The general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.
The given differential equation is 9yy′ = x. This is a separable equation, meaning it can be solved by separating the variables and integrating both sides. To solve the equation, we start by dividing both sides by 9y to get y′ = x/9y. Now, we can solve for y by integrating both sides with respect to x. This gives us y = (1/9)∫xdy + c, where c is a constant of integration.
To determine c, we can use the initial condition given, y(9) = 5. We substitute 9 for x, and 5 for y to get 5 = (1/9)∫9dy + c. We can solve for c by subtracting (1/9)∫9dy from both sides, giving us c = 5 - (1/9)∫9dy.
Finally, we can substitute c into our equation to get the solution, y = (1/9)∫xdy + (5 - (1/9)∫9dy). This is the general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.
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express each set using roster notation. then give the cardinality of the set. (a) p(∅) (b) p(p(∅)) (c) p(p(p(∅)))
The cardinality of the sets p(∅), p(p(∅)), and p(p(p(∅))) are 1, 2, and 4 respectively.
a)p(∅) = {x | x ⊆ ∅}
Cardinality of the set is 1, since there is only one subset of the empty set, which is the empty set itself.
b)p(p(∅)) = {x | x ⊆ {∅}}
Cardinality of the set is 2, since there are two subsets of the set containing the empty set, which are the empty set itself and the set containing the empty set.
c)p(p(p(∅))) = {x | x ⊆ {{∅}}}
Cardinality of the set is 4, since there are four subsets of the set containing the set containing the empty set, which are the empty set itself, the set containing the empty set, the set containing the set containing the empty set, and the set containing the empty set and the set containing the empty set.
The cardinality of the sets p(∅), p(p(∅)), and p(p(p(∅))) are 1, 2, and 4 respectively.
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can you guys please help without guessing?
Answer:
In order of appearance in the image:
Two solutions
No solutions
Infinite solutions
No solutions
Step-by-step explanation:
Let's evaluate the systems of equations one by one:
[tex]\left \{ {{x-y=3} \atop {3x+y=1}} \right.[/tex]
Let's solve this system of equations:
[tex]x=3+y\\3(3+y)+y=1\\9+4y=1\\4y=-8\\y=-2\\x=3-2\\x=1[/tex]
This system has two solutions! x = 1, y = -2
[tex]\left \{ {{y=5x-4} \atop {y=5x+13}} \right.[/tex]
This system of equations has no solutions because no x value exists that satisfies both equations.
[tex]\left \{ {{4g+r=12} \atop {8g=-2r+24}} \right. \\r=12-4g\\8g=-2(12-4g)+24\\8g=-24+8g+24\\8g=8g\\1=1\\[/tex]
This system of equations has infinite solutions. No matter what values you plug in for g and r, the solution is the same!
[tex]\left \{ {{3y+15x=-1} \atop {y=4-5x}} \right. \\3(4-5x)+15x=-1\\12-15x+15x=-1\\12=-1[/tex]
This system of equations has no solutions because no values exist that can satisfy both equations.
in a game a player throws a dart at the object shown here. if the player throws two darts, what is the probability they both land in a shaded region
The probability of an event happening is represented as a fraction, with the numerator being the number of favorable outcomes and the denominator being the total number of outcomes.
In this case, if the player throws two darts, the probability that both land in a shaded region is equal to the product of the probabilities of each dart landing in the shaded region.
If the shaded region is a circle with radius r and the darts are randomly thrown onto a larger circle with radius R, then the probability of a dart landing in the shaded region is given by:
P = (Area of shaded region) / (Area of larger circle) = (πr^2) / (πR^2)
So, the probability that both darts land in the shaded region is given by:
P = (πr^2 / πR^2) * (πr^2 / πR^2) = (πr^2 / πR^2)^2
Note that the specific values of r and R would depend on the particular game and the dimensions of the object.
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What’s the value of X?
Assuming these triangles are similar, first find the standard ratio between them by dividing the corresponding sides of triangle VUT by RSQ:
[tex]R=\frac{36}{54} =\frac{2}{3}[/tex]
Now we know that if we multiply any side of triangle RSQ by the ratio (2/3), we can find the corresponding side of triangle VUT. Using this logic, multiply side RQ by our common ratio to find what UT should equal:
[tex]24*\frac{2}{3} =UT[/tex]
[tex]16=UT[/tex]
Finally, set up an equation for this side:
[tex]x+5=16[/tex]
Solve for x:
[tex]x=11[/tex]
According to a research study, parents with young children slept 6.4 hours each night last year, on average. A random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. This data has a sample standard deviation of 0.9. (Assume that the scores are normally distributed.)
Researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year.
The null and alternative hypotheses are H0:μ=6.4 and Ha:μ>6.4, which is a right-tailed test.
The test statistic is determined to be t0=1.89
Using the partial t-table below, determine the critical value(s). If there is only one critical value, leave the second answer box blank.
df t0.10 t0.05 t0.025 t0.01 t0.005
... … … … … …
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.898
18 1.330 1.734 2.101 2.552 2.878
The critical value for a one-tailed test at the 5% significance level with 18 degrees of freedom is 2.878.
To determine this value, the researcher can use the partial t-table above. The first row of the table contains the degrees of freedom (df) and the last column (t0.005) contains the C. To find the critical value, the researcher would look for the row with df=18 and the column with t0.005. The value at the intersection of these two values is 2.878. Therefore, the critical value for this test is 2.878.
To compare the test statistic to the critical value, the researcher would subtract the test statistic from the critical value. If the difference is greater than 0, then the test statistic is greater than the critical value and the null hypothesis can be rejected. In this case, the difference is -0.988, which is less than 0. Therefore, the test statistic is less than the critical value and the null hypothesis cannot be rejected.
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95% of what number is 57
When buying advertiing time on televiion or in magazine, advertier calculate the cot per thouand (CPM) people reached by the ad. If the cot of advertiing wa $100,000 and the reach or circulation wa 10,000,000 people, what would be the CPM? (Note: M i the Roman numeral for 1,000. )
If the cost of advertising was $100,000 and the reach or circulation was 10,000,000 people, then the CPM is $10.
Cost per thousand (CPM), which is also called cost per mille, is a marketing word used to denote the price of 1,000 advertisement prints on one web page. If a publisher of a website charges $2.00 CPM, that means an advertiser must pay $2.00 for every 1,000 prints of its ad.
The CPM is calculated by dividing the cost of the advertisement by the number of people reached and then multiplying by 1000.
Given that the cost of advertising was $100,000 and the reach was 10,000,000 people, the CPM can be calculated as follows:
CPM = ($100,000 / 10,000,000) × 1000 = $10.
So, the CPM is $10.
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when there are fractions in an equation, how do you determine what number to multiply by in order to rewrite the equation into a simpler form?
To make an equation with fractions simpler we will be required to take up and LCM and cross-multiplication.
When an equation has fractions, there can be a case where each side, the LHS and the RHS, have multiple fractions with different denominators or even whole numbers.
In this case, first, you have to make sure to take an LCM for fractions on each side and make sure each side has only one denominator and all the constants and variables are a part of that fraction.
Then you have to take the denominator from each side and then multiply it with the numerator of the other. For example-
If an equation looks like [2x - 3]/5 = [4x + 8]/7
Here LHS has 5 as the denominator while RHS has 7
Hence, we will take 5 over to the RHS and 7 to LHS to get
7 X [2x - 3] = 5 X [4x + 8]
Now we have gotten our simpler form.
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ASAP I need a quick answer pls
Answer:
62 square feet.
Step-by-step explanation:
7*5=35, 9*3=27, 35+27=62
how do you solve for X in this equation 3/8 x - 17 = 10
Answer: x = 72
Step 1: Add 17 to both sides.
Step 2: Multiply both sides by 8/3.
help please!!!
Fill in the table below. Round your answers to the nearest thousandth.
(1) From Latoya's results, compute the experimental probability of landing on white. ~
(2) Assuming that the spinner is fair, compute the theoretical probability of landing on white.
(3) Assuming that the spinner is fair, choose the statement below that is true:
a. The experimental and theoretical probabilities must always be equal.
b. As the number of spins increases, we expect the experimental and theoretical
c. probabilities to become closer, though they might not be equal. As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.
1) The experimental probability of landing on white is; 18/50
2) The theoretical probability of landing on white is; 1/3
3) Assuming that the spinner is fair, the statement that is true is; probabilities to become closer, though they might not be equal.
How to find experimental probability?Theoretical probability is the term that is used to describe what we expect to happen based on math theory, whereas experimental probability refers to what actually happens when the actual situation is tried out as an experiment.
A) Total number of spins = 18 + 14 + 18
= 50
Thus, experimental probability of landing on white = 18/50
B) The theoretical probability of landing on white as there are only three colors is;
Prob = 1/3
C) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
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(a) What 3 by 3 matrix E₁₃ will add row 3 to row 1? (b) What matrix adds row 1 to row 3 and at the same time adds row 3 to row 1? (c) What matrix adds row 1 to row 3 and then adds row 3 to row 1?
The process of adding the matrix is explained blow.
Matrices are powerful tools used to analyze data and solve complex equations.
A 3x3 matrix, or E₁₃, is a matrix composed of 3 rows and 3 columns. It can be used to perform various operations, including adding two rows together.
(a) To answer the first question, a 3x3 matrix E₁₃ can add row 3 to row 1 by performing a row operation. This involves taking the second row and adding it to the first, thus adding the values on each row together.
(b) To answer the second question, a 3x3 matrix E₁₃ can add row 1 to row 3 and at the same time add row 3 to row 1 by performing a row exchange operation. This results in a 3x3 matrix where each value in the first row is equal to the corresponding value in the third row.
(c) To answer the third question, a 3x3 matrix E₁₃ can add row 1 to row 3 and then add row 3 to row 1 by performing two separate row operation and then taking the third row and adding it to the first, thus adding the values of each row together again.
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Uber charges you $10.75 plus $0.50 per mile for a trip to a Hornets game. Ashley paid $30 for her ride to the game. How many miles did she travel?
Solving a linear equation, we can see that her travel was 38.5 miles long.
How many miles did she travel?We know that Uber charges $10.75 as a fixed fee plus $0.50 per mile, then the cost for x miles is modeled by the linear function:
y = 10.75 + 0.5*x
We know that Ashley paid 30 dollars for her ride, then we need to solve the equation:
30 = 10.75 + 0.5x
30 - 10.75 = 0.5x
19.25 = 0.5x
19.25/0.5 = x = 38.5
So her travel was 38.5 miles.
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Solve for x. 6x² + 1 = 20 Round to the nearest hundredth.
Answer:
x = 1.78
Step-by-step explanation:
6x² + 1 = 20
6x^2 = 19
x^2 = 19/6
x = 1.78
Answer:
1.78
Step-by-step explanation:
6x² + 1 = 2
6x²=19
x²=19/6=3.167
x=√3.167 = 1.78
Comparing Theater Sales 200 150 100 50 0 Bud's Movies Theater Bud's Movies Super Cinema Theater Why is Figure B misleading? 1) Bars have more discrepancy. 2) Vertical scale does not begin with zero. Figure A 200 Sales 100 Super Cinema 50 50 Figure B 150 Sales
Graph B is misleading because Vertical scale does not begin with zero.
What is the average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given, Comparing Theater Sales 200 150 100 50 0 Bud's Movies Theater Bud's Movies Super Cinema.
1) Figure 1 will compare A looks Bars have more discrepancy Because rectangular columns seem to have a larger area.
2) vertical scale dose not begin with zero. The scale of Statistical tables generally Starts from 0.
therefore, Graph B is misleading because Vertical scale does not begin with zero.
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Complete question:
The function is continuous and So f(u)du = 6 What is the value of $xf(x2 – 1)dx? (A) 3/2(B) 3(C) 6(D) 12 (E) 24
If the function is continuous function and ∫0 to 8 f(u) du = 6, the value of ∫ 1 to 3 xf(x² - 1) dx is B) 3.
Given ∫0 to 8 f(u) du = 6 and we need to find the value of ∫ 1 to 3 xf(x² - 1) dx
We can say, u = x² - 1
Differentiating both sides
du = 2x dx
dx = du/2x
When x = 1,
u = 1² - 1 = 0
and when x = 3
u = 3² - 1 = 8
So, ∫ 1 to 3 xf(x² - 1) dx can be written as
∫ 1 to 3 xf(x² - 1) dx = ∫ 0 to 8 xf(u) du/2x
= 1/2∫ 0 to 8 f(u) du
It is given that ∫0 to 8 f(u) du = 6
So, ∫ 1 to 3 xf(x² - 1) dx = 1/2 x 6 = 3
Hence, the value of ∫ 1 to 3 xf(x² - 1) dx is 3.
