A bacteria culture starts with 100 bacteria and doubles in size every half hour.
(a) How many bacteria are there after 4 hours?
bacteria
(b) How many bacteria are there after t hours?
y = bacteria
(c) How many bacteria are there after 40 minutes? (Round your answer to the nearest whole number.)
bacteria
(d) Graph the population function.

Answer:

The normal vector is [tex]{\bf n} \ =\ 3{\bf i} -8{\bf j} +4{\bf k}[/tex]

Step-by-step explanation:

Let

[tex]{\bf b}=\langle\,x_1,\,y_1,\,z_1\, \rangle\,, \ \ {\bf r} = \langle\,x_2,\,y_2,\,z_2\, \rangle\,, \ \ {\bf s} = \langle\,x_3,\,y_3,\,z_3\, \rangle.[/tex]

The vectors

[tex]\overrightarrow{QR} \ = \ {\bf r} - {\bf b} \,, \qquad \overrightarrow{QS} \ = \ {\bf s} - {\bf b} \,,[/tex]

then lie in the plane. The normal to the plane is given by the cross product

[tex]{\bf n} = ({\bf r} - {\bf b})\times ( {\bf s} - {\bf b})[/tex]

We have the following points:

[tex]Q(-6,\,-4,\,-6)\,, \ \ R(-2,\,0,\,-1)\,, \ \ S(-2,\,1,\,1)\,.[/tex]

when the plane passes through [tex]Q,\, R[/tex], and [tex]S[/tex], then the vectors

[tex]\overrightarrow{QR} = \langle\, -2-(-6),\, 0-(-4),\, -1-(-6)\, \rangle\,, \overrightarrow{QS}= \langle\, -2-(-6),\, 1-(-4),\, 1-(-6)\, \rangle\,,\\\\\overrightarrow{QR} = \langle\, 4,\, 4,\, 5\, \rangle\,,\qquad \overrightarrow{QS}= \langle\, 4,\, 5,\, 7\, \rangle\,[/tex]

lie in the plane. Thus the cross-product

[tex]{\bf n} \ = \ \left|\begin{array}{ccc}{\bf i} & {\bf j} & {\bf k} \\ 4 & 4 & 5 \\ 4 & 5 & 7 \end{array}\right| \ = \begin{pmatrix}4\cdot \:7-5\cdot \:5&5\cdot \:4-4\cdot \:7&4\cdot \:5-4\cdot \:4\end{pmatrix} \ = \ 3{\bf i} -8{\bf j} +4{\bf k}[/tex]

is normal to the plane.

The normal vector to the plane passing through the points (-6,-4,-6), (-2,0,-1), and (-2,1,1) is (-6, -8, 4). This is found by obtaining two vectors from the given points and then taking the cross product of these vectors.

To find the vector normal to the plane passing through the points (-6, -4, -6), (-2, 0, -1), and (-2, 1, 1), we first need to find two vectors lying in the plane that originate from the same point. Let's take the first point as common and obtain the vectors AB and AC:

AB = B - A = (-2 - (-6), 0 - (-4), -1 - (-6)) = (4, 4, 5)

AC = C - A = (-2 - (-6), 1 - (-4), 1 - (-6)) = (4, 5, 7)

Now, we can find the normal vector to the plane by taking the cross-product of these two vectors. The cross product of two vectors provides a new vector which is perpendicular to the original vectors:

N = AB x AC = (4*7 - 5*5, 5*4 - 4*7, 4*5 - 4*4) = (-6, -8, 4)

Therefore, the normal vector to the plane is (-6, -8, 4).

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Answer:

The weight of the citation designation should be at 4.8432 pounds.

Explanation:

Given

Mean [tex]= 3.2 pounds.[/tex]

Standard deviation[tex]= 0.8 pound.[/tex]

Step 1:

Consider 'y' as one of the top weight, that is, [tex]y = 2 \% = 2.054 pounds.[/tex]

Let 'x' be the weight of the citation designation.

