The statements that are true are:
→ Line Segment KL ≅ Line Segment JM
→ Quadrilateral JKLM is a trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.
According to the given informationIn the quadrilateral JKLM
Using the distance formula, we can find the lengths of the line segments:
JK = √[(7-3)² + (8-5)²] = √58
KL = √[(13-7)² + (5-8)²] = √58
LM = √[(13-13)² + (0-5)²] = 5
JM = √[(13-3)² + (0-5)²] = √109
From this, we can analyze each statement:
a.) Line Segment KL ║ Line Segment JM
We can see from the sketch that the two line segments are not parallel. Therefore, statement a is false.
b.) Line Segment KL ≅ Line Segment JM
We found that the length of KL is equal to the length of JM. Therefore, statement b is true.
c.) Line Segment JK ≅ Line Segment LM
We can see from the sketch that the two line segments are not congruent. Therefore, statement c is false.
d.) Line Segment JK ║ Line Segment LM
We can see from the sketch that the two line segments are perpendicular. Therefore, statement d is false.
e.) Quadrilateral JKLM is a trapezoid.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. We can see from the sketch that line segments KL and JM are not parallel, but line segments JK and LM are parallel. Therefore, statement e is true.
f.) Quadrilateral JKLM is an isosceles trapezoid.
An isosceles trapezoid is defined as a trapezoid with congruent base angles and congruent non-parallel sides. We can see from the sketch that neither the base angles nor the non-parallel sides are congruent. Therefore, statement f is false.
Therefore, the statements that are true are b and e.
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Answer:
A) KL⎯⎯⎯⎯⎯∥JM⎯⎯⎯⎯⎯
C) JK⎯⎯⎯⎯⎯≅LM⎯⎯⎯⎯⎯⎯
E) Quadrilateral JKLM is a trapezoid.
F) Quadrilateral JKLM is an isosceles trapezoid.
Step-by-step explanation:
These where the correct answer I got when taking the assignment with that question
In how many ways can a committee of two men and one women be formed from a group of ten men and eight women?
Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman.
What is number?Numbers are mathematical units of measurement and labelling. It is a sign or collection of symbols that are used to represent a quantity, usually a real or integer number.
Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman. The idea of combination can be used to arrive to this number.
Calculating the number of possible combinations of a given number of things is done mathematically using the concept of combination. C(n,r) = n! / (r! (n - r)!), where n is the total number of items and r is the number of things to be picked at a time, is the formula used to compute it. In this instance, r is the number of persons to be picked, which is 3, and n is the total number of people to be chosen from the group, which is 18, consisting of 10 males and 8 women.
As a result, there are a total of 10 ways for men and 8 ways for women to form a committee of two men and one woman C(18,3) = 18! / (3! (18 - 3)!) = 18! / (3! 15!) = 1320.
Thus, there are 1320 different methods to create a committee of two men and one woman out of a group of ten men and eight women.
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PLEASE HELP!!! This is due tomorrow and I haven’t had the time to finish since I have after school activities
Answer:
y int: (0, -23)
Step-by-step explanation:
first you find the slope by taking two points and substituting it in rise over run ([tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex])
I used 25-13/-72+54 which eventually simplified to -2/3
You then use point slope form and plug in one pair of points
I used (-36,1) since it seemed the easiest
y-1=[tex]\frac{-2}{3}[/tex](x+36) point slope form: [tex]y-y_{1}=m(x-x_{1} )[/tex]
y-1= [tex]\frac{-2}{3} x-\frac{72}{3}[/tex]
y-1=[tex]\frac{-2}{3} x-24[/tex]
y=[tex]\frac{-2}{3} x-23[/tex]
the number without the variable is always y int regardless of the numbers in the equation
therefore, the y int is (0,-23)
what is trigonometry
trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)
Which of the following combinations of side lengths would NOT form a triangle with vertices X, Y, and Z? A. XY = 11 mm , YZ = 12 mm , XZ = 18 mm B. XY = 16 mm , YZ = 12 mm , XZ = 23 mm C. XY = 16 mm , YZ = 17 mm , XZ = 18 mm D. XY = 11 mm , YZ = 12 mm , XZ = 28 mm
the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.
How to solve the question?
To determine whether a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Let's check each option:
A. XY = 11 mm, YZ = 12 mm, XZ = 18 mm
To form a triangle, we need to check whether the sum of any two sides is greater than the third side. Let's check:
XY + YZ = 11 mm + 12 mm = 23 mm > XZ = 18 mm
YZ + XZ = 12 mm + 18 mm = 30 mm > XY = 11 mm
XY + XZ = 11 mm + 18 mm = 29 mm > YZ = 12 mm
All the combinations are greater than the third side, so a triangle can be formed with these side lengths.
