what is the median of this set of measurements? 10cm, 15cm, 15cm, 18cm, 20cm.

Answer:

[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} =  \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants.

Step-by-step explanation:

Consider the differential equation [tex]y''+6y'+9y = 4e^{x}[/tex]. To find the homogeneus solution, we assume that [tex]y = Ae^{rt}[/tex] and replace it in the equation [tex]y''+6y'+9y = 0[/tex]. If we do so, after using some properties of derivatives and the properties of the exponential function we end up with the equation

[tex]r^2+6r+9 = 0 = (r+3)^2[/tex]

which leads to r = -3. So, one solution of the homogeneus equation is [tex]y_h = c_1e^{-3x}[/tex], where c_1 is a constant.

To use the order reduction method, assume

[tex] y = v(x)y_h(x)[/tex]

where v(x) is an appropiate function. Using this, we get

[tex]y'= v'y+y'v[/tex]

[tex]y''=v''y+y'v'+y''v+v'y'=v''y+2v'y'+y''v[/tex]

Plugging this in the original equation we get

[tex]v''y+2v'y'+y''v + 6(v'y+y'v) +9vy=4e^{x}[/tex]

re arranging the left side we get

[tex]v''y+2v'y'+6v'y+v(y''+6y'+9y)=4e^{x}[/tex]

Since y is a solution of the homogeneus equation, we get that [tex]y''+6y'+9y=0[/tex]. Then we get the equation

[tex]yv''+(2y'+6y)v' = 4e^{x}[/tex]

We can change the variable as w = v' and w' = v'', and replacing y with y_h, we get that the final equation to be solved is

[tex] e^{-3x}w'+(6e^{-3x}-6e^{-3x})w =4e^{x}[/tex]

Or equivalently

[tex]w' = 4e^{4x}[/tex]

By integration on both sides, we get that w = e^{4x}+ k[/tex] where k is a constant.

So by integration we get that v = [tex]e^{4x}{4} + kx+d[/tex] where d is another constant.

Then, the final solution is

[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} =  \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants

Answer:

[tex]j^4k[/tex]

Step-by-step explanation:

[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]

Answer:

4

Step-by-step explanation:

give me brainliest

Answer: D

Step-by-step explanation:

Since we are not given the height of the trapezoid, we can split this into a triangle and a rectangle. We find the area of each and then add them together. In order to do so, we must use Pythagorean Theorem to find the missing length so that we can find the area.

a²+b²=c²

a²+4²=8²

a²+16=64

a²=48

a=√48

a=4√3

Now that we know the missing length of the triangle, we can find the area of the triangle and the rectangle.

Triangle

A=1/2bh

A=1/2(4)(4√3)

A=8√3

-----------------------------------------------------------------------------------------

Rectangle

A=lw

A=7(4√3)

A=28√3

With our areas, we can add them together.

4√3+28√3=36√3 cm²

Answer:

We want a line that passes through the point (4, 7/2)

and we have no other information of this line, so we can not fully find it, but we can find a general line.

We know that a line can be written as:

y = a*x + b.

Now we want that, when x = 4, we must have y = 7/2.

7/2 = a*4 + b

b = -a*4 + 7/2

Then we can write this line as:

y = a*x - a*4 + 7/2.

Where a can take any value, and it is the slope of our line.

Answer:

A

Step-by-step explanation:

Answer:

96 ft^2

Step-by-step explanation:

volume=l^3

l=4

4x4x4=64

Surface area (4x4)=16

16x6=96

Answer:

SA =96 ft^2

Step-by-step explanation:

The volume of a cube is given by

V = s^3

64 = s^3

Take the cube root of each side

64 ^ 1/3 = s^3 ^ 1/3

4 =s

The side length si 4

The surface area of a cube is

SA = 6 s^2

SA = 6 * 4^2

SA = 6 * 16

SA =96 ft^2

Answer:

7 donkeys

Step-by-step explanation:

Given

A system consisting of donkeys and tourists

Heads = 50

Legs = 114

Required

Calculate number of donkeys.

Represent donkeys with D and tourists with T.

By means of identification; donkeys and tourists (human) both have 1 head.

This implies that

Number of Heads = D + T

50 = D + T ----- Equation 1

While each donkey have 4 legs, each tourists have 2 legs.

This implies that

Number of legs = 4D + 2T

114 = 4D + 2T ---- Multiply both sides by ½

114 * ½ = (4D + 2T) * ½

57 = 4D * ½ + 2T * ½

57 = 2D + T ----- Equation 2

Subtract equation 1 from 2

57 = 2D + T

- (50 = D + T)

---------------------

57 - 50 = 2D - D + T - T

7 = D

Recall that D represents the number of donkeys.

