You must count the instances of each rule and the instances of each item in each rule separately using the data in the Excel file in order to determine the support, confidence, and lift of a rule.
Open the Excel file and look for the information on the options ordered for the specific model of car. This information will probably be presented as a table or a group of columns, where each row represents a distinct order and each column a different choice.
You must count the instances of the rule's components occurring together in the data in order to calculate the support for a rule. You would need to track how frequently the fastest engine choice and the traction control option are selected together, for instance, if the rule is "If the quickest engine, then traction control." This can be accomplished by counting the number of cells in a range that satisfy a specific condition using Excel's COUNTIF function.
The confidence in a rule is calculated by dividing the total number of times the items in the premise (the "if" component of the rule) occur by the total number of times the items in the rule. The number of times the fastest engine and traction control options are selected together must be divided by the total number of times the fastest engine option is ordered, for instance, if the rule is "If the fastest engine, then traction control."
You must divide the rule's confidence by the support of the item in the rule's conclusion to determine the lift of a rule (the "then" part of the rule). You would need to divide the rule's confidence by the support for the traction control option, for instance, if the rule is "If the quickest engine, then traction control."
To calculate the support, confidence, and lift for each of the rules, you can use the Excel formulas indicated above together with any other Excel functions or tools you are familiar with.
It is crucial to keep in mind that the precise formulas and processes you will need to follow will depend on the exact data and rules you are working with, so you might need to modify the following instructions to suit your personal needs.
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Let f(x) = 6x. The graph of f(x) is transformed into the graph of g(x) by a vertical compresion of 1/2 and a translation of 4 units up.
The equation for of graph of g(x) = 3x-4
Functionsy = afb(x +c) + d
where a represent the vertical stretch
b represent the horizontal stretch
c represent the horizontal translation
d represent the vertical translation
from the equation we are given g(x) has a vertical stretch and a vertical translation ( y-axis represent up and down therefore its a vertical translation)
The equation of g(x) is:
g (x) = 1/2(6x) - 4
g(x) = 3x-4
Therefore, the equation for of g(x) = 3x-4
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Which ordered pair is a solution to the equation?
-4x + 7 = 2y - 3
Choose 1 answer:
A Only (2, 1)
B Only (5, -5)
C Both (2, 1) and (5,-5)
D Neither
Answer: Neither (5/2, 0)
Step-by-step explanation:
-4x + 7 = 2y - 3
+3 +3
2y = -4x + 10
(Divide both sides by 2)
y = -2x +5
—————————————————
-4x + 7 = 2(-4x + 10) - 3
-4x + 7 = -8x + 20 - 3
-4x + 7 = -8x + 17
+8x -7 +8x -7
8x - 4x = 17 - 7
4x = 10
(Divide both sides by 4)
x = 5/2
—————————————
y = -2(5/2) + 5
y = -5 + 5
y = 0
——————————
Check Work:
-4x + 7 = 2y - 3
-4(5/2) + 7 = 2(0) -3
-10 + 7 = 0 - 3
-3 = -3 ✔️
exhibit 9-4 a random sample of 16 students selected from the student body of a large university had an average age of 25 years. we want to determine if the average age of all the students at the university is significantly different from 24. assume the distribution of the population of ages is normal with a standard deviation of 2 years. the test statistic is . a. 1.645 b. 2.00 c. 1.96 d. .05
It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.
If the average student age is not substantially different from 24 years, then the null hypothesis is tested, which is:
[tex]H_{0}[/tex] : μ = 24
If it differs from 24 years, the alternative premise is tested, so:
[tex]H_{1}[/tex] : μ ≠ 24
The z-distribution is utilized because we have the population's standard deviation. The test statistic comes from:
z = x - μ÷ σ/[tex]\sqrt{n}[/tex]
The parameters in this issue have the following values:
x(mean) = 25
μ = 24
σ = 2
n=16
As a result, the test statistic's value is:
z = 25-24÷ 2/[tex]\sqrt{16}[/tex]
z = 2
The probability of a sample mean older than 25 years determines the test's p-value, which is 1 less than the p-value of z = 2.
The p-value for z = 2 in the z-table is 0.9772; 1 - 0.9772 = 0.0228.
Given that the test's p-value is 0.0228 0.05, we may say that:
It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.
