Why does changing a subrtraction problem to an addition with the complement of 9 work

Answer:

The system will have no solution when [tex]k = -4[/tex] and [tex]h \neq 7.5[/tex].

Step-by-step explanation:

We can find these values by the Gauss-Jordan Elimination method.

The Gauss-Jordan elimination method is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

We have the following system:

[tex]-3x - 3y = h[/tex]

[tex]-4x + ky = 10[/tex]

This system has the following augmented matrix:

[tex]\left[\begin{array}{ccc}-3&-3&h\\-4&k&10\end{array}\right][/tex]

The first thing i am going to do is, to help the row reducing:

[tex]L_{1} = -\frac{L_{1}}{3}[/tex]

Now we have

[tex]\left[\begin{array}{ccc}1&1&-\frac{h}{3}\\-4&k&10\end{array}\right][/tex]

Now I want to reduce the first row, so I do:

[tex]L_{2} = L_{2} + 4L_{1}[/tex]

So:

[tex]\left[\begin{array}{ccc}1&1&-\frac{h}{3}\\0&k+4&10 - \frac{4h}{3}\end{array}\right][/tex]

From the second line, we have

[tex](k+4)y = 10- \frac{4h}{3}[/tex]

The system will have no solution when there is a value dividing 0, so, there are two conditions:

[tex]k+4 = 0[/tex] and [tex]10 - \frac{4h}{3} \neq 0[/tex]

[tex]k+4 = 0[/tex]

[tex]k = -4[/tex]

...

[tex]10 - \frac{4h}{3} \neq 0[/tex]

[tex]\frac{4h}{3} \neq 10[/tex]

[tex]4h \neq 30[/tex]

[tex]h \neq \frac{30}{4}[/tex]

[tex]h \neq 7.5[/tex]

The system will have no solution when [tex]k = -4[/tex] and [tex]h \neq 7.5[/tex].

Answer:

%82.5

Step-by-step explanation:

From point 1 we know that Moe´s grade just before taking the final exam represents 60% of the final grade. Then, using the information in the point 2 we can compute Moe´s final grade as follows:

[tex]FG=0.40*FE+0.60*0.45[/tex],

where FG is Moe´s Final Grade and FE is Moe´s final exam grade. Then,

[tex]\frac{ FG-0.60*0.45}{0.40}=FE[/tex].

So, in order to receive the passing grade average of 60% for the class Moe needs to obtain in his exam:

[tex]FE=\frac{ 0.60-0.60*0.45}{0.40}=0.825[/tex]

That is, he need al least %82.5 to obtain a passing grade.

Answer:

P(B) = 0.30

Step-by-step explanation:

This is a probability problem that can be modeled by a diagram of Venn.

We have the following probabilities:

[tex]P(A) = P_{A} + P(A \cap B) = 0.50[/tex]

In which [tex]P_{A}[/tex] is the probability that only A happens.

[tex]P(B) = P_{B} + P(A \cap B) = P_{B} + 0.15[/tex]

To find P(B), first we have to find [tex]P_{B}[/tex], that is the probability that only B happens.

Finding [tex]P_{B}[/tex]:

The problem states that P(A OR B) = 0.65. This is the probability that at least one of this events happening. Mathematically, it means that:

[tex]1) P_{A} + P(A \cap B) + P_{B} = 0.65[/tex]

The problem states that P(A) = 0.5 and [tex]P(A \cap B) = 0.15[/tex]. So we can find [tex]P_{A}[/tex].

