50.5 is what percent of 40.4

Let x = a + bi and y = c + di and z = f + gi. Which statements are true? Check all of the boxes that apply. x + y = y + x (x × y

Leni [432]

Answer:

<h3>The statements i) x+y=y+x</h3><h3> ,iv) (x+y)+z=x+(y+z)</h3><h3>and v) (x-y)-z = x-(y-z) are true </h3>

Step-by-step explanation:

Given that x = a + bi and y = c + di and z = f + gi

<h3>To check which statements are true :</h3><h3>i)x+y=y+x</h3><h3>Taking LHS x+y</h3>

Substitute the values of x and y we get

x+y=a+bi+c+di

<h3>x+y=(a+c)+(b+d)i=LHS</h3><h3>Taking RHS y+x</h3>

Substitute the values of x and y we get

y+x=c+di+a+bi
y+x=(c+a)+(d+b)i
y+x=(a+c)+(b+d)i=RHS
Therefore LHS=RHS

<h3>Therefore x+y=y+x statement is true </h3><h3>iv) (x+y)+z=x+(y+z)</h3><h3>Taking LHS (x+y)+z</h3>

Substitute the values of x ,y and z we get

(x+y)+z=(a+bi+c+di)+(f+gi)

<h3>(x+y)+z=(a+c+f)+(b+d+g)i=LHS</h3><h3>Taking RHS x+(y+z)</h3>

Substitute the values of x ,y and z we get

x+(y+z)=(a+bi)+(c+di+f+gi)

Therefore LHS=RHS

<h3>Therefore statement (x+y)+z=x+(y+z) is true</h3><h3>v) (x-y)-z = x-(y-z)</h3><h3>Taking LHS (x-y)-z</h3>

Substitute the values of x ,y and z we get

(x-y)-z=(a+bi-(c+di))-(f+gi)

=a+bi-c-di-f-gi

<h3>(x-y)-z=(a-c-f)+(b-d-g)i=LHS</h3><h3>Taking RHS x+(y+z)</h3>

Substitute the values of x ,y and z we get

x-(y-z)=(a+bi)-((c+di)-(f+gi))

x-(y-z)=a+bi-c-di-f-gi=RHS

Therefore LHS=RHS

<h3>Therefore statement (x-y)-z=x-(y-z) is true</h3><h3>Therefore the statements i) ,iv) and v) are true </h3><h3 />

4 0

3 years ago

Read 2 more answers

Leona is having a birthday party on Sunday. Jeanette wants to know how many people will be coming. Leona tells her that there wi

konstantin123 [22]

Answer:77 and 87

Step-by-step explanation:

7×6=42 + 5+7=35/\ 35+42=77(first outcome)

7×6=42 + 5×9=45/\42+45=87 (second outcome.

7 0

3 years ago

Karen calculates the volume of cylinder A with a radius of 3 inches, and a height of 6 inches. The volume of this cylinder is 54

Setler [38]

<span>B) The volume of cylinder B is twice the volume of cylinder A. </span>

8 0

3 years ago

Please help me in this question

charle [14.2K]

Number defective=4
number of non-defective=total-defective
=20-4
=16
the questions asked for 1 defective
so we choose only 1 defective from 4 defective items
4C1

and for 1 non-defective
we choose only 1 non-defective from 16 non-defective items
16C1

we choose 2 items from 20 items
so 20C2

answer:
probability= [(4C1) * (16C1)] /(20C2)
=32/95

6 0

3 years ago

A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent

siniylev [52]

Answer:

(a) P (p' > 0.25) = 0.

(b) P (0.15 < p' < 0.20) = 0.7784.

(c) P (133 < X < 171) = 0.2205

Step-by-step explanation:

Let <em>p</em> = proportion of business trip that were for internal company visit.

It is provided that 19% responded that it was for an internal company visit, i.e.

<em>p</em> = 0.19.

A sample of <em>n</em> = 950 business travelers are randomly selected.

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

Thus, the distribution of $\hat p$ is N (<em>μ</em> = 0.19, <em>σ </em>= 0.013).

(a)

Compute the probability that more than 25% of the business travelers say that the reason for their most recent business trip was an internal company visit as follows:

P (p' > 0.25) = P (Z > 4.62) = 0

*Use a <em>z</em>-table for the probability.

Thus, the probability that more than 25% of the business travelers say that the reason for their most recent business trip was an internal company visit is 0.

(b)

Compute the probability that between 15% and 20% of the business travelers say that the reason for their most recent business trip was an internal company visit as follows:

P (0.15 < p' < 0.20) = P (-3.08 < Z < 0.77)

= P (Z < 0.77) - P (Z < -3.08)

= 0.7794 - 0.0010

= 0.7784

*Use a <em>z</em>-table for the probability.

Thus, the probability that between 15% and 20% of the business travelers say that the reason for their most recent business trip was an internal company visit is 0.7784.

(c)

Compute the proportion of <em>X</em> = 133 and <em>X</em> = 171 as follows:

p' = 133/950 = 0.14

p' = 171/950 = 0.18

Compute the value of P (0.14 < p' < 0.20) as follows:

P (0.14 < p' < 0.18) = P (-3.85< Z < -0.77)

= P (Z < -0.77) - P (Z < -3.85)

= 0.2206- 0.0001

= 0.2205

*Use a <em>z</em>-table for the probability.

Thus, the probability that between 133 and 171 of the business travelers say that the reason for their most recent business trip was an internal company visit is 0.2205.

7 0

3 years ago