B. XY = 16 mm, YZ = 12 mm, XZ = 23 mm
Let's check whether the sum of any two sides is greater than the third side:
XY + YZ = 16 mm + 12 mm = 28 mm > XZ = 23 mm
YZ + XZ = 12 mm + 23 mm = 35 mm > XY = 16 mm
XY + XZ = 16 mm + 23 mm = 39 mm > YZ = 12 mm
Again, all the combinations are greater than the third side, so a triangle can be formed with these side lengths.
C. XY = 16 mm, YZ = 17 mm, XZ = 18 mm
Let's check whether the sum of any two sides is greater than the third side:
XY + YZ = 16 mm + 17 mm = 33 mm > XZ = 18 mm
YZ + XZ = 17 mm + 18 mm = 35 mm > XY = 16 mm
XY + XZ = 16 mm + 18 mm = 34 mm > YZ = 17 mm
All the combinations are greater than the third side, so a triangle can be formed with these side lengths.
D. XY = 11 mm, YZ = 12 mm, XZ = 28 mm
Let's check whether the sum of any two sides is greater than the third side:
XY + YZ = 11 mm + 12 mm = 23 mm < XZ = 28 mm
YZ + XZ = 12 mm + 28 mm = 40 mm > XY = 11 mm
XY + XZ = 11 mm + 28 mm = 39 mm > YZ = 12 mm
The first combination is less than the third side, so a triangle cannot be formed with these side lengths.
Therefore, the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.
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1. Calculate the perimeter, area and volume a) Classroom with Length=10m, breadth=8m and height=3m b) Box with Length=40cm, breadth=25cm and height=30cm c) Cabinet with length=80cm, breadth=70cm and height=2m Area Volume 26 a b C Perimeter
a) Classroom:
Perimeter = 2(length + breadth) = 2(10m + 8m) = 36m
Area = length x breadth = 10m x 8m = 80m^2
Volume = length x breadth x height = 10m x 8m x 3m = 240m^3
What is the perimeter, area and volume?b) Box:
Perimeter = 2(length + breadth) = 2(40cm + 25cm) = 130cm
Area = 2(length x breadth + length x height + breadth x height) = 2(40cm x 25cm + 40cm x 30cm + 25cm x 30cm) = 41500cm^2
Volume = length x breadth x height = 40cm x 25cm x 30cm = 30000cm^3
c) Cabinet:
Perimeter = 2(length + breadth) = 2(80cm + 70cm) = 300cm
Area = 2(length x breadth + length x height + breadth x height) = 2(80cm x 70cm + 80cm x 2m + 70cm x 2m) = 12640cm^2
Volume = length x breadth x height = 80cm x 70cm x 2m = 112000cm^3
Note: It's important to use consistent units in calculations. In this case, I converted the dimensions to a common unit (meters or centimeters) before performing the calculations.
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Project Option 1
For this option, you will work individually.
Instructions
For this option, you will work individually.
You’ve worked hard in this module to become a pro at equations! Now, you’ll put your skills to the test. Your job is to create an equations portfolio. The format is up to you. Be creative! You may use a slideshow, document, video, etc. As long as all of the parts of the project are addressed, the delivery is up to you.
Your portfolio must include a minimum of the following five types of equations and solutions:
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable. Once you have created each equation, you will solve it and show your work. Pretend that you are teaching the equations to a new pre-algebra student. Or you can actually teach them to a sibling or friend!
This is a total of 7 equations and solutions.
Equations are used to solve different types of problems in mathematics and in the real world.The five types of equation are 2x = 8,2y/2 = 8/2, (1/2)x + 2 = 3,3(x+4)= 21,0.4x + 1.2 = 2.6.
What is Equations Portfolio?
Equations are an essential part of mathematics and have various applications in real-world problems. In this portfolio, we will cover different types of equations and solve them step by step. This portfolio will cover one-step equations, equations with fractions, equations with the distributive property, and equations with decimals.
