(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".
Hypotheses: M(Penelope), D(Penelope)
Conclusion: M(Penelope)
Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:
From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)
From D(Penelope), we have M(Penelope)
So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".
Hypotheses: A(Penelope), ~D(Penelope)
Conclusion: ~M(Penelope)
Using modus tollens, which states that if P implies Q and Q is false, then P must be false,
we can conclude that M(Penelope) is false:
From A(Penelope) and "Every student who missed class or got a detention did not get an A",
we have ~M(Penelope) & ~D(Penelope)
From ~D(Penelope), we have ~M(Penelope)
So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
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assistance with This question please I’ll give you brainliest
Answer:
%6, 1/2, 0.6, 6/5
Step-by-step explanation:
Answer:
Bottom left option
Step-by-step explanation:
The four numbers present in this order are:
[tex]\frac{1}{2} = 0.5[/tex]
0.6
[tex]\frac{6}{5} = 1.2[/tex]
[tex]6 percent = \frac{6}{100}[/tex] = 0.06
The order of the numbers from least to greatest are:
6%, [tex]\frac{1}{2}[/tex], 0.6, [tex]\frac{6}{5}[/tex]
Please help me with this question.
The area of the rectangle will be equal to 11 square units.
Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.
A matrix is a structured table with columns and rows for arranging numbers, expressions, and even symbols. If the two matrices have equal row and column sizes, they can be added to, subtracted from, and multiplied element by element.
The area of the rectangle is calculated by finding the determinant of the matrix as below,
[tex]A = \left[\begin{array}{cc}3&-1&\\5&2&\\\end{array}\right][/tex]
A = ( 6 - ( -5 )
A = 6 + 5
Area = 11 square units
Hence, the value of the area of the rectangle is 11 square units.
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How do i rewrite the sum in the form a(b+c) such that the integers b and c have no common factor. 36+72
Ans:-
[tex] \: [/tex]
[tex] \underline{ \boxed{ \bold{12( 3 + 6 )}}}[/tex][tex] \: [/tex]
Int b nd c can be divide by 12
[tex] \: [/tex]
[tex] \rm 12 × 3 = \bold{36}[/tex][tex] \: [/tex]
[tex] \rm 12 × 6 = \bold{72}[/tex][tex] \: [/tex]
The Sum In The Form a( b + c ):-
[tex] \: [/tex]
[tex] \rm \bold{12 ( 3 + 6 )}[/tex][tex] \: [/tex]
[tex] \underline{ \rm \: 36 + 72 \: }[/tex][tex] \: [/tex]
hope it helps! :)
Need Help please, here is screenshot
1)
The axis of symmetry is x = -6.
2)
Vertex is (-6, 26).
3)
f(x) has a maximum value.
4)
f(x) is concave down.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
f(x) = -x² - 12x - 10
This is in the form of ax² + bx + c.
a = -1, b = -12, c = -10
The axis of symmetry is x = -b/2a
x = 12/(-2)
x = -6
Now,
f(x) = -x² - 12x - 10
f(x) = -(x² + 12x + 10)
f(x) = - { (x² + 12x + 36) - 36 + 10}
f(x) = -(x + 6)² + 26
This is in the form of f(x) = a (x - h)² + k
a = -1, h = -6, k = 26
Vertex = (h, k) = (-6, 26)
Now,
f(x) = -x² - 12x - 10
f'(x) = -2x - 12
f''(x) = -2
It is a negative value.
This means f(x) has a maximum value.
Now,
From the graph, we see that f(x) is concave down.
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1/4 of what is 1/5 thank you very much
Answer:
4/5
Step-by-step explanation:
Call our unknown variable ‘x’
X(1/4)=1/5
Therefor, x=4/5
The problem: Shawn thought of planning for his 18-year-old daughter going
off to college when she was born. Create a realistic compound interest
equation that shows the value of the investment that Shawn made using
A = P(1 + i
n)tn
The total value of the account after 18 years, deposit of $100,000 with monthly compounding and a rate of 5%, is given as follows:
$245,501.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
[tex]P = 100000, r = 0.05, n = 12, t = 18[/tex]
Hence the balance is given as follows:
A(18) = 100000 x (1 + 0.05/12)^(12 x 18)
A(18) = $245,501.
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Simplify 10 • (2 + 5).
25
17
70
100
Answer: 70
Step-by-step explanation: To find this answer, we must use PEMDAS. So, we have parentheses (adding) and multiplying. The P is first, so we solve for parentheses first. So, 2 + 5 = 7. So, now we multiply. 10 * 7 = 70. Therefore 70 is our answer. I hope this helped!
