Answer:
182859444
Step-by-step explanation:
You just have to times them together
a researcher wants to examine the effect of fertilizer and the effect of sunlight on the yield of tomatoes. she bought 60 tomato plants at a local garden store. she randomly assigned 30 tomato plants to be planted on the sunny side of the hill and 30 to be planted on the shady side. the 30 plants which are planted on the shady side are randomly assigned to one of three groups. the first group are grown with no fertilizer, the second group with a small amount of fertilizer, and the third group with a large amount of fertilizer. the 30 plants which are planted on the sunny side are likewise randomly assigned to one of three groups. the first group are grown with no fertilizer, the second group with a small amount of fertilizer, and the third group with a large amount of fertilizer. all tomato plants are planted at the same time and are all treated alike (in terms of how much they are watered, weeded, etc.), and the person who tends the plants does not know which group each is in. each plant is grown to maturity. the total weight of tomatoes obtained from each plant is recorded. Describe the design of the experiment (completely randomized or blocked).
Completely randomized over one factor (location), blocked by fertilizer
Blocked by fertilizer, blocked by location
Completely randomized over one factor (fertilizer)
Completely randomized over one factor (fertilizer), blocked by location
Completely randomized over two factors (fertilizer and location)
The design of the experiment is Completely randomized over two factors (fertilizer and location).
Randomization is a statistical technique used in experimental design to ensure that all possible combinations of the factors being studied are represented in the study groups. It is used to eliminate bias and control for confounding variables that may affect the outcome of an experiment.
The researcher randomly assigned the tomato plants to be planted on either the sunny or the shady side of the hill. This creates two groups or two levels of the factor "location". She also randomly assigned the tomato plants to one of three groups based on the amount of fertilizer given, creating three groups or three levels of the factor "fertilizer".
The random assignment of plants to the different groups for both factors helps to ensure that any differences in the yield of tomatoes is due to the independent variables (fertilizer and location) being tested, and not due to other extraneous factors.
Therefore, The design of the experiment is Completely randomized over two factors (fertilizer and location).
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my question was why the general solution of the linear second order homogeneous equation is represented as combination of two particular solutions
The general solution of a linear second order homogeneous equation is represented as the combination of two particular solutions.
This is because the linear second order homogeneous equation is of the form ax2+bx+c=0 and has two distinct roots, i.e. x1 and x2. The general solution of the equation can be written as y=C1y1+C2y2, where C1 and C2 are constants and y1 and y2 are the two particular solutions. The particular solutions can be derived from the two distinct roots of the equation using the formula y1=e^(x1*t) and y2=e^(x2*t). The constants C1 and C2 can be found by solving the linear combination of the two particular solutions for the given initial conditions of the equation. This gives the general solution of the linear second order homogeneous equation as a combination of the two particular solutions.
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At the store, there are 11 shelves with 27 pictures books and 12 shelves with 21 chapter books. How many fewer chapter books thank picture books does the store have
Answer:
45 fewer chapter books
Step-by-step explanation:
Picture books: 27 x 11= 297
Chapter books: 21 x 12= 252
297-252= 45
Indicate the equation of the given line in standard form. The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal. Show calculations.
The linear functions for each diagonal are given as follows:
Diagonal BD: y = x.Diagonal AC: y = -x.How to define the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For diagonal BD, the points are given as follows:
D(-3,-3) and B(3,3).
The slope is given by the change in y divided by the change in x, hence:
m = (3 - (-3))/(3 - (-3)) = 1.
Hence:
y = x + b.
When x = 3, y = 3, hence the intercept b is given as follows:
y = x.
The diagonals are perpendicular, meaning that the multiplication of their slopes is of -1, hence the slope of AC is of:
m = -1.
Hence:
y = -x + b
When x = -3, y = 3, hence the intercept b is given as follows:
3 = 3 + b
b = 0.
Hence the equation is:
y = -x.
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Doug smalley, a meteorologist, is married, earns $1,352.75 a week, and claims 1 allowance
The federal income tax withheld for Doug, given the fact Doug is married and claims 1 allowance is $ 149.
How to find the federal income tax withheld ?Using the Married Persons Weekly Payroll table, you can find the bracket that Doug Smalley belongs in which is $1, 350 - $ 1, 360.
