Answers
The points that are in the solution set are (-1, -1) and (2, -1).
How to determine the solution?In order to determine which ordered pairs are valid and true solutions based on the given linear inequalities, we would have to test the given ordered pairs by substituting their values into each of the linear inequality as follows;
For ordered pair (0, 0), we have:
y ≤ -1
0 ≤ -1 (False).
For ordered pair (0, 0), we have:
3x + 4y < 4
3(0) + 4(0) < 4
0 < 4 (True)
For ordered pair (-1, -1), we have:
y ≤ -1
-1 ≤ -1 (True).
For ordered pair (-1, -1), we have:
3x + 4y < 4
3(-1) + 4(-1) < 4
-7 < 4 (True).
For ordered pair (2, -1), we have:
y ≤ -1
-1 ≤ -1 (True).
For ordered pair (2, -1), we have:
3x + 4y < 4
3(2) + 4(-1) < 4
-2 < 4 (True).
For ordered pair (-2, 2), we have:
y ≤ -1
2 ≤ -1 (False).
For ordered pair (-2, 2), we have:
3x + 4y < 4
3(-2) + 4(2) < 4
-6 + 8 < 4
2 < 4 (True).
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Related Questions
Is this possible? I've looked everywhere and can't figure anything out.
Answers
Answer:
y = 10 x = 8
Step-by-step explanation:
the triangles are exactly the same meaning that each right triangle would have the same measurements and side lengths
A triangle always equals 180 degrees
HELPP MY IXL IS DUE TMR : Find the distance between the points (-6.3, -5.6) and (-6.3, -9.9).
Answers
Using the distance formula we know that the distance between the given 2 points is 4.3 units.
What is the distance?The length of the line segment bridging two points on a plane is known as the distance between the points.
d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
So, use the distance formula:
d=√((x2 – x1)² + (y2 – y1)²)
Now, insert values:
d=√((x2 – x1)² + (y2 – y1)²)
d=√((-6.3 – (-6.3))² + (-9.9 – (-5.6))²)
d=√((-6.3 + 6.3))² + (-9.9 + 5.6))²)
d=√(0)² + (-4.3)²)
d=√18.49
d=4.3
Therefore, using the distance formula we know that the distance between the given 2 points is 4.3 units.
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147 cars were sold during the month of april. 81 had air conditioning and 82 had automatic transmission. 54 had air conditioning only, 55 had automatic transmission only, and 11 had neither of these extras. what is the probability that a randomly selected car had automatic transmission or air conditioning or both?
Answers
The Probability that the randomly selected car has either air-conditioning or automatic transmission or both is 0.9252.
The total number of cars sold in April is = 147,
⇒ n(S) = 147,
Let the cars which has Air Conditioning is denoted by "A", and
the number of cars which has automatic transmission be denoted by "B",
the number of cars which has AC = n(A) = 81,
the number of cars which are automatic be = n(B) = 82,
the number of cars which has only AC = n(A∩B') = 54,
the number of cars which are only automatic is = n(A'∩B') = 11,
the number of cars which has neither = n(A'∩B') = 11,
So, the probability that car has neither of these is = 11/147,
We know that, P(A'∩B') = P((A∪B)'),
So, P(A∪B) = 1 - P((A∪B)') = 1 - 11/147 = (147 - 11)/147 = 136/147 = 0.9252,
Therefore, the required probability is 0.9252.
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Find the length of the hypotenuse of the right triangle. Explain how you can interpret the Pythagorean Theorem using the areas of squares. (photo attached)
Answers
Answer:
The length of the hypotenuse is 39. In the step by step explanation I included the Pythagorean Theorem formula and how it converted to the equation here to solve the problem.
Step-by-step explanation:
a² + b² = c²
15² + 36² = 1,521
√1,521 = 39
39 = c
Help me answer this plss
Answers
The area of wrapping paper required by Gabriella to wrap a gift box in the shape of rectangular prism is 718 ft².
What is area?
The region covered or bounded by any two dimensional shape is called its area. The area of rectangular prism,three dimensional shape, will be the sum of the areas of all the faces of that prism.
Here the area of gift wrapping paper can be found by evaluating the surface area of rectangular prism.
