A batch of 20 semiconductor chips is inspected by choosing a sample of 3 chips. Assume 10 of the chips do not conform to customer requirements. Round your answers to the nearest integer. a. How many different samples are possible? b. How many samples of 3 contain exactly one nonconforming chip? c. How many samples of 3 contain at least one nonconforming chip?

There are 11,238,513 ways Powerball tickets can be purchased.

There are 292, 201, 338 ways to win Powerball tickets.

Given

Number of white balls = 69

Number of white balls drawn = 5

Number of red balls = 26

Number of red balls drawn = 1

The combination is the way to select the number of objects from a group.

The formula is used to select the number of the object is;

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

Where n is the total number of objects and r is the number of selected objects.

1. How many possible different Powerball tickets can be purchased?

The number of ways Powerball tickets can be purchased is;

[tex]\rm = \ ^{69}C_5\\\\= \dfrac{69!}{(69-5)!. 5!}\\\\= \dfrac{69!}{64!.5!}\\\\= 11238513[/tex]

There are 11,238,513 ways Powerball tickets can be purchased.

2.  How many possible different winning Powerball tickets are there?

A number of ways to win Powerball tickets are there is;

[tex]\rm = \ ^{69}C_5 \times ^{26}C_1\\\\= \dfrac{69!}{(69-5)!. 5!} \times \dfrac{26!}{(26-1)!\times 1!}\\\\= \dfrac{69!}{64!.5!} \times \dfrac{26!}{25!.1!}\\\\= 11238513 \times 26\\\\= 292, 201, 338 ways[/tex]

There are 292, 201, 338 ways to win Powerball tickets.

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The total number of possible different Powerball tickets is 292,201,338, calculated by multiplying 11,238,513 combinations of white balls with the 26 possible red balls. There is only one winning combination for the Powerball jackpot, so there is only one possible winning Powerball ticket.

To calculate the total number of possible different Powerball tickets, we must consider the combination of white balls and the selection of the red Powerball. There are 5 white balls drawn from a set of 69, and this is a combination because the order does not matter. Therefore, the number of combinations of white balls is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of balls to choose from and k is the number of balls chosen. So, the calculation is C(69, 5) = 69! / (5!(69-5)!) = 11,238,513 combinations of white balls.

For the red Powerball, there is 1 ball drawn from a set of 26, and since there is only one ball, there are 26 possible outcomes. To find the total number of possible Powerball tickets, multiply the number of white ball combinations by the number of possible red balls: 11,238,513 × 26 = 292,201,338 possible Powerball tickets.

For part b, considering that there is only one winning combination, there is just one possible winning Powerball ticket.

To determine the number of subsets that can be formed from a set containing eleven elements, we use the formula [tex]2^n,[/tex] yielding [tex]2^11[/tex] = 2048 possible subsets.

The question is about finding the number of subsets that can be formed from a set containing eleven elements. To determine this, we employ the principle that for any set with n elements, the number of possible subsets is 2n. This includes both the empty set and the set itself as subsets.

Therefore, for a set with 11 elements, the number of possible subsets is 211 = 2048. This calculation reveals that one can form 2048 different subsets from a set of eleven elements. This includes all possible combinations of elements within the set, ranging from choosing no elements (the empty set) to choosing all eleven elements (the set itself).

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:

[tex]\sin x + \sqrt{1-\sin^2x}[/tex]

Step-by-step explanation:

Given: sin x + cos x

To change the given trigonometry expression in term of sine only.

Trigonometry identity:-

Expression: [tex]\sin x+\cos x[/tex]

We get rid of cos x from expression and write as sine form.

Expression: [tex]\sin x + \sqrt{1-\sin^2x}[/tex]        [tex]\because \cos x=\sqrt{1-\sin^2x}[/tex]

Hence, The final expression is only sine function.

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:  We should dispense 60 tablets.

Step-by-step explanation:

Given : A patient is to receive 2 tablets po ACHS for 30 days.

i.e. Dose for each day = 2 tablets

Number of days = 30

If a patient takes 2 tablets each day , then the number of tablets he require for 30 days will be :-

[tex]2\times30=60[/tex]   [Multiply 2 and 30]

Therefore, the number of tablets we should dispense = 60

Answer:

The rate is 4.9%.