[tex]y = \frac{x-mean}{standard\ deviation}[/tex]

[tex]=2.054 = \frac{x-3.2}{0.8}[/tex]

[tex]=2.054\times 0.8 = x-3.2[/tex]

[tex]=1.6432 = x-3.2[/tex]

[tex]x = 1.6432+3.2[/tex]

 [tex]x = 4.8432[/tex]

Thus, at 4.8432 pounds citation designation be established.

To learn more about citation, refer:

Final answer:

The citation catfish designation should be established at a weight of at least 4.84 pounds, which corresponds to the top 2% of a normal distribution given the mean is 3.2 pounds and the standard deviation is 0.8 pounds.

Explanation:

The weight at which a citation catfish designation should be established is calculated by identifying the z-score that corresponds to the top 2% of a normal distribution. Given that the average weight of a catfish is 3.2 pounds with a standard deviation of 0.8 pounds, we can use a z-table to find the z-score for the 98th percentile, which typically is around 2.05.

Using the z-score formula: z = (X - mean) / standard deviation, we rearrange to solve for the unknown X (catfish weight): X = z * standard deviation + mean. Plugging in the numbers: X = 2.05 * 0.8 + 3.2, we find that the citation catfish should weigh at least 4.84 pounds.

Answer:

Therefore,

[tex]AB=16.25\ units[/tex]

The Measurement of AB is 16.25 units.

Step-by-step explanation:

In Right Angle Triangle ABC

m∠C=90°

AC = 10.01    .....(Adjacent Side to angle A)

m∠A=52°

cos 52 ≈ 0.616

To Find:

AB = ? (Hypotenuse)

Solution:

In Right Angle Triangle ABC, Cosine Identity,

[tex]\cos A= \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}\\[/tex]

Substituting the values we get

[tex]\cos 52= \dfrac{AC}{AB}=\dfrac{10.01}{AB}[/tex]

But cos 52 ≈ 0.616 ....Given

[tex]AB=\dfrac{10.01}{0.616}=16.25\ units[/tex]

Therefore,

[tex]AB=16.25\ units[/tex]

The Measurement of AB is 16.25 units.

Answer:

a) Sample co-variance = -1.5

b) Sample correlation = -0.4404152

c) Weak negative relationship between X and Y.

Step-by-step explanation:

a) by sample co-variance = sum ((x - xbar)* (y-ybar)/n-1

#.... use the following program in R

x = c(7,8, 5, 3, 9)

y = c(7,5,9,7,7)

sv = sum((x-mean(x))*(y-mean(y)))/4

cor(x,y)

####################################

Final answer:

The number of tickets drawn at random can be calculated using the formula for the number of combinations.

Explanation:

To determine the number of tickets drawn at random in this scenario, we need to calculate the total number of possible outcomes. In this case, Maria is drawing marbles without replacement, meaning that the number of marbles in the bag decreases with each draw. We can use the formula for the number of combinations to calculate the total number of outcomes. The formula is nCr = n! / (r!(n-r)!), where n is the total number of marbles in the bag and r is the number of marbles drawn. In this case, n = 5+8+3 = 16 and r = 2. Therefore, the number of tickets drawn at random is 16C2 = 120.

Answer:

0.416 au

Step-by-step explanation:

Let y1=8sin(x) and y2=8cos(x), we must find the area between y1 and y2

[tex]\int\limits^\pi _0{(8cos(x)-8sin(x))} \, dx = 8\int\limits^\pi _0{(cos(x)-sin(x))} \, dx =\\8(sin(x)+cos(x)) evaluated(0-\pi )=\\8(sin(\pi )-sin(0))+8(cos(\pi )-cos(0))=\\8(0.054-0)+8(0.998-1)=8(0.054)+8(-0.002)=0.432-0.016=0.416[/tex]

Answer:

a) Profit = 84000

b) at break even number of pens sold = 46

Step-by-step explanation:

Profit = Selling price - Cost price

Total revenue generated = 99 * 1000

Total revenue generated = 99000

Total cost on making the pen  = 11 * 1000

Total cost on making the pen = 11000

Total cost including the initial cost = 11000 + 4000

Total cost including the initial cost =  15000

Profit = 99000 - 15000

Profit = 84000

Break even is when the cost are equal to Revenue thus no profit or loss

Revenue = total cost (break even)

9x = 1x + 4000

9x - x = 4000

8x = 4000

x = 500

At breakeven Revenue = 9 * 500

At breakeven Revenue =  4500

since one pen is sold at 99 therefore at break even number of pens sold = 4500/99 = 45.45( to 2 decimal place)

at break even number of pens sold = 46

To find the profit, substitute the selling quantity into the revenue and cost equations and subtract the cost from the revenue. To find the break-even point, set the profit to zero and solve for the selling quantity.

To find the profit, P, when the company sells 1000 pens, we first calculate the revenue by substituting x = 1000 into the revenue equation: R = 9x. Therefore, R = 9(1000) = 9000. Next, we calculate the cost by substituting x = 1000 into the cost equation: C = 1x + 4000. Therefore, C = 1(1000) + 4000 = 5000. Finally, we find the profit by subtracting the cost from the revenue: P = R - C. Therefore, P = 9000 - 5000 = 4000. The company's profit when selling 1000 pens is $4000.

To find the number of pens needed to break even, we set the profit to zero and solve for x. Therefore, P = R - C = 0. Substituting the revenue and cost equations, we have 9x - (1x + 4000) = 0. Simplifying this equation gives us 8x - 4000 = 0. Solving for x, we get x = 500. The company needs to sell 500 pens to break even.

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Answer:

(X and Y are real numbers)

p) X > 0

q) Y > 0

r)  XY > 0

s) (X > 0 ∧ Y > 0) ∨ (X = Y = 0)

Step-by-step explanation:

Lets assume that a pair of the propositions are true, and we will show that the other 2 are also true. There are 6 possible cases:

1) If p and q are true, then XY has to be positive because it is the product of positive numbers. And the first option of proposition s is true

2) If p and r are true, then Y = XY/X > 0 because it is the division of tow positive numbers, thus q is true. Since p and q are true, then so it is s.

3) If p and s are true, then option 2 of S is impossible, thus X > 0 and Y>0, hence q is true. SInce p and q are true, so is r.

4) If q and r are true, we can obtain X by dividing the positive numbers XY and Y, thus X>0, and p and s are true.

5) is q and s are true, an argument similar at the one made in 3) shows that both p and r are true.

6) if r and s are true, then the second part of s cant be true, therefore X>0 and Y>0, as a consecuence, p and q are true.

Now, lets show that, individually, no proposition implies the others:

p clearly doesnt imply q. X can be positive while Y is negative. Similarly Y can be positive while X is negative, thus q doesnt imply p either.

If XY > 0, then it can be that both X and Y are negative, thus r might not imply neither p nor q.

and if only s is true, then it may be that the second part is the one that is true, thereofre X=Y=0 and p, q and r are all false in this case.

As a consecuence, you need 2 of the propositions to be true so that all 4 are true, but as we show above, by having any pair of the propositions true, then all 4 are automaticallyy true.

Answer:

7

Step-by-step explanation:

Since the goal is to draw three marbles of the same colour, regardless of which colour that is, the worst possible scenario would be drawing two marbles of each color in the first six picks (2 red, 2 white and 2 blue). At this point, with the 7th pick, no matter what colour marble the student picks will form three of the same kind.

Therefore, the minimum number of marbles which students should take from the box to ensure that at least three of them are of the same colour is 7.

Final answer:

To ensure at least three marbles of the same color, a minimum of 349 marbles must be drawn from the box.

Explanation:

Question: What is the minimum number of marbles which students should take from the box to ensure that at least three of them are of the same color?

When considering the worst-case scenario, you would need to take marbles until you have at least 3 of the same color.

For this situation, where you have 203 red, 117 white, and 28 blue marbles:

It's possible that you could pick 202 red, 117 white, 27 blue, and still not have 3 of the same color. The next pick would guarantee 3 of the same color, giving a minimum of 349 marbles in total.

Answer:

1.242% probability that the second one selected is defective given that the first one was defective

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have

484 containers

7 are defective

a) What is the probability that the second one selected is defective given that the first one was defective?

After the first one was selected(defective), we have

483 containers

6 defective

6/483 = 0.01242

0.01242 = 1.242% probability that the second one selected is defective given that the first one was defective

Answer: The average speed of the plane is 600 miles per hour.

Step-by-step explanation:

The formula for determining average speed is expressed as

Average speed = total distance travelled/total time taken

The airplane flew from Chicago to San Francisco in 3.25 hours. Therefore, time = 3.25 hours

The cities are 1,950 miles apart. This means that the distance travelled is 1950 miles. Therefore,

Average speed = 1950/3.25 = 600 miles per hour.

Answer:

Speed = 600 mile per hour

Step-by-step explanation:

Given values:

Time = 3.25hours

Distance = 1950miles

Formula: speed = distance ÷ time

Therefore:

Speed = 1950 ÷ 3.25

Speed = 1950 ÷ 325/100

Speed = 1950 × 100/325

Speed= 195000/325

Speed = 600ml^h

Answer:

Step-by-step explanation:

given that the operations manager of a plant that manufactures tires wishes to compare the actual inner diameter of two grades of tires, each of which has a nominal value of 575 millimeters. A sample of five tires of each grade is selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are as follows:

Grade X

568 570 575 578 584

Mean = Total/5 = 575

Median = middle entry = 575

Mode = nil

Grade Y

573 574 575 577 578

Mean = sum/5 = 575.4

Median = middle entry =575

Mode = nil

Answer:

15.87% probability that no more than 80 customers walk into the coffee shop next Monday

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 100, \sigma = 20[/tex]

What is the probability that no more than 80 customers walk into the coffee shop next Monday?

This is the pvalue of Z when X = 80. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 100}{20}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

So there is a 15.87% probability that no more than 80 customers walk into the coffee shop next Monday

Answer:

A or C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = 3x-2

g(x) = 1/2(x²)

f(0) = 3x-2 = 3(0)-2 = 0-2 = -2

f(-1) = 3x-2 = 3(-1)-2 = -3-2 = -5

g(4) = 1/2(4²) = 1/2(16) = 8

g(-1) = 1/2(-1²) = 1/2(1) = 1/2

Answer:

68% of the dinosaurs' ages were within 1 standard deviation of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

What percentage of the dinosaurs' ages were within 1 standard deviation of the mean?

By the Empirical Rule, 68% of the dinosaurs' ages were within 1 standard deviation of the mean.

Final answer:

To find the probability of someone with periodontal disease having a heart attack, we can use conditional probability and Bayes' theorem. The probability of having a heart attack given that someone has periodontal disease is 79%. Using Bayes' theorem, we can calculate the probability of a person with periodontal disease having a heart attack.

Explanation:

To answer part A, we can use conditional probability. The probability of having a heart attack given that someone has periodontal disease is represented by P(heart attack | periodontal disease). According to the given information, 79% of people who have suffered a heart attack had periodontal disease. Therefore, P(heart attack | periodontal disease) = 0.79.

To answer part B, we can use Bayes' theorem. The probability of a person with periodontal disease having a heart attack is represented by P(heart attack | periodontal disease). According to the given information, the probability of having a heart attack in the community is 38%.

Therefore, P(heart attack) = 0.38. Let's use Bayes' theorem: P(heart attack | periodontal disease) = (P(periodontal disease | heart attack) × P(heart attack)) / P(periodontal disease). We know that P(periodontal disease | heart attack) = 0.79 from part A.

The probability of having periodontal disease in the community is represented by P(periodontal disease). In the given information, it says that only 33% of healthy people have periodontal disease. Therefore, P(periodontal disease) = 0.33. Substituting these values into Bayes' theorem, we can calculate P(heart attack | periodontal disease).

We start with the parent function

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

The first child function would be

[tex]g(x)=(2x)^2[/tex]

We have multiplied the input of the function by a constant: we have

[tex]g(x)=f(2x)[/tex]

This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.

The second child function would be

[tex]h(x)=(2x+6)^2[/tex]

We added 6 to  the input of the function: we have

[tex]h(x)=g(x+6)[/tex]

This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.

