The average is 9.99, the very first percentile is 8.01, as well as the upper quartile is 13.33 as a result.
The 4 quartiles are what?From smallest to highest number, 25% is the first quartile. Second quartile: 25.1% to 50% (till median) 51% to 75%, third quartile (above the median) 25% of the biggest values are in the fourth quartile.
The data must first be arranged in ascending order before we can calculate the median or quartiles of the provided data:
5.24, 6.02, 6.67, 7.30, 7.59, 7.99, 8.03, 8.35, 8.81, 9.45, 9.61, 10.37, 10.39, 11.86, 12.22, 12.71, 13.07, 13.59, 13.89, 15.42
There are a total of 20 data points, and the median is calculated as that of the average of a 10th and 11th pieces of data:
(9.61 + 10.37) / 2 = 9.99; median
The very first quartile (Q1) must be determined in order to determine.
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Explain in steps pls
Answer:
Step-by-step explanation:
2X3x2Xx
Given w=-68, e=-3, f=-4 what is e4-df?
Answer:
-12 + 4d
Step-by-step explanation:
(-3)4 - d(-4)
-12 - -4d
apprmixate the value of 1+1
The value of 1+1 is 2.
Describe addition?Addition is a fundamental operation in mathematics that involves combining two or more numbers or quantities to find a total or sum. The process of addition involves adding together individual digits, numbers, or quantities to find their sum or total.
In the simplest form of addition, two numbers are added together to find their sum. For example, 2 + 3 = 5, where 2 and 3 are the addends, and 5 is the sum. The order in which the addends are added does not affect the sum, so 3 + 2 = 5 as well.
Addition can be extended to more than two numbers by adding each pair of numbers in turn. For example, to find the sum of 2, 3, and 4, we can add 2 + 3 first, which equals 5, and then add 5 + 4 to get the final sum of 9.
Addition can be represented visually using symbols such as the plus sign (+) and the equals sign (=). The plus sign is used to indicate that two numbers are being added together, while the equals sign indicates that the sum has been found.
Addition is used in many different applications, from simple arithmetic to complex mathematical models. It is a fundamental skill that is taught early on in mathematics education and is essential for understanding more advanced concepts in algebra, calculus, and other branches of mathematics.
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $14.69 and the monthly cost for 57 minutes is $17.68 . What is the monthly cost for 39 minutes of calls?
The monthly cost for 39 minutes of calls is $15.34.
According to given conditions :We can use the two given data points to form two equations and then solve for the unknown coefficients of the linear function.
Let the monthly cost (in dollars) be denoted by C, and let the total calling time (in minutes) be denoted by T. Then we can write:
C = aT + b
where a is the slope of the line (representing the rate of change of cost per minute of calling time), and b is the y-intercept of the line (representing the fixed monthly cost).
Using the given data points (34, 14.69) and (57, 17.68), we can form the following two equations:
14.69 = 34a + b (equation 1)
17.68 = 57a + b (equation 2)
Subtracting equation 1 from equation 2, we get:
17.68 - 14.69 = 57a - 34a + b - b
2.99 = 23a
a = 2.99/23
a = 0.13 (rounded to two decimal places)
Substituting the value of a into equation 1 (or 2), we get:
14.69 = 34(0.13) + b
b = 14.69 - 4.42
b = 10.27
Therefore, the linear function that represents the monthly cost in terms of total calling time is:
C = 0.13T + 10.27
To find the monthly cost for 39 minutes of calls, we can substitute T = 39 into this function:
C = 0.13(39) + 10.27
C = 5.07 + 10.27
C = $15.34 (rounded to two decimal places)
Therefore, the monthly cost for 39 minutes of calls is $15.34.
What is cost price ?The cost price (CP) is the original price paid to purchase a product or asset. It is the total cost incurred to acquire or produce the item, including all direct and indirect costs such as the cost of raw materials, labor, overhead expenses, transportation, taxes, etc.
The cost price is an important factor in determining the profitability of a business or investment, as it directly affects the profit margin. The profit margin is the difference between the selling price (SP) and the cost price (CP), expressed as a percentage of the cost price.
