2. According to a well-known legend, the game of chess was invented many centuries ago in northwestern India by a certain sage. When he took his invention to his king, the king liked the game so much that he offered the inventor any reward he wanted. The inventor asked for some grain to be obtained as follows: just a single grain of wheat was to be placed on the first square of the chessboard, two on the second, four on the third, eight on the fourth, and so on, until all 64 squares had been filled. If it took just 1 second to count each grain, how long would it take to count all the grain due to him?

Answer:

Option D.

Step-by-step explanation:

Arianna kicks a soccer ball into the air with an initial velocity = 42 feet per second

If the starting height of the ball is 0 feet then we have to find the approximate maximum height the soccer ball attached.

Since we know vertical motion is represented by

v² = u² - 2gh

Where v = final velocity of the object

u = initial velocity of the object

g = gravitational force

h = h = maximum height achieved by the object

Here v = 0, u = 42 feet per second and g = 32 feet per second²

Now we plug in these values in the formula

0 = (42)² - 2(32)(h)

1764 = 64h

[tex]h=\frac{1764}{64}[/tex]

h = 27.56 feet

  ≈ 27.60 feet

Therefore, maximum height achieved by the soccer ball is 27.6 feet.

Option D is the answer.

Answer:

Option D is 2.76 ft

Step-by-step explanation:

Its correct

Answer:

Step-by-step explanation:

In order to solve the inequality, follow the simple steps:

–3(5y – 4) ≥ 17 .

Dividing both sides with -3:

5y - 4 ≤ -17/3 (the sign of the inequality becomes opposite whenever a negative number is either multiplied or divided on both the sides of the inequality).

Adding 4 on both sides:

5y ≤ -5/3

Dividing 5 on both sides:

y ≤ -1/3.

This shows that all the values of y less than and equal to -1/3 satisfy the inequality.

The number line has been attached. Since it involves ≤ sign, therefore, a filled circle will be used to plot the inequality. Less than means that all the values on the left hand side of the number line will be included. This is denoted with an arrow (see the diagram)!!!

Answer with explanation:

 It is given that, abc=1

[tex]\rightarrow \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}\\\\\rightarrow \frac{b}{b+ab+1}+\frac{c}{c+bc+1}+\frac{a}{a+ac+1}\\\\abc=1\\\\\rightarrow \frac{b}{b+ab+abc}+\frac{c}{c+bc+abc}+\frac{a}{a+ac+abc}\\\\\rightarrow \frac{1}{1+a+ac}+\frac{1}{1+b+ab}+\frac{1}{1+c+bc}\\\\\rightarrow \frac{1}{abc+a+ac}+\frac{1}{1+b+ab}+\frac{1}{1+c+bc}\\\\\rightarrow \frac{1+a}{a(bc+1+c)}+\frac{c}{c+bc+1}\\\\\rightarrow\frac{1+a+ac}{a(bc+1+c)}\\\\\rightarrow\frac{1+a+ac}{abc+a+ac)}\\\\\rightarrow\frac{1+a+ac}{1+a+ac)}\\\\=1[/tex]

Hence proved.

Answer:

ABC=1

Step-by-step explanation:

Answer:

42 in

Step-by-step explanation:

108 in = 2l + 2w

l = 12 in

108 = 24 + 2w

84 = 2w

w = 42

The width is 21 inches, leading to a length of 33 inches, which corresponds to option c.

To find the length of the rectangular poster, we will use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width. According to the question, we have a perimeter P of 108 inches and the length is 12 inches greater than the width. If we let w represent the width, then the length can be represented as w + 12. Plugging into the perimeter formula we get: 108 = 2(w + 12) + 2w.

Now, let's solve for w:

108 = 2w + 24 + 2w

108 = 4w + 24

108 - 24 = 4w

84 = 4w

w = 84 / 4

w = 21 inches

Now that we have the width, we can find the length by adding 12 inches:

Length = w + 12

Length = 21 + 12

Length = 33 inches

Therefore, the length of the poster is 33 inches, which corresponds to option c.