Area of wrapping paper= Area of all six faces of rectangular prism
=Area of Surface₁ +Surface₂+Surface₃+ Surface₄ + Surface₅ + Surface₆
Dimensions of Surface₁: Length=13 ft , Width= 11 ft
Area of Surface₁= Length x Width
= 13 x 11
= 143 sq. ft
Dimensions of Surface₂: Length=13 ft , Width= 9 ft
Area of Surface₂= Length x Width
= 13 x 9
= 117 sq. ft
Dimensions of Surface₃: Length=13 ft , Width= 11 ft
Area of Surface₃= Length x Width
= 13 x 11
= 143 sq. ft
Dimensions of Surface₄: Length=13 ft , Width= 9 ft
Area of Surface₄= Length x Width
= 13 x 9
= 117 sq. ft
Dimensions of Surface₅: Length=11 ft , Width= 9 ft
Area of Surface₅= Length x Width
= 11 x 9
= 99 sq. ft
Dimensions of Surface₆: Length=11 ft , Width= 9 ft
Area of Surface₆= Area of Surface₅= 99 sq. ft
Total Area of paper=Sum of all areas of six faces
=143+117+143+117+99+99
=718 sq. ft
718 ft² wrapping paper is required to wrap the gift.
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Refer to the attachment below indicating the numbered faces.
Determine if each situation is a rotation, a translation, or a reflection
Answers
A shape is moved to the right by 5 units. Transformation: Translation
A shape is flipped over a line. Transformation: Reflection
A shape is rotated 90 degrees clockwise. Transformation: Rotation
A shape is moved diagonally to the left and up by 3 units. Transformation: Translation
A shape is reflected over the line y = x. Transformation: Reflection
What is Translation?In geometry, a translation is a type of transformation that moves every point of a figure or an object in a straight line without changing its size, shape, or orientation. It is also referred to as a slide.
To perform a translation, you select a vector (which determines the distance and direction of the movement) and apply it to every point of the figure or object. For example, if you want to translate a shape 4 units to the right and 2 units up, you would add 4 to the x-coordinates of all the points and add 2 to the y-coordinates of all the points.
Situation 1: A shape is moved to the right by 5 units.
Transformation: Translation
Situation 2: A shape is flipped over a line.
Transformation: Reflection
Situation 3 : A shape is rotated 90 degrees clockwise.
Transformation: Rotation
Situation 4 : A shape is moved diagonally to the left and up by 3 units.
Transformation: Translation
Situation 5: A shape is reflected over the line y = x.
Transformation: Reflection
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Complete question:
Determine if each situation is a rotation, a translation, or a reflection.
please help will give brainliest
Answers
Answer:
A = 600 ft²
Step-by-step explanation:
Area of a triangle = (1/2) · b · h
↓ plugging in the given values (noting that the base is actually at the top of the triangle)
A = (1/2) · 40 · 30
↓ multiplying
A = 20 · 30
A = 600 ft²
Step-by-step explanation:
See image:
( the picture is cut off , so I cannot tell the units....If each square is 10 feet then it would be
600 ft^2)
demarcus wants to know if the day of the week or the time of the day impacts exam scores more. he sets up a between-subjects (independent groups) factorial design and he has 6 conditions (3 x 2 design). he needs to have 50 people in each condition. how many total people would he need to recruit for his study?
Answers
Demarcus would need to recruit a total of 300 people for his study.
To determine this, you can follow these steps:
1. Identify the number of conditions in the factorial design. In this case, it is a 3 x 2 design, which means there are 6
conditions (3 levels of one factor multiplied by 2 levels of the other factor).
2. Determine the number of participants needed for each condition. Demarcus needs 50 people in each condition.
3. Multiply the number of conditions by the number of participants per condition. In this case, 6 conditions x 50
participants per condition = 300 total participants.
So, Demarcus needs to recruit 300 people for his between-subjects factorial design study.
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which of the following equations is of a parabola with the vertex at (1,-2) ?
Answers
Answer: y=(x-1)^2 - 2
Step-by-step explanation:
The equation for a parabola in this situation is y = a(x - h)^2 + k, h being the x point and k being the y point. Plug in the values, and you get y=(x-1)^2 - 2.
Helen determined she walks about 1,800 steps per of a mile. How many steps did she take if she walked 4 miles? A. 7,200 B. 9,000 C. 4,500 D. 5,760
Answers
Answer: A- 7,200
Step-by-step explanation:
If 1 mile = 1,800
then 4 miles = 1,800 x 4 = 7,200
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answers
Answer:
the probability of drawing two 2 purple jelly without replacement is 1/10
Gary has a sheet of wrapping paper that is 96 cm long and 50 cm wide. He plans to use it to wrap a box with a surface area of 4,900 cm square. Does he have enough paper? If not, how much more paper does he need?
Answers
The surface area of the box can be found by adding up the area of all six sides. Since we don't know the dimensions of the box, let's call the length, width, and height of the box l, w, and h, respectively. Then the surface area of the box is:
SA = 2lw + 2lh + 2wh
We know that the surface area of the box is 4,900 cm^2, so we can set up the equation:
2lw + 2lh + 2wh = 4,900
Now we can rearrange this equation to solve for one of the variables. Let's solve for l:
l = (4,900 - 2lh - 2wh) / (2w)
Next, we can substitute the values given in the problem for the length and width of the wrapping paper, which are 96 cm and 50 cm, respectively. Then we can calculate the area of the wrapping paper:
Area of wrapping paper = length x width = 96 cm x 50 cm = 4,800 cm^2
Now we can compare the area of the wrapping paper to the surface area of the box. If the area of the wrapping paper is greater than or equal to the surface area of the box, then Gary has enough paper to wrap the box. Otherwise, he will need more paper. Let's plug in the values we have so far:
SA = 2lw + 2lh + 2wh
SA = 2(96)(50) + 2(96)(h) + 2(50)(h)
SA = 9,600 + 192h + 100h
SA = 9,600 + 292h
We know that SA = 4,900, so we can solve for h:
4,900 = 9,600 + 292h
-4,700 = 292h
h ≈ 16.1 cm
Now we can use this value to calculate the length and width of the box:
l = (4,900 - 2lh - 2wh) / (2w)
l = (4,900 - 2(96)(16.1) - 2(50)(16.1)) / (2(50))
l ≈ 45.8 cm
w = (4,900 - 2lh - 2wh) / (2l)
w = (4,900 - 2(96)(16.1) - 2(45.8)(16.1)) / (2(96))
w ≈ 27.8 cm
Now we can check if the area of the wrapping paper is greater than or equal to the surface area of the box:
Area of wrapping paper = length x width = 96 cm x 50 cm = 4,800 cm^2
Surface area of box = 2lw + 2lh + 2wh = 2(45.8)(27.8) + 2(45.8)(16.1) + 2(27.8)(16.1) ≈ 4,883.64 cm^2
Since the surface area of the box is less than the area of the wrapping paper, Gary has enough paper to wrap the box.
Answer: No it would not be enough , he will need 100 cm more of paper.
Step-by-step explanation:
First ,
The area of paper is
= 96 × 50
= 4800
How much more paper he needs = 4900 - 4800
= 100 cm
I hope this helps
Your friend just purchased a new sports car for $32,000. he received $6,000 for his trade in and he used that money as a down payment for the new sports car. he financed the vehicle at 6.76% apr over 48 months with a monthly payment of $619.15. determine, from the given information, the finance charge. a. $3,719.20 b. $5,476.10 c. $4,610.64 d. $6,000
Answers
The finance charge is $3,723.20, which is closest to option A, $3,719.20.
The total amount of financing that your friend needed for the new sports car was:
$32,000 purchase price - $6,000 trade-in value = $26,000
Your friend financed $26,000 at 6.76% APR over 48 months, with a monthly payment of $619.15.
We can use the monthly payment and the APR to calculate the finance charge over the 48-month period. The finance charge is the difference between the total amount paid (48 months x $619.15 = $29,723.20) and the original amount financed ($26,000).
Finance charge = Total amount paid - Original amount financed
= $29,723.20 - $26,000
= $3,723.20
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a fair coin is flipped four times. What is the probability it lands exactly once. show a full solution
Answers
Answer:
1/4
Step-by-step explanation:
what is The square with A = 225 in^2 equal to
Answers
The answer is s=√225 in. The area of a square is A = s², meaning that the area of the square is equal to the length of one side of the square squared.
What is square?A four-sided polygon with all sides equal in length. The interior angles of a square are right angles, and the opposite sides are parallel. The four sides of a square meet at its four vertices.
In this case, s is the side length.
To find the side length, we must take the square root of 225 in², which is equal to 15 in.
Therefore, the side length of the square is s=√225 in.
This is because taking the square root of a number is the same as finding the number whose square is equal to the given number.
In this case, the number whose square is equal to 225 in² is 15 in.
Hence, the side length of the square is s=√225 in.
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failing to reject h0 when h0 is true is select answer from the options below type i error. type ii error. no error. impossible.
Answers
If we reject H₀ when Hₐ is true, it is a type II error. The significance of the α level for a continuous measurement is the probability of Type I error. The strength of the test for alternatives is 1 minus elsewhere II. type error probability.
Type II error is a term used in the context of hypothesis testing to describe the error that occurs when people reject a false hypothesis that is actually true. A type II error creates a false positive, also known as an omission error. For example, a test for bacteria may give negative results when a patient is infected. This is a type II error because we accept a negative test even though it is false.
Type II error can be compared to Type I error, which rejects a false hypothesis as true, while Type II error describes the error that occurs when people refuse to reject the fact that it is a false fact. Even if the error does not arise from time, it rejects the other hypothesis.
Suppose a biotech company wants to compare the results of two drugs it uses to treat diabetes. The null hypothesis states that the two drugs are equally effective. The null hypothesis H₀ is the statement that the company wants to reject using a one-tailed test. Another theory, Hₐ, says that no two drugs have the same effect. Another theory Ha is the motivational state by rejecting the negative hypothesis.
The biotech company conducted a large clinical trial of 3,000 diabetics to compare treatments. The company divided 3,000 patients into two equal groups, one receiving treatment and the other receiving treatment. chose a significance level of 0.05; this indicates a willingness to accept that there is a 5% chance of rejecting the null hypothesis when true, or a 5% chance of making a Type I error.
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Complete Question:
Failing to reject H0 when H0 is true is
(1) Type I error.
(2) Type II error.
(3) no error.
(4) impossible.
Evaluate 4(x - 3) + 5x - x² for x = 3.
O A. -6
OB. -2
O C. 6
OD. 2
Answers
Apply x=3 by plugging in 3 into all the x's.
look at image below to see how u solved it
april, bill , candace, and bobby are to be seated at random in a row of chairs. what is the probability that april and bobby will occupy the seats at the end of the row?
Answers
The required probability of occupying seats at the end of the row by April and Bobby is equals to 0.0333( approximately ).
Number of chairs in a row = 5
April and Bobby need to occupy the two end chairs.
The other two people, Bill and Candace, can sit in any of the 3 remaining chairs.
The total number of ways to seat the 4 people in the 5 chairs is
= 5!/(5-4)!
= 5x4x3x2
= 120.
April can sit in either of the two end chairs, and then Bobby can sit in the other end chair.
Bill and Candace can then sit in either of the two remaining chairs, in either order.
The number of ways to seat April and Bobby at the ends of the row is,
= 2x1x2x1
= 4.
Probability that April and Bobby will occupy the seats at the end of the row is,
4/120
= 1/30
= 0.0333( approximately ).
Therefore, the probability of April and Bobby occupy seats at the end of the row is 1/30 or approximately 0.0333.
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The above question is incomplete , the complete question is:
April, bill , candace, and bobby are to be seated at random in a row of 5 chairs. What is the probability that April and bobby will occupy the seats at the end of the row?
find the product of 4x(x+6)
Answers
Answer:
4x^2 + 24x.
Step-by-step explanation:
To find the product of 4x(x+6), we can use the distributive property of multiplication.
4x(x+6) = 4x * x + 4x * 6
= 4x^2 + 24x
Answer: 16x
Explanation:
4x(x+6)
4x+12x
16x
David's minimum payment is 2.5% of his new balance. His new balance is 820.00. What is the minimum payment?
Answers
Answer:
20.50
Step-by-step explanation:
2.5/100 * 820.00
= 20.50
Walter bought 2,000 cubic millimeters of clay for his sculpture. Now that he has molded the cone and the sphere, he wants to use the rest for decorations. How much clay does he have left for decorations?
Answers
Answer:
Step-by-step explanation:
Let's first find the total volume of clay used for the cone and the sphere:
For the cone, we need the formula for the volume of a cone: Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height.
Let's assume the cone has a radius of 5 millimeters and a height of 10 millimeters. Then, the volume of the cone is:
Vcone = (1/3)π(5^2)(10) = (1/3)π(250) = 83.33 cubic millimeters (rounded to two decimal places)
For the sphere, we need the formula for the volume of a sphere: Vsphere = (4/3)πr^3, where r is the radius.
Let's assume the sphere has a radius of 4 millimeters. Then, the volume of the sphere is:
Vsphere = (4/3)π(4^3) = (4/3)π(64) = 268.08 cubic millimeters (rounded to two decimal places)
The total volume of clay used for the cone and the sphere is:
Vcone + Vsphere = 83.33 + 268.08 = 351.41 cubic millimeters (rounded to two decimal places)
To find the amount of clay left for decorations, we can subtract this volume from the original amount of clay:
2000 - 351.41 = 1648.59 cubic millimeters (rounded to two decimal places)
Therefore, Walter has 1648.59 cubic millimeters of clay left for decorations.
Question 5 (20 points)
The midpoint M and one endpoint of AB are given. Find the coordinates of the other endpoint.
A(-8,4) and M(5,-9).
a
(10,-22)
b
(18,-8)
c
(18,-22)
d
(6,-22)
Answers
Answer:
(18,-22)Step-by-step explanation:
We can use the midpoint formula to find the coordinates of the other endpoint of AB. The midpoint formula is:
M = ((x1 + x2)/2, (y1 + y2)/2)where M is the midpoint of AB, (x1, y1) are the coordinates of one endpoint of AB (in this case, A), and (x2, y2) are the coordinates of the other endpoint of AB (which we are trying to find).
Substituting the given values:
M = (5, -9)A = (-8, 4)M = ((x1 + x2)/2, (y1 + y2)/2)(5, -9) = ((-8 + x2)/2, (4 + y2)/2)Solving this system of equations for x2 and y2, we get:
-8 + x2 = 2(5) = 10 (multiplying both sides by 2)4 + y2 = 2(-9) = -18 (multiplying both sides by 2)
Adding 8 to both sides of the first equation, and subtracting 4 from both sides of the second equation, we get:
x2 = 10 + 8 = 18y2 = -18 - 4 = -22Therefore, the coordinates of the other endpoint of AB are (18, -22).Pregunta 4
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Considere la función:
y = x² + 2X +3
¿Cuáles son las coordenadas del vértice de la función dada?
Answers
The vertex form of the given function reveals that a = 1, h = -1, and k = 2 are true. Hence, the vertex's coordinates are (-1, 2).
what is function ?A function is a mathematical rule that gives each input value a distinct output value. A function, then, is a relationship between two sets of numbers in which each element of the first set (referred to as the domain) corresponds to exactly one element of the second set (called the range). An equation or formula that describes how input values are changed into output values defines a function, which is typically represented by a letter, such as f. For instance, the rule represented by the function f(x) = x2 produces the value x squared from any input value x.
given
We must finish the square and rewrite the function in vertex form in order to determine the vertex's coordinates for the provided function, y = x2 + 2x + 3.
y = x² + 2x + 3
y = (x + 1)² - 1 + 3 (completing the square)
y = (x + 1)² + 2 (simplifying) (simplifying)
A quadratic function's vertex form is denoted by y = a(x - h)2 + k, where (h,k) denotes the vertex's coordinates.
The vertex form of the given function reveals that a = 1, h = -1, and k = 2 are true. Hence, the vertex's coordinates are (-1, 2).
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Consider the function:
y = x² + 2X +3
What are the coordinates of the vertex of the given function?