Step-by-step explanation:

The compound interest formula is :

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

A = 73677.48

p = 73377.34

r = ?

n = 12

t = 1/12

Putting the values in formula we get;

[tex]73677.48=73377.34(1+\frac{r}{12})^{12*1/12}[/tex]

=> [tex]73677.48=73377.34(1+\frac{r}{12})^{1}[/tex]

=> [tex]\frac{73677.48}{73377.34} =(1+\frac{r}{12})[/tex]

=> [tex]1.004090=(\frac{12+r}{12})[/tex]

=> [tex]12.04908=12+r[/tex]

=> [tex]r = 12.04908-12[/tex]

r = 0.04908

or r = 4.9%

Therefore, the interest rate is 4.9%.

Final answer:

Explaining how to calculate the interest rate for an investment question.

Explanation:

To find the interest rate, subtract the initial amount from the final amount: $73,677.48 - $73,377.34 = $300.14. This represents the interest earned in one month.

Next, calculate the interest rate using the formula we get the :

Interest Rate = (Interest Earned / Initial Amount) x 100%.

Plugging in the values: Interest Rate = ($300.14 / $73,377.34) x 100% ≈ 0.409% or 0.4% to the nearest tenth.

Answer: D. 2.5

Step-by-step explanation:

Given : Line segment DF is dilated from the origin to create line segment D’F’ at D' (0, 10) and F' (7.5, 5).

The original coordinates for line segment DF are D(0, 4) and F(3, 2).

We know that the scale factor(k) is the ratio of the coordinates of the image points and the original points.

Then, [tex]k=\dfrac{\text{ y-coordinate of D'}}{\text{y-coordinate of D}}\\\\=\dfrac{10}{4}=\dfrac{5}{2}=2.5[/tex]

Hence, the scale factor was line segment DF dilated by = 2.5

Answer:

The answer to this is 2.5

Step-by-step explanation:

Well 1 i took the test and 2 if you mulitply the otginial coordinates by 2.5 then you will get the new cordiates

Answer:

i think the answer is 1,000

Step-by-step explanation:

Before the piper increased his volume, there were approximately 2530 rats. The final total (6578 rats), represents a 160 percent increase over this original amount.

The question is asking about the original number of rats before a 160 percent increase. In this scenario, you must remember that 6578 rats is equal to the original number of rats plus an extra 160 percent of the original number. Hence, 6578 rats signifies 260% of the original quantity of rats because inherently 100% represents the original quantity. To find the original number of rats, we'd divide the final quantity by 2.6. So, the original number of rats would be calculated by: 6578 ÷ 2.6 = 2530 rats approximately. Therefore, before the piper increased his volume, there were approximately 2530 rats.

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Answer:

As consequence of the Taylor theorem with integral remainder we have that

[tex]f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \int^a_x f^{(n+1)}(t)\frac{(x-t)^n}{n!}dt[/tex]

If we ask that [tex]f[/tex] has continuous [tex](n+1)[/tex]th derivative we can apply the mean value theorem for integrals. Then, there exists [tex]c[/tex] between [tex]a[/tex] and [tex]x[/tex] such that

[tex] \int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}dt = \frac{f^{(n+1)}(c)}{n!} \int^a_x (x-t)^n d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{n+1}}{n+1}\Big|_a^x[/tex]

Hence,

[tex] \int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{(n+1)}}{n+1} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} .[/tex]

Thus,

[tex] \int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} [/tex]

and the Taylor theorem with Lagrange remainder is

[tex] f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}[/tex].

Step-by-step explanation:

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 proposition: The sum of two odd numbers is an even number is true.

Step-by-step explanation:

A proof by contradiction is a proof technique that is based on this principle:

To prove a statement P is true, we begin by assuming P false and show that this leads to a contradiction; something that always false.

Facts that we need:

Proposition. The sum of two odd numbers is an even number

Proof. Suppose this proposition is false in this case we assume that the sum of two odd numbers is not even. (That would mean that there are two odd numbers out there in the world somewhere that'll give us an odd number when we add them.)

Let a, b be odd numbers. Then there exist numbers m, n, such that a = 2m + 1, b = 2n + 1 .Thus a + b = (2m + 1) + (2n + 1) = 2(m + n + 1) which is even. This contradicts the assumption that the sum of two odd numbers is not even.