Answer: y(x) = [tex]C_{1} e^{x} + C_{2} e^{\frac{-x}{2} }[/tex]

Step-by-step explanation:

2y ′′ − y ′ − y = 0

The characteristic equation is:

[tex]2r^{2} - r - 1 = 0[/tex]

[tex]2r^{2} - 2r + r - 1 = 0[/tex]

2r(r-1) + 1(r-1) = 0

(r-1)(2r+1) = 0

[tex]r_{1} = 1 , r_{2} = \frac{-1}{2}[/tex]

∴ there are two distinct roots

so the general equation is as follows:

y(x) = [tex]C_{1} e^{r_{1}x } + C_{2} e^{r_{2}x }[/tex]

y(x) = [tex]C_{1} e^{x} + C_{2} e^{\frac{-x}{2} }[/tex]

Answer:

g(-4) = -4

g(-2) = 1

g(1) = -4

Step-by-step explanation:

The value of the given function is -4 for all values of x other than -2 and 1 if x=-2

So,

For x=-4 the value of function will be -4.

g(-4) = -4

For x=-2

The value of function is -2.

g(-2) = 1

And for x=1, the value will be -4.

g(1) = -4 ..

Answer:

0.7564

Step-by-step explanation:

Let X be the event of watching a rented video at least once during a week,

Given,

The probability of watching a rented video at least once during a week was, p = 0.75,

So, the probability of not watching a rented video at least once during a week was, q = 1 - p = 0.25,

Binomial distributive formula,

[tex]P(x)=^nC_x p^x q^{n-x}[/tex]

Where,

[tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]

Hence, the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week,

P(X ≥ 5) = P(X=5) + P(X=6 )+ P(X=7)

[tex]=^7C_5 0.75^5 0.25^{7-5}+^7C_6 0.75^6 0.25^{7-6}+^7C_7 0.75^7 0.25^{7-7}[/tex]

[tex]=21 (0.75)^5 (0.25)^2 + 7 (0.75)^6 0.25 + 0.75^7[/tex]

[tex]=0.756408691406[/tex]

[tex]\approx 0.7564[/tex]

The probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week is 0.3015.

The probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week can be calculated using the binomial probability distribution formula:

P(X ≥ k) = 1 - P(X < k)

where X is the number of teenagers who watched a rented movie at least once, k is the minimum number of teenagers (5 in this case), and P(X < k) is the probability that less than k teenagers watched a rented movie at least once.

In this case, the probability that a randomly selected teenager watched a rented video at least once during a week is 0.75. Therefore, the probability that a randomly selected teenager did not watch a rented video at least once is 1 - 0.75 = 0.25.

Using the binomial probability distribution formula, we can calculate the probability that less than 5 teenagers watched a rented movie at least once:

P(X < 5) = C(7, 0) * (0.25)^0 * (0.75)^7 + C(7, 1) * (0.25)^1 * (0.75)^6 + C(7, 2) * (0.25)^2 * (0.75)^5 + C(7, 3) * (0.25)^3 * (0.75)^4 + C(7, 4) * (0.25)^4 * (0.75)^3

where C(n, r) is the number of combinations of n items taken r at a time:

C(n, r) = n! / (r! * (n-r)!)

Substituting the values and evaluating the expression, we get:

P(X < 5) = 0.698486328125

Therefore, the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week is:

P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.698486328125 = 0.301513671875

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Answer:$2.7 dollars per piece

Step-by-step explanation: Divide 113.40 by 42

$2.7 per piece is the answer.

$113.40 / 42 piece set of stainless steel = $2.7

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer: Slope would be,

[tex]-\frac{x^2}{y^2}[/tex]

Step-by-step explanation:

Here, the given curve,

[tex]x^3 + y^3=C^3[/tex]

[tex]\implies x^3 + y^3 - C^3=0[/tex]

In Barrow's method,

Steps are as follows,

Step 1 : put, x = x - e, y = y - a

[tex](x-e)^3 + (y-a)^3 - C^3=0[/tex]

[tex]x^3-3x^2e+3xe^2-e^3+y^3-3y^2a+3ya^2-a^3+C^3=0[/tex]

Step 2 : Reject terms which do not contain a or e,

[tex]-3x^2e+3xe^2-e^3-3y^2a+3ya^2-a^3=0[/tex]

Step 3 : Reject all terms in which a or e have exponent greater than 1,

[tex]-3x^2e-3y^2a=0[/tex]

Step 4 : Find the ratio of a : e,

[tex]-3y^2a=3x^2e[/tex]

[tex]\implies \frac{a}{e}=-\frac{x^2}{y^2}[/tex]

Hence, the slope of the given curve is [tex]-\frac{x^2}{y^2}[/tex]

Answer:

We need to put $801.88 amount in the bank.

Step-by-step explanation:

given that

t=3 yr

Need amount $850 after 3 yr so P= $850

Interest rate=2%

We know that for simple interest

[tex]P=A\left(1+\dfrac{rt}{100}\right)[/tex]

Where r is the Interest rate,t is the time,A is the present amount and P is principle amount after t time.

Here given that  P= $850

So now putting the values

[tex]850=A\left(1+\dfrac{2\times 3}{100}\right)[/tex]

So A=$801.88

We need to put $801.88 amount in the bank.

Answer:

To answer you question, we need the confidence internals formula, μ±Zc*(σ/[tex]\sqrt{N}[/tex]); N is the 20 psychology students, 0.5 the desviation standar and 4.3 is the medium based on national data, every fact in years.

Step-by-step explanation:

You need to consult the Zc value, you can find this table attached in this question; for 95%, we have a Zc value of 1.96.

Next step replace values: 4.3±1.96*(0.5/[tex]\sqrt{20}[/tex]) = 4.3±0.22 (rounding the result)

So, the confidence interval are:

4.08cm≤X≤4.52cm

Answer:

=SUM(C2:C4, C7)

Step-by-step explanation:

In excel 'C' represent the cell ( intersection of row and column ),

Also, '=sum( )' represents the function of addition in the excel,

Also, when we operate all consecutive cells from [tex]Cn[/tex] to [tex]Cm[/tex]

Then under the function formula we write [tex]Cn:Cm[/tex]

And, when we operate a cell [tex]Cn[/tex] with non consecutive cell [tex]Cl[/tex]

Then under the function formula we write [tex]Cn, Cl[/tex]

Hence, C2+C3+C4+C7 can be written as,

=SUM(C2:C4, C7)

Answer:

a. 50%

b. 33%  

c. 17% (I'm assuming the exercise is wrong and it has to say "white" instead of "red", because if not is the same as b.)

d. 67%

Step-by-step explanation:

a. We have a total of 18 balls, 13 are red and 5 are white. They are numbered from 1 to 18. In this case, we don't care about the color of the ball, we just need it to be not even. We have to count how many not even numbers are between 1 and 18, that is 9. So, the chances of getting a ball not even numbered are 9 in 18, that's

[tex]\frac{9}{18}*100=50\%[/tex]

b. Now we do care about the color of the ball. The red balls are numbered from 1 to 13, so we have 6 balls even numbered. That makes the chances 6 in 18 (we still have 18 in total), that's

[tex]\frac{6}{18}*100=33\%[/tex]

c. (I'm assuming the exercise is wrong and it has to say "white" instead of "red", because if not is the same as b.)

The white balls are numbered from 14 to 18, so we have 3 balls even numbered. That makes the chances 3 in 18,

[tex]\frac{3}{18}*100=17\%[/tex]

d. Let's notice that "the ball is neither red or even numbered" is the complement (exactly the opposite) of "the ball is red and even numbered", that means  

100% = Probability (ball red and even numbered) + Probability (ball neither red or even numbered)

So, Probability (ball neither red or even numbered) = 100% - Probability (ball red and even numbered) = 100% - 33% = 67%

Answer:

2 h 16 min 23 sec

Step-by-step explanation:

Hello

the time is expressed in the sexadecimal system, which uses the number 60 as an arithmetic base,hence

1 min=60 sec

1 hora =60  min

Now, we have

[tex](8 min + 31 sec)*17=136 min +527 sec\\\\\\we\ need\ to\ convert\ this\ in\ our\ base\ 60\, using\ a\ rule\ o\ three\\\\ 60 min=1\ hour\\136 min=x ?\\\\x=\frac{ 136 h}{60}\\ x=2.26 hours\\\\[/tex]

we take the whole part as an hour, and the decimal part is multiplied by 60 to get minutes

