Answer:
The marked price of the torchlight is Rs. 1960.
Step-by-step explanation:
The marked price (MP) of a torchlight is 40% more than the cost price (CP), so we can calculate the MP using the formula:
MP = CP + (CP x 40%)
The cost price of the torchlight is Rs. 1400, so the marked price is:
MP = 1400 + (1400 x 40%) = 1400 + 560 = 1960
The shopkeeper is selling the torchlight at a 20% discount, so we can calculate the selling price (SP) using the formula:
SP = MP - (MP x 20%)
The marked price of the torchlight is Rs. 1960, so the selling price is:
SP = 1960 - (1960 x 20%) = 1960 - 392 = 1568
So the marked price of the torchlight is Rs. 1960.
A company is planning to purchase a plot of land for $200,000 to build a factory. There are two options offered by a lending institution.
1. 20-year loan at 3.25% APR compound monthly
2. 30-year loan at 4.75% APR compound monthly
- Calculate the monthly payment for both options.
- Calculate the finance charge for both options.
- Determine which option is better for the company & explain why.
Answer:
1.) 20 yrs --> $1,045.63
30 yrs --> $1,204.08
2. See the attachment
3. See the attachment
Step-by-step explanation:
Please find the attachment for detail
An 8-foot ladder is leaning against a wall so that the top of the ladder is 5 feet above the ground. If a 15-foot ladder is leaned against the wall and forms the same angle with the wall, how high up the wall does this ladder reach? Enter your answer in the box. Show your answer to thousandths.
5. Use the graph to find the cost of 8 hats.
a. $7.50
b. $8.00
c. $60.00
d. $75.00
Answer:
c. $60
Step-by-step explanation:
Go along the x-axis until you get to 8, then go straight up until you hit the line, now go straight over to the left until you hit the y-axis. Your horizontal line will hit the y-axis at y=$60.
find the market equilibrium point for the following demand and supply functions. demand: p = −2q 280 supply: p = 8q 1
The market equilibrium point for the following demand and supply functions are, demand and supply p = 224.2
He estimated the market demand and supply function as follows demand : P = −2q + 280 (Equation-1)
supply: P = 8q + 1 (Equation-2)
We need to find the equilibrium price
The equilibrium price (EP) is the price where the demand for a product or service balances its supply. .
At equilibrium price
Demand function = supply function
−2q + 280 = 8q + 1
280 - 1 = 8q + 2q
279 = 10q
q = 279/10
q = 27.9
We can substitute equation-1,
The equilibrium price = −2q + 280
The equilibrium price = -2(27.9) + 280
The equilibrium price = -55.8 + 280
The equilibrium price = 224.2
We can substitute equation-2,
The equilibrium price = 8q + 1
The equilibrium price = 8(27.9) + 1
The equilibrium price = 223.2 + 1
The equilibrium price = 224.2
demand: p = 224.2
supply: p = 224.2
Therefore,
The market equilibrium point for the following demand and supply functions are, demand and supply p = 224.2
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the base radius and height of a right circular cylinder are measured as 8 cm and 16 cm, respectively, with a possible error in measurement of as much as 0.2 cm each. use the total differential to estimate the maximum error in the calculated volume of the cylinder.
The total differential to estimate the maximum error in the calculated volume of the cylinder is 200.96.
The base radius of a right circular cylinder are measured as 8 cm.
The height of a right circular cylinder are measured as 16 cm.
The possible error in measurement of as much as 0.2 cm each.
We have to calculate the maximum error in the calculated volume of the cylinder.
The formula of volume of cylinder is:
V = πr^2h
The value of dr = 0.2 and dh = 0.2. So;
dV(max) = ∂V/∂r dr + ∂V/∂dh dh
dV(max) = ∂(πr^2h)/∂r dr + ∂(πr^2h)/∂dh dh
On differentiating
dV(max) = 2πrh dr + πr^2 dh
r = 8 cm, π = 3.14 and h = 16 cm.