The third child function would be

[tex]l(x)=-(2x+6)^2[/tex]

We changed the sign of the previous function (i.e. we multiplied it by -1): we have

[tex]l(x)=-h(x)[/tex]

This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.

The fourth child function would be

[tex]m(x)=-(2x+6)^2+3[/tex]

We added 3 to previous function: we have

[tex]m(x)=l(x)+3[/tex]

This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.

Recap

Starting from the parent function [tex]y=x^2[/tex], we have to:

Note that the order is important!

Answer:

B

Step-by-step explanation:

i know the other answer was a little confusing, but they did more, so feel free to give them brainliest, just wanted to help clarify :)

edgenuity 2020

Answer:

hi guada!

Step-by-step explanation:

well the answer i think is 35.

180-155= 25

180-120-25=35

Answer:

[tex]\bar X = \frac{\sum_{i=1}^n x_i f_i}{n} = \frac{1220750}{500}=2441.5[/tex]

[tex] s= \sqrt{\frac{N \sum x^2 f -[\sum xf]^2}{N(N-1}}= \sqrt{\frac{500*3408029125 -[1220750]^2}{50*49}}=9341.2405[/tex]

Step-by-step explanation:

In order to find the mean and standard deviation we can create the following table:

Limits            Frequency(f)      x(midpoint)      x*f           x^2 *f

__________________________________________________

0-499                   9                   249.5         2245.5    560252.3

500-999              13                  749.5         9743.5     7302753

1000-1499           33                 1249.5       41233.5    51521258.25

1500-1999           115                1749.5       201192.5   351986278.8

2000-2499         125               2249.5      281187.5   632531281.3

2500-2999          81                2749.5      222709.5  612339770.3

3000-3499          47                3249.5      152726.5   496284761.8

3500-3999          45                3749.5      168727.5   632643761.3

4000-4499          22                4249.5      93489       397281505.5

4500-4999          10                 4749.5       47495      225577502.5

_____________________________________________________

Total                    500                               1220750     3408029125

We can calculate the mean with the following formula:

[tex]\bar X = \frac{\sum_{i=1}^n x_i f_i}{n} = \frac{1220750}{500}=2441.5[/tex]

And the standard deviation would be given by:

[tex] s= \sqrt{\frac{N \sum x^2 f -[\sum xf]^2}{N(N-1}}= \sqrt{\frac{500*3408029125 -[1220750]^2}{50*49}}=9341.2405[/tex]

Answer:

a) There is a 60% probability that he picks up a blue pen and recognizes it as blue.

b) There is a 62.5% probability that he chooses a pen and thinks it is blue.

c) Given that he thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.

Step-by-step explanation:

We have these following probabilities

A 75% probability that a pen is blue

A 25% probability that a pen is green

If a pen is blue, an 80% probability that the boy thinks it is a blue pen

If a pen is blue, a 20% probability that the boy thinks it is a green pen.

If a pen is green, a 90% probability that the boy thinks it is a green pen.

If a pen is green, a 10% probability that that the boy thinks it is a blue pen.

a) What is the probability that he picks up a blue pen and recognizes it as blue?

There is a 75% probability that he picks up a blue pen.

There is a 80% that he recognizes a blue pen as blue.

So

[tex]P = 0.75*0.8 = 0.6[/tex]

There is a 60% probability that he picks up a blue pen and recognizes it as blue.

b) What is the probability that he chooses a pen and thinks it is blue?

There is a 75% probability that he picks up a blue pen.

There is a 80% that he recognizes a blue pen as blue.

There is a 25% probability that he picks up a green pen

There is a 10% probability that he thinks a green pen is blue.

So

[tex]P = 0.75*0.80 + 0.25*0.10 = 0.625[/tex]

There is a 62.5% probability that he chooses a pen and thinks it is blue.

c) (Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?

There is a 62.5% probability that he thinks that he choose a blue pen.

There is a 60% probability that he chooses a blue pen and think that it is blue.

So

[tex]P = \frac{0.6}{0.625} = 0.96[/tex]

Given that he thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.

