A town's population has been growing linearly. In 2003, the population was 59.000 and the population has been growing by 1,700 people each year. a. Write a formula for the population x years after 2003. b. What will the town's population be in 2007? c. In what year will the population be 77,700 people?

Shown in the explanation

A Rhombus is a quadrilateral having four sides of equal length each. Here, we know that the vertices of this shape are:

[tex]W(7,2) \\ \\ X(5,-1) \\ \\ Y(3,2) \\ \\ Z(5,5)[/tex]

So the rhombus is named as WXYZ. To find its perimeter (P), we just need to find the length of one side and multiply that value by 4. By using the distance formula, we know that:

[tex]\overline{WX}=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2} \\ \\ W(7,2)=W(x_{1},y_{1}) \\ \\ X(5,-1)=X(x_{2},y_{2}) \\ \\ \\ \overline{WX}=\sqrt{(7-5)^2+(2-(-1))^2} \\ \\  \overline{WX}=\sqrt{(2)^2+(3)^2} \\ \\ \overline{WX}=\sqrt{4+9} \\ \\ \overline{WX}=\sqrt{13}[/tex]

Finally, the Perimeter (P) is:

[tex]P=4(\sqrt{13}) \\ \\ \boxed{P=4\sqrt{13}\ units}[/tex]

Answer:

4 13

Step-by-step explanation:

Answer:

1052.944 g

Step-by-step explanation:

Given:

Initial temperature of water = 15° C

Final temperature of water = 1° C

Mass of ice = 185 grams

Now,

Heat of fusion of ice = 333.55 J/g

Thus,

The heat required to melt ice = Mass of ice × Heat of fusion

or

The heat required to melt ice = 185 × 333.55 = 61706.75 J

Now,

for water the specific heat capacity= 4.186 J/g.°C

Heat provided = mass × specific heat capacity × Change in temperature

or

61706.75 = mass × 4.186 × (15 - 1)

or

61706.75 = mass × 58.604

or

mass = 1052.944 g

Hence, the mass that can be heated 1052.944 g

Answer:

Y=32.67°

Step-by-step explanation:

Supplement condition:

Y+(10x+4°)=180°     (1)

Complement condition:

Y+4x=90°      (2)

5*(2)-2*(1):

5Y +20x - 2Y -20x -8° =450°-360°

3Y=98°

Y=32.67°

Answer:

See below.

Step-by-step explanation:

2−4÷2+23 =

= 2 - 2 + 23

= 0 + 23

= 23

This is the answer of the problem you posted, where 23 is the number twenty-three. 23 is not an answer choice, so perhaps 23 is not the number twenty-three, but rather 2 to the 3rd power, 2^3.

2−4÷2+2^3 =

= 2 - 2 + 8

= 0 + 8

= 8

8 is one of the choices.

Answer:

The sum E (4 + 6 + 8 + 10 + 106) is greater than the sum O (-3 + 5 + 7 + 9 + 105) by 11. E equals 134 and O equals 123.

To compare the sums O and E without computing each sum directly, let's analyze each expression:

For O: -3 + 5 + 7 + 9 + 105
For E: 4 + 6 + 8 + 10 + 106

Group the pairs of numbers for simplicity:

Comparing the two:

Therefore, the sum E is greater than the sum O by 11.

Answer:

1/6

Step-by-step explanation:

Slope is [tex]\frac{\text{rise}}{\text{run}}=\frac{1}{6}[/tex].

Answer and Step-by-step explanation:

The U.S. Drug Enforcement Administration (DEA) has divided the sustances into five categories schedules, which they are:

Schedule 1 (I) drugs: substances with no accepted medical use so far and a high potential for abuse. This is the most dangerous schedule because they are considered to have a very high potential of severe psychological and physical dependence. Examples: Heroin, LSD, Methylenedioxymethamphetamine (ecstasy)

Schedule 2 (II)  drugs: substances with very controlled medical use with a abuse potential very high but less than Schedule 1 drugs. They are considered very dangerous, because they can lead to a severe psychological and physical dependence. Examples: Cocaine

Methamphetamine, Ritalin.

Schedule 3 (III) drugs: substances that are defined as drugs with a moderate to low potential for physical and psychological dependence. Their abuse potential is less than Schedule 1 and 2, but higher than Schedule 4. Examples: Vicodin, Anabolic steroids, Testosterone.

