Identify the radius and center.

x^2 + y^2 + 4y -21 =0

Answer:

[tex](4)^{20}[/tex]

Step-by-step explanation:

Total number of questions = 20

Possible options for each question = 4

Sample space contains the total number of possible outcomes.

For every question there are 4 possible ways to select an answer. This holds true for all 20 questions. Selecting an answer for a question is independent of other questions/answers,

According to the counting principle, the total number of possible outcomes will be the product of the number of possible outcomes of individual events. Possible outcomes for each of the 20 questions is 4. This means we have to multiply 4 twenty times to find the total number of possible outcomes.

So, the number of elements in the sample space would be:

[tex](4)^{20}[/tex]

Answer:

D.368 space ft squared

Step-by-step explanation:

Hello

The equation to find the area of ​​the rectangle is simply A = h * b. This means that the area of ​​a rectangle is equal to the product of its height (h) by its base (b), or of its length by its width

Let

A=h*b

h=23

b=16

A=23 ft*16 ft

A=368 ft squared

so, the answer is

D. 368 ft squared.

I hope it helps

Have a fantastic day.

Answer:

111,952,800 beats in 3 years

Step-by-step explanation:

71 beats/minute, 60 minutes/hour ~ 71x60=4,260 beats/hour

24 hours/day ~ 4,260x24=102,240 beats/day

365 days/year ~ 102,240x365=37,317,600 beats/ year

37,317,600x3=111,952,800 beats in 3 years

The heart beats 111952800 times in 3 years

From the given question, we just have to find the rate at which the heart beats.

Given;

we can start by solving how many minutes are in 1 year.

To do that, we have to multiply 60 minutes by 24 hours by 365 days

[tex]60*24* 365=525600\\ [/tex]

We have 525600 minutes in 1 year

Now, we can multiply this value by 71 to know the number of beats in 1 year.

[tex]525600 * 71 = 37317600[/tex]

The heart beats for 37317600 times in a year.

Let's multiply this value by 3 to know how many times it beats in 3 years.

[tex]37317600 * 3 = 11952800[/tex]

The heart beats 11952800 times in 3 years.

We are also asked to calculate 3.0, 3.00 and 3.000 years

In this case, 3.0 = 3.00 = 3.000  and the rate at which the heart beats is uniform or equal across the three times given.

learn more about rates here;

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Answer:

[tex]\frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C[/tex]

Step-by-step explanation:

Given differential equation,

[tex](x^2 + y^2) dx + (x^2 - xy) dy = 0[/tex]

[tex]\implies \frac{dy}{dx}=-\frac{x^2 + y^2}{x^2 - xy}----(1)[/tex]

Let y = vx

Differentiating with respect to x,

[tex]\frac{dy}{dx}=v+x\frac{dv}{dx}[/tex]

From equation (1),

[tex]v+x\frac{dv}{dx}=-\frac{x^2 + (vx)^2}{x^2 - x(vx)}[/tex]

[tex]v+x\frac{dv}{dx}=-\frac{x^2 + v^2x^2}{x^2 - vx^2}[/tex]

[tex]v+x\frac{dv}{dx}=-\frac{1 + v^2}{1 - v}[/tex]

[tex]v+x\frac{dv}{dx}=\frac{1 + v^2}{v-1}[/tex]

[tex]x\frac{dv}{dx}=\frac{1 + v^2}{v-1}-v[/tex]

[tex]x\frac{dv}{dx}=\frac{1 + v^2-v^2+v}{v-1}[/tex]

[tex]x\frac{dv}{dx}=\frac{v+1}{v-1}[/tex]

[tex]\frac{v-1}{v+1}dv=\frac{1}{x}dx[/tex]

Integrating both sides,

[tex]\int{\frac{v-1}{v+1}}dv=\int{\frac{1}{x}}dx[/tex]

[tex]\int{\frac{v-1+1-1}{v+1}}dv=lnx + C[/tex]

[tex]\int{1-\frac{2}{v+1}}dv=lnx + C[/tex]

[tex]v-2ln(v+1)=lnx+C[/tex]

Now, y = vx ⇒ v = y/x

[tex]\implies \frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C[/tex]

Answer with Step-by-step explanation:

Since we have given that

[tex]BA=I[/tex]

As we know that

AA⁻¹ = I (A is invertible matrix)

Multiplying A⁻¹ on the both the sides:

[tex]BAA^{-1}=IA^{-1}\\\\B=A^{-1}[/tex]

Using the above result, we get that

[tex]BA=I=AA^{-1}\\\\BA=AB[/tex]

Therefore, BA = AB

Hence, proved.