Answer:

(a) 0.48, (b) 0.625, (c) 0.1923

Step-by-step explanation:

First define

Probability a person is a democrat: P(D) = 0.4

Probability a person is a republican: P(R) = 0.6

Probability a person support the measure given that the person is a democrat: P(SM | D) = 0.75

Probability a person support the measure given that the person is a republican: P(SM | R) = 0.3

Now for the Theorem of total probabilities we have

(a) P(SM) = P(SM | D)P(D)+P(SM | R)P(R) = (0.75)(0.4)+(0.3)(0.6) = 0.48

and for the Bayes' Formula we have

(b) P(D | SM) = P(SM | D)P(D)/[P(SM | D)P(D)+P(SM | R)P(R)] = (0.75)(0.4)/0.48 = 0.625

Now let SMc be the complement of support the measure, i.e.,

P(SMc | D) = 0.25 : Probability a person does not support the measure given that the person is a democrat

P(SMc | R) = 0.7: Probability a person does not support the measure given that the person is a republican,

and also for the Bayes' Formula we have

(c) P(D | SMc) = P(SMc | D)P(D)/[P(SMc | D)P(D)+P(SMc | R)P(R)] = (0.25)(0.4)/[(0.25)(0.4)+(0.7)(0.6)] = 0.1/(0.52)=0.1923

Final answer:

This detailed answer covers the calculation of probabilities regarding support for gun control based on political affiliation in a certain town in the United States.

Explanation:

a) To find the probability that a randomly selected resident supports the measure, we calculate as follows: P(support) = P(support|Democrat) ∗ P(Democrat) + P(support|Republican) ∗ P(Republican) = 0.75 ∗ 0.40 + 0.30 ∗ 0.60 = 0.45 + 0.18 = 0.63.

b) The probability that a supporter is a Democrat can be found using Bayes' theorem: P(Democrat|support) = P(support|Democrat) ∗ P(Democrat) / P(support) = 0.75 ∗ 0.40 / 0.63 = 0.4762.

c) To find the probability that a non-supporter is a Democrat: P(Democrat|non-support) = P(non-support|Democrat) ∗ P(Democrat) / P(non-support) = 0.25 ∗ 0.40 / (1 - 0.63) = 0.1.

Answer:

[tex]x\ =\ \dfrac{21}{5}[/tex]

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

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

[tex]\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right][/tex]

[tex]R_2=>R_2-R_1\ and\ R_3=>R_3+R_1[/tex]

[tex]=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right][/tex]

[tex]R_2=>\dfrac{R_2}{5}[/tex]

[tex]=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right][/tex]

[tex]R_1=>R_1+2.R_2[/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right][/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right][/tex]

[tex]R_3=>\dfrac{R_3}{2}[/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right][/tex]

[tex]R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3[/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right][/tex]

So, from the above augmented matrix, we can write

[tex]x\ =\ \dfrac{21}{5}[/tex]

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

z = 2

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:

[tex]26^{39}[/tex] is greater.

Step-by-step explanation:

Given numbers,

[tex]26^{39}\text{ and }39^{26}[/tex]

∵ HCF ( 26, 39 ) = 13,

That is, we need to make both numbers with the exponent 13.

[tex]26^{39}=((13\times 2)^3)^{13}=(13^3\times 2^3)^{13}=(13^3\times 8)^{13}=(13^2\times 104)^{13}[/tex]

[tex](\because (a)^{mn}=(a^m)^n\text{ and }(ab)^m=a^m.a^n)[/tex]

[tex]39^{26}=((13\times 3)^2)^{13}=(13^2\times 3^2)^{13}=(13^2\times 9)^{13}[/tex]

Since,

[tex]13^2\times 104>13^2\times 9[/tex]

[tex]\implies (13^2\times 104)^{13} > (13^2\times 9)^{13}[/tex]

[tex]\implies 26^{39} > 39^{26}[/tex]

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

Final answer:

The expected value of the winnings on a $8 bet placed on a red number in European roulette is -$1.945, indicating an average loss.

Explanation:

The question concerns the expected value of winnings on a $8 bet placed on red in European roulette. In European roulette, there are 18 red numbers, 18 black numbers, and 1 green number (0), totaling 37 numbers. A bet on red will win if the ball lands on any of the red numbers. When betting $8 on red, the player will either win $8 or lose $8, since the payoff for winning is 1:1.

To calculate the expected value, we consider the probability of winning, P(Win), and the probability of losing, P(Lose). The probability of landing on red (and wining) is 18/37, and the probability of not landing on red (and losing) is 19/37 (which includes the 18 black and 1 green).

The expected value is calculated as follows:

EV = (amount won × P(Win)) + (amount lost × P(Lose))

EV = ($8 × 18/37) + (-$8 × 19/37)

EV = $2.16 + (-$4.11)

EV = -$1.95

Rounded to three decimal places, the expected value is -$1.945.

