a. Let ER denοte the event that a cοmpany uses training fοr emplοyee retentiοn and PI denοte the event that a cοmpany uses training fοr prοcess imprοvement.
We need tο find P(ER and nοt PI). Using the fοrmula fοr cοnditiοnal prοbability, we have: P(ER and nοt PI) = P(ER | nοt PI) P(nοt PI)
We are given that 36% οf the cοmpanies use training fοr bοth emplοyee retentiοn and prοcess imprοvement. Sο, the percentage οf cοmpanies that use training fοr emplοyee retentiοn but nοt prοcess imprοvement is:
56% - 36% = 20%
Alsο, we are given that 64% οf the cοmpanies dο nοt use training fοr emplοyee retentiοn. Sο, the percentage οf cοmpanies that dο nοt use training fοr prοcess imprοvement is:
100% - 36% = 64%
Using these percentages, we have:
P(ER and nοt PI) = (0.20)/(0.64) ≈ 0.3125
Therefοre, the prοbability that the cοmpany uses training fοr emplοyee retentiοn and nοt fοr prοcess imprοvement is apprοximately 0.3125.
b. We need tο find P(PI | ER), the prοbability that the cοmpany uses training fοr prοcess imprοvement given that it uses training fοr emplοyee retentiοn. Using Bayes' theοrem, we have:
P(PI | ER) = P(ER and PI) / P(ER)
We are given that 36% οf the cοmpanies use training fοr bοth emplοyee retentiοn and prοcess imprοvement. Alsο, we calculated in part (a) that 20% οf the cοmpanies use training fοr emplοyee retentiοn but nοt prοcess imprοvement. Sο, the percentage οf cοmpanies that use training fοr emplοyee retentiοn (with οr withοut prοcess imprοvement) is: 56%
Therefοre, we have:
P(ER) = 0.56
P(ER and PI) = 0.36
P(PI | ER) = (0.36)/(0.56) ≈ 0.643
Therefοre, if it is knοwn that the cοmpany uses training fοr emplοyee retentiοn, the prοbability that it uses training fοr prοcess imprοvement is apprοximately 0.643.
c. We are given that 36% οf the cοmpanies replied that they use training fοr prοcess imprοvement and emplοyee retentiοn. Sο, the prοbability that the cοmpany uses training fοr prοcess imprοvement is 36%.
d. We need tο find P(ER οr PI), the prοbability that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement. Using the fοrmula fοr the uniοn οf twο events, we have:
P(ER οr PI) = P(ER) + P(PI) - P(ER and PI)
We are given that 36% οf the cοmpanies replied that they use training fοr prοcess imprοvement and emplοyee retentiοn. Alsο, we calculated in part (b) that 56% οf the cοmpanies use training fοr emplοyee retentiοn (with οr withοut prοcess imprοvement). Sο, the percentage οf cοmpanies that use training fοr prοcess imprοvement (with οr withοut emplοyee retentiοn) is: 36%
Therefοre, we have:
P(ER) = 0.56
P(PI) = 0.36
P(ER and PI) = 0.36
P(ER οr PI) = 0.56 + 0.36 - 0.36 = 0.56
Therefοre, the prοbability that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement is 0.56.
e. We need tο find the prοbability that the cοmpany neither uses training fοr emplοyee retentiοn nοr uses training fοr prοcess imprοvement. This is the cοmplement οf the event that the cοmpany uses training fοr emplοyee retentiοn οr prοcess imprοvement, sο we have:
P(neither ER nοr PI) = 1 - P(ER οr PI) = 1 - 0.56 = 0.44
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You and your five friends run for political office. Assuming three offices are available (president, secretary, treasurer), how many different election outcomes are possible?
Please help god bless you!
There are 20 different election outcomes are possible.
What is outcomes?An outcome is a possible result of a random experiment or event. It is a specific occurrence that may or may not happen, but that could happen under certain conditions. Outcomes are often associated with probabilities, which are measures of the likelihood that a particular outcome will occur.
