40 coins = 7.75 how many are quarters
In Exercises 11-18, use analytic methods to find the extreme values of the function on the interval and where they occur. Identify any critical points that are not stationary points.
15. f(x) = sin(x + π/4), 0 ≤ x ≤ 7π/4
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]
Take Derivative of f(x):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).
[tex]f'(x)=\frac{d}{dx} [sin(x+\frac{\pi}{4})] \times \frac{d}{dx} (x+\frac{\pi}{4})[/tex]The derivative of sin(x) is cos(x), so we can write this as:
[tex]f'(x)=cos(x+\frac{\pi}{4})\times \frac{d}{dx} (x+\frac{\pi}{4})[/tex]Now, we can apply the power rule to x + pi/4.
[tex]f'(x)=cos(x+\frac{\pi}{4} ) \times 1[/tex] [tex]f'(x)=cos(x+\frac{\pi}{4} )[/tex]Critical Points: Set f'(x) = 0Now 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.
[tex]0=cos(x+\frac{\pi}{4})[/tex]Take the inverse cosine of both sides of the equation.
[tex]cos^-^1(0) = cos^-^1[cos(x+\frac{\pi}{4})][/tex]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.
[tex]\frac{\pi}{2} = x +\frac{\pi}{4}[/tex]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.
[tex]x=\frac{\pi}{2}- \frac{\pi}{4}[/tex][tex]x=\frac{2 \pi}{4}-\frac{\pi}{4}[/tex] [tex]x=\frac{\pi}{4}[/tex]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:
[tex]\frac{\pi}{4}, \frac{5 \pi}{4}[/tex] Sign Chart(?):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.
Critical Point Values:[tex]f(\frac{\pi}{4} )=sin(\frac{\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{\pi}{4} )=sin(\frac{2\pi}{4}) \\ f(\frac{\pi}{4} )=sin(\frac{\pi}{2}) \\ f(\frac{\pi}{4} )=1[/tex]There is a maximum value of 1 at x = pi/4.
[tex]f(\frac{5\pi}{4} )=sin(\frac{5\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{5\pi}{4} )=sin(\frac{6\pi}{4}) \\ f(\frac{5\pi}{4}) = sin(\frac{3\pi}{2}) \\ f(\frac{5\pi}{4} )=-1[/tex]There is a minimum value of -1 at x = 5pi/4.
Endpoint Values:[tex]f(0) = sin((0) + \frac{\pi}{4}) \\ f(0) = sin(\frac{\pi}{4}) \\ f(0) = \frac{\sqrt{2} }{2}[/tex]There is a maximum value of √2/2 at x = 0.
[tex]f(\frac{7\pi}{4} ) =sin(\frac{7\pi}{4} +\frac{\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(\frac{8\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(2\pi) \\ f(\frac{7\pi}{4} ) =0[/tex]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.
Stationary Points: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.
Three printing companies were rated on their performance using a percentage scale. This graph shows how they were
rated.
Printing Company Ratings
100
KEY
Q = Quicky Printing Company
80
R = Reliable Printers, Inc.
S = Superior Printing, Inc.
60
Rating Scale (%)
20
Q
S
Printing Company
Which company was rated the best?
a. There is insufficient information to determine which company was rated best.
Mark this and return
Save and Exit
Next
Submit
Answer:
D All three companies were rated to be equal
Step-by-step explanation:
got it right on EDG2020
MORE MATH FOR YOU GUYS! BUT FOR REAL PLS HELP! 20 PTS!!!
Answer: $94.50
Step-by-step explanation:
What are the characteristics of the F distribution
Ten percent of the engines manufactured on an assembly line are defective.
a. If engines are randomly selected one at a time and tested what is the probability that the first non defective engine will be found on the second trial?
b. What is the probability that the third non defective engine will be found on the fifth trial?
c. Find the mean and variance of the number of trials on which the first non defective engine is found.
d. Find the mean and variance of the number of trials on which the third non defective engine is found.
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
Y’ALL PLEASE HELP ME ON MY TEST PLEASE I’VE BEEN STRUGGLING TO UNDERSTAND THE CLASSES AND MY TEACHER WONT EVEN EXPLAIN ANYTHING JUST SAY “I don’t know what you want me to do.” LIKE EXPLAIN PLEASE. SOMEONE PLEASE JUST HELP ME ON MY TEST
Answer:
1. 4320
2. 248
3. -180
4. 1/8
If the class mark and class size of the class
interval are 25 and 10 respectively, then the
class interval is
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
How many times does 35 go into 100 please give correct answer max points.
Answer:
100/35 = 2
35 goes into 100 2 times
Step-by-step explanation:
One-eighth of a number is -4,200.
What is the number?
-42,800
-37,800
-33,600
-42,000
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
2(3x+10)=6x+20 does this equation have one solution or many ? Explain why
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:
Christina is buying a new rug for her bedroom. The rug's length is 8 yards, 2 feet, and 4 inches long. The rug's width is 1/4 of its length. What is the perimeter of the rug?
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
Pls help i dont get i t
The store is selling 6 oranges for $ 1.80. How much will it cost to buy 16 orange .Show work .
Answer:
$4.80
Step-by-step explanation:
6 oranges for 1.80
sp 6 divided by 1.80 comes out to 0.3 per orange
0.3 times 16 comes out to 4.80
therefor $4.80
Answer:
$4.80
Step-by-step explanation:
1.80/6=0.3
0.3=$0.30 for each orange
16×0.3=4.8
4.8=$4.80 for 16 oranges
Manny rolls a number cube labeled 1-6 and spins a spinner with four equal sections, labeled 1, 2, 3, and 4. If both numbers are odd, he wins. Otherwise, Gabriel wins. Use a list to find the sample space. Then find the probability that Gabriel wins.
a.
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;
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;
c.
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;
d.
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;
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
Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability the fourth defective engine will be found on the second trial?
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]
Consider the function. f(x) = 2x(x - 1)
What are the values of
f(0)=
f(3)=
f(-4)=
Answer:
3
Step-by-step explanation:
Please help 30 points plus brainlyist who does first
Determine which expressions can be simplified further, and which cannot. Sort the expressions into the correct
category
2x + 3y
Can Be Simplified
Cannot Be Simplified
x + x
4r +
7y + 1
4y + 4x
y + 2y
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
Directions : Find the indicated term of each arithmetic sequence.
Question :14th term: a = 4; d = -5
Answer:
The 14th term is -61.
Step-by-step explanation:
T(n) = 9-5n
T(14) = 9 - 5 * 14 = 9 - 70 = -61
someone please help me i am so bad with point slope stuff
Write the equation of the line that passes through the points (2,−6) and (6,-6).
Write the equation of the line that passes through the points (9,8)and (6,3).
Write the equation of the line that passes through the points (-9,-4) and (-9,-4).
What is the equation of the line that passes through the point (−8,5) and has a slope of 0?
What is the slope of the line that passes through the points (-2, 7)and (2, -5).
What is the slope of the line that passes through the points (6, -5)and (6, -8).
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!!
Find the value of x and y.
12
9
Гу
X=
y =
Answer:
this makes no sense give me the full question please
Step-by-step explanation:
simplify the given involving the indicated division.
Help and please show all your work I need this ASAP
Needdd helpp noww please
Giving extra points
Answer:
b
20
10
Step-by-step explanation:
graph the line with the equation y=-6/5x+1
Please help me out, I don’t usually ask for answers but this will mean the world too me
ksdfjsbjgdfg f sndm f
Answer:
Nice
Step-by-step explanation:
Answer:
hahhhh funny one nice :-)
Jesus has a total of $80 in his savings account he is withdrawing $10 from his savings account each week write an equation indicating his withdrawal from his savings account
A rectangle is 2 meters long and 50 centimeters wide. What is its perimeter, in centimeters?
Answer:
250 centimeters
Step-by-step explanation:
2 meters into centimeters is 200 so 200+50=250
Answer:
100cm
Step-by-step explanation:
Answer please thanks
Answer:
4. interphase
5. prophase
6. metaphase
45×(−10)×45 STEP explanation
Answer:
-20,250
Step-by-step explanation:
PEMDAS
Multiply left to right
45 * -10 * 45
45* -10
-450 * 45 =
-20,250