Profit Margin = (SP - CP) / CP * 100%
For example, if a product is sold for $100 and the cost price is $70, then the profit margin is:
Profit Margin = ($100 - $70) / $70 * 100%
Profit Margin = 30%
This means that for every $1 of cost, the business makes a profit of $0.30. The profit margin can be used to evaluate the efficiency and competitiveness of a business, and to compare the profitability of different products or investments.
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pls give diple working out :))
Answer:
x = 132°
Step-by-step explanation:
x and y lie on a straight line and sum to 180° , that is
x + y = 180°
x + 48° = 180° ( subtract 48° from both sides )
x = 132°
Using the digits 0-9 once, create accurate number line
The digits are arranged in increasing order from left to right, and that each digit is used exactly once.
What is a number line?
A number line is a visual representation of numbers arranged in a straight line from left to right or from right to left. It is a tool commonly used in mathematics to help visualize numerical relationships, such as addition, subtraction, multiplication, and division.
A typical number line starts at zero in the middle and extends infinitely in both directions, with positive numbers increasing to the right and negative numbers decreasing to the left. The distance between any two points on the number line represents the absolute difference between the corresponding numbers.
Here's a number line using the digits 0-9 exactly once:
-9 --- -8 --- -7 --- -6 --- -5 --- -4 --- -3 --- -2 --- -1 --- 0 --- 1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9
Note that the digits are arranged in increasing order from left to right, and that each digit is used exactly once.
Therefore, the digits are arranged in increasing order from left to right, and that each digit is used exactly once.
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Solve for 0
sin(0-70)=cos0
The solution of the trigonometric equation for θ is given as follows:
θ = 80º.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
sin(θ - 70) = cos(θ).
When two angles are complementary, that is, the sum of their measures is of 90º, we have that the sine of one angle is equals to the cosine of the other angle.
The angles for this problem are given as follows:
θ - 70.θ.As the sine of one is equals to the cosine of the other, they are complementary, hence the angle θ is obtained as follows:
θ - 70 + θ = 90
2θ = 160
θ = 160/2
θ = 80.
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Assume that military aircraft use ejection seats designed for men weighing between 132. 4132. 4 lb and 217217 lb. If women's weights are normally distributed with a mean of 168. 7168. 7 lb and a standard deviation of 48. 848. 8 lb, what percentage of women have weights that are within those limits
The percentage of women with weights that are within the limits is:
60.93%
What percentage of women have weights that are within those limits?Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:
z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74
z-score for upper limit = (217 - 168.7) / 48.8 = 0.99
Next, we can use a z-table to find the corresponding probabilities for these z-scores:
Probability for lower limit = 0.2296
Probability for upper limit = 0.8389
Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093
Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.
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Aircraft a has 147 more seats than aircraft be. If their total number of seats is 643, find the number of seats for aAircraft a has 147 more seats than aircraft B. If their total number of seats is 643, find the number of seats for each aircraft
Aircraft A has 496 seats and Aircraft B has 347 seats.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
To find the number of seats for each aircraft, we can use the equation 643 = 496 + 147. From this equation, we can see that aircraft A has 496 seats and aircraft B has 147 seats.
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Verify the identity using the definitions of the hyperbolic functions.
tanh x = (e^2x - 1)/(e^2x +1)
Hyperbolic tan x is verified to equal to
(e^2x - 1)/(e^2x +1)How to verify the expressionTo verify the identity using the definitions of the hyperbolic functions, we start with the definition of hyperbolic tangent:
tanh x = sinh x / coxh x = (e^x - e^-x) / (e^x + e^-x)
We can simplify this expression by multiplying the numerator and denominator by e^x:
tanh x = (e^x - e^-x) / (e^x + e^-x) * (e^x / e^x)
tanh x = (e^2x - 1) / (e^2x + 1)
We can see that this expression is equivalent to the given identity
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Find the volume of a sphere with a diameter of 18.8 cm, . Use 3.14 for π. Round your answer to the nearest tenth.
Answer:
volume of a sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
Radius = 18.8/2 = 9.4 cm
volume of the required sphere = [tex]\frac{4}{3} \pi (9.4)^{3}[/tex]
= [tex]\frac{4}{3}(3.14)(9.4)^{3}[/tex]
=3477.4 cm^3 (cor to nearest tenth)
What type of proofs did they use?
Bobby used deductive reasoning because he started with a stated fact and used logical steps to arrive at the desired conclusion.
Elaine used proof by contradiction because she made the assumption that the opposite of the desired conclusion and showed that it led to a contradiction, which gives further proof that the original assumption must be true.
What is deductive reasoning?Deductive reasoning is described as formal system in which an abstract structure is used for inferring theorems from axioms according to a set of rules.
The set rules are used for carrying out the inference of theorems from axioms, which are then seen as the logical calculus of the formal system.
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What is 40% as a fraction? Thanks in advance!!!!!!
It can be put as 40 / 100 as a fraction, which if you needed, it can be further simplified to 4 / 10, or even 8 / 20.
A square has an area of 400 square miles. What is the length of each side of the square? 10 mi 20 mi 30 mi 40 mi
Answer: The side of the square is 20 miles
Step-by-step explanation:
Since the area of square= side *side
given, area =400 square miles
400 = side *side
400= side²
√400=side
20 miles=side
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A person walks 1/4 miles in 1/12 hour. What is the person’s speed in miles per hour?
The speed of the person in miles per hour is S = 3 mph
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed of the person in miles per hour be S
Now , the distance traveled by the person D = 1/4 miles
The time taken by the person to travel ( 1/4 ) miles = 1/12 of an hour
Now , speed of the person in miles per hour S = distance traveled by the person D / time taken by the person to travel ( 1/4 ) miles
On simplifying , we get
The speed of the person in miles per hour S = ( 1/4 ) / ( 1/12 )
The speed of the person in miles per hour S = ( 1/4 ) x 12
The speed of the person in miles per hour S = 3 miles per hour
Hence , the speed is 3 mph
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After a 66% increase your salary is now $75,000. What was your original salary?
The original salary was approximately $45,180.72.
What is the formula for the starting amount?Prior to a percentage increase or decrease, one must ascertain the beginning value of an amount: The amount must be represented as a percentage of the initial sum. Determine one percent of the starting sum. The original value may be obtained by multiplying by 100 because 100% is the original sum.
We can use algebra to resolve this issue. Let x represent the starting wage.
The issue states that following a 66% raise, the new compensation is $75,000 Mathematically, this can be expressed as:
x + 0.66x = 75000
By merging similar phrases to simplify the left side, we obtain:
1.66x = 75000
Finally, by multiplying both sides by 1.66, we can find the value of x:
x = 75000/1.66
x ≈ 45,180.72
Hence, the initial wage was roughly $45,180.72.
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A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she takes 10 shots. Let x = the number of shots that she makes. What is the standard deviation for x?.
The standard deviation is 1.32
We can use the binomial distribution to calculate the probability of making a certain number of shots. The formula for the standard deviation of a binomial distribution is:
σ = √(np(1-p))
Where σ is the standard deviation, n is the number of trials (in this case, 10), p is the probability of success on each trial (0.39, or 39%), and (1-p) is the probability of failure on each trial (0.61, or 61%).
So, plugging in our values:
σ = √(10 * 0.39 * 0.61)
σ ≈ 1.32
In other words, if the player takes 10 free throws, we would expect her to make between 2 and 6 of them about 68% of the time.
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The bike store marks up the wholesale cost of all of the bikes they sell by 30%.
1. Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike?
2. If the bike is discounted by 20%, how much will Andre pay (before tax)?
Answer:
1. The wholesale cost of the bike is $93.75.
2. Andre will pay $100 before tax.
What is the answer to this problem?
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answer:
10x -25
Step-by-step explanation:
You want to simplify the expression ...
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x
SimplifyFirst, we use the distributive property to eliminate parentheses:
3x+6+x-2+8x-24+-4-4+x+1+-2x-4+6+7x+-8x
Now, we group x-terms and constant terms:
(3 +1 +8 +1 -2 +7 -8)x +(6 -2 -24 -4 -4 +1 -4 +6)
Finally, we perform the sums:
10x -25
__
Additional comment
This sort of problem can be described as "tedious, but not difficult."
4x−1<11 what is the answer
Answer:
Add 1 to both sides. Add 11 and 1 to get 12. Divide both sides by 4. Divide 12 by 4 to get 3.
f(x) = 4x − 12 what is the inverse
Answer:
f-1(x)=x4+3 this is your answer
A triangle has two sides that are 8 cm and 13 cm . What could be the length of the triangles third side?
Answer:
Third side > 13 - 8 = 5 cm. Therefore, the length of the third side is between 5 cm and 9 cm, respectively.
Step-by-step explanation:
Answer:21>c>5
Step-by-step explanation:
a+b>c>a-b
so,
13+8>c>13-8
21>c>5
Using repeated division method find the prime factors of 28
Answer:
Step-by-step explanation:
Finally, we got the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 28 are written as 2 × 2 × 7 or 22 x 7, where 2 and 7 are the prime numbers.
( 20 points!!) \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ simplify:
The value of the expression is -3/2, So correct option is A.
Describe Fraction?In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.
The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.
Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.
A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.
An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.
A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.
Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.
We can start by simplifying the expression inside the absolute value bars:
|1/6 - 3/4| = |(2/12) - (9/12)| = |-(7/12)| = 7/12
Now we can substitute this back into the original expression and simplify:
(7/4 - 8/3) - |1/6 - 3/4|
= (21/12 - 32/12) - 7/12 (converting fractions to have a common denominator)
= -11/12 - 7/12
= -18/12
= -3/2
Therefore, the value of the expression is -3/2.
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Answer:
What is Fraction ?
A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'.
A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.
An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.
A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.
Fractions are used in cooking, measuring, and financial calculations.
We can start by simplifying the expression inside the absolute value bars:
|1/6 - 3/4| = |(2/12) - (9/12)| = |-(7/12)| = 7/12
Now we can substitute
(7/4 - 8/3) - |1/6 - 3/4|
= (21/12 - 32/12) - 7/12 (converting fractions to have a common denominator)
= -11/12 - 7/12
= -18/12
= -3/2
Therefore, the value of the expression is -3/2.
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. About _____% of the area is between zequalsnegative 2. 2 and zequals2. 2 (or within 2. 2 standard deviations of the mean)
The area under the curve of the standard normal distribution is 98.61% of the area between equals negative 2. 2 and zequals2. 2
The area under the curve of a standard normal distribution between z = -2.2 and z = 2.2 is given by the integral of the normal distribution function from -2.2 to 2.2. This can be calculated using a table of standard normal probabilities or using a calculator with a normal distribution function.
The result is approximately 0.9861. To convert this to a percentage, simply multiply by 100: 0.9861 * 100 = 98.61%. Therefore, about 98.61% of the area is between z = -2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also known as the z-distribution or the unit normal distribution. It is often used in statistical tests, such as the z-test, t-test, and chi-square test. It is also used to determine confidence intervals, to calculate probabilities, and to measure the probability of a given event.
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PLEASE HELP THIS IS DUE IN AN HOUR an art supplies store sells boxes that contain colored pencils and markers. Each box has a colored pencil to marker ratio of 5 to 2. Complete the table or the missing number of colored pencils, markers, or total number of colored pencils and markers in each box for sale. *it's in box like | blank | 20 | blank |.... so on so fourth. also the blanks are what I need to figure out*
Number of Colored | blank | 20 | blank |
Pencils
Number of Markers | 6 | blank |blank|
Total Number of
Colored Pencils and | blank blank | 70 |
Markers in the Box
Answer:
Using the ratio given, we know that for every 5 colored pencils, there are 2 markers in each box.
Therefore:
The first blank represents the number of colored pencils in the box. Since the ratio of colored pencils to markers is 5 to 2, we can calculate that there are 5 colored pencils for every 2 markers. This means that for each box, there are 5/7 of the total number of items are colored pencils. So the missing value in the first row is 25.
The second row indicates that there are 20 items in the box. We know that the first row (colored pencils) has 25 items, and since the total number of items in the box is 20, the missing value in the second row (markers) is 20 - 25/5 = 15.
The third row represents the total number of colored pencils and markers in each box. We know that there are 25 colored pencils and 15 markers in each box, so the total number of items in each box is 40.
Therefore, the completed table would be:
Number of Colored | 25 | 20 | 25 |
Pencils
Number of Markers | 6 | 15 | 6 |
Total Number of
Colored Pencils and | 31 | 35 | 40 |
Markers in the Box
Lauren is working two summer jobs, making $24 per hour tutoring and making $8
per hour clearing tables. In a given week, she can work no more than 13 total hours
and must earn no less than $160. Also, she must work no more than 8 hours tutoring
and a maximum of 5 hours clearing tables. If a represents the number of hours
tutoring and y represents the number of hours clearing tables, write and solve a
system of inequalities graphically and determine one possible solution.
The system of inequalities of the given question is x>0, y>0 and 24x+8y=160
What are system of inequalities?
When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.
A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.
We are given that;
Price per hour for tutoring=$24
Price per hour for clearing tables=$8
Earning no less than $160
Work no more than in tutoring= 8hr
Maximum working for clearing table=5hr
Now,
x = number of hours tutoring y = number of hours landscaping
We cannot have negative values for either x and y, so xo and
x+y= total hours worked for both jobs combined
This total cannot exceed 11 hours
x+y≤11
Either x+y= 11 or x+y < 11
22x amount of money made from tutoring only = By amount of money made from landscaping only 22x+8y = total amount made from both jobs
24k+By 160 since he must make at least $160 Either 24x+8y = 160 or 24x+8y> 160
Therefore, the system of inequalities will be x>0,y>0,24x+8y=160
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a large company is being sued for false advertisement because 18% of the flashlights in its shipping boxes are defective, but the company claims that only 8% are defective. you plan to use hypothesis testing to determine whether there is significant evidence that the company is falsely advertising. part a: state the null and alternative hypotheses for the significance test. (2 points) part b: in the context of the problem, what would a type i error be? a type ii error? (2 points) part c: if the hypothesis is tested at a 10% level of significance instead of 5%, how will this affect the power of the test? (3 points) part d: if the hypothesis is tested based on the sampling of 100 boxes of flashlights rather than 1,000 boxes of flashlights, how will this affect the power of the test? (3 points) source stylesformatfontsize
The required solution for the hypothesis testing is shown.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here, we have,
Part A:
The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.
The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.
H0: p ≤ 0.05
Ha: p > 0.05
where p represents the proportion of defective batteries.
Part B:
A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.
A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.
Part C:
If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.
Part D:
If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.
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what is the area of a trapezoid with a height of 5 ft and bases of 10 ft and 14 ft?
The area of the Trepezium will be 60 feet².
What is a trepezium, exactly?
Trapezoids have two parallel sides and two oblique sides. It is also known as a Trapezium. A trapezoid is a four-sided closed shape or figure having a space-filling perimeter. It is a 2D figurine, not a 3D figure. The bases of a trapezoid are the sides that are parallel to one another. Legs, also known as lateral sides, are non-parallel sides. Its height is determined by the distance between its parallel sides.
Area of a trepezium=1/2*(a+b)*h
where h=height or distance between two parallel lines
a and b are two parallel lines.
Now,
Given that a=14 feet, b=10 feet and h=5 feet
then area=1/2*(10+14)*5
=24/2*5
=12*5
=60 ft²
hence,
The area of the Trepezium will be 60 feet².
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can someone please help me
Using trigonometric ratio, the value of tan V is √7 / 8
What is the value of tan VTo find the value of tan V, we have to use trigonometric ratio.
In the triangle, we have the opposite side and the hypothenuse. We can find the adjacent side using Pythagoras theorem.
Substituting the values into the formula;
w² = v² + x²
(√71)² = (√7)² + x²
71 = 7 + x²
x² = 71 - 7
x² = 64
x = √64
x = 8
The value of tan V;
tan V = opposite /adjacent
tan V = √7 / 8
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