Consider this bag of marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things? Make sure you show work, answer all questions and write in complete sentences.

Answer:

The company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass

Step-by-step explanation:

This is a classical problem that can be solved using a system of equations:

Let us first define our variables:

[tex]x[/tex] as the number of 100-pound bags which contain a mixture of rye and Kentucky bluegrass and,

[tex]y[/tex] as the number of 100-pound bags of bluegrass.

The problem tells us that in a week a total of 17 bags were sold, therefore, we can say that this number must be equal to the number of bags containing the mixture of rye and Kentucky bluegrass plus the number of bags containing bluegrass. Then, according to our variable names:

[tex]x+y=17[/tex]   (1)

The problem also says that the company got a receipt for $4,949 in total. Hence, this number has to be equal to the total number of bags that contain rye and Kentucky bluegrass seeds times its price plus the number of bags containing bluegrass multiplied by its price. Then,

[tex]235x+341y=4949[/tex]  (2)

Now we have the system of equations:

[tex]x+y=17[/tex]   (1)

[tex]235x+341y=4949[/tex]  (2)

Solving for [tex]x[/tex] in equation (1)

[tex]x+y=17\\x=17-y[/tex]   (3)

And substituting [tex]x[/tex] in equation (2)

[tex]235x+341y=4949\\235(17-y)+341y =4949\\3995 - 235y +341y=4949\\-235y+341y = 4949-3995\\106y=954\\y=\frac{954}{106}\\ y=9[/tex]

Then, substituting [tex]y=9[/tex] in equation (1):

[tex]x+y=17\\x+9=17\\x=17-9\\x=8[/tex]

Thus, the company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass.

8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.

Let's assume that:

x = number of bags of the 100-pound mixture of rye and Kentucky bluegrass sold

y = number of bags of the 100-pound bag of bluegrass sold

We can set up a system of equations based on the given information:

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Simplifying the equation in step 2 gives us -106y = -994. Solving for y, we get y = 9.

Substituting the value of y back into equation (1), we get x + 9 = 17. Solving for x, we get x = 8.

Therefore, 8 bags of the 100-pound mixture are sold, and 9 bags of the 100-pound bag of bluegrass are sold in a week.

Answer:

The probability that the person gets a speeding ticket is 0.27

Step-by-step explanation:

The probability that the person receives a speeding ticket is the probability that the person passes through any of the speed limits and the radar is operating at that time.

Let [tex]P(L_1)[/tex] is the probability that the person passes through radar [tex]L_{1}[/tex] and it is operating at that time is

[tex]P(L_{1})=P(1)\times P(2)[/tex]

Where

P(1) is the probability of person passes through [tex]L_{1}[/tex]

P(2) is probability that the radar is operating

[tex]P(L_1)=0.2\times 0.4=0.08[/tex]

Similarly the probabilities are calculated for other radars in the similar manner as

[tex]P(L_2)=0.1\times 0.3=0.03[/tex]

[tex]P(L_3)=0.5\times 0.2=0.1[/tex]

[tex]P(L_4)=0.2\times 0.3=0.06[/tex]

Thus the reuired probability of the reuired event is

[tex]P(E)=P(L_1)+P(L_2)+P(L_3)+P(L_4)\\\\P(E)=0.08+0.03+0.1+0.06=0.27[/tex]

When the girl is 45 ft away from the pole, the tip of her shadow is moving away from the light at a rate of approximately 4.8 ft/sec.

Given:

Height of the pole (h): 25 ft

Height of the girl (4 ft)

Rate of the girl walking away from the pole (dx/dt = 6 ft/sec)

Distance from the pole to the girl (x = 45 ft, when the girl is 45 ft away from the pole)

Objective:

Find the rate at which the tip of her shadow is moving away from the light (ds/dt) when the girl is 45 ft away from the pole.

Step 1: Set up the Similar Triangles Equation

s/x = h/(x + s)

Step 2: Differentiate both sides with respect to time t:

(1/x) * ds/dt - (s/x^2) * dx/dt = (h/(x + s)^2) * (dx/dt + ds/dt)

Step 3: Substitute Known Values:

Substitute x = 45, dx/dt = 6, and h = 25 into the equation.