[tex]P(A) = P_{A} + P(A \cap B)[/tex]

[tex]0.5 = P_{A} + 0.15[/tex]

[tex]P_{A} = 0.35[/tex]

Replacing it in equation 1)

[tex]P_{A} + P(A \cap B) + P_{B} = 0.65[/tex]

[tex]0.35 + 0.15 + P_{B} = 0.65[/tex]

[tex]P_{B} = 0.65 - 0.35 - 0.15[/tex]

[tex]P_{B} = 0.15[/tex]

Since

[tex]P(B) = P_{B} + P(A \cap B)[/tex]

[tex]P(B) = 0.15 + 0.15[/tex]

[tex]P(B) = 0.30[/tex]

Answer:

(a) [tex]\frac{dy}{(2y+1)}=tdt[/tex] (b) [tex]y=\frac{e^{t^2}+e^{2c}-1}{2}[/tex]

Step-by-step explanation:

(1) We have given [tex]\frac{dy}{dt}+ycost=0[/tex]

[tex]\frac{dy}{dt}=-ycost[/tex]

[tex]\frac{dy}{y}=-costdt[/tex]

Integrating both side

[tex]lny=-sint+c[/tex]

[tex]y=e^{-sint}+e^{-c}[/tex]

(2) [tex]\frac{dy}{dt}-2ty=t[/tex]

[tex]\frac{dy}{dt}=2ty+t[/tex]

[tex]\frac{dy}{dt}=t(2y+1)[/tex]

[tex]\frac{dy}{(2y+1)}=tdt[/tex]

On integrating both side  

[tex]\frac{ln(2y+1)}{2}=\frac{t^2}{2}+c[/tex]

[tex]ln(2y+1)={t^2}+2c[/tex]

[tex]2y+1=e^{t^2}+e^{2c}[/tex]

[tex]y=\frac{e^{t^2}+e^{2c}-1}{2}[/tex]

Answer:

[tex]8+27=17+18=35 cm=0.35 meter[/tex]

Step-by-step explanation:

[tex]8+27=35[/tex] cm

= [tex]17+18=35[/tex] cm as [tex]35-18=17[/tex] cm

Now as the final answer is in meters, so, we will convert 35 cm in meters.

100 cm = 1 meter

So, 35 cm = [tex]\frac{35}{100}=0.35[/tex] meters

Therefore, we can write the final expression as:

[tex]8+27=17+18=35 cm=0.35 meter[/tex]

Answer:

4:3

Step-by-step explanation:

You count up all the red marbles which equals 4 and put them on one side, then you add up all the rest of the marbles same color or not which equals 3 and put it on the other side of the 4

To find the probability, you need to calculate the number of ways to choose one Macintosh and one Windows computer from the given options and divide it by the total number of ways to choose two computers. The probability is 0.507.

To find the probability that the sample contains exactly one Windows machine and exactly one Macintosh machine, we can use the concept of combinations. There are a total of 30 computers, out of which 17 are Macintosh and 13 are Windows. The number of ways to choose one Macintosh and one Windows computer can be calculated by multiplying the number of ways to choose one Macintosh from 17 and the number of ways to choose one Windows from 13.

The number of ways to choose one Macintosh from 17 is C(17, 1) = 17 and the number of ways to choose one Windows from 13 is C(13, 1) = 13. Therefore, the total number of ways to choose one Macintosh and one Windows computer is 17 * 13 = 221.

The sample space is the total number of ways to choose two computers from 30, which is C(30, 2) = 435. So the probability of selecting exactly one Windows machine and exactly one Macintosh machine is 221 / 435 = 0.507.

Answer:

relative can take 2 tablets every six hours or 8 tablets a day without the amount being dangerous

Step-by-step explanation:

Given:

Amount of Tylenol per day that is dangerous = 2.3 g

1 g = 1000 mg

thus,

= 2.3 × 1000 mg

= 2300 mg

Amount of scored Tylenol tablets every six hours = 200 mg

Now,

for 6 hours intervals, total intervals in a day = [tex]\frac{\textup{24}}{\textup{6}}[/tex]  = 4

thus,

He takes Tylenol tablets 4 times a day

Now,

let x be the number of tablets taken in every interval

thus,

4x × 200 mg ≤ 2300

or

800x ≤ 2300

or

x ≤ 2.875

hence, relative can take 2 tablets every six hours or 8 tablets a day without the amount being dangerous

A person should take 2 tablets of 200mg Tylenol every six hours to keep the daily dose under the dangerous level of 2.3g.

