The exact value of A in the general solution y = A + cx is 75
How to determine the value of A in the general solutionFrom the question, we have the following parameters that can be used in our computation:
y = A + cx
The differential equation is given as
y - xy' = 75
When y = A + cx is differentiated, we have
y' = c
So, we have
y - xc = 75
Recall that
y = A + cx
So, we have
A + cx - xc = 75
Evaluate the like terms
A = 75
Hence, the value of A in the general solution is 75
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$120 is shared among 3 friends Ava, Ben, and Carlos. If Ava receives $20 less than
Ben, and Ben receives 3 times as much money as Carlos, how much money does
Carlos receive?
Answer:$20
Step-by-step explanation:
If Carlos had $20
Ben would have $60
And Ava would have $40
In a certain game of chance, a wheel consists of 40 slots numbered 00, 0, 1, 2,..., 38. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts (a) through (c) below. OU. ne sample space is 00, 0, 1, 2,..., 38). (b) Determine the probability that the metal ball falls into the slot marked 4. Interpret this probability, The probability that the metal ball falls into the slot marked 4 is 0.025 (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Type a whole number.) O A. If the wheel is spun 1000 times, it is expected that about of those times result in the ball landing in slot 4. O B. If the wheel is spun 1000 times, it is expected that exactly of those times result in the ball not landing in slot 4, (c) Determine the probability that the metal ball lands in an odd slot. Interpret this probability The probability that the metal ball lands in an odd slot is (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within (Type a whole number.) your choice O A. If the wheel is spun 100 times, it is expected that exactly of those times result in the ball not landing on an odd number, B. If the wheel is spun 100 times, it is expected that about of those times result in the ball landing on an odd number
(a) The sample space for this game is the set of numbers on the wheel are 00, 0, 1, 2, ..., 38.
For this game of chance with a wheel consisting of 40 slots, the sample space is defined as the set of all possible numbers that the metal ball can fall into. The numbers range from 00 to 38, including both the double zero and single-digit numbers.
(b) The probability of the ball landing in the slot marked 4 is 1/40, which is equivalent to 0.025 when rounded to four decimal places.
To determine the probability that the metal ball falls into the slot marked 4, we need to calculate the ratio of the favorable outcomes (the ball landing in slot 4) to the total number of possible outcomes.
There is only one slot marked 4, so the number of favorable outcomes is 1. The total number of possible outcomes is 40 since there are 40 slots on the wheel.
This means that if the game is played many times, we can expect the ball to land in slot 4 approximately 0.025 (or 2.5%) of the time.
(c) The probability that the metal ball lands in an odd slot is 0.5.
To determine the probability that the metal ball lands in an odd slot, we count the number of odd slots on the wheel. Odd numbers occur every other slot starting from 1, so there are a total of 20 odd slots on the wheel.
The probability of the ball landing in an odd slot is given by the ratio of the number of odd slots to the total number of possible outcomes. Therefore, the probability is 20/40, which simplifies to 1/2 or 0.5 when rounded to four decimal places.
This means that if the game is played many times, we can expect the ball to land in an odd slot approximately 0.5 (or 50%) of the time.
The correct choices are:
(b) If the wheel is spun 1000 times, it is expected that about 25 of those times result in the ball landing in slot 4.
(c) If the wheel is spun 100 times, it is expected that exactly 50 of those times result in the ball landing on an odd number.
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Question 9 Which of the following statements is correct about the simple shortest path problem? (Assume, for simplicity, that the graph is connected). O The problem is NP-hard if the graph contains a negative-length cycle. O The problem is ill-posed if the graph contains a negative-length cycle. O The problem is NP-hard if the graph contains arcs of negative length.
The statement that is correct about the simple shortest path problem is: The problem is ill-posed if the graph contains a negative-length cycle.
If the graph has a negative-length cycle, the shortest path will loop around that cycle an infinite number of times and, as a result, it is difficult to find the shortest path.
The Simple Shortest Path problem is a popular algorithmic issue in computer science. It is well-known that this issue may be solved in O(m log n) time using a variety of algorithms.
Dijkstra’s algorithm is a simple algorithm that is usually used to solve this issue. This algorithm works by maintaining a set of vertices that have already been visited while also maintaining a heap with all of the vertices that have yet to be explored.