(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)

Step 4: Solve for ds/dt:

Combine like terms and isolate ds/dt.

(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)

Step 5: Substitute x = 45 into the equation:

(1/45) * ds/dt - (4/2025) = (25/(90 + s)^2) * (6 + ds/dt)

Step 6: Solve for ds/dt:

ds/dt ≈ 4.8 ft/sec

You should expect to arrive at Terminal B approximately 17 minutes past the scheduled arrival time, factoring in remaining stops and travel times.

Let's calculate the expected delay in arrival at Terminal B.

Given:

- Scheduled departure from Terminal A: 9:18 a.m.

- Scheduled arrival at Terminal B: 10:03 a.m.

- Arrival at a stop on the route at 9:58 a.m.

- 5 more stops remaining, including the arrival at Terminal B.

- Average travel time between stops: 2 minutes

- Loading and unloading time: 1 minute

1. Total travel time from the current stop to Terminal B:

[tex]\[ 10:03 \text{ a.m.} - 9:58 \text{ a.m.} = 5 \text{ minutes} \][/tex]

2. Remaining stops:

[tex]\[ 5 \text{ stops} \times (2 \text{ minutes travel time} + 1 \text{ minute loading/unloading}) = 5 \text{ stops} \times 3 \text{ minutes per stop} = 15 \text{ minutes} \][/tex]

3. Total time from the current stop to Terminal B, including remaining stops:

[tex]\[ 5 \text{ minutes (travel time to Terminal B)} + 15 \text{ minutes (remaining stops)} = 20 \text{ minutes} \][/tex]

4. Determine how many minutes past the scheduled arrival time at Terminal B this would be:

[tex]\[ 20 \text{ minutes} - (10:03 \text{ a.m.} - 10:00 \text{ a.m.}) = 20 \text{ minutes} - 3 \text{ minutes} = 17 \text{ minutes} \][/tex]

Therefore, you should expect to arrive at Terminal B 17 minutes past the scheduled arrival time.

If the correct answer is indeed 10 minutes, then there might be a misunderstanding or a mistake in the problem statement.

You can expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time. This is calculated based on the average travel time and loading/unloading time for the remaining stops.

To determine how many minutes past your scheduled arrival time you should expect to arrive at Terminal B, let's break down the time required for the remaining stops.

Therefore, you should expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time.

Answer:

si

Step-by-step explanation:

por el telefono

−2x + 3y + 5z = −21

−4z = 20

6x − 3y = 0

do -4z=20 first

divide both sides by -4 to get z by itself

-4z/-4=20/-4

z=-5

Use z=-5 into −2x + 3y + 5z = −21

-2x+3y+5(-5)=-21

-2x+3y-25=-21

move -25 to the other side

sign changes from -25 to +25

-2x+3y-25+25=-21+25

-2x+3y=4

6x-3y=0

find x by eliminating y

Add the equations together

-2x+6x+3y+(-3y)=4+0

-2x+6x+3y-3y=4

4x=4

Divide by 4 for both sides

4x/4=4/4

x=1

Use x=1 into 6x − 3y = 0

6(1)-3y=0

6-3y=0

Move 6 to the other side

6-6-3y=0-6

-3y=-6

Divide both sides by -3

-3y/-3=-6/-3

y=2

Answer:

(1, 2, -5)

The formula for secant lines is the outside x the overall length is equal to the outside times the overall length of the second line.

A) 5*(x+5) = 6*10

SImplify:

5x +25 = 60

Subtract 25 from both sides:

5x = 35

Divide both sides by 5:

x = 35/5

x = 7

B) 3*8 = 4*(x+4)

Simplify:

24 = 4x +16

Subtract 16 from both sides:

4x = 8

Divide both sides by 4:

x = 8/4

X = 2

Hey!

----------------------------

Solution:

5 1/5% = 0.052

325 x 0.052 = 16.9

----------------------------

Answer:

D. 16.899...

----------------------------

Hope This Helped! Good Luck!

