Find the GCF.

36x3 and 48x4

Answer:

The correct option is 2.

Step-by-step explanation:

Given information: Height of both prism are same.

Right rectangular prism has base dimensions of 3 inches by 12 inches.

Volume of a right rectangular prism:

[tex]V=Bh[/tex]

where, B is base area and h is height of the prism.

The volume of right rectangular prism is

[tex]V=(3\times 12)\times h=36h[/tex]

Therefore the volume of right rectangular prism is 36h cubic inches.

An oblique rectangular prism has base dimensions of 4 inches by 9 inches.

Volume of a oblique rectangular prism:

[tex]V=Bh[/tex]

where, B is base area and h is height of the prism.

The volume of right rectangular prism is

[tex]V=(4\times 9)\times h=36h[/tex]

Therefore the volume of oblique rectangular prism is 36h cubic inches.

The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

Option 2 is correct .

The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

The formula for the Volume of a right rectangular prism is:

V = B * h

where,

B is base area.

h is height of the prism.

Thus:

V = 3 * 12 * h

V = 36h

Similarly, the volume of the oblique rectangle is:

V = Bh

V = 4 * 9 * h

V = 36h

Thus, we can see that the volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

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3x + y = -10. The standard form of the equation that is parallel to y = -3x + 3 and goes through point (-5, 5) is 3x + y = -10.

The equation is written in the slope-intercept form y = mx +b. So:

y = -3x + 3

The slope m = -3

Since the slopes of parallel lines are the same, we are looking for a slope line m = -3 and goes through point (-5, 5).

With the slope-intercept form:

y = mx + b

Introducing the slope m = -3:

y = -3x + b

Introducing the point (-5, 5):

5 = -3(-5) + b

5 = 15 + b

b= 5 - 15

b = -10

then

y = -3x -10

write the equation in standard form ax + by = c:

y = -3x -10

3x + y = -10

To find the standard form of the equation of a line that is parallel to y = -3x + 3 and passes through the point (-5, 5), let's follow these steps:
1. **Identify the slope**: Since parallel lines have the same slope, we can take the slope of the given line y = -3x + 3, which is -3.
2. **Use the point-slope form**: With the slope known and a point provided, we can use the point-slope form of the equation, which is:
  \[ y - y_1 = m(x - x_1) \]
  where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.
3. **Apply the point and slope**: Insert the slope (-3) and the point (-5, 5):
  \[ y - 5 = -3(x - (-5)) \]
  \[ y - 5 = -3(x + 5) \]
4. **Distribute the slope**: Multiply -3 by both terms inside the parentheses:
  \[ y - 5 = -3x - 15 \]
5. **Isolate y:** Add 5 to both sides of the equation to isolate y:
  \[ y = -3x - 15 + 5 \]
  \[ y = -3x - 10 \]
6. **Convert to standard form**: The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) should be non-negative. Arrange the terms:
  \[ 3x + y = -10 \]
So the standard form of the equation that is parallel to y = -3x + 3 and passes through the point (-5, 5) is \(3x + y = -10\).

Answer:

7 minutes

Step-by-step explanation:

g(x) = x^4 - 3x^2 + 4x - 5

g(2) = 2^4 - 3(2^2) + 4(2) - 5

g(2) = 16 - 3(4) + 4(2) - 5

g(2) = 16 - 12 + 8 - 5

16 - 12 = 4

4 + 8 = 12

12 - 5 = 7

input: 2

output: 7

ordered pair: (2,7)

By modeled function, the time taken to reach the school is 7 minutes.

A function which depicts the variation of a given dependent parameter represented by the variable in the function is known as a modeled function. For modeled function, we input the value of the dependent parameter in place of the given variable and the solution of function gives us the result of dependency.

Given that the time it takes to get to school, measured in minutes, is modeled using the function g(x) = [tex]x^{4} - 3x^{2} + 4x - 5[/tex] , where x is the number of stops the bus makes.

Also said that the bus makes 2 stops after we board.

Thus the dependent parameter is stop which is represented by the variable x in the modeled function g(x) and the solution of g(x) gives us the time period. We will get the time period by putting x = 2 in the modeled function.

