Answer:
Yes, Rolle's theorem can be applied
There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)
Step-by-step explanation:
Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable in the open interval, and f(a) = f(b) given that:
[tex]f(0)=-0^2+3\,(0)=0\\f(3)=-3^2+3\,(3)=-9+9=0[/tex]
Then there must be a c in the open interval for which f'(c) =0
In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:
[tex]f(x)=-x^2+3\,x\\f'(x)=-2\,x+3\\f'(c)=-2\,c+3\\0=-2\,c+3\\2\,c=3\\c=\frac{3}{2} =1.5[/tex]
There is a unique answer for c, and that is c = 1.5
Rolle's theorem is applicable if [tex]f(a)=f(b)[/tex] and $f$ is differentiable in $(a,b)$
since it's polynomial function, it's always continuous and differentiable..
and you can easily check that $f(0)=f(-3)=0$
so it is applicable.
now, $f'(x)=-2x+3=0 \implies x=\frac32$
there is only once value (as you can imagine, the graph will be downward parabola)
HELP ASAP ROCKY!!! will get branliest.
Answer:
work pictured and shown
Answer:
Last one
Step-by-step explanation:
● [ ( 3^2 × 5^0) / 4 ]^2
5^0 is 1 since any number that has a null power is equal to 1.
●[ (3^2 ×1 ) / 4 ]^2
● (9/4)^2
● 81 / 16
please help me in these question ????
A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
(b) How many samples have 3 red pens and 1 black pen?
(c) How many samples of size 4 contain at least two red pens?
(d) How many samples of size 4 contain
If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution.
1- What percentage of a cucumber give the crop amount between and 834 kg?
2- What the probability of cucumber give the crop exceed 900 kg ?
Answer:
Step-by-step explanation:
A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
12C4=12!/(4!*8!)=495
(b) How many samples have 3 red pens and 1 black pen?
5C3*7C1
5C3=5!/(3!*2!)=10
7C1=7!/(1!*6!)=7
=>5C3*7C1=10*7=70
(c) How many samples of size 4 contain at least two red pens?
(5C2*7C2)+(5C3*7C1)+(5C4*7C0)
5C2=5!/(2!*3!)=10
7C2=7!/(2!*5!)=21
5C3=5!/(3!*2!)=10
7C1=7!/(1!*6!)=7
5C4=5!/(4!*1!)=5
7C0=7!/(0!*7!)=1
=>(5C2*7C2)+(5C3*7C1)+(5C4*7C0)=285
(d) How many samples of size 4 contain at most one black pen?
(7C1*5C3)+(7C0*5C4)
7C1=7!/(1!*6!)=7
7C0=7!/(0!*7!)=1
5C3=5!/(3!*2!)=10
5C4=5!/(4!*1!)=5
=>(7C1*5C3)+(7C0*5C4)=(7*10)+(1*5)=75
MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO
Help
Step-by-step explanation:
Hi, there!!!
According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,
So, let's simply work with it,
Firstly, finding the area of rectangle,
length = 11cm.
breadth = 11cm.
now, area= length× breadth.
or, a = 11cm× 11cm.
a= 121cm^2
Now, let's work out the area of circle.
radius= 5cm
and pi. = 3.14 {using pi value as 3.14}
now,
area of a circle = pi× r^2
or, a= 3.14×5^2
or, a = 78.5 cm^2.
Therefore, The area of a circle is 78.5cm^2.
Now lastly finding the area of shadedregion,
area of shaded region = area of rectangle - area of circle.
or, area of shaded region = 121cm^2 - 78.5cm^2
Therefore, the area of shaded region is 42.5 cm^2.
Hope it helps...
The graph of F(x), shown below in pink, has the same shape as the graph of
G(x) = x3, shown in gray. Which of the following is the equation for F(x)?
Greetings from Brasil...
In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.
The translations are established as follows:
→ Horizontal
F(X + k) ⇒ k units to the left
F(X - k) ⇒ k units to the right
→ Vertical
F(X) + k ⇒ k units up
F(X) - k ⇒ k units down
In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.
