A woman forgot her bank ATM PIN but she was able to recall some of the pin.
1)the 1st digit is half of the 2nd pin
2)the sum of 2nd and 3rd is equal to 10
3)the 4th is equal to the 2nd plus 1
4)the sum of all digits is 23
show workings please
what is the ATM digit?

Answer:

[tex]y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]

Step-by-step explanation:

Solution:-

- Given is the 2nd order linear ODE as follows:

                      [tex]ty'' + ( 2t - 1 )*y' - 2y = 6t^2 . e^(^-^2^t^)[/tex]

- The complementary two independent solution to the homogeneous 2nd order linear ODE are given as follows:

                     [tex]y_1(t) = 2t - 1\\\\y_2 (t ) = e^-^2^t[/tex]

- The particular solution ( yp ) to the non-homogeneous 2nd order linear ODE is expressed as:

                    [tex]y_p(t) = u_1(t)*y_1(t) + u_2(t)*y_2(t)[/tex]

Where,

              [tex]u_1(t) , u_2(t)[/tex] are linearly independent functions of parameter ( t )

- To determine [  [tex]u_1(t) , u_2(t)[/tex] ], we will employ the use of wronskian ( W ).

- The functions [[tex]u_1(t) , u_2(t)[/tex] ] are defined as:

                       [tex]u_1(t) = - \int {\frac{F(t). y_2(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\\\u_2(t) = \int {\frac{F(t). y_1(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\[/tex]

Where,

      F(t): Non-homogeneous part of the ODE

      W [ y1(t) , y2(t) ]: the wronskian of independent complementary solutions

- To compute the wronskian W [ y1(t) , y2(t) ] we will follow the procedure to find the determinant of the matrix below:

                      [tex]W [ y_1 ( t ) , y_2(t) ] = | \left[\begin{array}{cc}y_1(t)&y_2(t)\\y'_1(t)&y'_2(t)\end{array}\right] |[/tex]

                      [tex]W [ (2t-1) , (e^-^2^t) ] = | \left[\begin{array}{cc}2t - 1&e^-^2^t\\2&-2e^-^2^t\end{array}\right] |\\\\W [ (2t-1) , (e^-^2^t) ]= [ (2t - 1 ) * (-2e^-^2^t) - ( e^-^2^t ) * (2 ) ]\\\\W [ (2t-1) , (e^-^2^t) ] = [ -4t*e^-^2^t ]\\[/tex]

- Now we will evaluate function. Using the relation given for u1(t) we have:

                     [tex]u_1 (t ) = - \int {\frac{6t^2*e^(^-^2^t^) . ( e^-^2^t)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_1 (t ) = \frac{3}{2} \int [ t*e^(^-^2^t^) ] \, dt\\\\u_1 (t ) = \frac{3}{2}* [ ( -\frac{1}{2} t*e^(^-^2^t^) - \int {( -\frac{1}{2}*e^(^-^2^t^) )} \, dt] \\\\u_1 (t ) = -e^(^-^2^t^)* [ ( \frac{3}{4} t + \frac{3}{8} )] \\\\[/tex]

- Similarly for the function u2(t):

                     [tex]u_2 (t ) = \int {\frac{6t^2*e^(^-^2^t^) . ( 2t-1)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_2 (t ) = -\frac{3}{2} \int [2t^2 -t ] \, dt\\\\u_2 (t ) = -\frac{3}{2}* [\frac{2}{3}t^3 - \frac{1}{2}t^2 ] \\\\u_2 (t ) = t^2 [\frac{3}{4} - t ][/tex]

- We can now express the particular solution ( yp ) in the form expressed initially:

                    [tex]y_p(t) = -e^(^-^2^t^)* [\frac{3}{2}t^2 + \frac{3}{4}t - \frac{3}{8} ] + e^(^-^2^t^)*[\frac{3}{4}t^2 - t^3 ]\\\\y_p(t) = -e^(^-^2^t^)* [t^3 + \frac{3}{4}t^2 + \frac{3}{4}t - \frac{3}{8} ] \\[/tex]

Where the term: 3/8 e^(-2t) is common to both complementary and particular solution; hence, dependent term is excluded from general solution.