Now putting the value
dV(max) = 2×3.14×8×16×0.2 + 3.14×(8)^2×0.2
dV(max) = 160.768 + 40.192
dV(max) = 200.96
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what is the coefficient of x2 in the taylor series for sin2x about x=0? responses
The coefficient of x² in the Taylor series for sin²x about x=0 is 1
If a Taylor Series is centred at 0, then the series is known as the Maclaurin series.
Maclaurin series is given by f(x) = [tex]\text{\Large$ \Sigma$}\limits^{\infty}_{k=0} \frac{f^{(k)}(a)}{k!}x^k[/tex]
f(x) = sin²x
We need coefficient of x², let us take n=5
f(x) = [tex]\text{\Large$ \Sigma$}\limits^{\infty}_{k=0} \frac{f^{(k)}(a)}{k!}x^k[/tex]
f^0(x) = sin²x => f^0(0) = 0
f^1(x) = 2 sinx cosx => f^1(0) = 0
f^2(x) = -2 sin²x + 2 cos²x => f^2(0) = 2
f^3(x) = -8 sinx cosx => f^3(0) = 0
f^4(x) = 8 sin²x - 8 cos²x => f^4(0) = -8
f^5(x) = 32 sinx cosx => f^5(0) = 0
f(x) = 0(x^0) + 0(x^1) + (2/2!)(x^2) + (0/3!)(x^3) + (-8/4!)(x^4) + (0/5!)(x^5)
f(x) = x^2 - (1/3)x^4
We can see that the coefficient of x² is 1.
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given the following codes, what would be the final value of z? x = 5 y = 7 z = x - y 2.00
Z would ultimately have a value of 2, since 5 minus 7 equals 2.
x = 5; y = 7; z = x - y z = 5; y z = 7; z = 2;Consequently, z's final value is 2.
Given that x is 5 and y is 7, the final value of z would be 2. These two numbers are divided by two, giving the answer 2. Subtraction is the action of comparing two integers to determine their differences. In this instance, since x and y differ by 2, the ultimate value of z is also 2. The solution is 2, which can alternatively be written as 5 - 7 = 2. In this case, the ultimate value of z is 2, since the difference between x and y is 2, which can be found using the useful mathematical technique of subtraction.
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The Firt Amendment include four baic right or freedom. What are they? Which of thee will be the focu of thi unit?
The four basic right that were included in the first amendment are Freedom of speech , Freedom of religion , Freedom of press and Freedom of assembly .
The First Amendment of the U.S. Constitution guarantees the following four basic rights:
(i) Freedom of Speech: This includes the right to express oneself freely, whether through oral or written communication.
(ii) Freedom of Religion: This protects an individual's right to practice their own religion or to not have a religion at all, without government interference.
(iii) Freedom of the Press: This protects the right of the media to publish and report the news without government censorship or restraint.
(iv) Freedom of Assembly: This allows individuals to gather and associate with others, including the right to form and participate in organizations and protest movements.
The given question is incomplete , the complete question is
The First Amendment include four basic right or freedom. What are they ?
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equation that can be used to solve for y, the length of the room is;
y² - 5y = 750
How to solve Algebra Expressions?The formula for the area of a rectangle is;
Area = L * W
where;
L is length
W is width
The width of the room is 5 feet less than the length of the room. Thus;
Width = Length - 5
If length is y, then;
Width = y - 5
Area = y(y - 5)
y(y - 5) = 750
y² - 5y = 750
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all piece must be assigned for the appropriate functional groups (ir) and protons (nmr) to earn full credit. 6. c5h10o
The correct answer is C5H10O which is also known as Methyl propyl ketone.
Methyl propyl ketone is a clear, colorless liquid with a nail polish-like smell. 45 °F flash point water soluble and less dense than water. consequently floats on water. 0.809 g/cm3 for density. heavier than air vapors.
