The cost of each large van is 22,323.53 and each small van is 36,117.65.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the cost of a large van and y be the cost of a small van.
The total cost of the vans for Location A is $228,500.
Location A buys 7 large and 2 small vans.
So we have a linear equation,
7x + 2y = 228,500
The total cost for Location B is $153,000.
Location B buys 2 large and 3 small vans.
So we have a linear equation,
2x + 3y = 153,000
Multiplying the first equation with 3 and the second equation with 2,
21x + 6y = 685,500
4x + 6y = 306,000
Subtracting,
17x = 379,500
x = 22,323.53
Substituting in one of the equation,
y = 36,117.65
Hence the cost of each large and small van are 22,323.53 and 36,117.65 respectively.
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Write an equation that gives the proportional relationship of the graph.
Responses
A y = 16
B y = 2x
C y = 6x
D y = 12x
The correct equation to gives the proportional relationship of the graph is,
⇒ y = 6x
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph is shown in figure.
Now, Let two points on the graph of line are (2, 12) and (4, 24).
Hence, The equation of line given the proportional relationship of the graph.
Thus, The equation of line is,
⇒ y - 12 = (24 - 12) / (4 - 2) (x - 2)
⇒ y - 12 = 12/2 (x - 2)
⇒ y - 12 = 6 (x - 2)
⇒ y - 12 = 6x - 12
⇒ y = 6x
Thus, The correct equation to gives the proportional relationship of the graph is,
⇒ y = 6x
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x-intercepts: (-2, 0), (3, 0)
y-intercept: (0, 4)
Answer: The x-intercepts of the line are points where the y-coordinate is equal to 0. The x-intercepts of this line are (-2, 0) and (3, 0). The y-intercept is the point where the x-coordinate is equal to 0, which in this case is (0, 4).
Step-by-step explanation:
The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account. What does the value 0.031 represent?
The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
The value 0.031 represents the interest rate, which means the annual compounded interest rate is 0.31%.
The value 0.031 represents the investment period, which means the investment is invested for 0.031 years.
The value 0.031 represents the investment period, which means the investment is invested for 3.1 years
In The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account, A. The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
What is the compound interest equation?The general compound interest equation is given as:
Formula:
A = P(1 + r/n)^nt
A = final amount or future value
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Compounding interest involves computing interest on both the principal and the accumulated interest.
On the other hand, the simple interest method does not compute interest on accumulated interest.
Thus, the correct representation of the value 0.031 is the compound interest rate as 3.1%.
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h. An even number, then drawing 1
2. Halston takes two pieces of fruit for a
snack. What is the probability that she chooses
two pieces of fruit that are not bananas?
FRUIT
Pear
AMOUNT
3
The probability of Halston choosing two pieces of fruit that are not bananas is 69 %
How to find the probability ?First, find the total number of fruit :
= 3 + 4 + 2
= 9 fruit
The probability of picking a fruit that is not a banana the first time is :
= ( 3 + 4 ) / 9
= 7 / 9
The probability of picking a fruit that is not a banana the second time is :
= ( 3 + 4 - 1 ) / 9
= 6 / 9
The probability that two fruits are picked that aren't bananas is:
= 7 / 9 x 6 / 9
= 69 %
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What is the annual interest for a principal of $4200 at a simple annual interest rate of 3%?
Answer:
$126Step-by-step explanation:
At a simple annual interest rate of 3%, the following formula might be used to determine the annual interest for a $4200 principal:
Interest is calculated as follows: Principal * Rate * Time
Where,
Capital = $4200
Rate = 3% (expressed as a decimal by dividing by 100) (expressed as a decimal by dividing by 100)
t = one year
When we enter the values, we obtain:
Interest is equal to $4200 multiplied by 0.03 times one.
Therefore, $126 would be the annual interest for a $4200 principal at a basic annual interest rate of 3%.
What is the constant of variation for the subscription cost based on the number of weeks?
$1.50
$7.50
$15.00
$30.00
The constant of variation for the subscription cost based on the number of weeks is $7.5.
What is Slope?
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
The straight line passes through the point
(4, 30), (8, 60) and (12, 90)
so, slope of line passing through the points
m = (60- 30)/ (8-4)
m = 30/ 4
m = 7.5
Thus, the constant of variation is $7.5.
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How to Convert 4 in Binary?
The binary representation of the number 4 is 101, which is a three-digit binary number where leftmost digit represents the MSB and the rightmost digit represents the LSB.
What is the binary representation?The binary fraction, 0.1, now has 1 added to it because the outcome is 1. The representation is finished because there is zero in the last decimal place of the number.
