Answer:
B.
Step-by-step explanation:
Took the test :}
(giving brainliest and 40 points) a package of trail mix weighs \frac {7}{8} pound. raisins make up \frac {1}{10} of the trail mix. how much of the trail mix, in pounds, is raisins? move numbers to the boxes to show the answer. if there is no whole number, enter () in the first box. \frac {\square }{\square } 0 1 7 8 10 18 39 40 70 80
Answer:
7/80 lb
Step-by-step explanation:
We are given that 1/10 of the 7/8 pound package is raisins.
__
The weight of raisins is ...
(1/10)(7/8 lb) = 7/80 lb
Let AU), 3,11) denote the set {b,b+s,b+28, . . . ,b+(n—1)s}. For instance, A(2, 3, 4) = {'2, 5,8, 11}. The variable names suggest b for beginning and s for skip value. (a) Write out the set A(1[},3,5). (h) Write out the set AU, 6, T). (c) Prove or disprove: Every element of AU, 6, 7) is prime. (d) What is the book's notation for the set A((], 1,6)? (e) Write out the set AU, 6, 7) fl A(10, 3, 5). (f) Write out the set A(2, 3, 4) U A((], 1, 6). (g) Write out the set A(2, 3, 4) x A(2, 3, 4). Bonus: Find values for b and s such that every elements of AU), 3, 5] is prime. 2. A logical staternent f (P, Q) is called a tautology if it is true for every combination of truth values for P and Q. A logical staternent f (P, Q) is called a contradiction if it is false for every combination of truth values for P and Q. (Please use the book's ordering of I} and 1 values for truth tables.) (a) Show that [P =) Q] A [P A -Q) is a contradiction. (b) Show that [PA (P =- (2)) =- Q is a tautology. (c) Show that P =) [Q =~ R) and (P A Q) => R are logically equivalent. 3. Logic with words. (a) Give the contrapositive of the statement, "If it's Tuesday, then I have class." ('0) Explain why both the original statement and the contrapositive in (a) are true for you. (c) Give the converse of the statement, "If it's Tuesday, then I have class." (d) Explain why the converse in (c) is false for you. (e) What can you say about a student's schedule for whom the converse in (c) is true? (f) What is the negation of "every good boy does fun"? (g) Prove or disprove: (3 n E Z) (Vm E Z) n < m2 (in words, there exists an integer n such that, for every integer m, n < 1112).
a) The set A(1, 3, 5) is {1, 4, 7, 10, 13}. This set starts with 1 and adds 3 to each element, so the next element is 1 + 3 = 4, then 4 + 3 = 7, and so on. It continues this pattern until the number of elements is reached, which in this case is 5.
b) The set A(U, 6, T) depends on the values of U and T, which are not provided in the question. Without these values, we cannot determine the set.
c) We cannot prove that every element of A(U, 6, 7) is prime because the values of U and n are not provided in the question. Without these values, we cannot determine the elements of the set and therefore cannot determine if they are prime.
d) The book's notation for the set A((], 1, 6) is A[1], 1, 6]. The square brackets indicate that the starting value is inclusive, while the round brackets indicate that the ending value is exclusive.
e) To write out the set A(U, 6, 7) U A(10, 3, 5), we need the value of U, which is not provided in the question. Without this value, we cannot determine the elements of the set.
f) To write out the set A(2, 3, 4) U A((], 1, 6), we first find the elements of each set separately. A(2, 3, 4) = {2, 5, 8, 11} and A[1], 1, 6] = {1, 7}. Taking the union of these sets gives us A(2, 3, 4) U A[1], 1, 6] = {2, 5, 8, 11, 1, 7}.
g) To write out the set A(2, 3, 4) x A(2, 3, 4), we multiply each element of the first set with each element of the second set. A(2, 3, 4) = {2, 5, 8, 11}. Multiplying each element by itself gives us {4, 25, 64, 121}.
For the bonus question, there is no way to find values for b and s such that every element of A(U, 3, 5) is prime. The set A(U, 3, 5) includes all elements starting from U and adding 3, so there will always be even numbers in the set, making it impossible for all elements to be prime.
2. (a) To show that [P = Q] A [P A -Q) is a contradiction, we can construct a truth table. The truth table will show that the statement is false for all combinations of truth values for P and Q, indicating that it is a contradiction.
(b) To show that [P A (P =- (2)) =- Q is a tautology, we can also construct a truth table. The truth table will show that the statement is true for all combinations of truth values for P and Q, indicating that it is a tautology.
(c) To show that P = [Q = R) and (P A Q) => R are logically equivalent, we can compare their truth tables. If the truth tables for both statements are the same, then they are logically equivalent.
3. (a) The contrapositive of the statement "If it's Tuesday, then I have class" is "If I don't have class, then it's not Tuesday."
(b) The original statement and its contrapositive are true for me because I have class on Tuesday and don't have class on other days of the week.
(c) The converse of the statement "If it's Tuesday, then I have class" is "If I have class, then it's Tuesday."
(d) The converse is false for me because I have class on other days of the week as well, not just on Tuesdays.
(e) If the converse of the statement is true for a student's schedule, it means that they only have class on Tuesdays and no other days of the week.
(f) The negation of "every good boy does fun" is "there is at least one good boy who does not do fun."
(g) To prove or disprove (3 n E Z) (Vm E Z) n < m2, we need to find an integer n such that, for every integer m, n < m2. However, this statement is false because there are infinite integers that do not satisfy this condition. For example, if n is a negative integer, it will not be less than any positive integer squared. Therefore, the statement is disproved.
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Express (4x3 + 5x + 1)/(x2 + 1) using long division method in the form q(x) + r(x)/b(x) where q(x) is the quotient, r(x) is the remainder, and b(x) is the divisor.
Answer:
4x + (x + 1) / (x^2 + 1)
Explanation:
We perform the long division
The result of the above long division tells is that
\(4x^3+5x+1=4x(x^2+1)+(x+1)\)If we now divide both sides by x^2 + 1, we get
\(\frac{4x^3+5x+1}{x^2+1}=\frac{4x(x^2+1)+(x+1)}{x^2+1}\)\(=\frac{4x(x^2+1)}{x^2+1}+\frac{(x+1)}{x^2+1}\)\(=4x+\frac{x+1}{x^2+1}\)Hence,
\(\boxed{\frac{4x^3+5x+1}{x^2+1}=4x+\frac{x+1}{x^2+1}\text{.}}\)Therefore, the first choice from the options is the correct answer!
Tommy travels –17 feet in 5 minutes.
What is Tommy's rate of change?
Tommy's average rate of change is given as follows:
-3.4 feet per second.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The parameters for this problem are given as follows:
Change in the output: -17 feet.Change in the input: 5 minutes.Hence the average rate of change is given as follows:
-17/5 = -3.4 feet per second.
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Luis and Arnold did their own car wash during the weekends this past Summer. They made a total of $1,200 together. They decided they were going to invest their money. So they invested in stocks for Tesla. The interest they are making is at 12%. How much money would they earn after 7 years?
Step-by-step explanation:
Amount they will earn=Principal+Interest
Interest=$1200×0.12×7=$1008
Amount=$(1200+1008)=$2208
80 POINTS! Help with this question please!!!! 80 POINTS!
Answer:
C. Translation 5 units left and 2 units down
Step-by-step explanation:
Let's take a look at A', which is (0, 0). This is the result of A, which is (5, 2) being transformed somehow. Notice that the x-coordinate moved 5 units to the left (from 5 to 0, which means we subtract 5 from 5). And, notice that the y-coordinate moved 2 units down (from 2 to 0, so we subtract 2 from 2).
Look to see if this works for the other two points:
B(6, 1): if we subtract 5 from the x-coordinate 6, we get 6 - 5 = 1, which matches the x-coordinate of the image B'. If we subtract 2 from the y-coordinate of B, which is 1, we get 1 - 2 = -1, which also matches the y-coordinate of B'. So, this works.
C(4, 5): if we subtract 5 from the x-coordinate 4, we get 4 - 5 = -1, which matches the x-coordinate of the image C'. If we subtract 2 from the y-coordinate of C, which is 5, we get 5 - 2 = 3, which also matches the y-coordinate of C'. So, this again works.
Therefore, we know that the transformation is a translation 5 units left and 2 units down, or C.
A picture will be shown below of a graph with the points in the table.
We only need to use (5, 2) and (0, 0) to solve this problem.
We take both points and see what it took for the old point to get to where the new point is (Shown in picture below).
Therefore, the answer is [ C. Translation 5 units left and 2 units down ]
Best of Luck!
11-4 skills practice areas of regular polygons and composite figures answers
The 11-4 skills practice areas of regular polygons and composite figures involve finding the areas of different geometric shapes using specific formulas and methods.
To find the area of regular polygons, you can use the formula (1/2) x apothem x perimeter.
For composite figures, you can break the shape into smaller, more manageable shapes like rectangles, triangles, or circles, and then calculate the area of each component before adding them together.
Hence, The 11-4 skills practice areas of regular polygons and composite figures teach you to find areas using the appropriate formulas and methods, improving your geometry understanding and problem-solving abilities.
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What is the mixed number used to represent 75?
Answer:
so you cant turn that into a mixed number i dont think
Step-by-step explanation:
Which one of the following is a characteristic of the classical approach to probability? a. Probabilities are based on outcomes observed from past experiments. b. None of the above c. Probabilities are based on opinion. d. Probabilities assume outcomes of an experiment are equally likely.
Answer:
d
Step-by-step explanation:
Classical approach traces back to the field where probability was first systematically employed, which is gambling (flipping coins, tossing dice and so forth). Gambling problems are characterized by random experiments which have n possible outcomes, equally likely to occur. It means that none of them is more or less likely to occur than other ones, hence they are said to be in a symmetrical position.
A rectangle has sides measuring (6x + 4) units and (2x + 11) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?
Answer:
Down Here ↓↓↓
Step-by-step explanation:
Hello!
A)
The area of a rectangle is L * W.
Area = (6x + 4)(2x + 11)Area = 12x² + 8x + 66x + 44Area = 12x² + 74x + 44B)
The degree of a polynomial is the value of the highest exponent. The degree of 12x² + 74x + 44 is 2, because 2 is the highest exponent.
C)
This demonstrates the closure property, as adding, subtracting, and or multiplying polynomials will give a polynomial.
during a 2-month trial period, a company institutes an exercise break for its workers to see if this will improve their sense of well-being. a random sample of 55 workers are randomly chosen: during the first month they don't take any exercise breaks; during the second month they take two exercise breaks during their work day. (a) which type of hypothesis test should be conducted?
The hypothesis test to conduct in this situation is a two-sample test for
means, specifically a paired-sample t-test.
This is because the same group of workers is being tested twice, under
two different conditions: without exercise breaks and with exercise breaks.
The two sets of data are dependent because they are coming from the
same group of individuals, and the goal is to determine if there is a
statistically significant difference in their well-being between the two
conditions.
A paired-sample t-test is appropriate because it can compare the means of
two related samples, and it takes into account the correlation between the
data points in each sample.
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suppose a line has slope -2/3 and passes through the point (1, 8). which other point must also be on the graph?
A (7, 4)
B (7, 12)
C (-5, 4)
D(-5, -12)
============================================
Explanation:
Use the slope and given point to find the y intercept
y = mx+b
8 = (-2/3)*(1) + b
8 = -2/3 + b
8 + 2/3 = b
24/3 + 2/3 = b
26/3 = b
b = 26/3
The equation of the line is y = (-2/3)x + 26/3
To confirm this, plug in x = 1 and we should get y = 8, due to the point (1,8)
y = (-2/3)x + 26/3
y = (-2/3)*1 + 26/3
y = -2/3 + 26/3
y = (-2+26)/3
y = 24/3
y = 8
So that verifies we have the correct equation.
--------------
Next, go through each answer choice to see if the x coordinate of the point leads to the y coordinate.
If we try x = 7, then,
y = (-2/3)x + 26/3
y = (-2/3)(7) + 26/3
y = -14/3 + 26/3
y = (-14+26)/3
y = 12/3
y = 4
This shows that (7,4) is on the line. Choice A is the answer
That rules out choice B.
----------------
If we tried x = -5, then,
y = (-2/3)x + 26/3
y = (-2/3)(-5) + 26/3
y = 10/3 + 26/3
y = 36/3
y = 12
meaning that (-5,12) is on the line. That rules out choices C and D.
Refer to the graph below. It visually confirms that of the four answer choices, only point A is on the line. I used GeoGebra to make the graph.
If a data point has a corresponding z-score of -1.5, then it is one and a half standard deviations above the mean value.
True or
False
A new television set was recently purchased for the common room in a residence hall for $520.00 including tax. If the tax rate is 4%, find the price of the television set before taxes.
Let's use the variable x to represent the price of the television set before taxes.
If the tax rate is 4%, then the original price is multiplied by 1.04, so it is equal 1.04x.
The final price is $520, so we have:
\(\begin{gathered} 1.04x=520 \\ x=\frac{520}{1.04} \\ x=500 \end{gathered}\)So the price before taxes is $500.00.
Today only, a table is being sold at a 24% discount. The sale price is 475$ What was the price yesterday?
Answer $625:
Step-by-step explanation:
Since the discount is 24% that means that $475 is 76% of the total
X is the 100% of the price (before sale)
475...............76%
x..........................100%
cross multiplication
76x = 475x100
76x = 47500
Divide both sides by 76
x= 625
What is the approximate volume of this sphere?
Don't forget to use the formula: V=43πr3
A 392.5 cm3
B 523.3¯ cm3
C 3,140 cm3
D 4,186.6¯ cm3
Answer: The correct answer is B. 523.3...cm^3
Step-by-step explanation:
4/3*pi*r^3 is the formula
first, divide the diameter by 2 to get the radius, now, you will begin solving.
4/3*5^3*3.14
5*5*5=125
4/3*125*3.14
125*3.14=392.5
4/3*392.5
523.3...
Dose anyone know this ??
if tyler paid 16 dollars per 4 tickets hw much would 1000 tickets cos 250 or 4000 dollars im cunfused
Answer:
16 per 4 tickets so that 4 a ticket so multiply 4 bye 1000 to get 4000
Step-by-step explanation:
Answer:
$4000 because the amount it costs is larger than the quantity, so the price will be more.
Step-by-step explanation:
Hope it helps! =D
geometric: you vs serena williams* you are playing serena williams (who has one hand tied behind her back) in tennis. your probability of losing is 98% and thus probability of winning is 2%. you will stop playing after you beat her. what is the probability you win on the 20th game played?
Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.
P(A) = f / N.
probability = 2%/100=0.0002
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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Jenny has a new puppy that weighs 4.21 pounds. Leon also has a new puppy, and his weighs 4.32 pounds. After one month, Jenny's puppy has gained 1.55 pounds, while Leon's has gained 1.47 pounds. Whose puppy currently weighs more?
Hurry pls
Answer:
Leon's puppy has gained the most weight.
model the decimal . then write percent and fraction equivalents .0.53
Decimal
Fraction
Percentage
0.53
53/100
53%
How many people out of 100,000 will survive until age 90?
Answer:
21,526 people
Step-by-step explanation:
y varies jointly as x and z. If y = 5 when x = 3 and z= 4, find y when x = 6 and z = 8.
Answer:
y = 20
Step-by-step explanation:
Given y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 5 when x = 3 and z = 4
5 = k × 3 × 4 = 12k ( divide both sides by 12 )
\(\frac{5}{12}\) = k
y = \(\frac{5}{12}\) xz ← equation of variation
When x = 6 and z = 8 , then
y = \(\frac{5}{12}\) × 6 × 8 = \(\frac{5}{12}\) × 48 = 5 × 4 = 20
568 + 396 is the same as
+ 400
Answer:
If your asking what plus 400 then it would be 564
Step-by-step explanation:
You had the first 2 numbers then subtract 400
564 is added with 400 to make 568 + 396 same as + 400.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
568 + 396 = x + 400
Solve for x.
568 + 396 = x + 400
Subtract 400 on both sides.
964 - 400 = x
x = 564
Thus,
568 + 396 is the same as 564 + 400.
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Which graph represents the function f(x)=√x+4-2?
Answer:
the top right graph
Step-by-step explanation:
I assume you mean the function is
f(x) = sqrt(x + 4) - 2
because for your function as you wrote it
f(x) = sqrt(x) + 4 - 2 = sqrt(x) + 2
none of the graphs apply.
to find the correct one we look at some specific points.
like x = 0, and when the square root will be 0 (x = -4).
normally we can see the right graph latest here already, but if not, then we have to pick a few more points.
so,
for x = 0 we get
sqrt(0 + 4) - 2 = 2 - 2 = 0
that means
f(0) = 0
now, when we look at the graphs, we see we are already finished. there is only one graph that goes through (0, 0).
the top right graph.
If is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with and being relatively prime positive integers, what is
The probability value of (m, n) is (1, 2^1005).
Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.
We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.
Thus, the probability is:
P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004
We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.
Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|
where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.
By the inclusion-exclusion principle:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)
where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.
This simplifies to:
(1/2) ⋅ (2^1004 + (-1)^1005)
Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).
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Complete question:
If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?
The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.
We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.
Thus, the probability is:
P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004
We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.
Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|
where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.
By the inclusion-exclusion principle:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)
where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.
This simplifies to:
\((1/2) * (2^{1004} + (-1)^1005)\)
Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)
Hence, (m, n) = (\(1, 2^{1005\)).
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Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet
If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.
Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.
We know that speed is the distance covered by an object in a particular period of time.
Speed=distance/time.
It is expressed as kilometers per hour or miles per hour, etc.
If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.
Distance=45 miles.
Time =distance/speed
=45/30
=1.5
Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.
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in the cost equation tc = f + vx, x is best described as the:
The cost equation is used to estimate total costs associated with a given level of activity or output, where f is the fixed cost and v is the variable cost per unit of activity. The variable cost component (vx) changes in proportion to the level of activity or output (x), whereas the fixed cost component (f) remains constant regardless of the level of activity.
In the cost equation tc = f + vx, x is best described as the level of activity or the quantity of the input variable. The cost equation is a mathematical representation of the relationship between the total cost of production and the level of activity or the quantity of the input variable. The variable x represents the number of units produced or the amount of resources used in the production process, which can be measured in terms of labor hours, machine hours, or any other relevant unit of measure. The variable v represents the variable cost per unit of activity, and f represents the fixed cost of production.
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Don Williams wised his small motorboat to go 5 miles upstream to his favorite fishing spot. Against the current, the trip takes 5/6 hour. With the current the trip takes 1/2 hour. How fast can the boat travel in still water ? What is the speed of the current in still water the boat speed is __ mph. The speed of the current is ___ mph
let s = speed in still water
let c = rate of the current
then
(s-c) = effective speed up-stream
and
(s+c) = effective speed down-stream
Write a distance equation for each way; dist = time * speed
5/6*(s-c) = 5
1/2 *(s+c) = 5
Now we get rid of the fractions
5(s-c)=30
s + c = 10
5s - 5c = 30
s + c = 10
siplifying:
s - c = 6 (1)
s + c = 10 (2)
adding:
2s = 16, then s = 8
8 mph is the boat speed in still water
According with (2):
8 + c = 10, then c = 2
2 mph is the speed of the current
what is the number of possible permutations of 8 objects Taken 3 at a time
The number of possible permutations of 8 objects taken 3 at a time is 336.
The formula for PermutationThe formula to calculate the permutation of 'n' object taken 'r' at a time is \(P_{r}=\dfrac{n!}{(n-1)!}\).
How to find the number of possible permutations?The formula for calculating the permutation is \(P_{r}=\dfrac{n!}{(n-r)!}\) where 'n' is the number of distinct objects taken 'r' at a time.
Thus we will substitute n=8 and r=3, we will get
\(P_{3}=\dfrac{8!}{(8-3)!}\\P_{3}=\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5!}\\P_{3}=\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}\\P_{3}=8\times 7\times 6\\P_{3}=336\)
So, the number of possible permutations of 8 objects taken 3 at a time is 336.
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