The question is asking how many 200 mg tablets of Tylenol can a person consume every six hours (which is four times a day), while keeping the daily dose under 2.3g, to avoid a risk level that can be dangerous. The first step is to convert the maximum safe dose from grams to milligrams, because the dose per tablet is given in milligrams. 2.3 g equals 2300 milligrams.

Then, to find out the number of safe tablets per dose, you divide the total safe amount by the number of doses per day. So, 2300 milligrams divided by 4 equals 575 milligrams per dose. Last but not least, to find out the number of tablets, you should divide the amount per dose by the amount in each tablet: 575 divided by 200 equals about 2.875.

Since you cannot take a fraction of a tablet, the safest number of tablets to take every six hours would be 2.

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The domain of the function represented in the graph is 30 SXS 60 or 30 to 60. Hence option C is correct.

Given that,

Five-year-old students at an elementary school were involved.

They were given a 30-yard head start in a race.

The graph represents the distance run by the average student in 30 seconds.

The graph is related to the age of the runner.

Since we can see that,

The graph starts from 30 yards and ends at 60 yards

Therefore,

The domain of the function represented in the graph is 30 SXS 60 or 30 to 60, which is option C.

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Answer:

(a) Set A = {1,2,3}

    Set B = {1,2,4,5}

(b) Set A Ç B = {1,2}

     Set A e B = {1,2}

Step-by-step explanation:

As per the question,

Given data :

A ∪ B = read as A union B = {1,2,3,4,5}

A ∩ B = read as A intersection B =  {1,2}

(a) An example of sets A and B such that A ∩ B = {1,2} and A U B = {1,2,3,4,5).

So, first draw the Venn-diagram, From below Venn diagram, One of the possibility for set A and set B is:

Set A = {1,2,3}

Set B = {1,2,4,5}

(b) An example of sets A and B such that A Ç B and A e B,

Set A Ç B read as common elements of set A in Set B.

Therefore,

Set A Ç B = {1,2}

Set A e B implies that which element/elements of A is/are present in set B.

Therefore,

Set A e B = {1,2}

Answer:  The proof is done below.

Step-by-step explanation:  Given that A is a 3 x 3 matrix such that det (A) = 9.

We are to prove the following :

[tex]det(3A^{-1})=3.[/tex]

For a non-singular matrix B of order n, we have two two properties of its determinant :

[tex](i)~det(B^{-1})=\dfrac{1}{det(B)},\\\\\\(ii)~det(kB)=k^ndet(B),~\textup{k is a scalar.}[/tex]

Therefore, we get

[tex]det(A^{-1})=\dfrac{1}{det(A)}=\dfrac{1}{9},[/tex]

and so,

[tex]det(3A^{-1})~~~~~~~[\textup{since A is of order 3}]\\\\=3^3det(A^{-1})\\\\=27\times\dfrac{1}{9}\\\\=3.[/tex]

Hence proved.

Answer:

The solutions of the quadratic equation are [tex]x_{1} = \frac{5 + \sqrt{13}}{6}, x_{2} = \frac{5 - \sqrt{13}}{6}[/tex]

Step-by-step explanation:

This is a second order polynomial, and we can find it's roots by the Bhaskara formula.

Explanation of the bhaskara formula:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

For this problem, we have to find [tex]x_{1} \text{and} x_{2}[/tex].

The polynomial is [tex]3x^{2} - 5x +1[/tex], so a = 3, b = -5, c = 1.

Solution

[tex]\bigtriangleup = b^{2} - 4ac = (-5)^{2} - 4*3*1 = 25 - 12 = 13[/tex]

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{-(-5) + \sqrt{13}}{2*3} = \frac{5 + \sqrt{13}}{6}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a} = \frac{-(-5) - \sqrt{13}}{2*3} = \frac{5 - \sqrt{13}}{6}[/tex]

The solutions of the quadratic equation are [tex]x_{1} = \frac{5 + \sqrt{13}}{6}, x_{2} = \frac{5 - \sqrt{13}}{6}[/tex]

Answer:

Ans. Effective annual rate=1.8928%

Annual Compound semi-annually=1.8839%

Step-by-step explanation:

Hi, this is the formula to find the effective annual rate for this zero-coupon bond.