Answer:

[tex]\frac{17}{64}\approx 0.27[/tex]

Step-by-step explanation:

We have been given a table to voters and their ages. We are asked to find the probability that a voter is younger than 45.

Voting age         Voters

17-29                       9

30-44                      8

45-64                    32

65+                        15

We can see from our given table that age of 17 (9+8) voters is between 17 to 44 years.

To find the probability that a voter is younger than 45, we will divide 17 by total number of voters.

[tex]\text{Total voters}=9+8+32+15=64[/tex]

[tex]\text{Probability that a voter is younger than 45}=\frac{17}{64}[/tex]

[tex]\text{Probability that a voter is younger than 45}=0.265625[/tex]

[tex]\text{Probability that a voter is younger than 45}\approx 0.27[/tex]

Therefore, the probability that a voter is younger than 45 is 0.27.

Answer: Hence, our required probability is [tex]\dfrac{1}{386206920}[/tex]

Step-by-step explanation:

Since we have given that

Numbers in a lottery = 60

Numbers to win the jackpot = 7 numbers

We need to find the probability to hit the jackpot:

So, our required probability is given by

[tex]P=\dfrac{^7C_7}{^{60}C_7}\\\\P=\dfrac{1}{386206920}[/tex]

This is a combination problem as we need to select 7 numbers irrespective of any arrangements.

Hence, our required probability is [tex]\dfrac{1}{386206920}[/tex

Answer:

10. México es un país con mucha gente (más de 130 millones de personas). Aunque es más grande, la Argentina tiene menos 45 millones de personas.

ARGENTINA NO ES TAN GRANDE COMO MÉXICO.

11. Ellos tienen cinco hijos y nosotros otros tenemos cinco hijos también.

ELLOS TIENEN TANTOS HIJOS COMO NOSOTROS.

12. Carlos no tiene mucho dinero, pero Felipe es rico.

CARLOS NO TIENE TANTO DINERO COMO FELIPE.

13. Linda es muy simpática, me gusta Dolores.

LINDA ES TAN SIMPÁTICA, PERO ME GUSTA DOLORES.

Answer:

cross sectional area of the wing's is = 3404.8 cm²

Step-by-step explanation:

using n= 5 to estimate area of the wing's

a = 160

taking sum of thickness at n = 1, 3, 5, 7, 9

so sum of the measurement of the thickness at the given position

19.9 +29.0 + 27.5 +20.9 + 9.1 = 106.4

so the thickness is 106.4/5

           = 21.28 cm

cross sectional area of the wing's is = 160 × 21.28

                                                            = 3404.8 cm²

Using the Midpoint Rule with 5 intervals, the estimated area of the airplane wing's cross-section can be obtained by dividing the total span into equal parts, calculating the midpoints of the measurements, and then adding up these individual areas.

To answer this question, we need to apply the Midpoint Rule - a method used in mathematics for approximating the definite integral of a function. The Rule works by estimating the area under the curve by rectangles, whose heights are determined by the function values at the midpoints of their bases.

Given n = 5, we divide the total measurement span (160 cm) into 5 parts. So, each part/subinterval is 32 cm.

We calculate the area of each part by multiplying its width (32 cm) by its midpoint height. For a sequence of measurements, the midpoints are obtained by averaging two consecutive measurements.

The midpoints for the given measurements are:

We then sum up the areas of all parts to get the estimated area of the airplane wing's cross-section.

