Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]
​

Answer:

The original dimensions of the park are:

(23/2) yards by 7 yards.

Step-by-step explanation:

Suppose that you have a given dimension X

if you want to reduce that dimension by a scale factor k, such that:

0 < k < 1

The reduced dimension is just:

X' = k*X

Now let's solve the problem:

We know that the dimensions on the blueprint are:

(23/147)yd by (3/14)yd

And the original dimensions are:

A yd by B yd

We know that, to get the blueprint dimensions, we reduced the original dimensions by a factor of 2/147

Then we just have that:

(2/147)*A = 23/147

(2/147)*B = 3/14

Now we just can solve these two equations for A and B

A = (23/147)*(147/2) = 23/2

B = (3/14)*(2/147) = (3/7)*(1/147) = 49/7 = 7

Then the original dimensions of the park are:

(23/2) yards by 7 yards.

Answer:

[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]

Step-by-step explanation:

We are given the function:

[tex]Q(x)=2x^2+5x-3[/tex]

And we want to find and simplify:

[tex]Q(a+h)-Q(a-h)[/tex]

Substitute:

[tex]=[2(a+h)^2+5(a+h)-3]-[2(a-h)^2+5(a-h)-3][/tex]

Expand:

[tex]\displaystyle =[2(a^2+2ah+h^2)+5a+5h-3]-[2(a^2-2ah+h^2)+5a-5h-3][/tex]

Distribute:

[tex]=[2a^2+4ah+2h^2+5a+5h-3]-[2a^2-4ah+h^2+5a-5h-3][/tex]

Distribute:

[tex]=(2a^2+4ah+2h^2+5a+5h-3)+(-2a^2+4ah-2h^2-5a+5h+3)[/tex]

Rewrite:

[tex]=(2a^2-2a^2)+(4ah+4ah)+(2h^2-2h^2)+(5a-5a)+(5h+5h)+(-3+3)[/tex]

Combine like terms:

[tex]=8ah+10h[/tex]

Hence:

[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]

Step-by-step explanation:

I think this is the ans and I have got this ans from brainly.

Answer:

option B

Step-by-step explanation:

Sum of interior angles of a polygon with n sides:

                                                                          [tex]= (n - 2 )\times 180[/tex]

[tex]Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180[/tex]

[tex]Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ[/tex]

                      [tex][ \ because \ straight \ line \ angle = 180^\circ \ ][/tex]

That is ,

[tex]Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9[/tex]

OR

Sum of exterior angles of a regular polygon = 360

Given 1 exterior angle of the regular polygon is  40

Therefore ,

               [tex]n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9[/tex]

Answer:

9

Step-by-step explanation:

Answer:

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

Step-by-step explanation:

We have the mean during an interval, so the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive.

This means that [tex]\mu = 3.3[/tex]

Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

This is P(X = 3). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 3) = \frac{e^{-3.3}*3.3^{3}}{(3)!} = 0.2209[/tex]

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

Answer:

[tex] \frac{1}{12} [/tex]

Step-by-step explanation:

[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]

So, if you divide 2/9 by 1/12, you'll get 8/3

Answered by GAUTHMATH

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2[tex]\pi[/tex]r             ( Calculate the total circumference)    

C = 2(8)[tex]\pi[/tex]

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

The arc length in approximate form is 33.49 radians.

[tex]s = r\times \theta[/tex]

where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.

Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]

For given question,

We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.

[tex]r=8~cm,~\theta=240^{\circ}[/tex]

First we convert angle in radians.

[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]

Using the formula of the arc length,

[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]

The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]

Substitute the value of [tex]\pi = 3.14[/tex]

So, the arc length would be,

[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians

Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

the arc length in approximate form is 33.49 radians.

Learn more about the arc length here:

https://brainly.com/question/16403495

#SPJ2

Answer:

[tex]\sqrt{x} -\frac{16}{\sqrt{x} }[/tex]

Step-by-step explanation:

Answer:

Hence the correct option is 3rd option. 40

Step-by-step explanation:

If two figures are similar, then the ratio of the corresponding sides is proportional.

[tex]\frac{15}{30} =\frac{20}{n} \\\\n=\frac{30 \times 20}{15} \\\\n= 40.[/tex]

Answer:

[tex]P(k)=0.2628[/tex]

Step-by-step explanation:

Given

[tex]n = 1693[/tex] --- sample size

[tex]k = 445[/tex] --- those that prefer chocolate ice cream to vanilla

Required

[tex]P(k)[/tex]

This is calculated as:

[tex]P(k)=\frac{k}{n}[/tex] --- probability formula

So, we have:

[tex]P(k)=\frac{445}{1693}[/tex]

[tex]P(k)=0.2628[/tex]