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the ph of a solution is measured eight times by one operator using the same instrument. she obtains the following data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16 and 7.18. calculate the a. sample mean b. sample variance and standard deviation c. coefficient of variation
a. sample mean = 7.1838
b. sample variance = 0.0004 and standard deviation = 0.0207
c. coefficient of variation = 0.29%
What is sample variance?
The expectation of a random variable's squared deviation from its population mean or sample mean is known as variance in probability theory and statistics. Dispersion is a measure of how far apart a group of numbers is from their mean value, and variance is a measure of dispersion.
A probability distribution's variance is defined as the mean of the squared deviation from the distribution's mean. The expected value, commonly known as the mean, is the value you will obtain on average if you take several samples of a probability distribution.
Solution Explained:
a) Mean x=∑x/n
=7.15+7.2+7.18+7.19+7.21+7.2+7.16+7.18/8
=57.47/8
=7.1838
b) Sample Variance S2=∑x2-((∑x)^2/n)/n-1
=(412.8531-(57.47)^2/8)/7
=412.8531-412.8501/7
=0.003/7
=0.0004
Sample Standard deviation S=√∑x^2-((∑x)^2)/n)/n-1
=√(412.8531-((57.47)^2/8))/7
=√412.8531-412.8501/ 7
=√0.003/7
=√0.0004 =0.0207
c) Coefficient of Variation (Sample) =
S/x X100%
=(0.0207/7.1838) X 100%
=0.29%
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Raise seven to the second power then find the sum of the result of Z
Answer: We write J raised to the 9th power as J9 (which means J multiplied by J a total of nine times). "Sum" means "add them" so J9 + K
Step-by-step explanation:
Four decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place.
The decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place include 0.237, 0.893, 0.475, and 0.652.
What is the definition of an even number?An even number is any number that can be divided exactly by two. Even numbers always have a last digit of 0, 2, 4, 6, or 8. Even numbers include 2, 4, 6, 8, 10, 12, 14, and 16.
Odd numbers are those that cannot be divided evenly by two. It cannot be evenly divided into two separate integers. When we divide an odd number by 2, we get a remainder. Odd numbers include 1, 3, 5, 7, and so on.
A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.
A prime number is a whole number greater than one with only the number one and itself as factors. A factor is a whole number that can be divided into other numbers evenly.
In this case, 0.237, 0.893, 0.475, and 0.652 have an even number in the tenths place which is the first place after the decimal point. Also, there's an odd number in the hundredths place, and a prime number in the thousandths place.
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Complete question
Write four decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place
Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector
If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.
Vector:A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.
Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.
Scalar Multiplication:Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).
For quaternion scalars and matrices:
λ = 2 A = [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
2A = 2[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] × 2 = A2
Subspace:In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
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To explain that the expression 20m−60n+20 can be written as 20(m−3n), John first factors 20m as 20 ⋅ m and 60n as 20 ⋅ 3n, and leaves 20 unchanged. Then, he factors 20 from each term of the expression 20m−60n+20 and puts the remaining factors together within a pair of brackets.
• Explain why John’s reasoning is incorrect.
• Factor 20m−60n+20
• Explain how you found the answer.
The expression 20 m−60 n+20 can be written as 20(m−3 n +1).
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Given expression,
20 m−60 n+20
can be factorized as
20(m−3 n +1).
A) John’s reasoning is incorrect because he has not included the constant term in the expression.
B) 20 m−60 n+20 can be factorized as 20(m−3n +1).
C) The expression can be factorized by taking common from each and every term of the expression.
Therefore,The expression 20 m−60 n+20 can be written as 20(m−3 n +1).
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given r(x)=x^3-4x^2+4x-6, find the value of r(2). what does your answer tell you about x-2 as a factor of r(x)?
The Value of r(2) is -6 and x-2 is not a factor of r(x).
What is the value of a function on a Variable?
A real-valued function of a real variable is a function that takes as input a real number, commonly represented by the variable x, for producing another real number, the value of the function, commonly denoted f(x).
What is Factor?
A factor of polynomial P(x) is any polynomial that divides evenly into P(x).
How to find out the value of r(x)?
Given r(x)=x^3-4x^2+4x-6,
Put x = 2 ,
r(2)=2^3-4(2)^2+4(2)-6
r(2)=8-16+8-6
r(2)=-6
As we see that x=2 is not equal to zero,
implies x-2 does not divide r(x) evenly.
thus x-2 is not a factor of given r(x).
a rectangle has a length of 1 inches and a width of 6 inches whose sides are changing. the length is increasing by 4 in/sec and the width is shrinking at 2 in/sec. what is the rate of change of the perimeter?
