Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of .

The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is

[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]

where T is the set

[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]

(a) I've attached an image of the integration region.

[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]

(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.

Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:

[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]

[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]

Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.

Answer:

Desmos could come in handy

Answer:

The function is  continuous at  x = 36

Step-by-step explanation:

From the question we are told that

      The  function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]  

       The  point at which continuity is tested is  x =  1

Now from the definition  of continuity ,

   At function is continuous at  k if  only  

       [tex]\lim_{x \to k}f(x) = f(k)[/tex]

So

      [tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]

                            [tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

                             [tex]= 7.2[/tex]

Now  

     [tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

     [tex]f(36) = 7.2[/tex]

So  the given function is continuous at  x =  36

because

          [tex]\lim_{x \to 36}f(x) = f(36)[/tex]

Answer:

252 miles

Step-by-step explanation:

19.99 + .80x = 221.59

,80x = 201.60

x = 252

Answer:

18 cm.

Step-by-step explanation:

The circumference of a circle is found by calculating 2 * pi * r.

In this case, the circumference is 36 pi cm.

2 * pi * r = 36 * pi

2 * r = 36

r = 36 / 2

r = 18 cm.

Hope this helps!

Answer:

18 centimeters

Step-by-step explanation:

The circumference of a circle can be found using the following formula.

[tex]c=2\pi r[/tex]

We know the circumference is 36π cm, therefore we can substitute 36π in for c.

[tex]36\pi= 2 \pi r[/tex]

We want to find r, the radius. Therefore, we must get r by itself. First, divide both sides of the equation by pi.

[tex]36\pi / \pi = 2 \pi r / \pi\\\\36= 2 \pi r / \pi\\\\36=2r[/tex]

Next, divide both sides of the equation by 2.

[tex]36=2r \\\\36/2=2r/2\\\\36/2=r\\\\18=r\\\\r=18 cm[/tex]

The radius of Circle O is 18 centimeters.

Answer:  a=24

Step-by-step explanation:

Lets find the line's  formula (equation of the line).

As known the general formula of any straight line (linear function) is

y=kx+b

Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7

(Xb;Yb)- are the coordinates of point B

(Xa;Ya) are the coordinates of point A

Now lets find the coefficient b.  For this purpose we gonna use the coordinates of any point A or B.

We will use A

7=-2/7*3+b

7=-6/7+b

b=7 6/7

So the line' s  equation is y= -2/7*x+7 6/7

Now we gonna find the value of a usingcoordinates of point C.

Yc=1,  Xc=a

1=-2/7*a+7 6/7

2/7*a= 7 6/7-1

2/7*a=6 6/7

(2/7)*a=48/7

a=48/7: (2/7)

a=24

Answer:

a=24

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

when you plug in 9 for k. you do 6(9) which is 54. then add 12 to 54 and thats ur answer, 66.

Answer:

-2, b, a+c

Step-by-step explanation:

Answer:

-2, b, a+c

Step-by-step explanation:

By looking at where A and C are on the number line, we can tell that A is a negative number close to zero and C is a positive number a little greater than four. This means that if we add the two together, we'll get a positive number a little below four.

By looking at the number line, we can tell that the value of B is a positive number a little below the number three.

Now that we know that B is less than A+C, and we know where -2 is on the number line (two marks to the left of zero) we can decide the least to greatest values.

Since negatives are always less than positives, we know that -2 has the smallest value. Next, we know that B is lower on the number line than A+C. So, in order, from least to greatest, the answer is:

-2, B, A+B

Hope this helps!! <3 :))

Answer:

Following are the given series for all x:

Step-by-step explanation:

Given equation:

[tex]\bold{J_0(x)=\sum_{n=0}^{\infty}\frac{((-1)^{n}(x^{2n}))}{(2^{2n})(n!)^2}}\\[/tex]

Let   the value a so, the value of [tex]a_n[/tex]  and the value of [tex]a_(n+1)[/tex]is:

[tex]\to a_n=\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}[/tex]

[tex]\to a_{(n+1)}=\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}[/tex]

To calculates its series we divide the above value:

[tex]\left | \frac{a_(n+1)}{a_n}\right |= \frac{\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}}{\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}}\\\\[/tex]

           [tex]= \left | \frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2} \cdot \frac {2^{2n}(n!)^2}{(-1)^2n x^{2n}} \right |[/tex]

           [tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)!^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |[/tex]

           [tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\= \left | \frac{x^{2n}\cdot x^2}{2^{2n} \cdot 2^2(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\[/tex]

           [tex]= \frac{x^2}{2^2(n+1)^2}\longrightarrow 0 <1[/tex]   for all x

The final value of the converges series for all x.

Answer:

The answer is 0.267949192

Step-by-step explanation:

I hope that is enough numbers.

Answer:

There are 80 10th graders in the school

Step-by-step explanation:

Let the number of 10th graders be x

There are 25% fewer 11th graders

That mean x - 25% of x

x -0.25x = 0.75x

There are 20% more 11th graders than 12th graders

So if number of 12th graders = y, then

0.75x = y + 20/100 * y = y + 0.2y = 1.2y

Since ;

0.75x = 1.2y

then y = 0.75x/1.2 = 0.625x

So let’s add all to give 190

x + 0.75x + 0.625x = 190

2.375x = 190

x = 190/2.375

x = 80

Answer:

consistent independent

Step-by-step explanation:

This is a graph of consistent independent equations

The lines cross and there is one solution

Inconsistent equations never cross and there is no solutions

Consistent dependent equations are equations of the same line

Answer:

Linear

Step-by-step explanation:

This is a graph of linear system of equation.