So, D = 7 implies that

The total number of donkeys are 7

Answer:

please see the attached picture for full solution...

Hope it helps...

Good luck on your assignment....

Answer:

[tex]\dfrac{15}{19}[/tex]

Step-by-step explanation:

The soccer player so far has made 15 penalty kicks in 19 attempts.

Therefore:

Total Number of trials =19

Number of Successes =15

Therefore, the relative frequency probability that she will make her next penalty​ kick is:

[tex]=\dfrac{\text{Number of Successes}}{\text{Total Number of Trials}} \\=\dfrac{15}{19}[/tex]

Answer: B, 1 mile / 5280 ft.

Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).

Answer:

Step-by-step explanation:

Given the equation j – 16 = 7, If Nolan is using substitution to determine if 23 is a solution to the equation, then Nolan need to make j the subject of the formula from the equation. The following statements must therefore be made by Nolan.

First, Nolan must substitute for the value of j in the equation.

To simplify, Nolan must subtract the value of  7 from both sides to have;

j – 16 - 7= 7 - 7

j – 23 = 0

Then Nolan must add 23 to both sides of the equation to get the value of j as shown;

j – 23 + 23 = 0+23

j = 23

23 is therefore a solution to the equation

Answer:First, Nolan must substitute 23 for j.To simplify, Nolan must subtract 16 from 23. 23 is a solution of the equation.

Step-by-step explanation:

I got it right on Edge

Answer:

  A) 10, -3.73, -6.035, -6.259 . . . cm/s

  B) -6.2832 cm/s

Step-by-step explanation:

A) For problems like this, where repeated evaluation of a function is required, I find a graphing calculator or spreadsheet to be an appropriate tool. The attached shows that we defined the position function ...

  p(t) = 2sin(πt) +5cos(πt)

and a function for computing the average velocity from t=1. For some time interval ending at t2, the average velocity is ...

  Va(t2) = Δp/Δt = (p(t2) -p(1))/(t2 -1)

Then, for example, for t2 = 2, the average velocity on the interval [1, 2] is ...

  Va(2) = (p(2) -p(1))/(2 -1) = ((2sin(2π) +5cos(2π)) -(2sin(π) +5cos(π)))/(1)

  = (2·0+5·1 -(2·0 +5·(-1)) = 10 . . . . matches the table value for x1 = 2.

Then the average velocity values for the intervals of interest are ...

  1) [1, 2]   Va = 10

  2) [1, 1.1]   Va = -3.73

  3) [1, 1.01]   Va = -6.035

  4) [1, 1.001]   Va = -6.259

__

B) Sometimes a better estimate is obtained when the interval is centered on the point of interest. Here, we can compute the average velocity on the interval [0.999, 1.001] as a better approximation of the instantaneous velocity at t=1. That value is ...

  [0.999, 1.001]   Va = -6.283175*

Our estimate of V(1) is -6.2832 cm/s.

The exact value is -2π ≈ -6.2831853... cm/s

__

* This is the average of the Va(0.999) and Va(1.001) values in the table.

Answer:

Step-by-step explanation:

The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm

This means that the required length of computer chips is between 1.1cm - 1.3cm

Where 1.1cm = [1.2 - 0.1]

1.3cm = [1.2 + 0.1]

Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.

The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:

- The length of the chips.

The length of the chips his production team produces should be tailored to meet the length specification of his client.

Step-by-step explanation:

Joe mama

Answer:

False, it is easier to isolate x.

Step-by-step explanation:

6y+x=3

x=3-6y

Answer:

Pillows:

Blankets:

Pet Beds:

Step-by-step explanation:

18 + 45 + 27 = 90 (there are 90 students)

18 out of 90 = 20%

45 out of 90 = 50%

27 out of 90 = 30%

Hope this helps!

Answer:

solution,

[tex]5x + 8 - 3x = - 10 \\ or \: 5x - 3x + 8 = -10 \\ or \: 2x + 8 = -10 \\ or \: 2x = -10 - 8 \\ or \: 2x = -18\\ or \: x = \frac{-18}{2 } \\ x = -9[/tex]

hope this helps..

Good luck on your assignment

Answer:

x = -9

Step-by-step explanation:

5x + 8 - 3x = -10

Rearrange.

5x - 3x + 8 = -10

Subtract like terms.

2x + 8 = -10

Subtract 8 on both sides.