One-step equations are equations that can be solved in one step. For example, if we have the equation 2x = 8, we can solve it by dividing both sides by 2. Let's solve two one-step equations,
3x = 15
Dividing both sides by 3
3x/3 = 15/3
x = 5
Again,
2y = 8
Dividing both sides by 2
2y/2 = 8/2
y = 4
Equations with fractions are equations that contain fractions. To solve these equations, we need to clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. Let's solve two equations with fractions:
(1/2)x + 2 = 3
Subtracting 2 from both sides
(1/2)x = 1
Multiplying both sides by 2 (LCM of 1/2)
(1/2)x × 2 = 1 × 2
x = 2
(2/3)y - 1 = 3
Adding 1 to both sides
(2/3)y = 4
Multiplying both sides by 3 (LCM of 2/3)
(2/3)y × 3 = 4 × 3
y = 6
Equations with distributive property are equations that involve distributing a number or a variable to the terms inside the parentheses. Let's solve an equation with the distributive property,
3(x + 4) = 21
Distributing 3 to (x + 4)
3x + 12 = 21
Subtracting 12 from both sides
3x = 9
Dividing both sides by 3
x = 3
Equations with decimals are equations that contain decimal numbers. To solve these equations, we need to clear the decimals by multiplying both sides of the equation by a power of 10. Let's solve an equation with decimals,
0.4x + 1.2 = 2.6
Subtracting 1.2 from both sides
0.4x = 1.4
Multiplying both sides by 10 (power of 10 for one decimal place)
0.4x × 10 = 1.4 × 10
4x = 14
Dividing both sides by 4
x = 3.5
Now let's solve a real-world problem using an equation,
Sarah has $500 in her bank account. She wants to buy a dress for $120 and save the rest of the money. How much money will Sarah save?
Let x be the amount of money Sarah saves.
Total money = $500
Money spent on the dress = $120
Money saved = Total money - Money spent on the dress
x = 500 - 120
x = 380
Therefore, Sarah will save $380.
In conclusion, equations are used to solve different types of problems in mathematics and in the real world.
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The five types of equation are 2x = 8,2y/2 = 8/2,(1/2)x + 2 = 3,3(x + 4) = 21,0.4x + 1.2 = 2.6.
What is Equations Portfolio?Equations are an essential part of mathematics and have various applications in real-world problems. In this portfolio, we will cover different types of equations and solve them step by step. This portfolio will cover one-step equations, equations with fractions, equations with the distributive property, and equations with decimals.
One-step equations are equations that can be solved in one step. For example, if we have the equation 2x = 8, we can solve it by dividing both sides by 2. Let's solve two one-step equations,
3x = 15
Dividing both sides by 3
3x/3 = 15/3
x = 5
Again,
2y = 8
Dividing both sides by 2
2y/2 = 8/2
y = 4
Equations with fractions are equations that contain fractions. To solve these equations, we need to clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. Let's solve two equations with fractions:
(1/2)x + 2 = 3
Subtracting 2 from both sides
(1/2)x = 1
Multiplying both sides by 2 (LCM of 1/2)
(1/2)x × 2 = 1 × 2
x = 2
(2/3)y - 1 = 3
Adding 1 to both sides
(2/3)y = 4
Multiplying both sides by 3 (LCM of 2/3)
(2/3)y × 3 = 4 × 3
y = 6
Equations with distributive property are equations that involve distributing a number or a variable to the terms inside the parentheses. Let's solve an equation with the distributive property,
3(x + 4) = 21
Distributing 3 to (x + 4)
3x + 12 = 21
Subtracting 12 from both sides
3x = 9
Dividing both sides by 3
x = 3
Equations with decimals are equations that contain decimal numbers. To solve these equations, we need to clear the decimals by multiplying both sides of the equation by a power of 10. Let's solve an equation with decimals,
0.4x + 1.2 = 2.6
Subtracting 1.2 from both sides
0.4x = 1.4
Multiplying both sides by 10 (power of 10 for one decimal place)
0.4x × 10 = 1.4 × 10
4x = 14
Dividing both sides by 4
x = 3.5
Now let's solve a real-world problem using an equation,
Sarah has $500 in her bank account. She wants to buy a dress for $120 and save the rest of the money. How much money will Sarah save?
Let x be the amount of money Sarah saves.
Total money = $500
Money spent on the dress = $120
Money saved = Total money - Money spent on the dress
x = 500 - 120
x = 380
Therefore, Sarah will save $380.
In conclusion, equations are used to solve different types of problems in mathematics and in the real world.
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Graph the solution of the inequality.
3.5
Find the measure of the line segment indicated, assume that lines which appear tangent, are tangent.
Find FS
Possible answers —>
A. 17
B. 21
C. None of the other answers are correct
D. 18
E. 45
The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18
What is the properties of intersecting chordsThe property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
UF × FS = VF × FT
8(10x - 1) = 9 × 16
80x - 8 = 144
80x = 144 + 8 {collect like terms}
80x = 152
x = 152/80 {divide through by 80}
x = 1.9
FS = 10(1.9) - 1 = 18
Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18
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Ned collected rocks at the beach. He placed 12 ounces of rocks in each of 4 different bags. How many ounces of rocks Ned collect?