Answer:

16,9

Step-by-step explanation:

To convert from a percentage to a decimal, move the decimal point twice to the left:

5,2% = 5⅕%

5,2% → 0,052

[tex](0,052)(325) = 16,9[/tex]

I am joyous to assist you anytime.

Answer:

See explanation

Step-by-step explanation:

Each ounce of fruit will supply

Each ounce of nuts will supply

Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.

Then x ounces of fruit will supply

and y ounces of nuts will supply

Every package must provide

A. You get the system of three inequalities

[tex]\left\{\begin{array}{l}x+y\ge 7\\ 2x+y\ge 11\\x+y\le 10\end{array}\right.[/tex]

B. See attached diagram

[tex]\begin{array}{cccc}&\text{Protein}&\text{Carbohydrates}&\text{Fat}\\\text{Fruit}&x&2x&x\\\text{Nuts}&y&y&y\\&\text{at least 7}&\text{at least 11}&\text{no more than 10}\end{array}[/tex]

Three inequalities were formulated: 1x + 1y ≥ 7 for protein, 2x + y ≥ 11 for carbohydrates and x + y ≤ 10 for fat, with x being fruit and y being nuts. These needs to be graphed to find a feasible region that meets all conditions. A table summarizing the needed unit amount per ounce for protein, carbohydrates, and fats for both fruits and nuts was also provided.

To solve your question, first, let's express the given conditions as inequalities:

Graphing

these inequalities would result in a feasible region that should fulfill all conditions.

The following table summarizes this:

Fruit

Nuts

Requirements per package

Protein1 unit per ounce1 unit per ounceAt least 7 unitsCarbohydrates2 units per ounce1 unit per ounceAt least 11 unitsFat1 unit per ounce1 unit per ounceNo more than 10 units

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Answer:

$24,166.67

Step-by-step explanation:

Let carry out the breakdown:

So Norman Jean makes a flat rate of $25 per hour, also she works 35 hours per week.

From the above statement Jean will make => 25 × 35 = $875 in a single week without commission.

For Jean to make $4500 in a week, we derive an equation for this:

875 + x = 4500;

x is the amount of commission Jean has to get in a week to make up to $4500 in that week => x = 4500-875; x = $3625.

Let y be the amount of sales Jean has to make to get a commission of x, we derive the following equation: 0.15 × y = x.

y = x ÷ 0.15 => 3625 ÷ 0.15

y = 24166.67.

So for Jean to meet her target of $4500 in a single week, Jean needs to make a sale worth $24,166.67.

The amount of sales that Norma needs to make in a week in order to earn $4500 in a week is; 24167

We are told that;

Norma Jean makes $25 per hour

Total time worked per week = 35 hours

Commision on total sales = 15%

Basic amount earned for the 35 hours in a week = 25 * 35 = $875

Now, if the amount of sales she makes that earns her commision is x, then it means for her to earn $4500 in a single week;

875 + 0.15x = 4500

0.15x = 4500 - 875

x = (4500 - 875)/0.15

x = 24166.67

Approximating to a whole number is;

x = 24167 sales

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Answer:

Step-by-step explanation:

2x+1 ≤ 3(x+1)/2

2x+1 ≤ 3x+3/2

Multiply by 2 on both sides

4x+2 ≤ 3x + 3

Subtract 2 on both sides

4x ≤ 3x + 1

Subtract 3x from both sides

x ≤ 1

I think this is what you were asking?

Answer:

a) 0.0613 b)0.0803

Step-by-step explanation:

Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.

p = 0.025

Let's consider that an applicant is not be able to repay  his or her installment loan as a ''success''

p (success) = 0.025

Last month she made 40 loans ⇒ n = 40

For the poisson approximation to the binomial we need to calculate n.p that  will be the λ parameter in our poisson approximation

[tex]n.p=40.(0.025)=1[/tex]

λ=n.p=1

Let's rename λ = j

In our poisson approximation :

[tex]f(k,j)=\frac{e^{-j} .j^{k} }{k!}[/tex]

f(k,j) is the probability function for our poisson variable where we calculated j,e is the euler number and k is the number of success :

