Determine the angles made by the vector V= (-35)i + (-41)j with the positive x-and y-axes. Write the unit vector n in the direction of V. Answers: ex= 9,0y i n =

Step-by-step explanation:

(a) 4 and 11

   binary equivalent of 4 in 5 bit = 00100

   binary equivalent of 11 in 5 bit = 01011

   decimal number 4 in 2's complement form = 11100

   decimal number 11 in 2's complement form = 10101

now,

        1 1 1 0 0

     + 1 01 0 1

    1 1 000 1

Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

(b) 6 and 14

   binary equivalent of 6 in 5 bit = 00110

   binary equivalent of 14 in 5 bit = 01110

   decimal number 6 in 2's complement form = 11010

   decimal number 14 in 2's complement form = 10010

now,

        1 1 0 1 0

     + 1 00 1 0

    1 0 1 1 0 0

Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

(c) -13 and 12

   binary equivalent of -13 in 5 bit = 10011

   binary equivalent of 12 in 5 bit = 01100

   decimal number -13 in 2's complement form = 01101

   decimal number 12 in 2's complement form = 10100

now,

        0 1 1 0 1

     + 1 0 1 0 0

    1 0 0 0 0 1

Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

(d) -4 and 8

   binary equivalent of -4 in 5 bit = 11100

   binary equivalent of 8 in 5 bit = 01000

   decimal number -4 in 2's complement form = 00100

   decimal number 8 in 2's complement form = 11000

now,

        0 0 1 0 0

     + 1  1 0 0 0

       1  1  1 0 0

Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will  not be overflow.

(e) -2 and -9

   binary equivalent of -2 in 5 bit = 11110

   binary equivalent of -9 in 5 bit = 10111

   decimal number -2 in 2's complement form = 00010

   decimal number -9 in 2's complement form = 01001

now,

        0 0 0 1 0

     + 0  1 0 0 1

       0  1  0 1 1

Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will  not be overflow.

(f) -9 and -14

   binary equivalent of -9 in 5 bit = 10111

   binary equivalent of -14 in 5 bit = 10010

   decimal number -9 in 2's complement form = 01001

   decimal number -10 in 2's complement form = 01110

now,

        0 1 0 0 1

     + 0 1  1 1  1

       1  1  000

Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will  not be overflow.

To convert decimal numbers to 5-bit 2's-complement numbers, convert each number to binary and add them.

(a) For 4, convert to binary: 00100. For 11, convert to binary: 01011. Add the binary numbers: 00100 + 01011 = 01111. Since the sum is positive, there is no overflow.

(b) For 6, convert to binary: 00110. For 14, convert to binary: 01110. Add the binary numbers: 00110 + 01110 = 10100. Since the sum is negative, there is overflow.

(c) For -13, convert to binary: 10011. For 12, convert to binary: 01100. Add the binary numbers: 10011 + 01100 = 11111. Since the sum is negative, there is no overflow.

(d) For -4, convert to binary: 11100. For 8, convert to binary: 01000. Add the binary numbers: 11100 + 01000 = 00100. Since the sum is negative, there is overflow.

(e) For -2, convert to binary: 11110. For -9, convert to binary: 10111. Add the binary numbers: 11110 + 10111 = 101001. Since the sum is positive, there is overflow.

(f) For -9, convert to binary: 10111. For -14, convert to binary: 10010. Add the binary numbers: 10111 + 10010 = 110001. Since the sum is negative, there is overflow.

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Answer:

The first one: It is in the 500,000 place.

The second one: It is in the 50 place.

Step-by-step explanation:

Answer:

  all except 5/6

Step-by-step explanation:

All of the numbers listed are in the set of integers, except for the fraction 5/6. It is a rational number, but not an integer.

___

If by "part of integers" you mean that the number can be multiplied by some integer value to make an integer, then 5/6 is "part of 5". It is 1/6 of the integer 5.

Answer:    [tex]\dfrac{1}{36}[/tex]

Step-by-step explanation:

We know that when two events A and B are independent , then the probability of getting A and B will be :-

[tex]P(A\cap B)=P(A)\times P(B)[/tex]

In a fair dice,total outcomes =6

Number of 2's =1

Then, the probability of getting a 2 =[tex]\dfrac{1}{6}[/tex]

If you roll one die two times, then the probability of getting a 2 on the first roll and a 2 on the second roll will be:-

[tex]\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{36}[/tex]

Hence, the probability of getting a 2 on the first roll and a 2 on the second roll=[tex]\dfrac{1}{36}[/tex]

Answer:

About 139,764,705.9 users were added, on average, per year, from 1995 to 2012.

Step-by-step explanation:

The problem states that in june 2012, about 2.4 billion people used the internet - 100 times more than the number of people who used it in June 1995.

So, in June 2012, 2.4 billion people used the internet.

In June 1995, [tex]\frac{2,400,000,000}{100} = 24,000,000[/tex] = 24 million people used the internet.

About how many people were added on average each year from 1995 to 2012?

[tex]2012 - 1995 = 17[/tex]. There were 17 years between 1995 and 2012.

[tex]2,400,000,000 - 24,000,000 = 2,376,000,000[/tex]. There were  2,376,000,000 internet users added during this 17-year period. To find this number per year, we solve the following rule of three:

1 year - x users

17 years - 2,376,000,000 users

[tex]17x = 2,376,000,000[/tex]

[tex]x = \frac{2,376,000,000}{17}[/tex]

[tex]x = 139,764,705.9[/tex]

About 139,764,705.9 users were added, on average, per year, from 1995 to 2012.

Answer:

In order to maximize the profit pairs of pants jackets, the manufactures should make 6 pants and 3 jackets.

Step-by-step explanation:

This problem can be solved by a system of first order equations:

I am going to say that [tex]x[/tex] is the number of pants and [tex]y[/tex] is the number of jackets that the manufacturer should make.

The profit will be maximized when all the avaiable time of the sewing operator and the cutter time has been used.

The problem states that there are 60 minutes of sewing operator time available. It takes 8 minutes to sew one pair of ski pants and 4 minutes to sew one jacket. So:

[tex]8x + 4y = 60[/tex]

We can simplify this equation by 4. So:

[tex]2x + y = 15[/tex]

The problem also states that there are 48 minutes of cutter time available. Cutters take 4 minutes on pants and 8 minutes on a jacket. So:

[tex]4x + 8y = 48[/tex]

Again simplifying by 4,

[tex]x + 2y = 12[/tex].

Now we have to solve the following system:

[tex]2x + y = 15[/tex]

[tex]x + 2y = 12[/tex]

I am going to write y as a function of x in the first equation, and replace it in the second.

[tex]y = 15 - 2x[/tex]

[tex]x + 2y = 12[/tex]

[tex]x + 2(15 - 2x) = 12[/tex]

[tex]x + 30 - 4x = 12[/tex]

[tex]-3x = -18[/tex]

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3}[/tex]

[tex]x = 6[/tex]

Now, replacing

[tex]y = 15 - 2x = 15 - 2(6) = 15 - 12 = 3[/tex]

In order to maximize the profit pairs of pants jackets, the manufactures should make 6 pants and 3 jackets.

Answer with explanation:

Let us assume that the 2 functions are:

1) f(x)

2) g(x)

Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that

[tex]\frac{d}{dx}\cdot f(x)<0\\\\\frac{d}{dx}\cdot g(x)<0[/tex]

Now the sum of the 2 functions is shown below

[tex]y=f(x)+g(x)[/tex]

Diffrentiating both sides with respect to 'x' we get

[tex]\frac{dy}{dx}=\frac{d}{dx}\cdot f(x)+\frac{d}{dx}\cdot g(x)\\\\[/tex]

Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus

[tex]\frac{dy}{dx}<0[/tex]

Thus the sum of the 2 functions is also a concave function.

Part 2)

The product of the 2 functions is shown below

[tex]h=f(x)\cdot g(x)[/tex]

Diffrentiating both sides with respect to 'x' we get

[tex]h'=\frac{d}{dx}\cdot (f(x)\cdot g(x))\\\\h'=g(x)f'(x)+f(x)g'(x)[/tex]

Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.

Answer:

d = 6 sin(2π/7 t + 3π/2)

Step-by-step explanation:

Equation for simple harmonic motion is:

d = A sin(2π/T t + B) + C

where A is the amplitude,

T is the period,

B is the horizontal shift (phase shift),

and C is the vertical shift.

Given that A = 6, T = 7, and C = 0:

d = 6 sin(2π/7 t + B)

At t = 0, the buoy is at d = -6:

-6 = 6 sin(2π/7 (0) + B)

-1 = sin(B)

3π/2 = B

d = 6 sin(2π/7 t + 3π/2)

Notice you can also use cosine instead of sine and get a different phase shift.

d = 6 cos(2π/7 t + π)

You can even use phase shift properties to simplify:

d = -6 cos(2π/7 t)

Any of these answers are correct.

The equation modeling the displacement d of the buoy as a function of time is d(t) = 6 * sin(2π/7 * t) - 6.

To model the displacement d of the buoy as a function of time t, we can use the equation:

d(t) = A * sin(2π/T * t) + C

where A is the amplitude, T is the period, t is the time, and C is the vertical displacement at t = 0 seconds.

In this case, the amplitude A is 6ft, the period T is 7 seconds, and the vertical displacement at t = 0 seconds C is -6ft and the buoy initially moves upward. Therefore, the equation modeling the displacement as a function of time is:

d(t) = 6 * sin(2π/7 * t) - 6

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Answer:

1) $329.66

2) $8011.20

3) 3.2%

4) 4

Step-by-step explanation:

Simple interest formula: I = P*r*t

the simple interest on the loan: $875 at 6.85% for 5 years 6 months

5 years 6 months = 5,5 years

6.85% = 0.0685

I = 875*0.0685*5.5 = 329.66

the total amount due for the simple interest loan: $6400 at 5.3% for 4 years 9 months.

4 years 9 months = 4 + 9/12 = 4 + 0.75 = 4.75

5.3% = 0.053

I = 6400*0.053*4.75 = 1611.20

Total amount due: 6400+1611.20 = 8011.20

the interest rate on a loan charging $960 simple interest on a principal of $3750 after 8 years.

I = 960

P = 3750

t = 8

960 = 3750*r*8

960 = 30000*r

r = 0.032

r = 3.2%

the term of a loan of $350 at 4.5% if the simple interest is $63.

P = 350

r = 4.5% = 0.045

I = 63

t = ?

63 = 350*0.045*t

63 = 15.75*t

t = 4

Answer:

The equation does not have a real root in the interval [tex]\rm [0,1][/tex]

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if [tex]f[/tex] is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in [tex]\rm [0,1][/tex], which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval [tex]\rm [0,1][/tex], which means to evaluate the equation in 0 and 1:

[tex]f(x)=x^3-3x+8\\f(0)=8\\f(1)=6[/tex]

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval [tex]\rm [0,1][/tex]. I attached a plot of the equation in the interval [tex]\rm [-2,2][/tex] where you can clearly observe how the graph does not cross the x-axis in the interval.  

Answer:

The amount is sufficient to make 75 tarts.

Step-by-step explanation:

We have been given that a recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart and 1 cup of hazelnuts weighs 4 ounces.

The half cup of hazelnuts will weigh 2 ounces [tex](\frac{4}{2}=2)[/tex].

1 kg equals 35.274 ounces.

[tex]\text{5 kg}=5\times 35.274\text{ ounces}[/tex]

[tex]\text{5 kg}=176.37\text{ ounces}[/tex]

Since each tart needs  ½ cup of hazelnuts and half cup of hazelnuts will weigh 2 ounces, so we will divide 176.37 ounces by 2 to find number of tarts.

[tex]\frac{176.37}{2}=88.185\approx 88[/tex]

Since we can make 88 tarts from 5 kg hazelnuts, therefore, the 5-kilogram bag of hazelnuts be sufficient to make 75 tarts.

Answer:

The area is given by the following integral: [tex]\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx[/tex], which can be approximated by: 0.265313

Step-by-step explanation:

A normal distribution is defined as:

[tex]f(x)=\frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}[/tex]

, where the greek letter sigma stands for the standard deviation and mu for the mean. Since in our problem we have a mean = 31.5 and a standard deviation = 11, then we can write this function as:

[tex]f(x)=\frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}}[/tex]

Now, we need to find the area below this function, between 35 and 45, and in order to do this, we need to integrate the function. The normal distribution does not has an exact closed form integral, therefore we will have to solve the integral in a software that allows for numerical calculations (I used the online software Wolfram|Alpha).

[tex]\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx =0.265313[/tex]

Answer:

infinitely many

Step-by-step explanation:

there were too many lines

Answer:

The correct option is D) Infinitely many.

Step-by-step explanation:

Consider the provided graph.

The system of equation has the solution at the point where the line intersects.

Now consider the graph of the equation 2x = 2y-6 and y = x+3

By observing the graph it can be concluded that the graph of 2x = 2y-6 and y = x+3 has the same line.

A system of equation have infinitely many solutions if each equations refers to the same line.

Since 2x = 2y-6 and y = x+3 refer the same line. The system has infinitely many solutions.

Hence, the correct option is D) Infinitely many.

Answer:

It will take Amy approximately 5.28 hours to count to 19,000.

Step-by-step explanation:

The first step to solve this problem is finding how many minutes it takes for Amy to count to 19,000. In each minute, she counts 60 numbers. So

1 minutes - 60 numbers

x minutes - 19,000 numbers

[tex]60x = 19,000[/tex]

[tex]x = \frac{19,000}{60}[/tex]

[tex]x = 316.7 minutes[/tex]

It is going to take 316.7 minutes for Amy to count to 19,000. How many hours are 316.7 minutes? Each hour has 60 minutes, so:

1 hour - 60 minutes

x hours - 316.7 minutes

[tex]60x = 316.7[/tex]

[tex]x = \frac{316.7}{60}[/tex]

[tex]x = 5.28[/tex]

It will take Amy approximately 5.28 hours to count to 19,000.

Answer:

The nurse should set the IV pump to deliver 125 ml/hr.

Step-by-step explanation:

The problem states that a nurse is preparing an IV pump to administer 250ml over 2 hours. So how many ml should be administered each hour?

This problem can be solved by this following rule of three.

250 ml - 2 hours

x ml -  1 hours

[tex]2x = 250[/tex]

[tex]x = \frac{250}{2}[/tex]

[tex]x = 125[/tex]ml.

The nurse should set the IV pump to deliver 125 ml/hr.

To determine the intermittent IV infusion rate, divide the total volume of the fluid (dextrose 5% water) by the total time of infusion. Here, it would be 250 ml divided by 2 hours, which equals 125 ml per hour.

To determine how many ml per hour a nurse should set the IV pump to deliver dextrose 5% water (D5W), you should divide the total volume by the total time. In this case, the total dextrose volume is 250 ml and it should be infused over 2 hours. Using the formula:

So, the nurse should set the IV pump to deliver 125 ml per hour of dextrose.

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Answer:

The volume of this tank is [tex]V = 10956.30 ft^{3}[/tex], using [tex]\pi = 3.14[/tex]

Step-by-step explanation:

A tank has the format of a cylinder.

The volume of the cylinder is given by:

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

In which r is the radius and h is the heigth.

The problem states that the diameter is measured carefully to be 15.00 ft. The radius is half the diameter. So, for this tank

[tex]r = \frac{15}{2} = 7.50[/tex] ft

The height of the tank is 62 ft, so [tex]h = 62[/tex].

The volume of this tank is:

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

[tex]V = pi*(7.5)^2*62[/tex]

[tex]V = 10956.30 ft^{3}[/tex]

The volume of this tank is [tex]V = 10956.30 ft^{3}[/tex], using [tex]\pi = 3.14[/tex]

Answer:

a) You should invest $6941.90 today.

b) The effective annual interest rate is 11%.

c) t is approximately 6.

Step-by-step explanation:

These are compound interest problems. The compound interest formula is given by:

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

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

a) How much would you invest today to have $9500 in 8 years if the effective annual rate of interest is 4%?

Here, we want to find the value of P when [tex]A = 9500, t = 8, n = 1, r = 0.04[/tex].

[tex]9500 = P(1 + \frac{0.04}{1})^{8}[/tex]

[tex]P = \frac{9500}{1.3685}[/tex]

[tex]P = 6941.90[/tex].

You should invest $6941.90 today.

b) Suppose that an investment of $5750 accumulates to $11533.20 at the end of 13 years, then the effective annual interest rate is i= ?

Here, we have that [tex]A = 11533.20, P = 5750, t = 13, n = 1[/tex], and we want to find the value of i, that is r on the formula above the solutions.

[tex]11533.20 = 5750(1 + r)^{13}[/tex]

[tex]\sqrt[13]{11533.20} = \sqrt[13]{5750(1 + r)^{13}}[/tex]

[tex]2.05 = 1.94(1 + r)[/tex]

[tex]r = 0.11[/tex]

The effective annual interest rate is 11%.

c) At an effective annual rate of interest of 5.3%, the present value of $7425.70 due in t years is $3250. Determine t.

Here, we have that [tex]A = 7425.70 + 3250 = 10675.7, P = 7425.7, r = 0.053, n = 1[/tex] and we have to find t. So

[tex]10675.7 = 7425.7(1 + \frac{0.053}{1})^{t}[/tex]

[tex](1 + 0.053)^{t} = \frac{10675.7}{7425.7}[/tex]

[tex](1.0553)^{t} = 1.4377[/tex]

We have that:

log_{a}a^{n} = n

So

[tex]log_{1.0553} (1.0553)^{t}  = log_{1.0553} 1.4377[/tex]

[tex]t = 5.95[/tex]

t is approximately 6.

Answer:

Total inventory: $175,000

Inventory in the stockroom: $35,000.

Inventory on the selling floor: $140,000.

Step-by-step explanation:

Let x be the the total inventory.

We have been given that in the Holiday Shop the manager wants 20% of the total inventory in the stockroom. You placed $35,000 of inventory in the stockroom.

We can set an equation such that 20% of x equals $35,000.

[tex]\frac{20}{100}\cdot x=\$35,000[/tex]

[tex]0.20x=\$35,000[/tex]

[tex]\frac{0.20x}{0.20}=\frac{\$35,000}{0.20}[/tex]

[tex]x=\$175,000[/tex]

Since $35,000 of inventory in the stockroom, so we will subtract $35,000 from $175,000.

[tex]\text{Amount of the inventory on the selling floor}=\$140,000[/tex]

Therefore, $140,000 of the inventory on the selling floor.

Answer:

5mL would be required to provide a patient with 0.25 mg of the drug substance.

Step-by-step explanation:

The problem states that an injectable solution contains 25μg of a dug substance in each 0.5 mL, and asks how many milliliters would be required to provide a patient with 0.25 mg of the drug substance.

So, the first step is the conversion of 25ug to mg, since the problem asks the answer in mg.

Each mg has 1000ug. So

1mg - 1000ug

xmg - 25ug

1000x = 25

[tex]x = \frac{25}{1000}[/tex]

x = 0.025 mg

It means that each 0.5mL of the solution contains 0.025mg of the drug. How many milliliters would be required to provide a patient with 0.25 mg of the drug substance.

0.5mL - 0.025mg

xmL - 0.25mg

0.025x = 0.5*0.25

[tex]x = \frac{0.5*0.25}{0.025}[/tex]

x = 10*0.5

x = 5mL

5mL would be required to provide a patient with 0.25 mg of the drug substance.

Final answer:

To provide a patient with 0.25 mg of a drug substance, 5 mL of the injectable solution is required when the solution concentration is 25μg per 0.5 mL.

Explanation:

If an injectable solution contains 25μg of a drug substance in each 0.5 mL, the question asks how many milliliters would be required to provide a patient with 0.25 mg of the drug substance. First, it is important to convert 0.25 mg to micrograms (μg) because the concentration of the drug is given in micrograms. Knowing that 1 mg = 1000 μg, we have:

0.25 mg = 0.25 × 1000 μg = 250 μg.

Next, if 25 μg is in 0.5 mL, we find how many times 25 μg goes into 250 μg to determine the volume needed:

250 μg / 25 μg/mL = 10 times

Since 25 μg is contained in 0.5 mL:

10 × 0.5 mL = 5 mL.

Therefore, 5 mL of the injectable solution is required to provide a patient with 0.25 mg of the drug substance.

Answer:

The value of x is [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Given,

[tex]\frac{1}{250}:2=\frac{1}{150}:x[/tex]

[tex]\frac{1/250}{2}=\frac{1/150}{x}[/tex]

[tex]\frac{1}{500}=\frac{1}{150x}[/tex]

By cross multiplication,

[tex]150x = 500[/tex]

[tex]x=\frac{500}{150}=\frac{500\div 50}{150\div 50}=\frac{10}{3}[/tex]

Final answer:

The probability that exactly 10 representatives from the first company and 12 from the second company will be chosen is about 1.288%, calculated using the hyper geometric probability formula.

Explanation:

The question asks for the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen to make presentations at an industry conference. This can be solved using the hypergeometric probability distribution since we are dealing with two groups and selections without replacement. The first group (G1) consists of 12 representatives from the first company, and the second group (G2) consists of 20 representatives from the second company.