The algorithm then picks the vertex with the lowest cost from the heap and processes all of its neighbours.
The cost of each neighbour is calculated by adding the weight of the edge connecting the current vertex to the neighbour vertex to the cost of the current vertex.
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HELP! Ill vote brainliest and 60 pts is on the line!
The Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, was used to solve the equation. 2x2 − 8x + 7 = 0. Fill in the missing denominator of the solution.
4 plus or minus the square root of 2, all over blank
−16
2
4
14
Answer:
2
Step-by-step explanation:
[tex]2x^2-8x+7=0\\\\[/tex]
a=2
b=-8
c=7
[tex]\frac{8+ \sqrt{16-4(2)(7)} }{4}[/tex]
4±[tex]\sqrt{2}[/tex] /2
Answer:
The answer is 2 hope this helps :3
Step-by-step explanation:
Find the area of a circle with a radius of 3.
Answer:
A =28.26
Step-by-step explanation:
Using the area formula
A = pi r^2
We use pi = 3.14 and the radius is 3
A = 3.14 * (3)^2
A = 3.14 *9
A =28.26
Let A = [(4,1,0):(1,0.-2); (0,1.-5)). Then A is a basis for
A. R4
the above vector space
B. R2
the above vector space
C. R3
the above vector space
D. None of the mentioned
A form a basis for R3.
To show that the columns of A form a basis for R3 , we need to show that they are linearly independent and span R3.
To show linear independence, we need to find constants c1 , c2 and c3 , not all zero , such that c1(4,1,0) + c2 (1,0,-2) + c3(0,1,-5) = (0,0,0).
This gives us a system of linear equations , which we can write in augumented matrix form as :
[4 1 0 | 0]
[1 0 1 | 0]
[0 -2 -5 | 0]
we can use row operations to reduce this matrix to row echelon form:
[4 1 0 | 0]
[0 -2 -5 | 0]
[0 0 1 | 0]
From this we can see that the only solution is c1 = c2 = c3 = 0, which means that columns of A are linearly independent.
To show that the columns of A span R3 , we can take any vector
(x, y, z) in R3 and write it as a linear combination of the columns of A :
(x, y, z) = a(4,1,0) + b(1,0,-2) + c(0,1,-5)
Solving for a , b and c, we get
a = (4x - y)/ 14
b = (2y + 5z - 2x)/ 14
c = -z/ 14
Since we can express any vector in R3 as a linear combination of the columns of A, they span R3 .
Therefore , the columns of A form a basis for R3.
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Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.
please prove that empty sets and singletons are always connected ?
Both the empty set (∅) and singleton sets are considered connected. The empty set is connected by definition, and a singleton set is connected because it cannot be divided into two non-empty open sets.
The statement that empty sets and singletons are always connected is true. Let's prove it for both cases:
1. Empty Set (∅):
The empty set (∅) is considered connected by definition. A set is said to be connected if there are no two non-empty open sets whose union is the set and whose intersection is empty. Since the empty set does not contain any elements, there are no open sets to consider, and thus it satisfies the definition of connectedness. In other words, there are no non-empty sets to separate the empty set, making it connected.
2. Singleton Set ({x}):
A singleton set, which contains only one element, is also connected. To prove this, let's assume the singleton set {x} is not connected. This means there exist two non-empty open sets A and B such that {x} is the union of A and B, and A and B have an empty intersection.
Since A and B are non-empty and their union is {x}, it means that each of them contains at least one point from the singleton set {x}. However, since the intersection of A and B is empty, it implies that A and B cannot contain any additional points other than x. This contradicts the assumption that A and B are open sets since they do not contain any points other than x.
Therefore, the assumption that {x} is not connected leads to a contradiction. Hence, {x} must be connected.
In conclusion, both the empty set and singleton sets are always connected.
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the object was turned 45 degrees around a fixed point that's called?
Answer:
A transformation that turns a figure around a fixed point, called the center of rotation. hope this helps
Step-by-step explanation:
The line graph shows the balance for a business on each day. How much more of a loss occurred on Friday than on Thursday?
A. $0
B. $2.50
C. $5
D. $10
Answer: this link will help you out
Step-by-step explanation: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/constructing-linear-models-real-world/v/word-problem-solving-4
COMPUTER FONT
1. What is the difference between sequence and series? 2. How do you solve series and sequence questions? 3. What is counting and probability in math? 4. What are the 3 principles of counting?
