The value of c in the equation 6,098×c=5,695,532 is 934
The given equation is 6,098×c=5,695,532
We have to find the value of c
c is the variable in the equation
6,098×c=5,695,532
Divide both sides by 6098
c=5,695,532/6098
c=934
Hence, the value of c in the equation 6,098×c=5,695,532 is 934
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write as a single fraction 1/1_x+2/1+x
To combine two divisions, we got to have a common denominator. In this case, ready to utilize the distributive property to induce a common denominator of (1+x) for both divisions:
1/(1x) + 2/(1+x) = 1/(1x*(1+x)) + 2x/(x(1+x))
Directly able to combine the two divisions by counting their numerators and composing them over the common denominator:
1/(1x(1+x)) + 2x/(x(1+x)) = (1+2x)/(x(1+x))
In this way, the given expression as a single division is:
(1+2x)/(x(1+x))
Writing 1/(1 + x) + 2/(1 + x) as a single fraction , we get 3/(1 + x)
Writing the expression as a single fractionFrom the question, we have the following parameters that can be used in our computation:
1/1_x+2/1+x
Express the fractions properly
So, we have
1/(1 + x) + 2/(1 + x)
Take the LCM of the fractions
So, we have
(1 + 2)/(1 + x)
Evaluate the sum of like terms
3/(1 + x)
Hence, the solution is 3/(1 + x)
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A student made two patterns to show multiplication of a decimal by powers of ten. The equations shown for both patterns are incorrect.
Pattern A
3.675 • 10 = 3.6750
3.675 • 100 = 3.67500
3.675 • 1,000 = 3.675000
Pattern B
3.675 • 0.1 = 3.0675
3.675 • 0.01 = 3.00675
3.675 • 0.001 = 3.000675
Explain why the equations in each of the patterns are false. Include in your explanation the values that should appear on the right side of each equation in both patterns to make the equations true.
Enter your explanation in the box provided.
How to get full credit:
Reasoning component: 2 points
Correctly explains why Pattern A is incorrect
Correctly explains why Pattern B is incorrect
Computation component: 2 points
Correct values for Pattern A
Correct values for Pattern B
The multiplication of decimals are wrong in he solution
How to multiply correctlyThe equations are false because the student is carrying out the wrong multiplication of decimal points
The correct multiplication should be:
Pattern A
3.675 • 10 = 36.75
3.675 • 100 = 367.5
3.675 • 1,000 = 3,675
Pattern B
3.675 • 0.1 = 0.3675
3.675 • 0.01 = 0.03675
3.675 • 0.001 = 0.003675
Hence the student has to solve this correctly because the previous values are wrong
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Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the differential equation dP/dt = c ln(K/P) P where c is a constant and K is the carrying capacity.
The rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.
The Gompertz function is a solution of the differential equation:
dP/dt = c ln(K/P) P
where P(t) is the population at time t, c is a constant, and K is the carrying capacity, i.e., the maximum population that can be sustained by the available resources.
To solve this differential equation, we can use separation of variables:
dP/P ln(K/P) = c dt
Integrating both sides, we get:
∫ dP/P ln(K/P) = ∫ c dt
Integrating the left-hand side requires a substitution. Let u = ln(K/P), then du/dP = -1/P and the integral becomes:
-∫ du/u = -ln|u| = -ln|ln(K/P)|
The right-hand side is just:
c t + C
where C is an arbitrary constant of integration.
Putting these together, we get:
-ln|ln(K/P)| = ct + C
Taking the exponential of both sides, we get:
|ln(K/P)| = e^(-ct-C)
Using the absolute value is unnecessary, since ln(K/P) is always positive, so we can drop the absolute value and write:
ln(K/P) = e^(-ct-C)
Solving for P, we get:
P = K e^(-e^(-ct-C))
This is the Gompertz function, which gives the population as a function of time, under the assumption that the rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.
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A supervisor is setting up a display of cereal boxes. The ratio of frosted to unfrosted cereals in the display is 5: 7. Approximately what percent
of the cereal boxes are unfrosted?
A) 40.0%
B) 41.7%
C) 58.3%
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 45% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?
(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b) The expected number of available places when the limousine departs is 0.338.
How to solveLet the random variable Y represent the number of passenger reserving the trip shows up.
The probability of the random variable Y is, p = 0.70.
Success in this case an be defined as the number of passengers who show up for the trip.
The random variable Y follows a Binomial distribution with probability of success as 0.70.
(a)
It is provided that n = 6 reservations are made.
Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:
P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)
= 0.4202
Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
The expected number of available places when the limousine departs is 0.338.
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please help with this
Step-by-step explanation:
by using Pythagoras theorem you can find the answer
[tex] {a}^{2} + {b }^{2} = {c}^{2} \\ {9 }^{2} + {x}^{2} = {24 }^{2} \\ 81 + {x}^{2} = 576 \\ {x }^{2} = 576 - 81 \\ {x }^{2} = 495 \\ \sqrt{ {x}^{2} } = \sqrt{495 } \\ x = 22.2485954613[/tex]
Answer:
3√55
Step-by-step explanation:
Because this is a right triangle we can use Pythagorean theorem to find the missing side length. Pythagorean theorem states the a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides. In this case 24 is the hypotenuse
x^2 + 9^2 = 24^2
x^2 + 81 = 576
Subtract 81 from both sides to isolate the x
x^2 = 495
Find the square root of both sides
√x^2 =√495
Now factor √495 to simplify
x = √3· 3 · 5 · 11
There is a pair of 3's so we move them to the outside of the radical
x = 3√5·11
x = 3√55
Help really confused
1. let s be the set of all positive integers n such that n2 is a multiple of both 24 and 108. which of the following integers are divisors of every integer n in s ? indicate all such integers. a. 12 b. 24 c. 36 d. 72
We know that n^2 is a multiple of both 24 and 108, which means it must be a multiple of their least common multiple (LCM). The LCM of 24 and 108 is 216.
So, n^2 must be a multiple of 216. This means that n must be a multiple of the square root of 216, which is 6√6.
Therefore, every integer n in s must be of form 6√6 * k, where k is a positive integer.
To find the divisors of every integer n in s, we need to find the common factors of all such expressions.
We can express 6√6 as 2√6 * 3. So, every integer n in s can be written as 2√6 * 3 * k.
The divisors of every integer n in s must be factors of 2√6 and 3.
The factors of 2√6 are 1, 2, √6, and 2√6.
The factors of 3 are 1 and 3.
Therefore, the integers that are divisors of every integer n in s are 2 and 3, which are both positive integers.
So, the correct answer is none of the given options (a, b, c, d).
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Use technology to find points and then graph the function y=(1/2)^x-4, following the instructions below
Because the equation of the asymptote is given as y = -4, the points on the function y = (1/2)ˣ -4 are:
Vertical Aymptote : x = 0
y-intercept: (0,3)
x-intercept: (-2.32, 0). See the attached graph.
How is the above derived ?
As x approaches zero and the base of the exponent in y = ((1/2)ˣ - 4 becomes increasingly small, the function value approaches infinity from the right side while simultaneously approaching zero from the left side.
This phenomenon is known as a vertical asymptote at x=0.
Note that the in the function:
y = (1/2)ˣ -4 , where x = 0
y = y(1/2)^0 - 4
y = 1 - 3
y = -3
Hence the y intercept is -3
To dertive the x-intercept,
we set y to zero.
0 = (1/2)^x -4
(1/2)^x = 4
Using Log we can solve x to be = -2.32
Thus, it is correct to state that the points are:
Vertical Asymptote : x = 0
y-intercept: (0,3)
x-intercept: (-2.32, 0).
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Write the equation for each translation of the graph of y = 1 2 x − 2 + 3. one unit up
The equation for translation of the graph given is y = |x/2-2| + 4
Given is a function y = |x/2-2| + 3, it is translated one unit up, we need to find the translated function.
We know that, f(x) + k moves f(x) by k units up.
So, y = |x/2-2| + 3 → y = |x/2-2| + 3 + 1
y = |x/2-2| + 4
Hence, the equation for translation of the graph given is y = |x/2-2| + 4
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Your job is to randomly select integrated circuits, and then test them in sequence until you find the first failure. let be the total number of tests, and assume that all tests are independent with probability of failure. Identify the type of random variable and its parameter(s).
The type of random variable in this scenario is a geometric random variable. Its parameter is the probability of failure for each integrated circuit being tested.
The type of random variable you're dealing with in this scenario, where you are testing integrated circuits in sequence until you find the first failure, is called a Geometric Random Variable. This type of random variable represents the number of trials needed for the first success (or failure, in this case) in a series of independent Bernoulli trials with the same probability of failure. The parameter for a Geometric Random Variable is the probability of failure, denoted as p. In summary, the type of random variable in this problem is a Geometric Random Variable, and its parameter is the probability of failure (p).
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1. Line a: y = −4x + 7
Line b: x = 4y + 2
Line c: -4y + x = 3
Non of the lines is perpendicular rather they are parallel to each other
What is a perpendicular line?Perpendicular lines are straight lines that make an angle of 90° with each other
But Parallel lines are coplanar lines on a plane that do not intersect and are always the same distance apart. In two dimensions, parallel lines have the same slope and can be written as an equation if we know a point on the line and an equation of the given line.
The given equations are
1. Line a: y = −4x + 7
Line b: x = 4y + 2
Line c: -4y + x = 3
Solving each of them
line 1: y = −4x + 7
making y the subject
y = −4x + 7
Line 2: x = 4y + 2
making y the subject
4y = x -2
y = (x-2)/4
line 3: -4y + x = 3
making y the subject of the relation
-4y = -x + 3
y =( x - 3)/4
From the answers the lines are not perpendicular as their values are not the same
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the equation of a line is y + 4 =6x + 13. what is the value of y at the point where the line crosses the y-xais?
Answer:
y = 9
Step-by-step explanation:
When a line crosses the y-axis, it crosses at point (0,y).
Substitute x = 0 in to the line equation we get:
y + 4 = 0 + 13
So y = 13 - 4 = 9
The line crosses the y-axis at point (0,9)
38. Make a stem and left plot of following data of Video game scores:
{542, 529, 564, 531, 456, 540, 522, 548, 531}
Answer:
Below
Step-by-step explanation:
There is an image uploaded below of the stem-and-leaf plot of the video game scores!
HELP ON MATH!ITS FOR A GRADE
Answer: about 25 km2 to 35 km2
Step-by-step explanation:
hope this helps ;)
Answer: About 40 to 50 km^2
Step-by-step explanation:
So basically area is length x width so you want to count the squares for the length then multiply by the number of squares for the width which is 8 x 5 which equals 40
What is the surface area of the pyramid
(A) 38 cm2
(B) 76 cm2
(C) 100 cm2
(D) 152 cm2
The surface area of the given pyramid is 76 cm². Option B is correct.
We can start by finding the area of each triangular face of the pyramid. The area of a triangle can be calculated using the formula:
Area = 0.5 * base * height
where the base is the length of one side of the triangle (which is equal to the base length of the pyramid in this case), and the height is the slant height of the triangle (which is given as 5 for one face and 5.5 for the other face).
Area of the first triangular face = 0.5 * 6 * 5 = 15
Area of the second triangular face = 0.5 * 4 * 5.5 = 11
To find the surface area of the pyramid, we need to add the area of the base to the sum of the areas of the triangular faces. The area of the base is simply the area of a rectangle, which can be calculated using the formula:
Area = length * width
where length and width are the dimensions of the base of the pyramid.
Area of the base = 6 * 4 = 24
Therefore, the total surface area of the pyramid is:
Total surface area = Area of base + Sum of areas of triangular faces
Total surface area = 24 + 2*15 + 2*11
Total surface area = 76 cm²
Hence, the surface area of the given pyramid is 76 cm².
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evaluate the numerical expression the quantity 3 to the power of five sixths end quantity over the quantity 3 to the power of one sixth end quantity. cube root of 6 cube root of 9 square root of 9 square root of 27
The cube root of a number is a special value that when cubed gives the original number.
We can simplify the given expression as follows:
(3^(5/6)) / (3^(1/6)) = 3^((5/6) - (1/6)) = 3^(4/6) = 3^(2/3)
Next, we can simplify the expression cube root of 6 * cube root of 9 as follows:
cube root of 6 * cube root of 9 = cube root of (6 * 9) = cube root of 54
We can simplify the expression square root of 9 * square root of 27 as follows:
square root of 9 * square root of 27 = square root of (9 * 27) = square root of 243
Since 243 can be factored as 3^5, we have:
square root of 243 = square root of (3^5) = 3^(5/2)
Therefore, the final expression becomes:
(3^(2/3)) / cube root of 54 * 3^(5/2)
We can simplify the denominator as:
cube root of 54 * 3^(5/2) = cube root of (54 * 3^3) = cube root of (2^3 * 3^6) = 6 * 3^2 = 54
Thus, the final expression simplifies to:
(3^(2/3)) / 54
which cannot be further simplified.
Therefore, the final answer is:
(3^(2/3)) / 54
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Ash can dig 5 holes in 2 hours, and Bruce can dig 9 holes in 5 hours. How many holes can they dig in 15 hours if they work together?
If Ash can dig 5 holes in 2 hours, and Bruce can dig 9 holes in 5 hours. The number of holes they can dig is: 64.5 holes .
How to find the number of holes?Ash rate:
5 holes / 2 hours
= 2.5 holes per hour
Bruce rate
9 holes / 5 hours
= 1.8 holes per hour
Number of holes they can dig together in one hour
2.5 holes per hour + 1.8 holes per hour
= 4.3 holes per hour
Now let find the number of holes they can dig in 15 hours,
4.3 holes per hour x 15 hours
= 64.5 holes
Therefore, Ash and Bruce can dig 64.5 holes.
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Solve by taking the square root of both sides. (3x+3)^2 =25
The answer is 3x+3 = ±5 when the square roots of both sides of the equation (3x+3)² = 25 are taken. Both x = 2/3 and x = -8/3 are possible answers to the "x" equation.
The squared term on one side of the equation must first be isolated in order to solve (3x+3)²= 25 by calculating the square roots of both sides we get:
(3x+3)²= 25
The result of taking the square root of both sides will:
3x+3 = ±5
Two potential equations result from simplifying the right side:
3x+3 = 5 or 3x+3 = -5
The right side can be simplified into one of two equations:
3x = 2
x = 2/3
Solving for x in the second equation, we get:
3x = -8
x = -8/3
Therefore, the answer to the equation (3x+3)² = 25 are x = 2/3 and x = -8/3.
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Members of a baseball team raised 967.50 to go to a tournament they rented a bus for 450.00 and budgeted 28.75 per player for meals they will spend all the money they raised
The equation is 967.50 = 450 + 28.75p which models the situation. The team could bring 18 players to the tournament.
Setting up an equation based on the given information.
Let p be the number of players on the team.
Then the total amount of money spent on meals will be 28.75p.
The total amount of money spent on the bus and meals will be 450 + 28.75p.
Since they spent all the money they raised, the equation models the situation as follows:
967.50 = 450 + 28.75p
To solve for p, subtract 450 from both sides:
517.50 = 28.75p
Then divide both sides by 28.75:
p = 18
Therefore, the team could bring 18 players to the tournament.
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The complete question is as follows:
Members of a baseball team raise $967.50 to go to a tournament. They rented a bus for $450.00 and budgeted $28.75 per player for meals. They will spend all the money they raised.
Write and solve an equation that models the situation and could be used to determine the number of players, p, the team could bring to the tournament.
George performs an experiment where he flips a coin 2 times. If he performs this experiment 100 times, what is the best prediction for the number of repetitions of the experiment that will result in both the two filps landing on heads?
Answer:
The probability of getting heads on a single coin flip is 1/2. The probability of getting heads on two coin flips in a row is (1/2) * (1/2) = 1/4. Therefore, if George performs this experiment 100 times, we can expect that he will get both flips landing on heads about 25 times
Step-by-step explanation:
451,501,388,428,510,480, 390 which data values are outliers
Answer: To determine if any of these data values are outliers, you would first need to calculate the median and interquartile range (IQR) of the data set. You can then use the following rule to identify potential outliers:
- Any data value that is less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR) is a potential outlier.
Assuming the data set is in order, the median is 451.5 and the first and third quartiles are 389 and 495, respectively. The IQR is therefore 495 - 389 = 106. Using the rule above, we can check each data value to see if it is a potential outlier:
- 451 is not a potential outlier.
- 501 is not a potential outlier.
- 388 is not a potential outlier.
- 428 is not a potential outlier.
- 510 is not a potential outlier.
- 480 is not a potential outlier.
- 390 is not a potential outlier.
Therefore, there are no outliers in this data set.
Step-by-step explanation:
A) In how many ways can 7 men and 7 women can sit around a table so that men and women alternate. Assume that all rotations of a configuration are identical hence counted as just one.
B) In how many ways can 8 distinguishable rooks be placed on a 8 x 8 chessboard so that none can capture any other, namely no row and no column contains more than one rook?
To arrange the 7 men and 7 women alternately around a table, we can first place the men in a circular manner. Since there are 7 men, there will be 6! ways to arrange them (considering that rotations are identical). Next, we can place the women in the 7 available spaces between the men.
A) In how many ways can 7 men and 7 women sit around a table so that men and women alternate? Assume that all rotations of a configuration are identical and hence counted as just one.
First, we can choose the position of the men around the table in 7! ways. Then, we can place the women in the remaining positions in 7! ways as well. However, we need to account for the fact that men and women must alternate. We can do this by fixing the position of one gender (say, men) and arranging the other gender (women) in the spaces in between. We have 7 spaces in between the men, so we can arrange the women in these spaces in 7! ways. However, we must also account for the fact that we could have started with women and arranged men in the spaces in between. Therefore, the total number of ways to arrange 7 men and 7 women around a table so that men and women alternate is:
2 * 7! * 7! * 7! = 20,160,000
B) In how many ways can 8 distinguishable rooks be placed on a 8 x 8 chessboard so that none can capture any other, namely no row and no column contains more than one rook?
First, we can place the first rook in any of the 64 squares on the board. Then, we must place the second rook in a square that is not in the same row or column as the first rook. There are 14 squares in the same row or column as the first rook, so there are 50 squares remaining for the second rook to be placed in. We continue in this manner, placing each subsequent rook in a square that is not in the same row or column as any of the previously placed rooks. Therefore, the total number of ways to place 8 distinguishable rooks on an 8 x 8 chessboard so that none can capture any other is:
64 * 50 * 36 * 25 * 20 * 15 * 10 * 5 = 3,416,748,800
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The table below shows the number of jumping jacks completed after a given period of time in minutes.
Common difference between jumping jacks is 50
The slope of line that connects 3 rd and 4th point is 50
The slope is constant.
The common difference between jumping jacks is 50
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
m=100-500/2-1=50
The slope of line that connects 3 rd and 4th point
Slope = 200-150/4-3=50
The slope of line that connects 1 st and 4th point
slope = 200-50/4-1
=150/3=50
The slope is constant
jumping jacks completed after a given period of time in minutes is linear so it is constant
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The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at most 47,500 miles? Show your answer to four decimal places (for example, 0.3217).
The probability that a randomly selected tire will have a life of at most 47,500 miles is 0.9332, or 93.32%.
To find the probability that a randomly selected tire will have a life of at most 47,500 miles, we need to calculate the z-score and use a standard normal distribution table.
The formula for the z-score is:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
Plugging in the values given in the problem, we get:
z = (47,500 - 40,000) / 5,000
z = 1.5
Using a standard normal distribution table, we can find that the probability of a z-score being less than or equal to 1.5 is 0.9332.
Therefore, the probability that a randomly selected tire will have a life of at most 47,500 miles is 0.9332 (or 93.32%) to four decimal places.
To answer your question, we will use the normal distribution, mean, standard deviation, and Z-score. Given that the life expectancy of the tire is normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles, we will find the probability of a tire having a life of at most 47,500 miles.
First, we calculate the Z-score using the formula: Z = (X - μ) / σ, where X is the value we're interested in (47,500 miles), μ is the mean (40,000 miles), and σ is the standard deviation (5,000 miles).
Z = (47,500 - 40,000) / 5,000 = 7,500 / 5,000 = 1.5
Now, we look up the Z-score of 1.5 in a standard normal distribution table or use a calculator with a cumulative distribution function (CDF). The CDF value for a Z-score of 1.5 is approximately 0.9332.
So, the probability that a randomly selected tire will have a life of at most 47,500 miles is 0.9332, or 93.32%.
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In the box below, type in all of the names possible for this shape. Some words may not be used.Why did you give the shape the names that you did? Explain using sides and angles.
The names possible for the shape are
Quadrilateral - this means a four sided figure
Parallelogram - Opposite sides are parallel to each other
Rhombus - The vertex angles are not all equal to each other
What is a quadrilateral?A polygon with four sides and angles is known as a quadrilateral. This two-dimensional plane shape features straight borders that connect at its four vertices, also referred to as corners.
A rhombus is a parallelogram because the opposites sides are parallel to each other
Geometrically speaking, a rhombus denotes a specific kind of quadrilateral encompassing four equal-lengthed border lines.
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This season, the probability that the Yankees will win a game is 0.55 and the
probability that the Yankees will score 5 or more runs in a game is 0.56. The
probability that the Yankees lose and score fewer than 5 runs is 0.34. What is the
probability that the Yankees would score fewer than 5 runs when they lose the game?
Round your answer to the nearest thousandth.
The probability that the Yankees would score fewer than 5 runs when they lose the game is 0.45.
Let A be the event that the Yankees win a game, B be the event that they score 5 or more runs, and C be the event that they lose and score fewer than 5 runs.
Using the total probability rule, we can find the probability of losing and scoring fewer than 5 runs:
P(C) = P(Lose and Score fewer than 5 runs) = P(Lose and not Score 5 or more runs) = P(not A and not B) = 1 - P(A) - P(B) + P(A and B)
P(C) = 1 - 0.55 - 0.56 + P(A and B)
To find P(A and B), we can use the fact that P(A and B) = P(B|A) * P(A), where P(B|A) is the conditional probability of scoring 5 or more runs given that they win.
We are not given this conditional probability directly, but we can find it using Bayes' theorem:
P(B|A) = P(A and B) / P(A) = (0.55 * 0.56) / 0.55 = 0.56
Substituting this value into the equation for P(C), we get:
P(C) = 1 - 0.55 - 0.56 + 0.56
P(C) = 0.45
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The surface area of a cylinder is 378π square centimeters. The radius is 7 cm. Apply the formula SA=2B+Ph to find the height of the cylinder
We have the formula for the surface area of a cylinder:
SA = 2πrh + 2πr^2
Given that the surface area is 378π cm^2 and the radius is 7 cm, we can plug in these values and solve for the height:
378π = 2π(7)(h) + 2π(7)^2
378π = 14πh + 98π
280π = 14πh
h = 20 cm
Therefore, the height of the cylinder is 20 cm.
Solve the equation
r/2-6=14
I'm giving brainliest answer to the first answer!
Formulate but do not solve the following exercise as a linear programming problem.
National Business Machines manufactures two models of portable printers: A and B. Each model A costs $120 to make, and each model B costs $140. The profits are $25 for each model A and $40 for each model B portable printer. If the total number of portable printers demanded per month does not exceed 3000 and the company has earmarked not more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profits P in dollars?
To formulate this problem as a linear programming problem, we need to identify the decision variables, objective functions, and constraints.
Decision Variables:
Let x be the number of model A printers manufactured per month, and y be the number of model B printers manufactured per month.
Objective Function:
The objective is to maximize monthly profits, which can be expressed as P = 25x + 40y.
Constraints:
1. The total number of printers demanded per month cannot exceed 3000, so we have the constraint x + y ≤ 3000.
2. The company has earmarked not more than $600,000/month for manufacturing costs, so the cost constraint is 120x + 140y ≤ 600,000.
3. The number of printers manufactured must be non-negative, so x ≥ 0 and y ≥ 0.
Therefore, the linear programming problem is:
Maximize P = 25x + 40y
Subject to:
x + y ≤ 3000
120x + 140y ≤ 600,000
x ≥ 0, y ≥ 0
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