Final answer:

The answer provides the probabilities related to a color-blind boy picking and identifying blue and green pens accurately.So,a)The overall probability is 0.75 * 0.80 = 0.60,b)0.62,c)0.968.

Explanation:

a) What is the probability that he picks up a blue pen and recognizes it as blue?

Let's calculate this by considering the probabilities given:

Probability of picking a blue pen: 75/100 = 0.75

Probability of recognizing a blue pen as blue given it is blue: 0.80

The overall probability is 0.75 * 0.80 = 0.60.

b) What is the probability that he chooses a pen and thinks it is blue?

This includes both him picking a blue pen and thinking it is blue or picking a green pen and mistakenly thinking it is blue. It can be calculated as 0.75 * 0.80  + 0.25 * 0.10 = 0.62

c) Given he thinks he chose a blue pen, what is the probability he actually chose a blue pen?

This involves computing the conditional probability using Bayes' theorem:

P(chose blue pen | thinks it's blue) = P(chose blue pen and thinks it's blue) / P(thinks it's blue) = (0.75 * 0.80) / 0.62 = 0.968.

Answer:

16 ways

Step-by-step explanation:

We are given that

Total cards=52

Total queen in deck of cards=4

Total cards of heart=13

We know 1 card of queen is heart

Number of ways drawing one card of heart out of 13=[tex]13C_1[/tex]

Using combination formula ;[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

Number of ways drawing one card of heart out of 13=[tex]\frac{13!}{1!12!}=\frac{13\times 12!}{12!}=13[/tex]

Number of ways of drawing one card of queen out of 4=[tex]4C_1=\frac{4!}{3!}[/tex]

Number of ways of drawing one card of queen out of 4=[tex]\frac{4\times 3!}{3!}=4[/tex]

Total number of ways of drawing one card out of 52 cards=[tex]13+4-1=16[/tex]

Answer:

equivalent price/ gallon = 13.98 US$ / gallon

Step-by-step explanation:

Assuming that the exchange rate is 1.762 US$ /€ , then

thus

equivalent price/ gallon =   liters/gallon * euros / liter * dollars/euro

equivalent price/ gallon = 3.78541178 liters/ gallon *  2.096 € /liter * 1.762 US$ /€ = 13.98 US$ / gallon

equivalent price/ gallon = 13.98 US$ / gallon

if the actual price would be different from the equivalent , then there would be an arbitrage opportunity ( profit with no risk)

To find the price per gallon in France converted to dollars, multiply the price per liter by liters per gallon to get the Euro amount, then convert to dollars using the exchange rate. The result is approximately $13.97 per gallon.

The question asks to determine the price of gasoline per gallon in France when converted to Euros, considering the given petrol price per liter and the exchange rate. To calculate this, we will first convert the price from liters to gallons and then convert Euros to the equivalent value in using the exchange rate.

Therefore, the equivalent price of gasoline per gallon in France, when converted to dollars, is approximately $13.97.

Answer: 27! - [22! * 6!]

Step-by-step explanation:

Decorations available = 12 blue ballons, 9 Green Lanterns and 6 red ribbons

To determine the number if ways of arrangement for if the ribbons must not be together, we must first determine the number of possible ways to arrange these decorations items if there are no restrictions.

Total number of ways to arrange them = [12+9+6]! = 27! = 1.089 * 10^28

If this ribbons are to be arranged distinctively by making sure all six of them are together, then we arrange the 6 of them in different ways and consider the 6ribbons as one entity.

Number of ways to arrange 6 ribbons = 6!.

To arrange the total number of entity now that we have arranged this 6ribbons together and taking them as one entity become: = (12 + 9 + 1)!. = 22!

Number of ways to arrange if all of the ribbons are taken as 1 and we have 22 entities in total becomes: 22! * 6!.

Hence, to arrange these decoration items making sure no two ribbons are together becomes:

= 27! - (22! * 6!)

= 1.08880602 * 10^28

To arrange the decorations, first calculate the number of ways to arrange the balloons and lanterns, then use the concept of stars and bars to calculate the number of ways to place the ribbons. The product of these two calculations gives the total number of ways to arrange the decorations.

