The assumed mean method is used to determine the mean or arithmetic mean of grouped data. If there is a large amount of data available, this method is suggested over calculating the mean directly.
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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Ms. Powell’s class voted on where to go for a field trip. The museum received 11 votes, and the aquarium received 16 votes. What is the ratio of votes for the aquarium to votes for the museum? Suppose 3 students who voted to go to the aquarium changed their votes to the museum. How would the ratio change?
2909/2000
Based on the given conditions, formulate: 16 divided by 11
Evaluate the equation/expression: 1.4545
Convert decimal into fraction: 14545/10000
Reduce the fraction: 2909/2000
Answer: 2909/2000
What is the nature of roots x2 5 0?
The nature of the roots of the equation x^2 - 5 = 0 is real and unequal.
We know that the general form of a quadratic equation is:
ax^2 + bx + c =0
The equation we have is:
x^2 - 5 = 0
Comparing the given equation with the general form of a quadratic equation, we get that:
a = 1, b= 0, and c = -5
If D = b^2 - 4ac > 0, then we say that the roots of the quadratic equation are real and unequal.
Here, (0)^2 - 4x1x(-5) = 20 >0,
hence we conclude that nature of the roots of the equation x^2 - 5 = 0 is real and unequal.
The question is incomplete, the complete question is:
x^2 - 5 = 0.
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What is the solution of y 3x 5?
The linear equation y = 3x + 5 has an infinitely many solutions.
Define the term solution of linear equation?We looked for as many solutions as possible to the given equation.
y = 3x + 5 is a linear equation with two variables as of ax + by + c = 0.
Thus,
Put x = 0, y = 0 + 5 = 5. Thus, (0, 5) is one solution.Put x = 1, y = 3 × 1 + 5 = 8. Thus, (1, 8) is another solution.Put y = 0, 3x + 5 = 0, x = -5/3. Thus, (-5/3, 0) is another solution.We are aware that for various values of x, we obtain varied values for y. As a result, any value that may be used to replace x with in given equation will result in another answer. As a result, there are an infinite number of unique solutions that can be derived by replacing x in the above linear equation with real numbers.A linear equation with two variables hence has an endless number of solutions.
y = 3x + 5 thus has an endless number of solutions.
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The correct question is-
What is the solution of y = 3x + 5?
What is multiplicative formula?
Answer:
like a ratio
Step-by-step explanation:
A multiplicative comparison involves comparing two quantities such that when one is multiplied by a specified number, the other is produced. For example, Sam has twice as many balloons as Sid. Sid has 3 balloons.
What is root formula?
Answer:Square Root Formula
The square root formula of a number, x is given as,
√x = x1/2
Suppose, x is any number such that, x = y × y, the formula to calculate the square root of x will be,
√x = √(y × y) = y
where, y is the square root of any number x. This also means that if the value of y is an integer, then x would be a perfect square.
Step-by-step explanation:
How many pyramids can fit inside a rectangular prism if both figures have the same measure of bases?
3 pyramids can fit inside a rectangular prism if both figures have the same measures of bases.
what is pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.
The ratio of volume of pyramid and a prism is 1:3 when they have the same base and height.
A cylinder with the same radius and height is precisely filled with the contents of three conical cups. A prism with the same base and height as three rectangular-base pyramids is exactly filled with their contents.
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A rhombus, which is a quadrilateral with 4 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are (2, 0), (7, 0), (5, 4), and (10, 4). How long is each side of the rhombus?.
Answer:
5 units
Step-by-step explanation:
You want to know the side length of the rhombus with vertices (2, 0), (7, 0), (5, 4), and (10, 4).
Side lengthYou can find the length of the horizontal edges by counting the grid squares, or by subtracting the x-coordinates:
7 -2 = 5
10 -5 = 5
The slanted sides are each the hypotenuse of a 3-4-5 right triangle, so are also 5 units long. (You expect all of the sides of the rhombus to be the same length.)
Each side is 5 units long.
The answer is 5, 4.47, 5, and 8.94.