Step 1

[tex]8min*17=136 min =2.26 h\\\\2.26h = 2\ h + 0.26h(\frac{60 min}{1 h}) \\2.26h =2h+15.6 min\\\\[/tex]

we repeat the procedure to leave the minutes as a whole part

[tex]2.26\ h =2\ h+15\ min + 0.6\ min*(\frac{60 \sec}{1 m} )\\2.26\ h =2\ h\ 15\ min\ 36\ sec[/tex]

Step 2

[tex]\\527\s*(\frac{1 min}{ 60\ sec})=8.78\ min\\ \\8.78\ min= 8\min\0.78\ min\\8.78\ min=8\ min\ 0.78\min(\frac{60\ seg}{min})\\8.78\min=8\ min \ 47\ sec\\\\now, add\\\\8 min *17 =2\ h\ 15\ min\ 36\ sec\\31 sec *17 =8\ min \ 47\ sec\\(8\ min\ 31\ sec)*17=2\ h\ 15\ min\ 83\ sec\\83 s(\frac{1 min}{60 sec})=1.38 min\\1.38\ min\ =1\ min\ 0.38\ min*(\frac{60 sec}{1\ min})\\1.38\ min=1\min\ 23 s.\\( 8min 31 sec)*17=2 h 16 min 23 sec[/tex]

Have a great day

Answer:

see below

Step-by-step explanation:

a

y = 2x -3

Standard form is Ax + By =C  where A is a positive integer and B and C are integers

Subtract 2x from each side

y-2x = 2x-2x -3

-2x+y = -3

We want A to be positive

Multiply each side by -1

2x -y = 3

This is in standard form

b

y = 2/3 x -7

Subtract 2/3x from each side

y-2/3x = 2/3x-2/3x -7

-2/3x+y = -7

We want A to be positive integer

Multiply each side by -3

-3*(-2/3x+y) = -7*-3

2x -3y = 21

c

y = -3x +1/2

Add 3x to each side

3x +y = -3x+3x +1/2

3x+y = 1/2

Multiply each side by 2

2(3x+y) = 1/2*2

6x+2y = 1

Answer:

[tex]\frac{3}{28}[/tex]

Step-by-step explanation:

Te meaning of without replacement is once the ball is picked from the stock it cannot be put back

Hre there are total 8 balls and 3 white balls

probability of picking 1st white is [tex]\frac{3}{8}[/tex]

now only 2 white and total is 7( one ball has already been picked)

therefore probability of picking 2nd white ball is [tex]\frac{2}{7}[/tex]

both the action are independent events

therefore, probability of picking 2 white balls is  [tex]\frac{3}{8}[/tex] × [tex]\frac{2}{7}[/tex]

= [tex]\frac{3}{28}[/tex]

Answer:[tex]\frac{3}{28}[/tex]

Step-by-step explanation:

Given a box contains 3 White ,2 green,2 red & 1 Blue marble

We have to draw two marbles without replacement

therefore for first draw we have 3 white marble to choose among 8 marbles

i.e.

[tex]_{1}^{3}\textrm{C}[/tex]  choices among the total of [tex]_{1}^{8}\textrm{C}[/tex] options

For second draw we 2 white marbles left therefore no of ways in which a white marble can be choosen is

[tex]_{1}^{2}\textrm{C}[/tex]

Therefore required probability is =[tex]\frac{favourable\ outcome}{Total\ outcome}[/tex]

P[tex]\left ( required\right )[/tex]=[tex]\frac{3\times2}{8\times7}[/tex]

P[tex]\left ( required\right )[/tex]=[tex]\frac{3}{28}[/tex]

Answer with explanation:

Given : The probability of grocery bags are classified as plastic = 0.97

(a) f two bags are chosen at random.

Then , the probability that both grocery bags are plastic​ is given by :-

[tex]^2C_2(0.97)^2(1-0.97)^0=0.9409[/tex]

(b) If five grocery bags are chosen at random.