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Answer:

d1=69.12 lbs/cbf, d2=1.32 lbs/cbf

Step-by-step explanation:

Hello

to make the conversion we will need

1" = 1 inch

12 inch = 1 feet

1 kg= 2. 20 lbs

Point 1, step 1

convert inch to feet

[tex]15"=15 inch*(\frac{1 feet}{12 in})=\frac{5}{4} ft\\ 20"=20 inch*(\frac{1 feet}{12 in})=\frac{5}{3}ft\\d=\frac{m(lbs)}{v(cbf)}\\ d=\frac{180 lbs}{\frac{5}{4} ft*\frac{5}{4} ft*\frac{5}{3} ft}\\ d=69.12\ lbs/cbf[/tex]

Point 2, step 2

[tex]90kg=90kg*\frac{2.2 lbs}{1 kg} =198 lbs\\\\d=\frac{m}{v}\\ d=\frac{198 lbs}{150 cbf}\\d=1.32\ lbs/cbf[/tex]

I hope it helps

Answer:

1120 possible ways

Step-by-step explanation:

In order to find the answer we need to be sure what equation we need to use.

From the given example, let's consider initially only men. Because you have a total of 8 men and we need to chose only 3 men, let's suppose that the 3 chosen men are A, B, and C.

Because A,B,C is the same as choosing C,B,A, which means it doesn't matter the order of the chosen men, we need to use a 'combination equation'.

Because we have two groups (women and men) then we have:

Possible ways = 8C3 * 6C3 (which are the combinations for women and men respectively). Remember that:

nCk=n!/((n-k)!*k!) so:

Possible ways = 8!/((8-3)!*3!) * 6!/((6-3)!*3!) = 56* 20 = 1120.

In conclusion, there are 1120 possible ways.

The standard error of the mean can be calculated by dividing the population standard deviation, which is 22, by the square root of the number of observations, which is 230.

In mathematics, the standard error of the mean is calculated by dividing the population standard deviation by the square root of the number of observations in the sample. In this case, the population standard deviation is given as 22, and the sample size is 230 observations.

The formula to calculate the standard error of the mean is:

Standard Error of the Mean = Population Standard Deviation / √(Number of Observations)

Plugging in the given values, this translates as:

Standard Error of the Mean = 22 / √230

Therefore, the standard error of the mean of this sample can be calculated as above. This represents the measure of statistical accuracy of the estimate of the sample mean, providing an indication of the precision of your results.

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The standard error of the mean is 1.449.

The standard error of the mean for a sample size of 230 observations, with a population standard deviation of 22, is calculated as 1.449.

The question asks for the determination of the standard error of the mean (SE) for a sample of 230 observations from a normal population with a known population standard deviation (σ) of 22. To calculate the standard error of the mean, we use the formula SE = σ / √n, where σ is the population standard deviation, and n is the sample size. In this case, n = 230.

So, SE = 22 / √230. Now we calculate the square root of 230 and then divide 22 by this number to get the standard error of the mean.

Therefore, the standard error of the mean is 1.449.

Answer: 1.758 is the lower bound of the 95% confidence interval for the mean number of TV's.

Step-by-step explanation:

Given that,

n = 10

Number of TV each household have = {2 , 0 , 2 , 2 , 2 , 2 , 1 , 5 , 3 , 2}

Standard Deviation(SD) = 0.55

95% Confidence Interval,  = 0.05

Follows normal distribution,

Mean = [tex]\bar{X} = \frac{2+0+2+2+2+2+1+5+3+2}{10}[/tex]

= [tex]\frac{21}{10}[/tex]

= 2.1

Therefore, 95% Confidence Interval are as follows:

[tex]\bar{X}\pm Z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}}[/tex]

[tex]2.1\pm 1.96 \times \frac{\0.55}{\sqrt{10}}[/tex]

Hence,

Lower bound = 2.1- 1.96 ×  [tex]\frac{\0.55}{\sqrt{10}}[/tex]

                      = 2.1- 1.96 × 0.174

                      = 1.758

Answer:

a.The profit is 40000 when sales are 10000 units.

b.Break-even point quantity and revenue=6000

c.When profits are at P9,000, sales are 6900

d.Fixed cost must decrease

e.The volume of sales to cover the fixed cost is 1500 units

f.If the firm want to break-even at a lower number of units, then the price will rice

Step-by-step explanation:

a.Profit is the difference between sales and cost

Profit= price* sales -((Variable cost * sales) +Fixed cost)

Profit when sales are 10000 units must be

P=40*10000-((30*10000)+60000)

P=400000-(300000+60000)=400000-360000

Profit=40000

The profit is 40000 when sales are 10000 units.