The formula for calculating hyper geometric probability is:

[tex]P(X = k) = (C(G1, k) * C(G2, n - k)) / C(G1 + G2, n)[/tex]

Where:

To find the probability, we calculate:

[tex]P(X = 10) = (C(12, 10) * C(20, 12)) / C(32, 22)[/tex]

Plugging in the values gives us:

[tex]P(X = 10) = (C(12, 10) * C(20, 12)) / C(32, 22)[/tex]

= [tex](66 * 125,970) / 645,122,40[/tex]

=[tex]8,309,820 / 645,122,40[/tex]

=[tex]0.01288 or 1.288%[/tex]

Therefore, the probability that exactly 10 representatives from the first company and 12 from the second will be chosen is about 1.288%.

The probability that exactly 10 representatives from the first company and 12 from the second company will be chosen is approximately 0.0716%. This is calculated using the combination formula and the hypergeometric distribution.

We will use the concept of combinations and the hypergeometric distribution.

The total number of ways to select 22 representatives out of 32 (12 from the first company and 20 from the second company) is given by the combination formula  [tex]\( C(n, k) = \frac{{n!}}{{k!(n-k)!}} \)[/tex] . This reflects the entire sample space.

Therefore, the probability P is calculated as:

[tex]\[ P = \frac{{C(12,10) \times C(20,12)}}{{C(32,22)}} \][/tex]

Using a calculator or computing these values manually, we find:

C(12,10) = 66

C(20,12) = 125,970

C(32,22) = 1,166,803,110

Thus, the probability P becomes:

[tex]\[ P = \frac{{66 \times 125,970}}{{1,166,803,110}} \][/tex]

After computation, we get:

[tex]\[ P \approx 0.000716 \][/tex]

Therefore, the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen is approximately 0.000716, or 0.0716%.

Answer:

we are applying 70 ml during the whole day

Step-by-step explanation:

First, it is necessary to calculate the percentage of the drug that is left in the evening. This is calculated as:

100% - (35% + 25%) = 100% - 60% = 40%

Because,  35% is the percentage of the drug apply at the morning and 25% is percentage of the drug apply at afternoon.

Then, 40% is the percentage of the drug that is left in the evening and it is equivalent to 28 mL. So, the milliliter that we apply during the whole day are the milliliters equivalent to the 100%. We can calculate this by a rule of three as:

40% -------------------- 28 mL

100% -------------------    X

Where X are the milliliters that we apply during the whole day. Solving for X, we get:

[tex]X=\frac{100*28}{40}=70 mL[/tex]

Answer:

The final depth of Melissa is 14 meters below the surface

Step-by-step explanation:

In this kind of problems, involving directions, etc, usually one position is the positive direction and the other position is the negative direction.

In our problem, we suppose that the surface is the positivo zero, above the surface is the positive position(positive depth) and below the surface is the negative directions(negative depth).

The problem states that Melissa is 29 meters below the surface. So, her initial position is 29 meters in the negative direction, so it is equal to -29.

Then, the problem states that Melissa rises upward 15 meters. Upward is the positive direction, so she moved to the positive direction. It means that we are going to do -29+15 = -14 meters.

It means that the final depth of Melissa is 14 meters below the surface

Answer:

If you purchase it, you will save 16.67% of the original price.

Step-by-step explanation:

Percentage problems can be solved as a simple rule of three problem:

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

A percentage problem is an example where the relationship between the measures is direct.

The problem states that the model you really like happens to be on sale for $1200 and it's original price is $1400. It means the you saved $1400-$1200 = $200. Thus, the problem wants to know how much $200 is of $1200. So, we have the following rule of three

$1200 - 100%

200 - x%

1200x = 200*100

[tex]x = \frac{20000}{1200}[/tex]

x = 16.67%.

If you purchase it, you will save 16.67% of the original price.

Use the divergence theorem.

[tex]\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+5\,\vec k\implies\mathrm{div}\vec F(x,y,z)=2[/tex]

By the divergence theorem,

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F\,\mathrm dV[/tex]

where [tex]R[/tex] is the region with boundary [tex]S[/tex].