Step 1: Determine the length of the sides using the distance formula.The distance formula is d = √(x2-x1)^2 + (y2-y1)^2
Step 2: Calculate the length of the first side. To do this, plug in the coordinates for the two points that make up the first side into the distance formula. This side is formed by the points (2, 0) and (7, 0).d = √(7-2)^2 + (0-0)^2
d = √(5)^2 + (0)^2
d = √(25) + (0)
d = 5
Step 3: Calculate the length of the second side. To do this, plug in the coordinates for the two points that make up the second side into the distance formula. This side is formed by the points (7, 0) and (5, 4).d = √(5 - 7)^2 + (4 - 0)^2
d = √(-2)^2 + (4)^2
d = √4 + 16
d = √20
d = 4.47
Step 4: Calculate the length of the third side. To do this, plug in the coordinates for the two points that make up the third side into the distance formula. This side is formed by points (5, 4) and (10, 4).d = √(10 - 5)^2 + (4 - 4)^2
d = √25 + 0
d = 5
Step 5: Calculate the length of the fourth side. To do this, plug in the coordinates for the two points that make up the fourth side into the distance formula. This side is formed by the points (10, 4) and (2, 0).d = √(2 - 10)^2 + (0- 4)^2
d = √(-8)^2 + (-4)^2
d = √64 + 16
d = √80
d = 8.94
Therefore, each side of the rhombus has a length of 5, 4.47, 5, and 8.94.
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please help it’s due today by 10pm
The size of the angle C is θ = 56°, given that BC and DE are tangents to the circle.
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
Considering the Isosceles triangle ∆AOB and its exterior angle ∠BOD;
∠BOD = 180° - 2(48) {exterior angle of a triangle equals 2 opposite interior angles}
∠BOD = 96°
If the line DE is extended to line BC at E' we will have a quadrilateral BODE' and a triangle ∆CE'D, hence;
∠B = ∠D = 90° (angles between radius and lines tangent to the circle)
so;
∠BOD + ∠OBD + ∠ODE' + ∠BE'D = 360° {sum of interior angles of a quadrilateral}
96° + 90° + 90° + ∠BE'D = 360°
276° + ∠BE'D = 360°
∠BE'D = 360° - 276° {subtract 276° from both sides}
∠BE'D = 84°
Considering triangle ∆CE'D;
∠DE'C = 180° - 84° {sum of angles on a straight line}
∠DE'C = 96°
We thus derive θ using the triangle ∆CE'D;
θ = 180° - (28 + 96)° {sum of interior angles of a triangle}
θ = 180° - 124°
θ = 56°
In conclusion, we have derived the size of the angel θ as 56° by proper application of the tangent to a circle theorem.
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a restaurant offers the following limited lunch menu. main courses: turkey, spaghetti, meatloaf, shrimp, hamburger vegetables: peas, squash, cauliflower, eggplant beverages: coffee, tea, milk, soda, shakes desserts: sundaes, mousse, pie, brownies if one item is selected from each of the four groups, in how many ways can a meal be ordered? there are ways a meal can be ordered
800 ways meal be ordered.
There are 5 main courses to choose from, so there are 5 ways to choose a main course. There are 4 vegetables to choose from, so there are 4 ways to choose a vegetable. There are 5 beverages to choose from, so there are 5 ways to choose a beverage. And there are 4 desserts to choose from, so there are 4 ways to choose a dessert.
The total number of ways to order a meal is the product of the number of choices for each category.
So there are 5 * 4 * 5 * 4 = 800 ways to order a meal.
Hence, 800 ways meal be ordered.
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Given y1(t) = t^2 is a solution to: t^2y'' - 4ty' + 6y = 0, t > 0 find another solution using the method of reduction of order.
For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.