CH3 – CH2 —C—CH? C–CH2–CH3 Molecular Formula: C5H100 Molecular Weight: 86.1 Name: 3-pentanone
CsH10 (4pts) IR C=O overtone 2941cm-1 C-H symmetric and asymmetric stretching of (-CH3 & -CH2-) 1716 cm-1 C=O stretch of K
6. C5H10O
CH3 – CH2 – CH-6-H CH: Molecular Formula: C5H100 Molecular Weight: 86.1 Name: 2-methylbutanal
IR C=0 Overtone Orman mu C-H Aldehyde Doublet stretch C-H symmetric and asymmetric stretching of sp3 carbon C=0 stretch HNMR
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Factor out a negative 1 from each expression
1: 7 + (-6)
2: -4 - (5 + 3)
3: -9 - 1
4: 8 - (-6)
5: 3 + (-4 + 8)
Use the distributive property to show that your answers to Questions one through 5 are
correct.
Factoring out negative 1 from the expression -4-(5+3) is -1(12).
What are factors?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
A) 7+(-6)
= 7-6
= 1
2) -4-(5+3)
= -4-8
= -12
= -1(12)
3) -9-1
= -10
= -1(10)
4) 8-(-6)
= 8+6
= 14
5) 3+(-4+8)
= 3+4
= 7
Therefore, factoring out negative 1 from the expression -4-(5+3) is -1(12).
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Which measurements represent the side lengths of a right triangle?
Right Triangle
NOT a Right Triangle
6 cm, 8 cm, 10 cm
12 cm, 35 cm, 37 cm
4 cm, 6 cm, 10 cm
10 cm, 24 cm, 26 cm
Answer:
(a) {6, 8, 10} cm
(b) {12, 35, 37} cm
(d) {10, 24, 26} cm
Step-by-step explanation:
You want to know which of the given sets of dimensions could be those of a right triangle.
6, 8, 10 cm12, 35, 37 cm4, 6, 10 cm10, 24, 26 cmPythagorean theoremA set of side lengths will form a right triangle if they satisfy the Pythagorean theorem:
a² +b² = c²
Application6² +8² = 36 +64 = 100 = 10² . . . . . {6, 8, 10} forms a right triangle
12² +35² = 144 +1225 = 1369 = 37² . . . . . {12, 35, 37} forms a right triangle
4 + 6 = 10 . . . . . {4, 6, 10} doesn't even form a triangle
10² +24² = 100 +576 = 676 = 26² . . . . . {10, 24, 26} forms a right triangle
__
Additional comment
For three side lengths to form a triangle, the sum of the two short sides needs to be longer than the longest side. (This is the triangle inequality.)
Lengths 4, 6, 10 do not meet that requirement.
You may notice that the long sides of these triangles differ in length by 2 units. The short side is twice the square root of their average. This relation will hold for any right triangles having long sides that differ by 2.
{6, 8, 10} ⇒ 6 = 2·√9
{12, 35, 37} ⇒ 12 = 2·√36
{10, 24, 26} ⇒ 10 = 2·√25
Along the same lines, if the longest sides differ by 1, the short side is the square root of their sum.
What is the rule for the following pattern by 9 18 12 24 18 36 30?
The rule for the pattern is to add 6 to each number.
What is the rule for the following pattern by 9 18 12 24 18 36 30?The pattern for this sequence is that it follows a multiplication by two rule. This means that each term in the sequence is twice the previous term. This rule is also known as the exponential rule, because each term is the result of multiplying the previous term by two.This pattern is an example of exponential growth, which is defined as a growth rate that increases by a fixed rate over a period of time. In this case, the fixed rate is a multiple of two, and the growth rate is increasing by a factor of two each time.Exponential growth is important in mathematics and science because it can be used to predict the growth of populations, the spread of disease, the growth of financial investments, and the growth of technology. It is also important in the study of natural phenomena such as climate change and the evolution of life.Exponential growth can be represented as a graph, which will show a curved line with a steep slope. This is because the growth rate is increasing exponentially. As the sequence progresses, the rate of growth will become increasingly steep.The rule for this pattern is that each term is twice the previous term, and this type of pattern is called exponential growth. It is important in mathematics, science, and other fields because it can be used to predict the growth of populations, the spread of disease, the growth of financial investments, and the growth of technology.To learn more about the exponential rule refer to:
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Which of the following terms completes the sentence below?