When looking at this bracket, we see that the federal income tax withheld for a person in this bracket, who claims 1 withholding allowance, is $ 149.
The federal income tax for Doug Smalley who earns $ 1, 352.75 a week in 2016, is therefore $ 149.
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The full question is:
Use the Married Persons Weekly Payroll table to find the federal income tax withheld. Doug smalley, a meteorologist, is married, earns $1,352.75 a week, and claims 1 allowance.
the linear system l has augmented matrix which is row equivalent to the following. how many solutions does l have?
The linear system l has one solution. This can be determined by examining the augmented matrix to find the row echelon form. The row echelon form is a matrix with zeroes below the leading entries and all the leading entries are in different columns.
By converting the augmented matrix into the row echelon form, we can identify the number of variables and the number of equations. Since there are three equations and three variables in the row echelon form, the linear system l has one solution. The row echelon form of the given augmented matrix is
[tex]$\begin{bmatrix}1&-3&2&3\\0&-5&-9&-10\\0&0&4&5\end{bmatrix}$[/tex]
By counting the number of equations and variables in the row echelon form, it can be seen that there is only one solution for the linear system l. This is because the number of equations is equal to the number of variables, indicating that there is a single solution.
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the linear system l has an augmented matrix which is a row equivalent to the following. how many solutions does l have?
[tex]$\begin{bmatrix}1&-3&2&3\\-3&8&-11&-14\\2&-7&5&7\end{bmatrix}$[/tex]
A bank representative studies compound interest, so she can better serve customers. She analyzes what happens when $2,000 earns interest at a rate of 4% for 3 years. Part a) Find the ending balance if it is compounded continuously. Part b) Find the interest earned if it is compounded continuously
The ending balance if the amount is compounded continusoly is $6,244.84
The interest earned is $4,244.84.
What is the ending balance and the interest?If an amount is compounded continuously, it means that both the amount invested and the interest earned increases in value infinitely over the investment period.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateInterest = future value - amount invested
2000 x e^0.04 x 3 = $6,244.84
Interest = $6,244.84 - $2000 = $4,244.84
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• The floor in a computer lab has a width of 6x – 9 and a length of 6x + 9. Find the area of the floor. Each tile that will cover the floor has an area of 24x2- 12x – 36. Divide the two areas and tell how many tiles will be needed to cover the floor?
Answer: The area of the floor can be found by multiplying the width and the length.
Area of the floor = (6x - 9)(6x + 9) = 36x^2 - 63x - 81
The area of each tile can be found by evaluating the expression 24x^2 - 12x - 36.
Area of each tile = 24x^2 - 12x - 36
To find out how many tiles are needed to cover the floor we need to divide the area of the floor by the area of each tile.
Number of tiles needed = (36x^2 - 63x - 81) / (24x^2 - 12x - 36)
The division is simplified by canceling out common factors between the numerator and denominator, the number of tiles is a fraction that can't be simplified any further.
So the answer is (36x^2 - 63x - 81) / (24x^2 - 12x - 36) tiles are needed to cover the floor.
Step-by-step explanation:
Humber Practice Skills - Estimating REVISION AVAILABLE 2.29 + 9.11 15.381-5.414 7.631.11 + 5.99 5.734 + 6.893 18.355-4.411 Answer the following Estimate the sum or difference of the following decimal numbers by rounding to the nearest tenth. ? CALCULATOR AMI RIGHT E Criteria O Search hp Learning 33 NCFE M DON'T KNOW RESET ROU 11:21 24/01/2023
The solution to the expression with decimals rounded to the nearest tenth is: -2
Examine the hundredth number to round the decimal number to the nearest tenth. If the number is more than 5, multiply it by one. If it is less than 5, leave the tenth place value alone and eliminate any numbers after the tenth. 4.624, for example, is 4.6 rounded to the closest tenth.
Thus, given the expression:
2.29 + 9.11 + 15.381 - 5.414 - 7.631.11 + 5.99 - 5.734 + 6.893 - 18.355 -4.411
We first round them up to the nearest tenths is:
2.1 + 9.1 + 15.4 - 5.4 - 7.6 + 6.0 - 5.7 + 6.9 - 18.4 - 4.4 = -2
Thus, it is correct to state that the version of the above-given expression resolved to the nearest tenths (2.1 + 9.1 + 15.4 - 5.4 - 7.6 + 6.0 - 5.7 + 6.9 - 18.4 - 4.4) = -2
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what is the sum of -3 and -12 ?