Then , the probability that all five grocery bags are plastic​ is given by :-

[tex]^5C_5(0.97)^5(1-0.97)^0\approx0.8587[/tex]

(c) The probability of getting paper = 1-0.97=0.03

The probability that at least one of five randomly selected grocery bags is paper :-

[tex]P(x\geq1)=1-P(0)\\\\1-^5C_0(0.03)^0(0.97)^5\\\\=1-(0.03)^0(0.97)^5=0.1412659\approx0.14>0.05[/tex]

Thus , it would not be unusual that at least one of five randomly selected grocery bags is paper.

Probability is used to determine the chances of an event

[tex]p = 97\%[/tex] -- chances that a bag is plastic

(a) Both plastics selected are plastic

This is calculated as:

[tex]P(2) = p^2[/tex]

So, we have:

[tex]P(2) = (97\%)^2[/tex]

[tex]P(2) = 0.9409[/tex]

Hence, the probability that both grocery bags are plastic is 0.9409

(b) All five are plastic

This is calculated as:

[tex]P(5) = p^5[/tex]

So, we have:

[tex]P(5) = (97\%)^5[/tex]

[tex]P(5) = 0.8587[/tex]

Hence, the probability that all five grocery bags are plastic is 0.8587

(c) At least one of the five is paper

The probability that none of the five is paper is the same as the probability that all five is plastic.

So:

[tex]P(None) = 0.8587[/tex]

Using complement rule,

[tex]P(At\ least\ 1) = 1 - P(None)[/tex]

So, we have

[tex]P(At\ least\ 1) = 1 - 0.8587[/tex]

[tex]P(At\ least\ 1) = 0.1413[/tex]

Hence, the probability that at least one grocery bags is paper is 0.1413

The above probability is greater than 0.05

Hence, it would not be unusual that at least one of five randomly selected grocery bags is paper.

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Answer:

Option A

Step-by-step explanation:

Given that in a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r^2 is reported as .40.

r square, being the coefficient of determination explains the variablity of one variable due to the variability of the other.  Here Mobility explains 40% variation in the number of friends is right answer.

Option B is wrong because r = ±6324, so cannot say positive or negative.

Similarly option c is wrong because we are unsure whether negative correlation.  Option d is wrong since 16% is not right .

Answer:

The amount would be $ 3600.

Step-by-step explanation:

Given,

The invested amount, P = $ 2000,

Annual rate of interest, r = 4 %,

Time, t = 20 years,

So, the simple interest would be,

[tex]I=\frac{P\times r\times t}{100}[/tex]

[tex]=\frac{2000\times 4\times 20}{100}[/tex]

[tex]=\frac{160000}{100}[/tex]

[tex]=\$1600[/tex]

Hence, the amount of money after 20 years,

[tex]A=P+I[/tex]

[tex]=2000+1600[/tex]

[tex]=\$ 3600[/tex]

Answer:

The probability that mike will guess​ correctly is 0.0027397 or [tex]\frac{1}{365}[/tex].

Step-by-step explanation:

Consider the provided information.

The number of days in a year is 365 (Ignore leap​ years).

[tex]Probability = \frac{favorable\ outcomes}{possible\ outcomes}[/tex]

Here, favorable outcomes is 1 and total number of outcomes are 365.

Substitute these value in above formula.

[tex]Probability = \frac{1}{365}[/tex]

[tex]Probability = 0.0027397[/tex]

Thus, the probability that mike will guess​ correctly is 0.0027397 or [tex]\frac{1}{365}[/tex].

Probability of an event represents the chances of occurrence of that event.

The probability that Mike will guess Kelly's birth date correctly (ignoring leap years) is [tex]\dfrac{1}{365} \approx 0.00027[/tex]

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}[/tex]

Where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Since we know that in a year (non leap year), there are 365 days, and Kelly's birthday can be on any one of those date, so the total number of days to chose from is 365 and since birthday of Kelly is going to be on single day of whole year, so favorable case is only single.