To convert 10 to binary, we can use the following steps:
Divide the decimal number 10 by 2. The remainder is 0, while the quotient is 5.
Write the remainder (0) as the least significant bit (LSB) of the binary representation.
To Divide the quotient (5) by 2. The remainder is 1, while the quotient is 2.
Write down the remainder (1) as the next bit in the binary representation.
As a result, 4 is represented in binary as 101
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The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
The surface area of the rectangular prism is 174 in²
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism.
Given is a net for a rectangular prism, we need to find the surface area of the rectangular prism,
We know that,
The surface area of the rectangular prism = 2(lxb+bxh+hxl)
Length = l, height = h and b = breadth
Therefore, here we have, l = 9 in, b = 3 in and h = 5 in
Surface area = 2(9x3+3x5+5x9)
= 2(27+15+45)
= 2x87
= 174 in²
Hence, the surface area of the rectangular prism is 174 in²
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Factor out the GCF of 18x^3y^4+24x^2y^5
Geometry two-column proof please help
A two-column table method used to prove that the segments of the triangle are proportional, AE/EC = BD/DC, can be presented as follows;
Statement [tex]{}[/tex] Reasons
1. AD bisects ∠BAC[tex]{}[/tex] Given
2. AE = ED [tex]{}[/tex] Given
3. ∠BAD ≅ ∠DAE [tex]{}[/tex] Definition of bisected angle ∠BAC
4. ΔADE is an isosceles Δ [tex]{}[/tex] Definition of isosceles triangle
5. ∠ADE ≅ ∠DAE [tex]{}[/tex] Base angles of an isosceles triangle
6. AB ║ DE [tex]{}[/tex] Converse of alternate int. ∠ theorem
7. AE/EC = BD/DC [tex]{}[/tex] Thales theorem
What is a proportional relationship?A proportional relationship is one in which the elements of each ordered pair in the relationship are in the same proportion.
The details of the reasons used to prove the proportionality of the segments of the triangle are presented as follows;
Definition of bisected angle ∠BAC
An angle is bisected by a segment that divides it into two angles of the same measure.
Definition of isosceles triangle
An isosceles triangle is a triangle that has two sides that are congruent, or which have the same length.
Base angles of an isosceles triangles
The base angles of an isosceles triangle are congruent.
Converse of the alternate interior angle theorem
The converse of the alternate interior angles theorem states that if the alternate interior angles formed between two lines and a transversal are congruent, then the lines are parallel
Thales theorem
The Thales theorem states that a line drawn parallel to one of the sides of a triangle, such that it intersects the other two sides, then the line divides the other two sides proportionately.
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Scott is trying to decide which amusement park to go to during vacation. Amusement park A costs $2.50 per ride with a $40 entry fee. Amusement park B costs $4.00 per ride with a $30 entry fee. Which inequality can be used to find x, the minimum number of rides Scott has to go on so that the total charge at amusement park A costs less than the total charge at amusement park B?
The minimum number of rides Scott has to go on is 7 or more rides.
What is inequality ?
An inequality is a mathematical statement that compares two quantities, expressing that one is greater than, less than, or equal to the other. Inequalities are often represented using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
According to the question:
Let's start by finding an expression for the total cost of each amusement park in terms of the number of rides, x. For Amusement Park A, the total cost is:
Total cost for Amusement Park A = 40 + 2.5x
This is because there is a $40 entry fee plus $2.50 for each ride.
For Amusement Park B, the total cost is:
Total cost for Amusement Park B = 30 + 4x
This is because there is a $30 entry fee plus $4.00 for each ride.
To find the minimum number of rides Scott has to go on so that the total charge at amusement park A costs less than the total charge at amusement park B, we can set up an inequality comparing the total cost of the two amusement parks:
40 + 2.5x < 30 + 4x
This inequality is saying that the total cost for Amusement Park A is less than the total cost for Amusement Park B. We want to solve for x, which represents the minimum number of rides that Scott has to go on to make Amusement Park A cheaper than Amusement Park B.
To solve for x, we can simplify the inequality:
40 + 2.5x < 30 + 4x
10 < 1.5x
6.67 < x
So the minimum number of rides Scott has to go on to make Amusement Park A cheaper than Amusement Park B is 7 (rounded up from 6.67). Therefore, if Scott goes on 7 or more rides, Amusement Park A will be cheaper than Amusement Park B.
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QUIZ 4-2: PARALLEL LINES & TRANSVERSALS
Identify each angle pair, and tell whether each set is congruent or
supplementary.
1. Type:
or
2. Type:
or
3. Type:
supplementary?
supplementary?
or supplementary?
21 and 27
21 and 23
22 and 2
1. <1 and <7 are supplementary.