Answer: The sum is -15
Step-by-step explanation:
5. If the bakery sold 144 cupcakes, write an inequality to represent the possible number of cakes sold
The required inequality to represent the possible number of cakes sold is Cupcakes ≥ 144.
What is inequality?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
According to question:
Write an inequality to illustrate the potential amount of cakes sold if the business sold 144 cupcakes.
So,
Bakery can sold 144 cupcakes and more
Cupcakes ≥ 144
Thus, required inequality is Cupcakes ≥ 144.
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Examine quadrilateral FGHI below. In order to determine the length of each * 5 points
side of the parallelogram, which of the following equations would need to
be used? Select two that apply.
The equations for the sides of the parallelogram would be
8x - 6 = 9x
y + 10 = 11y
Option (A) and (C) are correct.
What is a parallelogram?
A parallelogram is a four-sided shape with opposite sides that are parallel and congruent. In other words, opposite sides of a parallelogram are of equal length and parallel to each other. Additionally, opposite angles in a parallelogram are also congruent. It has two pairs of parallel sides. It can be thought of as a rectangle with opposite sides that are not necessarily at right angles to each other.
As the property of the parallelogram says
"Opposite sides of the parallelogram are equal"
So we can write
8x - 6 = 9x
y + 10 = 11y
Hence, The equations for the sides of the parallelogram would be
8x - 6 = 9x
y + 10 = 11y
Option (A) and (C) are correct.
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Julio is buying a car. He makes a down payment of 20%
and he makes arrangements to finance the remaining
$14,000
What is the dollar amount of Julio's down payment?
Julio's down payment would be 20% of the total cost of the car. If he is financing $14,000 of the remaining cost, the total cost of the car would be $14,000 / (1 - 0.20) = $14,000 / 0.80 = $17,500. Therefore, Julio's down payment would be $17,500 * 0.20 = $3,500.
What is a percentage in plain English?
A percentage is a portion of a total stated as a number between 0 and 100 as opposed to being expressed as a fraction. The percentages of everything are 100%, nothing is 0%, 50% of something is 50%, and nothing is 0%. To calculate the percentage, divide the component by the total and multiply the result by 100.
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Using percentage, Julio's down payment would be $3,500.
What does a % mean in everyday terms?In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.
Julio's down payment would be 20% of the total cost of the car.
If he is financing $14,000 of the remaining cost,
the total cost of the car would be
$14,000 / (1 - 0.20)
= $14,000 / 0.80
= $17,500.
Therefore, Julio's down payment would be $17,500 * 0.20 = $3,500.
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if sum a n and sum b n are series with positive terms, and lim a n/b n does not exist, and sum b n diverges, then sum a n diverges
Since lim a n/b n does not exist, it means that the ratio between a n and b n can be larger or smaller depending on the terms.
This implies that the rate of growth of a n and b n are not necessarily the same. If the series b n diverges, it means that the terms of b n increase without bound. Therefore, the terms of a n will also increase without bound, and sum a n will also diverge.
Formally, if lim a n/b n = ∞, then ∑ a n is divergent. We can prove this by contradiction. Suppose ∑ a n converges. Then by the comparison test, lim a n/b n must converge and be finite, which is a contradiction. Therefore, ∑ a n must diverge.
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the quality control manager at a factory records the number of equipment breakdowns each day. let the random variable y represent the number of breakdowns in one day. the standard deviation of y is 0.28. which of the following is the best interpretation of the standard deviation? responses the number of breakdowns on a randomly selected day is expected to be 0.28.
The best interpretation for the given standard deviation as per given information is given by :
Option D. On an average, the number of breakdowns per day varies from the mean by about 0.28.
As given in the question,
Standard deviation represents the measure of the data in a given set which varies or deviates from the mean. In the given information, the standard deviation of y is 0.28 for the number of equipment breakdowns each day means that on an average, the number of breakdowns each day deviates by 0.28 about the mean.This represents that the most of the data exists in the range of 0.28 above or below the mean. Standard deviation is a method to present the data which spread , it also help in learning the distribution of the given data set.Therefore, the best interpretation of standard deviation is :
Option D. On an average, the number of breakdowns per day varies from the mean by about 0.28.