To fill out a function's______
and after each of the function's
, you will need to use test numbers before
and asymptotes.
O A. rational equation; values
OB. sign chart; values
OC. rational equation; zeros
O D. sign chart; zeros
Answer:
D. sign chart; zeros
Step-by-step explanation:
To fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes
What is Number system?A number system is defined as a system of writing to express numbers.
The term that completes the sentence and makes it grammatically and conceptually correct is "sign chart; zeros".
To fill out a function's sign chart; zeros and after each of the function's zeros, you will need to use test numbers before and after the zero to determine the sign of the function on each interval.
Hence, to fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes
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Which of the following would be classified as categorical data?
Choose the correct answer below.
A. Hair color
B. Number of suitcases on a plane
C. Tree height
D. Amount of rainfall
Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.
Statistical information made up of categorical variables—data that have been divided into categories—is known as categorical data. A set of grouped data is one of example. More specifically, countable qualitative data or quantitative data clustered within predetermined intervals could be used to create category data. The information is condensed into a probability table. However, the word "categorical data," which is used to describe data sets, is used when discussing data analysis. It should be noted that although the data set includes some categorical variables, it may also include non-categorical variables.
Categorical data is a collection of information that is divided into groups. I.e, if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical. This data is called categorical because it may be grouped according to the variables present in the biodata such as sex, state of residence, etc.
A. Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.
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What is the quotient?
49 ÷ 3
This model describes the division calculation.
What do I put in the boxes
The value of 49 ÷ 3 is 16 remainder 1
How to evaluete the quotientFrom the question, we have the following parameters that can be used in our computation:
49 ÷ 3
This can be interpreted as
49 divided by 3
Dividing 49 by 3 can be done using the given model
From the model, we have
49 ÷ 3 = (30 + 19) ÷ 3
This gives
49 ÷ 3 = (30 + 18 + 1) ÷ 3
So, we have
49 ÷ 3 = 16 1/3
So, the result is 16 remainder 1
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Determine all intervals on which f(x)[tex]\leq[/tex]0.
The required interval for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
From the graph, the portion of the function below the axis shows the f(x) ≤ 0.
So the interval where f(x) ≤ 0, from the graph, is given as,
(-∞, -2) and (2, 7)
Thus, the required intervals for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).
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you have 28 cards and 10 envelopes (labeled 1,2, ..,10). in how many ways can you put the 28 cards into the envelopes if:
The number of permutations of putting the 28 cards into the envelopes is 1024.
A permutation is the arrangement of objects in a specific order. When we are counting the number of permutations of a set of objects, we are finding the total number of ways that the objects can be arranged.
In your question, you have 28 cards and 10 envelopes. To find the number of permutations of putting the 28 cards into the envelopes, we need to consider a few factors.
Firstly, each envelope can only hold a maximum of
=> 28/10 = 2 cards.
Secondly, the order in which the cards are placed into the envelopes matters,
Since each envelope can only hold a maximum of 2 cards, we have two options for each envelope: either 0 cards or 2 cards.
We can use a binary code of 0 and 1 to represent this, where 0 means the envelope is empty and 1 means the envelope has 2 cards.
Therefore, the total number of permutations can be calculated as
=> 2¹⁰ = 1024
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A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $28. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Based on the information, it can be inferred that this salesperson must make sales equivalent to $28,000 to obtain an equal profit with both options.
How to find the amount of money that he would have to sell to make the same profit with both options?To find the amount of money that we must sell to have the same profit with both options we must carry out the following mathematical procedure.