Schedule 4 (IV) drugs: substances with a abuse potential low and their risk of dependence is also low. Examples: Xanax, Valium , Ativan.

Schedule 5 (V) drugs: substances abuse potential lower potential than Schedule 4 (IV) and they are made with limited amounts of some narcotics. They are used for analgesic purposes, antidiarrheal and less serious conditions. Examples: Lomotil, Robitussin

Answer:

The EMV of the project is $25,500.

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 multiplied by each probability

So, in our problem

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

The problem states that the project has a 60% of super success earning $50,000. So

[tex]P_{1} = 0.6*50,000 = 30,000[/tex]

The project has a 15% chance of mediocre success earning $20,000. So

[tex]P_{2} = 0.15 * 20,000 = 3,000[/tex]

The project has a 25% probability of failure losing $30,000. So

[tex]P_{3} = 0.25*(-30,000) = -7,500[/tex]

[tex]EMV = P_{1} + P_{2} + P_{3} = 30,000 + 3,000 - 7,500 = 25,500[/tex]

The EMV of the project is $40,500.

Answer: 38760

Step-by-step explanation:

Given : The number of employees in the company = 20

The number of employees will be selected by company owner to give bonus = 6

We know that the combination of n things taking r at a time is given by :-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Then, the number of different sets of employees could receive bonuses is given by :-

[tex]^{20}C_6=\dfrac{20!}{6!(20-6)!}\\\\=\dfrac{20\times29\times18\times17\times16\times15\times14!}{(720)14!}=38760[/tex]

Hence, the number of different sets of employees could receive bonuses is  38760.

Answer:

The correct definition of statistics is D.

Step-by-step explanation:

The field of statistics is divided into descriptive and inferential statistics. This description "Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions." corresponds to the description of Descriptive statistics and this part "In​ addition, statistics is about providing a measure of confidence in any conclusions."  is the description of Inferential statistics.

Final answer:

To calculate the difference in earnings between the two investments, we can use the compound interest formula to find the future value of each investment. The first investment would earn $2,353,121.65 more than the second investment.

Explanation:

To calculate the difference in earnings between the two investments, we need to calculate the future value of each investment. For the first investment, we have $22,000 invested for 40 years at an annual interest rate of 14%. Using the compound interest formula:

FV = PV * (1 + r)^n

FV = $22,000 * (1 + 0.14)^40 = $2,889,032.39

For the second investment, we have $22,000 invested for 40 years at an annual interest rate of 7%. Using the compound interest formula:

FV = PV * (1 + r)^n

FV = $22,000 * (1 + 0.07)^40 = $535,910.74

The difference in earnings between the two investments is:

$2,889,032.39 - $535,910.74 = $2,353,121.65

Linear pair makes a straight line.

A. are vertical angles.

B. are vertical angles

C. make a right angle

D. makes a straight line of TR

The answer is D.

Answer:

1. 405000: Number of significant digits 3. 405

2. 0.0098: Number of significant digits 2. 98

3. 39.999999: Number of significant digits 8. 39999999

4. 13.00: Number of significant digits 4. 1300

5. 80,000,089: Number of significant digits 8. 80000089

6. 55430.00: Number of significant digits 7. 5543000

7. 0.000033: Number of significant digits 2. 33

8. 620.03080: Number of significant digits 8. 62003080

[tex]1. \hspace{3} 70000000000 = 7\times10^{10}\\2. \hspace{3} 0.000000048 = 4.8\times10 ^{-8}\\3. \hspace{3} 67890000 = 6.789\times10^7\\4. \hspace{3} 70500 = 7.05\times10^4\\5. \hspace{3} 450900800 = 4.509008\times10^8\\6. \hspace{3} 0.009045 = 9.045\times10^{-3}\\[/tex]

Step-by-step explanation:

The significant digits in a real number refer to the digits that are held in the gutter to determine their accuracy. That is, those relative values that could be determined with certainty. Therefore, the answers are:

1. 405000: Number of significant digits 3. 405

2. 0.0098: Number of significant digits 2. 98

3. 39.999999: Number of significant digits 8. 39999999

4. 13.00: Number of significant digits 4. 1300

5. 80,000,089: Number of significant digits 8. 80000089

6. 55430.00: Number of significant digits 7. 5543000

7. 0.000033: Number of significant digits 2. 33

8. 620.03080: Number of significant digits 8. 62003080

[tex]1. \hspace{3} 70000000000 = 7\times10^{10}\\2. \hspace{3} 0.000000048 = 4.8\times10 ^{-8}\\3. \hspace{3} 67890000 = 6.789\times10^7\\4. \hspace{3} 70500 = 7.05\times10^4\\5. \hspace{3} 450900800 = 4.509008\times10^8\\6. \hspace{3} 0.009045 = 9.045\times10^{-3}\\[/tex]

The question asks to find the significant digits in several numbers and to convert different sets of numbers into scientific notation. The answers provide the number of significant digits for each number and the respective numbers in scientific notation. Significant digits provide precision in measurements, and scientific notation is useful for representing very large or very small numbers.

Part 1: Significant digits are crucial in science because they tell us how accurate a measurement is. Zeros can sometimes not be significant, as they might just be placeholders.

Part 2: Converting these numbers into scientific notation gives us:

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Convert 55% to a decimal by moving the decimal point two places to the left:

55% = 0.55

Now multiply:

3650.00 x 0.55 = 2,007.50

Answer:

840

Step-by-step explanation:

Total number of gifts (teddy bears)= 4

Total number of nieces = 7

We need to find the number of ways to give the 4 teddy bears to 4 of the 7 nieces, where no niece gets more than one teddy bear.

Number of possible ways to give first teddy = 7

It is given that no niece gets more than one teddy bear.

The remaining nieces are = 7 - 1 = 6

Number of possible ways to give second teddy = 6

Now, the remaining nieces are = 6 - 1 = 5

Similarly,

Number of possible ways to give third teddy = 5

Number of possible ways to give fourth teddy = 4

Total number of possible ways to distribute 4 teddy bears is

[tex]Total=7\times 6\times 5\times 4=840[/tex]

Therefore total possible ways to distribute 4 teddy bears are 840.

Final answer:

There are 35 different ways to give 4 identical teddy bears to 4 of the 7 nieces where no niece receives more than one teddy bear. The calculation is done using combinations formula C(7, 4).

Explanation:

To determine the number of different ways the 4 teddy bears can be given to 4 out of 7 nieces where each niece gets only one teddy bear, we use combinations. Combinations are a way of selecting items from a group, where the order does not matter. In mathematics, this is denoted as C(n, k), which represents the number of combinations of n items taken k at a time.

In this case, we want to find C(7, 4), because we have 7 nieces (n=7) and we are choosing 4 of them (k=4) to each receive one teddy bear. This is calculated by:

C(7, 4) = 7! / (4! * (7-4)!) => C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3!). Since 4! in the numerator and denominator cancel each other out, it simplifies to:

C(7, 4) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different ways to give the 4 identical teddy bears to 4 of the 7 nieces when no niece gets more than one teddy bear.

Answer:

It is a straight horizontal line where the line is only on 0.5.

Step-by-step explanation:

Answer:

a) 0.2

b) 0.2

c) 0.5

Step-by-step explanation:

Let [tex]S[/tex] be the event "the car stops at the signal.

In the attached figure you can see a tree describing all possible scenarios.

For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus

[tex]P(a)=0.4\times0.5=0.2[/tex]

For the second one the blue path describes the situation

[tex]P(b)=0.4\times 0.5=0.2[/tex]

For the las situation the sum of the two green path will give us the answer

[tex]P(c)=0.6\times 0.5 + 0.4\times 0.5=0.3+0.2=0.5[/tex]

Answer:

a) 0.3

b) 0.1

c) 0.3

Step-by-step explanation:

Lets call:

a = stop at first signal,  b = stop at second signal

The data we are given is P(a) = 0.4, and P(b)=0.5

Stoping at least at one is the event (a or b) = a ∪ b

P(a U b) = 0.6 is the other data we are given

a) Stoping at both signals is the event (a and b = a ∩ b)

The laws of probability say that:

P(a ∪ b)= P(a) + P(b) - P( a ∩ b) = 0.4 + 0.5  - P( a ∩ b) = 0.6

Then we get P( a ∩ b) = 0.3

b) The event is (a and not b) = a ∩(¬b).

P( a ∩(¬b) ) = P(a) - P( a ∩ b) = 0.1

c) The event is (a or b) without the cases in which (a and b)

P(a ∪ b) - P( a ∩ b) = 0.3

The Venn diagram can help you understand how the events are related to each other

To find the value of n, we can use the concept of combinations. By setting up and solving an equation using the combination formula, we find that the value of n is 6.

To find the value of n, we can use the concept of combinations. Since Columba has 2 dozen (24) each of n different colored beads, the total number of beads she has is 24n. If she can select 20 beads with repetitions allowed in 230,230 ways, we can set up the equation:

24n choose 20 = 230,230

To solve this equation, we need to use the concept of combinations. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items, r is the number of items being selected, and ! represents the factorial function.

Plugging in the values, we have:

24n! / (20!(24n-20)!) = 230,230

Simplifying the equation, we get:

n! / (20!(n-20)!) = 10

To find the value of n, we can try different values of n and calculate the factorial on both sides of the equation. Starting with n = 2, we have:

2! / (20!(2-20)!) = 1 / (20!(18)!) = 1 / (20!(18!)) = 1 / (20 * 19) = 1 / 380 = 0.00263

Since this value is smaller than 10, we need to try a larger value of n. By trying different values, we find that when n = 6, the equation holds:

6! / (20!(6-20)!) = 6! / (20!(14)!) = 720 / (20 * 19 * 18 * 17 * 16 * 15 * 14!) = 720 / (20 * 19 * 9 * 17 * 16 * 15) = 720 / 9909000 = 0.00007

Therefore, the value of n is 6.

Answer: she must walk for 72.8 s

Hi!

Lets say that with the cart she rides a time T1 (28 s) for a distance D1, then the average speed in the cart is V1 = D1 / T1 =  3.10 m/s. We can calculate D1 = (28 s )* (3.10 m/s) = 86.8 m

She then walks a time T2 for a distance D2, with average speed

V2 = D2 / T2 = 1.30 m/s

For the entire trip, we have average speed:

V3 = (D1 + D2) / (T1 + T2) = 1.80 m/s

We can solve for T2:

(1.8 m/s) *( 28s + T2) = 86.8 m  +  D2 = 86.8 m + (1.3 ms) * T2

Doing the algebra we get: T2 = 72,8 m/s

This question involves an application of the concept of average speed. Knowing that the average speed for the entire trip was 1.80 m/s, we first determined the distance covered while riding the golf cart. Using this, we set up an equation that allowed us to solve for the time spent walking to maintain the given average speed.

In order to solve this problem, we'll have to apply the formula for average speed, which is total distance covered (d) divided by the total time (t) taken.

Firstly, let's determine the distance covered while riding the golf cart. The golfer rides at an average speed of 3.10 m/s for 28.0 s. Therefore, she covers a distance of (average speed)x(time) = (3.1 m/s)(28.0 s) = 86.8 m.

Let's denote the time she walks as 't2'. The total time of the trip equals the sum of the time spent in the cart and the time spent walking: 28.0 s + t2.

Similarly, the total distance covered equals distance covered with the cart plus distance covered walking, which is 86.8 m + 1.30 m/s * t2.

Given the average speed for the entire trip is 1.80 m/s, we can write:

1.80 m/s = (total distance) / (total time)

1.80 m/s = (86.8 m + 1.30 m/s * t2) / (28.0 s + t2).

This equation could be solved for t2 to calculate how long the golfer needs to walk.

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Step-by-step explanation:

Consider the provided information.

Division by zero is not defined in our number system.

You can understand this if you think about how division and multiplication are related.

For example:

4 divided by 2 is 2 because  2 times 2 is 4

Now 4 divided by 0 is x would mean that  0 times x = 4

But there is no value for x so that 0 times x =4. Because 0 times a number is 0.  

Or

4/0 means Into how many groups of zero could you separate  four blocks?

It doesn't matter how many zero groups you have, as they'd never add up to four.

0+0+0+0=0.

You can add zero billions time still add up to zero.

That the reason behind "division by zero is not allowed in our number system."

Answer:

The level curves F(t,z) = C for any constant C in the real numbers

where

[tex]F(t,z)=z^3t^2+e^{tz}-4t+2z[/tex]

Step-by-step explanation:

Let's call

[tex]M(t,z)=2tz^3+ze^{tz}-4[/tex]

[tex]N(t,z)=3t^2z^2+te^{tz}+2[/tex]

Then our differential equation can be written in the form

1) M(t,z)dt+N(t,z)dz = 0

To see that is an exact differential equation, we have to show that

2) [tex]\frac{\partial M}{\partial z}=\frac{\partial N}{\partial t}[/tex]

But

[tex]\frac{\partial M}{\partial z}=\frac{\partial (2tz^3+ze^{tz}-4)}{\partial z}=6tz^2+e^{tz}+zte^{tz}[/tex]

In this case we are considering t as a constant.

Similarly, now considering z as a constant, we obtain

[tex]\frac{\partial N}{\partial t}=\frac{\partial (3t^2z^2+te^{tz}+2)}{\partial t}=6tz^2+e^{tz}+zte^{tz}[/tex]

So, equation 2) holds and then, the differential equation 1) is exact.

Now, we know that there exists a function F(t,z) such that

3) [tex]\frac{\partial F}{\partial t}=M(t,z)[/tex]  

AND

4) [tex]\frac{\partial F}{\partial z}=N(t,z)[/tex]

We have then,

[tex]\frac{\partial F}{\partial t}=2tz^3+ze^{tz}-4[/tex]

Integrating on both sides

[tex]F(t,z)=\int (2tz^3+ze^{tz}-4)dt=2z^3\int tdt+z\int e^{tz}dt-4\int dt+g(z)[/tex]

where g(z) is a function that does not depend on t

so,

[tex]F(t,z)=\frac{2z^3t^2}{2}+z\frac{e^{tz}}{z}-4t+g(z)=z^3t^2+e^{tz}-4t+g(z)[/tex]

Taking the derivative of F with respect to z, we get

[tex]\frac{\partial F}{\partial z}=3z^2t^2+te^{tz}+g'(z)[/tex]

Using equation 4)

[tex]3z^2t^2+te^{tz}+g'(z)=3z^2t^2+te^{tz}+2[/tex]

Hence

[tex]g'(z)=2\Rightarrow g(z)=2z[/tex]

The function F(t,z) we were looking for is then

[tex]F(t,z)=z^3t^2+e^{tz}-4t+2z[/tex]

The level curves of this function F and not the function F itself (which is a surface in the space) represent  the solutions of the equation 1) given in an implicit form.

That is to say,

The solutions of equation 1) are the curves F(t,z) = C for any constant C in the real numbers.

Attached, there are represented several solutions (for c = 1, 5 and 10)

Answer:

Number of members having previous work experience = 18

Step-by-step explanation:

As given in question,

Total number of new members hired = 27

Since, two-thirds had previous retail work experience

So,

[tex]the\ fraction\ of\ members\ having\ previous\ work\ experience\ =\ \dfrac{2}{3}[/tex]

[tex]So,\ the\ number\ of\ members\ having\ previous\ work\ experience\ =\ \dfrac{2}{3}\times\ total\ number\ of\ members\ hired[/tex]

                                              [tex]=\ \dfrac{2}{3}\times 27[/tex]

                                                = 18

So, the number of new members hired having work experience = 18

Final answer:

Two-thirds of the 27 new executive training program members had previous retail work experience, which equals to 18 members.

Explanation:

To calculate how many of the new executive training program members have previous retail work experience, we can use simple multiplication.

As two-thirds of the 27 new members had previous retail experience, we would calculate this as follows:

Number with experience =
2/3 of 27
Number with experience = 27 × (2/3)
Number with experience = 18

Therefore, out of the 27 new members, 18 have previous retail work experience.

Answer:

There were 49 people that chose chocolate and vanilla twist.

Step-by-step explanation:

This problem can be solved by building a Venn diagram of this set, where:

-A is the number of the people that tasted the vanilla

-B is the number of the people that tasted the chocolate.

The most important information in this problem is that some of those people tasted both. It means that [tex]A \cap B = x[/tex], and x is the value we want to find.

The problem states that 97 people tasted the vanilla sample of frozen yogurt.  This includes the people that tasted both samples. It means that x people tasted the chocolate and vanilla twist and 97-x people tasted only the vanilla twist.

72 people tasted the chocolate, also including the people that tasted both samples. It means that x people that tasted the chocolate and vanilla twist and 72-x that tasted only the chocolate twist.

So, recapitulating, there are 120 people, and

97-x  tasted only the vanilla twist.

72 - x tasted only the chocolate twist

x people tasted both

So

97 - x + 72 - x + x = 120

-x = 120 - 72 - 97

-x = -49 *(-1)

x = 49

There were 49 people that chose chocolate and vanilla twist.

To find out how many people chose the chocolate and vanilla twist, we need to subtract the number of people who tasted only vanilla and only chocolate from the total number of people who tasted the frozen yogurt.

To find out how many people chose the chocolate and vanilla twist, we need to subtract the number of people who tasted only vanilla and only chocolate from the total number of people who tasted the frozen yogurt. We know that 97 people tasted vanilla and 72 people tasted chocolate. However, some people chose the chocolate and vanilla twist, so we need to subtract the overlapping cases.

To calculate the number of people who chose the chocolate and vanilla twist, we can use the principle of inclusion-exclusion. We add the number of people who tasted only vanilla and the number of people who tasted only chocolate, and then subtract the total number of people who tasted the frozen yogurt.

Using the formula:

(# of people who tasted vanilla) + (# of people who tasted chocolate) - (# of people who tasted both) = Total # of people who tasted the frozen yogurt

97 + 72 - X = 120

X = 97 + 72 - 120

X = 169 - 120

X = 49

Therefore, 49 people chose the chocolate and vanilla twist.

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The diameter of 4.3 cm equals 1.677 inches and 43 millimeters. This is calculated by using the conversion factors of 0.39 for inches and 10 for millimeters.

To convert diameter from centimeters to inches and millimeters, we use the conversion factors that 1 cm equals 0.39 inches and 1 cm equals 10 millimeters.

First, let's convert into inches. Multiply the given diameter (4.3 cm) by the conversion factor (0.39). 4.3 cm * 0.39 = 1.677 inches.

Next, let's convert into millimeters. Multiply the given diameter (4.3 cm) by the conversion factor (10) for millimeters. 4.3 cm * 10 = 43 millimeters.

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Answer:

slope = -5 ÷ 4

Step-by-step explanation:

The equation of line can be written as,

y = mx + c

where, m is slope

and c is intercept of line.

So, transforming the given equation in above standard equation.

5x + 4y - 1 = 0

⇒ 4y = -5x + 1

⇒ [tex]y = \frac{-5}{4}x +\frac{1}{4}[/tex]

Now comparing this equation with standard equation. We get,

[tex]m =\frac{-5}{4}[/tex]

and [tex]c = \frac{1}{4}[/tex]

Hence, Slope =  [tex]m =\frac{-5}{4}[/tex]

Answer:

The resultant velocity of the airplane is 213.41 m/s.

Step-by-step explanation:

Given that,

Velocity of an airplane in east direction, [tex]v_1=210\ mph[/tex]

Velocity of wind from the north, [tex]v_2=38\ mph[/tex]

Let east lies in the direction of the positive x-axis and north in the direction of the positive y-axis.

We need to find the resultant velocity of the airplane. Let v is the resultant velocity. It can be calculated as :

[tex]v=\sqrt{v_1^2+v_2^2}[/tex]

[tex]v=\sqrt{(210)^2+(38)^2}[/tex]

v = 213.41 m/s

So, the resultant velocity of the airplane is 213.41 m/s. Hence, this is the required solution.

Final answer:

The resultant velocity of the airplane, combining its eastward direction and the northward wind, is approximately 213.4 miles per hour at an angle of 10.3 degrees north of east.

Explanation:

The student's question relates to the concept of resultant velocity, which is a fundamental topic in Physics. When two velocities are combined, such as an airplane's velocity and wind velocity, the outcome is a vector known as the resultant velocity. To calculate this, one must use vector addition.

The airplane has a velocity of 210 miles per hour due east, which can be represented as a vector pointing along the positive x-axis. The wind has a velocity of 38 miles per hour from the north, represented as a vector along the positive y-axis. To find the resultant velocity, these two vectors must be combined using vector addition.

Mathematically, the resultant vector [tex]\\(R)[/tex] can be found using the Pythagorean theorem if the vectors are perpendicular, as in this case:
[tex]\[ R = \sqrt{V_{plane}^2 + V_{wind}^2} \][/tex]

Where \\(V_{plane}\\) is the velocity of the airplane and [tex]\(V_{wind}\)[/tex] is the velocity of the wind.

The direction of the resultant vector can be determined by calculating the angle [tex]\(\theta\)[/tex] it makes with the positive x-axis using trigonometry, specifically the tangent function:
[tex]\[ \theta = \arctan\left(\frac{V_{wind}}{V_{plane}}\right) \][/tex]

By substituting the given values:

The resultant velocity (magnitude) is then calculated by:

[tex]\[ R = \sqrt{(210)^2 + (38)^2} = \sqrt{44100 + 1444} = \sqrt{45544} \][/tex]

This yields a resultant speed of approximately 213.4 miles per hour.

The direction \\(\theta\\) will be:

[tex]\[ \theta = \arctan\left(\frac{38}{210}\right) \][/tex]

Using a calculator, one finds that [tex]\(\theta\)[/tex] is approximately 10.3 degrees north of east.

Answer:  a)   2.27 g     and     b)  15384

Step-by-step explanation:

Given : An effervescent tablet has the following formula:

acetaminophen 325 mg,

calcium carbonate 280 mg,

citric acid 900 mg,

potassium bicarbonate 300 mg, and

sodium bicarbonate 465 mg.

a) When we add all quantities together , we get

The total weight of the ingredients in each tablet = [tex]325 +280+900+300+465=2270[/tex]

Since, 1 gram = 1000 mg

Then, [tex]1\ mg=\dfrac{1}{1000}\ g[/tex]

Now, [tex]2270\ mg=\dfrac{2270}{1000}\ g=2.27\ g[/tex]

∴ The total weight of the ingredients in each tablet = 2.27 g

b. 1 kg = 1000g and 1 g = 1000 mg

Then, 1 kg = [tex]1000\times1000=1000,000\ mg[/tex]

⇒ 5 kg = 5000,000 mg

Now, The number of  tablets could be made with a supply of 5 kg of acetaminophen will be :

[tex]\dfrac{5000000}{325}=15384.6153846\approx15384[/tex]

Hence, the number of  tablets could be made with a supply of 5 kg of acetaminophen= 15384

The total weight of the ingredients in the effervescent tablet is 2.27 g. With a supply of 5 kg of acetaminophen, you could produce approximately 15,385 tablets.

To answer the student's questions, we start by calculating the total weight of the tablet:
acetaminophen: 325 mg, calcium carbonate: 280 mg, citric acid: 900 mg, potassium bicarbonate: 300 mg, and sodium bicarbonate: 465 mg.
Adding all these quantities together gives a total of 2270 mg or 2.27 g per tablet.

Now for the second question, to find out how many tablets you can make from 5 kg of acetaminophen, we need to determine how much acetaminophen is in a single tablet. We know that each tablet contains 325 mg of acetaminophen, so if we have 5 kg of it, we first convert the 5 kg into milligrams (since the amount in each tablet is given in milligrams).
There are 1,000,000 milligrams in a kilogram, so 5 kg = 5 x 1,000,000 = 5,000,000 mg.
We then divide this total quantity by the amount of acetaminophen in each tablet: 5,000,000 mg / 325 mg/tablet = approximately 15,385 tablets.

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Answer:

[tex]\left\{11, 21\right\} \times \left\{1, 1.5, 2\right\} = \left\{ (11, 1), (11, 1.5), (11, 2), (21, 1), (21, 1.5), (21, 2)\right\}[/tex]

Step-by-step explanation:

The Cartesian product between two discrete sets, is given by all possible ordered pairs originated with the combinations of the elements of the two sets, thus the requested Cartesian product is:

[tex]\left\{11, 21\right\} \times \left\{1, 1.5, 2\right\} = \left\{ (11, 1), (11, 1.5), (11, 2), (21, 1), (21, 1.5), (21, 2)\right\}[/tex]

[tex]A = (11, 1)\\B = (11, 1.5)\\C = (11, 2)\\D = (21, 1)\\E = (21, 1.5)\\F = (21, 2)\\[/tex]

You can see the attached file

Answer: The required value would be 0.000013.

Step-by-step explanation:

Since we have given that

0.001 % of [tex]\dfrac{4}{3}[/tex]

As we know that

To remove the % sign we should divide it by 100.

Mathematically, it would be expressed as

[tex]\dfrac{0.001}{100}\times \dfrac{4}{3}\\\\=\dfrac{0.004}{300}\\\\=0.000013[/tex]

Hence, the required value would be 0.000013.

Answer:

The set of solutions is [tex]\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}[/tex]

Step-by-step explanation:

The augmented matrix of the system is [tex]\left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right][/tex].

We will use rows operations for find the echelon form of the matrix.

Now we solve for the unknown variables:

The system has a free variable, the the system has infinite solutions and the set of solutions is [tex]\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}[/tex]