[tex]EffectiveAnnualRate=\sqrt[n]{\frac{FaceValue}{Price} } -1[/tex]

n= years to maturity

That is:

[tex]EffectiveAnnualRate=\sqrt[8]{\frac{50,000}{43,035} } -1=0.018928[/tex]

Means that the effective interest rate is 1.8928% effective annual

Now, let´s find the compound interest rate.

First, we have to turn this rate effective semi-annually

[tex]Semi-AnnualRate=(1+0.018928)^{\frac{1}{2} }  -1=0.00942[/tex]

0.942% effective semi annual

To turn this into a semi-annual, compounded semi-annually, we just have to multiply by 2, so we get.

1.8839% compounded semi-annually

Best of luck

Answer:

[tex]\frac{7}{6}[/tex]

Step-by-step explanation:

[tex]-4\frac{1}{2} + 5\frac{2}{3} =[/tex]

For the first term you have to multiply 2x(-4) and add 1, for the second term you have to multiply 3x5 and add 2.

[tex]\frac{2(-4)+1}{2} + \frac{3(5)+2}{3} =[/tex]

[tex]-\frac{9}{2} +\frac{17}{3} =[/tex]

Now you need to find the lowest common multiple between the denominators, just cross multiply as it is shown:

[tex]-\frac{9}{2} (\frac{3}{3} )+\frac{17}{3} (\frac{2}{2} )=[/tex]

[tex]-\frac{27}{6} +\frac{34}{6} = \frac{7}{6}[/tex]

finally you get the result by doing a substraction = 7/6, or 1[tex]\frac{1}{6}[/tex]

Answer:

Turning point has coordinates [tex]\left(\dfrac{27}{13},\dfrac{8}{13}\right)[/tex]

Step-by-step explanation:

Gandalf the Grey started in the Forest of Mirkwood at a point P(3, 0) and began walking in the direction of the vector [tex]\vec{v}=-3i+2j.[/tex] The coordinates of the vector v are (-3,2). Then he changed the direction at a right angle, so he was walking in the direction of the vector [tex]\vec{u}=2i+3j[/tex] (vectors u and v are perpendicular).

Let B(x,y) be the turning point. Find vectors PB and BQ:

[tex]\overrightarrow{PB}=(x-3,y-0)\\ \\\overrightarrow {BQ}=(5-x,5-y)[/tex]

Note that vectors v and PB and vectors u and BQ are collinear, so

[tex]\dfrac{x-3}{-3}=\dfrac{y}{2}\\ \\\dfrac{5-x}{2}=\dfrac{5-y}{3}[/tex]

Hence

[tex]2(x-3)=-3y\Rightarrow 2x-6=-3y\\ \\3(5-x)=2(5-y)\Rightarrow 15-3x=10-2y[/tex]

Now solve the system of two equations:

[tex]\left\{\begin{array}{l}2x+3y=6\\ -3x+2y=-5\end{array}\right.[/tex]

Multiply the first equation by 3, the second equation by 2 and add them:

[tex]3(2x+3y)+2(-3x+2y)=3\cdot 6+2\cdot (-5)\\ \\6x+9y-6x+4y=18-10\\ \\13y=8\\ \\y=\dfrac{8}{13}[/tex]

Substitute it into the first equation:

[tex]2x+3\cdot \dfrac{8}{13}=6\\ \\2x=6-\dfrac{24}{13}=\dfrac{54}{13}\\ \\x=\dfrac{27}{13}[/tex]

Turning point has coordinates [tex]\left(\dfrac{27}{13},\dfrac{8}{13}\right)[/tex]

The coordinates of the point where Gandalf makes the turn are (5, 5).