Thus,

if E = Selecting Kelly's birth date correctly,

Then

[tex]P(E) = \dfrac{1}{365} \approx 0.00027[/tex]

Thus,

The probability that Mike will guess Kelly's birth date correctly (ignoring leap years) is [tex]\dfrac{1}{365} \approx 0.00027[/tex]

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First,

We are dealing with parabola since the equation has a form of,

[tex]y=ax^2+bx+c[/tex]

Here the vertex of an up - down facing parabola has a form of,

[tex]x_v=-\dfrac{b}{2a}[/tex]

The parameters we have are,

[tex]a=-5,b=-10, c=6[/tex]

Plug them in vertex formula,

[tex]x_v=-\dfrac{-10}{2(-5)}=-1[/tex]

Plug in the [tex]x_v[/tex] into the equation,

[tex]y_v=-5(-1)^2-10(-1)+6=11[/tex]

We now got a point parabola vertex with coordinates,

[tex](x_v, y_v)\Longrightarrow(-1,11)[/tex]

From here we emerge two rules:

So our vertex is minimum value since,

[tex]a=-5\Longleftrightarrow a<0[/tex]

Hope this helps.

r3t40

Answer:

The probability is 0.66.

Step-by-step explanation:

Given,

The chance of encountering a car crash on the road is stated as 66​%,

That is, out of 100% cases the percentage of the number of car crash cases is 66%,

⇒ Total outcomes = 100%, favourable outcome = 66 %

So, the probability of occurrence a car crash = [tex]\frac{66\%}{100\%}[/tex]

[tex]=\frac{66/100}{100/100}[/tex]

[tex]=\frac{66}{100}[/tex]

[tex]=0.66[/tex]

Where, 0 < 0.66 < 1.

Hence, the indicated degree of likelihood as a probability value between 0 and 1 inclusive is 0.66.

Answer:

(a) [tex]P_{t}=3(2)^{6t}[/tex]

(b) [tex]3(2)^{42}[/tex]

(c) 28.07 minutes

Step-by-step explanation:

A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.

That means sequence formed will be 3, 6, 12, 24............

We can easily say that this sequence is a geometric sequence having common ratio (r) = [tex]\frac{T_{2}}{T_{1}}=\frac{6}{3}[/tex]

r = 2

Now we know the explicit formula of a geometric sequence is given by

[tex]P_{t}=P_{0}(r)^{\frac{60t}{10}}=P_{0}(r)^{6t}[/tex]

Where a = Initial population = 3 bacteria

r = common ratio = 2

and t = time in hours

So explicit formula will be [tex]P_{t}=3(2)^{6t}[/tex]

(a) Now we have to calculate the size of population after t hours

[tex]P_{t}=3(2)^{6t}[/tex]

(b) We have to find the size of population after 7 hours or 420 minutes

[tex]P_{t}=3(2)^{6\times7}[/tex]

= [tex]3(2)^{42}[/tex]

After 7 hours bacteria population will be [tex]3(2)^{42}[/tex]

(c) Time to reach population as 21

By the explicit formula

[tex]21=3(2)^{6t}[/tex]

[tex]2^{6t}=\frac{21}{3}=7[/tex]

Now we take log on both the sides of the equation

[tex]log(2^{6t})=log(7)[/tex]

6t log2 = log 7

6t(0.301) = 0.845

t(1.806) = 0.845

t = [tex]\frac{0.845}{1.806}=0.468[/tex] hours

Or t = 0.468×60 = 28.07 minutes

Therefore, after 28.07 minutes bacterial population will be 21

The bacteria population grows following an exponential pattern, therefore the population after t hours can be calculated using the exponential growth formula with the initial population as 3 and each cell dividing every 10 minutes. To calculate the time when the population reaches a certain size, solve the exponential growth equation for t.

The growth of bacteria population can be described as exponential growth, with each cell dividing into two every 10 minutes. Given the initial population as 3 bacteria, we would need to calculate the number of divisions that occur within the specified time frame to calculate the population after t hours.

(a) To find the population after t hours, we convert the hours to minutes (since each division occurs every 10 minutes) and then calculate the number of divisions. Each bacterial division results in a doubling of the population, so we use the formula for exponential growth: N = N0 * 2^n, where N0 is the initial population (3), and n is the number of divisions (6t, because t hours is 60t minutes and each division occurs every 10 minutes, making a total of 6t divisions per hour). So the population after t hours is N = 3 * 2^(6t).

