Use any method to multiply (3a + 2b - c)(a - b + 2c).

Answer:

a)

X      P[X]

0       5/14

1        15/28

2       3/28

b)

The expected value is 0.75

Step-by-step explanation:

Ok, we know that out of 8 cameras, 3 are defective.

So first let's find the probability for a camera randomly selected to be defective.

This is just the quotient between the number of defective cameras and the total number of cameras.

p = 3/8

then the probability that a camera is not defective is:

q = 5/8.

Ok, now we draw 2 cameras at random from the box.

We can define X as the number of defective cameras in these two drawn, we can have 3 possible values of X.

X = 0  (neither of the cameras is defective)

X = 1 (one of the cameras is defective)

X = 2 (both of the cameras is defective).

Let's find the probabilities for each case.

X = 0.

In this case, we first draw a non-defective camera, with a probability of:

P = 5/8.

The second camera drawn must be also non-defective, but now there are 4 non-defective cameras in the box and a total of 7 cameras (because one was already drawn).

Then the probability now is:

Q = 4/7

The joint probability is the product of the two individual probabilities:

P[0] = P*Q = (5/8)*(4/7) = (5/14)

X = 1

Here we have two cases:

the first is defective and the second is non-defective

the first is non-defective and the second is defective

So we just have a factor of 2, to consider both cases

Assuming the first case

Probability of drawing first a defective camera is equal to the quotient between the number of defective cameras  and the total number of cameras:

P = 3/8

For the second draw we want to get a non-defective camera, here the probability is equal to the number of non-defective cameras remaining (5) and the total number of cameras (7, because we drawn one)

Q = 5/7

The joint probability, taking in account the permutation, is

P[1] = 2*P*Q = 2*(3/8)*(5/7) = (15/28)

finally, for X = 2

This is the case where we draw two defective cameras, we can use a similar approach as the one used in the first case:

For the first camera:

P = 3/8

For the second camera:

Q = 2/7

Joint probability:

P[2] = (3/8)*(2/7) = 3/28

then we have the table:

X      P[X]

0       5/14

1        15/28

2       3/28

b)

The expected value for an event that has the outcomes:

{x₁, x₂, ..., xₙ}

Each one with the correspondent probability

{p₁, p₂, ..., pₙ}

is defined as:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

Then in our case, the expected value is just:

EV = 0*P[0] + 1*P[1] + 2*P[2]

EV = 0  + 15/28  + 2*3/28

EV = (15 + 6)/28 = 21/28 = 0.75

Step-by-step explanation:

answer is in photo above

Answer:

-2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The importer needs to make the payment in the VND each time so the importer may enter into hedge to protect himself from the appreciation of the VND against the dollar, now if the importer enters into the forward contract of the hedge and he come across the reverse situation that means the VND is depriciating that means if the hedger would not have entered into a forward contract then they would have benefited more.

Lets convert above above rate in per VND rate to understand better.

E_USD/VND = 1/21000 = 0.000048

F_USD/VND = 0.000047

Ee_USD/VND = 0.000045

so as we can see above if we had enter into a hedge contract we have to pay the 0.000047 per VND and if we would not have enter into the contract we would have to pay the 0.000045 per VND hence cost of Hedging is 0.00002 USD per VND.

Answer:

y= -6/7

Step-by-step explanation:

.............. I did it, trust me

Answer:

z (max) =  17461.54  $

x₁   =  29.23 acres

x₂  =  0

x₃  =  3.07

Step-by-step explanation: INCOMPLETE QUESTION.

