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Related Questions
other form to write 600,000+80,000+10
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hope this helps
or 680,010
Find the particular solution of the differential equation dydx+ycos(x)=5cos(x) satisfying the initial condition y(0)=7.
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[tex]e^{\sin x}\dfrac{\mathrm dy}{\mathrm dx}+ye^{\sin x}\cos x}=5e^{\sin x}\cos x[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[e^{\sin x}y\right]=5e^{\sin x}\cos x[/tex]
[tex]e^{\sin x}y=5\displaystyle\int e^{\sin x}\cos x\,\mathrm dx[/tex]
[tex]e^{\sin x}y=5e^{\sin x}+C[/tex]
[tex]y=5+Ce^{-\sin x}[/tex]
With [tex]y(0)=7[/tex], we have
[tex]7=5+Ce^{-\sin 0}\implies 7=5+C\implies C=2[/tex]
so that the particular solution is
[tex]y=5+2e^{-\sin x}[/tex]
The provided differential equation is a first-order linear differential equation, which can be solved using an integrating factor. After solving, the particular solution satisfying the initial condition y(0)=7 is y=e^(-sin(x))(5sin(x)+7).
Explanation:The differential equation provided is a first-order linear differential equation, which can be solved using an integrating factor. In this case, dy/dx + ycos(x) = 5cos(x), the integrating factor is e^(∫ cos(x) dx) = e^sin(x). Multiplying everything by the integrating factor, we get (ye^sinx)' = 5cos(x)e^sin(x).
Then we can integrate on both sides to get ye^sin(x) = 5sin(x) + C, where C is the constant of integration. To find the particular solution, we can use the initial condition y(0)=7. By substituting these values, we can solve for C. Substituting x=0 and y=7 yields C=7. Thus, the particular solution is y=e^(-sin(x))(5sin(x)+7).
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Devaughn is 13 years older than Sydney. The sum of their ages is 77 . What is Sydney's age?
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A parallelogram has an area of 48 m². If the base is 12 m long, what is the height?
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a class voted for either kayaking, fishing, or hiking as their favorite summer activity. if hiking got 17% percent of the vote and fishing got 33%, what percentage of the class voted kayaking?
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100-17-33
Just the difference after subtraction
The percentage of the class that voted for kayaking is 50%.
Given data:
To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.
Hiking got 17% of the vote.
Fishing got 33% of the vote.
Let x be the percentage of the class that voted for kayaking.
Since the total percentage of votes is 100%:
17% + 33% + x = 100%
On solving for x:
x = 100% - (17% + 33%)
x = 100% - 50%
x = 50%
Hence, 50% of the class voted for kayaking.
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4a + 6b=10
2a - 4b =12
What is 12a?
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4a + 6b = 10
2a - 4b = 12
First make both a terms equal
2a · 2 - 4b · 2 = 12 · 2
4a - 8b = 24
Subtract both expressions to cancel out the a term.
4a + 6b = 10
-4a - 8b = 24
14b = -14
b = -1
Now put the value in one of the equations and solve
2a - 4 · -1 = 12
2a + 4 = 12
2a = 8
a = 4
Since a = 4, 12a = 48.
The answer is 48
Hope this helps! :)
A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus
holds 40 students and 3 teachers and cost $1200 to rent. Each van holds 8 students and 1 teacher
and costs $100 to rent. The school has at least 400 students wanting to go, but at most 36 teachers.
What is the minimum transportation cost?
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A bus can hold 40 students and 3 teachers.
A van can hold 8 students and 1 teacher.
The number of students riding in buses and vans is at least 400, therefore
40x + 8y ≥ 400 (1)
The number of teachers riding in buses and vans is at most 36, therefore
3x + y ≤ 36 (2)
Write (1) and (2) as
y ≥ 50 - 5x (3)
y ≤ 36 - 3x (4)
The equality portion of the solution of (3) and (4) is
36 - 3x = 50 - 5x
2x = 14
x = 7 => y = 36 - 3*7 = 15
A graph of the inequalities indicates the acceptable solution in shaded color, as shown below.