Putting x = 2 in g(x), we get -

⇒ g(x) = [tex]2^{4} - 3*2^{2} + 4*2 - 5[/tex]

⇒ g(x) = 16 - 12 + 8 - 5

∴  g(x) = 7

Thus the time period is 7 units.

Therefore, by modeled function, the time taken to reach the school is 7 minutes.

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Answer:

Pool will be filled in 280 hours

Step-by-step explanation:

Inlet pipe fills in  40 hours = 1 pool

Inlet pipe fills in 1 hours = [tex]\frac{1}{40}[/tex]

Drain pipe empty in 42 hours = 1 pool

Drain pipe empty in 1 hour =  [tex]\frac{1}{42}[/tex]

If both pipes are opened together

 then in pool fills in 1 hour =  [tex]\frac{1}{40}[/tex] -  [tex]\frac{1}{42}[/tex]

      on simplifying the right side ,we get  [tex]\frac{42-40}{(40)(42)}[/tex]

                                                                 =      [tex]\frac{2}{(40)(42)}[/tex]

                                                                 =     [tex]\frac{1}{840}[/tex]

      [tex]\frac{1}{840}[/tex]  pool fills in 1 hour

                       1 pool will be filled in 840 hours

    [tex]\frac{2}{3}[/tex]     pool is filled

empty pool =  1 - [tex]\frac{2}{3}[/tex] =  [tex]\frac{1}{3}[/tex]

therfore  [tex]\frac{1}{3}[/tex] pool will be filled in     [tex]\frac{1}{3}[/tex]X 840 =

                                                                                           = 280 hours

The  calculations indicate that 280 hours is the  time required to fill 2/3 of the pool with both pipes open.

Inlet Pipe Rate:

The inlet pipe can fill the pool in 40 hours.

Therefore, the rate of the inlet pipe is 1/40 pool per hour.

Drain Pipe Rate:

The drain pipe can empty the pool in 42 hours.

Therefore, the rate of the drain pipe is 1/42 pool per hour.

Combined Rate when both pipes are open:

The net rate when both pipes are open is the difference between their individual rates:

Net rate = (1/40) - (1/42)

Simplify the Net Rate:

Find a common denominator for 40 and 42, which is 840:

Net rate = (42 - 40) / 840 = 2/840 = 1/420

Time to Fill 2/3 of the Pool:

Set up the equation: Net rate * Time = 2/3

Substitute the net rate: (1/420) * Time = 2/3

Cross-multiply to solve for time: Time = (2/3) * (420/1) = 280

Therefore, it takes 280 hours to fill 2/3 of the pool when both the inlet and drain pipes are open.

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Answer:

Step-by-step explanation:

The temperature at a given altitude is

y = 36 - 3x

The temperature on the surface of the planet is the point (0,t) where t is the temperature for the given height.

y = 36 - 3*0

y = 36

So at the surface of the planet is 36 degrees C.

======================

Effectively it is the slope of the equation which is - 3

So ever km going up will mean a loss of 3 degrees. I think they want you to write -3

Answer:

15 miles per hour

Step-by-step explanation:

Average Speed is:

Average Speed = Total Distance/Total Time

Going uphill, she took 12 minuets, that is hours is 12/60 = 0.2 hours

We know D = RT, Distance = Rate(speed) * Time

Thus,

D = 10mph * 0.2 hr = 2 miles

So, total distance (uphill and downhill) = 2 + 2 = 4 miles

Downhill the time she took is

D = RT

2miles = 30mph * T

T = 2/30 = 1/15 hours = 1/15 * 60 = 4 minutes

Hence total time is 12 + 4 = 16 minutes

Note: 16 minutes = 16/60 = 4/15 hours

Now

Average Speed = Total Distance/Total Time

Average Speed = 4 miles/ 4/15 hours = 15 mph

Answer:

The Answer is 15.00000000000000000... miles per hour

Step-by-step explanation: You do tis by doing your work and not checking for answers

Answer:

[tex]x=1/4(y-2)^{2}-1[/tex]

Step-by-step explanation:

Use Vertex form: [tex]x=a(y-k)^{2}+h[/tex]

Given: vertek (h, k)=(-1, 2)  

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

A point:(x , y) = (3, 6)

[tex]3 = a (6-2)^{2} -1[/tex]

16a=4, a=1/4

The equation is : [tex]x=1/4(y-2)^{2}-1[/tex]

Answer:

(-10,-10)

Step-by-step explanation:

9x-9y=0

3x-4y=10

In elimination, we want both equations to have the same form and like terms to be lined up.  We have that.  We also need one of the columns with variables to contain opposites or same terms. Neither one of our columns with the variables contain this.  

