The cold water faucet can fill a sink in 2 minutes. The drain can empty a full sink in 3 minutes. If the faucet were left on and the drain was left open, how long would it take to fill the sink?

Answer:

Induction

Step-by-step explanation:

This is an example of induction. When you take a (possibly false) conclusion according to the information you know. In this case, since you dont know of any case of a biology student not going for picnic, then you conclude that every biology student go for picnic .

 It isnt deduction because the reasoning is not based on logic, rather, it is based on the partial information you know. You can argue that, since you know many students that went for a picninc, then the whole class should go to the picnic because they organized it that way, however you might need a bit more of information to reach this conclussion, for example, that the teacher went with them. Maybe, for example, a small group of students decided to go elsewhere instead.

There isnt inaccurate information here. It is incomplete, yes, but it doesnt lack accuracy: all you know is true. There isnt innacurate information.

Answer:he borrowed $22000 from bank 1.

He borrowed $2000 from bank 2

Step-by-step explanation:

Let x represent the amount of money that he borrowed from bank 1.

Let y represent the amount of money that he borrowed from bank 2.

Bobby Borrowed 24,000 from two different banks to start a business. This means that

x + y = 24000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

Considering the money borrowed from bank 1,

P = x

R = 4%

T = 1

I = (x × 4 × 1)/100 = 0.04x

Considering the money borrowed from bank 2,

P = y

R = 5.5%

T = 1

I = (y × 5.5 × 1)/100 = 0.055y

if the total interest after 1 year was $990, it means that

0.04x + 0.055y = 990 - - - - - -1

Substituting x = 24000 - y into equation 1, it becomes

0.04(24000 - y) + 0.055y = 990

960 - 0.04y + 0.055y = 990

- 0.04y + 0.055y = 990 - 960

0.015y = 30

y = 30/0.015 = $2000

Substituting y = 2000 into

x = 24000 - y, it becomes

x = 24000 - 2000

x = 22000

Final answer:

The departure time in Riyadh when flying to Manila can be calculated by subtracting the flight duration from the arrival time in Manila.

Explanation:

To determine the time in Riyadh when you left for Manila, we need to calculate the time difference between the two cities. We know that when it's 11:00 a.m. in Riyadh, it's 4:00 p.m. in Manila, giving us a time difference of 5 hours. Since your flight duration is 11 hours and 40 minutes, we need to subtract this time from the arrival time in Manila to find the departure time in Riyadh. Subtracting 11 hours and 40 minutes from 2:00 a.m. on Monday gives us 2:00 p.m. on Sunday. Therefore, it was 2:00 p.m. on Sunday in Riyadh when you left for Manila.

Answer:

 B: Based on the data, this is an example of correlation.

Step-by-step explanation:

It's the correct answer because there somewhat related and as the ice cream trucks get more sales the weather gets warmer. They both have a positive increase.

Based on the data, this is an example of correlation and causation. Option A is correct

Correlation is defined as the two things depends on each other.

Here,

People would like to buy ice cream in warm weather this statement is correlation and causation is people would like to by ice cream cause the increase in temperature.  

Thus, Based on the data, this is an example of correlation and causation.

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Answer: 2miles/ 2.5miles.

Step-by-step explanation:

If rentals for a car costs $35

subtracting this $35 from budget of $85 gives us

$85-$35= $50

By travelling one mile, we subtract $20, we're then left with

$50 - $20 = $30.

By travelling another mile, we subtract another $20, which gives

$30-$20= $10.

Since this $10 is not enough to cater for another mile, the maxmimum number of miles is 2miles.

But if allowed in halves, the $10 can cover half a mile and the longest possible distance she can travel is 2.5miles

Answer:

C. The term linear refers to a straight line, and r measures how well a scatter plot fits a straight-line pattern

Step-by-step explanation:

In statistics, when two variables are being investigated, the location of the co-ordinates on a rectangular co-ordinates ystem is called a scatter diagram.

The amount of linear correlation between two variables is expressed by a coefficient of correlation, given the symbol r. This is defined in terms of the deviations of the co-ordinates of two variables from their mean values and is given by the product-moment formula

For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists.

