Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)
Here is the full question.
The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.
A. The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)
B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)
Answer:
a. x ≅ 337 seconds.
b. P(x > 337 ) = 0.1056
Step-by-step explanation:
A.
Given that ;
Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17 ) seconds = 317 seconds ( since 60 seconds make 1 minute.
Standard deviation: [tex]\sigma[/tex] = 12 seconds.
Only the fastest 5% of all runners qualify
The objective is to determine the qualifying time in seconds
Let's look for the Z-score of 0.95;
The Z-score is 1.645 from the tables
[tex]x= ( \sigma * z ) + \mu[/tex]
[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]
x ≅ 337 seconds.
B. Given that the standard deviation = 12 seconds
Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds
he objective is to find P(x > 337 ) i.e the proportion of boys from this region who qualify to run in this event in the state meet.
we are using command normalcdf (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)
we have P(x > 337 ) = 0.1056
In football seasons, a team gets 3 points for a win, 1 point for a draw and 0 points for a
loss. In a particular season, a team played 34 games and lost 6 games. If the team had a
total of 70 points at the end of the season, what is the difference between games won and lost
Answer:
The difference between the games won and lost = 21 - 6 =15
Step-by-step explanation:
According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.
A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.
The team played a total of 34 games.
Total games played = 34
Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,
34 - 6 = 28 games was won or draw
Let
the number of games won = x
the number of game drew = y
3x + y = 70.............(i)
x + y = 28................(ii)
x = 28 - y
insert the value of x in equation(i)
3(28 - y) + y = 70
84 - 3y + y = 70
84 - 70 = 3y -y
14 = 2y
divide both sides by 2
y = 14/2
y = 7
insert the value of y in equation(ii)
x + y = 28
x = 28 - 7
x = 21
The team won 21 games , drew 7 games and lost 6 games.
The difference between the games won and lost = 21 - 6 =15
outline the procedure for finding the probabilities of any given compound event
Explanation:
We will discuss the probability of any given Compound event under two broad heading. Exclusivity and Dependence.
Two or more events are mutually exclusive if they cannot occur at the same time.
In mutually excusive events,
[tex]P(A \cap B)=0[/tex]
The probability of two mutually exclusive events is given as:
P(A or B)=P(A)+P(B)
If however the two events can occur at the same time, they are mutually inclusive and: [tex]P(A \cap B)\neq 0[/tex].
For mutually inclusive events A and B,
[tex]P(A or B)=P(A)+P(B)-P(A \cap B [/tex].
Two events are independent if the outcome of one does not affect the outcome of the other.
For two independent events, the probability of A and B,
[tex]P(A \cap B)=P(A) \times P(B)[/tex].
Two events are not independent if the outcome of one affect the outcome of the other.
For two dependent events, if A is dependent of B, we say that the probability of A given B,
[tex]P(A|B)=\dfrac{P(A) \cap P(B)}{P(B)}[/tex].
average of a data set was 40, and that standard deviation was 10, what else could you derive from that information.
Answer:
[tex] \bar x = 40, s =10[/tex]
And from these values we can estimate the sample variance like this:
[tex] s^2 = 10^2 =100[/tex]
And we can also estimate the coeffcient of variation given by:
[tex] \hat{CV} =\frac{s}{\bar x}[/tex]
And replacing we got:
[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]
And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar x = 40, s =10[/tex]
And from these values we can estimate the sample variance like this:
[tex] s^2 = 10^2 =100[/tex]
And we can also estimate the coeffcient of variation given by:
[tex] \hat{CV} =\frac{s}{\bar x}[/tex]
And replacing we got:
[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]
And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.
1) Ethan, Amir, Victoria, and Kayla share
3 apples equally. What fraction of an
apple does each friend get?
Answer:
3 apples / 4 people
3/4
to check divide fractions
Multiply reciprocal
3/1 x 4/1
3/1 / 1/4 = 3/4
3/4 x 4 = 12/4 = 3 apples
3/4 is the answer
Hope this helps
Step-by-step explanation:
What is the approximate length of minor arc LM? Round to
the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters
Answer:its 15.7
Step-by-step explanation:
Answer:
15.7
Step-by-step explanation:
A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a standard deviation of 6.5. What percentage of the class has an exam score of A- or higher (defined as at least 90)? Type your calculations along with your answer for full credit; round your final percentage to two decimal places.
Answer:
6.18% of the class has an exam score of A- or higher.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 80, \sigma = 6.5[/tex]
What percentage of the class has an exam score of A- or higher (defined as at least 90)?