The rate of change of the perimeter is 4 in/sec .
In the question ,
it is given that ,
the length of the rectangle is [tex]=[/tex] 1 inch
the width of the rectangle is = 6 inch
the rate of increasing length is (dL/dt) = 4 in/sec
rate of shrinking width is (dW/dt) = -22 in/sec ,
We know that the perimeter of the rectangle is = 2(L + W) ,
that is , P = 2L + 2W ,
Differentiating perimeter with respect to time "t" ,
we get ,
dP/dt = 2 × ( dL/dt) + 2 × (dW/dt )
Substituting the values from above ,
we get ,
= 2 × (4) + 2 × (-2)
= 8 - 4
= 4
Therefore , the required rate of change is = 4 in/sec .
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What is the slope of the line that passes through the points (-5, 8) and (-5, 4)? Write your answer in simplest form.
If the bond angle between two adjacent hybrid orbitals is 120°, which is the hybridization?.
If the bond angle between two adjacent hybrid orbitals is 120° the hybridization is Sp2 hybridization .
Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.
sp2 hybridization
There are other ways to combine the orbitals than sp3 hybridization when an excited state carbon atom is produced. As opposed to the three p orbitals in the sp3 hybridization, the s orbital only interacts with two p orbitals in the sp2 hybridization. As a result, three orbitals are combined to create three hybrid orbitals, also known as sp2 hybrid orbitals.
The sp2 hybridization occurs when the s orbital is mixed with only two p orbitals as opposed to the three p orbitals in the sp3 hybridization
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The number 100 went into a machine (input), and
after an increase of 60%, a number came out
(output).
What number was output of the machine?
Answer:
outpot=160
Step-by-step explanation:
outpot= 100+ 100×0.6=160
(I NEED HELP URGENTLY, THIS IS DUE TOMORROW!)
The table represents a proportional relationship.
A. Find the constant of proportionality:
B: Write a equation to represent the relationship. Equation: y=
The constant of proportionality is 1/3 and the equation is y = 1/3x
A. The constant of proportionalityThe table of values represents the given parameter
From the table of values, we have the following ordered pair
(x, y) = (3, 1)
The constant of proportionality (k) is then calculated as
k = y/x
So, we have
k = 1/3
B: The equation to represent the relationship.Recall that, we have
k = y/x
Substitute k = 1/3
y/x = 1/3
So, we have
y = 1/3x
Hence, the equation is
y = 1/3x
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a sample of 60 information system managers had an average hourly income of $45.80 with a standard deviation of $7.00. what is the lower limit for the 95% confidence interval estimate for the average hourly wage of all information system managers? round your answer to two decimal places.
The lower limit for the 95%confidence interval for the given mean and standard deviation is equal to 39.03.
As given in the question,
Sample size 'n' = 60
Mean 'μ' = $40.80
Standard deviation 'σ' = $7.00
Using z-score table of normal distribution
z-value for 95%confidence interval = 1.96
Formula used
Confidence interval
= μ ± ( z-value × σ ) /√n
= 40.80 ± (1.96 × 7)/√60
= 40.80 ± (13.72 /7.75)
= 40.80 ±1.770
Lower limit of the confidence interval is equal to :
40.80 - 1.770 = 39.03
Upper limit of the confidence interval is equal to :
40.80 + 1.770 = 42.57
Therefore, the lower limit for the 95% confidence interval is equal to 39.03.
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Which pairs of figures are congruent? Which pairs are similar?
Answer:
Step-by-step explanation:
B becuase the way the angle is
vv7 of 107 of 10 items 10:32 skip to resources question the height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?
The kiwi as per the given relation of ostrich and kiwi's height is equal to 22inches tall.
As given in the question,
Ostrich height is equal to 108 inches
Let us consider 'x' inches be the height of the kiwi.
Ostrich is 20inches more than four times of x.
Ostrich height = 20 + 4x
⇒ 108 = 20 + 4x
Subtract 20 from both the sides we get,
108 - 20 = 20 + 4x -20
⇒ 88 = 4x
Divide by 4 on both the sides we get,
88/ 4 = 4x / 4
⇒ x = 22 inches
Therefore, as per the given relation of ostrich and kiwi's height , kiwi is 22inches tall.