2x = -10 - 8

2x = -18

Divide 2 into both sides.

x = -18/2

x = -9

Answer:

(a) 2.81%

(b) 0.5%

Step-by-step explanation:

We have the following information from the statement:

P = 64 + - 0.9

(a) We know that the perimeter is:

P = 2 * pi * r

if we solve for r, we have to:

r = P / 2 * pi

We have that the formula of the area is:

A = pi * r ^ 2

we replace r and we are left with:

A = pi * (P / 2 * pi) ^ 2

A = (P ^ 2) / (4 * pi)

We derive with respect to P, and we are left with:

dA = 2 * P / 4 * pi * dP

We know that P = 64 and dP = 0.9, we replace:

dA = 2 * 64/4 * 3.14 * 0.9

dA = 9.17

The error would come being:

dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811

In other words, the error would be 2.81%

(b) tell us that dA / A <= 0.01

we replace:

[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01

solving we have:

2 * dP / P <= 0.01

dP / P <= 0.01 / 2

dP / P <= 0.005

Which means that the answer is 0.5%

Answer:

As the P-value is very low, we can conclude that there is enough evidence to support the claim that the survival rate is significantly higher when the seatbelt is used.

Step-by-step explanation:

We have a hypothesis test that compares the survival rate using the seatbelt versus the survival rate not using it.

The claim is that the survival rate (proportion) is significantly higher when the seatbelt is used.

Then, the null hypothesis is that the seatbelts have no effect (both survival rates are not significantly different).

The P-value is the probabilty of the sample we have, given that the null hypothesis is true. In this case, this value is 0.0001.

This is very low, what gives enough evidence to claim that the survival rate is significantly higher when the seatbelt is used.

EASY!

Answer: 17/16 or 1 1/16

Step-by-step explanation:

BRO IT'S ELEMANTARY FRACTIONS!!!!

Answer:

Step-by-step explanation:

Answer:

a. They are empty set.

b. they are finite set.

Solution,

a. A={ prime number between 6 and 7}

There are not any number between 6 and 7.

So there will be no Elements.

A={ }

It is empty set.

Empty set are those set which doesn't contain any Element.

b.B={multiples of 2 less than 20}

B={2,4,6,8,10,12,14,16,18}

It is a finite set.

Finite set are those set which we can count easily.

Hope this helps...

Good luck on your assignment...

Answer:

0| 2

1| 2

2| 0 0 3 9

3| 2 4 4 4 8 8

4| 2 2 4 5 5 6 7

Step-by-step explanation:

Same as the other similar questions

hope this helps!

Let's think:

1 ton ------------ 1000 kilograms

3.2 tons ----------- x kilograms

Multiply in cross

1 . x = 1000 . 3.2

x = 3200

So 3.2t = 3200 kilograms

Answer:

It is 2902.99 to be exact

Step-by-step explanation:

Answer:

0.48% probability that all four are new

Step-by-step explanation:

The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Total of 10 homes, so N = 10.

We want 4 new, so x = 4.

In total, there are 4 new, so k = 4.

Sample of four homes, so n = 4.

Then

[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]

0.48% probability that all four are new

The calculated probability is "0.0048".

From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.

Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.

X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.

[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]

[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]

                   [tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]

Using the excel function:

[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex]  for calculating the [tex]P_{X} (4)[/tex]:

[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]

[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]

Find out more information about the probability here:

brainly.com/question/2321387

Answer:

a. P(x=0)=0.2967

b. P(x=1)=0.4444

c. P(x=2)=0.2219

d. P(x=3)=0.0369

Step-by-step explanation:

The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).

The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants)  by the total amount of restaurants from where we can pick (15 restaurants):

[tex]p=\dfrac{5}{15}=0.333[/tex]

Then, we can model the probability that k meals cost more than $50 as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\[/tex]

a. We have to calculate P(x=0)

[tex]P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\[/tex]

b. We have to calculate P(x=1)

[tex]P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\[/tex]

c. We have to calcualte P(x=2)

[tex]P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\[/tex]

d. We have to calculate P(x=3)

[tex]P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\[/tex]

Answer:

[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]

Step-by-step explanation:

when the equation is like y = ax + b

the slope is a

in this case we have

[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]

so the slope is

[tex]\dfrac{4}{5}[/tex]

Answer:

20-39 ⇒ 5

40-59 ⇒ 3

60-79 ⇒ 5

80-99 ⇒ 10

Answer:

20-39: 5

40-59: 3

60-79: 5

80-99: 10

Step-by-step explanation:

If you just added up, you can find all the values.

Answer:

1/3

Step-by-step explanation:

hello,

probability of 1 = 1/6

probability of 2 = 1/6

probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0

so the answer is 2/6=1/3