As the problem statement establishes:  "Each crop requires labor, fertilizer, and insecticide"  and information about quantities and availability does not exist. To build a model and that such model would be feasible I copy from the internet the following data. We assume the problem is to maximize the number of acres to plant with a maximum of profit ( we will use as profit the numbers 550  ;  350 ; 450 for  acres of corn, peanuts, and cotton)

Then z =  550*x₁  +  350*x₂  +  450*x₃    to maximize

                                            labor (h)      fertilizer ( tn)    Insecticide (Tn)

acres of corn         (x₁)               2                     4                        3

acres of peanut     (x₂)              3                     3                        2

acres of cotton      (x₃)              2                     1                         4

Availability         acres 40       120                120                      100

Constraints:

1) Size of the farm 120 acres

x₁  +  x₂   +   x₃   ≤   40

2) labor   120 h

2*x₁  +  3*x₂  +  2*x₃    ≤   120

3) Fertilizer  120 Tn

4*x₁  +  3*x₂  +  1*x₃      ≤   120

4) Insecticide 100 Tn

3*x₁   +  2*x₂  +  4*x₃     ≤  100

The Model is:

z =  550*x₁  +  350*x₂  +  450*x₃    to maximize

Subject to:

x₁  +  x₂   +   x₃   ≤   40

2*x₁  +  3*x₂  +  2*x₃    ≤   120

4*x₁  +  3*x₂  +  1*x₃      ≤   120

3*x₁   +  2*x₂  +  4*x₃     ≤  100

x₁    ≥   0  ;   x₂   ≥   0  ;   x₃   ≥   0

After 3 iterations using an on-line solver optimal solution is:

z (max) =  17461.54  $

x₁   =  29.23 acres

x₂  =  0

x₃  =  3.07

Answer:

Step-by-step explanation:

tan x= opp./adj.

tan x = 12/5 so

     x = tan^-1 (12/5)

second choice

Answer:

B

Step-by-step explanation:

Answer:

Therefore, 7/4 simplified to lowest terms is 7/4.

Answer:

Robert had 78 coins or c=78

Answer:

Step-by-step explanation:

Let the number is x, then we have:

Answer:

28.45

Step-by-step explanation:

33.04-1.75=31.29

31.29/1.10=28.45

Answer:

The answer is "Option 2".

Step-by-step explanation:

Please find the complete question in the attached file.

When there is a mean value k in a set of data. Otherwise, we will assert with certainty that at least one of the values is k. They can't say anything at all about the maximum or even the minimum using knowledge only. Nevertheless, we know that certain numbers cannot be over and that all numbers cannot be below than mean. Mean also no value throughout the data set must be equal.

Step-by-step explanation:

The volume of a hemisphere is given by :

[tex]V=\dfrac{2}{3}\pi r^3[/tex]

Taking differentiation,

[tex]\dfrac{dV}{dr}=2\pi r^2[/tex]

So,

[tex]dV=2\pi r^2\times dr[/tex]

Put r = 21 m and dr = 0.03 cm = 0.0003 m

[tex]dV=2\pi \times 21^2\times 0.0003\\\\dV=0.831\ m^3[/tex]

Hence, this is the required solution.

Answer:

Step-by-step explanation:

the equation is 8 cause 10 equals 8

Given:

Principal = $14850

Rate of interest = 4% compounded semiannually.

Time = 3 years

To find:

The amount after 3 years.

Solution:

Formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest in decimal, n is the number of times interest compounded and t is the number of years.

The interest is compounded semiannually, so n=2.

Putting [tex]P=14850, r=4, n=2, t=3[/tex] in the above formula, we get

[tex]A=14850\left(1+\dfrac{0.04}{2}\right)^{2(3)}[/tex]

[tex]A=14850\left(1+0.02\right)^{6}[/tex]

[tex]A=14850\left(1.02\right)^{6}[/tex]

On further simplification, we get

[tex]A=14850(1.12616242)[/tex]

[tex]A=16723.511937[/tex]

[tex]A\approx 16723.51[/tex]

Therefore, the amount in the account after three years is $16723.51.

Answer:

The answer is A

Step-by-step explanation: a net of a pyramid will always have a square and 4 triangles around it.