If A(0, 4), B(5, y), and AB = 13. What is y?
The required value of y for the given segment AB is given as y = 16, -8.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
here,
A(0, 4), B(5, y), and AB = 13.
Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]
Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12
y = 16, -8
Thus, the required value of y for the given segment AB is given as y = 16, -8.
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Write the equation of the function graphed below:
An equation of the function graphed above include the following: f(x) = 2∛x - 4.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Additionally, a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate of the pre-image or parent function.
By critically observing the graph of the function shown above, we can logically deduce that it is a cube root function that has been vertically shifted by a scale factor of 2 units and then translated downward by 4 units. Therefore, this can be modeled by this equation as follows;
f(x) = 2∛x - 4.
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Give the solution of the equation x+5/3=15
Answer:
x = 40/3
Step-by-step explanation:
x+5/3=15
x + 5/3 = 45/3
x = 40/3
Let's check
40/3 + 5/3 = 15
45/3 = 15
15 = 15
SO, x = 40/3 is the correct answer.
Q1: For triangle ABC use the Triangle Proportionality Theorem to solve for x. Show all of your work for full credit.
Q2: What is the perimeter of triangle ABC? Show all of your work for full credit.
The value of x in the triangle is 17 .
The perimeter of the triangle ABC is 86 units.
How to use triangle proportionality theorem to find side of a triangle?Triangle Proportionality Theorem states that If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
Therefore, let's use the theorem to find the value of x in the triangle.
Hence,
20 / 4 = 2x - 4 / 6
cross multiply
120 = 4(2x - 4)
120 = 8x - 16
120 + 16 = 8x
136 = 8x
divide both sides by 8
x = 136 / 8
x = 17
Hence, let's find the perimeter of the triangle ABC.
perimeter of the triangle ABC = 24 + 26 + 2(17) - 4 + 6
perimeter of the triangle ABC = 50 + 30 + 6
perimeter of the triangle ABC = 86 units
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Please answer!!!
question: What is the triangle's base, b?
Answer:
b = 8 cm
Step-by-step explanation:
Area: 1/2*base*height
1/2*base*3=12
3*base=24
base=24/3
base=8 cm
random variables and have the following distribution. x2 f(x1,x2) 0.00 10.00 20.00
x1 5.00 0.20 0.14 0.06
10.00 0.11 0.07 0.12
20.00 0.08 0.02 0.20
Find P(X +Y s 4). (write up to first decimal place)
P(X + Y < 4) = 0.53 rounded to the first decimal place.
To find the probability P(X + Y < 4),
we need to find the values of x1 and x2 that satisfy the condition
X + Y < 4, and then sum up the corresponding probabilities in the table.
We can start by plotting the points (x1, x2) on a graph and finding the region where X + Y < 4.
This region can be determined by shading in the portion of the graph that is below the line X + Y = 4.
Next, we need to find the values of x1 and x2 in the table that fall within this region and sum up their probabilities.
This gives us P(X + Y < 4) = 0.20 + 0.14 + 0.11 + 0.08 = 0.53.
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A population, f(x), after x years may be modeled with f(x)=2(3)^x. What is the initial amount , growth rate, domains and range?
2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and range of the function is all positive real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is:
f(x) = 2(3)ˣ
To find the initial amount, we need to find f(0):
f(0) = 2(3)⁰ = 2(1) = 2
So the initial amount is 2.
To find the growth rate, we can use the formula:
growth rate = (f(x) - f(0)) / f(0) × 100%
= (2(3)ˣ - 2) / 2 × 100%
= (3ˣ - 1) × 100%
So the growth rate is (3ˣ - 1)×100%.
The domain of the function is all real numbers because the function is defined for all values of x.
The range of the function is all positive real numbers because the function is always positive for any value of x.
Specifically, the range of the function is (0, infinity).
Hence, 2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and range of the function is all positive real numbers
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Find f(a + 5).
f(x) = x² + 7
Answer:
[tex]f(x) = {x}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {(a + 5)}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {a}^{2} + 25 + 10a + 7 \\ \dashrightarrow \: \: \boxed{ f(a + 5) = {a}^{2} + 10a + 32}[/tex]
hope helpful! :)
Let the vector space P2 have the inner product
⟨p,q⟩=∫4−4p(x)q(x)dx
Find the following for p=2x, q=5x2.
Solution
(i) ⟨p,q⟩=
(ii) d(p,q)=
(iii) ∥p∥=
(iv) ∥q∥=
Do the values in the table represent a proportional relationship?
Answer:
Yes
Step-by-step explanation:
Yes, they do since if you multiply the y by 2.5 it will give you all the answers you entered
Tell whether the triangles are congruent. Explain your reasoning.
Answer:
Yes because there all the same shape the size dosent effect the shape of it.
Step-by-step explanation:
Answer:
101. ΔABC congruent to ΔDEF
102. ΔJKL not congruent to ΔMNO
Step-by-step explanation:
Q 101
Triangle ABC has 3 sides equal to each of the three sides of DEF
The corresponding two angles of ABC and DEF are also equal
So the third angle of ABC ∠B must be equal to the third angle of DEF so we have three sides equal, three angles equal, hence congruent
ΔABC congruent to ΔDEF
Q 102
We have JL = MP = 1.9
m∠J = m∠M = 24°
The other two angles are not correspondingly equal
This only makes one side equal and one angle equal. Not sufficient to make it congruent
Hence ΔJKL not congruent to ΔMNO
#1. Which situation represents an example of a non-proportional Equation? A. A farmer sells fresh peaches for $0.71 a pound. B. Michael's Pizza charges a $5 fee for the delivery of each pizza. C. Emiliano's cell phone plan charges $40 per gigabyte of data used. D. The temperature in the morning was 49 F, and it increased by 3 F every hour.
When two variables' ratios are equivalent, proportional relationships between them emerge.The right response is option c.A $50 membership fee plus a $20 monthly cost is required to use a gym.
What is a proportional relationship?Because b, the w intercept, is zero in the linear exhaustion of a line, y=mx+b, a proportionate relationship would be something like y=mx+0.IHaving said that, the equation for a line is as follows: so that y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y-intercept).Therefore, this is a y=0.10x for b) (because it is only charging per amount of texts, and nothing else, there is again no b value, so the y-intercept is 0, crossing the origin).(YET AGAIN, THIS IS NOT THE ANSWER)c) y=20x+50 (x is the number of months, and depending on how many months you go to the gym, the amount of money you spend there is determined). Additionally, you must include the $50 cost of the gym membership.In this instance, the b value or y-intercept would be 50 because 50 is being added to the 20x.To learn more about proportional relationship refer
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How many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 25% antifreeze to get a mixture that is 40% antifreeze? Use the six-step method.
You need
gallons.
(Round to the nearest whole number.)
Answer:
Step-by-step explanation:
7877
Answer:
180 gallons is needed.
Step-by-step explanation:
A hose fills a hot tub at a rate of 3.99 gallons per minute. How many hours will it take to fill a 275-gallon hot tub?
The time taken to fill a 275-gallon hot tub is 69 minutes.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A hose fills a hot tub at a rate of 3.99 gallons per minute.
This means,
3.99 gallons = 1 minute
Multiply 275/3.99 on both sides.
275 gallons = 275/3.99 x 1 minute
275 gallons = 69 minutes
Thus,
It will take 69 minutes to fill a 275-gallon hot tub
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According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this
is the parameter value for the population. If a simple random sample of size were taken, what is the approximate
probability that , the proportion who exercise at least five days per week, is higher than 0.30?
The probability that the proportion of a sample is higher than 0.30 can be estimated using the Central Limit Theorem (CLT) which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a large sample size (n >= 30), we can use the normal distribution to approximate the distribution of the sample means.
Assuming the sample size is large, the standard error (SE) of the sample mean is given by
SE = sqrt(p * (1 - p) / n), where p is the population proportion (0.27) and n is the sample size.
With this information, we can find the Z-score corresponding to 0.30 using the formula: Z = (0.30 - 0.27) / SE
Since we don't know the sample size, we'll assume a conservative sample size of 30.
With a sample size of 30, the SE is approximately 0.039, and the Z-score is approximately 0.77.
Using a standard normal table, we can find the probability of a Z-score being greater than 0.77 is approximately 0.22.
Therefore, the approximate probability that the proportion who exercise at least five days per week is higher than 0.30 is 0.22.
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Please help me with this question.
The center of mass coordinates of the given plane is -
COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex], [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}
What is center of mass?The center of mass is the point at which the whole mass of the body or system can be considered to be concentrated.
Given is the plane with the equation -
ρ(x, y) = (1 + x/2)
We can write the center of mass as -
X{C.M.} = [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex]
Y{C.M.} = [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]
Therefore, the center of mass coordinates of the given plane is -
COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex], [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}
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A new sidewalk will be 4 feet wide, 140 feet long, and filled to a depth of 6 inches (0.5foot) with concrete. How many cubic yards of concrete are needed?
Answer: 93 [tex]\frac{1}{3}[/tex] yards³
Step-by-step explanation:
We will find the volume in feet with this formula:
V = LWH
V = LWH
V = (140)(4)(0.5)
V = 280 feet³
There are 3 feet in a yard, and the question asks for yards, so we will divide:
280 feet³ / 3 = 93 [tex]\frac{1}{3}[/tex] yards³
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katie rents a car while spending her vacation travelling in australia. when she returns the car, she has driven 1400 miles and used about 56 gallons of gas. if gas costs an average of $5.099 per gallon, estimate how much she spent on fuel.
Katie spent approximately $285.544 on fuel during her vacation in Australia.
The Average Cost is the per unit cost of the product received by dividing the total cost (TC) by the total output (Q). By per unit cost of production, we mean that all the fixed and variable costs are considered for calculating the average cost. Thus, it is also called Per Unit Total Cost.
Symbolically, the average cost is expressed as:
AC = TC/Q
To estimate how much Katie spent on fuel, you need to multiply the number of gallons of gas she used (56 gallons) by the average cost of gas per gallon ($5.099):
56 gallons × $5.099/gallon = $285.544
So, Katie spent approximately $285.544 on fuel during her vacation in Australia.
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Solve and reduce to lowest terms 2/7 x 5/6
Answer:
5/21
Step-by-step explanation:
2 x 5 = 10
--------
7 x 6 = 42
10 / 42 in simplest form is 5/21
Crossfire Company segments its business into two regions—East and West. The company prepared a contribution format segmented income statement as shown below: Total Company East West Sales $ 910,000 $ 650,000 $ 260,000 Variable expenses 637,000 468,000 169,000 Contribution margin 273,000 182,000 91,000 Traceable fixed expenses 133,000 70,000 63,000 Segment margin 140,000 $ 112,000 $ 28,000 Common fixed expenses 56,000 Net operating income $ 84,000 Required: 1. Compute the companywide break-even point in dollar sales. 2. Compute the break-even point in dollar sales for the East region. 3. Compute the break-even point in dollar sales for the West region. 4. Prepare a new segmented income statement based on the break-even dollar sales that you computed in requirements 2 and 3. Use the same format as shown above. What is Crossfire’s net operating income (loss) in your new segmented income statement? 5. Do you think that Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region?
1. Companywide break-even point in dollar sales = $910,000
2. Break-even point in dollar sales for the East region = $391,667
3. Break-even point in dollar sales for the West region = $225,000
How did we get the values?Companywide break-even point in dollar sales: Total fixed expenses / Contribution margin ratio = $189,000 / (273,000/910,000) = $910,000
Break-even point in dollar sales for the East region: Traceable fixed expenses / Contribution margin ratio = $70,000 / (182,000/650,000) = $391,667
Break-even point in dollar sales for the West region: Traceable fixed expenses / Contribution margin ratio = $63,000 / (91,000/260,000) = $225,000
New segmented income statement based on the break-even dollar sales:
Total Company
Sales $910,000
Variable expenses 637,000
Contribution margin 273,000
Traceable fixed expenses 133,000
Segment margin 140,000
Common fixed expenses 56,000
Net operating income $ 84,000
Total East
Sales $391,667
Variable expenses 258,250
Contribution margin 133,417
Traceable fixed expenses 70,000
Segment margin 63,417
Total West
Sales $225,000
Variable expenses 154,500
Contribution margin 70,500
Traceable fixed expenses 63,000
Segment margin 7,500
Net operating income in the new segmented income statement: $84,000
Yes, Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region as these expenses benefit both regions and affect the profitability of each region.
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8n = 120 − 8(5 + 2)
can someone help me with this, im too lazy lol
Answer:
Step-by-step explanation: First, do the multiplication inside the parenthesizes so 8x5 is 40, and 40+2 is 42. 120-42=78
8n=78
n=9.75
two different ways to represent the expression -1/3x -17/3
Answer: -1/x-17 -1-17x
Step-by-step explanation:
the retail price of a tv is $600. The discount is 25% and tax is7%. how much do you pay for the tv?
Answer:
$ 481.50
Step-by-step explanation:
Discount:
Discount = 25% of retail price of TV
= 0.25 * 600
= $ 150
Price after discount = Retail price - discount
= 600 - 150
= $ 450
Tax:
Tax = 7% of 450
= 0.07 * 450
= $ 31.50
Amount to be paid:
Amount needs to be paid = price after discount + tax
= 450 + 31.50
= $ 481.50