2. <1 and <3 are supplementary.
3. <2 and <6 are congruent angles.
What are Supplementary Angles and Congruent Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, they are angles that "complete" each other, forming a straight line. If two angles are supplementary, they are said to be "supplementary to each other."
Congruent angles are angles that have the same measure. They are written with the symbol "≅" and are read as "is congruent to." Two angles are congruent if they have the same degree measure.
1. Angles 1 and 7 add up to 180 degrees, therefore, they are supplementary.
2. Also, angles 1 and 3 are supplementary.
3. Angles 2 and 6 are corresponding angles, therefore, they are congruent angles.
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Check that the EAN-13 barcode of Mr. Chips Nacho Cheese Flavor (100 g) 4-800016-653094 is valid or invalid.
Final Answer:
(The final answer of your computation)
Therefore, the EAN-13 code is
The EAN-13 code of Mr. Chips Nacho Cheese Flavor (100 g) 4-800016-653094 is valid.
To check the validity of the EAN-13 barcode, we need to perform a computation based on the numbers in the code. The EAN-13 code consists of 13 digits, where the first digit represents the number system, the next five digits represent the manufacturer code, the following five digits represent the product code, and the last digit is the check digit.
The check digit is calculated based on the previous 12 digits using a specific algorithm.
For the given EAN-13 code 4-800016-653094, we can extract the previous 12 digits as 480001665309. To calculate the check digit, we need to multiply the first, third, fifth, etc. digits by 3, and the second, fourth, sixth, etc. digits by 1, and then sum these products. In this case, the calculation is as follows:
(4x3) + 8 + (0x3) + 0 + (0x3) + 1 + (6x3) + 6 + (5x3) + 3 + (0x3) + 9 = 74
The check digit is then the smallest number that, when added to the sum above, results in a multiple of 10. In this case, the check digit is 6, since 74 + 6 = 80, which is a multiple of 10.
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(66-6)divided by 12+ 5with exponent of 2
Answer:30
Step-by-step explanation:
use the word Pemdas
P-parenthesis
e-exponent
m-Multiplication
d-divide
a-Add.
s-Subtract.
What does surface analysis chart show?
Answer:
Step-by-step explanation:
A surface analysis chart is a type of weather map that displays information about the current pressure and wind patterns over a particular region. The chart provides a snapshot of the weather conditions at a specific point in time and helps meteorologists to identify and track the location, movement, and development of high- and low-pressure systems, fronts, and other weather features.
The surface analysis chart typically shows a map of the Earth's surface with various meteorological symbols and information, including isobars (lines of equal pressure), fronts (boundaries between different air masses), and wind direction and speed. The chart may also include information about temperature, precipitation, and cloud cover.
Surface analysis charts are used in weather forecasting, air traffic control, and other applications where an understanding of current weather conditions is important. They provide important information for short-term weather forecasting, such as predicting the location of fronts and the development of thunderstorms, and for long-term weather planning, such as determining the most suitable routes for shipping or aviation.
Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack. No Snack 12% Fruit. 23% Chips · 18% Cheese 15% Veggies 17% L Cookies 15%
The number of students that have veggies as a snack is equal to 51 students.
What is a circle graph?In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.
Since there are 300 students at York Middle School, the number of students that have veggies as a snack can be calculated as follows;
Number of students that had veggies = 17/100 × 300
Number of students that had veggies = 0.17 × 300
Number of students that had veggies = 51 students.
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Standard Questions
Question Progress
10
Karim is 2.03 metres tall.
Lucas is 1.59 metres tall.
Carlo is taller than Lucas by half the difference between Karim's height and
Lucas's height.
How tall, in metres, is Carlo?
Answer:
.28
Step-by-step explanation:
you subtract Lucas's from karim's hight wich is .56 then devid in by 2 wich is .28
identify each of Mr. Nicholson’s earning opportunities as arithmetic or geometric. For each opportunity, include the common difference or ratio. In your final answer, use complete sentences to explain how you identified each opportunity as arithmetic or geometric.
Mr. Nicholson accepts a job that pays an annual salary of $60,000. In his employment contract, he is given the option of choosing a) an annual raise of $3,500 or b) an annual raise of 5% of his current salary.
The sequence types are (a) arithmetic seqience and (b) geometric seqience
How to determine the sequence typea) an annual raise of $3,500
Given that the annual rase ie $3500
This is an arithmetic seqience
And it means that there will be an addition of $3500 in the salary each year
So, we have
Common difference = 3500
b) an annual raise of 5% of his current salary.
Given that the annual rase is 5% of the current salary
This is a geometric seqience
And it means that the raise would be 5% of previous salary
So, we have
Common ratio = 1.05
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What are some conversion factors?