b.The break-even point quantity and revenue is when profit=0

So,  Profit= price* sales -((Variable cost * sales) +Fixed cost)

If profit is 0, then (Variable cost * sales) +Fixed cost =price* sales

30x +60000=40x

10x=60000

x=60000/10=6000

Break-even point quantity and revenue=6000

c. Profit= price* sales -((Variable cost * sales) +Fixed cost)

9000=40x -(30x +60000)=40x -30x -60000)

9000 +60000=40x-30x

69000=10x

x=6900 units

d. break even at sales volume of 500 units

(Variable cost * sales) +Fixed cost =price* sales

30*500+FC=40*500

1500+FC=2000

FC=2000-1500

FC=500 Fixed cost must decrease

e.The volume of sales to cover the fixed cost

To only cover fixed cost, sales have to be 60000

Fixed cost =price* sales

Sales=Fixed cost/price

Sales 60000/40=1500 units

f. If the firm want to break-even at a lower number of units, then the price will rice

Remember that break-even formula is

(Variable cost * sales) +Fixed cost =price* sales

Variable an fixed cost remain constant, if sales go down,  then price must go up.

Answer:

Step-by-step explanation:

Answer: 2730

Step-by-step explanation:

Given : The number of applicants  =15

The number of posts for which candidates have been applied = 3

To find the number of selections we use permutations since here order matters.

The permutations of n things taking m at a time is given by :-

[tex]^nP_m=\dfrac{n!}{(n-m)!}[/tex]

Then , the required number of ways is given by [Put n = 15 and m = 3] :-

[tex]^{15}P_3=\dfrac{15!}{(15-3)!}\\\\=\dfrac{15\times14\times13\times12!}{12!}\\\\15\times14\times13=2730[/tex]

Hence, the number of ways the selection can be made = 2730

Hence, the probability is:

            [tex]\dfrac{1}{6^4}\ or\ 0.000772[/tex]

It is given that:

A fair die is rolled four times. A 2 is considered​ "success," while all other outcomes are​ "failures."

This means that the probability of 4 successes is the outcome such that each of the four die will result in the outcome 2.

Also, the probability of 2 in each of the die is: 1/6

( since, there are total 6 outcomes in a die {1,2,3,4,5,6} and out of which there is only one '2' )

Also, we know that the outcome on one die is independent on the other this means that  the probability of 4 successes is:

[tex]=\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\\\\\\\\=\dfrac{1}{6^4}\\\\\\=0.000772[/tex]

Final answer:

The probability of rolling a 2 four times in a row on a fair six-sided die is found by multiplying the probability of a single 2 (which is 1/6) four times, giving us a final probability of 1/1296 or approximately 0.0008.

Explanation:

To find the probability of rolling a 2 on a six-sided die four times in a row, we consider each roll as an independent event. The probability of rolling a 2 on each individual roll is 1/6, since there are six faces on the die and only one face with a 2 on it.

Since these events are independent, the joint probability of all four events occurring is the product of the individual probabilities:

Probability of 4 successes (rolling a 2 four times) = (1/6) * (1/6) * (1/6) * (1/6) = 1/1296.

This is computed by multiplying the probability of a single success, 1/6, four times since the dice rolls are independent events. Therefore, the probability of obtaining four successes is quite low at approximately 0.0008 when rounded to four decimal places.

Answer:

Option A. If I eat an apple then I am hungry.

Step-by-step explanation:

we know that

To form the converse of the conditional statement, interchange the hypothesis and the conclusion.

In this problem

The hypothesis is "If I am hungry"

The conclusion is "l eat an apple."

therefore

interchange the hypothesis and the conclusion

The converse of "If I am hungry then l eat an apple." is

"If  l eat an apple then I am hungry"

Answer:the 1 one, A. " If I am hungry then I eat an apple"

Step-by-step explanation:

Answer:

$2,800 was invested at 9%.

$7,200 was invested at 6%.

Step-by-step explanation:

Usually, you need to assign variables to the unknowns you are looking for. Then follow the statements you are given to write equations. Then solve the equation  or system of equations.

What are we being asked? The amount invested at each rate.

Assign variables:

Let x = amount invested at 6%

Let y = amount invested at 9%

Since we have two unknowns, we need two equations.