1. The difference between a sequence and a series is that a sequence is an ordered list of numbers, while a series is the sum of the terms in a sequence.
2. To solve series and sequence questions, various techniques can be used, such as finding patterns, using formulas, or applying mathematical operations like addition, subtraction, multiplication, or exponentiation.
3. Counting and probability are branches of mathematics that deal with quantifying and analyzing the likelihood of events. Counting involves determining the number of possible outcomes in a given situation.
4. The three principles of counting are the multiplication principle, the addition principle, and the principle of complementary counting.
1. A sequence is an ordered list of numbers, typically denoted as a₁, a₂, a₃, ..., where each term in the sequence is identified by its position or index. For example, {1, 3, 5, 7, 9} is a sequence. On the other hand, a series is the sum of the terms in a sequence. For instance, the series corresponding to the sequence mentioned earlier would be 1 + 3 + 5 + 7 + 9.
2. To solve series and sequence questions, it is important to look for patterns or relationships between the terms. For sequences, one can identify a pattern and use it to generate subsequent terms. In series, formulas or techniques like finding the sum of an arithmetic or geometric progression can be applied.
3. Counting involves determining the number of possibilities or outcomes in a given situation. It can involve simple counting principles or more complex techniques like combinations and permutations. Probability, on the other hand, deals with quantifying the likelihood of events. It uses mathematical calculations to determine the probability of specific outcomes or events occurring.
4. The three principles of counting are fundamental rules used in counting problems:
The multiplication principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are 'm x n' ways to do both.
The addition principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are 'm + n' ways to choose one of the two options.
The principle of complementary counting states that if there are 'm' ways to do something, then there are 'm' ways not to do it. By subtracting the number of ways not to do something from the total number of possibilities, one can determine the desired outcome.
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Find the measure of each number angle:
Answer:
12. 6= 68°
15. 4= 52°
Step-by-step explanation:
12.
since 5= 22°
5+6= 90° since it Is a right angle
6= 90-22
therefore 6 is 68°
15.
since 3 is 38°
and 3+4= 90° since it is a right angle
4= 90-38
therefore 4 is 52°
The figures are similar. Find X
Answer:
hi
Step-by-step explanation:
i think so
hope it helps
have a nice day
What is the measure of this angle?
Answer:
25
Step-by-step explanation:
Answer:
? = 25°
Step-by-step explanation:
all triangle interior angles added together = 180°, so:
? = 180° - 119° - 36°
? = 25°
find cos B in the triangle
Question 1 of 5 The Ridgeport school district collected data about class size in the district. The table shows the class sizes for five randomly selected kindergarten and seventh-grade classes. Number of students in randomly selected class Mean Mean absolute deviation Kindergarten 18, 20, 21, 19, 22 20 1.2 27, 32, 33, 33, 35 32 2 Seventh grade Based on these data, which statement is true?
sorry I couldn't fit the answer in it
Answer:
C is the correct answer
Step-by-step explanation:
Based on the data provided, the correct statement is:
A. The average size of a seventh-grade class is larger and varies more than that of a kindergarten class.
Here's the explanation:
1. Average class size:
The mean (average) class size for kindergarten is given as 20, while for the seventh grade, it is given as 32. Since 32 is greater than 20, we can conclude that the average size of a seventh-grade class is larger than that of a kindergarten class.
2. Variation in class sizes:
The mean absolute deviation (MAD) is provided as 1.2 for kindergarten and 2 for the seventh grade. The MAD measures the average amount by which each data point differs from the mean. A higher MAD indicates greater variability. In this case, the MAD for the seventh grade (2) is higher than that for kindergarten (1.2), indicating that the class sizes in the seventh grade vary more than those in kindergarten.
Therefore, the average size of a seventh-grade class is larger and varies more than that of a kindergarten class.
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consider the partially completed anova table shown. supposing all groups are of the same size, how many values are in each group of the data set this is based on?
The number of values in each group of the data set would be equal to the degrees of freedom for each group plus one.
In order to determine the number of values in each group of the data set based on the partially completed ANOVA table, we need to consider the total number of observations and the number of groups.