A conversion factor is a mathematical expression that is used to convert a quantity from one unit of measure to another. It is a ratio that expresses the relationship between two different units of measurement.
There are many conversion factors used to convert one unit of measure to another. Here are some common conversion factors that you may find useful:
1 inch = 2.54 centimeters
1 foot = 0.3048 meters
1 mile = 1.609 kilometers
1 pound = 0.4536 kilograms
1 ounce = 28.35 grams
1 gallon = 3.785 liters
1 liter = 1000 milliliters
1 meter = 100 centimeters
1 kilometer = 1000 meters
1 square meter = 10.764 square feet
1 cubic meter = 35.315 cubic feet
1 atmosphere = 101.3 kilopascals
These are just a few examples of the many conversion factors that are used in various fields of science, engineering, and everyday life. It's important to know and use the appropriate conversion factor when converting units of measure to ensure accurate and meaningful results.
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Antonio is researching the growth of E. coli bacteria cells. The population of cells present at each hour in the table in the chart below. If P represents the size of the population at any time (t), what is the domain in the context of the problem situation?
If you can only pick one answer, the most correct choice would be (d) all real numbers up to and including 2, and any other values for which we have data.
This choice is the most general and inclusive, as it covers all possible values of time, including non-integer values, and any other values for which we have data on the population of E. coli bacteria.
However, if the answer choices are restricted to the given options, the most appropriate answer would be (c) all integers up to and including 2, and any other values for which we have data, since the given table only provides data for integer values of time up to 2 hours.
Steve had
48
4848 chocolates but decided to give
8
88 chocolates to each of his
�
ff coworkers.
How many chocolates does Steve have left?
Write your answer as an expression.
The number of chocolates that Steve have left is 4848 - 88 chocolates
What are algebraic expressions?Algebraic expressions are expressions having a composition of terms, variables, coefficients, factors and constants.
They are also composed of mathematical operations, such as;
ParenthesesBracketAdditionSubtractionMultiplicationDivisionFloor divisionFrom the information given, we have that;
The total number of chocolates is 4848The chocolates given are 88Then, the number of chocolates he has is 4848 - 88
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At the end of the summer, a store marks down all the outdoor furniture 20%. A family bought 4 chairs that originally cost $100 each. How much was the cost of the 4 chairs?
Answer:
$320
------------------
Original price of 4 chairs:
100*4 = 400Cost after mark down by 20%:
400*(100 - 20)/100 = 400*0.8 = 320Jacinta notices a pattern when she multiplies fractions. Her pattern is
written below.
When you multiply with
fractions, the product is less
than each of the two factors.
Is Jacinta's pattern correct for the fractions you worked with in Questions A
and B? Explain your reasoning.
When two positive fractions are multiplied the product is always less than the factors.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole. In mathematics, fraction is a number that is expressed as a proportion, as 1/2 or 2/3. The number on the bottom represents the total number of parts of one unit, while the number on the top is the portion of the unit being considered.
here,
Let's assume an example,
1 / 8 × 1 / 9 = 1 / 72
So as we see in the above example,
1 / 8 and 1/ 9 is a positive fractions and their product is less than their own factors.
Thus, when two positive fractions are multiplied the product is always less than the factors.
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Jacinta's pattern is correct for question A.
Jacinta's pattern is not correct for question B.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
Jacinta's:
Fractions are 1/3 and 1/5 (say).
Product.
= 1/3 x 1/5
= 1/15
Now,
1/15 < 1/3
1/15 < 1.5
For Question A:
We can assume that,
The fractions are 1/3 and 3/4.
Their product.
= (1/3) x (3/4)
= 3/12
= 1/4
1/4 < 1/3
1/4 < 3/4.
So,
Jacinta's pattern is correct.
For Question B.
The fractions are 2/5 and 4/7.
Their product.
= (2/5) x (4/7)
= 8/35
We see that,
8/35 < 2/5
8/35 > 4/7
So,
Jacinta's pattern is not correct.
Thus,
Jacinta's pattern is correct for question A.
Jacinta's pattern is not correct for question B.
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The complete question.
A) The two fractions are 1/3 and 3/4
B The two fractions are 2/5 and 5/7
Sally is 12 years old and Uncle Mike is three times as old. How many years must pass before her Uncle Mike is only twice as old as Sally? How many years ago was Uncle Mike 7 times as old?
Answer:
Uncle Mike was 7 times as old as Sally 17 years ago.
Step-by-step explanation:
Let's call Uncle Mike's current age "x."
Sally is 12 years old, so x = 12 * 3 = 36 years old.