To arrange the balloons, lanterns, and ribbons in a row without any two ribbons being next to each other, we need to consider their positions separately. We can arrange the balloons and lanterns first, making sure no two ribbons are adjacent. The number of ways to arrange the balloons and lanterns is (12+1)C12 x (9+1)C9 = 13C12 x 10C9 = 13 x10 = 130.

Now, let's place the ribbons using the concept of stars and bars. We can consider the spaces between the balloons and lanterns as 'bars' and the ribbons as 'stars.' Since there are 13 spaces between the 12 balloons and lanterns, we have 13 bars. We need to place 6 ribbons (stars) in these 13 spaces. The number of ways to do this is (13-6+1)C6 = 8C6 = 28.

The total number of ways to arrange the decorations is the product of the number of ways to arrange the balloons and lanterns and the number of ways to place the ribbons. Therefore, the answer is 130 x 28 = 3640.

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Answer:

0.50

Step-by-step explanation:

The probability that a customer has purchased a cup of coffee given that they have also purchased a piece of cake is determined by the percentage of customers who purchase both coffee and cake (20%) divided by the percentage of customers who purchase cake (40%):

[tex]P(Coffee|Cake) = \frac{P(Coffee\cap Cake)}{P(Cake)}\\P(Coffee|Cake) =\frac{0.20}{0.40}=0.50[/tex]

50% of the customers also purchased coffee given that they have purchased a piece of cake.

Final answer:

To find the probability that a customer purchased a cup of coffee given they purchased a cake, we use conditional probability, resulting in a 50% chance.

Explanation:

The question requires us to use conditional probability to find the probability that a customer who purchased a piece of cake also purchased a cup of coffee. The known probabilities are that 70% of customers purchase coffee, 40% purchase cake, and 20% purchase both.

To find the probability that a customer purchased coffee given they purchased cake, we use the formula for conditional probability: P(A|B) = P(A ∩ B) / P(B), where A is the event 'customer buys coffee' and B is the event 'customer buys cake'. Given P(A ∩ B) = 20% or 0.2, and P(B) = 40% or 0.4, the calculation is P(A|B) = 0.2 / 0.4.

So, the conditional probability is 0.5 or 50%.

Answer:

This is an "Experiment" type of study

Step-by-step explanation:

Researchers use various methods or techniques to conduct research and draw conclusions from it. Some of these methods are given below

1. Experiment

2. Observational study

3. Anecdotal evidence

1. Experiment: In this type of study, researchers have control over their setup and they can give directions or apply any treatment on their subjects.

2. Observational study: In this type of study, researchers cannot give directions or apply any treatment on their subjects but rather they can only observe what is going on.

3. Anecdotal evidence: Also refers to experience and can be defined as personal experience based on something.

The study that we are given is clearly an example of "experiment" since half of the participants were to told walk 2 miles a day for 6 weeks. The researchers have control over their subjects in this case and they gave directions to their subjects to do this and that.

This could have been an observational study if researchers had selected 10 people who walked 2 miles a day for 6 weeks and 10 people who did not walk 2 miles a day for 6 weeks and simply measured their blood pressure and come to a conclusion. This way, it would have been a case of observational study.

Answer:

Experiment

Step-by-step explanation:

Experimental study design is a type of study design in which the investigator or researcher is in complete control of the research environment. For example, a researcher may want to assess the effects of certain treatments on some experimental units. The researcher or investigator decides the type of treatment, the type of experimental unit to use, the time, the allocation and assessment procedures of the treatment and effects respectively. In Experimental study design, the investigator or researcher is in complete control of the exposure and the result should therefore provide a stronger evidence of an association or lack of association between an exposure and a health problem than would an observational study where the investigator or researcher is usually a passive observer as he only observes and analyses facts and events as they occur  naturally or anecdotal evidence which is just someones personal experience or testimony without scientific proof that can be based on some measurement or experimentation.