To find the point where Gandalf makes a right angle turn, we need to find the intersection of the line formed by the vector v and the line connecting points P and Q. The equation of the line formed by the vector v is given by y = 2x - 3. The equation of the line connecting points P and Q is given by y = x. To find the intersection point, we can solve these two equations simultaneously. Substituting y = 2x - 3 into y = x, we get x = 5. Substituting x = 5 into y = x, we get y = 5. Therefore, the coordinates of the point where Gandalf makes the turn are (5, 5).

Answer:

a) Mode: 2 Median: 3 Mean: 4.6

b) Mode: 7 Median: 8 Mean: 9.6

c) Just added 5 to values. General below.

Step-by-step explanation: 2, 2, 3, 6, 10

a) Mode: 2 (Most apperances)

Median: 3 (odd data, middle number)

Mean: (2+2+3+6+10)/5 = 23/5 = 4.6

b) + 5

Data: 7,7,8,11,15

Mode: 7 (Most apperances)

Median: 8 (odd data, middle number)

Mean: (7+7+8+11+15)/5 = 48/5 = 9.6

c) The results from (b) is (a) + 5

In general: Let's add x to the same data provided:

2+x, 2+x, 3+x, 6+x, 10+x,

For the mode, it does not matter, the number with most apperances will continue to be the mode + x

For the median, same thing. It is just the median + x

For the mean, same thing. For the set of 5 numbers:

(2+x + 2+x + 3+x + 6+x + 10+x)/5 =

(23+5x)/5

23/5 + 5x/5 =

23/5 + x

For example, If it was 6 numbers, we would add 6 times that number and divide it by 6, adding x to the mean.

To compute the mode, median, and mean of a data set, count the frequency of each number, arrange the data in order, and find the middle value. Adding the same constant to each data value affects the mean but does not change the mode or median.

To compute the mode, median, and mean of the data set {2, 2, 3, 6, 10}, we can follow these steps:

After adding 5 to each data value, the new data set becomes {7, 7, 8, 11, 15}.

In general, when the same constant is added to each data value in a set, the mode remains unchanged, the median remains unchanged, and the mean is affected by adding the constant to each value. The mean increases when the constant is positive and decreases when the constant is negative.

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Answer:

182 of these adults did not do any of these three activities last Friday night.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the adults that watched TV

-The set B represents the adults that hung out with friends.

-The set C represents the adults that ate pizza

-The set D represents the adults that did not do any of these three activities.

We have that:

[tex]A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)[/tex]

In which a is the number of adults that only watched TV, [tex]A \cap B[/tex] is the number of adults that both watched TV and hung out with friends, [tex]A \cap C[/tex] is the number of adults that both watched TV and ate pizza, is the number of adults that both hung out with friends and ate pizza, and [tex]A \cap B \cap C[/tex] is the number of adults that did all these three activies.

By the same logic, we have:

[tex]B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)[/tex]

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

This diagram has the following subsets:

[tex]a,b,c,D,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)[/tex]

There were 510 adults suveyed. This means that:

[tex]a + b + c + D + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 510[/tex]

We start finding the values from the intersection of three sets.

Solution:

43 watched TV, hung out with friends, and ate pizza:

[tex]A \cap B \cap C = 43[/tex]

47 hung out with friends and ate pizza, but did not watch TV:

[tex]B \cap C = 47[/tex]

29 watched TV and hung out with friends, but did not eat pizza:

[tex]A \cap B = 29[/tex]

28 watched TV and ate pizza, but did not hang out with friends:

[tex]A \cap C = 28[/tex]

161 ate pizza

[tex]C = 161[/tex]

[tex]C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)[/tex]

[tex]161 = c + 28 + 47 + 43[/tex]

[tex]c = 43[/tex]

196 hung out with friends

[tex]B = 196[/tex]

[tex]196 = b + 47 + 29 + 43[/tex]

[tex]b = 77[/tex]

161 watched TV

[tex]A = 161[/tex]

[tex]A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)[/tex]

[tex]161 = a + 29 + 28 + 43[/tex]

[tex]a = 61[/tex]

How may 18-24 year olds did not do any of these three activities last Friday night?