Now we follow the statements to write equations.

"you invested in $10,000, part at 6% annual interest and the rest at 9% annual interest."

The total investment is $10,000, so the sum of our two investments, each at an interest rate is $10,000.

First equation:

x + y = 10,000

We have dealt with the two amounts that were invested. Now we deal with the interest earned.

x amount invested at 6% yields 6% of x in interest in 1 year.

6% of x as a decimal is 0.06x.

y amount invested at 9% yields 9% of y in interest in 1 year.

9% of y as a decimal is 0.09y.

The total interest earned at the two rates is 0.06x + 0.09y.

We are told the total interest is $684, so that gives us the second equation.

0.06x + 0.09y = 684

We now have a system of two equations in two unknowns.

x + y = 10,000

0.06x + 0.09y = 684

Let's use the substitution method to solve the system of equations.

We solve the first equation for x:

x = 10,000 - y

Now we replace x of the seconds equation by 10,000 - y.

0.06x + 0.09y = 684

0.06(10,000 - y) + 0.09y = 684

Distribute the 0.06.

600 - 0.06y + 0.09y = 684

0.03y + 600 = 684

0.03y = 84

y = 2,800

$2,800 was invested at 9%.

x + y = 10,000

x + 2,800 = 10,000

x = 7,200

$7,200 was invested at 6%.

Check:

Let's see if 6% of $7,200 plus 9% of $2,800 adds up to $684.

0.06(7200) + 0.09(2800) = 432 + 252 = 684

Yes it does, so our answer is correct.

Answer:

2,652

Step-by-step explanation:

51*52=2652

Final answer:

To solve the given differential equation y'''+4y''-16y'-64y=0 with initial conditions, we can use the characteristic equation method. By finding the roots of the characteristic equation and applying the initial conditions, the general solution is obtained as y(t) = (-16/21)e^(-8t) + (8/21)e^(2t) + (8/21)e^(-4t).

Explanation:

To solve the given differential equation, we can use the characteristic equation method. We first find the characteristic equation by substituting y = e^(mt) into the differential equation, which gives us the equation (m^3 + 4m^2 - 16m - 64)e^(mt) = 0. Since e^(mt) is never zero, we can simplify the equation to m^3 + 4m^2 - 16m - 64 = 0.

Using a numerical method or factoring, we find that the roots of the characteristic equation are m = -8, m = 2, and m = -4. Therefore, the general solution to the differential equation is y(t) = c1e^(-8t) + c2e^(2t) + c3e^(-4t), where c1, c2, and c3 are constants determined by the initial conditions.

Using the given initial conditions y(0) = 0, y'(0) = 26, and y''(0) = -16, we can solve for the constants. Substituting t = 0 into the general solution and its derivatives, we get the equations c1 + c2 + c3 = 0, -8c1 + 2c2 - 4c3 = 26, and 64c1 + 4c2 + 16c3 = -16. Solving these equations, we find c1 = -16/21, c2 = 8/21, and c3 = 8/21.

Therefore, the solution to the differential equation is y(t) = (-16/21)e^(-8t) + (8/21)e^(2t) + (8/21)e^(-4t).

[tex]f(4+h)-f(4)=(4+h)^2-10-(4^2-10)\\f(4+h)-f(4)=16+8h+h^2-10-16+10\\f(4+h)-f(4)=h^2+8h[/tex]

Answer:

[tex]f (4 + h) -f (4) = h ^ 2 + 8h[/tex]

Step-by-step explanation:

We have the following quadratic function.

[tex]f (x) = x ^ 2-10[/tex]

We must find the following expression

[tex]f (4 + h) -f (4) =[/tex]

First we must find [tex]f (4 + h)[/tex]

Then substitute [tex]x = (4 + h)[/tex] in the quadratic equation:

[tex]f (4 + h) = (4 + h) ^ 2 -10\\\\f (4 + h) = 16 + 8h + h ^ 2 -10\\\\f (4 + h) = h ^ 2 + 8h +6[/tex]

Now we find [tex]f(4)[/tex]. Replace [tex]x = 4[/tex] in the function [tex]f (x)[/tex]

[tex]f (4) = (4) ^ 2-10\\\\f (4) = 16-10\\\\f (4) = 6[/tex]

Finally we have to:

[tex]f (4 + h) -f (4) = h ^ 2 + 8h +6 - 6[/tex]

[tex]f (4 + h) -f (4) = h ^ 2 + 8h[/tex]

The average wait time in line at Renuka Jain's Car Wash is approximately 7.69 minutes, and the average number of customers waiting in line is approximately 1.54 cars.