(b) To find the size of the population after 7 hours, we substitute t = 7 into the formula, to get N = 3 * 2^(6*7) = 3 * 2^42.

(c) To find out when the population reaches 21, we equate N to 21 in the formula and solve for t. So, 21 = 3 * 2^(6t). Solving this equation gives the time t in hours when the population will reach 21.

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Answer with explanation:

Suppose, A={(a,b),(b,a), (c,d),(d,c),(p,q),(q,p),(a,a),(b,b)}

A Relation M is Symmetric , if (p,q)∈M , then (q,p)∈M.

⇒It is given that, R and S are symmetric Relation  on a Set A.

⇒If R is symmetric, then if (a,b)∈R, means,(b,a)∈R.So, R={(a,b),(b,a)}.

⇒If S is Symmetric, then if (c,d)∈S, means,(d,c)∈S.So, S={(c,d),(d,c)}.

⇒R ∩ S ={(a,b),(b,a),(c,d),(d,a)}

⇒If you will look at the elements of Set , R∩S, there is (a,b)∈ R∩S,so as (b,a)∈ R∩S.Also, (c,d)∈ R∩S,so as (d,a)∈ R∩S.

Which shows Relation in the set ,  R∩S is symmetric.

Answer:

f(9) =5

Step-by-step explanation:

We have an input x and an output f(x)

The input in the last row is 9 and the output is 5

The input x=9 and the output f(9) =5

f(9) =5

The correct option is (a) because [tex]f(9)=5[/tex].

Important information:

The function notation of a point [tex](x,f(x))[/tex] or [tex](x,y)[/tex] is [tex]f(x)=y[/tex].

Using the definition of function notation. The function notation of given ordered pairs [tex](2,6),(7,3)[/tex] and [tex](9,5)[/tex] are:

[tex]f(2)=6[/tex]

[tex]f(7)=3[/tex]

[tex]f(9)=5[/tex]

Thus, option (a) is correct and the other options are incorrect.

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Answer:

Step-by-step explanation:

Divisibility rule when a number is divisible by 11:

Take the alternating sum of digits in a number read from left to right .If that is divisible by 11 then the the given number is divisible by 11.

It is a divisibility rule of 11.

Let 1342 is a number .The number is divisible by 11 or not

Alternating sum of digits  =1-3+4-2=0

The alternating sum of digits is divisible by 11 .

Therefore, the number 1342 is divisible by 11.

Let a number 2728

Alternating sum of digits = 2-7+2-8=-11.

The alternating sum of digits is divisible by 11 .

Therefore, the number 2728 is divisible by 11.

The rule for determining divisibility by 11 involves alternately adding and subtracting a number's digits; if the result is 0 or divisible by 11, the original number is too. Examples illustrate the application of the divisibility test.

Rule for Divisibility by 11

The rule for determining when a number is divisible by 11 is quite straightforward. To apply the rule, you alternate between adding and subtracting the digits of the number in question from left to right. If the resulting sum (which may be negative) is 0 or divisible by 11 itself, then the original number is divisible by 11. For example, consider the number 2728. Apply the rule like this: 2 - 7 + 2 - 8 = -11. Since -11 is divisible by 11, 2728 is also divisible by 11.

Examples

Another example: Take the number 5831. Using the rule: 5 - 8 + 3 - 1 = -1, which is not divisible by 11, hence 5831 is not divisible by 11.

This divisibility test is a fantastic example of how certain mathematical rules are used to quickly determine properties of numbers without needing to perform long divisions.

Answer: 0.0427

Step-by-step explanation:

Given : The area under the standard normal curve to the left of z = -1.72 is​ 0.0427

We know that the normal curve is a bell shaped curve that is symmetric such that half of the data falls to the left of the mean (Mean lies at the middle of the curve) and half of data falls to the right.

Now, z=-1.72 lies on the left side and z=1.72 lies right side.