Answer:angular speed=471.429rad/sec

Step-by-step explanation:

One revolution is :

2×pi×radians

Then 4500 revolution will be:

2×pi×4500rad= 9000pi rad

1minutes = 60seconds

So the angular speed is :

=(9000×pi rad) / minutes

=9000×(22/7)rad /60seconds

=471.42857143 rad/sec

=471.429rad/sec to 3 d.p

The angular speed of the blade is [tex]471[/tex] radian per minute.

In one revolution, angle made is [tex]2\pi[/tex] radian.

In 4500 revolutions = [tex]2\pi *4500=9000\pi[/tex] radian.

We know that ,

1 hour = 60 minute.

Angular speed = [tex]\frac{9000\pi radian}{60minute} =\frac{9000*3.14}{60}=471radian/minute[/tex]

Therefore, the angular speed of the blade is [tex]471[/tex] radian per minute.

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Answer:

Therefore, the following results are not possible:

A) green offspring only

B) yellow offspring only

D) green and yellow offspring.

Step-by-step explanation:

We know that feather color in budgies is determined by two different genes. For blue color are combinations yyBB or yyBb. For white color is combination yybb.  

By combining these two colors we can not get green and yellow.  

Because green and yellow colors are  in this form:

Green: YYBB, YyBB, or YYBb

Yellow: YYbb or Yybb.

Therefore, the following results are not possible:

A) green offspring only

B) yellow offspring only

D) green and yellow offspring.

A) When x increases by 1 unit, y increases by 4 units.

B) When x decreases by 5 units, y decreases by 20 units.

Use the concept of linear equation defined as:

The equation having degree one is called a linear equation.

The point-slope of the linear equation is:

y = mx + c

The given  equation is:

y = 4x - 3

A) To find the corresponding change in y when x increases by 1 unit,

Use the given equation y = 4x - 3.

By substituting x+1 in place of x, we get

y = 4(x+1) - 3.

Simplifying this expression,

y = 4x + 4 - 3,

y = 4x + 1.

Comparing this equation with the original equation,

That the coefficient of x is the same (4),

Which means that the rate of change remains constant.

Therefore, when x increases by 1 unit, y will increase by 4 units.

B) Similarly, to find the corresponding change in y when x decreases by 5 units,

Substitute x-5 in place of x in the original equation.

This gives us y = 4(x-5) - 3.

Simplifying further, we get

y = 4x - 20 - 3,

y = 4x - 23.

Comparing this equation with the original equation,

Again the coefficient of x remains the same (4), indicating a constant rate of change.

Therefore, when x decreases by 5 units, y will decrease by 20 units.

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Final answer:

For the equation y = 4x - 3, an increase of x by 1 unit results in an increase of y by 4 units, and a decrease of x by 5 units results in a decrease of y by 20 units, due to the slope of the line being 4.

Explanation:

The equation in question is y = 4x - 3.

A) Change in y when x increases by 1 unit:

For the linear equation given, the coefficient in front of x represents the slope of the line, which is 4. This indicates that for every 1 unit increase in x, y will increase by 4 units (since the slope is the rate of change of y with respect to x). Therefore, if x increases by 1 unit, y will increase by 4 units.

B) Change in y when x decreases by 5 units:

If x decreases by 5 units, we again use the slope of the line to determine the change in y. Since the slope is 4, a decrease in x by 5 units will result in a decrease in y by 20 units (5 units × 4 = 20 units).

Answer:888 cubic centimeters

Step-by-step explanation:

The formula for determining the volume of a rectangular prism is expressed as

Volume = length × height × width

Length = 10 centimeters

Width = 8 centimeters

Height = 12 centimeters

Therefore, the volume of the rectangular prism would be

10 × 8 × 12 = 960 centimeters³

A rectangular hole with a length of 2 centimeters and a width of 3 centimeters is cut through the prism. The height of the hole would also be 12 centimeters.

Therefore, the volume of the rectangular hole would be

2 × 3 ×12 = 72 cm³

the volume of the resulting figure would be

960 - 72 = 888 cm³

ANSWER: Adult tickets: 200  Student tickets:400

STEP-BY-STEP EXPLANATION:

n = number of adult tickets sold

2n = number of student tickets sold

2n(1.25) + n(1.75) = $850

2.50n + 1.75n = $850

4.25n = $850

n = 200

2n= 2 × 200= 400

Answer:

The average life of the mice that are placed on this diet is less than 40 months.

Step-by-step explanation:

Consider the provided information.

When 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40.

The null and alternative hypothesis are:

[tex]H_0:\mu=40\\H_a:\mu<40[/tex]

64 mice that are placed on this diet have an average life is 38 months with a standard deviation of 5.8 months.

Therefore, [tex]n = 64, \bar x=38\ and\ \sigma=5.8[/tex]

Use the formula: [tex]z=\dfrac{\bar x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]

Substitute the respective values in the above formula.

[tex]z=\dfrac{38-40}{\frac{5.8}{\sqrt{64} }}[/tex]

[tex]z=-\dfrac{2}{\frac{5.8}{8}}\approx-2.76[/tex]

Now using the table [tex]P(Z<z)=0.029[/tex]

The p value is smaller than 0.05 so reject the null hypothesis.

Therefore, the average life of the mice that are placed on this diet is less than 40 months.

The reciprocal of n must be less than –10

Solution:

Given n denotes a number to the left of 0 means n < 0.

Square of n is less than [tex]\frac{1}{100}[/tex] means [tex]n^2<\frac{1}{100}[/tex].

Therefore, we have [tex]n<0[/tex] and [tex]n^2<\frac{1}{100}[/tex].

⇒ [tex]n^2<\frac{1}{100}[/tex]

Taking square root on both sides, we get

⇒ [tex]n<\± \frac{1}{10}[/tex]

⇒[tex]\frac{-1}{10}<n<\frac{1}{10}[/tex]

⇒ But we know that n < 0, so [tex]n<\frac{1}{10}[/tex] false.

It should be [tex]\frac{-1}{10}<n[/tex].

To equal the expression, multiply both sides of the equation by –10n.

⇒ [tex]-\frac{1}{10} \times\frac{-10}{n}>n \times\frac{-10}{n}[/tex]   (symbol < changed to > when multiply by minus)

⇒ [tex]\frac{1}{n}>-10[/tex]

Hence, the reciprocal of n must be less than –10.

Answer:

C) 0.45

Step-by-step explanation:

Given that a population mean is 0.45, standard deviation is 0.001 and margin of error stands at 0.5% we have the following

0.45 + 0.001 = 0.451

Population mean with standard deviation is 0.451.

0.451 * 0.5% = 0.448745

We now reduce the number to two decimals and get the final marigin of error

0.45 as result

Answer:

Confirmation it is 0.45

Step-by-step explanation:

The cost of one granola bar is $0.60 and cost of one apple is $0.35

Step-by-step explanation:

Let,

Cost of one granola bar = x

Cost of one apple = y

According to given statement;

4x+y=2.75     Eqn 1

2x+3y=2.25   Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+3y=2.25)\\4x+6y=4.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 1 from Eqn 3

[tex](4x+6y)-(4x+y)=4.50-2.75\\4x+6y-4x-y=1.75\\5y=1.75[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{1.75}{5}\\y=0.35[/tex]

Putting y=0.35 in Eqn 2

[tex]4x+0.35=2.75\\4x=2.75-0.35\\4x=2.40[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{2.4}{4}\\x=0.60[/tex]

The cost of one granola bar is $0.60 and cost of one apple is $0.35

Keywords: linear equation, elimination method

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The cost of one granola bar is $0.60, and the cost of one apple is $0.35.

To solve the problem, we need to set up a system of linear equations based on the information given:

Georgia paid $2.75 for 4 granola bars and 1 apple.

Addison paid $2.25 for 2 granola bars and 3 apples.

Let G be the cost of one granola bar and A be the cost of one apple.
4G + A = 2.75
2G + 3A = 2.25

Multiply the first equation by 3
3(4G + A = 2.75)
=> 12G + 3A = 8.25
(12G + 3A) - (2G + 3A) = 8.25 - 2.25
10G = 6
G = 0.60
Substitute the value of G back into the first equation,
4(0.60) + A = 2.75
2.40 + A = 2.75
A = 0.35

Therefore, the cost of one granola bar is $0.60 and the cost of one apple is $0.35.

Answer:

Byte

Step-by-step explanation:

We use byte to represent 1 and 0 in computing..