Answer:
48 ounces
Step-by-step explanation:
12*4= 48
the mean iq of the population of osu students is 100. a random sample of 5 students will be taken from the population, but the first student scored 150. what do expect the average to be for the 5 students?
Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.
Explain average
The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.
According to the given information
Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:
Y = (X1 + X2 + X3 + X4 + X5) / 5
Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:
E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)
Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:
E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4
Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:
E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)
Thus, we can simplify the expression as:
E(Y|X1=150) = (4E(X) / 4) = E(X) = 100
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Fifteen children split $9 among themselves so that each child receives the same amount. How much did each child receive?
The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.
Total number of children is equal to 15
Total amount of money distributed among 15 children = $9
To find out how much each child receives,
We can divide the total amount of money by the number of children.
In this case, there are 15 children and $9 to split.
So, the amount of money each child receives is equal to,
(Total amount of money )/ ( total number of children )
= $9 ÷ 15
= $0.60
Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.
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What is the exact area of the trapezoid?
Answer:
135.07 mm2
Step-by-step explanation:
height = 10.39 mm
area = 135.07 mm2
Which comparison is not correct?
A. 1 > -9
B. 3 < 6
C. -8 > -6
D. -3 < 4
Answer:
The comparison that is not correct is:
C. -8 > -6
This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.
The other comparisons are correct:
A. 1 > -9 (true, because 1 is greater than -9)
B. 3 < 6 (true, because 3 is less than 6)
D. -3 < 4 (true, because -3 is less than 4)
write a equation of the line that passes through (2,7) and (0,-5)
Answer:
To write the equation of the line that passes through the points (2, 7) and (0, -5), we can use the slope-intercept form of a linear equation, which is:
y = mx + b
Where m is the slope of the line, and b is the y-intercept.
First, we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) = (2, 7) and (x2, y2) = (0, -5)
m = (-5 - 7) / (0 - 2)
m = -12 / -2
m = 6
So the slope of the line is 6.
Next, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Where (x1, y1) = (2, 7)
y - 7 = 6(x - 2)
Simplifying this equation, we get:
y - 7 = 6x - 12
y = 6x - 5
So the equation of the line that passes through the points (2, 7) and (0, -5) is y = 6x - 5.
Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
3 out of 7 questions. PLEASE help me.
Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar
Transforming the circles(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:
Translate the solid circle 2 units to the left and 2 units down.Dilate the solid circle by a scale factor of 2.Therefore, the blank spaces should be filled as follows:
Translate the solid circle 2 units to the left and 2 units down.
Dilate the solid circle by a scale factor of 2.
(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.
This is because all circles are similar
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If quadrilateral PQRS is a parallelogram, line segment QR is ≅ to line segment QT, and m∠TQR=60°, which angles are congruent to ∠S? Select all that apply.
a.) ∠P
b.) ∠PQR
c.) ∠RQT
d.) ∠QRT
e.) ∠SRQ
f.) ∠TQR
From the given information, you can deduce that triangle QTR is equilateral and equiangular (all angles are 60 degrees)
b, c, d, and f are true
The opposite angles of a parallelogram are congruent (b)
If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent (d)
Angle RQT is congruent to angle QRT, and angle QRT is congruent to angle S. By the transitive property, angle RQT is congruent to angle S (c)
Transitive property, like c (f)
I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these is true?
The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).
Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:
V_small = π(2²)(4) = 16π cubic inches
Using these dimensions, we can calculate the volume of the larger can using the same formula:
V_large = π(6²)(12) = 432π cubic inches
Now, let's compare the volumes of the small and large cans. We have:
V_large = 432π cubic inches > 16π cubic inches = V_small
Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:
V_large = 432π cubic inches 3
V_small = 3(16π) cubic inches = 48π cubic inches
We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.
Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.
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Complete Question:
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?
a) The radius of the larger can will be 5 inches.
b) The volume of the larger can will be 3 times the volume of the smaller can
c) The radius of the larger can will be 8 inches.
d) The volume of the larger can is 3 times the volume of smaller can
9.12 movie lovers, part ii. suppose an online media streaming company is interested in building a movie recommendation system. the website maintains data on the movies in their database (genre, length, cast, director, budget, etc.) and additionally collects data from their subscribers ( demographic information, previously watched movies, how they rated previously watched movies, etc.). the recommendation sys- tem will be deemed successful if subscribers actually watch, and rate highly, the movies recommended to them. should the company use the adjusted r2 or the p-value approach in selecting variables for their recommendation system?