Given solution to t²y'' - 4ty' + 6y = 0 is
y₁(t) = t²
Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,
y₂ = vt²
y₂' = 2vt + t²v'
y₂'' = 2v + 2tv' + 2tv' + t²v''
y₂'' = 2v + 4tv' + t²v''
Substituting this
t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0
t⁴v'' = 0
v'' = 0
v' = c, c is a constant
v = ct
Therefore, y₂(t) = ct×t²
y₂ (t) = ct³
Therefore general solution will be y(t) = c₁t² + c₂t³
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FL
Intro
2
2
y
E
What is the y-coordinate of point D after a translation of
(x, y) - (x+6, y - 4)?
D'(3.5,
Done
Answer:
(3,1)
Step-by-step explanation:
(x+ 6, y -4)
The x tells us the movements are right or left. Right would be a positive movement and left would be a negative movement.
The y tells us the movements are up or down. Up would be a positive movement and down would be a negative movement.
D is at the point ( -3,5)
(x + 6, y -4) Is telling us that from the point of D, move right 6 spaces and down 4 spaces. You will know be at the point (3,1).
helpp, please!
Andre wanted to measure the width of a creek by his camp but cannot get to the other side of the creek. Andre decided to construct two triangles to determine the width of the creek indirectly. Sighting the position of a tree on the opposite bank of the creek and placing 4 wooden pegs at point N, O, P, and Qas shown in the figure such that MN is perpendicular to NP, NP is perpendicular to PQ, and O is the midpoint of NP. Andre claims that AMNO and AQPO are congruent.
Part A: Provide a valid argument, using geometry theorems or postulates, to validate Andre's claim that AMNO and APQO are congruent.
Part B: Which segment should Andre measure to determine the width of the creek? Explain why.
Answer:
Step-by-step explanation:
Part A: you can just restate parts of the text to make a vaild argument or you can make you own
Part B: he should measure N, O, P and Qas
Triangles MNO and QPO are congruent. To find the width of the creek, Andre should find the measurement of NP
What is congruent triangles?When two triangles are congruent, their corresponding three sides and their three angles match precisely.
Given that
O is the midpoint of NP,
NP is perpendicular to MN, and
NP is perpendicular to PQ.
When two lines intersect at a specific point, the opposite angles formed in this situation are equal.
a) Then ∠MNP =∠QPO=90°
∠MON=∠QOP
Also, NO = OP (by the definition of midpoints)
Therefore, Triangles MNO and QPO are congruent by ASA rule
And,
b) To find the width of the creek, Andre should find the measurement of NP, because according to the figure the width is represented by NP. He should find NO and OP and then add it.
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PLEASE HELP Identify the factorization of 36 + 25x^2.
!!WILL HAVE IMAGINARY NUMBERS!!
Answer:
x = (6 i)/5 or x = -(6 i)/5
Step-by-step explanation:
Solve for x:
25 x^2 + 36 = 0
Subtract 36 from both sides:
25 x^2 = -36
Divide both sides by 25:
x^2 = -36/25
Take the square root of both sides:
Answer: x = (6 i)/5 or x = -(6 i)/5
How do you tell if a system has no solution or infinitely many?
The system of linear equations are said to have no solution if they are parallel to each other or have infinitely many solutions if they are coincident.
Considering two system of equations:
y1 = mx +c and y2 = px+ q.
The lines are said to be parallel if their slopes m and p are equal but the y intercepts c and q are not equal. Which further concludes that the system of equations has no solution.
The lines are said to be coincident if their slopes m and p are equal along with the y intercepts c and q being equal. And hence we conclude that the system of equations have infinitely many solutions.
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Population density is the number of people per unit of area. The population density of a certain region is 50 people per square kilometer. If the region covers 26 square kilometers, what is the population of the region?
The population of the region is 1300 people.
How to calculate the population?It should be noted that population simply means the number of people on a particular region or area. Population density is the number of people per unit of area.
Since the population density of a certain region is 50 people per square kilometer and the region covers 26 square kilometer, the population will be:
= Number of square kilometers × Number of region
= 50 × 26
= 1300
The population is 1300 people.
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What does it mean to be closed under addition and subtraction?