The minimum cost of renting buses and vans is
7*$1200 + 15*$100 = $9900
Answer: The minimum cost is $9,900
Tickets for a school play sold for $7.50 for each adult and $3 for each child the total receipts for the 113 tickets sold were $663 find the number of adult ticket sold
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a+c=113
Write a literal equation for c using the second equation.
c=-a+113
Substitute the value of c into the first equation
7.5a+3(-a+113)= 663
7.5a-3a+339=663
4.5a+339=663
4.5a=324
a=72
Final answer: 72 adult tickets sold
Check by finding the value of c and plugging both values in
(72)+c=113
c=41
7.5(72)+3(41)
663
True
You have taken over an abandoned drilling project. After drilling for 2 hours, the depth is 110 feet. After 5 hours, the depth has increased to 114.5 feet. Write an equation in the form y = mx + b to describe the relationship between x, the hours of drilling, and y, the depth of the well.
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slope = (114.5 - 110) / (5 - 2) = 4.5 / 3 = 1.5
y = mx + b
slope(m) = 1.5
use either of ur points..(2,110)...x = 2 and y = 110
now we sub and find b, the y int
110 = 1.5(2) + b
110 = 3 + b
110 - 3 = b
107 = b
so ur equation is : y = 1.5x + 107 <==
A rectangular prism has the following dimensions: l = 5a , w = 2a ,
h = ( a^3 - 3a^2 + a ) Use the formula V = l ⋅ w ⋅ h to find the volume of the rectangular prism.
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The volume of a shape is the amount of space in it.
The volume of the rectangular prism is: [tex]\mathbf{10a^5 -30a^4 + 10a^3}[/tex]
The dimensions of the rectangular prism are:
[tex]\mathbf{l = 5a}[/tex]
[tex]\mathbf{w = 2a}[/tex]
[tex]\mathbf{h = (a^3 - 3a^2 + a)}[/tex]
The volume (v) of the rectangular prism is:
[tex]\mathbf{v = l\cdot w \cdot h}[/tex]
So, we have:
[tex]\mathbf{v = 5a \cdot 2a \cdot (a^3 -3a^2 + a)}[/tex]
[tex]\mathbf{v = 10a^2 \cdot (a^3 -3a^2 + a)}[/tex]
Expand
[tex]\mathbf{v = 10a^5 -30a^4 + 10a^3}[/tex]
Hence, the volume of the rectangular prism is: [tex]\mathbf{10a^5 -30a^4 + 10a^3}[/tex]
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A researcher computes a 2 x 3 factorial anova. in this example, how many interactions can be observed?
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The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign.
Upper a 18a 18?-footfoot ladder is leaning against a building. if the bottom of the ladder is sliding along the pavement directly away from the building at 22 ?feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 44 feet from the? wall?
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So we are assuming a distance of 4 feet, similarly a rate of change in x equal to 2ft/s.
check the picture.
let [tex]h(x)= \sqrt{ 18^{2}- x^{2} } = (18^{2}- x^{2})^{ \frac{1}{2}} [/tex]
be the function of the height of the ladder with respect to x, the distance of the bottom of the ladder to the wall.
We want [tex] \frac{dh}{dt} [/tex], the rate of change of h with respect to t.
h is a function of x and x is a function of t, so we keep this in mind as we derivate h with respect to t:
[tex] \frac{dh}{dt}= \frac{dh}{dx} \frac{dx}{dt}= \frac{1}{2} (18^{2}- x^{2})^{ -\frac{1}{2}}(-2x) \frac{dx}{dt} [/tex]
we substitute [tex] \frac{dx}{dt}=2[/tex] and x=4:
[tex]\frac{dh}{dt}=\frac{1}{2} (18^{2}- 4^{2})^{ -\frac{1}{2}}(-2)*(4)*2= \frac{-8}{ \sqrt{18^{2}- 4^{2}} } = \frac{-8}{17.5}= -0.46[/tex] ft/s
(APEX) If a product is equal to zero, we know at least one of the factors must be zero. And the constant factor cannot be zero. So set each binomial factor equal to 0 and solve for x, the width of your project (-2x^-6x-4)
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(x-q)(x-r) = 0
where q and r are the roots of the equation. Because their product is zero, the Zero Product Property states that x-q - 0 and x-r = 0
Thus, for the given equation above, a = -2, b = -6 and c=-4. Then, we find the roots using the quadratic formula.
[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]
[tex]x= \frac{-(-6)+/- \sqrt{ (-6)^{2}-(-2)(-4) } }{2(-2)} [/tex]
x = -1 and -2. That means q=-1 and r=-2. Hence, the two binomials are (x+1) and (x+2).
Express the ratio of A's to N's in the word SAVANNAH, in simplest form
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The t value for a 99% confidence interval estimation based upon a sample of size 10 is
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For a sample size of 10, the t-value is about 3.25 (from tables) at a 99% confidence interval.
Explanation:
When the standard deviation for the population is not known, the confidence interval estimate for the population mean is performed with the Student's t-distribution.
The confidence interval for the mean is calculated as
[tex](\Bar{x}- t\frac{s}{\sqrt{n}} , \, \Bar{x}+ t\frac{s}{\sqrt{n}} [/tex]
where
[tex]\Bar{x}[/tex] = sample mean,
s = sample standard deviation,
t = t-value (provided in tables),
n = sample size.
When reading the t-value, (n-1) is called the df or degrees of freedom.
The [tex]\( t \)[/tex]-value for a 99% confidence interval based on a sample size of 10 is 3.2498.
To find the [tex]\( t \)[/tex]-value for a 99% confidence interval estimation based on a sample size of 10, we need to use the [tex]\( t \)[/tex]-distribution table or a calculator. The [tex]\( t \)[/tex]-distribution is used when the sample size is small (typically [tex]\( n < 30 \)[/tex]) and the population standard deviation is unknown.
Given:
- Confidence level: 99%
- Sample size [tex](\( n \)): 10[/tex]
The degrees of freedom [tex](\( df \))[/tex] are calculated as:
[tex]\[ df = n - 1 = 10 - 1 = 9 \][/tex]
To find the critical [tex]\( t \)[/tex]-value for a 99% confidence interval with 9 degrees of freedom, we look for the [tex]\( t \)[/tex]-value that corresponds to the area in the tails of the distribution. For a 99% confidence interval, the area in each tail is:
[tex]\[ \frac{1 - 0.99}{2} = 0.005 \][/tex]
So we need the [tex]\( t \)[/tex]-value such that 0.5% of the distribution is in each tail.
Using a [tex]\( t \)[/tex]-distribution table or a calculator, we find the [tex]\( t \)[/tex]-value for 9 degrees of freedom and a 99% confidence interval (or 0.5% in each tail).
The [tex]\( t \)[/tex]-value for 9 degrees of freedom at the 99% confidence level is approximately:
[tex]\[ t_{0.005, 9} \approx 3.2498 \][/tex]
Thus, the [tex]\( t \)[/tex]-value for a 99% confidence interval based on a sample size of 10 is approximately 3.2498.
A rubber ball has a radius of about 2.86 in. Can the ball be packaged in a box shaped like a cube with a volume of 125 in3?
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volume of the ball = 4/3 * PI *r^3 =
4/3 * 3.14 * 2.86^3 = 97.99 cubic inches
this is less than the volume of the box, so yes it will fit
On a busy day you clock into work at 6:45 a.m .You clock out for lunch at 12:30 p.m how long did you work before lunch
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The student worked for 5 hours and 45 minutes before taking a lunch break, calculated by finding the difference between the clock-in time of 6:45 a.m. and the lunchtime of 12:30 p.m.
Explanation:The student worked for a certain number of hours before taking a lunch break. To calculate the duration of work before lunch, we subtract the start time from the end time. The student clocks in at 6:45 a.m. and clocks out at 12:30 p.m. for lunch.
First, we convert the time worked to a 24-hour format: 6:45 a.m. remains the same but 12:30 p.m. is 12:30 in 24-hour time. Now, we calculate the time difference:
From 6:45 a.m. to 7:45 a.m. is 1 hour.7:45 a.m. to 12:30 p.m. is 4 hours and 45 minutes.Adding up the hours and minutes, we get a total of 5 hours and 45 minutes worked before lunch.
Two linear equations are shown.
What is the solution to the system of equations?
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2 + 5 = 4/3x - 1/3x
7 = x
y = 1/3(7) + 2
y = 7/3 + 2
y = 7/3 + 6/3
y = 13/3
solution is : (7,13/3) <=
Answer:
B.
Step-by-step explanation:
What happens when you apply the power rule for integration to the function f(x)=1/x?
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Integrating [tex] \int\ {x^{-1} } \, dx [/tex] will give the effect of
[tex] \frac{x^{-1+1} }{-1+1} = \frac{ x^{0} }{0} [/tex], which is undefined since we cannot divide by '0'
The conclusion is that to integrate [tex]f(x)= \frac{1}{x} [/tex] we don't use the power rule. We use instead
[tex] \int\ { \frac{1}{x} } \, dx =ln(x)[/tex]
In the rhombus, m<1=8y-6. Find the value of y. Please help!!
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Answer: 12
The value of y= 12.
Step-by-step explanation:
We know that the diagonal of rhombus are perpendicular bisector of each other.
i.e. the angle made at the intersection of diagonal is 90 degrees.
Thus , for the given figure m∠1 = 90°
Since it is given that m∠1 = 8y-6
Thus , 8y-6= 90
⇒8y=96 [Adding 6 both sides]
⇒ y = 12 [Dividing both sides by 8]
Hence, the value of y= 12.
A class tossed coins and recorded 165 heads and 172 tails. What is the experimental probability of tails?
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172/337 is the experimental probability of tails.
Hope this helps!
Answer:
Probability of tails = 0.51
Step-by-step explanation:
Probability is the ratio of number of favorable outcome to the total number of outcomes.
Total number of outcomes = Total number of heads + Total number of tails
= 165 + 172 = 337
Number of favorable outcome = Total number of tails = 172
[tex]\texttt{Probability}=\frac{172}{337}=0.51[/tex]
In the triangle XYZ, IF WZ=24, then WY is:
12.
24.
48.
None of the choices are correct.
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Which should equal 105 to prove that f // g ?
A
B
C
D
Please hurry !!
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since you have the 75, we know that a would equal 105 for line g , since a line = 180 degrees
so to make line f parallel with g it needs the same angles with line n as line g has
so if a = 105, then angle d would also need to be 105
The answer is D
Manuel is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
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Use an Addition or Subtraction Formula to simplify the equation. sin(3θ) cos(θ) − cos(3θ) sin(θ) = Square root 2/2 Find all solutions in the interval [0, 2π). (Enter your answers as a comma-separated list.)
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[tex]\sin2\theta=\dfrac1{\sqrt2}[/tex]
[tex]\implies2\theta=\dfrac\pi4+2n\pi,\,2\theta=\dfrac{3\pi}4+2n\pi[/tex]
[tex]\implies\theta=\dfrac\pi8+n\pi,\,\theta=\dfrac{3\pi}8+n\pi[/tex]
where [tex]n[/tex] is any integer. To take only the solutions within the interval [tex]0\le\theta<2\pi[/tex], we solve
[tex]0\le\dfrac\pi8+n\pi<2\pi\implies\dfrac18+n<2\implies n<\dfrac{15}8\implies n=0,\,n=1[/tex]
[tex]\implies\theta=\dfrac\pi8,\,\theta=\dfrac\pi8+\pi=\dfrac{9\pi}8[/tex]
[tex]0\le\dfrac{3\pi}8+n\pi<2\pi\implies \dfrac38+n<2\implies n<\dfrac{13}8\implies n=0,\,n=1[/tex]
[tex]\implies\theta=\dfrac{3\pi}8,\,\theta=\dfrac{11\pi}8[/tex]
Answer: For 0 ≤Ф≥ 2π (where π= 180°)
∴ Ф = 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5°
Step-by-step explanation:
sin(3Ф)cos(Ф) - cos(3Ф)sin(Ф) = √2/2
sin(3Ф - Ф) =√2/2
3Ф -Ф = sin∧-1{√2/2}
2Ф = 45°
∴ Ф = 22.5°
Which statement is true?
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f(x) = 9x-6
g(x) =√(x-4)
(f0g)(x) = f(g(x)) exist if g(x) exist and f(g(x)) exist.
g(1) no exist because : √(1-4) =√(-3) ... no real
conclusion : 1 is not in the domain of : f0g
What is the equation of the line that passes through (4,3) and (2,2)
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Answer:
The equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].
Step-by-step explanation:
Given information: The line passes through the point (4,3) and (2,2).
If a line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the point (4,3) and (2,2), so the equation of line is
[tex]y-3=\frac{2-3}{2-4}(x-4)[/tex]
[tex]y-3=\frac{-1}{-2}(x-4)[/tex]
[tex]y-3=\frac{1}{2}(x-4)[/tex]
Using distributive property, we get
[tex]y-3=\frac{1}{2}(x)+\frac{1}{2}(-4)[/tex]
[tex]y-3=\frac{1}{2}(x)-2[/tex]
Add 3 on both sides.
[tex]y=\frac{1}{2}(x)-2+3[/tex]
[tex]y=\frac{1}{2}(x)+1[/tex]
Therefore the equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].
A water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R)equals=0.53. The clay probability is P(C)equals=0.21. The sand probability is P(S)equals=0.26. If the soil is rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand.
Given the test is positive, what is the probability that the soil is clay, P(clay | positive)? Use Bayes' rule to find the indicated probability.
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To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Given the probabilities of the different types of soil and the accuracy of the test in each soil type, we can calculate the probability using the law of total probability and Bayes' rule.
Explanation:To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Bayes' rule states that P(A|B) = (P(B|A) * P(A)) / P(B), where P(A|B) is the probability of event A happening given that event B has occurred, P(B|A) is the probability of event B happening given that event A has occurred, P(A) is the probability of event A happening, and P(B) is the probability of event B happening. In this case, event A is that the soil is clay and event B is that the test result is positive.
Given that the soil is clay, the test gives a positive result with 48% accuracy. Therefore, P(B|A) = 0.48. The probability of the soil being clay is P(A) = 0.21. To find P(B), we need to consider the probabilities of the test result being positive in each type of soil.
If the soil is rock, the test gives a positive result with 35% accuracy, so the probability of the test result being positive in rock soil is P(B|rock) = 0.35. Similarly, if the soil is sand, the test gives a positive result with 75% accuracy, so the probability of the test result being positive in sand soil is P(B|sand) = 0.75. We can calculate P(B) using the law of total probability: P(B) = P(B|rock) * P(rock) + P(B|clay) * P(clay) + P(B|sand) * P(sand).
Plugging in the given values, we have P(B) = 0.35 * 0.53 + 0.48 * 0.21 + 0.75 * 0.26. Now we can substitute the values into Bayes' rule:
P(clay | positive) = (P(positive | clay) * P(clay)) / P(positive) = (0.48 * 0.21) / P(B).
So the probability that the soil is clay given a positive test result is (0.48 * 0.21) / P(B).
A set of equations is given below:
Equation A: y = x + 1
Equation B: y = 4x + 5
Which of the following steps can be used to find the solution to the set of equations?
x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1
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Answer:
x + 1 = 4x + 5
Step-by-step explanation:
To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".
A hardware store customer requests a square slab of tile that measures 12.8 feet wide. The width of each side of the slab of tile is __________ inches.
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1 foot = 12 inches
12.8 x 12 = 153.6 inches each side