We are looking for years that must pass before Uncle Mike is only twice as old as Sally. So we need to find the age when x = 2 * (12 + n), where n is the number of years that have passed. Solving for n:
36 = 2 * (12 + n)
36 = 24 + 2n
12 = 2n
n = 6
So, six years must pass before Uncle Mike is only twice as old as Sally.
To find out how many years ago Uncle Mike was 7 times as old as Sally, we need to find the age when x = 7 * (12 - m), where m is the number of years ago. Solving for m:
36 = 7 * (12 - m)
36 = 84 - 7m
120 = 7m
m = 17
So, Uncle Mike was seven times as old as Sally 17 years ago.
What is the standard form of this number?
Answer:
450.092
Step-by-step explanation:
4 × 100 = 400
5 × 10 = 50
9 × 1/100 = 0.09
2 × 1/1000 = 0.002
400 + 50 + 0.09 + 0.002 = 450.092
give an example of a negative correlation curve
Plotting the relationship between the number of hours studied and exam results reveals a negative correlation curve, where the exam results get worse as the number of hours studied rises.
The point (10,70) would be plotted on the negative correlation curve, for instance, if a student spent 10 hours studying and received a 70 on their exam. A downward sloping negative correlation curve would result as study time increased and exam score decreased. A graph illustrating the relationship between two variables, where an increase in one variable is accompanied by a drop in the other, is called a negative correlation curve. Numerous various types of situations, such as the amount of hours studied and exam results, might demonstrate this type of link. Exam scores typically decline as the amount of study time increases.
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A pair of parallel lines divide a parallelogram as shown in the diagram into three regions with the same area. If one of the three regions is an equilateral triangle with perimeter $1$, then what is the perimeter of the original parallelogram?
The perimeter of the original parallelogram is 22/9 * √3
What is the perimeter of the original parallelogram?The vertices of the parallelogram are A, B, C, and D, with AB parallel to CD and AD parallel to BC.
The parallel lines intersect the sides of the parallelogram at E, F, G, and H.
The side length of the equilateral triangle is s.
The three regions have the same area, hence, the area of each region is 1/3 of the total area of the parallelogram.
Let's the area of the parallelogram as A.
The area of the equilateral triangle is (s²√3)/4
This area is one-third of A
(s²√3)/4 = A/3
s² = 4A/(3√3)
Considering the whole parallelogram;
AB is parallel to CD, hence, triangle AEF is similar to triangle BGF
Also, AD is parallel to BC, hence, triangle ADE is similar to triangle BCF.
AE/EB = BF/FG AD/DE
AE/EB = BC/CF
Expressing AE, BF, AD, and BC in terms of s:
AE = s/3 (perimeter of the equilateral triangle is 1)
EB = 2s/3
BF = 2s/3
FG = s/3
AD = (2s + 2EB)/3
AD = (2s + 4s/3)/3
AD = 10s/9
DE = (2s + 2AE)/3
DE = (2s + 2s/3)/3
DE = 8s/9
BC = (2s + 2FG)/3
BC = (2s + s/3)/3
BC = 7s/9
CF = (2s + 2BF)/3
CF = (2s + 4s/3)/3
CF = 10s/9
Now we can find the perimeter of the parallelogram:
Perimeter = 2(AB + AD)
Perimeter = 2(EB + BC)
Perimeter = 2(2s/3 + 7s/9)
Perimeter = 4s/3 + 14s/9
Perimeter = (22s/9)
Substituting s² = 4A/(3√3) from the earlier equation, we get:
Perimeter = (22/9)√3
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You select a marble without looking and then put it back. If you do this 12 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
Answer:
the answer is number of orange marble/number of times
which might be 1/12 because you didn't specify
I need some help please - The box plot shows the test scores of students in Mr. Lenard’s class. What is the most appropriate measure of center?
The most appropriate measure of center is median.
option B.
Which parameter is the most appropriate for the measure of center?
The choice of measure of center (i.e., the most appropriate way to summarize the "typical" value of a dataset) depends on the distribution of the data and the research question being addressed. In general, the most commonly used measures of center are the mean and the median.
The mean is the arithmetic average of a dataset, and is often used as the measure of center for datasets that follow a normal or symmetrical distribution, where the data are roughly evenly distributed around a central value.
The median, on the other hand, is the middle value of a dataset when the values are arranged in order from smallest to largest.
For the given data, it is not evenly distributed but it is arranged from the smallest to the largest, so we can use median as the most appropriate measure of center.
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factorise using common factor method 2x-8
Answer:
2(x-4)
Step-by-step explanation:
2 is common and (x-4) is the leftover.. simple as that.