We can do a multiplication to the second equation so that the first terms of each are either opposites or sames. It doesn't matter which.  I like opposites because you just add the equations together. So I'm going to multiply the second equation by -3.

I will rewrite the system with that manipulation:

9x-9y=0

-9x+12y=-30

----------------------Add them up!

0+3y=-30

     3y=-30

       y=-10

So now once you find a variable, plug into either equation to find the other one.

I'm going to use 9x-9y=0 where y=-10.

So we are going to solve for x now.

9x-9y=0 where y=-10.

9x-9(-10)=0  where I plugged in -10 for y.

9x+90=0  where I simplified -9(-10) as +90.

9x     =-90 where I subtracted 90 on both sides.

x=       -10 where I divided both sides by 9.

The solution is (x,y)=(-10,-10)

Answer:

  z = 2.00

Step-by-step explanation:

This is a number many statistics students memorize.

95.44% of the distribution lies within 2 standard deviations of the mean.

Answer:

z = 2.00

Step-by-step explanation:

The value of z such that "0.9544" of the area lies between −z and z rounded to two decimal places is z = 2.00.

Answer:

The answer is 9

Answer:

Step-by-step explanation:

9

Answer:

The answer is 1.94

You need to have 1.94 hours a week to loose a monthly weight of 3 pounds

Answer:

The dimensions on the blueprints are 0.9 inches and 0.8 inches

Step-by-step explanation:

* Lets explain the relation between the drawing dimensions and

 the real dimensions

- A scale drawing make a real object with accurate sizes reduced

 or enlarged by a certain amount called the scale

- Ex: If the scale drawing is 1 : 10, so anything drawn with the size of

 1 have a size of 10 in the real so a measurement of 15 cm on the

 drawing will be 150 cm on the real

- In a scale drawing, all dimensions have been reduced by the same

 proportion

* Lets solve the problem

- On a set of blueprints for a new home, the contractor has

  established a scale of 0.5 in : 10 ft

∵ The drawing scale ratio must be in same unit

∴ Change the feet to inch

∵ 1 foot = 12 inches

∴ 10 feet = 10 × 12 = 120 inches

∴ The scale is 0.5 inches : 120 inches

- Simplify the scale by multiply it by 2

∴ The scale is 1 in : 240 in

- Lets find the dimensions on the blueprints

∵ The real dimensions are 18 feet and 16 feet

- Change the feet to inches

∴ 18 feet = 18 × 12 = 216 inches

∵ 16 feet = 16 × 12 = 192 inches

∵ The scale is 1 : 240

∴ 1/240 = x/216 ⇒ use cross multiplication

∴ 240 x = 216 divide both sides by 240

∴ x = 0.9 inch

∵ The scale is 1 : 240

∴ 1/240 = y/192 ⇒ use cross multiplication

∴ 240 y = 192 divide both sides by 240

∴ y = 0.8 inch

* The dimensions on the blueprints are 0.9 inches and 0.8 inches

Answer:

Initial velocity is zero.

Step-by-step explanation:

According to second equation of motion

    [tex]s=ut+\frac{1}{2} at^2[/tex]

where s = distance traveled  

           t = time taken

          a = acceleration

          u = initial velocity

here in the question we have

      s = 10 m

     t = 1 second

    a = 20[tex]ms^{-2}[/tex]

plugging the known value in order to find the unknown which is u (initial velocity)

[tex]10=u(1)+\frac{1}{2} (20)(1)^2[/tex

10 = u +10

gives u =0

therefore initial velocity is zero.

Answer:

Depth below sea level is the independent quantity,

Water pressure is the dependent quantity

Step-by-step explanation:

An independent quantity is a variable that can be changed in an experiment. While, dependent quantity results from the independent quantity or we can say, that depends upon the independent quantity.

Here,

The water pressure increases 0.44 pounds per square inch (0.44 psi) with each increase of one foot in depth below sea level,

So, for measuring the water pressure we took depth below sea level as a variable,

⇒ Depth below sea level is the independent quantity,

While, with increasing depth by 1 foot the pressure is also increase by 0.44 pounds per square inches ⇒ pressure depends upon the depth

⇒ Water pressure is the dependent quantity.

Answer:The best answer I think is depth, water pressure

Step-by-step explanation:

[tex]b[/tex] - the side of a square

[tex]a=b\sqrt2\\b=\dfrac{a}{\sqrt2}\\\\b=\dfrac{a\sqrt2}{2}[/tex]

Answer:

a√2 / 2.

Step-by-step explanation:

Using the Pythagoras Theorem;

a^2 = s^2 + s^2 where s is the length of each side of the square.

2s^2 = a^2

s^2 = a^2 / 2

s =  √(a^2 / 2)

= a / √2

= a√2 / 2 .

Answer:

  19.3%

Step-by-step explanation:

Assuming the events are independent, the probability of all five is ...

  0.72^5 ≈ 0.19349 ≈ 19.3%

Answer: 19.3%

Step-by-step explanation:

If we randomly select 5 students, we know that each of them has a probability of 72% of finding a job in that year (or 0.72 in decimal form)

The joint probability in where the 5 of them have found a job, is equal to the product of the 5 probabilities:

P = 0.72*0.72*0.72*0.72*0.72 = 0.72^5 = 0.193

Where because all the students are in the same result, the number of permutations is only one.

If we want the percentage form, we must multiplicate it by 100%, and we have that P = 19.3%

Answer:

16

Step-by-step explanation:

i know because i did the test

Answer:

16 for people with ads i really need brainliest

Step-by-step explanation:

Answer:

First mechanic: 20 hours

Second mechanic: 15 hours

Step-by-step explanation:

First we create two equations where:

x - hours of first mechanic

y - hours of second mechanic

x+y=35

115x+45y=2975

Then, we multiply both sides of the first equation by 45, and then subtract it from the second equation:

45x+45y=1575

|115x+45y=2975

-|45x+45y = 1575

70x = 1400

x=20 hours

Now we know for how many hours the first mechanic worked. Now we just need to subtract that from the combined total to find the second mechanic's hours:

35-20=15 hours

Answer:

58 miles per hour

Step-by-step explanation:

First you need to divide 80 by 10 to see how many miles she was over the speed limit.

80/10 = 8 miles over the speed limit.

The speed limit was 50, so 50 + 8 = 58 miles.

So Cathy was driving at 58 miles per hour

Answer:

58mph

Step-by-step explanation:

Given:

Each mph over the speed limit gets fined $10

or mathematically, rate of fine = $10/mph

also, total fine was $80.

Number of mph over the speed limit,

= total fine ÷ rate of fine

= $80 ÷ $10/mph

= 8 mph.

Given that the speed limit was 50 mph, Cathy's final speed,

= speed limit + number of mph over speed limit

= 50 + 8

= 58 mph

Answer:

  see below

Step-by-step explanation:

Option 1: the two solution sets overlap at x=1.

Option 2: the two solution sets do not overlap; no solution.

Option 3: together, the two set describe all real numbers.

Answer:

146 degrees

Step-by-step explanation:

The measure of the arc is the measure of the central angle that the arc is created from.

The central angle has a measure of 146 degrees so that is the measure of the arc there.

Answer:

  a)  73.52%

  b)  Regular membership is growing faster

Step-by-step explanation:

a)  r(t) = r0·1.047^(12t) . . . . regular members after t years, where r0 is the initial value of regular members at t=0.

Equivalently, this is ...

  r(t) = r0·(1.047^12)^t ≈ r0·1.7352^t

This shows the effective annual growth rate for regular members is 73.52%.

__

b) The 74% yearly growth rate of regular members is higher than the 65% yearly growth rate of VIP members. Regular membership is growing faster.

Answer:

  B.  3y = 6

Step-by-step explanation:

(6x +5y) -(6x +2y) = (16) -(10)

6x +5y -6x -2y = 6 . . . eliminate parentheses

(6-6)x +(5-2)y = 6 . . . . add like terms

3y = 6 . . . . . . . . . . . simplify

Answer:

x^2 -6x+44

Step-by-step explanation:

Develop form of (x-3)^2 is x^2 - 6x +9

Then y= x^2 -6x +9 + 35

So, y= X^2 -6x +44

Answer:

[tex]y=x^2 -6x+44[/tex]

Step-by-step explanation:

The standard form of a quadratic equation is:

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

In this case we have the following quadratic equation in vertex form

[tex]y=(x-3)^2+35[/tex]

Now we must rewrite the equation in the standard form.

[tex]y=(x-3)(x-3)+35[/tex]

Apply the distributive property

[tex]y=x^2 -3x -3x +9+35[/tex]

[tex]y=x^2 -6x+9+35[/tex]

[tex]y=x^2 -6x+44[/tex]

the standard form of the equation is: [tex]y=x^2 -6x+44[/tex]

Answer:

Step-by-step explanation:

E

Answer:

B

Step-by-step explanation:

Edge

Answer:

  d = 8t

Step-by-step explanation:

A lot of math is about matching patterns. Here, the pattern you can match is given in the problem statement:

  d = 6t  . . . . . equation for distance traveled at 6 miles per hour

You are asked to write an equation for distance traveled at 8 miles per hour. You can see the number 6 in the above equation matches the "miles per hour" of the traveler. This should give you a clue that when the "miles per hour" changes from 6 to 8, the number in the equation will do likewise.

The equation you want is ...

  d = 8t . . . . . equation for distance traveled at 8 miles per hour

The distance traveled by a person biking at 8 miles per hour is represented by the equation d = 8t, where d is the distance, and t is the time in hours. For example, if they bike for 2 hours, they will have traveled 16 miles.

The question is about calculating the distance traveled by a person who can bike at a rate of 8 miles per hour. This can be represented by the equation d = rt, where d is the distance, r is the rate, and t is the time.

In this case, the rate (r) is 8 miles per hour. Therefore, the equation becomes: d = 8t, meaning the distance travelled is equal to 8 times the amount of time spent biking.

For example, if the person bikes for 2 hours, we would substitute 2 for t in the equation, which would look like this: d = 8 * 2. The resulting distance (d) is 16 miles.

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Answer:

15, 18, 21, 24, 27

Step-by-step explanation:

Five multiples of 3 means we have 5 terms we are adding together to = 105.

For the sake of having something to base each one of these terms on, let's say that the first term is 3.  It's not, but 3 is a multiple of 3 and we have to start somewhere.  These terms go up by the next number that is divisible by 3.  After 3, the next number that is divisible by 3 is 6.  The next one is 9, the next is 12, the last would be 15.

Let's then say that 3 is the first term, and we are going to say that is x.

To get from 3 to 6, we add 3.  Therefore, the second term is x + 3.

To get from 3 to 9, we add 6.  Therefore, the third term is x + 6.

To get from 3 to 12, we add 9.  Therefore, the fourth term is x + 9.

To get from 3 to 15, the last term, we add 12.  Therefore, the last term is x + 12.

The sum of these terms will then be set to equal 105:

x + (x + 3) + ( x + 6) + ( x + 9) + ( x + 12) = 105

We don't need the parenthesis to simplify so we add like terms to get

5x + 30 = 105.  Subtract 30 from both sides to get

5x = 75 so

x = 15

That means that 15 is the first multiple of 3.  

The next one is found by adding 3 to the first:  so 18

The next one is found by adding 6 to the first:  so 21

The next one is found by adding 9 to the first:  so 24

The last one is found by adding 12 to the first:  so 27

15 + 18 + 21 + 24 + 27 = 105

Notice that all the numbers are, in fact, consecutive multiples of 3 as the instructions stated.

The five consecutive multiples of 3 that sum up to 105 are 15, 18, 21, 24, and 27.

The question posed is regarding five consecutive multiples of 3. The sum of these multiples equals 7x15 (or 105). Let's call the first multiple of 3 as '3x'. Therefore, the five consecutive multiples can be represented as 3x, 3x+3, 3x+6, 3x+9, 3x+12.

The sum of the five consecutive multiples then is 15x + 30 (comprising 5 times 'x', plus 30 from the sum of 3, 6, 9, and 12). We know that this sum equals 105, so we can set up the following equation:
15x + 30 = 105.

Solving this equation for 'x' gives:
x = 5. This means the first multiple is 3x, or 3x5 = 15. The next multiples are therefore 15+3 (18), 18+3 (21), 21+3 (24) and 24+3 (27).

So, the five multiples of 3 that yield a sum of 105 are 15, 18, 21, 24, and 27.

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Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

[tex](f+g)'=f'+g'[/tex] Sum rule.

[tex](cf)'=cf'[/tex] Constant multiple rule.

[tex](x^n)'=nx^{n-1}[/tex] Power rule.

[tex](x)'=1[/tex] Slope of y=x is 1.

[tex]f(x)=12x^2+8x[/tex]

[tex]f'(x)=(12x^2+8x)'[/tex]

[tex]f'(x)=(12x^2)'+(8x)'[/tex] by sum rule.

[tex]f'(x)=12(x^2)+8(x)'[/tex] by constant multiple rule.

[tex]f'(x)=12(2x)+8(1)[/tex] by power rule.

[tex]f'(x)=24x+8[/tex]

Now we need to find the derivative function evaluated at x=9.

[tex]f'(9)=24(9)+8[/tex]

[tex]f'(9)=216+8[/tex]

[tex]f'(9)=224[/tex]

In case you wanted to use the formal definition of derivative:

[tex]f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]

Or the formal definition evaluated at x=a:

[tex]f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}[/tex]

Let's use that a=9.

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]

We need to find f(9+h) and f(9):

[tex]f(9+h)=12(9+h)^2+8(9+h)[/tex]

[tex]f(9+h)=12(9+h)(9+h)+72+8h[/tex]

[tex]f(9+h)=12(81+18h+h^2)+72+8h[/tex]

(used foil or the formula  (x+a)(x+a)=x^2+2ax+a^2)

[tex]f(9+h)=972+216h+12h^2+72+8h[/tex]

Combine like terms:

[tex]f(9+h)=1044+224h+12h^2[/tex]

[tex]f(9)=12(9)^2+8(9)[/tex]

[tex]f(9)=12(81)+72[/tex]

[tex]f(9)=972+72[/tex]

[tex]f(9)=1044[/tex]

Ok now back to our definition:

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}[/tex]

Simplify by doing 1044-1044:

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}[/tex]

Each term has a factor of h so divide top and bottom by h:

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}[/tex]

[tex]f'(9)=\lim_{h \rightarrow 0}(224+12h)[/tex]

[tex]f'(9)=224+12(0)[/tex]

[tex]f'(9)=224+0[/tex]

[tex]f'(9)=224[/tex]

Final answer:

To find the probability of selecting 5 non-defective widgets from 25 produced, we consider the independent probabilities of selecting a non-defective widget for each selection and multiply them together.Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.

Explanation:

To find the probability of selecting 5 widgets where none are defective, we need to consider the probability of selecting a non-defective widget for each of the 5 selections.

The probability of selecting a non-defective widget from the 25 produced is (25-5)/25 = 20/25 = 4/5.

Since the selections are independent, we can multiply the probabilities. So the probability of selecting 5 non-defective widgets is (4/5)⁵ = 1024/3125.

Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.

Answer:

revolutions per minute for 16 inches is 946 / minute

revolutions per minute for 14 inches is 1081 / minute

Step-by-step explanation:

Given data

radius = 16 inch

speed = 90 mph  = 90/60 = 1.5 miles/minute = 1.5 × 5280 feet /12 inches = 95040 inches /minute

radius 2 = 14 inches

to find out

revolutions per minute

solution

first we calculate the circumference of the wheel i.e. 2×[tex]\pi[/tex]×radius

circumference = 2×[tex]\pi[/tex]×16

circumference = 32[tex]\pi[/tex]

we know that revolution is speed / circumference

revolution = 95040/32[tex]\pi[/tex]

revolution = 945.38 / minute

we have given radius 14 inches than revolution will be i.e.

revolution = speed / circumference

circumference = 2×[tex]\pi[/tex]×14

circumference = 28[tex]\pi[/tex]

revolution =  95040/ 28[tex]\pi[/tex]

revolution = 1080.43 / minute