The company should use the adjusted R² approach to select variables for their recommendation system, as it will better account for the influence of multiple variables and help create a more accurate model for predicting subscriber's movie ratings.
To build a successful movie recommendation system for the online media streaming company, it's important to consider the appropriate statistical approach for selecting variables.
In this case, the company should use the adjusted R² approach instead of the p-value approach.
The adjusted R² approach is more suitable for this scenario because it measures the proportion of variance in the dependent variable (subscriber's ratings) that is predictable from the independent variables (movie and subscriber data).
Adjusted R² takes into account the number of variables and adjusts for overfitting, which is important when dealing with a large dataset, like the one the streaming company has.
It helps in identifying the most influential factors and creating a model that better predicts movie ratings.
On the other hand, the p-value approach focuses on the statistical significance of individual variables, which might lead to including variables that are significant but not necessarily the best predictors for movie ratings.
This could result in a less accurate recommendation system.
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Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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A rectangular garden has a walkway around it. The area of the garden is 4(4.5x+3.5). The combined area of the garden and the walkway is 5.5(6x+5). Find the area of the walkway around the garden as the sum of two terms.
The product of two terms gives the walkway's area around the garden: 15x+13.5.
Define rectangleA rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.
Area of garden = 4(4.5x + 3.5) = 18x+14
The combined area of the garden and the walkway = 5.5(6x+5) =33x+27.5
The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:
Aw=combined area -Area of garden
=33x+27.5-18x-14
=15x+13.5
Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.
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I need this answer asap can someone help??
The shortest driving distance between the stadium and the animal shelter is given as follows:
10 blocks.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates are given as follows:
Animal shelter: (-3,3).Stadium: (6,2).Since the spaces are filled by houses, we cannot apply the formula, hence the shortest distance is:
6 - (-3) + 3 - 2 = 9 + 1 = 10 blocks.
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Kendra and her family went on a camping trip to Buffalo Springs State Park. This graph
shows how much fuel they used to cook food each day.
Amount of fuel
xx
←+ +
0
1
Submit
4
X
** ++
x X
2
Liters
314
How much fuel did they use in all?
Write your answer as a fraction, mixed number, or whole number.
liters
* Kendra and her family used:
** 4 liters of fuel on day 1
*** 3 liters of fuel on day 2
**** 2 liters of fuel on day 3
***** 4 liters of fuel on day 4
So in total they used:
4 + 3 + 2 + 4 = 13 liters of fuel
Therefore, the amount of fuel they used in all is:
13 liters
Gia made a garden stone shaped like a regular octagon with the dimensions shown. Find the area of the octagon.
5.5 in.
4.6 in
The area of the garden which is same as the shape of an octagon would be = 101.2in².
How to calculate the area of an octagon?To calculate the area of an octagon the formula that can be used is given below;
Area of an octagon = (number of sides × length of one side × apothem)/2
For an octagon = 8 sides
apothem = 5.5in
Length of one side = 4.6in
Area = 8×4.6×5.5/2
= 202.4/2
= 101.2in²
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ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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May anyone help with this question
Rounding to the nearest hundredth, the arc length of one slice is approximately 53.67 feet.
What is arc length?Arc length is the distance along the curved line or arc of a circle, measured in linear units such as centimeters, feet, or meters. It is calculated as the product of the radius of the circle and the angle subtended by the arc at the center of the circle, expressed in radians.
Here,
Since the circle is divided into eight equal slices, each slice is 360/8 = 45 degrees. The arc length of one slice can be calculated using the formula:
Arc length = (angle/360) x 2πr
where angle is the central angle in degrees, r is the radius of the circle, and π is the constant pi.
In this case, the diameter of the circle is 137 feet, so the radius is half of that, or 68.5 feet.
Substituting the given values into the formula, we get:
Arc length = (45/360) x 2 x 3.14 x 68.5
Arc length = 0.125 x 2 x 3.14 x 68.5
Arc length = 0.785 x 68.5
Arc length = 53.67 feet
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lee had scored the following points in his first 8 games 12,14,14,15,8,10,3,15 enter the number of points lee needs to score in the nest game to increase his keam score to 13 points PLS ANSER FASTE
Is the triangle equilateral, isoscele, or scalene?
Answer: This triangle is isoscele
Step-by-step explanation:
angles of triangles- does anyone know how to do this?
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°
(4) m∠1=88°m∠2=42° m∠3=113°
What is an angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.
Define triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles.
(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)
(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)
(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)
(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)
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