Thus, if you were to place a $8 bet on red in European roulette, you would expect to lose, on average, $1.945 per game, as the expected value is negative.

Answer:

3.33 milliliters.

Step-by-step explanation:

We have been given that a 125-mL container of amoxicillin contains 600 mg/5 mL.

First of all, we will find amount of mg's of amoxicillin per ml as:

[tex]\text{Concentration of amoxicillin per ml}=\frac{\text{600 mg}}{\text{5 ml}}[/tex]

[tex]\text{Concentration of amoxicillin per ml}=\frac{\text{120 mg}}{\text{ml}}[/tex]

Now, we will use proportions as:

[tex]\frac{\text{1 ml}}{\text{120 mg}}=\frac{x}{\text{400 mg}}[/tex]

[tex]\frac{\text{1 ml}}{\text{120 mg}}\times \text{400 mg}=\frac{x}{\text{400 mg}}\times \text{400 mg}[/tex]

[tex]\frac{\text{400 ml}}{120 }=x[/tex]

[tex]\text{3.33 ml}=x[/tex]

Therefore, 3.33 milliliters would be used to administer 400 mg of amoxicillin.

To administer a 400mg dose of amoxicillin, using a solution where 5 mL contains 600 mg, approximately 3.33 mL of the solution would be needed. This was determined by setting up a proportion based on the known ratio of 600 mg of amoxicillin to 5 mL of solution.

First, we need to set up a ratio to find out how many milligrams (mg) of amoxicillin are in one milliliter (mL). We know that there are 600 mg in 5 mL, so the ratio is 600 mg:5 mL, which simplifies to 120 mg:1 mL. This tells us there are 120 mg of amoxicillin in each mL of solution.

To calculate how many mL are needed to administer 400 mg of amoxicillin, we can set up a proportion, using the known ratio of 120 mg:1 mL and the unknown value of 400 mg:x mL. The proportion would be set up as follows: 120/1 = 400/x. Solving for x, we find that x equals approximately 3.33 mL.

So, if you need to give a dose of 400mg of amoxicillin, you would need to administer about 3.33 mL of the amoxicillin solution.

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By the binomial theorem we know that

[tex]1 = (.4 + .6)^8 \\ = {8 \choose 0} (.4)^{8} (.6)^{0} + {8 \choose 1} (.4)^{7} (.6)^{1} +{8 \choose 2} (.4)^{6} (.6)^{2} + {8 \choose 3} (.4)^{5} (.6)^{3} + {8 \choose 4} (.4)^{4} (.6)^{4} \\ + \quad {8 \choose 5} (.4)^{3} (.6)^{5} + {8 \choose 6} (.4)^{2} (.6)^{6} + {8 \choose 7} (.4)^{1} (.6)^{7} + {8 \choose 8} (.4)^{0} (.6)^{8}[/tex]

The probability that exactly 5 of 8 support the incumbent is the term

 [tex]{8 \choose 5} (.4)^{3} (.6)^{5}[/tex]

So at least five of eight support is the sum of this term and beyond,

[tex]p={8 \choose 5} (.4)^{3} (.6)^{5} + {8 \choose 6} (.4)^{2} (.6)^{6} + {8 \choose 7} (.4)^{1} (.6)^{7} + {8 \choose 8} (.4)^{0} (.6)^{8}[/tex]

No particularly easy way of calculating that except popping it into Wolfram Alpha which reports

[tex]p = \dfrac{ 46413}{78125}[/tex]

Shouldn't half the terms work out to .6 ?  Interestingly it's not exactly .6 but pretty close at .594.

The total probability of at least five residents supporting the candidate, denoted as P(X≥5), is calculated by summing the probabilities of exactly five, six, seven, and eight residents supporting the candidate.

To find the probability of at least five out of eight randomly selected residents supporting the incumbent candidate when 60% of the community supports them, calculate and sum the binomial probabilities for exactly five to eight residents supporting the candidate.

The student is asking for the probability of at least five out of eight randomly selected community members supporting the incumbent candidate, given that 60% of the eligible voting residents support the candidate. This is a binomial probability problem because each selection is a Bernoulli trial with only two possible outcomes (support or do not support) and the probability of a resident supporting the candidate is constant (60%).

To calculate this probability, we will sum the probabilities of exactly five, six, seven, and eight residents supporting the candidate:

Calculate the probability of exactly 5 residents supporting the candidate using the binomial probability formula: P(X = 5) = (8 choose 5) * (0.6)^5 * (0.4)^3.

Repeat the process for P(X = 6), P(X = 7), and P(X = 8).

Finally, sum these probabilities to get the total probability of at least five residents supporting the candidate: P(X \\u2265 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8).

This sum provides the required probability.

Answer:

  c(x) = 1000 +40x

Step-by-step explanation:

The total cost c will be the sum of the fixed cost and the product of the variable cost per pair and the number of pairs.

  c(x) = 1000 +40x

The mathematical model for total cost of production at the O'Neill Shoe Manufacturing Company is determined by both fixed and variable costs and can be represented as C = 1000 + 40x, where x is the number of pairs of shoes produced.

The total cost of producing a certain number of shoes includes both fixed costs and variable costs. In the case of the O'Neill Shoe Manufacturing Company, the fixed cost, which is incurred regardless of the number of shoes produced, is $1,000. This pertains to the production setup cost. The variable cost, on the other hand, depends on the quantity of shoes produced. It's given as $40 per pair of shoes. Therefore, the total cost (C) for producing x pairs of shoes can be presented as: C = 1000 + 40x. In this equation, 1000 represents the fixed cost while 40x corresponds to the variable cost of producing x number shoes.

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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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Answer:

The function is a parabola described by: [tex]y = 1 +\frac{(x-2)^{2}}{8}[/tex]

Step-by-step explanation:

Since a directrix and a focus are given, then we know that they are talking about a parabola.

We know that the distance from any point in a parabola (x, y), to the focus is exactly the same as the distance to the directrix. Therefore, in order to find the required equation, first we will compute the distance from an arbitrary point on the parabola (x, y) to the focus (2, 1):

[tex]d_{pf} = \sqrt{(x-2)^2+(y-1)^2}[/tex]

Next, we will find the distance from an arbitrary point on the parabola (x, y) to the directrix (y= -3). Since we have an horizontal directrix, the distance is easily calculated as:

[tex]d_{pd}=y-(-3)=y+3[/tex]

Finally, we equate the distances in order to find the parabola equation:

[tex]\sqrt{(x-2)^2+(y-1)^2}=y+3[/tex]

[tex](x-2)^2+(y-1)^2=(y+3)^2[/tex]

[tex](x-2)^{2} +y^{2}-2y+1=y^{2}+6y+9[/tex]

[tex](x-2)^{2}-8=8y[/tex]

[tex]y = \frac{(x-2)^{2}}{8}-1[/tex]

Answer:

1) [tex]7 x 10^{15} J[/tex]

2) [tex]40.5[/tex] days

Step-by-step explanation:

1) First of all we use [tex]1MJ=1x10^{6}J[/tex] so the total energy will be [tex]7x10^{9} kg * 1x10^{6} \frac{J}{kg} =7x10^{15}J[/tex].

2)Then we use [tex]1W=1\frac{J}{s}[/tex] and [tex]Time=\frac{7 x 10^{15} J }{2x10^{9}J/s} =3.5x10^{6}s[/tex] or [tex]3.5x10^{6}s*\frac{1h}{3600s}*\frac{1day}{24h} =40.5 days[/tex]

Answer:

1) Base - 5

2) Base - 1.2

3) Base - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

To find : Write the base number for each expression ?

Solution :

Base number is defined as the number written in exponent form [tex]a^n[/tex]

which tells you to multiply a by itself, so a is the base of power n.

1) [tex]5^{12}[/tex]

In number [tex]5^{12}[/tex] the base is 5 as the power is 12.

2) [tex]1.2^{2}[/tex]

In number [tex]1.2^{2}[/tex] the base is 1.2 as the power is 2.

3) [tex](\frac{1}{3})^{2}[/tex]

In number  [tex](\frac{1}{3})^{2}[/tex] the base is [tex]\frac{1}{3}[/tex] as the power is 4.

The base number for 5^12 is 5, for 1.2^2 is 1.095, and for (1/3)^4 is 0.577.

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Answer:

Step-by-step explanation:

Estimated because there is no number that can go into 5 and 8 evenly

Answer:

This is the reduced row-echelon form

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&0&2&-3\\0&0&0&1&-4&7\end{array}\right][/tex]

from the augmented matrix

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\2&-4&8&3&10&7\\3&-6&10&6&5&27\end{array}\right][/tex]

Step-by-step explanation:

To transform an augmented matrix to the reduced row-echelon form we need to follow this steps:

1. Write the system of equations as an augmented matrix.

The augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable.