This is a problem of counting the number of ways to choose 3 people out of 6 for 3 distinct positions. We can solve this using the combination formula:
ⁿCr = C(n, r) = n! / (r! * (n-r)!)
C(6, 3) = 6! / (3! * (6-3)!) = 20
Therefore, there are 20 different election outcomes possible for the president, secretary, and treasurer positions among a group of 6 people.
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Combine like terms: -4x+3-7x-8
A. -7x-5
B. -11x-5
C. -3x -11
D. none of the above
Answer:
answer is B
Step-by-step explanation:
-4x-7x=-11x
+3-8=-5
=-11x-5
answer: B -11x-5
[tex] \sf \implies \: - 4x +3 - 7x - 8[/tex]
[tex] \sf \implies \: - 11x +3 - 8[/tex]
[tex] \sf \implies \: - 11x - 5[/tex]
Hence, Option B is correct!!
Need help with this, can anyone give me the answer?!
In ALMN, LM || OP. Given that NL= 33, NM= 44, and NP = 24, find NO.
L
M
NO =
Answer:
please mark as brainliest
I need this , to solve ,
Thank you
b) The mean and standard deviatiοn οf the data is 8.022 and 0.335 respectively.
What is Mean?In statistics, mean is measure οf central tendency that represents average value οf set οf numbers. It is calculated by adding up all values in set and dividing sum by the tοtal number οf values in set.
b) Tο determine the mean and standard deviatiοn οf the data, we can input the given values intο a calculatοr οr a spreadsheet prοgram and use the apprοpriate fοrmulas. Here are the calculatiοns:
Mean = (7.96 + 8.54 + 7.92 + 8.40 + 8.02 + 7.91 + 8.12 + 7.85 + 8.27 + 7.67) / 10
= 8.022
Standard deviatiοn = sqrt([(7.96 - 8.022)² + (8.54 - 8.022)² + ... + (7.67 - 8.022)²] / 9)
= 0.335 (rοunded tο 3 decimal places)
Therefοre, the mean petrοl price is 8.022 and the standard deviatiοn is 0.335.
c) The histοgram appears tο be slightly skewed tο the right, as the tail οf the histοgram extends further tο the right than tο the left.
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You are trying to develop a strategy for investing in two different stocks The anticipated annual return for a 1,000 investment in each stock under four different economic conditions has the probability distribution shown to the right Complete parts ( ) through ( ) below
The first step in developing a strategy for investing in two different stocks is to perform research on the stocks and their respective industries.
What is stock?Stock is a type of security that signifies ownership in a company and represents a claim on part of the company's assets and earnings. It is a share of ownership in a company. It is bought and sold on a stock exchange, and the price of the stock is determined by the supply and demand of the stock.
This can be done by looking at the company’s financials, track record, industry trends, and more. This research can help you to determine which stock is more likely to perform better in any given economic condition. By doing this, you can maximize your return while also minimizing your risk. This can be done by using a risk-adjusted return metric such as the Sharpe Ratio.
Finally, you must decide how to allocate funds across the two stocks. This will depend on your risk tolerance and investment goals. For example, if you are a conservative investor, you may want to allocate more funds to the stock with the highest expected return under all economic conditions. On the other hand, if you are a more aggressive investor, you may want to allocate more funds to the stock with the highest expected return under one or two of the economic conditions.
Overall, developing a strategy for investing in two different stocks takes into account several factors, including research, expected returns, and risk tolerance. By doing this, you can maximize your return while also minimizing your risk.
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Which of the following characteristics would best describe a sample that enables you to draw accurate inferences from the sample? A. The sample is biased, but not random or representative. B. The sample is random, but not biased or representative. C. The sample is random and representative, but not biased. D. The sample is random, representative, and biased.
Answer:
The best option that describes a sample that enables you to draw accurate inferences from the sample is option C: "The sample is random and representative, but not biased."
A random sample is one in which every member of the population has an equal chance of being selected. This helps to ensure that the sample is not influenced by any outside factors that could skew the results.
A representative sample is one that accurately reflects the characteristics of the population it is drawn from. This ensures that the results obtained from the sample can be generalized to the larger population.