The set of rational numbers is closed under addition, subtraction, multiplication, and division (division by zero is not defined) because if you complete any of these operations on rational numbers, the solution is always a rational number. -1 and 1.
What is a closed set ?
A Closed Set Math has a way of explaining a lot of things, and one of those explanations is called a closed set.
Closure property holds for addition and multiplication of whole numbers. The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number. The difference between any two whole numbers may or may not be a whole number. Hence, the whole numbers are not closed under subtraction.
According to the given question:
A set is closed under addition if you can add any two numbers in the set and still have a number in the set as a result. A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set.
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How do you find the inverse of a function with an inequality?
Remove the parentheses before performing the reverse operations of addition and subtraction, Remove the parentheses before reversing the process of division and multiplication, Flip The Inequality Sign When Adding, Subtracting, or Multiplying By A Negative Number.
What is a function?An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the input x.A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.Hence, Remove the parentheses before performing the reverse operations of addition and subtraction, Remove the parentheses before reversing the process of division and multiplication, Flip The Inequality Sign When Adding, Subtracting, or Multiplying By A Negative Number.
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In the figure, j∥k and m∠2 = 117°.
What is the m∠3?
Enter your answer in the box. |__|
Step-by-step explanation:
angle3 is the supplementary angle to angle2.
that means together they are 180°.
180 = 117 + angle3
angle3 = 180 - 117 = 63°
What is the equation in slope-intercept form of the line that crosses the x-axis at 36 and is perpendicular to the line represented by y equal minus 4 over 9 x plus 5?.
The equation in slope-intercept form of the line that crossed the x-axis at 36 and is perpendicular to the line represented by y = -4/9x + 5 is y = 9/4 ( x ) + 36
Given :
line equation is y = -4/9 x + 5
We have to find the line equation which is perpendicular to the given line in slope intercept form.
y = mx + c where m is slope and c is intercept.
slope m = -4/9
perpendicular slope = -1/m
= -1 / -4 / 9
= 9 / 4
x - intercept of x - axis = 36
so the equation is y = 9/4 ( x ) + 36 .
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the national average family size was reported as 3.18. a random sample of 24 families in one school district had a mean of 3.83 and a standard deviation of 1.43. at the 5% level of significance, does the average family size in this school district differ from the national average? assume the distribution is approximately normal.
As pert the t-test there is sufficient evidence that the average family size in this school district differ from the national average.
Let us assume null and alternate hypothesis.
H₀ = Average family size is 3.18
Hₐ = Average family size is not 3.18
The value of t = (Sample Mean - 3.18) / s/√n
where,
Sample Mean = 3.83
n = 24
s = 1.43
So, t = (3.83 - 3.18) / (1.43 / √24)
t = 2.2268
Degree of freedom = n - 1 = 23
The p-value = 0.0360
As the p-value <0.05, so the null hypothesis will be rejected.
Therefore, there is enough proof to conclude that this school district's average family size is different from the national average.
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please give a step by step explanation
∡ABD and ∡BAD = ∡55°
As we can see Δ ABD is isosceles
so,
∡ABD = ∡BAD (let us assume them to be ∡F)
Therefore
∡ABD+∡BAD+∡ADB = 180°
2∡F+∡ADB = 180°
2∡F + 70° = 180°
∡F = 55°
∡ABD = ∡BAD = 55°
Now
∡ABD + ∡CBD = 180° (Supplementary Angles)
55° + ∡CBD = 180°
∡CBD = 125°
As the sum of all the angles in a triangle is 180°
∡BDC +∡DCB +∡CBD = 180°
∡BDC + 29° +125° = 180°
Hence
∡BDC = 26°
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How to find x+y?
(Explain pls, thank you!