Since, normal curve is symmetric and the magnitude of the values if same , then the area under the standard normal curve to the left of z = -1.72 is​  equals to the area to the right of z = 1.72 is 0.0427

Therefore, the area under the standard normal curve to the right of z = 1.72  is 0.0427

The area under the standard normal curve to the right of z=1.72 is 0.9573 or 95.73%, which can be calculated by subtracting the area to the left of z from 1 (1 - 0.0427 = 0.9573).

The area under the standard normal curve to the left of z=-1.72 is 0.0427. This essentially means that 4.27% of all observations fall under this score. Conversely, the area to the right of the z-score represents the proportion of observations that are greater than z. In a normal distribution, the sum of the areas to the left and to the right of a z-score must always equal to 1 (0.0427 + x = 1), because all possible outcomes are accounted for by a normal distribution. Hence, we can find out the area to the right by simply subtracting the area to the left from 1. So, the area under the standard normal curve to the right of z=1.72 is 1 - 0.0427 = 0.9573 or 95.73%.

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Answer:

The P(x=45) is more that the P(x=20). Therefore x=45 successes is more likely to get.

Step-by-step explanation:

Given information: n=100 and p=1/3.

According to the binomial distribution, the probability of getting r success in n trials is

[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]

where, n is total trials, p is probability of success and q is probability of failure.

Total trials, n = 100

Probability of success, p = [tex]\frac{1}{3}[/tex]

Probability of failure, q = [tex]1-\frac{1}{3}=\frac{2}{3}[/tex]

The probability of 20 successes is

[tex]P(x=20)=^{100}C_{20}\times (\frac{1}{3})^{20}\times (\frac{2}{3})^{100-20}[/tex]

[tex]P(x=20)=\frac{100!}{20!(100-20)!}\times (\frac{1}{3})^{20}\times (\frac{2}{3})^{80}\approx 0.001257[/tex]

The probability of 45 successes is

[tex]P(x=45)=^{100}C_{45}\times (\frac{1}{3})^{45}\times (\frac{2}{3})^{100-45}[/tex]

[tex]P(x=45)=\frac{100!}{45!(100-45)!}\times (\frac{1}{3})^{45}\times (\frac{2}{3})^{55}\approx 0.004296[/tex]

The P(x=45) is more that the P(x=20). Therefore x=45 successes is more likely to get.

The probability that exactly two telephones will end up being replaced under warranty is found to be 0.147.

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Suppose the total number of telephones be x.

Then, the telephones submitted under warranty is 20% × x = 0.2x.

The number of telephones to be repaired is 60% × 0.2x = 0.12x

And, those to be replaced  are given as 40% × 0.2x = 0.08x.

Now, the probability of exactly two units being replaced out of 10 is given by binomial distribution as,

P(Exactly two units being replaced) = ¹⁰C₂(0.08)²(0.92)⁸

⇒ P(Exactly two units being replaced) = 0.147

Hence, the probability for the given case is obtained as 0.147.

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To solve this problem, we can use the concept of conditional probability. Given that 20% of telephones are submitted for service while under warranty and of these, 60% can be repaired and 40% must be replaced with new units, we can calculate the probability that exactly two telephones will be replaced under warranty.

To solve this problem, we can use the concept of conditional probability. Let's break down the information given:

Now, let's calculate the probability that exactly two telephones will be replaced:

Therefore, the probability that exactly two telephones will end up being replaced under warranty is approximately 0.0572, or 5.72%.

Answer:

The average daily sales rate for candy is 37.4.

Step-by-step explanation:

We know that,

[tex]\text{Inventory turnover }= \frac{\text{Total sale}}{\text{Average inventories}}[/tex]

[tex]\implies \text{Total sale}=\text{Inventory turnover }\times \text{Average inventories}[/tex]

Given,

Inventory turnover of candies = 3.3,

Average inventories = 340

So, sale of candies = 3.3 × 340 = 1122

Now,

[tex]\text{Average daily sales rate}=\frac{\text{total sale}}{\text{Number of days}}[/tex]

Since, 1 month = 30 days ( approx ),

Hence, the  average daily sales rate for candy = [tex]\frac{1122}{30}[/tex]=37.4