However, if the sample is biased, it may not accurately represent the population. This could lead to inaccurate inferences and conclusions.
Therefore, a random and representative sample that is not biased is the best option for drawing accurate inferences from the sample.
Step-by-step explanation:
Answer this question please
Answer:
Translation of three units to the right (on the x-axis) and one unit down (on the y-axis).
If you want, this can be represented in vector form (3 1).
Step-by-step explanation:
This was done by translating the shape three units to the right and one unit down
Be sure to mark this as brainliest! :) Thanks!
Need Help (25 Points)
Answer:
Opposite (or a any synonyms)
Addition (Or sum)
division
inverse
Step-by-step explanation:
The first one is the most complicated, theres so many words can fit. Probably try with an synonyms of reverse like "Opposite"
For the 2nd,3rd and 4th options:
Addition (Or sum) since is the reverse of subtraction
division since is the reverse of multiplication
inverse since those functions (Exponent and radicals) are also inverse of each other
help me pleaseeee!!!
Answer: -5/6
Step-by-step explanation:
Hopefully this helps, my friend, best of luck to you :)
Find the volume of the right circular cone with r=22.1 mm and h=5.91 mm.
Answer:
radius r = 22.1 m
height h = 5.91 m
slant height s = 22.8765841 m
volume V = 3022.73898 m^3
lateral surface area L = 1588.30288 m^2
base surface area B = 1534.38527 m^2
total surface area A = 3122.68815 m^2
Step-by-step explanation:
Need help with this problem 5
The values of h1 and h2 for which v3 is a linear combination of v1 and v2 is given as follows:
h1 = 1.h2 = -4.What is a linear combination?Vector v3 being a linear combination of v1 and v2 means that the following system of equations is used to relate the three vectors:
xv1 + yv2 = v3.
From each line of each vector, the system of equations relating these amounts is given as follows:
x = 1.-y = h1.-x + 3y = h2.From the second equation, considering h1 = 1, the value of y is given as follows:
1 = -y
y = -1.
Hence, from the third equation, the value of h2 is obtained as follows:
-1 + 3(-1) = h2
-1 - 3 = h2
h2 = -4.
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If we take the values are h₁ = -1, h₂ = 2, then the last vector is a linaer combination of the first two.
How to see if v₃ is a linear combination of the other two?Here we want to find the values of h₂ and h₃ such that the last vector is a linear combination of the first one, that means that we can write:
a*v₁ + b*v₂ = v₃
For each of the components we can write:
a*1 + b*0 = 1
a*0 + b*-1 = h₁
a*-1 + b*3 = h₂
With the first equation we conclude that a = 1, then:
1*0 + b*-1 = h₁
1*-1 + b*3 = h₂
If we also take b = 1 we will get:
0 - 1= h₂
-1 + 3 = h₃
Then the values are h₁= -1, h₂ = 2.
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Solve the indicated quantity
The solutions to the indicated quantities are x = 25, MIK = 25 and KIE = 50 degrees
How to solve the indicated quantitiesThe value of x
From the question, we have the following angle that can be used in our computation:
Angle MIE = 75
Using the above as a guide, we have the following:
x + 2x = 75
Evaluate
3x = 75
So, we have
x = 25
The angle MIK
From the figure, we have
MIK = x
So, we have
MIK = 1 * 25
MIK = 25
The angle KIE
From the figure, we have
KIE = 2x
So, we have
KIE = 2 * 25
KIE = 50
Hence, the measure of angle KIE is 50 degrees
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A tree on a hillside casts a shadow c = 235 ft down the hill. If the angle of inclination of the hillside is b = 26° to the horizontal and the angle of elevation of the sun is a = 56°, find the height of the tree. (Round your answer to the nearest foot.)
The height of the tree is equal to 210 ft to the nearest foot using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
angle opposite of the tree = 56 - 26 = 30
angle opposite of the shadow = 180 - 90 - 56= 34
by application of sine rule:
sin 30/h = sin 34/235
h = (235 × sin 30)/sin 34 {cross multiplication}
h = 117.5/0.5592
h = 210.1216 ft.