Answer:

Option 1

Step-by-step explanation:

(3m/n)⁴ = (3⁴×m⁴)/n⁴

= 81m⁴/n⁴

Answer: $b(abc+5ab)+b(c+a)$ = - 18

Step-by-step explanation:

If $a = $ - 1, $b = $3 and $c = $- 5, then

abc = - 1 × 3 × - 5 = 15

5ab = 5 × - 1 × 3 = - 15

Then,

$b(abc+5ab) = 3(15 - 15)

Opening the brackets, it becomes

3 × 0 = 0

(c + a)$ = - 5 - 1 = - 6

Then,

b(c+a)$ = 3 × - 6 = - 18

Therefore,

$b(abc+5ab)+b(c+a)$ = 0 + (- 18)

$b(abc+5ab)+b(c+a)$ = 0 - 18 = - 18

Final answer:

After substituting the given values into the expression and simplifying, the result of the calculation is -18.

Explanation:

To calculate b(abc+5ab)+b(c+a) with given values of a=-1, b=3, and c=-5, first, substitute these values into the expression:

b(abc+5ab)+b(c+a) = 3((-1)(3)(-5)+5(-1)(3))+3((-5)+(-1))

Next, simplify inside the parentheses:

3((15)+(-15))+3(-6)

Now, simplify further:

3(0)+3(-6)

This reduces to:

0 - 18

And the final result is:

-18

Answer:

the probability is 0.32 (32%)

Step-by-step explanation:

defining the event W= has extended warranty , then

P(W)= probability of purchasing the basic model * probability of purchasing extended warranty given that has purchased the basic model + probability of purchasing the deluxe model * probability of purchasing extended warranty given that has purchased the deluxe model = 0.3 * 0.44 + 0.7 * 0.40 = 0.412

then using the theorem of Bayes for conditional probability and defining the event B= has the basic model , then

P(B/W)= P(B∩W)/P(W)= 0.3 * 0.44/0.412 =0.32 (32%)

where

P(B∩W)= probability of purchasing the basic model and purchasing the extended warranty

P(B/W) = probability of purchasing the basic model given that has purchased the extended warranty

Final answer:

Using Bayes' theorem, there is approximately a 32% chance that a customer who purchased an extended warranty has a basic model camera.

Explanation:

The question asks us to calculate the probability of a randomly selected purchaser having a basic model given that they have an extended warranty. We can use Bayes' theorem to solve this. Let's denote B as the event of buying a basic model, D as the event of buying a deluxe model, and W as the event of purchasing an extended warranty. From the information provided, we can infer :

P(B) = 0.30 (30% of cameras sold are basic models)

P(D) = 1 - P(B) = 0.70 (since if it's not a basic model, it's a deluxe model)

P(W|B) = 0.44 (44% of basic model buyers purchase an extended warranty)

P(W|D) = 0.40 (40% of deluxe model buyers purchase an extended warranty)

We are interested in P(B|W), the probability that a randomly selected purchaser who bought an extended warranty has a basic model. Using Bayes' theorem:

P(B|W) = (P(W|B) * P(B)) / ((P(W|B) * P(B)) + (P(W|D) * P(D)))

Plugging in the values:

P(B|W) = (0.44 * 0.30) / ((0.44 * 0.30) + (0.40 * 0.70))

P(B|W) = (0.132) / (0.132 + 0.28)

P(B|W) = 0.132 / 0.412 = approximately 0.320

So, there is approximately a 32% chance that a customer with an extended warranty has purchased a basic model camera.

Answer:

2.17

Step-by-step explanation:

As the population variance is known we can calculate population standard deviation and so, z-test statistic will be used.

[tex]z=\frac{xbar-pop mean}{\frac{pop SD}{\sqrt{n} } }[/tex]

population variance=σ²=0.36

population standard deviation=σ=√0.36=0.6

The value of population mean can be achieved through null hypothesis.

Null hypothesis : μ=7.4

Alternative hypothesis : μ≠7.4

population mean=μ=7.4

xbar=7.5

n=170

z=(7.5-7.4)/(0.6/√170)

z=0.1/(0.6/13.038)

z=0.1/0.046

z=2.17

Thus, the calculated z-test statistic is 2.17.