Express the product of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]

Answer:

Step-by-step explanation:

Scholarship and grants are money given to the candidates to support his financial needs in school. It will serves as the means of revenue for the student.

Revenue generated = Grant + Scholarship amount

Revenue generated = $350 + $400

Revenue generated= $750

Total money needed to be spent in school = Tuition + fees

If tuition is $113.67 per credit hour and I used 15 credit hours, total amount of tuition paid = 15* $113.67 =  $1705.05

Total fees =  $660

Total money needed to be spent in school = $1705.05 + $660

Total money needed to be spent in school =  $2365.05

Amount I will need to pay for classes next semester = Total money that will be spent - (grant+scholarship)

=  $2365.05 - $750

= $1615.05

Hence, the amount I will need to pay for classes next semester is  $1615.05

Answer:

-84 + 10i

Step-by-step explanation:

Standard Complex Form: a + bi

Step 1: Evaluate

√-100 = √-1 x √100 = i x 10 = 10i

-84 = -84

Step 2: Combine

10i - 84

Step 3: Rearrange

-84 + 10i

Answer:

Last Option

Step-by-step explanation:

√-100 - 84

(√(100×-1)) - 84

(√100)(√-1)-84

√-1 = i

10i - 84 or -84 + 10i

Answer:

dddddd okaksy ogvurn

Step-by-step explanation:

d

Answer:

Step-by-step explanation:

[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]

Answer:

C. $37.76

Step-by-step explanation:

30% of $49.95

=30/100×49.95

=$14.99

selling price = 49.95 -14.99

= $34.96

8% sales tax included

=8/100×34.96

=$2.80

new price= 34.96+2.80

=$37.76

[tex]|\Omega|=5\cdot4=20[/tex]

a)

[tex]|A|=3\cdot2+2\cdot1=8\\\\P(A)=\dfrac{8}{20}=\dfrac{2}{5}[/tex]

b)

[tex]|A|=3\cdot2+2\cdot3=12\\\\P(A)=\dfrac{12}{20}=\dfrac{3}{5}[/tex]

c)

[tex]|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{20}=\dfrac{3}{10}[/tex]

d)

[tex]|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{20}=\dfrac{1}{10}[/tex]

Answer:

The two numbers are 1 and 2.

Step-by-step explanation:

Let the two numbers be a and b.

One number is twice another, so let's let b=2a.

Their reciprocals are 3/2. Thus:

[tex]\frac{1}{a}+\frac{1}{b} =\frac{3}{2}[/tex]

Substitute and solve for a:

[tex]\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}\\[/tex]

Combine the fractions by forming a common denominator by multiplying the left term by 2:

[tex]\frac{2}{2a} +\frac{1}{2a}=\frac{3}{2}[/tex]

Combine and cross-multiply:

[tex]3/2a=3/2\\6a=6\\a=1\\b=2(1)=2[/tex]

Thus, the two numbers are 1 and 2.

Answer:

16x^2 - 64

Step-by-step explanation:

(4x − 8)(4x + 8)

We recognize that this is the difference of squares

(a-b) (a+b) = a^2 - b^2

                 =(4x)^2 - 8^2

                 =16x^2 - 64

No, that is not a function.

To be a function, each different input (x) needs a different output (y)

In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.

Answer: no

Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.

Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.

Ask yourself, do any of the ordered pairs

in this relation have the same x-coordinate?

Well by looking at this relation, we can see that two

of the ordered pairs have the same x-coordinate.

In this case, the x-coordinate of 3 appears twice.

So no, this relation is not a function.

Answer:

A: 19

Step-by-step explanation:

For this, we can complete the square. We first look at the first 2 terms,

t^2 and -6t.

We know that [tex](t-3)^2[/tex] will include terms.

[tex](t-3)^2 = t^2 - 6t + 9[/tex]

But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:

[tex]m(t) = (t-3)^2 - 9 +28[/tex]

[tex]m(t) = (t-3)^2 +19[/tex]

Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.

Answer:

800= about 1.76 lbs

700= about 1.54 lbs

(there are about 453.5 grams in a pound

Step-by-step explanation:

Answer:

800 grams = 1.76  pounds

700 grams =  1.54  pounds

Step-by-step explanation:

i googled it

It is.........................................................

One way to prove this without a truth table is to use a conditional proof. We assume the portion p ^ (p --> q). If that's true, then so is p and p-->q

Using p and p-->q, the modus ponens rule allows us to derive q. It says that if p is true and p --> q, then q must be true as well.

Since we arrive at q, we have found the conclusion we're after. The assumption (p ^ (p-->q)) leads to q, and therefore the entire statement (p ^ (p-->q)) --> q is true for any combination of p,q.

Answer:

108 : 145

Step-by-step explanation:

253 - 108 = 145

Ratio of those who receive 2 weeks of paid vacation is 108

Ratio of those paid vacation is not 2 weeks is 145

108 : 145

This question is incomplete because it lacks the required diagram. Please find attached the diagram required to answer the question.

Answer:

14 feet

Step-by-step explanation:

The volume of a cone = 1/3 πr²h

In the above question, we are given the volume = 314 cubic feet

the height is given in the attached diagram = 6ft

Step 1

We find the radius.

From the formula for the volume of a cone, we can derive the formula for radius of the cone.

Radius of the cone = √(3 × V/π × h

π = 3.14

Radius of the cone = √( 3 × 314 /3.14 × 6

Radius of the cone = √942/3.14× 6

Radius = √50

= 7.0710678119feet

Step 2

Diameter of the cone = Radius of the cone × 2

= 7.0710678119 × 2

= 14.142135624 feet

Approximately to the nearest foot = 14 feet

Therefore, the diameter of the cone to the nearest foot = 14 feet.

Answer:

(a) Probility Distribution

Outcome   probability

$1               5/15 = 1/3

$5              4/15

$10             3/15 = 1/5

$20            5/15 = 1/3

(b) P($9 or less) =  3/5

Step-by-step explanation:

(a) Probility Distribution

Outcome   probability

$1               5/15 = 1/3

$5              4/15

$10             3/15 = 1/5

$20            5/15 = 1/3

Any other denomination

                  0

(b)

ways to draw $9 or less in a single draw

P($1) = 1/3

P($5) = 4/15

P($9 or less) = P($1) + P($5) = 1/3 + 4/15 = 9/15 = 3/5

Answer:

18

Step-by-step explanation:

Given that:

y∞ xz

y=kxz. Where k is constant

When z=196 and x= 2 then y= 7

7=(196)(2)k

7=392k

k=1/56

There fore y=(1/56)xz

When x=3 and z =336

y=(1/56)xz

y=(1/56)(336)(3)

y=18

if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Value of y varies jointly with x and z.

y ∞ xz

y=kxz.

Where k is constant

When z=196 and x= 2 then y= 7

Let us find the value of k

7=(196)(2)k

7=392k

Divide both sides by 7

k=1/56

y=(1/56)xz

When x=3 and z =336

y=(1/56)xz

y=(1/56)(336)(3)

y=18

Hence,  the value of y when x = 3 and z = 336 is 18.

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ2

Answer:

Step-by-step explanation:

From the given information;

Angela took a general aptitude test and scored in the 90th percentile for aptitude in accounting.

What percentage of the scores were at or below her score?

The percentage of scores that were at or below her score is

Percentage P = 90%

This benchmark is more than average, so we can typically say more of the scores were at or below her score

What percentage were above?

Since The percentage of scores that were at or below her score is

Percentage P = 90%

Then the percentage of the scores that were above will be : (100 -90)%

= 10 %

We can see here that  less percentage of score were above Angela's Score.

Answer:

the percentage of  bearings   that will  not be acceptable = 7.3%

Step-by-step explanation:

Given that:

Mean = 0.499

standard deviation = 0.002

if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.

Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )

= ( 0.496 , 0.504)

If x represents the diameter of the bearing , then the probability for the  z value for the random variable x with a mean and standard deviation can be computed as follows:

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]

From the standard normal tables

[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]

[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]

By applying the concept of probability of a  complement , the percentage of bearings will now not be acceptable

P(not be acceptable)  = 1 - P(acceptable)

P(not be acceptable)  = 1 - 0.927

P(not be acceptable)  = 0.073

Thus, the percentage of  bearings   that will  not be acceptable = 7.3%

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

Assuming the cube is closed, you can use the divergence theorem:

[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]

where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].

We have

[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]

so the flux is 0.

Answer:

Step-by-step explanation:

5x - 15 = 5(-4x - 3)

Multiply the terms in the bracket

5x - 15 = - 20x - 15

Group like terms

Send the constants to the right side of the line and those with variables to the left side

That's

5x + 20x = - 15 + 15

Simplify

25x = 0

Divide both sides by 25

We have the final answer as

Hope this helps you

Answer:

x=0

Step-by-step explanation:

5x - 15 = 5(-4x - 3)

To find the solution to this equation, we have to get x by itself on one side of the equation.

First, distribute the 5 on the right side. Multiply each term by 5.

5x - 15= (5*-4x) + (5*-3)

5x-15 = -20x + (5*-3)

5x-15= -20x -15

Next, add 20x to both sides of the equation.

(5x+20x) -15 = (-20x+20x) -15

(5+20x) -15 = -15

25x -15=-15

Next, add 15 to both sides of the equation.

25x -15 +15 = -15+15

25x= -15+15

25x=0

Finally, divide both sides of the equation by 25.

25x/25=0/25

x= 0/25

x= 0

The solution to this equation is x=0

Answer

Is it C I may have done my math wrong lol

Step-by-step explanation:

you can only see values of [tex] x[/tex] Ranging from $-3$ to $3$ and they're included, so domain is $[-3,3]$

and $y$ values ranging from $-2$ to $4$ but $-2$ is not included so range is $(-2,4]$

Answer: Option C.

Step-by-step explanation:

The lengths of our triangle are:

9, 10 and √130.

If the triangle is a triangle rectangle, by the Pitagoream's theorem we have:

A^2 + B^2 = H^2

in this case H is the larger side, this must be √130.

then:

A and B must be 9 and 10.

9^2 + 10^2 = (√130)^2

81 + 100 = 130

This is false, so this is NOT a triangle rectangle, the hypotenuse is shorter than it should be.

Now, we have some kind of rule:

 if A^2 + B^2 = H^2 then we have one angle of 90° and two smaller ones. (triangle rectangle)

 if A^2 + B^2 > H^2 then all the angles are smaller than 90°, this is an acute triangle.

 if A^2 + B^2 < H^2 then we have one angle larger than 90°, this is an obtuse angle.

(H is always the larger side, A and B are the two shorter ones).

In this case:

81 + 100 > 130

Then this must be an acute angle.

Answer:

16 bags for the first(30% pure) and 64 bags of the second(80% pure)

Step-by-step explanation:

If they are mixed in a ratio of x bags to y bags

(0.3x+0.8y)/(x+y) = 0.7

0.3x + 0.8y = 0.7(x+y)

Multiply both sides with 10

3x + 8y = 7(x+y)

4x = y ——(1)

x + y = 80 ——(2)

Solve simultaneously

x + 4x = 80

5x = 80

x = 16 bags

y = 4x = 64 bags

Answer:

3.25 US Quarts

Step-by-step explanation:

Answer:

the equation is not correct, u have to write like

ax'3+bx'2+cx+d

Answer:

x=-2 and x=0

Step-by-step explanation:

So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.

First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x

Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in

So, in conclusion I believe the answer to be x=-2 and x=0

Answer: A,C, and D

Step-by-step explanation:

Answer:

the answer to this question may be option B, C and D

The larger metallic object is initially at rest, so the velocity is 0 when t = 0. The speed changes after t = 3 seconds.

Answer:

It would be the last one.

Step-by-step explanation:

It says the object is initially at rest, so you look for a table with 0 m/s and you find the last table had been at rest for 0 -2  seconds. The small rocky object initially had a speed of 90 m/s and then decreased to 36 m/s as its energy transferred to the metallic object. The metallic object's speed from time 4-6s with the small rocky object equals the small rocky initial speed.

Rocky Object initial speed = 90 m/s

Rocky Object new speed = 36 m/s

Large metallic object speed after collision = 64 m/s.

64 m/s + 36 m/s = 90 m/s

Large metallic object speed after collision + Rocky Object new speed

= Rocky Object initial speed

You can also test this for kinetic energy.

Answer:

Policeman A = 56 tickets

Step-by-step explanation:

Policemen A + B = 70

If Policeman B hands out x no of tickets...

Then Policeman A hands out 4x no of tickets

meaning...

x + 4x = 70

5x = 70

x = 70/5

x = 14

Therefore Policeman A hands out..

4x = 4 × 14 = 56 tickets