Compute the latter integral in cylindrical coordinates, taking

[tex]\begin{cases}x=r\cos\theta\\y=y\\z=r\sin\theta\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dy[/tex]

[tex]\displaystyle\iint_R2\,\mathrm dV=2\int_0^{2\pi}\int_0^1\int_0^{2-r\cos\theta}r\,\mathrm dy\,\mathrm dr\,\mathrm d\theta=\boxed{4\pi}[/tex]

Answer:

You should take 2 tablets of Aspirin.

Six tablets is not the correct dosage.

You should get 4 tablets.

Step-by-step explanation:

You wake up with a fever! All you can find at the store is Aspirin, and the bottle says to take 162 mg. The bottle also says each tablet has 81 mg in each tablet. How many tablets should you take?

This can be solved by this following rule of three.

1 tablet - 81mg

x tablets - 162mg

[tex]81x = 162[/tex]

[tex]x = \frac{162}{81}[/tex]

[tex]x = 2[/tex]

You should take 2 tablets of Aspirin.

The doctor orders 120 mg of medicine to be given twice a day. The nurse comes in with 6 tablets and tells you that there are 30 mg in each tablet. Is this the correct dosage?

We need to see how many mg are in 6 tablets. If there are 120mg in 6 tablets, this is the correct dosage. We verify this by the following rule of three:

1 tablet - 30mg

6 tablets - x mg

[tex]x = 30*6[/tex]

[tex]x = 180[/tex]mg.

In 6 tablets, there are 180mg. So, it is not the correct dosage.

If not, how many tablets should you get?

Knowing that each tablet has 30mg, in how many tablets are there 120mg?

1 tablet - 30 mg

x tablets - 120 mg

[tex]30x = 120[/tex]

[tex]x = \frac{120}{30}[/tex]

[tex]x = 4[/tex]

You should get 4 tablets.

Answer:

  C)  [tex]\dfrac{2}{3}(6+s)[/tex]

Step-by-step explanation:

The distributive property lets you factor out the common factor of 2/3. The result is ...

   [tex]\dfrac{2}{3}(6+s)[/tex]

Answer: 18.75%

Step-by-step explanation:

The percent strength of a solution is given by :-

[tex]\% \text{ Strength}=\dfrac{\text{Mass of solute in g}}{\text{Volume of solution in mL}}\times100[/tex]

Given :  A solution of ibuprofen contains 150g in 800mL .

Then, the percent strength of this solution will be :-

[tex]\% \text{ Strength}=\dfrac{150}{800}\times100\\\\\Rightarrow\ \% \text{ Strength}=18.75\%[/tex]

Hence, the percent strength of this solution = 18.75%

Answer:

0 is not an element of an empty set.

Step-by-step explanation:

We are asked to determine whether 0 is not an element of an empty set.

We know that an empty set is an unique set having no elements. The cardinality of an empty set is 0.

Cardinality stands for the count of element is an set. An empty set is denoted by symbols ∅ or { }.

The empty set is like an empty container. The container is there, but nothing is in it.

When 0 is an element of a set, then its cardinality would be 1.

Therefore, 0 is not an element of an empty set.

Answer:

The EMV of this project is -17,500

Step-by-step explanation:

The EMV of the project is the Expected Money Value of the Project.

This value is given by the sum of each expected earning/cost multiplied by each probability.

So, in our problem

[tex]EMV = P_{1} + P_{2} + P_{3} + P_{4}[/tex]

The problem states that there is a 25% chance of Snowmaggedon which will delay the project at a cost of $35,000. Since this is a cost, [tex]P_{1}[/tex] is negative.

[tex]P_{1} = 0.25*(-35,000) = -8,750[/tex]

There is a 10% chance of cost of construction materials dropping saving the project $70,000. A saving is an earning, so [tex]P_{2}[/tex] is positive

[tex]P_{2} = 0.10*70,000 = 7,000[/tex]

There is a 10% probability a labor strike will occur delaying the schedule with a cost of $40,000.

[tex]P_{3} = 0.10*(-40,000) = -4,000[/tex]

There is a 80% chance of new regulations mandated calling for higher inspection standards which will cost an additional $15,000 to mitigate

[tex]P_{4} = 0.80*(-15,000) = -12,000[/tex]

[tex]EMV = P_{1} + P_{2} + P_{3} + P_{4} = -8,750 + 7,000 - 4,000 - 12,000 = -17,500[/tex]

The EMV of this project is -17,500