[tex]f(k,1)=\frac{e^{-1} .1^{k} }{k!}[/tex]

For a) We are looking the probability of 3 success :

[tex]f(3,1)=\frac{e^{-1} .1^{3} }{3!}=0.0613[/tex]

For b) We are looking for the probability of at least 3 success

If ''L'' is the number of success

[tex]P(L\geq 3)=1-P(L\leq 2)[/tex]

[tex]P(L\leq 2)=P(L=0)+P(L=1)+P(L=2)[/tex]

[tex]P(L\leq 2)=f(0,1)+f(1,1)+f(2,1)[/tex]

[tex]P(L\leq 2)=e^{-1} +e^{-1}+\frac{e^{-1}}{2} =e^{-1}(1+1+\frac{1}{2} )[/tex]

[tex]P(L\geq 3)=1-P(L\leq 2)=1-e^{-1}(1+1+\frac{1}{2} )=0.0803[/tex]

The probability that three loans will default is 0.0613

The probability that at least 3 loans will default is 0.0803

Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.

p = 0.025

Hence, we consider that an applicant is not able to repay his or her installment loan as a ''success''

p (success) = 0.025

Last month she made 40 loans ⇒

n = 40

For the Poisson approximation to the binomial, we need to calculate n.p which will be the λ parameter in our Poisson approximation

n.p= 40.(0.025) =1

λ=n.p=1

Let's rename λ = j

In our Poisson approximation :

f(k,1) = e^-j.j^k/k!

Hence, the probability of 3 success is:

f(3,1)= e^-1.1^3/3!

=0.0613.

The probability of at least 3 successes is:

If  ''L'' is the number of successes.

P(L≥ 3) = 1- P(L≤ 2)

P(L≥ 3)= 0.0803.

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Answer:

Step-by-step explanation:

let x and y be the distances of each car from the intersection after sometime.

let x<y

then y-x=7

and y+x=13

add 2y=20

y=10

x=13-10=3

slower car travels 3 miles and faster car travels 10 miles

Answer:

You require 10 helpers

Step-by-step explanation:

The problem could be solved in many ways ( like using an optimization software) but I propose you this.

Start with production of large cakes.  In the time kitchen is available one helper could make, if only works in large cakes:

(2 large cakes / 1 hour) * (3 hours ) = 6 large cakes

So with 3 helpers using all their 3 hours we would have

3 helpers *6 large cakes /helper  = 18 large cakes.

We need 2 more large cakes so we can use one more helper and in his first hour he can produce

(2 large cakes / 1 hour) * (1 hour ) = 2 large cakes

The 4th helper has two hours of work left so he can produce small cakes.

(35 small cakes/hour* 2 hours = 70 small cakes.

With 4 helpers we have the 20 large cakes and 70 small ones. We still have to makes

700 - 70 = 630 small cakes left

In the 3 hour period a helper can make

(35 small cakes / 1 hour) * (3 hours ) = 105 large cakes

So if 1 helper does  105 large cakes  we would need to finish production with

630 / 105 =  6 helpers

So in total we have 3 helpers in only large cakes 6 in only small cakes and one helper doing both - total 10 helpers

Final answer:

The correct general form of the equation of a circle with a center at (-2, 1) is x² + y² - 4x + 2y - 4 = 0, as it aligns with the pattern of the standard circle equation upon completion of the square.

Explanation:

The general form of the equation of a circle on a coordinate plane with a center at (-2, 1) can be found using the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Since we do not have the radius given, our primary goal is to expand and arrange the given options to match this standard form and check which one relocates the center to (-2, 1).

The equation that matches this pattern would be x² + y² - 4x + 2y - 4 = 0. Here's why: when you complete the square to revert it back to the standard equation, you'll add 4 to both sides to get (x - (-2))² + (y - 1)² = 4, which indicates a center at (-2, 1) when you compare with the standard equation.

Answer:

so, the figure here is a cylinder with a semi sphere on the top, we know the height of whole structure, and the radius of the semi sphere, which is the same as the radius of the cylinder (you can see it because the radius of the semisphere is constant, and you can thin on it as half a sphere over a cylinder).

First, the cylinder will be the structure without the semi sphere, so his height will be te total height minus the radius of the semi sphere, which is 0.9μm.

so now we know the height and the radius of the cylinder, the surface or the sides of it is 2*3.14*r*h = 2*3.14*0.9μm*0.1μm = 0.5662[tex]μm^{2}[/tex].

The surface area of the cylindrical part of the microvillus is calculated by multiplying pi (3.14) with the diameter (0.1μm) and height (1.0μm) to yield a result of 0.314μm².

To calculate the surface area of the cylindrical 'sides' of the microvillus, which we can consider to be a cylinder without its top and bottom parts, the formula used is: π * diameter * height. In this case, the diameter of the microvillus is 0.1μm (which is the diameter of the hemispherical top) and the height is 1.0μm.

Substitute these values into the formula:

Surface area = π * diameter * height = 3.14 * 0.1μm * 1.0μm = 0.314μm².

Thus, the surface area of the cylindrical part of the microvillus is 0.314 micrometers squared.

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Answer:

The same amount of applesauce, nuts, flour, and raisins is used.

Step-by-step explanation:

Have you ever heard of the question, "which weighs more, a pound of steel, or a pound of feathers?" And then everyone is shocked when they weigh the same, even though they both were said to weigh a pound?

This question is like that.

One cup of each is used, so they are all a cup, which means an equal amount of all of them were used.

9 + -20 + -16= 2of course it’s going to be a negative 27 because wen u had a positive u lost 20 and then lost another 16 now u owe 27 which is -27 in your pockets

The simplified result is -$27.

To describe the gambler's situation using positive and negative numbers, we use the following expression:

$9 - $20 - $16

We can simplify this step-by-step:

First, add the positive and negative amounts: $9 - $20 = -$11

Then, subtract the next amount: -$11 - $16 = -$27

Therefore, the simplified result is -$27.

Answer:

The given statement is true.

Step-by-step explanation:

Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisions : TRUE statement.

Statistics helps the people to use limited sample to make accurate conclusions about a greater population. In stats we use tables, charts and graphs to present the data to draw some conclusions.

The shortest path the gecko can take is 20 feet long, consisting of 8 feet along the ceiling and 12 feet along the opposite side wall.

Distances:

Gecko to ceiling edge: 1 foot

Ceiling edge to opposite wall edge: 10 feet (room width)

Opposite wall edge to fly: 1 foot

Path calculation:

Ceiling path: 1 foot (to edge) + 8 feet (along edge) = 9 feet

Side wall path: 1 foot (to edge) + 11 feet (remaining wall) = 12 feet

Shortest path:

Add ceiling and wall paths: 9 feet + 12 feet = 20 feet

Therefore, the shortest path for the gecko is 20 feet long.

Answer:

C. y = 115 000(1.05)^x

Step-by-step explanation:

The formula for the amount accrued on an investment earning compound interest is

[tex]A = P(1 + r)^{t}[/tex]

where

P = the amount of money invested (the principal)

r = the interest rate per period expressed as a decimal fraction

t = the number of periods

In this problem,  

P = $115 000

r =  5 % = 0.05

By 2010, Luca's house will have increased in value for three years. Its value will be  

[tex]A = 115000(1 + 0.05)^{3}\\\text{The correct formula for the value of his home x years after 2010 is}\\ y = 115000(1.05)^{x}[/tex]

Answer:

C: y = 115,000(1.05)x

Step-by-step explanation:

(havn’t actually did any math, but this is just process of elemination.)

{I’m just looking at the end of these, because the start is all the same}

if the number with the (perenthese) is below 1, it is a decreas, and the problem says it’s increasing by 5%. (1.5) Is equal to 50% increase so that means your answer would be (1.05) Because anything times 1 is the larger number, but when u add that 0.5, it’s raising the number up by 5%.

Answer:

True

Step-by-step explanation:

f is odd if the graph of f is symmetric with respect to the origin.

f is even if and only if f(-x) = f(x) for all x in the domain of f.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

%33.75

Step-by-step explanation:

I put the answer that the other person answered and I got it wrong so here is the right answer!