The value of x+y is 289
What is an expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Given is an expression, x²+74x+2021=y²
On solving, we get
x²+2×37x + 37² = y²-652
(x+37)²= y²-652
(x+37)²- y² = -652
(x+y+37) (x-y+37) = 289 × -2
Thus, x+y+37 = 289......(i)
x-y+37 = -2.......(ii)
Solving the equations, we get
x = 125 & y=164
Therefore,
x+y = 125+164
= 289
Hence, The correct answer is x+y = 125+164 = 289
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as sunee improves her algebra skills, she takes 0.8 times as long to complete each homework assignment as she took to complete the preceding assignment. if it took her 70 minutes to complete her first assignment, find how long it took her to complete the fifth assignment. find the total time she took to complete her first five homework assignments
According to the sum of n terms in geometric progression, the total time she took to complete her first five homework assignments is 219 minutes.
The time taken to complete first assignment is 70 minutes.
She takes 0.8 times as long to complete each homework assignment as she took to complete the preceding assignment.
This shows that the given series is in geometric progression, where
a = first term = 70
r = common ratio = 0.8
The sum of first n terms in geometric progression is given by,
Sₙ = a (rⁿ - 1) / r - 1
S₅ = 70 (0.8⁵ - 1) / 0.8 - 1
S₅ = 219
Therefore, the total time she took to complete her first five homework assignments is 219 minutes.
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I need HUUUGGGE help
A square church hall had an area of 289m². What is half the perimeter?
Answer:
34 m
Step-by-step explanation:
s=side of square
A=Area of square
P = Perimeter of square
s*s = A
s*s = 289
s^2 = 289
s = [tex]\sqrt{289}[/tex]
s = 17 m
P = s + s + s + s
P = 4s
P = 4(17)
P = 68 m
68/2 = 34 m
When scale factor is greater than 1 your image gets?
By Dilation, if the scale factor is greater than 1 image gets enlarged.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.
Enlargement is the term used when a dilatation results in a larger image.
Reduction occurs when a dilatation results in a smaller picture.
As the scale factor of given question is greater than 1 it is Enlargement.
By Dilation, if the scale factor is greater than 1 image gets enlarged.
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please can you solve this question
since we have our two medians, we need to add them up 1st then divide the sum by two;
50+60
2
= 110
2
= 55
55 is the median
determine whether the following statement is true or not. the center of a confidence interval is always the point estimate for the population parameter. group of answer choices true false
The given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.
What is a confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
The point estimate for the population parameter is always the value at the center of a confidence range.
You have a 5% probability of being incorrect with a 95% confidence interval.
We have a 10% probability of being incorrect with a 90% confidence interval.
A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
Therefore, the given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.
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How do you find the mode in math examples?
The most common occurrence of a number or the one that does so most frequently is known as the mode of the data.
What do we mean by mode?A set of data values' mode is the value that appears the most frequently.
The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable.
In other words, it is the value that will be sampled most frequently.
The number that appears the most frequently, or the one that does so most frequently.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers {4, 2, 4, 3, 2, 2}.
Therefore, the most common occurrence of a number or the one that does so most frequently is known as the mode of the data.
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A florist ordered a shipment of red, blue, and white carnations to use for table decorations at a banquet. The ratio of red : blue : white carnations in the shipment is 3:1:2. There are 60 white carnations in the shipment. What is the total number of carnations in the shipment? 120 carnations 180 carnations 240 carnations 360 carnations.
As per the given ratio, the total number of flowers in shipment is 180.
The term Ratio in math basically compares quantities, which means that it shows the value of one quantity with respect to the other quantity.
Here we have given that the florist ordered a shipment of red, blue, and white carnations to use for table decorations at a banquet.
And we need to find the total number of carnations in the shipment.
While we looking into the given question, we know that the ratio of red : blue : white carnations in the shipment is 3:1:2.
Here we aloo know that there are 60 white carnations in the shipment
Then let us consider if a and b are two values, their ratio will be a:b,
Then the ratio of flowers is written as
=> red: blue: white = 3:1:2
Where red flowers are 3x, and the blue flowers are x, and the white flower are 2x.
So, the total number of flowers = 3x+x+2x = 6x
When we apply the value of whit\te flowers = 60
Then the value of x is calculated as,
=> 2x = 60
=> x = 30
Therefore, the total number of flowers = 6x = 6×30 = 180
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