- The general solution is the superposition of complementary and particular solution as follows:

                    [tex]y_g(t) = y_c(t) + y_p(t)\\\\y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]

Answer:

A --- unless d is supposed to be "y= -7x + 2"

Step-by-step explanation:

The slope is m in y=mx + b

So:

a. y= -2x + 11 slope= -2

b. y= x + 4 slope= 1

c. y= -x + 7 slope= -1

d. y= -7 + 2 (I don's see an x but if there were an x I assume that the slope would equal -7)

The higher the m value, the steeper the slope because it is m/1

So, -2/1 is steeper than 1/1 or -1/1

Answer: Choice C

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

3/10≠3/5*1/4

so event A and B are not independent.

Answer:

[tex]cos150 = -\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

Recall the unit circle. At 150 deg, the point value is (-sqrt3/2, 1/2)

Remember the cosine is always the x-value, and sine is always the y-value.

This means that cosine will be -sqrt3/2.

Answer:

option 3

Step-by-step explanation:

x = 2 is a vertical line with an x-intercept of (2, 0) so the answer is Option 3.

Answer:

Option 3

Step-by-step explanation:

The value of x will always be 2. Y can be anything it wants to be and x will still be 2 no matter what, You could pick multiple points on the line for each graph, and only Option 3 will have x always being 2.

Answer is 5 calories/min

75 divided by 15 is 5

Answer:five cal per min.15 in five groups equals ''75''

Step-by-step explanation:

[tex]y = {x}^{2} - 18 \\ y + 18 = {x}^{2} \\ square \: root \: both \: sides \: \\ \sqrt{y + 18} = \sqrt{ {x}^{2} } [/tex]

[tex]x = \sqrt{y + 18} [/tex]

Answer:

√y + 18 = x

Step-by-step explanation:

Let us solve it now.

y = x² - 18

Take -18 to the left side

y + 18 = x²

Now remove the square of x

√y + 18 = x

Answer:

i dont really know what it is

Answer:

The data support the hypothesis that the proportion of defectives is lower for robots than humans.

Step-by-step explanation:

To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.

From the data given:

Total number of cables a robot assembled = 507

Defectives = 9

To get the defect rate =  the number of defects divided by the total number of cables, multiplied by 100.

Defect rate =  (9 / 507) x 100 = 0.01775 x 100

Defect rate for the robot = 1.775‬%

From the question, a robot was used and the defect rate after the calculation is 1.775‬%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745‬ defectives.

x / 507 = 3.5%

x (defectives) = 17.745‬

Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.

The smaller angle, inside the bold lines, is -90 degrees.

The larger angle, outside the bold lines, is 270 degrees.

Angles can be measured in increments between -90° and 630°.

Two straight lines are considered to be intersecting if they come together at the same point. The intersection of two lines is known as the junction point. When two lines intersect, four angles are produced. The sum of the four angles is always 360 degrees.

Two straight lines that cross one other and produce right angles are called perpendicular lines. There are four right angles created when two perpendicular lines cross.

There are two types of angle connections produced when lines intersect:

Congruent opposite angles

Nearby angles are helpful

The information is

Let O (0, 0) be the origin, where the y and x axes must connect.

Thus, the angles on the four quadrants of the axis are produced.

The fourth quadrant's crossing lines create an angle that is given by For, the anticlockwise measure, A = -90°.

B = 360n - 180° for the clockwise measure, and n = 3 in this case.

Hence, when we simplify, we obtain

The second angle has a length of = 630°.

As a result, the angles are 90° and 630°.

Go here to find out more about angles created by intersecting lines.

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Answer:

x = -30/7

Step-by-step explanation:

-7x+3y=30

Let y=0

-7x +0 = 30

Divide by -7

-7x /-7 = 30/-7

x = -30/7

Answer:

[tex]-\frac{30}{7}[/tex]

Step-by-step explanation:

y equals zero => y = 0

-7x+3y=30

-7x +3.0 = 30

-7x + 0 = 30

-7x = 30

-7x/-7 = 30/-7

x = -30/7

Hope this helps ^-^

Hey there!