The question is incomplete. The complete question is
" The function f is continuous and ∫0 to 8 f(u) du=6. What is the value ∫ 1 to 3 xf(x² - 1) dx? (A) 3/2 (B) 3 (C) 6 (D) 12 (E) 24 "
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NEED HELP WITH 2 QUESTIONS WILL MARK BRAINLIEST!!!
you have 3/4 yard of wire. you use 1/3 yard to make an electric circuit. how much wire do you have left?
Answer: 5/12th or 0.41666666666 yards of wire
Step-by-step explanation:
this is my math... not an explanation
3, 6, 9, 12,
4, 8, 12,
4/12-9/12=5/12
Answer:
Step-by-step explanation:
Melissa buys framing to go around the perimeter of her rectangular painting that measures inches by 8 1/4 inches. 10 1/4 Each inch of framing costs $0.45. What is the total cost for the framing? Show your work.
The total cost of the framing measuring 8 1/4 inches by 10 1/4 is $16.65
How to determine the cost of the framingThe total perimeter of the framing is solved by the formula
= perimeter of the frame * price of each framing
perimeter of the framing is equal to perimeter of rectangle
= 2 * (length + width)
= 2 * (10 1/4 + 8 1/4)
= 37 inch
The cost of the framing
Since the unit cost of the framing is $0.45 per inch then the total cost is
= 0.45 * 37
= $16.65
The framing will cost $16.65
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Plot the point (1 and 1/2, 5 ) in the coordinate plane
Plot the point (1 and 1/2, 5 ) in the coordinate plane is Attached below.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, the point (1 and 1/2, 5 ) in the coordinate plane
Since, Point at x = 1 1/2 the value of y = 5
In coordinate plane,
x = 1 1/2 represents that Point is 1 1/2 units right to the origin point that is (0, 0).
And y = 5 represents that Point is 5 units upward to the origin point that is (0, 0).
therefore, the graph of (1 1/2 , 5) is attached below.
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What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
In accordance with the above, the scale that relates these two figures is 1:4, that is to say that each unit of the large figure is reduced four times.
How to find the scale that relates these two figures?To find the scale that relates these two figures we must know the measures of one of its sides. In this case we have the measure of the side of the rectangle, which in the large rectangle is equal to 6 and in the small rectangle is equal to 1.5
Based on the above information, we must divide the larger number into the smaller number and the result of this operation will be the scale of the model.
6 / 1.5 = 4So, the scale would be 1:4 because the distances of the small model represent a quarter of the original distance of the figure.
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What is the percentage increase from 520 to 800
153,9 % d'augmentation
The area of a rectangle is 44 square units. Its length measures 11 units. Find the length of its diagonal
The length of the diagonal of the rectangle is 11.7 units.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that the area of a rectangle is 44 square units. Its length measures 11 units.
Area = L x W
44 = 11 x W
W = 4 units
D² = W² + L²
D = √ ( 11² + 4 ²)
D = √ ( 121 + 16)
D = 11.7 units'
Therefore, the measure of the diagonal is 11.7 units.
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find the surface area of 9 3 3 pyramid
The surface area of the pyramid is 1377 square units
What is surface area of a pyramid?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
To find the surface area of a pyramid, we use the formula SA=B+12ps, where B is the area of the base, p is the perimeter of the base, and s is the slant height
height = 9
length = 3
width = 3
therefore s = √9²+3²
s = √81+9
s = √90
s = 9.5 units
Base area = l×w = 3 × 3 = 9 units
perimeter of the base = 2( 3+3) = 2×6 = 12
Surface Area = 9 + 12× 12× 9.5
SA = 9 + 1368
SA = 1377 square units
Therefore the surface area of the pyramid is 1377 square units
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What is the equation of this graph compared to parent graph? vertical shift= number added or subtracted to function.
Graphs can be shifted vertically in both straight and curved lines.
What is the equation for vertical shift?Graphs can be vertically moved in both linear and curvilinear directions. Add or remove a number from the constant to change the equation's graph vertically. G(x) = f(x) + c and G(x) = f(x) - c are the formulas for an upward and a downward shift, respectively.
Given a function f, a new function g(x) = f(x - h) is created, where h is a constant. This new function is a horizontal shift of the original function f. Graph shifts to the right if h is positive. If h is low, the graph will move to the left.
Given a function f(x), a new function g(x) = f(x) + k is created, which is a vertical shift of the original function f(x). The output values all shift outward by k units. The graph will move upward if k is positive. The graph will tilt downward if k is negative.
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1. What is the solution to the simultaneous equation? 2x +y= 1
2. Find the value of 4y-x given that (x, y) is the solution of the linear simultaneous equation.
3. From the graph find the positive value of y when x=2
Answer:
its 4
Step-by-step explanation:
In the transformation AABCAA'B'C', the prelmage of B' Is Type the answer in the space provided.
In the transformation ABC A'B'C', the preimage of B' is B.
What is the transformation about?It's a triangle, ABC. ABC is changed so that the resulting image is A'B'C'. It should be noted that there are many other forms of transformations, including dilation, vertical shift, horizontal shift, rotation about a point, reflection on a line, etc.
Corresponding vertices will be matched in all transformations. In other words, A will change to A', B to B', and C to C'.Preimage of B' would just be B itself due to the transformation's ability to maintain image similarity and convert vertices appropriately.
In conclusion, it is B.
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In the transformation ABC A'B'C', the preimage of B' is ____
consider the function f (x, y) = 1 x2 y2. draw a contour map for f (x, y).
A two-dimensional surface with all the points of equal value is shown in a contour map for the function f (x, y). It is used to illustrate how the function changes in relation to the two variables.
1. On the two-dimensional coordinate plane, create a grid.
2. Give each of the x and y coordinates a value.
3. Determine the value of f (x, y) for every pair of x and y.
4. Plot the grid points based on the values of f. (x, y).
5. To create the contour map, connect the points with equal values along a curved line.
In a two-dimensional plane, a contour map is a graphical representation of a function that displays all the points with identical values. It is used to illustrate how the function changes in relation to the two variables. Draw a grid on the two-dimensional coordinate plane and give values to the x- and y-coordinates before drawing a contour map for a function f (x, y). Once this is done, determine the value of f (x, y) for each pair of x and y, and plot the points on the grid using those values (x, y). To complete the contour map, draw a curved line connecting the points of equal value. The contour map will display the function's regional extrema as well as any locations where it is rising or decreasing locally. Additionally, it can be used to pinpoint regions of the plane where the function's value is constant. For seeing and comprehending the behaviour of functions of two variables, contour maps are a useful tool.
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What is the value of N in N - 7/7 = 8 ?
What is the value of N in N - 7/7 = 8 ?
A 10
B 11
C 9
D 8
Answer:
A. 10
Step-by-step explanation:
The correct way to solve the equation is:
N - 7/7 = 8
N = 8 + 7/7
N = 8 + 1
N = 9 + 1
N = 10
So the value of N is 10.
Graph the curves y = x^5 and x = y(y - 1)^2 Find their points of intersection correct to one decimal place. find the smallest x-value and the largest x-value
The points of intersection are (-0.4, -0.2) and (2.8, 16.8). The smallest x-value is -0.4 and the largest x-value is 2.8.
To graph the curves y = x^5 and x = y(y - 1)^2, first plot the points on the graph for y = x^5. This can be done by substituting in values for x and then finding the corresponding values for y. For example, when x = -3, y = -3^5 = -243. When x = 0, y = 0^5 = 0. When x = 3, y = 3^5 = 243. After plotting the points, draw a smooth curve connecting them. Next, plot the points on the graph for x = y(y - 1)^2. This can be done by substituting in values for y and then finding the corresponding values for x. For example, when y = -2, x = -2(-2 - 1)^2 = -2(-3)^2 = 18. When y = 0, x = 0(0 - 1)^2 = 0(-1)^2 = 0. When y = 4, x = 4(4 - 1)^2 = 4(3)^2 = 36. After plotting the points, draw a smooth curve connecting them. The curves intersect at two points. The points of intersection are (-0.4, -0.2) and (2.8, 16.8). The smallest x-value is -0.4 and the largest x-value is 2.8.
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