The complete question is :
The height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?
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a summer squash, spinach, and leek frittata recipe requires 6 ounces of spinach. if the ep unit cost of the ingredient is $2.25 per pound, what is the total cost of the ingredient?
The total cost of the ingredient is $0.84 for 6 ounces.
Define fixed cost.
The cost or expense known as fixed cost is unaffected by a short-term horizon's growth or reduction in the number of units produced or sold. To put it another way, it refers to a cost that is linked to a time period rather than a specific economic activity.
It can be viewed as costs that a business must pay regardless of the volume of business activity, such as the number of units produced or sales made. One of the two main parts of the overall manufacturing cost is the fixed cost.
Solution Explained:
Given,
1 pound = $2.25
Since 1 pound = 16 ounces
So, 16 ounces = 2.25
1 ounce = 2.25/16 = 0.14
Therefore, 6 ounces = 0.14 X 6 = 0.84
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Assume that the probability a child is a boy is 0.51 and that the sexes of children born into family are independent. What is the probability that a family of five children hasa. exactly three boys?b. all girls?c. at least one girl?
a) Probability of exactly three boys is 0.3185
b) Probability of at least one boy is 0.9717
c) Probability of at least one girl is 0.9655
d) Probability of all of same sex is 0.06275
What is probability?
Probability refers to potential. A random event's occurrence or the outcome is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.The potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.a) Probability of exactly three boys
Choose 3 out of 5 in C(5,3)=10 ways
So probability is:10*0.51^3*0.49^2
~0.3185
(b) Probability of at least one boy
p(at least one boy)=1-p( all girls)
=1-0.49^5
=0.9717
c) Probability of at least one girl
p(at least one girl)=1-p( all boys)
=1-0.51^5
=0.9655
d) Probability of all of same sex
p(all of same sex)=p(all boys)+p(all girls)=
0.51^5+0.49^5
=0.06275
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The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7%. Find the total cost of the set and the tax.
The total cost of the set and the tax is 2653.6 dollars.
How to find the total cost of the set and the tax?The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7 percent.
Therefore, the total cost of the set and the tax can be calculated as follows:
tax = 7% of 2480
tax = 7 / 100 × 2480
tax = 17360 / 100
tax = $173.6
Therefore, let's find the total cost of the set and tax.
total cost = 173.6 + 2480
total cost = 2653.6 dollars
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Help please 17. G(9)+h(-14)
Answer:
15
Step-by-step explanation:
Given functions:
[tex]g(x)=14-\dfrac{2}{3}x[/tex]
[tex]h(x)=-x-7[/tex]
g(9) means to substitute x = 9 into function g(x):
[tex]\begin{aligned}\implies g(9)&=14-\dfrac{2}{3}(9)\\&=14-\dfrac{18}{3}\\&=14-6=8\end{aligned}[/tex]
h(-14) means to substitute x = -14 into function h(x).
[tex]\begin{aligned}\implies h(-14)&=-(-14)-7\\&=14-7\\&=7\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies g(9)+h(-14)&=8+7\\&=15\end{aligned}[/tex]
As one calculation:
[tex]\begin{aligned}\implies g(9) + h(-14)&=\left(14-\dfrac{2}{3}(9)\right)+\left(-(-14)-7\right)\\&=\left(14-\dfrac{18}{3}\right)+\left(14-7\right)\\&=\left(14-6\right)+\left(14-7\right)\\&=8+7\\&=15\end{aligned}[/tex]
theo started watching a movie at 19:30 The movie was 1 hour 56 minutes long,but part-way through he paused it for 12 minutes what was the time the movie finished
Answer: 21:38 on a 24 hour clock and 9:38 on a 12 hour clock
Step-by-step explanation:
So if Theo started the movie at 7:30 and the movie was 1 hour 56 minutes, and he paused half way for 12 minutes, we can conclude that the total time taken to watch the movie/break was 2 hours and 8 minutes.
Now we just add that time
7:30 + 2 hours and 8 minutes = 9:38
On a 24 hour clock the answer would be 21:38
an efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster. to test it, volunteers are selected. half of the volunteers will use the new chair and half will use their old chairs. each volunteer types a randomly selected passage for 2 minutes and the number of correct words typed is recorded. choose the correct answer below. a. the data are independent and not paired. b. the data are paired where the pairing involves the volunteers who use the new chair and the volunteers who use their old chair. c. the data are paired where the pairing involves the random passages the volunteers type
with the help of Advanced Placement statistics correct answer is option B.
what is Advanced Placement statistics?
In the United States, the College Board's Advanced Placement programme offers a college-level high school statistics course known as Advanced Placement Statistics.
explanation:
The data are paired where the pairing involves the volunteers who use the new chair and the volunteers who use their old chair.
hence the correct option is B by Advanced Placement statistics
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2. how long does it take to cook a potato? consider a cylindrical potato, sliced into thin slices with thicknesses l
The boundary value and initial value statement are,
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].
What is Initial Value Problem?
In multivariable calculus, an initial value problem is an ordinary differential equation that also includes an initial condition that identifies the value of the unknown function at a specific location in the domain. An initial value problem is frequently solved when modelling a system in physics or another scientific field.
Consider a cylindrical potato, sliced into thin slices with thickness L = 1 cm, much smaller than the diameter slices.
Initial temperature [tex]T_i = 20^o[/tex]
Final temperature = [tex]T_f = 75^o[/tex]
Now we have to solve the given cases.
Consider the heat equation,
q = k(∂T / ∂x) ..(1)
(a) Now we have to find the boundary value
Boundary Value:
[tex]T_i = 20^oc, T_f = 75^oc\\[/tex]
⇒ ΔT = [75 - 20]
⇒ΔT = 55°c
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex]
Hence, the boundary value and initial value statement are,
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].
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Complete question:
Complete question is attached below,
You have a bag with five different colored marbles in it; red, green, blue, orange, and purple. Each marble has an equal chance of
being drawn from the bag and a marble is replaced after each draw.
After four draws from the bag what is the probability that you have seen both the red and green marbles at least once?
This question is based on the probability. Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.
Given:
There are 5 marbles in a bag. Each marble is a different color. The colors are: red, orange, green, blue, purple. Two marbles are randomly drawn from the bag without replacement.
We need to determined the probability that the red marble is drawn first and the white marble is drawn second.
According to the question,
It is given that, there are 5 different marbles. In the first draw, you have a one out of 5 chance of getting the red is 1/5 .
In the second draw, there are 4 marbles remaining, so a one out of 4 chance of drawing a white marble i.e. 1/4.
Now, calculating the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.
⇒ 1/5 × 1/4 = 1/20
Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.
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Find the 70th term of the arithmetic sequence
Answer:
753
Step-by-step explanation:
Arithmetic sequences are sequences that change by a constant factor.
Explicit Rule
The formula that describes an arithmetic sequence is called the "explicit rule". This formula is f(x) = f(1) + d(x-1). Sometimes the rule will be written with [tex]a_{n}[/tex] instead of f(x) but the equations are still the same.
In this equation, f(1) is the first term of the sequence, d is the common difference, and x is the term. The common difference is the factor that the sequence changes by.
Setting Up the Equation
To set up the equation, we need to find f(1) and d.
The first term, f(1), is directly given to us in the equation. The first term written is -6, so f(1)=-6.
It is slightly more difficult to find d. But, one easy way to find d is by subtracting terms. Take the second term, 5, and subtract the first term, -6.
5 - (-6) = 11So, d = 11. Each term in the sequence increases by 11.
The final equation is f(x) = -6 + 11(x-1).
Finding the 70th Term
Now, all we have to do is plug 70 in for x. To find any term in the sequence, all you have to do is plug the term number in for x.
f(70) = -6 + 11(70-1)f(70) = 753The 70th term in the sequence is 753.
write a quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3).
The quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3) is; y = 0.2x² - 2.2x + 2
How to write the standard form of the quadratic equation?
The standard form of a quadratic equation is;
y = ax² + bx + c
where a, b and c are constants
Thus, for the coordinate (10,0), we have;
0 = a(10)² + b(10) + c
100a + 10b + c = 0 -----(1)
For the coordinate (1,0), we have;
0 = a(1)² + b(1) + c
a + b + c = 0 -----(2)
For the coordinate (4,3), we have;
3 = a(4)² + b(1) + c
16a + b + c = 3 ------(3)
Using online simultaneous equation, we have;
a = 0.2 and b = -2.2 and c = 2
The quadratic function is;
y = 0.2x² - 2.2x + 2
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a. Lin is using the diagram to prove the statement, "If a parallelogram has one
right angle, it is a rectangle." Given that EFGH is a parallelogram and angle
HEF is a right angle, write a statement that will help prove angle FGH is also
a right angle.
b. Han then states that the 2 triangles created by diagonal BG must be congruent.
Help Han write a proof that triangle EHG is congruent to triangle GFE.
The congruence of the angles and triangles are proven as follows;
a. The composition angles of FGH are alternate interior angles to the composition angles of angle AHEF
b. The three sides of triangle ∆EHG are congruent to the three sides of triangle ∆GFE, therefore, triangles ∆EHG and ∆GFE are congruent by SSS congruency rule
What are congruent triangles?The lengths of the three sides of triangles that are congruent.
a. The shape of quadrilateral EFGH = A parallelogram
The measure of angle HEF = 90°
Angle HEF = 90°
Angle HEF = Angle HED + Angle DEF
Angle HED is congruent to angle FGD (Alternate interior angles theorem)
Angle HED = angle FGD
Angle DEF is congruent to angle DGH (Alternate interior angles theorem)
Angle DEF = angle DGH
Angle FGH = Angle FGD + Angle DGH
Angle FGH = Angle HED + Angle DEF (Substitution property)
Angle FGH = Angle HEF (Transitive property)
Angle FGH = Angle HEF = 90°
Therefore, the statement that will help prove angle FGH is also a right is that angle FGH is the sum of angles FGD and angle DGH which are alternate interior angles to angles HED and DEF which makes up angle HEF, which is a right angle.
b. The two-column method can be used to prove that triangle EHG and triangle GFE are congruent as follows;
Statement. Reason
EF is congruent to HG. Opposite sides of a parallelogram are congruent
EH is congruent FG Opposite sides of a parallelogram are congruent
EG is congruent to EG Reflexive property of congruency
∆EHG is cong. to ∆GFE SSS, Side-Side-Side, congruency rule
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about 22% of the population of a large country is allergic to pollen. if two people are randomly selected, what is the probability that both will be allergic to pollen? (round your answer to two decimal places) what is the probability that at least one person is allergic to pollen? (round your answer to two decimal place
The probability that both will experience allergies to pollen is 0.0484, and the probability that at least one will is 0.9516.
The following information is provided in the question:
A large country has a pollen allergy rate of about 22%.
As a result, the probability of people has a chance of having an allergy is 0.22.
P(allergic) = 0.22
P(Not allergic) = 1 - 0.22 = 0.78
If A and B are independent even, then,
P(A∩B) = P(A) × P(B)
Two people are randomly selected.
a) P( both will be allergic to pollen)
Since these are independent events,
P(both will be allergic to pollen)= P(allergic)*P(allergic)
= 0.22*0.22 = 0.0484
b) P(at least one person is allergic to pollen)
= 1 - P(both are not allergic to pollen)
= 1 - P(P(not allergic)*P(not allergic))
= 1 - (0.22*0.22)
= 0.9516
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pls help :( The table shows the sizes of Farmer Reuben's fields. Use the table and a separate sheet of paper to help you answer each question.
The areas of each of Reuben's fields are given as follows:
Corn Field: 24,000 square feet.Wheat Field: 140,000 square feet.Barley Field: 40,000 square feet.Hence the total area of all of Reuben's fields is given as follows:
204,000 square feet.
How to obtain the areas of the fields?The areas of the fields is given by the multiplication of each of the dimensions of the field, as the fields have a rectangular format.
Then the total area is obtained as the sum of the areas of each field.
The dimensions of each field are given as follows, from the table given by the image at the end of the answer:
Corn Field: 400 feet by 60 feet.Wheat Field: 700 feet by 200 feet.Barley Field: 200 feet by 200 feet.Hence the areas of each of the fields are given as follows:
Corn Field: 400 x 60 = 24,000 square feet.Wheat Field: 700 x 200 = 140,000 square feet.Barley Field: 200 x 200 = 40,000 square feet.Then the total area is given as follows:
24,000 + 140,000 + 40,000 = 204,000 square feet.
Missing InformationThe problem asks for the areas of each field and the total area.
The dimensions are given by the image shown at the end of the answer.
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