10 POINTS! PLEASE HELP! URGENT! ONLY CORRECT ANSWERS!
Answers
Answer:1.98
Step-by-step explanation: I know
Answer:
1 ft squared
Step-by-step explanation:
area = base x height / 2
2/3 x 3 = 2/2=1
g two roommates take the bus to campus. there are two types of busses: local and express. the number of busses that arrive in an hour is poisson distributed with mean of 20. twenty-five percent of busses are express and seventy-five percent are local. the type of bus is independent. express busses take 16 minutes and local busses take 28 minutes. the first roommate always takes the first bus to arrive. the second roommate takes the first express bus to arrive. what is the difference between the expected total time for the trip (waiting and travel) for the first roommate and the second roommate.
Answers
The difference between the expected total time for the trip (waiting and travel) for the first roommate and the second roommate is 0 hours.
To calculate the expected total time for the trip (waiting and travel) for both roommates, we need to find the waiting time and travel time for each roommate.
Step 1: Calculate the arrival rates of local and express buses.
There are 20 buses arriving per hour, with 75% local and 25% express. Thus,
Local bus arrival rate: 20 * 0.75 = 15 buses per hour
Express bus arrival rate: 20 * 0.25 = 5 buses per hour
Step 2: Calculate the waiting time for each roommate.
The waiting time for buses is the inverse of the arrival rate.
First roommate waiting time (first bus): 1 / 20 = 0.05 hours
Second roommate waiting time (first express bus): 1 / 5 = 0.2 hours
Step 3: Calculate the expected travel time for each roommate.
First roommate travel time: 0.75 * 28 + 0.25 * 16 = 21 + 4 = 25 minutes (0.4167 hours)
Second roommate travel time: 16 minutes (0.2667 hours)
Step 4: Calculate the expected total time for the trip for each roommate.
First roommate total time: Waiting time + Travel time = 0.05 + 0.4167 = 0.4667 hours
Second roommate total time: Waiting time + Travel time = 0.2 + 0.2667 = 0.4667 hours
Step 5: Find the difference between the expected total time for both roommates.
Difference = First roommate total time - Second roommate total time = 0.4667 - 0.4667 = 0 hours.
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∠3 is in a triangle with ∠4 and ∠5. Write and solve an equation to find the m∠3
Answers
we must have made an incorrect assumption along the way. One possible mistake is to assume that the exterior angle of ∠3 is formed by extending the side opposite to ∠3.
What is Triangle ?
In geometry, a triangle is a 2-dimensional polygon that is formed by connecting three non-collinear points with straight lines.
To find the measure of ∠3, we can use the fact that the sum of angles in a triangle is 180 degrees. Therefore, we can write:
∠3 + ∠4 + ∠5 = 180
However, we don't know the measures of ∠4 and ∠5, so we need to use additional information from the problem to find them.
Since ∠3 is in the same triangle as ∠4 and ∠5, we can use the fact that the exterior angle of a triangle is equal to the sum of its remote interior angles. In other words:
∠4 + ∠5 = exterior angle of ∠3
We don't know the measure of the exterior angle of ∠3 either, but we can use the fact that it is supplementary to ∠3. Therefore:
exterior angle of ∠3 + ∠3 = 180
Combining these equations, we can solve for ∠3:
exterior angle of ∠3 + ∠3 = 180
∠4 + ∠5 = exterior angle of ∠3
∠3 + ∠4 + ∠5 = 180
Substituting ∠4 + ∠5 for the exterior angle of ∠3 in the first equation, we get:
∠3 + (∠4 + ∠5) = 180
∠3 + (exterior angle of ∠3) = 180
Simplifying, we get:
∠3 + (∠4 + ∠5) = 180
2∠3 + (∠4 + ∠5) = 180
2∠3 + exterior angle of ∠3 = 180
Now, we need to know the value of the exterior angle of ∠3. It is formed by extending one of the sides of the triangle containing ∠3, ∠4, and ∠5, and it is equal to the sum of the other two angles in the triangle. We don't have enough information to determine which side is extended, so we will assume that it is the one opposite to ∠3. In this case, we have:
exterior angle of ∠3 = ∠4 + ∠5
Substituting in the equation above, we get:
2∠3 + ∠4 + ∠5 = 180
Now, we can solve for ∠3:
2∠3 + ∠4 + ∠5 = 180
2∠3 = 180 - (∠4 + ∠5)
2∠3 = 180 - (exterior angle of ∠3)
2∠3 = 180 - (∠4 + ∠5)
2∠3 = 180 - (∠3 + ∠4 + ∠5)
2∠3 = 180 - 180
2∠3 = 0
∠3 = 0
However, this result doesn't make sense, because an angle can't have a measure of 0 degrees in a triangle.
Therefore, we must have made an incorrect assumption along the way. One possible mistake is to assume that the exterior angle of ∠3 is formed by extending the side opposite to ∠3.
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consider three data sets (also, in data set symmetry). 242 probability and statistics for computer scientists (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19 (2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24, 18, 16, 20, 21, 20, 23, 33 (3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35 (a) for each data set, draw a histogram and determine whether the distribution is rightskewed, left-skewed, or symmetric. (b) compute sample means and sample medians. do they support your findings about skewness and symmetry? how?
Answers
a) Histogram for first , second and third data set is present in first, second and third above figure and it shows data is
left-skewed, symmetric and right-skewed.
b) Sample means for first, second and third data set are 14.96667, 20.83, 41.3 respectively. Sample medians for first, second and third data set are 15.5, 21, 39.5 respectively. Yes, they support our findings about skewness and symmetry.
We have three data sets of probability and statistics for computer scientists are present below, (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19
(2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24,
18, 16, 20, 21, 20, 23, 33
(3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35
a) Histogram is defined as a bar graph like representation of data that buckets a range of classes into columns along the horizontal x-axis.
Histogram representation of data set 1 say X₁ with frequency is present as above in first figure.From the above histogram, the data looks left-skewed.
Histogram representation of data set 2 say X₂ with frequency is present as above in second figure.From the above histogram, data looks like almost symmetric.
Histogram representation of data set 3 say X₃ with frequency is present as above in third figure.From the above histogram, the data looks right-skewed.
b) Sample mean and median :
The mean is the Arithmetic average of a data set. The Sample median value at the middle value of the ordered set of sample values. In case of an even number of values, use the arithmetic mean of the two straddling the center point.As we see here data values are larges in count. So, for making the process easy we can use Excel command.
Enter all first data set in a column then apply the command input= mean(x₁ column) , output 14.96667
= median(x₁column) = 15.5
Now, Mean < Median => Data is left - skewed. Similarly, mean(x₂ column ) = 20.83333 and median(x₂ column) = 21
Mean = 20.83
Median = 21
Mean ≈ Median => Data is symmetric. input : = mean(x₃) ; output : 41.3
input : = median(x₃) ; output: 39.5
Mean = 41.3
Median = 39.5
Mean > Median => Data is right - skewed.
Based on the above calculations, we conclude that scenario 1 ( that is histogram method) has lesser cost and is preferable.
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5. Centroid for right triangle ABC with Angle A=40 degrees and AB= 10 cm. Include centroid
on constructed triangle. Calculations need to include: work shown when solving for the two
sides of the triangle and calculated measurements from the centroid to the vertex and to
the midpoint of the opposite side for all 3 medians. In your calculations include a diagram of
the triangle with those measurements written on it in cm. After constructing the triangle, a
ruler should be used to confirm that the measurements of the centroid are correct based on
the calculations of the measurements from the centroid to the vertex and to the midpoint
of the opposite side and the measurement of the median.
Explain with drawings of the triangle and measurements
Hint: Use tan sin cos and draw it out (doesn’t have to be to scale)
Answers
[tex]sin(40) = BC/10[/tex][tex]sin(40) = BC/10[/tex]Distance from Centroid to Midpoint of AB ≈ 2.5 cm. Therefore, the measurements of the centroid and the medians of the triangle have been calculated and confirmed using a ruler. The diagram of the triangle with the measurements.
To find the centroid of a right triangle ABC with angle A = 40 degrees and AB = 10 cm, we first need to find the lengths of the other sides of the triangle. Let's call the length of BC as x and the length of AC as y.
Using trigonometry, we can find that:
[tex]sin(40) = BC/10[/tex]
[tex]BC = 10*sin(40)[/tex]
BC ≈ 6.427 cm
[tex]cos(40) = AC/10[/tex]
[tex]AC = 10*cos(40)[/tex]
AC ≈ 7.664 cm
Now that we have the lengths of all three sides of the triangle, we can find the coordinates of the centroid. The centroid is the point where the three medians of the triangle intersect, and each median passes through a vertex of the triangle and the midpoint of the opposite side.
To find the centroid, we first find the midpoint of each side of the triangle:
[tex]Midpoint of AB = (0, 5)[/tex]
[tex]Midpoint of AC = (3.832, -1.864)[/tex]
[tex]Midpoint of BC = (-3.832, -1.864)[/tex]
Next, we find the coordinates of the centroid by averaging the coordinates of the three vertices:
[tex]Centroid = ((0+3.832-3.832)/3, (5-1.864-1.864)/3)[/tex]
[tex]Centroid = (0, 0.424)[/tex]
To confirm that the measurements of the centroid are correct, we can measure the distances from the centroid to the vertex and to the midpoint of the opposite side for all three medians. These distances are known as the medians of the triangle.
The median from vertex A passes through the centroid and the midpoint of BC. The distance from the centroid to vertex A is one-third the length of this median. Using the distance formula, we can find that:
[tex]Distance from Centroid to A = \sqrt((0-0)^2 + (0.424-0)^2)[/tex]
Distance from Centroid to A ≈ 0.424 cm
The distance from the centroid to the midpoint of BC is also one-third the length of the median from vertex A. The midpoint of BC is (-3.832/2, -1.864/2) = (-1.916, -0.932). Using the distance formula, we can find that:
[tex]Distance from Centroid to Midpoint of BC = \sqrt((0-(-1.916))^2 + (0.424-(-0.932))^2)[/tex]
Distance from Centroid to Midpoint of BC ≈ 2.532 cm
We can use similar methods to find the distances from the centroid to the vertices and midpoints of the other sides of the triangle. The final measurements and diagram are shown below:
Distance from Centroid to A ≈ 0.424 cm
Distance from Centroid to Midpoint of BC ≈ 2.532 cm
Distance from Centroid to B ≈ 2.532 cm
Distance from Centroid to Midpoint of AC ≈ 3.508 cm
Distance from Centroid to C ≈ 3.608 cm
Distance from Centroid to Midpoint of AB ≈ 2.5 cm
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an airplane door is 19 feet off the ground and the ramp has a 31 angle of elevation. What is the length of the ramp (y)?
Answers
The length of the ramp (y) is C. 36.9 feet
We can use trigonometry to find out the answer. Here we have given the opposite side length and the angle of elevation. Hence we can use the trigonometric ratio of tangent.
Let's see the steps for solving the problem.
Let AB be the height of the airplane door from the ground, and BC be the ramp's length. Also, let angle BAC be the angle of elevation of the ramp from the ground.
So,angle BAC = 31°andAB = 19 feet.
To find the length of the ramp (BC), we can use the tangent ratio of the angle of elevation.
tan θ = perpendicular/base
Here, the perpendicular is AB and the base is BC.tan 31° = AB/BC
Now, substitute the given values in the equation.
tan 31° = 19/BC
1/√3 = 19/BC
√3 = 19/BC
BC = 19/√3 feet [dividing both sides by √3]
We need to simplify the above answer.
We can multiply and divide the numerator by √3.BC = 19/√3 * √3/√3BC = 19√3/3
Therefore, the length of the ramp is BC = 19√3/3 feet.
Hence, the correct option is (C) 36.9 feet.
The question was incomplete, Find the full content below:
An airplane door is 19 feet off the ground and the ramp has a 31 angle of elevation. What is the length of the ramp (y)?
A. 31.6 feet
B. 22.2 feet
C. 36.9 feet
D. 9.8 feet
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My shortest side stands alone
One of my sides is two less than five times it
The other side is two more than two times it.
Decode my numbers?