The above question is incomplete , the complete question is:
The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?
A. The number of breakdowns on a randomly selected day is expected to be 0.28.
B. The number of breakdowns on a randomly selected day will be 0.28 away from the mean.
C. The average number of breakdowns per day for a random sample of days is expected to be 0.28
D. On average, the number of breakdowns per day varies from the mean by about 0.28.
E. The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.
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Select all of the conditions that prove that a quadrilateral is a rectangle.
A) Both pairs of opposite sides are congruent.
B) One pair of opposite sides is longer than the other pair of sides.
C) The diagonals bisect each other.
D) The diagonals are congruent.
E) The diagonals are perpendicular.
only C) The diagonals bisect each other, and E) The diagonals are perpendicular are the two conditions that prove that a quadrilateral is a rectangle.
What is the quadrilateral?
A quadrilateral is a four-sided polygon, which means it has four straight edges and four angles. Quadrilaterals can come in many different shapes and sizes and can be classified based on their properties. Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombi, and trapezoids.
A quadrilateral is a rectangle if it satisfies the following conditions:
C) The diagonals bisect each other.
E) The diagonals are perpendicular.
A) Both pairs of opposite sides are congruent, is not a necessary condition for a quadrilateral to be a rectangle, as a rectangle can have different side lengths.
B) One pair of opposite sides is longer than the other pair of sides, is not a necessary condition for a quadrilateral to be a rectangle, as a rectangle can have equal side lengths.
D) The diagonals are congruent, is not a necessary condition for a quadrilateral to be a rectangle, as a rectangle can have diagonals of different lengths.
So, only C) The diagonals bisect each other, and E) The diagonals are perpendicular are the two conditions that prove that a quadrilateral is a rectangle.
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The area of a triangle is 48 square inches. If the base of the triangle is 8 inches, what is the height?
Answer:
height = 12
Step-by-step explanation:
The formula for the area of a triangle is: [tex]\frac{1}{2}(b*h)[/tex] = A
A = area of a triangle
b = base
h = height
The problem states that the area (A) of triangle is 48, and the base (b) is 8, so we can plug those values into the equation above:
48 = [tex]\frac{1}{2}(8*h)[/tex]
Let's solve for h now:
48 = [tex]\frac{1}{2}8h[/tex]
48 = 4h
h = 48/4
h = 12
Answer:
12 inches
Step-by-step explanation:
Formulae (Area of a triangle): 1/2 × Measure of Base × Measure of Height
Given Information:
Area of triangle = 48 in²Measure of Base = 8 inSubstitute the information into the formula to create an equation;
⇒ 1/2 × Measure of Base × Measure of Height = Area of a triangle⇒ 1/2 × 8 in × Measure of Height = 48 in²Solve the equation to find out the measure of the height;
⇒ 4 in × Measure of Height = 48 in²⇒ Measure of Height = (48 in²)/(4 in)⇒ Measure of Height = (48 in)/(4) = 12 inchesTherefore, the measure of the height is 12 inches.
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6 1/5 multiplied by 2 2/3 equals
Answer:1325
Step-by-step explanation:
help math slope thingy
The machine can make 20 soda bottles each minute.
How to calculate the number of soda bottles?In Mathematics and Geometry, the slope of any straight line simply refers to the rate of change and it can be calculated by using this mathematical equation (expression);
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points located on the line:
Points on the x-coordinate = (5, 7).Points on the y-coordinate = (100, 140).Substituting the given points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (140 - 100)/(7 - 5)
Slope (m) = 40/2
Slope (m) = 20.
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A line passes through the point (-8, -9) and has a slope of Write an equation in slope-intercept form for this line.- 5/4
The equation in slope-intercept form for this line is y = -5/4x + 3.
What is the slope-intercept form of the line?
The slope-intercept form is a way of representing the equation of a straight line in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). The slope of a line represents the steepness of the line, and the y-intercept represents the point at which the line crosses the y-axis.