Answer:

A = 192 in²

Step-by-step explanation:

Base = 4 ft

Height = 4 in

Convert the length of the base to inches:

4 ft = 4 ×12 = 48 in

Formula for the area of a rectangle: A = l × w (in this instance, 'l' is the height)

4 × 48 = 192 in²

Answer:

A =192 in^2

Step-by-step explanation:

Change the 4 ft to inches

4 * 12 = 48 inches

A = l*w

A = 48*4

A =192 in^2

Answer:

a) The CDF of X/Y is calculated as:

[tex]F_{z} (\zeta) = \frac{\zeta}{\zeta + 2}[/tex] for [tex]0 < \zeta < \infty[/tex]  

[tex]F_{z} (\zeta) = 0[/tex] for [tex]\zeta \leq 0[/tex]

Note: Z = X/Y

b) Probability that A finishes before B = 1/3

Step-by-step explanation:

For clarity and easiness of expression, this solution is handwritten and attached as a file. Check the complete solution in the attached file.

Answer:

A

Step-by-step explanation:

(2,1) - only one in the table. Remember (x,y)

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The point of diminishing returns (x , y ) is  (11, 21462)

Step-by-step explanation:

From the question we are told that

     The function is  [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]

Here R(x)  represents revenue (in thousands of​ dollars) and  x  represents the amount spent on advertising​ (in thousands of​ dollars).

           Now  differentiating  R(x) we have  

               [tex]R'(x) = -3x^2 +66x + 800[/tex]

Finding the second derivative of R(x)

              [tex]R''(x) = -6x +66[/tex]

at  inflection point    [tex]R''(x) = 0[/tex]

    So      [tex]-6x +66 = 0[/tex]

=>           [tex]x= 11[/tex]

    substituting value of x into R(x)

     [tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]

      [tex]R(x) = 21462[/tex]

Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is

     (11, 21462)

Answer:

6 less than a number is equal to 1 and 4 tenths

Step-by-step explanation:

Answer:

a.vertical translation

Here is the full question .

We are interested in finding an estimator for [tex]Var (X_i )[/tex] and propose to use :

[tex]\hat {V} = \bar {X}_n (1- \bar {X} )_n[/tex]

Now; we are interested in the basis of [tex]\hat V[/tex]

Compute :

[tex]E \ \ [ \bar V] - Var (X_i) =[/tex]

Using this; find an unbiased estimator [tex][ \bar V][/tex] for [tex]p(1-p) \ if \ n \geq 2[/tex]

Write [tex]bar \ x{_n} \ for \ X_n[/tex]

Answer:

Step-by-step explanation:

[tex]\bar X_n = \dfrac{1}{n} {\sum ^n _ {i=1} } \\ \\ E(X_i) = - \dfrac{1}{n=1} \sum p \dfrac{1}{n}*np = \mathbf{p}[/tex]

[tex]V(\bar X_n) = V ( \dfrac{1}{n_{i=1} } \sum ^n \ X_i )} = \dfrac{1}{n^2} \sum ^n_{i=1} Var (X_i) \\ \\ = \dfrac{1}{n^2} \ \sum ^n _{i=1} p(1-p) \\ \\ = \dfrac{1}{n^2}*np(1-p) \\ \\ = \dfrac{p(1-p)}{n}[/tex]

[tex]E( \bar X^2 _ n) = Var (\bar X_n) + [E(\bar X_n)]^2 \\ \\ = \dfrac{p(1-p)}{n}+ p \\ \\ = p^2 + \dfrac{p(1-p)}{n} \\ \\ \\ \hat V = \bar X_n (1- \bar X_n ) = \bar X_n - \bar X_n ^2 \\ \\ E [ \hat V] = E [ \bar X_n - \bar X_n^2] \\ \\ = E[\bar X_n ] - E [\bar X^2_n] \\ \\ = p-(p^2 + \dfrac{p(1-p)}{n}) \\ \\ = p-p^2 -\dfrac{p(1-p)}{n}[/tex]

[tex]=p(1-p)[1-\dfrac{1}{n}] = p(1-p)\dfrac{n-1}{n}[/tex]

[tex]Bias \ (\bar V ) = E ( \hat V) - Var (X_i) \\ \\ = p(1-p) [1-\dfrac{1}{n}] - p(1-p) \\ \\ - \dfrac{p(1-p)}{n}[/tex]

Thus; we have:

[tex]E [\hat V] = p(1-p ) \dfrac{n-1}{n}[/tex]

[tex]E [\dfrac{n}{n-1} \ \ \bar V] = p(1 -p)[/tex]

[tex]E [\dfrac{n}{n-1} \ \ \bar X_n (1- \bar X_n )] = p (1-p)[/tex]

Therefore;

[tex]\hat V ' = \dfrac{n}{n-1} \bar X_n (1- \bar X_n)[/tex]

[tex]\mathbf{ \hat V ' = \dfrac{n \bar X_n (1- \bar X_n)} {n-1}}[/tex]

Hope this helps!

Stay safe, have a good day :D

Answer:

67

Step-by-step explanation:

Using triangle property

127+x=180

x=53

53+60+y=180

113+y=108

y=67

Answer:

The answer is C.

Step-by-step explanation:

For a function, we do a vertical line test. If there is more than one point in one single x-position, it is not a function. Example, the ordered pairs (1, 1) and (1, 2) do NOT describe a function because there are more than one point on x=1.

Answer:   b) 1510 vehicles

Step-by-step explanation:

Total: 5 miles x 5280 ft per mile = 26,400

Cars: 80% of vehicles are cars with a length of 13.5 =  0.8(13.5)v = 10.8v

Trucks: 20% of vehicles are trucks with length of 20 = 0.2(20)v = 4v

Between: Distance between two vehicles is 3: (3/2)v = 1.5v

Total  = Cars + Trucks + Between

26,400 = 10.8v + 4v + 1.5v

26,400 = 16.3v

1619.6 = v

the closest number of all of the options is (b) 1510

Answer:

C. The trails are not independent.

The probability of drawing one marble will not be independent of others thus option (c) is correct.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Drawing 5 marbles from a bag with 10 red, 8 green, and 12 yellow marbles without replacement.

In without replacement, the remaining balls in each draw will go to be decreased thus they will be dependent events so binomial distribution will not be applied.

Hence "One marble's likelihood of being drawn won't be independent of the other marbles".

For more information about the probability,

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Answer:

[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]

Step-by-step explanation:

For a hyperbolic mirror the two foci are 42 cm apart.

The distance between the foci = 2c.

Therefore:

The distance of the vertex from one focus = 6 cm

The distance of the vertex from the other focus = 36 cm

2a=36-6=30

Now:

[tex]c^2=a^2+b^2\\21^2=15^2+b^2\\b^2=21^2-15^2\\b^2=216\\b=6\sqrt{6}[/tex]

If the transverse axis lies on the y-axis, and the hyperbola is centered at the origin. Then the hyperbola has an equation of the form:

[tex]\dfrac{y^2}{a^2} -\dfrac{x^2}{b^2}=1[/tex]

Therefore, the equation of the hyperbola is:

[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]

Answer:

  3.84 units

Step-by-step explanation:

By the properties of angle bisectors, ...

  WZ/ZX = WY/YX

Solving for WY, we have ...

  WY = (YX)(WZ)/(ZX) = (6.5/6)(WZ)

The length YZ is ...

  YZ = 8 = WY +WZ

  8 = (6.5/6)(WZ) +WZ = 12.5/6(WZ) . . . . substitute for WY

  WZ = 8(6/12.5) . . . . multiply by 6/12.5

  WZ = 3.84

Answer:

The correct answer is indeed 3.84 units

Step-by-step explanation:

I just took the test and got it correct hope this helps ☺

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that [tex]p = 0.42[/tex]

Three Americans are randomly selected

This means that [tex]n = 3[/tex]

What is the probability that none of them voted in the last election

This is P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]

19.51% probability that none of them voted in the last election

Answer:

B

The mode is 11 and 3

The Median is 10

The mean is 12

Answer:

5.625 = 45/8 = 5 5/8

Step-by-step explanation:

4yd^2

2yd^2

6yd^2

Step-by-step explanation:

Rule: height x base/2

The area of the big triangle=2 x 4/2 = 4 yd^2

The area of the small one= 2 x2/2 =2yd^2

The total area of the trapezoid is the sum of these areas= 2+4=6yd^2

Answer:

40%

Step-by-step explanation:

To find the answer to this, you first can find out what percentage of students did wear spirit shirts. To do this you can divide 135 by 225 to give you 0.6. To convert the decimal into a percentage you can simply multiply by 100, giving you 60%. Then to find the percentage of students that did not wear spirit shirts, you can subtract 60 from 100, giving you 40%.