Answer:

33.75

Step-by-step explanation:

Answer:

Marta's house is 3.10 miles from Latanya's house

Step-by-step explanation:

Marta's house is at 3.1 miles fron Latanya's house.

From 12:30pM to 3:30pM there are a total of 3 hours, remember that.

Let's say that the distance between the two houses is D, then we can write the equations:

12mi/h*t₁ = D

2.5mi/h*t₂ = D

These are equations of the form:

speed*time = distance

Where t₁ is the time that Latanya takes to arrive to Marta's house, and t₂ is the time that they take to arrive to Latanya's house.

We know that the total time of this is 3 hours, and they spent 90 minutes = 1.5 hours in Marta's house, then:

t₁ + t₂ + 1.5 = 3

t₁ + t₂ = 3 - 1.5 = 1.5

Now we have a system of equations:

12*t₁ = D

2.5*t₂ = D

t₁ + t₂ =  = 1.5

We can write:

D/12 = t₁

D/2.5 = t₂

And replace that in the last equation:

D/12 + D/2.5 = 1.5

2.5*D + 12D = 1.5*2.5*12

14.5D = 45

D = 45/14.5

D = 3.10 miles

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Answer:

a = 14

Step-by-step explanation:

Since QR = QP then the triangle is isosceles and

QS is a perpendicular bisector, thus

RS = SP ← substitute values

3a = a + 28 ( subtract a from both sides )

2a = 28 ( divide both sides by 2 )

a = 14

Answer:

  1)  60°, 75°, 120°, 105°

  2)  101.5 m

Step-by-step explanation:

1) The sum of ratio units is 4+5+8+7 = 24, which corresponds to the sum of angles, 360°. Then each ratio unit must stand for 360°/24 = 15°. Multiplying the given ratio units by 15° gives the angle measures:

__

2) The similarity statement and the scale factor mean ...

  MJ : TQ = 4 : 7

  7·MJ = 4·TQ . . . . . . . . . "cross multiply"

  TQ = 7/4×MJ = 7/4(58 m) . . . . . divide by 4, substitute the value of MJ

  TQ = 101.5 m

Answer:

  x = (c -mp)/g

Step-by-step explanation:

Subtract the term not containing x, then divide by the coefficient of x.

  gx +mp = c . . . . . given

  gx = c - mp . . . . . subtract mp

  x = (c -mp)/g . . . . divide by g

_____

Comment on the process

This process can be described various ways. A usual description is "get the x term by itself on one side of the equal sign, then divide by the x-coefficient."

I like a more general description of the solution to "solve for" problems: undo what is done to the variable, in reverse order.

Here, the variable x is multiplied by g, then added to mp. To undo those operations (in reverse order), first we undo the addition of mp. We accomplish that by subtracting mp, or by adding the opposite of mp, as you wish.

Having done that, we undo the multiplication by g by dividing by g.

  (gx)/g = (c -mp)/g

  x = (c -mp)/g

The steps we actually perform here are identical to the steps in "get the x-term by itself, ...". However, the process we have described can be applied to any sort of equation, not just a 2-step linear equation.

Answer:

Stratified Sampling

Step-by-step explanation:

Since Keri divides the day into different strata and each unit is selected from each strata randomly. So, it is Stratified Sampling.

Further, In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.

Answer:

Step-by-step explanation:

[tex]i=\sqrt{-1}\to i^2=-1\\\\(3+\sqrt{-16})(6-\sqrt{-64})\\\\\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\sqrt{-64}=\sqrt{(64)(-1)}=\sqrt{64}\cdot\sqrt{-1}=8i\\\\(3+4i)(6-8i)\\\\\text{use FOIL}\ (a+b)(c+d)=ab+ac+bc+bd\\\\=(3)(6)+(3)(-8i)+(4i)(6)+(4i)(-8i)\\\\=18-24i+24i-32i^2\qquad\text{cancel}\ 24i\\\\=18-32(-1)=18+32=50[/tex]