A line can be represented by two points (x1, y1) and (x2, y2) the slope can be calculated by the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the line passes through the point (-8, -9) and has a slope of -5/4, we can use the point-slope form of the equation of a line to find the equation of this line:
y - y1 = m(x - x1)
y - (-9) = (-5/4)(x + 8)
y = (-5/4)x + (-9) + (2*9)
y = (-5/4)x + 3
Hence, the equation in slope-intercept form for this line is y = -5/4x + 3.
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A shipping container will be used to transport several 100-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 5400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 100-kilogram crates that can be loaded into the shipping container.
The inequality to determine the number of 100-kilogram crates that can be loaded into the shipping container is 27500 ≤ 5400 + 100x
How to represent a situation with inequality?A shipping container will be used to transport several 100-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 5400 kilograms have already been loaded into the container.
Therefore, the inequality that can be used to determine x, the number of 100-kg crates that can be loaded into the shipping container can be calculated as follows:
27500 ≤ 5400 + 100x
where
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A teacher in a summer school program notices that her students seem less able to pay attention
when the temperature in the classroom gets warmer. The teacher decides to record the
temperature every day (utilizing Fahrenheit degrees) to track classroom heat conditions. The
measurement of the temperature used here used here is
1.
2.
3.
C
Nominal
r
Ordinal
Interval
Save
Ratio
The level of measurement used for the temperature is given as follows:
Interval.
How to obtain the levels of measurement of the data?There are four levels of measurement for the data, given as follows:
Nominal.Ordinal.Interval.Ratios.The measures of central tendency for each level are given as follows:
Nominal: ModeOrdinal: Mode and median.Interval: Arithmetic mean, mode and median.Ratios: Arithmetic mean, geometric mean, mode and median.For the temperature, we obtain the arithmetic mean, hence it has the level of measurement of interval.
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The augmented matrix of linear system has been reduced by rOw operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system: Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice 0 A: The solution set has exactly one element; (Type integers or simplified fractions 0 B. The solution set has infintely many elements The solution set is empty:
The original matrix's rank > the augmented matrix's rank. So the option C "the solution set is empty" is correct.
The matrix is
[tex]\left [ \begin{matrix}1 & 7&3 & -4\\ 0& 1& -1 & 3\\ 0& 0 & 0& 2\\ 0&0 & 1&1 \end{matrix} \right ][/tex]
To determine the solution set we simplify the given matrix by performing the row operations.
[tex]R_{4}\leftrightarrow R_{3}[/tex]
[tex]\left[\left.\begin{matrix}1 & 7 &3 \\ 0& 1 & -1\\ 0& 0 & 1\\ 0&0 &0 \end{matrix}\right|\begin{matrix}-4\\ 3\\ 1\\ 2\end{matrix}\right][/tex]
The rank of main matrix = 3
The rank of augmented matrix = 4
The rank of main matrix < The rank of augmented matrix
So, there is no solution. The solution set is empty.
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The complete question is:
The augmented matrix of linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system:
[tex]\left [ \begin{matrix}1 & 7&3 & -4\\ 0& 1& -1 & 3\\ 0& 0 & 0& 2\\ 0&0 & 1&1 \end{matrix} \right ][/tex]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice.
A: The solution set has exactly one element
B. The solution set has infinitely many elements
C. The solution set is empty
4(5x-3)-3(2x-5)=17 solve for x.
Answer:
x=1
Step-by-step explanation:
4(5x-3)-3(2x-5)=17
20x-12-6x+15=17
14x+3=17
-3. -3
14x=14
/14. /14
x=1
Please help! Anything helps with this one thank you!
The coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².
What is congruency?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given are two figures as shown in the image attached.
{ 1 } -
The image in question {12} cannot be proved congruent by AAS congruence rule.
{ 2 } -
For the triangles shown in question {13}, we can prove the triangles congruent by AAS rule as -
90° = 90° { Equal right angles }
Sides opposites to right angles are equal. So, the angles opposite to these angles {let x° and y°} will be equal. We can write -
x° = y°
Two equal sides given
Hence, triangles are proved AAS congruent rule.
Therefore, the triangles along with their respective congruency proofs are given above.
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find the bake if x and y
The value of x is 76°. The solution has been obtained using the properties of hexagon.
What is a hexagon?
A closed, two-dimensional, six-sided polygon in geometry is called a hexagon. It has six vertices, which together create six internal angles, and six line segments. The total of a hexagon's internal angles is 720°.