1. We must calculate how much you would earn with option A in a week.
$28 * 40 = $1,120
2. We must make a rule of three to find a value of which 4% is equal to 1,120
4% - $1,120100% - x100% * $1,120 / 4 = $28,000Based on the above, the salesperson must sell $28,000 to make the same profit on both options in one week.
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We have two mass storage devices, A and B with the same specs. Each can store N bits, but read/write operations are slow. We mitigate this problem by turning the two devices into a storage array: data is alternatingly written to A and B. The array can now store 2N bits, and read and write at almost twice the speed of the individual devices, assuming that the time it takes to send data to A and B is negligible, compared to the time it takes each device to write the data.There is however a flaw in this plan. Since data is distributed over two devices, the total chance of failure has now doubled. The failure of just one device causes the failure of the array.We could eliminate this problem by copying all of A's data redundantly to an additional devices C, and all of B's data to an additional device D. This insures against single and double drive failure, but at the cost ofdoubling the required amount of storage devices.We decide that simultaneous drive failure is sufficiently unlikely to ignore that possibility, and we will guard against data loss from single drive failure only. This requires only one extra device C, as follows:We abstract each device as a list of bits, A= a1, a2,..., aN, B=b1, b₂,... bNand C=C1, C2,..., CN.Then for each k=1...N, C storesCk=ak XOR bkHere, XOR is the bitwise exclusive or operation.(a) (2 points) With this scheme, if bit k fails on device A or B (not both), it can be reconstructed from bit k on device C. Explain.(b) (2 points) Would the same reconstruction property still hold if you used logical AND instead of XOR? Explain your answer.(c) (2 points) Would the same reconstruction property still hold if youused logical inclusive OR instead of XOR? Explain your answer.
The best mathematical operation to use when considering the probability of data loss from single drive failure is XOR.
Data storage is a critical process, as any data loss could have disastrous consequences.
The XOR technique uses one extra device (C) to store the exclusive OR result of the data stored on devices A and B. This means that for each bit k, the value of Ck is the exclusive OR of ak and bk.
This means that if bit k fails on device A or B (not both), it can be reconstructed from bit k on device C. This is because the exclusive OR of two identical bits is 0 and the exclusive OR of two different bits is 1, which can be used to reconstruct the failed bit from the other one.
The same cannot be said of the AND or OR technique. If we use the AND technique, the value of Ck would be the logical AND of ak and bk.
In this case, the failed bit could not be reconstructed from the other bit, as the logical AND of two identical bits is the same bit and the logical AND of two different bits is 0.
The same problem applies for the OR technique, as the value of Ck would be the logical OR of ak and bk, and the failed bit could not be reconstructed from the other bit.
Thus, XOR is the best mathematical operation to use when considering the probability of data loss from single drive failure.
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PLS HELP ME!!!!
2 x3x5² is the prime factorization of what composite number? OA) 120 OB) 180 OC) 450 OD) 600
2³ × 3 × 5² is the prime factorization of the composite number 600.
What is the composite number?Composite numbers are whole numbers that can be divided evenly by numbers other than 1 or themselves. For example, 4 is a composite number because it can be divided evenly by 1, 2, and 4. Other examples of composite numbers are 6, 8, 9, 10, 12, 14, 15, and so on.A composite number is a positive integer that has more than two divisors. It is the product of two or more prime numbers. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, 16 and so on.
2³ × 3 × 5² = 2 × 2 × 2 × 3 × 5 × 5
= 600
Thus, 2³ × 3 × 5² is the prime factorization of the composite number 600.
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Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Be sure to consider whether the units are appropriate to the statement, as well as whether the stated amount makes any sense. For example, a statement that someone is 15 feet tall uses the units (feet) appropriately, but does not make sense because no one is that tall. I know a professional bicyclist who weighs 220 kilograms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to the nearest tenth as needed.) O A. This statement does not make sense because 220 kilograms = pound(s), which is an unreasonable weight for a professional bicyclist. OB. This statement makes sense because 220 kilograms = pound(s), which is a reasonable weight for a professional bicyclist. OC. This statement does not make sense because a kilogram is not a unit of mass.