The most basic unit of computing is the 'bit', which can be represented as either 1 (on) or 0 (off). This binary information is used in digital circuits to perform tasks in computing devices. The use of bits was crucial to the development of modern computing.

The most fundamental unit of computing is the bit, which is represented as an on (1) or off (0) value. In digital circuits found in modern devices, transistors behave like switches that can be either on or off, encoding information in a binary code of ones and zeros. These bits are utilised to perform a variety of tasks like data manipulation and transmission of signals. Over time, scientists have found ways to amplify the computing capacity of bits by integrating vast collections of transistors on single silicon wafers, creating the integrated circuits (IC), which is foundational to the modern digital computer revolution.

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Answer:B

Step-by-step explanation:

Given

Right circular cone is inscribed in a hemisphere so that the base of the cone coincides with base of hemisphere

Height of cone is equal to radius of hemisphere

so ratio of the height of cone to the radius of the hemisphere is 1:1

Answer: The amount of fine F as a function of the driving speed x would be

[tex]25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75[/tex]

Step-by-step explanation:

Since we have given that

Maximum speed = 75 mi/hr

Minimum speed = 50 mi/hr

Fine for every mile per hour above the maximum speed or below the minimum speed = $25

So, Amount of fine for below the minimum speed would be

[tex]25(50-x)\ ;\ 0\leq x<50[/tex]

Amount of fine for above the maximum speed would be

[tex]25(x-75)\ ;\ x> 75[/tex]

There will be no fine in between the following range:

[tex]0\ ;\ 50\leq x\leq 75[/tex]

Hence, the amount of fine F as a function of the driving speed x would be

[tex]25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75[/tex]

The function that represents the given situation is required.

The required function is

[tex]f(x)=\begin{cases}25(50-x) & \text{ if } 0\leq x<50 \\0 & \text{ if }  50\leq x\leq75\\25(x-75) & \text{ if } x>75 \end{cases}[/tex]

Let [tex]x[/tex] be the speed of the car

Maximum speed limit is 75 mi/h

Minimum speed limit is 50 mi/h

Any speed above the maximum speed and any speed below the minimum speed the fine is $25 dollar per mile per hour.

[tex]f(x)=25(50-x),\ 0\leq x<50[/tex]

[tex]f(x)=25(x-75),\ x>75[/tex]

There is no fine if the speed is between the given limits.

[tex]f(x)=0,\ 50\leq x\leq75[/tex]

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Answer: Simple random

Step-by-step explanation:

Since , the company randomly selects customers and asks them about their level of satisfaction with the company.

So the chances for each customer to get selected are equal.

This technique of sampling is known as simple random sampling .

Definition:

Here , the probability for each individual to get selected is equal as [tex]\dfrac{1}{N}[/tex] , where N = Population size.

In the rest of sampling method (convenience , systematic , stratified and cluster) , the individuals in the population do not have equal chances to get selected. .

The type of sampling used is Cluster Sampling.

The type of sampling used in this scenario is Cluster Sampling.

Cluster sampling involves dividing the population into smaller groups or clusters, and then selecting a random sample of clusters to survey.

In this case, the customers are grouped based on their respective clusters in the customer database, and then a random sample of 30 clusters is selected to participate in the satisfaction survey.

Answer:

The answer to your question is below

Step-by-step explanation:

*A(x)=3x³ + 2x² - x           This polynomial is not divisible by (x - 1)

                                       Factor completely    3x(x + 1)(3x - 1)

*B(x)=5x³ - 4x² - x            This polynomial is divisible by (x - 1)

                                       factor completely   3x(x - 1)(5x + 1)

*C(x)=2x³ - 3x² + 2x - 1     This polynomial is divisible by (x - 1)

                                        Synthetic division      2   - 3  + 2  -1      1

                                                                                   2    -1    1                

                                                                            2    -1      1    0

*D(x)=x³ + 2x² + 3x + 2   This polynomial is not divisible by (x - 1)

                                        Synthetic division    1    2   3   2   1

                                                                                1    3   6                      

                                                                           1    3   6   8                  

Answer:

B(x) and C(x)

Step-by-step explanation:

B(x) and C(x)

Answer:

[tex]V_{avg} = \frac{ln2}{e} = 0.255fts^{-1}[/tex]

Step-by-step explanation:

The question asks for the average velocity and not the instantaneous velocity (which would have meant to differentiate). So, the right formula is

[tex]V_{avg} = \frac{s(t_{2}) - s(t_{1} ) }{t_{2} -t_{1} } =[/tex]

From the question, [tex]t_{1}[/tex] corresponds to e seconds and [tex]t_{2}[/tex] corresponds to 2e seconds. So, we have

[tex]V_{avg} = \frac{ln(2e) - ln(e)}{2e - e}[/tex]

One of the laws of logarithms says that

[tex]ln(\frac{a}{b} )= ln(a) - ln(b). \\\\ Therefore, ln(2e) - ln(e) = ln(\frac{2e}{e} ) = ln(2)[/tex]

[tex]V_{avg} = \frac{ln(2)}{e} = 0.2550fts^{-1}[/tex] ≅ [tex]0.255fts^{-1}[/tex]

Answer:

Step-by-step explanation:

The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, that he works.

The domain of a function are the set of possible values of x, the independent variable that satisfies the function.

Fernando works between 12 and 25 hours each week. It means that the statement that best represents the domain of this function for any given week would be

12 ≤ x ≤ 25

The statement that best represents the domain of this function for any given week would be 12 ≤ x ≤ 25.

The function is a type of relation, or rule, that maps one input to a specific single output.

Fernando works between 12 and 25 hours each week.

The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, he works.

The domain is the set of values x for which the given function is defined.

Or The independent variable that satisfies the function.

The statement that best represents the domain of this function for any given week would be 12 ≤ x ≤ 25.

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Answer:

It would take skinny cat 6 mins to reach fat cat.

Step-by-step explanation:

Given:

Speed of Fat cat = 75 yd/min

Speed of skinny cat = 100 yd/min

We need to find the time taken by skinny cat to reach fat cat.

Let the distance covered by both be 'd'.

Also let the time taken by Fat cat to cover distance 'd'  be 't' mins.

Now we know that skinny cat started 2 mins later so time taken by Skinny cat will be [tex]t-2 \ mins[/tex].

Now we know that;

Distance is equal to speed times time.

framing in equation form we get;

Distance cover by fat cat = [tex]75t[/tex]

Distance cover by skinny cat = [tex]100(t-2) =100t-200[/tex]

Both distance have to made same since we need to find the time required more to reach the other cat.

[tex]100t-200=75t[/tex]

Combining like terms we get;

[tex]100t-75t=200\\\\25t =200[/tex]

Dividing both side by 25 we get;

[tex]\frac{25t}{25}=\frac{200}{25}\\\\t = 8\ mins[/tex]

Time taken by skinny cat = [tex]t-2 =8-2=6 \ mins[/tex]

Hence it would take skinny cat 6 mins to reach fat cat.

Skinny Cat catches up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am. This is calculated by determining the head start that Fat Cat has and the faster pace at which Skinny Cat moves.

We are presented with a problem where two cats, one named Fat Cat and the other Skinny Cat, start at different times and move at different speeds. Fat Cat starts at 9:00 am moving at 75 yards per minute, and Skinny Cat starts at 9:02 am moving at 100 yards per minute. The question is to find out how long it takes for Skinny Cat to catch up to Fat Cat.

So, Skinny Cat will catch up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am.

Answer:

Angle bisector

Step-by-step explanation:

Given that a food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets.

We have to find out where she should park her truck on a perpendicular bisector, and angle bisector, a median, or an altitude

We know the perpendicular bisector is the locus of points equidistant form two points.

But here two streets can be treated as straight lines only.

The angle bisector of two lines will have all the points on the bisector.

Median is not applicable since here no triangle is there neither altitude

So right answer is angle bisector.

She should park her  truck on  the angle bisector of angle formed by intersection of two roads.

Answer:

50.75 units

Step-by-step explanation:

In this problem

Triangles HFM and PST are similar

we know that that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

step 1

Find the scale factor

Let

z ----> the scale factor

[tex]z=\frac{HF}{PS}[/tex]

substitute the given values

[tex]z=\frac{14}{8}=1.75[/tex]

step 2

Find the perimeter of triangle PST

[tex]P=8+9+12=29\ units[/tex]

step 3

Find the perimeter of triangle HFM

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor

so

[tex]29(1.75)=50.75\ units[/tex]

Answer:

a. A = {RRR,LLL,SSS}

b. B = {RLS, RSL, LSR, LRS, SRL, SLR}

c. C = {RRS, RRL, RSR, RLR, LRR, SRR}

d. D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}

e. C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}

C n D = {RRS, RRL, RSR, RLR, LRR, SRR}

Step-by-step explanation:

a..

All three vehicles go in the same direction

This means that all the three vehicles either go straight, or right or left at the same time.

So, A { {RRR, LLL, SSS}

b..

All three vehicles take different directions

Thus means that all the vehicle take different routes

If a vehicle takes the the straight direction, the other 2 vehicles take right and left directions respectively

So, B = {RLS, RSL, LSR, LRS, SRL, SLR}

c..

Exactly two of the three vehicles turn right

This means that two vehicles take right direction while the last vehicle either tske the straight route or left route.

C = {RRS, RRL, RSR, RLR, LRR, SRR}

d..

Exactly two vehicles go in the same direction.

The means that if two vehicles pass straight direction then the third vehicle takes either the right or left direction.

Also, if two vehicles pass right direction, the third vehicle either takes the left direction or straight direction

Lastly, if two vehicles pass left direction then the third vehicle either pass the straight direction or right direction.

D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}

e. C U D = the union of items in C and D without repetition

So,

C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}

C n D = Common items in C and D

C n D = {RRS, RRL, RSR, RLR, LRR, SRR}

List outcomes in D'.D' = List outcomes in C ∪ D.C ∪ D = List outcomes in C ∩ D.C ∩ D =

The question presents various scenarios of successive vehicles choosing directions. Outcomes are determined in cases where all vehicles choose the same direction, all choose different directions, exactly two choose right, exactly two choose the same direction (any), and the negation of the latter case. The outcomes of combining these scenarios (union and intersection) are also defined.

The events refer to the outcomes of the directions three successive vehicles could potentially take. There are three possibilities: right (R), left (L), or straight (S).

(a) Event A where all three vehicles go in the same direction, would include these outcomes: A = {RRR, LLL, SSS}.

(b) Event B where all three vehicles take different directions, would look like this: B = {RLS, RSL, LRS, LSR, SRL, SLR}.

(c) Event C where exactly two of the three vehicles turn right would include these outcomes: C = {RRS, RRL, SRR, LRR, RSR, RLR}.

(d) Event D where exactly two vehicles go in the same direction, would include these outcomes: D = {RRS, RRL, SRS, SSL, LRL, LLR, RRS, RLS, RSS, LSS, SLL, LLS, SSR, SRL, SRR, LLR, LRS, LRR}.

(e) Event D' which stands for everything that's not in event D, includes these outcomes: D' = {RLS, SLR, LRS, RSL, LSR, SRL}.

The union of events C and D, C ∪ D, combines the outcomes of both C and D, but without repetition: C ∪ D = {RRS, RRL, SRS, SSL, LRL, LLR, RRS, RLS, RSS, LSS, SLL, LLS, SSR, SRL, SRR, LLR, LRS, LRR, RSR, RLR}.

Finally, the intersection of event C and D, C ∩ D, includes only outcomes common to both C and D: C ∩ D = {RRS, RRL, SRR, LRR, RSR, RLR}.

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Answer:

40.112

Step-by-step explanation:

Answer:

DIRECT WAY EXCEL

"=NORM.DIST(75,80,3,TRUE)"

And we got: [tex] P(X\leq 75)= 0.04779[/tex]

OTHER WAY

[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]

And we can find this probability using the normal standard table or excel:

[tex]P(Z<-1.67)=0.04779[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(80,3)[/tex]  

Where [tex]\mu=80[/tex] and [tex]\sigma=3[/tex]

And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:

[tex] P(X\leq 75)[/tex]

One way to do this in excel is with the following formula:

"=NORM.DIST(75,80,3,TRUE)"

And we got: [tex] P(X\leq 75)= 0.04779[/tex]

And the other way is use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]

And we can find this probability using the normal standard table or excel:

[tex]P(Z<-1.67)=0.04779[/tex]