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]y = 3[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{"The value of 9-y twice as much as the value of y" can be written as:}}\\\\9-y = 2y[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'y'...}}\\\\9-y=2y\\------------\\\rightarrow 9 -y + y = 2y + y\\\\\rightarrow 9 = 3y\\\\\rightarrow \frac{9=3y}{3}\\\\\rightarrow 3 = y\\\\\rightarrow \boxed{y = 3}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

-18

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

Let the four consecutive integers be x, (x + 1), (x + 2) & (x + 3)

Smallest integer = x

According to the given condition:

[tex]x + (x + 1) + (x + 2) + (x + 3) = 3x \\ \\ 4x + 6 = 3x \\ \\ 4x - 3x = - 6 \\ \\ x = - 6 \\ \\ Sum\: of\: the\:integers \\=4x + 6 = 4( - 6) + 6 \\ \\ = - 24 + 6 \\ \\ = - 18[/tex]

Answer:

The photo is not clear post a clear photo then i will see that

Answer:

per = 28 units

area 32 sq units

Step-by-step explanation:

Answer:

10 Ghuups I believe. I am sorry if this is wrong

Answer:

503.75, 504.75, 505.75, 506.75

Step-by-step explanation:

x+(x+1)+(x+2)+(x+3)=2021

4x+6=2021

4x=2015

x=503.75

so it would be

503.75+504.75+505.75+506.75= 2021

Answer:

189 ft²

Step-by-step explanation:

Here is the formula...

1/2 * 6 * 36 + 81

Hope this helps

Step-by-step explanation:

so  the equation in standard form that models the given scenario is

2x + 3y = 24

Answer:

0.9984

Step-by-step explanation:

we have shape parameter for the first component as 2.1

characteristics life = 100000

for this component

we have

exp(-2000/100000)².¹

= e^-0.0002705

= 0.9997

for the second component

shape parameter = 1.8

characteristic life = 80000

= exp(-2000/80000)¹.⁸

= e^-0.001307

= 0.9987

the reliability oif the system after 2000  events

= 0.9987 * 0.9997

= 0.9984

Answer:

Tisco: 12 for £5.16

Azda: 12 for £5.04

Azda has the better value.

Step-by-step explanation:

Tisco: 3 for £1.29

Multiply both numbers by 4.

12 for £5.16

Azda:

4 for £1.68

Multiply both numbers by 3.

12 for £5.04

Azda has the better value.

Answer:

False

Step-by-step explanation:

Each f(x) increases by 8 therefore this equation is a linear function. If you where to graph it would be a straight line

Hope this helped :)

Answer:

False

Step-by-step explanation:

The slope is the same between all pounts which means the function is linear.

Hope this helps!

Answer:

The answer is $1.50/bottle.

Step-by-step explanation:

To get the unit price, you need to divide the total by the amount of bottles.

[tex]9.00/6=1.50[/tex]

Answer:

(x+5)(x-3) / (x+5)(x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

Answer:

There is no significant evidence to support the claim that college women have more credit card debt than college men

Step-by-step explanation:

Given :

women n1 =32 x1= 781 s1 = 1489 men n2 = 38 x2 = 435 s2 = 1026

H0 : μ1 = μ2

H0 : μ1 > μ2

Assume unequal variance :

The test statistic :

(x1 - x2) / √(s1²/n1) + (s2²/n2)

T= (781 - 435) / √(1489²/32) + (1026²/38)

T = 346 / 311.42740

Test statistic = 1.111

Degree of freedom, df

(s1²/n1+s2²/n2)²÷1/(n1-1)*(s1²/n1)²+1/(n2-1)*(s2²/n2)²

The Pvalue :

(s1²/n1+s2²/n2)² = ((1489²/32) + (1026²/38))² = 9406484230.6884765625

1/(n1-1)*(s1²/n1)²+1/(n2-1)*(s2²/n2)²:

1/31(1489^2/32)^2 + 1/37(1026^2/38)^2 = 1.755926E8

df = 9406484230.6884765625 / 1.755926E8 = 53.569

df = 54

The Pvalue, from t score ;

Pvalue(1.111, 54) = 0.136

Pvalue > α ; Hence, we fail to reject the null ; There is no significant evidence to support the claim that college women have more credit card debt than college men

Answer:

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Step-by-step explanation:

Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:

[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]

[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]

[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Answer:

Step-by-step explanation:

√121 = 11

√900 = √30^2 = 30

∛125 = ∛5^3 = 5

∛729 = ∛9^3 = 9

Answer:

x < 16

Step-by-step explanation:

Let the number be x

Four time the number = 4x

Eight less than four times the number = 4x - 8

Eight less than four times the number is less than 56,

          that is , 4x - 8  < 56

                      4x - 8 + 8 < 56 + 8                    [ adding both sides by 8 ]

                        4x + 0 < 64

                              4x < 64                             [ divide both sides by 4 ]

                                 x < 16