The statement 'I know a professional bicyclist who weighs 220 kilograms' does not makes sense because 220 kilograms = 485.017 pounds, which is not a reasonable weight for a professional bicyclist.
Therefore the answer is A. This statement does not makes sense because 220 kilograms = 485.017 pound(s), which is an unreasonable weight for a professional bicyclist.
A kilogram is a unit of mass and is commonly used to measure the weight of individuals. One kilogram is equivalent to approximately 2.205 pounds, so 220 kilograms is equivalent to 485.6 pounds, which is off the weight range of many professional cyclists, who typically have a low body fat percentage and high muscle mass. Therefore, it is not possible for a professional cyclist to weigh 220 kilograms and this statement does not makes sense.
--The question is not readable, the question is given below--
"Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Be sure to consider whether the units are appropriate to the statement, as well as whether the stated amount makes any sense.
For example, a statement that someone is 15 feet tall uses the units (feet) appropriately, but does not make sense because no one is that tall.
I know a professional bicyclist who weighs 220 kilograms.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to the nearest tenth as needed.)
A. This statement does not make sense because 220 kilograms = pound(s), which is an unreasonable weight for a professional bicyclist.
B. This statement makes sense because 220 kilograms = pound(s), which is a reasonable weight for a professional bicyclist.
C. This statement does not make sense because a kilogram is not a unit of mass."
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how many hexadecimal strings of length 9 have exactly three a’s, no b’sand two 7’s
There are approximately 368,739,406 possible hexadecimal strings of length 9 with exactly three a’s, no b’s and two 7’s.
Hexadecimal is a numbering system that uses 16 symbols (0-9 and A-F) instead of the standard 10 symbols in decimal.
A hexadecimal string of length 9 with exactly three a’s, no b’s and two 7’s can be represented as
=> XaXaXaX7X7,
where X can be any of the hexadecimal symbols other than a and 7.
To calculate the number of possible combinations, we need to calculate the number of possible values for X.
In total, there are 16 possible hexadecimal symbols, but we need to subtract 3 (a’s) and 2 (7’s) to find the number of possible values for X.
So, the number of possible values for X is
=> 16-3-2 = 11.
With 9 positions to fill and 11 possible values for X, the total number of combinations is 11⁹, which is approximately 368,739,406.
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Short Explanation:Marcelino did not win the game 2 day ago. Marcelino did not win the game yeterday. Therefore, Marcelino will win the game today
This is a false conclusion. Just because Marcelino did not win the game 2 days ago or yesterday, it does not necessarily mean he will win the game today. There could be many other factors at play that determine the outcome of the game.
Marcelino Game Win False ConclusionThis statement is referring to a hypothetical game and the outcome of it, but the conclusion that Marcelino will win today is not logically deduced from the information given (that Marcelino did not win 2 days ago or yesterday). The outcome of a game can be influenced by many factors such as the skill level of the players, the strategies used, and luck. Simply not winning in the past does not guarantee a win in the future.
This statement is not related to mathematics. It is a logical conclusion based on the given information about a hypothetical game, but the conclusion does not follow logically from the information provided.
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a one story house recently sold for $348,000. what is the price per square foot of the house, if the house measures 25' x 68'…?
The price per square foot of the house is $51.18.
The price per square foot of the house is determined by taking the total price of the house, $348,000, and dividing it by the total square footage of the house, 25' x 68' and we get $51.18.
For example- The total square footage is 1700, so when divided into the total cost, $348,000, the price per square foot of the house is $204.71. This means that for every square foot of the house, the buyer paid $204.71. The total cost of the house is a combination of the price per square foot in addition to any additional fees, such as taxes and closing costs.
When purchasing a home, it is important to know the price per square foot as this can help to determine the value of the home.
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Find the perimeter of the isosceles trapezoid pictured above. Round to the nearest hundredth. Do not label your answer.
The perimeter of the isosceles trapezoid is 30.94 cm
How to find the perimeter of the isosceles trapezoid?An isosceles trapezoid is a type of trapezoid where the two sides that are parallel to each other (known as the bases) are of equal length.
The perimeter of an isosceles trapezoid is the sum of the lengths of all four sides.
slant side = √(4²+2²) = 4.47 cm
Note: all sides are identical (check the attached image)
Perimeter = 9 + 4.47 + (2 + 9 + 2) + 4.47 = 30.94 cm
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Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 =____.
Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.
Given log 630 ≈ 1.898 and log 62 ≈ 0.387,
We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387
And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086
So, log 615 ≈ 2.086
In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.
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if p(x)=(4x−5)(4x 5), what are the zeros of the polynomial?
The zeros of the polynomial p(x)=(4x−5)(4x + 5) are x = 5/4 and x = -5/4
We know that the zeros of a polynomial are the points where the polynomial becomes zero.
To find the zeros of polynomial P(x), equation the polynomial to zero P(x) = 0 and find the solutions of the equation P(x) = 0
Here, the polynomial is p(x)=(4x-5)(4x + 5)
To find the zeros of polynomial p(x) we equate p(x) to zero.
We get,
p(x) = 0
(4x - 5)(4x + 5) = 0
We solve above equation for x.
⇒ (4x - 5)(4x + 5) = 0
⇒ (4x - 5) = 0 OR (4x + 5) = 0
⇒ 4x = 5 OR 4x = -5
⇒ x = 5/4 OR x = -5/4
Therefore, x = 5/4 and x = -5/4 are zeros of p(x)
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From a station, hikers Oliver and Roel, who both have uniform hiking, speed walk in opposite directions - Oliver speed walks eastward whereas Roel speed walks westward. After walking 3 kilometers each, both take left turns at different angles. Oliver at angle 30° and Roel at 40°. Both continue hiking and cover another 4 kilometers each after taking a rest. Which of the hikers is farther from their station? Why?
Oliver is farther from the station.
The distance from the station for each hiker can be calculated using the Law of Cosines.Let's call the initial distance from the station for Oliver and Roel as d1 and d2, respectively. The Law of Cosines states:
d1^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(30°)
d2^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(40°)
By solving the above equations, we can determine the distances d1 and d2. The hiker who is farther from the station will have the larger value of d1 or d2.
In this case, it can be seen that d1 > d2, meaning Oliver is farther from the station than Roel.
This is because the angle of 30° is larger than the angle of 40°, so the cosine of 30° is smaller than the cosine of 40°.
Therefore, Oliver is farther from the station.
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a city worker inspected 200 homes in dairy city. during that inspection, 120 homes were found to violate one or more city codes. the city worker released a statement that 60% of dairy city's 3,000 homes are in violation of city codes. this is .
If the city worker released the statement that 60% of dairy city's 3,000 homes are in violation of city codes , then the City Worker's statement is an example of : (d) Statistical Inference .
The Statistical Inference involves making generalizations about a population based on a sample.
In this case, the city worker has taken a sample of 200 homes out of the total 3,000 homes in Dairy City, and based on that sample, the City Worker is making an inference about the proportion of homes in violation of city codes for the entire population of Dairy City.
The statement is not a census as a census would involve collecting data from every single unit in the population, in this case every single home in Dairy City.
The given question is incomplete , the complete question is
A city worker inspected 200 homes in dairy city. during that inspection, 120 homes were found to violate one or more city codes. the city worker released a statement that 60% of dairy city's 3,000 homes are in violation of city codes.
The City Worker's statement is an example of :
(a) Census
(b) An experiment
(c) Descriptive Statistics
(d) Statistical Inference
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