This is 1 subtracted by the pvalue of Z when X = 90. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 80}{6.5}[/tex]
[tex]Z = 1.54[/tex]
[tex]Z = 1.54[/tex] has a pvalue of 0.9382
1 - 0.9382 = 0.0618
6.18% of the class has an exam score of A- or higher.
Identify the exponential function for this graph. (Be sure to look at the scales
on the x- and y-axes.)
The required exponential function will be F(x)= [tex]4(0.5)^{x}[/tex]
Hence, Option A is the correct.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
From the assumption graph as shown in attached figure, we can determine that when x = 0 then y = 4.
Also, we can closely observe that the graph represents decay
exponential function.
The reason is that when the value of x increases, the graph of the particular function decreases.
But, the rate of decay must be less than 1 for decay exponential function because if it is greater than 1, then it would represent the exponential growth function.
Hence, the option B and D should be completely ruled out as these values represent the exponential growth.
And from graph, it is clear that when x = 0 then y = 4
The exponential function will be F(x)= [tex]4(0.5)^{x}[/tex]
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2y + 5x – z = 4y + 6x solve for y
(show work)
Answer:
y = -z/2 - x/2
Step-by-step explanation:
2y + 5x – z = 4y + 6x
-5x. -5x
2y - z = 4y + x
+z. +z
2y = 4y + z + x
-4y -4y
-2y = z + x
÷-2. ÷-2
y = -z/2 - x/2
When writing expressions for complex numbers, what does i represent?
Answer:
see below
Step-by-step explanation:
i is the imaginary number and it represents the square root of -1
..
..................
[tex]1. \: (x - y) {2} \\ = {x}^{2} - 2xy + {y}^{2} \\ 2. \: (a + b) ^{2} \\ = {a}^{2} + 2ab + {b}^{2} \\ 3. \: (2x + 3y) ^{2} \\ = {(2x)}^{2} + 2.2x.3y + (3y) ^{2} \\ = {4x}^{2} + 12xy + {9y}^{2} \\ 4.(3x - 2y) ^{2} \\ = (3x) ^{2} - 2.3x.2y + (2y) ^{2} \\ = {9x}^{2} - 12xy + {4y}^{2} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
a) x^2−2xy+y^2
b) a^2 -ab+b^2
c)4x^2+12xy+9y^2
d)9x^2 -12xy+4y^2
Step-by-step explanation:
a) x^2−2xy+y^2
b) a^2 -ab+b^2
c)4x^2+12xy+9y^2
d)9x^2 -12xy+4y^2
We rewrite (x-y)^2 as (x-y) (x-y) to show and always see + sign at start for question a ) and question b)
a) x*x+x(−y)−yx−y(−y) = x^2−2xy+y^2
b) a^2 becomes a^2 -ab as a^2 -ab+b^2
c) As shown in notes attached and this will help you most.
d) the reasons we keep +4y is because -2y becomes -2y-2y and creates a plus.
A researcher conducts two studies on the effectiveness of a peer mentoring program. Self-evaluation ratings among participants before, during, and after the program were measured in both studies. In Study 1, 12 participants were observed, and in Study 2, 16 participants were observed. If Fobt = 3.42 in both studies, then in which study will the decision be to reject the null hypothesis at α= 0.05 level of significance?
Answer:
Study 2
Step-by-step explanation:
Okay, so in this question we are given the data or parameters or information Below;
=>" two studies were conducted on the effectiveness of a peer mentoring program."
=> "Self-evaluation ratings among participants before, during, and after the program were measured in both studies."
=> In Study 1, 12 participants were observed"
=> "Study 2, 16 participants were observed."
=> " If Fobt = 3.42 in both studies"
Say Vo = study 2 and V1 = study 1.
Hence, Vo: not effective.
V1 = effective.
The study in which the decision will be to reject the null hypothesis at α= 0.05 level of significance is the STUDY 2.
This is because the value of F > f-critical.
You have already a 1000 cash on your hand. You have also a 1000 cash in bank and you withdraw half of 500, so, it means you withdraw 250. Now, you have a 1000 cash on hand plus 250 that you have been withdraw from the bank, all in all you have 1250 now in your hand.
Answer: At the end, you have $750 remaining in the bank.
Step-by-step explanation:
I guess you want to know how much is left in the bank.
initially
Hand : $1000
Bank: $1000
you withdraw $250 from the bank:
Hand: $1000 + $250 = $1250
Bank: $1000 - $250 = $750
Express the following ratio in its simplest form.
4:12
Answer:
3:12
Step-by-step explanation:
Answer:
1:3
Step-by-step explanation:
Think 4:12 as a fraction for a moment, it would be 4/12. Now completely simplify 4/12, you get 1/3. Now put 1/3 as a ratio, it would be 1:3.
Please mark BRAINLIEST, thanks!
simplify 2x+x+x+2y times 3y times y
Answer:
12 x y² + 6 y³
Step-by-step explanation:
Step(i):-
Given ( 2 x + x + x + 2 y ) times 3 y times y
( 2 x + x + x + 2 y ) × 3 y × y = ( 4 x + 2 y) × 3 y × y = ( 4 x + 2 y) 3 y²
By applying Distributive property
( a + b ) c = a . c + b . c
= 4 x . 3 y² + 2 y . 3 y²
= 12 x y² + 6 y³
Final answer:-
( 2 x + x + x + 2 y ) times 3 y times y = 12 x y² + 6 y³
A random sample pulled 43 catfish from a large lake. They were marked and released. A second sample pulled out 88 catfish. Seventeen had been marked. Calculate the estimated population
Answer: 114
Step-by-step explanation: You have 43 new catfish then you catch 88 but 17 of them have already been marked so you do not want to count those in the estimated population again because they have already been counted so you take 88 minus 17 and you get 71 new fish. So then you add the first new sample of fish 43 and then you add the second new sample of fish 71 and then you get 114
Evaluate the function h(t) =|t +2| + 3; find h(6)
Answer:
11
Step-by-step explanation:
h(t) =|t +2| + 3
Let t=6
h(6) =|6 +2| + 3
= |8| +3
=8+3
= 11
please help me on this work please !
Please help. I’ll mark you as brainliest if correct!
Answer:
[tex]\sqrt{-6} \sqrt{-384}=\sqrt{(-6)(-384)}=\sqrt{2304}=48\\ a=48\\b=0[/tex]
or
[tex]a=-48\\b=0[/tex]
both solutions are correct because root square has two solutions, one positive and one negative.
Answer:
a= -48
b=0
Step-by-step explanation:
[tex]\sqrt[]{-6} = i\sqrt{6}[/tex]
[tex]\sqrt{-384} =i\sqrt{384}[/tex]
[tex](i\sqrt{6} )(i\sqrt{384} )[/tex]
[tex]i^{2} \sqrt{2304}[/tex]
(-1)(48) = -48
a + bi
a= -48
b= 0
Please help
Convert 200 cm to cm
Answer:
to cm it's still 200 if you mean to metre 2m
Step-by-step explanation:
Answer:
It would still be 200
Step-by-step explanation:
HELP...it has timer
Answer:
lily has a larger ratio
Step-by-step explanation:
42,000 as a multipul of a power of 10
Answer:
[tex] 4.2 \times {10}^{4} [/tex]
Step-by-step explanation:
[tex]42000 = 4.2000 \times \times {10}^{4} \\ = 4.2 \times {10}^{4} [/tex]
no guess please explain
Find the diameter and radius of a circle with a circumference of 65.98 Please help
Answer:
21 and 10.5 respectively
Step-by-step explanation:
Remember circumference of a circle is given as;
C= 2×π×r; r is raduis
r = C / 2×π
=65.98/(2×3.142)= 10.50
D= 2× r = 2× 10.50= 21.0( D represent diameter)
Note π = 3.142 a known constant
how do you add 9 in 1 6 + 2 1/12
Step-by-step explanation:
9 + 1/6 + 2 1/12
9 + 2.25
11.25
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
Answer:
When x is 2, y is 16
Step-by-step explanation:
If y is 48 and x is 6, then y is 8 when x is 1.
Because of this, when x is 2, y will be 16.
Please mark Brainliest
What’s the correct answer for this question ?
Answer:
C
Step-by-step explanation:
It closely resembles to a sphere.
The perimeter of the rectangle is below 76 units. Find the length of side AD. AB on rectangle 3y + 3 CB 2y
Answer:
14 units
Step-by-step explanation:
The perimeter of a figure is the sum of the lengths of all the sides.
Here, we know that ABCD is a rectangle, so by definition, AB = CD and AD = BC. We also are given that AB = 3y + 3 and BC = 2y, which means that:
AB = CD = 3y + 3
AD = BC = 2y
Adding up all the side lengths and setting that equal to the perimeter, which is 76 units, we get the expression:
AB + CD + AD + BC = 76
(3y + 3) + (3y + 3) + 2y + 2y = 76
10y + 6 = 76
10y = 70
y = 7
We want to know the length of AD, which is written as 2y. Substitute 7 in for y:
AD = 2y = 2 * 7 = 14
The answer is thus 14 units.
~ an aesthetics lover
Answer:
14
Step-by-step explanation:
The perimeter of a rectangle is found by
P = 2 (l+w)
P = 2( 3y+3+2y)
Combine like terms
P = 2(5y+3)
We know the perimeter is 76
76 = 2(5y+3)
Divide each side by 2
76/2 = 2/2(5y+3)
38 = 5y+3
Subtract 3 from each side
38-3 = 5y+3-3
35 = 5y
Divide each side by 5
35/5 = 5y/5
7 =y
We want the length of AD = BC = 2y
AD = 2y=2*y = 14
Let:T : ℝ3→ℝ3 be the transformation that projects each vector x=(x1,x2,x3)onto the plane
x2=0,
so
T(x)=(x1 ,0 ,x3). Show that T is a linear transformation.
The first property for T to be linear is
T(0) =_________________________________________________
Check if this property is satisfied for T.T(x1, x2, x3) =(x1, 0,x3)
T(0,0,0) = ( _____ ,_____, _,_______) ,
So, is the first property satisfied?
Yes 0r No
The second property for T to be linear is T(cu+dv)=______(see choices below)___________________________________________for all vectors(u and v)i n the domain of T and all scalars c, d
cT(u)+dT(v)
dT(u)+cT(v)dT(u)−cT(v)
cT(u)−dT(v)
for all vectors
u,
v in the domain of T and all scalars c, d.
Check if this property is satisfied for T. Let u=(u1, u2, u3) and v =(v1, v2, v3).
T(cu+dv)=(cu1+dv1, 0, cu3+dv3) =(cu1, _______, _________) +(dv1, ________, _________)
Factor out the scalar in each ordered triple.
T(cu+dv) = ____(u1, 0, u3) + ______(v1, 0,v3)
Further simplify the previous equation.
T(cu+dv) = c
▼
(choices pick one)
T(v)
T(u)+d
▼
(choices for the arrow above pick one)
T(v)
T(u)
So, is the second property satisfied?
Yes
No
Thus, T ▼
is
is not
linear.
Answer:
Step-by-step explanation:
A linear transformation must satisfy the following properties.
- T(0) = 0.
- For vector a,b then T(a+b) = T(a) + T(b).
- For a vector a and a scalar r, it must happen that T(ra) = rT(a)
In this case we have that T(a,b,c) = (a,0,c).
Note that T(0) = T(0,0,0) = (0,0,0) = 0. So, the first property holds.
Let [tex] a=(a_1,a_2,a_3), b=(b_1,b_2,b_3) [/tex]. Then
[tex]T(a+b) = T((a_1+b_1,a_2+b_2,a_3+b_3)) = (a_1+b_1,0,a_3+b_3) = (a_1,0,a_3)+(b_1,0,b_3) = T(a) + T(b)[/tex]
So the second property holds.
Finally, let r be a scalar and let [tex] a=(a_1,a_2,a_3)[/tex]. Then
[tex] T(ra) = T((ra_1,ra_2,ra_3)) = (ra_1,0,ra_3) = r(a_1,0,a_3)= rT(a)[/tex]
So, the three properties hold, and therefore, T is a linear transformation.
It is true that T represents a linear transformation
How to determine if T is a linear transformationA linear transformation is such that have the following properties
T(0) = 0.If u and v are vectors, then T(u+v) = T(u) + T(v).If u is a vector and r is a scalar, then T(ru) = rT(u)For the first property, we have:
T(x1,x2,x3) = (x1,0,x3)
The above property becomes
T(0) = T(0,0,0)
T(0) = (0,0,0)
T(0)= 0.
So, we can conclude that the first property of the linear transformation is satisfied
For the second property, we make use of the following:
u = (u1, u2, u3) and b = (v1,v2,v3)
The above property becomes
T(u + v) = T(u1 + v1, u2 + v2, u3 + v3)
Expand
T(u + v) = T(u1 + v1, 0, u3 + v3)
Expand
T(u + v) = (u1,0,u3) + (v1, 0, v3)
Simplify
T(u + v) = T(u) + T(v)
The above means that the second property is also satisfied
Recall that:
u = (u1, u2, u3)
So, we have:
T(ru) = (ru1, ru2, ru3)
Where r is a scalar
Expand
T(ru) = (ru1, 0, ru3)
Further, expand
T(ru) = r(u1, 0, u3)
So, we have:
T(ru) = rT(u)
The above means that, the third property is also satisfied
Hence, T represents a linear transformation
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Complete the point- slope equation of the line through (8, -8 and (9, 8). Y - 8 =