The ANOVA table consists of three main components: "Source of Variation," "Sum of Squares (SS)," and "Degrees of Freedom (df)." The "Source of Variation" represents the different factors or groups in the data set, while the "Sum of Squares" measures the variability within each group. The "Degrees of Freedom" represents the number of independent pieces of information available for estimating the population parameters.
In this case, since all groups are of the same size, we can determine the number of values in each group by examining the "Degrees of Freedom" column. The degrees of freedom for each group is the group size minus one (df = group size - 1). By adding one to the degrees of freedom for each group, we obtain the number of values in each group.
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If you add Natalie's age and Fred's age, the result is 39 If you add Fred's age to 3 times Natalie's age, the result is 69 Write and solve a system of equations to find how old Fred and Natalie are
Answer:
Natalie is 15
Fred is 24
Step-by-step explanation:
You would first create equations to represent the problem. You would then solve for a variable (I chose to solve for y). I subtracted each equation from each other which helped me isolate y, which equaled 15. I then substituted y for 15 which allowed me to isolate x, which gave me 24.
(the equations)
x + y = 39
x + 3y = 69
(solving for y)
x + 3y = 69 - x + y = 39
x-x +3y -y = 69 - 39
2y = 30
y = 15
(solving for x)
x + 15 = 39
x +15 -15 = 39 -15
x = 24
what is the fraction for 0.875?
Answer:
7/8
Step-by-step explanation:
Answer:
7/8
Step-by-step explanation:
simplify 875/1000
Priya has 5 pencils, each x inches in length. When she lines up the pencils end to end, they measure 34.5 inches. Select ALL the equations that represent this situation. *
Answer:
Equation b and c represent the situation.
Please help thanks!!!
For question 3, you don’t need to calculate it. Please explain the steps of how you would work it out.
Answer:
30 or 780 is your answer for the first one. i dont know how to work out the answer for the 2 one im sorry :(
Step-by-step explanation:
13+12+5 = 30
13 x 12 x 5 = 780
I would go for 780
it seems more like to be the answer
47 students have a dog 76 students have a cat a) Represent this data in a Venn diagram in the box provided (3) b) How many students have both a dog and a cat?
Answer:
89 people
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest.
Answer:
(-6, -7)
Step-by-step explanation:
For the x coordinates:
-1 - 4 = -5
-1 + -5 = -6
For the y coordinates:
-5 + -3 = -2
-5 + -2 = -7
I don't know how to explain it well sorry
Evaluate the following expression will give branliest
256 to the power of 5/8
Answer:
32
Step-by-step explanation:
The formula needed to solve this question by hand is:
[tex]x^{\frac{m}{n}} =\sqrt[n]{x^{m}}[/tex]
256^(5/8) = 8th root of 256^5
256^(5/8) = 8th root of 1280
256^(5/8) = 32
A bank charges a fee of 0.5% per month for having a checking account. Stephani’s account has $325 in it. Which function models the balance of Stephani’s account, B(t), in dollars, as a function of time, t, in months?
a: B(t) = 325(0.0995)t
b: B(t) = 325(0.005)t
c: B(t) = 0.05(325)t
d: B(t) = 325 + 12(0.005)t
The required, function that models the balance of Stephani's account is
[tex]B(t) = 325(0.005)^t[/tex]. Option B is correct.
The function that models the balance of Stephani's account, B(t), in dollars, as a function of time, t, in months, can be determined using the given information.
Given:
Bank charges a fee of 0.5% per month for having a checking account.
Stephani's account has $325 in it.
The function that models the balance of Stephani's account, B(t), in dollars, as a function of time, t, in months, is:
b: [tex]B(t) = 325(0.005)^t[/tex]
In this function, the initial balance is $325, and the bank charges a fee of 0.5% per month, which is equivalent to 0.005 as a decimal. The exponent "t" represents the number of months, and with each passing month, the balance is reduced by 0.5%.
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Question 8 Given f(x) = cosh(x) = €¯x+e² find 2 df (4) dx
The value of df(4)/dx is (-e⁻⁴ + e⁴)/2 when function f(x) is cosh(x).
To find df(4)/dx, we need to differentiate the function f(x) = cosh(x) with respect to x.