We know that sum of angles on a straight line is 180°.
So, on the first line with angle 60°, the other angle will be
180° - 60° = 120°
Similarly, on the second line with angle 64°, the other angle will be
180° - 64° = 116°
Similarly, on the third line with angle 36°, the other angle will be
180° - 36° = 144°
Similarly, on the fourth line with angle 48°, the other angle will be
180° - 48° = 132°
Similarly, on the fifth and sixth lines with angle x°, the other angles will be
180° - x° = (180-x)°
We know that sum of angles of interior angles of a hexagon is 720°
Therefore,
⇒ 120° + 116° + 144° + 132° + (180-x)° + (180-x)° = 720°
⇒ 512° + 180° - x° + 180° - x° = 720°
⇒ 872° - 2x° = 720°
⇒ 2x° = 152°
⇒ x = 76°
Hence, the value of x is 76°.
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Suppose the sample space for a continuous random variable is 0 to 100. If
the area under the density curve for the variable from 0 to 15 is 0.20, what is
the area under the density curve from 15 to 100?
The area under the density curve from 15 to 100 is 0.80.
How can you determine a continuous random variable's density?With pdf f and cdf f, consider X to be a continuous random variable.
By definition, integrating the pdf yields the cdf: F(x)=x∫−∞f(t)dt.
By differentiating the cdf, one may find the pdf according to the Fundamental Theorem of Calculus: f(x) = ddx[F(x)]
An interval or group of intervals makes up the sample space of a continuous random variable, X.
1- 0.20 0.80
[tex]\int\limits^[/tex] f(x) dx from 0 to 100 = 1
[tex]\int\limits^[/tex] f(x) dx from 0 to 15 + int 15 ^ 100 =1
[tex]\int\limits^[/tex] d from 15 to 100 =1-0.20=0.80.
The area under the density curve from 15 to 100 is 0.80.
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help me please asap!!
The scale factor for the dilation in this problem is given as follows:
2.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
As the side lengths are changed, with a dilation the figure loses it's congruence relative to the original figure.
The equivalent side lengths in this problem are given as follows:
AD, with length 8 - 0 = 8.DE, with length 8 - 4 = 4.The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:
k = 8/4 = 2.
(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).
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Find the equation of the regression line for the given data and use it to predict the value of y for x = −2.5. Round to the nearest thousandth.
x: -5, -3, 4, 1, -1, -2, 0, 2, 3, -4
y: -10, -8, 9, 1, -2, -6, -1, 3, 6, -8
For your data, the regression equation for Y is:
Y = 2.09697X - 0.55152
What is Linear function?
A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.
Given, a data set
x: -5, -3, 4, 1, -1, -2, 0, 2, 3, -4
y: -10, -8, 9, 1, -2, -6, -1, 3, 6, -8
Sum of X = -5
Sum of Y = -16
Mean X = -0.5
Mean Y = -1.6
Sum of squares (SSₓ) = 82.5
Sum of products (SP) = 173
Regression Equation = Y = bX + a
b = SP/SSₓ = 173/82.5 = 2.09697
a = Mₓ - bMₓ = -1.6 - (2.1*-0.5) = -0.55152
Y = 2.09697X - 0.55152
For x = 2.5 the value of y:
y = 2.09697* 2.5 - 0.55152
y = 4.69
Therefore, For your data, the regression equation for Y is:
Y = 2.09697X - 0.55152
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given: pr is parralel to vo; ro is parralel to pv; pr is congruent to ro prove: angle 1 and angle 2 are complementary
According to the information ∠1 and ∠2 are complementary to each other.
∠1 ⊥ ∠2
Since PR is parallel to VO and RO is parallel to PV, it follows that PR is congruent to RO. This means that ∠1 and ∠2 are supplementary angles and thus, complementary.
Since PR // VO and RO // PV, then by the Transitive Property of Congruence, VO // PV.
Since PR ≅ RO and VO // PV, then by the Corresponding Angles Postulate, ∠1 ≅ ∠2.
Since ∠1 and ∠2 are congruent, then by the definition of complementary angles, ∠1 and ∠2 are complementary.
Thus, ∠1 and ∠2 are complementary.
∴ ∠1 and ∠2 are complementary
Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
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