Given that Renuka​ Jain's Car Wash takes a constant time of 3.0 minutes for its automated car wash cycle, and cars arrive following a Poisson distribution at the rate of 12 cars per hour (meaning one car every 5 minutes on average), we can calculate the average wait time in line and the average number of customers waiting in line.

To find the average wait time, we use the formula for the wait time in a M/M/1 queue: W = 1/(μ - λ), where λ is the arrival rate and μ is the service rate. We have λ = 12 cars/hour = 0.2 cars/minute, and μ = 1 car/3 mins = 0.33 cars/minute. Thus, the average wait time is W = 1/(0.33 - 0.2) = 7.69 minutes.

For the average number of customers in the line, we use the formula L = λW, where L is the average number of customers in the line, λ is the arrival rate and W is the average wait time. L = 0.2 cars/minute * 7.69 minutes = 1.54 cars.

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Answer:

True.

Step-by-step explanation:

We can represent an odd number by 2n + 1 where n = 0, 1, 2, 3, 5 etc.

Substituting:

a^2 + a = (2n + 1)^2 + 2n + 1

=  4n^2 + 4n + 1 + 2n + 1

= 4n^2 + 6n + 2

= 2(2n^2 + 3n + 1)

which is even because any integer multiplied by an even number is even.

This is also true if we use a negative odd integer:

We have 4n^2 + 4n + 1  - 1 - 2n

= 4n^2 + 2n

=  2(2n^2 + n(.

The statement is true. For any odd integer 'a', the expression 'a² + a' will always be even. This is because when 'a' (in the form of 2n+1 where n is any integer) is squared and added to 'a', the result is a number that is divisible by two, hence an even number.

Your statement is true. If a is any odd integer, then a² + a is indeed even. Here's why:

Any odd number can be expressed in the form 2n+1, where n is any integer. So, when you square this you get (2n+1)² = 4n² + 4n + 1, which simplifies to 2(2n² + 2n) + 1. This is an odd number.

Then, if you add a (which is 2n+1), you get 2(2n² + 2n) + 1 + 2n + 1, which simplifies to 2(2n² + 3n + 1). This is divisible by 2, which means it's an even number. Therefore, the expression a² + a represents an even number.

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Answer:

The required probability is approximately 0.3467.

Step-by-step explanation:

Let X represents the event of making an online purchase,

Given,

The probability of making an online purchase, p = 0.35,

While, the probability of not making the online purchase, q = 1 - p = 0.65,

Hence, by the binomial distribution 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 most 3 of them has made an online purchase is,

P(x ≤ 3) =P(x=0) + P(X=1) + P(X=2) + P(x=3)

[tex]= ^{12}C_0 p^0 q^{12-0}+^{12}C_1 p^1 q^{12-1}+^{12}C_2 p^2 q^{12-2}+^{12}C_3 p^3 q^{12-3}[/tex]

[tex]=(0.65)^{12}+12(0.35)(0.65)^{11}+66(0.35)^2(0.65)^{10}+220(0.35)^3(0.65)^9[/tex]

[tex]=0.346652696179[/tex]

[tex]\approx 0.3467[/tex]

To find the probability that at most 3 people in a sample of 12 have made an online purchase, use the binomial probability formula.

To find the probability that at most 3 people in a sample of 12 have made an online purchase, we can use the binomial probability formula. The formula is P(X ≤ k) = Σ{k=0}^{k} (nCk) * p^k * (1-p)^(n-k), where n is the sample size, k is the number of successes, p is the probability of success, and (nCk) is the combination.

In this case, n = 12, k ≤ 3, p = 0.35. So, the probability is:

Then, you can sum up these probabilities to find the total probability that at most 3 people have made an online purchase.

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Answer:

[tex]\frac{6x^2+3}{2x^3+3x}[/tex]

Step-by-step explanation:

You need to apply the chain rule here.