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\2&-4&8&3&10&7\\3&-6&10&6&5&27\end{array}\right][/tex]

2. Make zeros in column 1 except the entry at row 1, column 1 (this is the pivot entry). Subtract row 1 multiplied by 2 from row 2 [tex]\left(R_2=R_2-\left(2\right)R_1\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\0&0&2&-1&8&-13\\3&-6&10&6&5&27\end{array}\right][/tex]

3. Subtract row 1 multiplied by 3 from row 3 [tex]\left(R_3=R_3-\left(3\right)R_1\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\0&0&2&-1&8&-13\\0&0&1&0&2&-3\end{array}\right][/tex]

4. Since element at row 2 and column 2 (pivot element) equals 0, we need to swap rows. Find the first non-zero element in the column 2 under the pivot entry. As can be seen, there are no such entries. So, move to the next column. Make zeros in column 3 except the entry at row 2, column 3 (pivot entry). Divide row 2 by 2 [tex]\left(R_2=\frac{R_2}{2}\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&3&2&1&10\\0&0&1&-1/2&4&-13/2\\0&0&1&0&2&-3\end{array}\right][/tex]

5. Subtract row 2 multiplied by 3 from row 1 [tex]\left(R_1=R_1-\left(3\right)R_2\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&7/2&-11&59/2\\0&0&1&-1/2&4&-13/2\\0&0&1&0&2&-3\end{array}\right][/tex]

6. Subtract row 2 from row 3 [tex]\left(R_3=R_3-R_2\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&7/2&-11&59/2\\0&0&1&-1/2&4&-13/2\\0&0&0&1/2&-2&7/2\end{array}\right][/tex]

7. Make zeros in column 4 except the entry at row 3, column 4 (pivot entry). Subtract row 3 multiplied by 7 from row 1 [tex]\left(R_1=R_1-\left(7\right)R_3\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&-1/2&4&-13/2\\0&0&0&1/2&-2&7/2\end{array}\right][/tex]

8. Add row 3 to row 2 [tex]\left(R_2=R_2+R_3\righ)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&0&2&-3\\0&0&0&1/2&-2&7/2\end{array}\right][/tex]

9. Multiply row 3 by 2 [tex]\left(R_3=\left(2\right)R_3\right)[/tex]

[tex]\left[\begin{array}{cccccc}1&-2&0&0&3&5\\0&0&1&0&2&-3\\0&0&0&1&-4&7\end{array}\right][/tex]

Answer: I don't know if you wanted to write sin(4x) or [tex]sin^{4} (x)[/tex] , but here we go:

ok, sin(4x) = sin(2x + 2x), and we know that:

sin (a + b) = sin(a)*cos(b) + sin(b)*cos(a)

then sin (2x + 2x) = sin(2x)*cos(2x) + cos(2x)*sin(2x) = 2cos(2x)*sin(2x)

So 2*cos(2x)*sin(2x) is equivalent of sin(4x)

If you writed [tex]sin^{4} (x)[/tex] then:

[tex]sin^{4} (x) = sin^{2} (x)*sin^{2} (x)[/tex]

and using that: [tex]sins^{2} (x) = \frac{1-cos(2x)}{2}[/tex]

we have: [tex]sin^{2} (x)*sin^{2} (x) = \frac{(1-cos(2x))*(1-cos(2x))}{4} = \frac{1-2cos(2x) + cos^{2}(2x) }{4}[/tex]

and using that: [tex]cos^{2} (x) = \frac{1 + cos(2x)}{2}[/tex]

[tex]\frac{1-2cos(2x) + cos^{2}(2x) }{4} = \frac{1-2cos(2x) + \frac{1+cos(4x)}{2} }{4}[/tex]

You can keep simplifying it, but there is your representation of [tex]sin^{4} (x)[/tex]  that does not contain powers of trigonometric functions greater than 1.

To write an equivalent expression for sin(4x) without powers of trigonometric functions greater than 1, use the trigonometric identity sin(2x) = 2sin(x)cos(x). Apply this identity twice to get 4sin(x)cos(x)(cos^2(x) - sin^2(x)).

To write an equivalent expression for sin(4x) that does not contain powers of trigonometric functions greater than 1, we can use the trigonometric identity sin(2x) = 2sin(x)cos(x). By applying this identity twice, we get:

Therefore, an equivalent expression for sin(4x) that does not contain powers of trigonometric functions greater than 1 is 4sin(x)cos(x)(cos^2(x) - sin^2(x)).

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