Using the chain rule, the derivative of f(x) with respect to x is given by:
df(x)/dx = d/dx [cosh(x)]
To differentiate cosh(x), we can use the derivative of e^x, which is e^x, and apply the chain rule:
df(x)/dx = d/dx (e⁻ˣ + eˣ)/2
Applying the chain rule to each term separately:
df(x)/dx = (d/dx [e⁻ˣ ] + d/dx [eˣ))/2
The derivative of e⁻ˣ is -e⁻ˣ, and the derivative of eˣ is eˣ:
df(x)/dx = (-e⁻ˣ+ eˣ)/2
Now, to find df(4)/dx, we substitute x = 4 into the derivative:
df(4)/dx = (-e⁻⁴ + e⁴)/2
This is the value of df(4)/dx for the function f(x) = cosh(x).
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The length of a 1-inch paperclip is about 1.6 x 10−5 miles. It takes about 1.5 x 1010 paperclips linked together to reach the moon. What is the approximate distance to the moon?
Answer:
Distance from the moon is 2.4 × 10⁵ miles
Step-by-step explanation:
Length of 1-inch paperclip = [tex]1.6\times 10^{-5}[/tex] miles
Number of paperclips used to reach the moon = 1.5 × 10¹⁰
Total distance from the moon = Number of paper clips used × Length of one clip
= (1.5 × 10¹⁰) × (1.6 × 10⁻5)
= (1.5 × 1.6) (10¹⁰× 10⁻⁵)
= 2.4 × 10⁽¹⁰⁻⁵⁾ miles
= 2.4 × 10⁵ miles
Distance from the moon is 2.4 × 10⁵ miles.
An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59–75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59.
(a) Test the hypotheses H0: u= 22.5 versus H1: u does not = 22.5, using alpha= 0.05. Find the P-value.
(b) Check the assumption that interior temperature is normally distributed.
(a) To test the hypotheses H0: μ = 22.5 versus H1: μ ≠ 22.5, a t-test can be used with a significance level of α = 0.05. The sample mean of the interior temperatures is calculated as 22.496, and the sample standard deviation is computed as 0.402.
Using these values, we can calculate the t-statistic, which is given by (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size)). Plugging in the values, we have (22.496 - 22.5) / (0.402 / sqrt(5)), resulting in a t-statistic of -0.020.
Next, we determine the degrees of freedom, which is the sample size minus 1, giving us 4.
Using the t-distribution table or a t-distribution calculator, we find the critical t-value for a two-tailed test with α = 0.05 and 4 degrees of freedom to be approximately ±2.776.
Since the absolute value of the calculated t-statistic (0.020) is less than the critical t-value (2.776), we fail to reject the null hypothesis.
(b) To check the assumption of normal distribution for the interior temperatures, a graphical method such as a histogram or a Q-Q plot can be used. Additionally, statistical tests such as the Shapiro-Wilk test can be employed to formally assess normality.
Know more about (a) To test the hypotheses H0: μ = 22.5 versus H1: μ ≠ 22.5, a t-test can be used with a significance level of α = 0.05. The sample mean of the interior temperatures is calculated as 22.496, and the sample standard deviation is computed as 0.402.
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A student saves $15 per week toward the purchase of a guitar. Her grandmother gives her $50 to help her reach her goal. Which function can be used to find the amount in dollars the student has saved after x weeks?
y=15x+50 it should look something like that
The Lewis family and the Pham family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 30 L per hour. The water output rate for the Pham family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1475 L. How long was each sprinkler used?
The Lewis family used their sprinkler for 30 hours, while the Pham family used theirs for 25 hours.
Let's assume x represents the number of hours the Lewis family used their sprinkler, and y represents the number of hours the Pham family used their sprinkler. We can set up a system of equations based on the given information.
Equation 1: x + y = 55 (The combined total of hours)
Equation 2: 30x + 25y = 1475 (The total water output in liters)
To solve this system of equations, we can use substitution or elimination methods. By solving Equation 1 for x and substituting it into Equation 2, we get:
30(55 - y) + 25y = 1475
1650 - 30y + 25y = 1475
-5y = -175
y = 35
Substituting the value of y into Equation 1, we find:
x + 35 = 55
x = 20
Therefore, the Lewis family used their sprinkler for 20 hours, while the Pham family used theirs for 35 hours.
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