There are few other requirements:

You will need to know how to differentiate [tex]\ln(u)[/tex].

You will need to know how to differentiate polynomials as well.

So here are some rules we will be applying:

Assume [tex]u=u(x) \text{ and } v=v(x)[/tex]

[tex]\frac{d}{dx}\ln(u)=\frac{1}{u} \cdot \frac{du}{dx}[/tex]

[tex]\text{ power rule } \frac{d}{dx}x^n=nx^{n-1}[/tex]

[tex]\text{ constant multiply rule } \frac{d}{dx}c\cdot u=c \cdot \frac{du}{dx}[/tex]

[tex]\text{ sum/difference rule } \frac{d}{dx}(u \pm v)=\frac{du}{dx} \pm \frac{dv}{dx}[/tex]

Those appear to be really all we need.

Let's do it:

[tex]\frac{d}{dx}\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot \frac{d}{dx}(2x^3+3x)[/tex]

[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (\frac{d}{dx}(2x^3)+\frac{d}{dx}(3x))[/tex]

[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (2 \cdot \frac{dx^3}{dx}+3 \cdot \frac{dx}{dx})[/tex]

[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (2 \cdot 3x^2+3(1))[/tex]

[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (6x^2+3)[/tex]

[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{6x^2+3}{2x^3+3x}[/tex]

I tried to be very clear of how I used the rules I mentioned but all you have to do for derivative of natural log is derivative of inside over the inside.

Your answer is [tex]\frac{dy}{dx}=\frac{(2x^3+3x)'}{2x^3+3x}=\frac{6x^2+3}{2x^3+3x}[/tex].

[tex]x=2[/tex]

Represent the sentence mathematically. [tex]2(x-3)=-2[/tex]

Distribute. [tex]2x+(2*-3)=2x-6=-2[/tex]

Add 6 on both sides. [tex]2x=-2+6=4[/tex]

Divide both sides by 2. [tex]x=2[/tex]

Answer:

P=0.3726 or 37.26%

Step-by-step explanation:

The success, with 41% of probability of occurring, is that the employee believes the ​ company's president possesses low ethical standards. For more than 8 and less than 12 successes, it means the probability of having  9, 10 or  11 successes (all these summed).

The formula is:

[tex]b(x;n,p)= \ _nC_x*p^x*(1-p)^{n-x}[/tex]

Where x is the number of successes,n the number of trials, p the probability of success,[tex]_nC_x[/tex] refers to the combinations that can occur,  and it's formula is:

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

Calculating each case:

[tex]b(9,20,0.41)=\frac{20!}{9!(20-9)!}*0.41^9*(1-0.41)^{20-9}=0.1658[/tex]

[tex]b(10,20,0.41)=\frac{20!}{10!(20-10)!}*0.41^{10}*(1-0.41)^{20-10}=0.1267[/tex]

[tex]b(11,20,0.41)=\frac{20!}{11!(20-11)!}*0.41^{11}*(1-0.41)^{20-11}=0.0801[/tex]

Adding each case:

[tex]P=0.1658+0.1267+0.0801= 0.3726[/tex]

To find the probability that more than eight but fewer than twelve employees believe the company's president possesses low ethical standards, use the binomial probability formula. Calculate the probabilities for each value of k, and then sum them up to find the final probability.

To find the probability that more than eight but fewer than twelve of the 20 sampled employees believe the company's president possesses low ethical standards, we need to use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where:

In this case, we want to find the probability that more than eight but fewer than twelve employees believe the president possesses low ethical standards. So we need to calculate the probabilities for k = 9, 10, and 11 and then sum them up:

P(X > 8 and X < 12) = P(X = 9) + P(X = 10) + P(X = 11)

Calculating each probability:

P(X = 9) = C(20, 9) * 0.41^9 * (1-0.41)^(20-9)

P(X = 10) = C(20, 10) * 0.41^10 * (1-0.41)^(20-10)

P(X = 11) = C(20, 11) * 0.41^11 * (1-0.41)^(20-11)

Once we have the individual probabilities, we can sum them up to find the final probability.

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Answer:

4 Pairs.

Explanation:

A vertical angle is a set of two opposite angles, they show up when two lines intersect. Their sum is also 180°.

Answer:

4 Pairs

Step-by-step explanation: