
To know more about surface area,
https://brainly.com/question/28016184
#SPJ1
help me please, i need to turn this in quick and im struggling.
Answer:
3) 0.75
5)96 pens
Step-by-step explanation:
3) 5 percent *15 =
( 5:100)*15 =
( 5*15):100 =
75:100 = 0.75
5) 48/4= 12
12*8=96
solve using quadratic equations (x+3)^2=25
Answer:
x=2 or x=−8
Step-by-step explanation:
A portfolio of claims contains 10 each of bodily injury, property damage, worker's compensation and comprehensive claims. Five claims are randomly drawn from this portfolio. Find the probability that the selected claims contain exactly three claims from one coverage and exactly two claims from one of the other coverages.
The value of P is approximately 0.0082027.
To find the probability of selecting exactly three claims from one coverage and exactly two claims from one of the other coverages, we need to calculate the total number of ways to choose three claims from one coverage and two claims from another coverage, and divide it by the total number of ways to choose five claims from the portfolio.
First, let's calculate the total number of ways to choose three claims from one coverage and two claims from another coverage. We have 10 bodily injury claims and 10 property damage claims to choose from, so the number of ways to choose three claims from one coverage is 10 choose 3 (denoted as C(10, 3)), and the number of ways to choose two claims from another coverage is 10 choose 2 (denoted as C(10, 2)). Multiplying these two combinations gives us the total number of ways to choose three claims from one coverage and two claims from another coverage.
Next, let's calculate the total number of ways to choose five claims from the portfolio. We have a total of 10 bodily injury claims, 10 property damage claims, 10 worker's compensation claims, and 10 comprehensive claims to choose from, so the number of ways to choose five claims from the portfolio is 40 choose 5 (denoted as C(40, 5)).
Finally, to find the probability, we divide the total number of ways to choose three claims from one coverage and two claims from another coverage by the total number of ways to choose five claims from the portfolio.
Therefore, the probability that the selected claims contain exactly three claims from one coverage and exactly two claims from one of the other coverages can be calculated as:
P = (C(10, 3) * C(10, 2)) / C(40, 5)
P = (C(10, 3) * C(10, 2)) / C(40, 5)
ChatGPT
To solve the expression P = (C(10, 3) * C(10, 2)) / C(40, 5), we can substitute the values into the combination formulas and perform the calculations:
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
C(10, 2) = 10! / (2!(10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45
C(40, 5) = 40! / (5!(40-5)!) = 40! / (5! * 35!) = (40 * 39 * 38 * 37 * 36) / (5 * 4 * 3 * 2 * 1) = 658,008
Now, we can substitute these values into the expression:
P = (C(10, 3) * C(10, 2)) / C(40, 5) = (120 * 45) / 658,008
Performing the calculation:
P = 5,400 / 658,008
Simplifying the fraction:
P ≈ 0.0082027
Therefore, the value of P is approximately 0.0082027.
To learn more about probability
https://brainly.com/question/13604758
#SPJ11
The point T( – 1,2) is rotated 180° clockwise around the origin. What are the coordinates of the resulting point, T'?
The coordinates of the resulting point, T' after the point T( – 1,2) is rotated 180° clockwise around the origin is (1, -2).
To rotate a point 180° clockwise around the origin, you can apply the following transformations:
Reflect the point across the x-axis by negating its y-coordinate.
Reflect the point across the y-axis by negating its x-coordinate.
Starting with T( – 1,2), we first reflect the point across the x-axis, which gives us T'( – 1, -2). Then, we reflect T' across the y-axis, which results in T''(1, -2).
The transformation can be represented as follows:
T' = (x, -y)
T'' = (-x, -y)
Therefore, the final coordinates of T'' are (1, -2).
Learn more about the coordinates at
https://brainly.com/question/16634867
#SPJ4
Determine if the triangles are similar by Angle-Angle similarity
The triangles are similar by Angle-Angle similarity since they are congruent.
What is Angle-Angle Similarity?According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.
Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.
In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
Learn more about triangles on:
https://brainly.com/question/17335144
#SPJ1
Functions x(t) and h(t) have the waveforms shown in Fig. 2.12. Determine and plot y(t) = x(t) * h(t) using the following methods. (a) Integrating the convolution analytically. (b) Integrating the convolution graphically. 2.12 Functions x(t) and ht) have the waveforms shown in Fig.P2.12. Determine and plot yt=xt*h(t using the following methods (a) Integrating the convolution analytically (b) Integrating the convolution graphically x(t) h(t) 2 0 0 0 t(s) 0 LS 1 1 2 Figure P2.12:Waveforms for Problem 2.12
y(t) = 2t^2 - 12t + 16 for 0 ≤ t ≤ 2, and y(t) = 0 otherwise, using both methods of integrating the convolution.
To determine and plot y(t) = x(t) * h(t), where * represents convolution, using the given waveforms, we can use two methods: (a) integrating the convolution analytically and (b) integrating the convolution graphically.
(a) Integrating the convolution analytically:
The convolution of two functions f(t) and g(t) is given by the integral of the product of the two functions over all possible values of the variable t:
f(t) * g(t) = ∫ f(τ)g(t-τ) dτ
where τ is a dummy variable of integration.
Using this formula, we can compute y(t) = x(t) * h(t) as follows:
y(t) = ∫ x(τ)h(t-τ) dτ
= ∫ x(τ)h(2-t-τ) dτ (since h(t) is non-zero only for 0 ≤ t ≤ 2)
= ∫ x(τ)h(2-t)h(τ-t+2) dτ (using the time reversal property of h(t))
= h(2-t) ∫ x(τ)h(τ-t+2) dτ (since h(2-t) is constant w.r.t τ)
= 2(2-t) ∫ 2(τ-t+2) dτ (since x(t) is constant w.r.t τ and h(τ-t+2) is zero outside the interval [t-2, t])
= (2-t) [τ^2-2tτ+8τ] from τ=0 to τ=2-t
= 2t^2 - 12t + 16 for 0 ≤ t ≤ 2
= 0 otherwise
(b) Integrating the convolution graphically:
To integrate the convolution graphically, we can plot x(t) and h(t) on the same graph and slide h(t) along the t-axis, multiplying it with x(t) at each value of t and adding up the products to obtain y(t).
From the given waveforms, we can plot x(t) and h(t) on the same graph as follows:
x(t) is a rectangular pulse of width 1 and amplitude 2, centered at t=0.5.
h(t) is a triangular pulse of base width 2 and peak amplitude 1, centered at t=1.
Now, we slide h(t) along the t-axis and multiply it with x(t) at each value of t as shown in the attached image. At t=0, h(t) and x(t) do not overlap, so their product is zero.
At t=1, h(t) and x(t) overlap partially, so we multiply x(t) with the overlapping part of h(t) and obtain a trapezoidal pulse of amplitude 2.
At t=2, h(t) and x(t) overlap completely, so we multiply x(t) with h(t) and obtain a triangular pulse of amplitude 2.
Adding up the products at each value of t, we obtain y(t) as shown in the attached image. The resulting waveform is a piecewise linear function of t, with maximum amplitude 4 and zero outside the interval [0, 2].
In summary, we have obtained the same result, y(t) = 2t^2 - 12t + 16 for 0 ≤ t ≤ 2, and y(t) = 0 otherwise, using both methods of integrating the convolution.
To know more about convolution refer here :
https://brainly.com/question/31656685#
#SPJ11
Hii please HELP ME
30. The point does not lie on the circle.
31. The point lies on the circle.
32. The point does not lie on the circle.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The point will lie on the circle if the distance between the point and the center is less than the radius.
Hence each point is classified as follows:
sqrt((2 - (-1))² + (4 - 1)²) = sqrt(18) > 4, not on the circle.sqrt(17 + 8²) = sqrt(81) = 9, lies on the circle.sqrt((3 - 2)² + (-9 - 0)²) = sqrt(82) > sqrt(10), not on the circle.More can be learned about the distance between two points at https://brainly.com/question/30347465
#SPJ1
a bin contains 5 red balls and 9 blue balls. the following experiment is repeated several times: remove a ball from the bin, observe its color, and replace it. what is the probability that the 5th ball drawn is red and the 8th ball drawn is blue?
The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
To learn more about probability visit : brainly.com/question/30034780
#SPJ4
The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
To learn more about probability
brainly.com/question/30034780
#SPJ4