The two lines represent different equations connected with each other.

They intersect at a common point showing the solution to the system of equation.

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

Answer:

9e -3

Step-by-step explanation:

Perform the indicated multiplication:

6 e + 3 (e-1) = 6e + 3e - 3

This, in turn, simplifies to

9e -3, or 3(3e - 1).

Answer:

ANSWER: 9e-3

Step-by-step explanation:

6e+3(e−1)

As we need to simplify the above expression:

First we open the brackets :

3(e-1)=3e-33(e−1)=3e−3

Now, add it to 6e.

So, it becomes,

$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$

Hence, equivalent expression would be 9e-3.

Answer:

The value of x= 20

Step-by-step explanation:

I believe the question is ,"60% of x is us, find x"

So , if the percentage of x to 60 is 12.

60/100 * x = 12

0.6 *x = 12

Dividing both sides by 0.6

X= 12/0.6

X= (12/6) *(10)

X= 2*10

.x= 20

The value of x= 20

Answer:

Step-by-step explanation:

The slope of a line is found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope and

(x1 , y1) and ( x2 , y2) are the points

Substituting the above values into the above formula we have

Slope of the line that passes through

(0,1) and (-8, -7) is

[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]

Hope this helps you

Answer:

6:10 pm

Step-by-step explanation:

she skate for 2 h and 14 min so,

8:24- 2:14

=6:10 pm

Answer:

Step-by-step explanation:

Let us first generate the frequency table from the information given:

Hurricane number(X)       Frequency(f)                f(X)

6                                            9                                   54

8                                            13                                  104

12                                           16                                  192

14                                            12                                168

Total                                     ∑(f) = 50                          ∑f(x) =518

In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:

Let the last frequency be f

9 + 3 + 16 + f = 50

38 + f = 50

f = 50 - 38 = 12

Now, calculating mean:

[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]

Therefore mean number of hurricanes = 10.4 (to one decimal place)

Answer:

5

Step-by-step explanation:

There will be five equal part because Iyene takes 2 parts and nokob takes 3 parts

Thus, the total parts which have been shared is 2+3=5

Further more, every part is

[tex] \frac{280}{5} = 56[/tex]

Hence, there is 5 parts have been shared and every part is 56 dollars

Answer:

5 equal parts

Because one of the dudes will get 2 and the other one will get 3 parts

3+2 is 5

280/5=56 (1 part)

so iyene will get 56*2=112 and nokob will get 56*3=168

Answer:

I just answered it

Step-by-step explanation:

Answer:

The probability is  [tex]P( X \le 4 ) = 0.0054[/tex]

Step-by-step explanation:

From the question we are told that

   The percentage that are on time is  p =  0.76

   The  sample size is n =  11

Generally the percentage that are not on time is

     [tex]q = 1- p[/tex]

     [tex]q = 1- 0.76[/tex]

     [tex]q = 0.24[/tex]

The  probability that no more than 4 of them were on time is mathematically represented as

        [tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]

=>     [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]

[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]

[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]

[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]

[tex]P( X \le 4 ) = 0.0054[/tex]

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

Answer:

A. –f(x)

Step-by-step explanation:

The transformation of a reflection about the x-axis is

f(x) -> -f(x).

So the answer is

A. –f(x)

Answer:

Regular hourly rate for Brandon is $30

Step-by-step explanation:

Let the payment for regular hours be $x

given that

Brandon is paid 150% of his regular hourly rate for overtime hours

payment for overtime hours = 150% of payment for regular hours

payment for overtime hours = 150/100 * x = 3x/2

Given that He is paid \$45.00 an hour for overtime hours

thus,

3x/2 = 45

=> x = 45*2/3 = 30

Thus,  regular hourly rate for Brandon is $30

Answer:

-23

Step-by-step explanation:

16x² - 106x - 105

factoring X

14 x -120 = -1680

14 - 120 = -106

16x² + 14x - 120x - 105

(16x² + 14x) -(120x - 105)

factor out 2 and -15 to get the same expression (8x + 7)

2x(8x + 7) - 15(8x + 7)

(8x + 7)(2x - 15)

a = 7

b = -15

a + 2b

7 + (-15 x 2)

7 + (-30)

= -23

Answer:

The 2 Gallon Tank is Enough

Step-by-step explanation:

A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.

There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.

[tex]8 * 2 = 16[/tex]

So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.

Answer:

2 gallon tank

Step-by-step explanation:

16 pints is the same as 2 US gallons

Answer:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 1 to 3.

= -196.5

Step-by-step explanation:

Given

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to infinity

The expression that includes all terms up to order 3 is:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to 3.

= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)

= -125/2 + 100000/6 - 759375/5040

= -62.5 + 16.67 - 150.67

= - 196.5

Answer:

476 workers

Step-by-step explanation:

Men: women : total

3          4           3+4 = 7

We want 204 men

204/3 =68

Multiply each by 68

Men: women : total

3*68    4*68      7*68

204        272      476

Answer:

There are 476 workers

Step-by-step explanation:

Answer:

Total distance travel by train =  70 km

Step-by-step explanation:

Given:

Speed of train = 70 km/h

Total time taken = 60 min = 60 / 60 = 1 hour

Find:

Total distance travel by train

Computation:

Distance = Speed × Time

Total distance travel by train = Speed of train × Total time taken

Total distance travel by train = 70 × 1

Total distance travel by train =  70 km