We can find the value of D from the following equation:

[tex]a + b + c + D + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 510[/tex]

[tex]61 + 77 + 43 + D + 29 + 28 + 47 + 43 = 510[/tex]

[tex]D = 510 - 328[/tex]

[tex]D = 182[/tex]

182 of these adults did not do any of these three activities last Friday night.

To find the number of 18-24 year olds who did not do any of the three activities last Friday night, we can use the principle of inclusion-exclusion. By subtracting the number of people who did at least one of the activities from the total number of participants, we find that 455 individuals did not participate in watching TV, hanging out with friends, or eating pizza.

To find the number of 18-24 year olds who did not do any of the three activities (watch TV, hang out with friends, eat pizza), we need to subtract the number of people who did at least one of these activities from the total number of participants. We can use the principle of inclusion-exclusion to solve this problem.

Let's define:

From the given information, we know:

To find the number of people who did not do any of these activities, we can use the formula:

n(A' ∩ B' ∩ C') = n(U) - n(A) - n(B) - n(C) + n(A ∩ B) + n(A ∩ C) + n(B ∩ C) - n(A ∩ B ∩ C)

Substituting the known values, we have:

n(A' ∩ B' ∩ C') = 510 - 161 - 196 - 161 + 28 + 29 + 47 - 43

n(A' ∩ B' ∩ C') = 455

Therefore, there were 455 18-24 year olds who did not do any of the three activities last Friday night.

Answer: 120

Step-by-step explanation:

The total number of digits from 1 to 9 = 10

The number of digits from less than 5 (0,1,2,3,4)=5

Since repetition is not allowed so we use Permutations , then the number of 3-digit different codes will be formed :-

[tex]^5P_3=\dfrac{5!}{(5-3)!}=\dfrac{5\times4\times3\times2!}{2!}=5\times4\times3=60[/tex]

The number of digits from greater than 4 (5,6,7,8,9)=5

Similarly, Number of 3-digit different codes will be formed :-

[tex]^5P_3=60[/tex]

Hence, the required number of 3-digit different codes = 60+60=120

Answer:

Step-by-step explanation:

Write expressions for the number of students in each major. Then write the equation needed to relate them the way the problem statement says they are related.

For year y, the number of students in each major is ...

1) Engineering is twice Business:

  120 +22y = 2(105 -4y) . . . . . Engineering is double Business in year y

  120 +22y = 210 -8y . . . . . . . eliminate parentheses

  120 +30y = 210  . . . . . . . . . . add 8y

  4 + y = 7 . . . . . . . . . . . . . . . . divide by 30

  y = 3  . . . . . . . . subtract 4

In 3 years there will be 2 times as many students majoring in Engineering than in Business.

__

2) Engineering is twice Biology:

  120 +22y = 2(98 +6y) . . . . Engineering is double Biology in year y

  120 +22y = 196 +12y . . . . . eliminate parentheses

  120 +10y = 196 . . . . . . . . . . subtract 12y

  10y = 76 . . . . . . . . . . . . . . . .subtract 120

  y = 7.6 . . . . . . divide by 10

In 8 years there will be 2 times as many students majoring in Engineering than in Biology.

Answer:

Step-by-step explanation:

We know that multiplication product of two given positive real number will always be positive real number and if one of the real number is negative, the multiplication product will always be negative.

so for the given condition, if [tex]x > 0[/tex] and [tex]y > 0[/tex], [tex]x[/tex] and [tex]y[/tex] are both positive real numbers

hence their multiplication product [tex]xy[/tex] will also be a positive number.

∴ [tex]xy > 0[/tex]

Answer:  2399760

Step-by-step explanation:

The concept we use here is Partial derangement.

It says that for m things , the number of ways to arrange them such that k things are not in their fixed position is given by :-

[tex]m!-^kC_1(m-1)!+^kC_2(m-2)!-^kC_3(m-3)!+........[/tex]

Given digits : 0,1,2,3,4,5,6,7,8,9

Prime numbers = 2,3,5,7

Now  by Partial derangement the number of ways to arrange 10 numbers such that none of 4 prime numbers is in its original position will be :_

[tex]10!-^4C_1(9)!+^4C_2(8)!-^4C_3(7)!+^4C_4(6)!\\\\=3628800-(4)(362880)+\dfrac{4!}{2!2!}(40320)-(4)(5040)+(1)(720)\\\\=3628800-1451520+241920-20160+720\\\\=2399760[/tex]

Hence, the number of  ways can the digits 0,1,2,3,4,5,6,7,8,9 be arranged so that no prime number is in its original position = 2399760

Answer:

Domain : D{-∞,∞} the reals.

Step-by-step explanation:

The function is plotted in the image.

[tex]  f(x) = -3.15 * x + 723.45 [tex]

the linear functions usually have a domain from - infinite to infinite, the domain when is a piece wise function or discontinuous, the domain is defined in the pieces where is defined.

In this case there is no restriction so the function is continuous.

Step-by-step explanation:

.454 kilograms= 1 pound.

Multiply .454 by 160

4.54

160

--------

000

2724 0<--Place marker

45400<--Double Place Marker

- - - - - - - -

72640 <-- Add

To find decimal point, count decimal place (Number of digits after the decimal on both numbers you multiply together) In this case, it's 2 ( 5 and 4 in 4.54) So, you count two spaces from right to left in your answer and tah dah!

72.640 (Zero isn't needed- just a placemarker)

Hope I was helpful :)

Answer:

The horsepower required is 235440 watt.

Step-by-step explanation:

To find : What horsepower is required to lift an 8,000 pound aircraft six feet in two minutes?

Solution :

The horsepower formula is given by,

[tex]W=\frac{mgh}{t}[/tex]

Where, W is the horsepower

m is the mass m=8000 pound

g is the gravitational constant g=9.81

t is the time t= 2 minutes

h is the height h=6 feet

Substitute all values in the formula,

[tex]W=\frac{8000\times 9.81\times 6}{2}[/tex]

[tex]W=\frac{470880}{2}[/tex]

[tex]W=235440[/tex]

Therefore, The horsepower required is 235440 watt.

Answer:

A 1.4% of the total connectors are expected to fail during the warranty period.

Step-by-step explanation:

Let's assume a population of 1000 connectors (to make the math easiest) and let's analize the dry connectors.  

Of the 1000 connectors, 900 are kept dry. and of that number, 9 are the ones that fails during the warranty period.  (90% of 1000 is 900. 1% of 900 is 9)

Of the 1000 connectors, 100 are wet. And of that number, 5 are connectors that will fail during the warranty period. (10% of 1000 is 100, and 5% of 100 is 5)

So overall we have 14 connectors that will fail from 1000 connectors.

That is a 1.4% of the total samples.

Answer

-16

Step By Step explanation

Answer:

[tex] - 12 - 3 \times ( - 8 + ( { - 4)}^{2} - 6) + 2[/tex]

[tex] - 12 - 3 \times ( - 8 + 16 - 6) + 2[/tex]

[tex] - 12 - 3 \times (8 - 6) + 2[/tex]

[tex] - 12 - 3 \times 2 + 2[/tex]

[tex] - 12 - 6 + 2[/tex]

[tex] - 12 - 4[/tex]

[tex] - 16[/tex]

Answer:

a) Yes.

b) Yes.

Step-by-step explanation:

Meredith and Hillary both want coffe, but they don't know if the other two people do, therefore they can't know if everyone want coffee. If they didn't want coffee, their answer would have been just "no".

Aly knows that she doesn't want coffee, therefore she knows that not everyone wants coffee.

Hillary and Meredith said 'I don't know' which implies they don't know if everyone wants coffee because they themselves do not want it. Aly confirmed that not everyone wants coffee. Therefore, neither Hillary nor Meredith got a coffee.

We have a logical puzzle where Hillary, Meredith, and Aly are deciding whether they want coffee. The key to solving this puzzle is understanding the implications of their statements to the waiter's question: "Does everyone want coffee?"

Hillary says, "I don't know." This means Hillary cannot be sure that everyone wants coffee, so there are two possibilities: either she does not want coffee or she doesn't know the preferences of the others. Meredith also responds with "I don't know," implying the same possibilities for her.

Finally, Aly states, "Not everyone wants coffee." This is the definitive answer that tells us at least one person does not want coffee. Since Aly knows for sure that not everyone wants coffee, it implies that either she does not want coffee herself or knows of someone else who doesn’t. Given that Hillary and Meredith both said they did not know, they could not have communicated their preference to Aly.

Therefore:

Answer:

136 units

65x - 8840

Step-by-step explanation:

Given,

The production cost function is,

[tex]C(x) = 195x + 8840[/tex]

Revenue function,

[tex]R(x)=260x[/tex]

So, profit would be,

P(x) = Revenue - cost

= 260x - 195x - 8840

= 65x - 8840

In break even condition,

Profit, P(x) = 0

65x - 8840 = 0

65x = 8840

⇒ x = 136.

Hence, the break even quantity is 136 units.

The break-even quantity is 1360 units, where the revenue equals the cost. The profit function is given by P(x) = R(x) - C(x).

To find the break-even quantity, we need to find the point where the revenue function equals the production cost function. So we set R(x) equal to C(x) and solve for x:

260x = 195x + 88408

Simplifying the equation, we get:

65x = 88408

x = 1360

Now we analyze the break-even quantity. The break-even quantity is the point at which the firm's revenue equals its cost. In this case, it occurs at 1360 units. At this quantity, the firm's total revenue will equal its total cost, resulting in zero profit.

To find the profit function, we subtract the cost function C(x) from the revenue function R(x). The profit function can be expressed as:

P(x) = R(x) - C(x)

Answer:

Age of Alice=25 years

Age of Jane=20 years

Step-by-step explanation:

We are given that the age of Jane is 80 % of the age Alice.

We have to find the age of Jane and Alice.

Let x be the age of Alice

According to question

Age of Jane=80% of Alice=80% of x=[tex]\frac{80}{100}\times x=\frac{4x}{5}[/tex]

[tex]x+\frac{4x}{5}=45[/tex]

[tex]\frac{5x+4x}{5}=45[/tex]

[tex]\frac{9x}{5}=45[/tex]

[tex]x=\frac{45\times 5}{9}=25[/tex]

Age of Alice=25 years

Age of Jane=[tex]\frac{4}{5}\times 25=20 years[/tex]

Age of Jane=20 years

Answer:

62 inches

Step-by-step explanation:

Let x be the height ( in inches ) of Ivan,

∵ Marcia is 5 inches shorter than Ivan,

height of Marcia = x - 5,

Marcia is  twice as tall as Sally-Jo,

height of sally-jo = [tex]\frac{x-5}{2}[/tex]

Mom is 2 inches taller than Ivan.

⇒ height of mom = x + 2,

Mom is 3 inches shorter than Dad,

height of dad = x + 2 + 3 = x + 5,

So, mean height of family is,

[tex]\frac{x+x-5+\frac{x-5}{2}+x+2+x+5}{5}[/tex]

[tex]=\frac{2x+2x-10+x-5+2x+4+2x+10}{10}[/tex]

[tex]=\frac{9x-1}{10}[/tex]

According to the question,

x + 5 = 74 ( 1 ft = 12 in )

x = 69

Hence, mean height of the family = [tex]\frac{9\times 69-1}{10}[/tex]

[tex]=\frac{620}{10}[/tex]

= 62 inches