Answer:

1.632 ft^3

Step-by-step explanation:

3.4 times .8 times .6 = 1.632 ft.

therefore the volume of the rectangle is 1.632 ft^3

Answer:

28,705,185

Step-by-step explanation:

The answer is 28,705,185

The solution is 28,705,185

The number is given from the equation A = 28,705,185

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = twenty eight million, seven hundred and five thousand, one hundred and eighty five

Substituting the values in the equation , we get

Twenty eight million = 28,000,000

Seven hundred and five thousand = 705,000

One hundred and eighty five = 185

Now , the value of A = 28,000,000 + 705,000 + 185

On simplifying the equation , we get

A = 28,705,185

Therefore , the value of A is 28,705,185

Hence , the number is 28,705,185

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Step-by-step explanation:

the answer is in the image above

The volume of the original cube is 1000 cubic units.

The volume of a cube is equal to the product of length, width and height of a cube.

Let the length of side of the original cube = L

The surface area of the original cube A₁ = 6 L²

When increase the side length of a certain cube by 4

The surface area of the increased cube A₂ = 6 (L + 4)²

The surface area increases by 576

So, 6(L + 4)² - 6 L² = 576

6(L² + 16 + 8L) - 6 L² = 576

Divided by 6 both the sides,

L² + 16 + 8L - L² = 96

16 + 8L = 96

8L = 96 - 16

8L = 80

L = 80/8

L = 10

So, the length of side of the original cube = L = 10 units

The volume of the original cube = L³

The volume of the original cube = (10)³

The volume of the original cube = 1000 cubic units

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Answer:

its 2/3 because if u divied the width u get that

Step-by-step explanation:

you welcome i tried

Answer:

New functinon is g(x) = (1/32)x^5

Step-by-step explanation:

If you horizontally stretch the quadratic parent function, f(x) = x^2, by a factor

of 5, the equation of the new function will be g(x) = (x/5)^2, or g(x) =  (1/32)x^5

Answer:

0.999945 = 99.9945% probability that at least two of the alarms are triggered.

Step-by-step explanation:

For each alarm, there are only two possible outcomes. Either it is triggered, or it is not. The probability of an alarm being triggered is independent of any other alarm, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A home security system is designed to have a 90% reliability rate.

This means that [tex]p = 0.9[/tex]

Suppose that 6 home equipped with this system experience an attempted burglary.

This means that [tex]n = 6[/tex]

Find the probability that at least two of the alarms are triggered.

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.9)^{0}.(0.1)^{6} = 0.000001[/tex]

[tex]P(X = 1) = C_{6,1}.(0.9)^{1}.(0.1)^{5} = 0.000054[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.000001 + 0.000054 = 0.000055[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.000055 = 0.999945[/tex]

0.999945 = 99.9945% probability that at least two of the alarms are triggered.

Answer:

C

Step-by-step explanation:

that is the procedure above

The area of this circle with a radius of 13 inches is, C)530.66 inches

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

A circle with center A is given and the length of the line segment(radius),

AB = AD = AC = 13 inches.

We know, The area of a circle is,

= πr².

= π(13)² sq in.

= 530.66 sq in.

We can also find the perimeter or the circumference of the circle by the formula 2πr,

= 2π×13.

= 26π.

= 81.64 inches.

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Answer:

x = 40

3x=120

x+40 = 120

Step-by-step explanation:

The angles are vertical angles which means they are equal

3x= x+80

Subtract x from each side

3x-x =x+80-x

2x = 80

Divide by 2

2x/2 = 80/2

x = 40

3x = 3(40) =120

x+80 = 40+80 = 120

Answer:

6z^2 + 2z + 10

6 (3^2) + 2(3) + 10

6(9) + 6 + 10

54 + 16= 70

Answer:

16/3

Step-by-step explanation:

When multiplyin fractions by whole numbers, you can make the whole number a fraction by simply making the denominator 1, than you will multiply numerators by numerators and denominators by denominators, therefore

8 x 2 = 16

1 x 3 = 3

16/3

Answer:

that's my answer

Step-by-step explanation:

i hope it helps

Answer:

13

Step-by-step explanation:

pythagorean theorm calculator

enter the values for each leg

Answer:

actually, the answers are "No, the slopes are not equal"

and "Yes, the slopes are negative reciprocals".

Reason: just did it!!!!

Answer:

"No, the slopes are not equal"

and "Yes, the slopes are negative reciprocals".

Step-by-step explanation: