If a bag contains 12 quarters, 6 dimes and 18 nickels what is the part to whole ratio of nickels to all coins?

Answer:

Absolute maximum of 1 at x = pi/4 ; [tex](\frac{\pi}{4}, \ 1)[/tex]

Absolute minimum of -1 at x = 5pi/4 ; [tex](\frac{5\pi}{4} , \ -1)[/tex]

Local maximum of √2/2 at x = 0 ; [tex](0, \ \frac{\sqrt{2} }{2} )[/tex]

Local minimum of 0 at x = 7pi/4 ; [tex](\frac{7\pi}{4}, \ 0)[/tex]

No critical points that are not stationary points.

Step-by-step explanation:

[tex]f(x)=sin(x+\frac{\pi}{4} ), \ 0 \leq x\leq \frac{7 \pi}{4}[/tex]

Let's start by taking the derivative of the function.

Use the power rule and the chain rule to take the derivative of f(x).

The derivative of sin(x) is cos(x), so we can write this as:

Now, we can apply the power rule to x + pi/4.

Now that we have the first derivative of [tex]f(x)=sin(x+\frac{\pi}{4})[/tex], let's set the first derivative to 0 to find the critical points of this function.

Take the inverse cosine of both sides of the equation.

Inverse cosine and cosine cancel out, leaving us with x + pi/4. The inverse cosine of 0 is equal to 90 degrees, which is the same as pi/2.

Solve for x to find the critical points of f(x). Subtract pi/4 from both sides of the equation, and move x to the left using the symmetric property of equality.

Since we are given the domain of the function, let's use the period of sin to find our other critical point: 5pi/4. This is equivalent to pi/4. Therefore, our critical points are:

Since this is a sine graph, we don't need to create a sign chart to check if the critical values are, in fact, extreme values since there are many absolute maximums and absolute minimums on the sine graph.

There will always be either an absolute maximum or an absolute minimum at the critical values where the first derivative is equal to 0, because this is where the sine graph curves and forms these.

Therefore, we can plug the critical values into the original function f(x) in order to find the value at which these extreme values occur. We also need to plug in the endpoints of the function, which are the domain restrictions.

Let's plug in the critical point values and endpoint values into the function f(x) to find where the extreme values occur on the graph of this function.

There is a maximum value of 1 at x = pi/4.

There is a minimum value of -1 at x = 5pi/4.

There is a maximum value of √2/2 at x = 0.

There is a minimum value of 0 at x = 7pi/4.

We need to first compare the critical point values and then compare the endpoint values to determine whether they are maximum or minimums.

A critical point is called a stationary point if f'(x) = 0.

Since f'(x) is zero at both of the critical points, there are no critical points that are not stationary points.  

Answer:

0

Step-by-step explanation:

From the given information;

Let x be the number of trails on which the [tex]r^{th}[/tex] defective occurs.

Let the probability that an occurrence of a defective be p = 0.10

Suppose x is a random variable that follows a negative binomial distribution with parameters r and p.

Then the probability mass function of X can be expressed as:

[tex]P(X=x) = \bigg (^{x-1}_{r-1} \bigg)p^r (1 - p) ^{x-r} \ \ \ \ ; x=r, \ r+1 , \ r+2 , ...[/tex]

[tex]P(X=x) = \bigg (^{x-1}_{r-1} \bigg)(0.10)^r (1 - 0.10) ^{x-r}[/tex]

[tex]P(X=x) = \bigg (^{x-1}_{r-1} \bigg)(0.10)^r ( 0.90) ^{x-r} \ \ ... \ \ (1)[/tex]

We are to find the probability of the fourth defective engine will be found on the second trial.

i.e. r =  4 and x = 2

[tex]P(X=2) = \bigg (^{2-1}_{4-1} \bigg)(0.10)^4 ( 0.90) ^{2-4}[/tex]

[tex]P(X=2) = \bigg (^1}_{3} \bigg)(0.10)^4 ( 0.90) ^{-2}[/tex]

[tex]P(X=2) = \bigg (\dfrac{1!}{3!(1-3)!} \bigg)(0.10)^4 ( 0.90) ^{-2}[/tex]

[tex]\mathbf{P(X=2) = 0}[/tex]

Answer:

Nice

Step-by-step explanation:

Answer:

hahhhh funny one nice :-)

Answer:

(5,5)

Step-by-step explanation:

left 5 is -5 and right 8 is +8.

-5+8=3

2+3=5

When talking about left and right, you change the x-coordinate, when up and down, y-coordinate.

Overall, (5,5)

Answer:

5,5

Step-by-step explanation:

since we are not changing the height of the point and just moving side to side, the y intercept does not change. Once you move 5 units to the left, your new point is -3,5 but then when you move 8 to the right it switches to positive again and the new point is 5,5

Answer:

2k+s-2

im assuming

Answer:

b

20

10

Step-by-step explanation:

Answer:

2(3x+10) = 6x+20

6x+20 = 6x+20

6x = 6x

x = x

This has an infinite amount of solutions

Step-by-step explanation:

Answer:

this makes no sense give me the full question please

Step-by-step explanation:

Answer:

20 yards, 6 feet

Step-by-step explanation:

Width of the rug is [tex]\frac{1}{4}[/tex] of the length:

[tex]\frac{1}{4}[/tex] × 8 yards = 2 yards

[tex]\frac{1}{4}[/tex] × 2 feet = [tex]\frac{1}{2}[/tex] foot = 6 inches

[tex]\frac{1}{4}[/tex] × 4 inches = 1 inch

P = 2( l + w )

2 × l = 16 yards, 4 feet, 8 inches

2 × w = 4 yards, 1 foot, 2 inches

P = 20 yards, 5 feet, 12 inches = 20 yards, 6 feet

Answer:

The 14th term is -61.

Step-by-step explanation:

T(n) = 9-5n

T(14) = 9 - 5 * 14 = 9 - 70 = -61

Answer:

2 and 5 because dilation always have the same angles and they can increase and decrease in size

Step-by-step explanation:

But I am not sure so if I am wrong I am sorry I did a test like this

Answer:

The class interval is: 20-30

Step-by-step explanation:

Let l be the lower class limit and u be the upper class limit.

Then according to given statement that class mark is 25

[tex]\frac{l+u}{2} = 25\\l+u = 50\ \ \ Eqn\ 1[/tex]

And

Class size is 10

So, the second equation will be:

[tex]u-l = 10\ \ \ \ Eqn\ 2[/tex]

Adding equation 1 and 2

[tex]l+u+u-l = 50+10\\2u = 60\\\frac{2u}{2} = \frac{60}{2}\\u = 30[/tex]

Now putting u =30 in equation 1

[tex]l+u = 50\\l+30 = 50\\l = 50-30\\l = 20[/tex]

A class interval is written in the form that lower limit comes first and upper limit comes second.

So,

20-30

Hence,

The class interval is: 20-30

Answer:

1.) y = -6

2.) y = 5/3x - 7

3.) y = 5

4.) y = -3x + 1

5.) x = -3

Step-by-step explanation:

So the equation you want to use is this:   [tex]\frac{y2-y1}{x2-x1}[/tex]

1.) Plug in

[tex]\frac{-6 - (-6)}{6 - 2} \\\\\frac{0}{4} = 0\\[/tex]

This line is zero slope to find the y-intercept get one of you points and plug them and the slope into this equation y = mx+ b. We will use (2,-6)

-6 = 0(2) + b (b represents y-intercept) (0*2=0)

-6 = b

So the equation is y = -6

2.) Do the same thing.

[tex]\frac{3-8}{6-9} \\\\\frac{-5}{-3} =\frac{5}{3}[/tex]

It's positive because when you divide a negative by a negative you get a positive. Plug in a point (6, 3) y = mx + b (b represents y-intercept)

3 = 5/3(6) + b (5/3*6 = 10)

3 = 10 + b (subtract 10 on both sides)

-7 = b

y = 5/3x - 7

3.) For this one you are just going to point slope form. y - y1 = m(x - x1)

Plug in

y - 5 = 0(x - (-8))

y - 5 = 0 (add 5 to both sides)

y = 5

4.) Do [tex]\frac{y2 - y1}{x2 - x1}[/tex] for this one

Plug in

[tex]\frac{-5 - 7}{2 - (-2)} \\\\\frac{-12}{4} = -3[/tex]

So the slope is -3. Plug into y = mx + b with the point (2, -5)

-5 = -3(2) + b (b represents y-intercept)

-5 = -6 + b (add 6 to both sides)

1 = b

The equation is y = -3x + 1

5.) Do the same thing as #4

[tex]\frac{-8 - (-5)}{6 - 6} \\\\\frac{-3}{0}[/tex]

This slope is undefined

Since you can't divide by 0 the equation would be

x = -3

Hope this helps ya!!

Answer:

Step-by-step explanation:

expresion can be simplified is they have like terms such as

x+x=2x

y+2y=3y

expresions can NOT be simplified if they have difrerent variables or just one number suchh as

2x+3y

7y+1

4y+4x

I do not know what is 4r+

Answer:

can - y +2y

9x+6x

4x+x

can't 4y+4x

7y+1

2x+3y

Answer:

3

Step-by-step explanation:

Answer:

100/35 = 2

35 goes into 100 2 times

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

b.

1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;

Step-by-step explanation:

IT'S B

Answer:

D All three companies were rated to be equal

Step-by-step explanation:

got it right on EDG2020

Answer:

250 centimeters

Step-by-step explanation:

2 meters into centimeters is 200 so 200+50=250

Answer:

100cm

Step-by-step explanation:

Answer:

-20,250

Step-by-step explanation:

PEMDAS

Multiply left to right

45 * -10 * 45

45* -10

-450 * 45 =

-20,250

Answer:

33,600

Step-by-step explanation:

take -4200 and multiply it by 8. You'd do this since the equation to get -4200 is

x(1/8) = -4200

multiply both sides by 8 to get rid of the fraction and you get x=33,600

Answer:

1. 4320

2. 248

3. -180

4. 1/8

Answer:

a) the probability that the first non-defective engine will be found on the second trial is 0.09

b) probability that the third non-defective engine will be found on the fifth trial is 0.00486

c) the Mean is 1.1111  and Variance is 0.1235  

d) the Mean is 3.3333and Variance is 0.3704  

Step-by-step explanation:

Firstly;

Let x be the number of trail on which the rth defective occurs

Also let the probability that an occurrence of a defective be p = 0.10

Here, x follows negative binomial distribution with parameters r and p

The probability mass function of X is as follows:

P(X = x) = [ x -1  p^r ( 1 - p)^(x-r)       ; x = r, r + 1, r + 2, ...

                 r - 1 ]

=   [ x -1  (0.10)^r ( 1 - 0.10)^(x-r)

     r - 1 ]

= [ x -1  (0.10)^r ( 0.9)^(x-r)  ..........n 1..... let this be equatio

    r - 1 ]

This represents the probability that the rth success occurs on the xth trail.  

a)

probability that the first non-defective engine will be found on the second trial?

Substitute r = 1 and x = 2 in equation 1  

P(X = 2)  = [ 2 - 1   (0.10)¹ ( 0.90 )²⁻¹

                   1 - 1 ]

= (0.10) × (0.90)

= 0.09

Therefore, the probability that the first non-defective engine will be found on the second trial is 0.09

b)

probability that the third non-defective engine will be found on the fifth trial?

So we substitute r = 3 and x = 5 in equation 1  

P(X = 5) = [ 5 - 1  (0.10)³ ( 0.90)⁵⁻³

                  3 - 1 ]

=    [ 4    (0.10)³ ( 0.9)²

      2 ]

= 0.00486

Therefore, probability that the third non-defective engine will be found on the fifth trial is 0.00486

Now the formula for the mean of the negative binomial distribution is as follows:  

Mean u = r / p    ------- let this be equation 2

The formula for the variance of the negative binomial distribution also is as follows:  

Variance α² = rq / p²   ---------- let this be equation 3

so

c)

the mean and variance of the number of trials on which the first non-defective engine is found.  

First, let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10  

Now we substitute r = 1, p = 0.90 and q = 0.10 in equation 2 & 3simultaneously,

the mean and variances are as follows;

Mean = r/p = 1/0.90 = 1.1111

Variance = rq/p² = (1)(0.10) / (0.90)² = 0.1235  

Therefore the Mean is 1.1111  and Variance is 0.1235  

d)

the mean and variance of the number of trials on which the third non-defective engine is found  

Let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10

Now we substitute r = 3, p = 0.90 and q = 0.10 in equation (2) and (3) simultaneously,

the mean and variances are;

Mean = r/p = 3/0.90 = 3.3333

Variance = rq/p² = (3)(0.10) / (0.90)² = 0.3704

Therefore the Mean is 3.3333 and Variance is 0.3704