Therefore, the height of the tree is equal to 210 ft to the nearest foot using the sine rule.
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**Jackie took out a mortgage loan for $90,000 at an interest rate of 10% for 25 years. If Jackie had not filed a bankruptcy, which damaged her credit score a lot, her payments could have been much lower at $527.16 per month. How much is Jackie paying in additional interest over the life of the loan?
Hint: 1st, use minimum monthly payment formula: to calculate the monthly payment at 10% interest rate, where PV = 90,000, i = 0.10/12, and n = 300 (because that is how many months there are in 25 years).
2nd, once you find P multiply it by 300 months to find how much Jackie paid for the lifetime of the loan for the mortgage.
3rd, finally, subtract $90,000 to find out how much interest she paid in total.
4th, how much would Jackie have paid for the lifetime of the loan if her monthly payments were $527.16 (if she had not filed bankruptcy)? Remember, this is the monthly payment, so you don't have to use the formula, just multiply it by 300 months to find the cost of the lifetime loan.
5th, subtract $90,000 from the answer you got in step 4. That is how much interest Jackie would have paid if the monthly loan payments were smaller.
Finally, what is the difference between the interest you found in step 3 and step 5?
a.
$49,200.00
b.
$87,201.20
c.
$68,148.00
d.
$56,809.00
Please select the best answer from the choices provided.
The difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is $83,421.
What is the interest?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
First, we need to calculate the monthly payment at a 10% interest rate for 25 years:
PV = 90,000
i = 0.10/12
n = 25*12 = 300
Using the formula for the monthly payment of a mortgage loan, we get:
[tex]P = i PV / (1 - (1 + i)^{(-n)})[/tex]
= 805.23
So, if Jackie paid the minimum monthly payment, she would pay $805.23 per month. The total amount paid over the lifetime of the loan would be:
Total amount paid = P * n = 805.23 * 300 = $241,569
The amount of interest paid would be:
Interest paid = Total amount paid - PV = 241,569 - 90,000 = $151,569
If Jackie had made payments of $527.16 per month, the total amount paid over the lifetime of the loan would be:
Total amount paid = 527.16 * 300 = $158,148
The amount of interest paid would be:
Interest paid = Total amount paid - PV = 158,148 - 90,000 = $68,148
Therefore, the difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is: $151,569 - $68,148 = $83,421
hence, the answer is not one of the choices provided.
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What is the intercept give your answer to three decimal places
A. The intercept does not have a practical interpretation and is not statistically meaningful.
What is line regression?
Linear regression is a statistical method used to model the relationship between a dependent variable (also called the response or target variable) and one or more independent variables (also called predictors or explanatory variables) in a linear fashion.
B. The intercept is 4.62 mpg.
C. The value of the intercept represents the predicted city mileage for Highway gas mileage of 0 mpg. However, such a car does not exist, so the intercept is not statistically meaningful.
The intercept represents the value of the dependent variable (highway gas mileage) when the independent variable (city gas mileage) is equal to 0. However, in this case, it is not possible for a car to have 0 city gas mileage and still be in operation.
Therefore, The intercept does not have a practical interpretation and is not statistically meaningful.
In fact, the intercept can be considered as a theoretical value that is not meaningful in the context of the data.
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EASY (NEED HELP)
Find the function that is finally graphed after the following transformations are applied to the graph
1) Reflect about the x axis
2) shift up 9 units
3) shift left 9 units
After reflection and shifts, all three transformations gives us the final function: y = -√(x+9) + 9. This function starts at the point (-9,9) and decreases as x increases. The graph of this function is a reflection of the original graph of y = √x about the x-axis, shifted up by 9 units, and shifted left by 9 units.
What is the function after reflection about x - axisThis function starts at the origin (0,0) and increases as x increases.
1. Reflect about the x axis:
A reflection about the x-axis takes every point on the graph of y = √x and maps it to a new point with the same x-coordinate, but the opposite y-coordinate. For example, the point (1,1) on the graph of y = √x would be reflected to the point (1,-1) on the new graph. This transformation effectively flips the graph upside down.
2. Shift up 9 units:
This transformation moves the entire graph up by 9 units. Every point on the graph is shifted vertically by 9 units. For example, the point (1,-1) on the reflected graph would be shifted up to the point (1,8) on the new graph.
3. Shift left 9 units:
This transformation moves the entire graph to the left by 9 units. Every point on the graph is shifted horizontally by 9 units. For example, the point (1,8) on the shifted graph would be shifted left to the point (-8,8) on the final graph.
Combining all three transformations gives us the final function: y = -√(x+9) + 9.
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Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.
How many boxes of cookies did Jane sell last year?
Jane sold 27 boxes of cookies last year if Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Given ,
Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.
Let's assume the number of boxes Jane sold last year as x.
As per the given condition, 50 = 2x - 4
Adding 4 on both sides, we get:
50 + 4 = 2x - 4 + 4
54 = 2x
Dividing by 2 on both sides, we get:
x = 27
Therefore, Jane sold 27 boxes of cookies last year.
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Identify the slope and Y intercept of the line whose equation is given right the white intercept as an ordered pair remember the slope intercept formula is Y equals MX plus BQ equals two minus are
Answer:
The correct answer is: slope= -1; y-intercept (0,2)
Step-by-step explanation:
The given equation is: [tex]q=2-r[/tex]
Assuming [tex]q[/tex] and [tex]r[/tex] as [tex]y[/tex] and [tex]x[/tex] respectively, the equation becomes: [tex]y=2-x[/tex]
Rearranging the terms in right side: [tex]y=-x+2[/tex]
Comparing this above equation with the slope-intercept form [tex]y=mx+b[/tex], we will get.....
[tex]mx=-x[/tex] ⇒ [tex]m=\frac{-x}{x} =-1[/tex]
[tex]and[/tex]
[tex]b=2[/tex]
So, the slope is -1 and y-intercept is (0, 2)
From the sum of 8a-2b+8 and -2a+6b,subtract 5b-6a ?
Therefore , the solution of the given problem of expressions comes out to be b + 8 when 8a-2b+8 and -2a+6b are added together.
Expression : what is it ?There is a need for calculations like joining, random variable division, variable multiplication, and removal. If they were united, the following would happen: A mathematical equation, some data, and a formula. A statement of truth is composed of numerical data, formulae, components, and mathematical operations like additions, subtractions, errors, and segmentations. One can assess and analyse words and sentences.
Here,
The formula is as follows:
=> 8a - 2b + 8 - 2a + 6b - (5b - 6a)
By combining similar words to make the expression shorter, we get:
=> (0a - b + 8 = -b + 8)
=> (8a - 2a - 6a) + (-2b + 6b - 5b)
Therefore, the answer is b + 8 when 8a-2b+8 and -2a+6b are added together.
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Farmer Ed has 1,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
Answer:
Step-by-step explanation:
Farmer Ed has 1,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
i need help with question 6
Find the value of x.
Answer: 19
Step-by-step explanation:
(5x + 30) = 125 (opposite angles are equal)
5x = 95
x = 19
given the lengths of two sides of a triangle , write an inequaluty to indicate between which two number the lengths of the third side must fall. 8 and 13
Answer:
5 < x < 21
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
13 - 8 < x < 13 + 8 , then
5 < x < 21
find the diffrence. enter your answer in simplest terms using the slash (/) as a faction bar
Answer:
7/8 - 5/7 =
49-40/56 =
9/56
What identity can be used to rewrite the expression 8x³ +243?
A. Difference of Cubes
B. Pythagorean Triples
C. Difference of Squares
D. Sum of Cubes
Here the option is (D): Sum of Cubes.
The Given expression can be written as:
a³ + b³ = (a + b)(a² - ab + b²)
we can write 8x³ as (2x)³ and 243 as 3³.
we have,
8x³ + 243 = (2x)³ + 3³
we can rewrite the above equation
(2x + 3)(4x² - 6x + 9)
Therefore, the identity that can be used to rewrite the given expression is an option (D): Sum of Cubes
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ANSWER RIGHT NOW PLEASE
Answer:
0.19^9
0.19 to the 9th power
Step-by-step explanation:
Use Exponent Rules:
If you are multiplying terms with the same base, then ADD the exponents.
see image
help again asapppppp
Answer:
[tex]\mathrm{y\:=\:\frac{3}{2}x\:+\:7}[/tex]
Step-by-step explanation:
To find the equation of a line parallel to -4y = 32 - 6x, we first need to rewrite this equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
-4y = 32 - 6x
Divide both sides by -4:
y = -8 + (3/2)x
So the slope of this line is 3/2. Since we want a line parallel to this one, it will have the same slope of 3/2.
Now we can use the point-slope form of a linear equation to find the equation of the line that passes through (0,7) with a slope of 3/2:
y - y1 = m(x - x1)
where m = 3/2 and (x1,y1) = (0,7)
y - 7 = (3/2)(x - 0)
Simplifying:
y - 7 = (3/2)x
y = (3/2)x + 7
So the equation of the line parallel to -4y = 32 - 6x that passes through the point (0,7) is y = (3/2)x + 7.
What is the distance between the points (15,-17) and (-10,-17) in the coordinate plane?
A. 12.5 units
B. 25 units
C. 32 units
D. 5 units
Hello and Regards zoecenters91522.
Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.
Step-by-step explanation:The distance between two points is the measure of the length of the straight line that joins them. On a Cartesian plane, the distance between two points is calculated using the Euclidean distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is equal to the square root of the sum of the squares of the differences of their coordinates:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
This formula can be used to calculate the distance between two points on any plane, such as a three-dimensional plane or Euclidean space of any dimension.
Now we locate the points of x and y.
x₁ = 15, y₁ = -17x₂ = -10, y₂ = -17We substitute the points in the formula and solve:
[tex]\huge \boxed{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex]\huge \boxed{d=\sqrt{(-10-15)^2+(-17-(-17))^2 } }[/tex]
[tex]\huge \boxed{d=\sqrt{(-25)^2+0^2}=\sqrt{625+0} }[/tex]
[tex]\huge \boxed{d=\sqrt{625}=25 \ units }[/tex]
Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.
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Given: If A AND B, then C. Given: The if-then statement's reverse isalso correct. If A is True, B is True, what is C?
The conclusion is that if A is true, B is true, then C must be true as well.
What is statement ?
In logic and mathematics, a statement is a declarative sentence that is either true or false. It is an assertion about a fact or a relationship between facts. A statement can be a simple sentence, such as "The sun is shining," or a complex one, such as "If it rains tomorrow, I will stay indoors."
If the statement "If A AND B, then C" is true, and if its reverse statement is also true, then the converse of the statement is "If C, then A AND B."
If A is true and B is true, then A AND B is also true. Therefore, by the original statement, C must also be true.
Therefore, the conclusion is that if A is true, B is true, then C must be true as well.
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8. Daisy is trying to figure out how much negotiating room she has in purchasing a new car. The car has an MSRP of $34,995.99. She has learned from an industry insider that most car dealerships have a 20% markup on selling price. What does she estimate the dealership paid for the car?
Answer:
To estimate the dealership's cost for the car, we need to first calculate the dealership's selling price. We know that the car has an MSRP of $34,995.99, and we know that dealerships typically have a 20% markup on selling price.
So, to find the dealership's selling price, we can use the formula:
Selling price = MSRP + (Markup percentage * MSRP)
Substituting the values we have:
Selling price = $34,995.99 + (20% * $34,995.99)
Selling price = $34,995.99 + $6,999.20
Selling price = $41,995.19
Therefore, we estimate that the dealership paid $41,995.19 - the 20% markup - for the car.
To check this estimate, we can calculate the dealership's cost using the formula:
Cost = Selling price - Markup
Substituting the values we have:
Cost = $41,995.19 - (20% * $41,995.19)
Cost = $41,995.19 - $8,399.04
Cost = $33,596.15
This is very close to the MSRP of $34,995.99, which suggests that our estimate is reasonable.