F(X) = X³
4 units horizontal to the left: F(X + 4)
3 units vertical to the bottom: F(X + 4) - 3
So,
F(X) = X³
F(X + 4) - 3 = (X + 4)³ - 3The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted
What happens when a function is transformed?Every modification may be a part of a function's transformation.
Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).
If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:
Vertical shift, often known as phase shift:
Y=f(x+c) with a left shift of c units (same output, but c units earlier)
Y=f(x-c) with a right shift of c units (same output, but c units late)
Vertical movement:
Y = f(x) + d units higher, up
Y = f(x) - d units lower, d
Stretching:
Stretching vertically by a factor of k: y = k f (x)
Stretching horizontally by a factor of k: y = f(x/k)
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) = x³
And , the transformed function has coordinates as A ( -4 , -3 )
So , when function is shifted 4 units to the left , we get
g' ( x ) = ( x + 4 )³
And , when the function is shifted vertically by 3 units down , we get
f ( x ) = ( x + 4 )³ - 3
Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3
To learn more about transformation of functions click :
https://brainly.com/question/26896273
#SPJ7
will rate you brainliest
Answer:
[tex] \frac{11x}{3y} [/tex]
Step-by-step explanation:
[tex] \frac{7x}{3y} + \frac{12x}{9y} [/tex]
Make both a single fraction by adding together.
[tex] \frac{3(7x) + 1(12x)}{9y} [/tex]
[tex] \frac{21x + 12x}{9y} [/tex]
[tex] \frac{33x}{9y} [/tex]
Simplify
[tex] \frac{3(11)x}{3(3y)} [/tex]
[tex] \frac{11x}{3y} [/tex]
Relating a Polynomial Identity to Pythagorean Triples
In this activity you'll relate polynomial identities with Pythagorean triples. Answer the following questions
based on this triangle with side lengths x^2 – 1, 2x, and x^2 + 1.
Answer:
Step-by-step explanation:
Hello, please consider the following.
For x > 1, we can apply Pythagoras theorem as below.
[tex]\text{Let's estimate this sum of two squares.} \\\\(2x)^2+(x^2-1)^2=4x^2+x^4-2x^2+1=x^4+2x^2+1\\\\\text{Let's estimate this square, now.} \\\\(x^2+1)^2=x^4+2x^2+1\\\\\text{The two expressions are equal, meaning.} \\\\(2x)^2+(x^2-1)^2=(x^2+1)^2\\\\\text{Using Pythagoras' theorem, we can say that this is a right triangle.}[/tex]
Thank you
A train leaves the station traveling north at 75 mph 2 hours later a second train leaves on a parallel track and travels north at 125 mph how far from the station will they meet
Answer:
At 3 hours, the trains will be equidistant from the station.
Step-by-step explanation:
The first train leaves at 75 miles per hour and has a 2 hour head start. This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.
To solve when they will be near each other, we set up an equation to solve for t.
150 + 75t = 125t
150 = 50t
3 = t
So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.
Cheers.
What is the slope of the line shown below?
A.
B.
C.
-
D.
3
Answer:
D
Step-by-step explanation:
Option D is correct. Slope of the line shown in the graph is 3.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=(y₂-y₁)/(x₂-x₁)
The line is passing through point (2, 2) and (4, 8).
Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.
Plug in the values in slope formula:
Slope = (8-2)/(4-2)
=6/2
=3
Hence, slope of the line shown in the graph is 3. Option D is correct.
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ4
Is {(4,2),(4,-2),(9,3),(9,-3)} a function
Answer:
no
Step-by-step explanation:
If any x-value is repeated, the relation is not a function. Both x=4 and x=9 are repeated values, so this relation is not a function.
Find the values of x which satisfy the following inequation:
x3 – x² <12x
Answer:
x< -3 and 0 < x < 4
Step-by-step explanation:
x^3 – x² <12x
Subtract 12x from each side
x^3 -x^2 - 12x< 0
Factor
x( x^2 -x-12) <0
Factor
x( x-4) ( x+3) < 0
Using the zero product property
x=0 x=4 x=-3
We have to check the signs regions
x < -3
-( -) (-) < 0 True
-3 to 0
-( -) (+) < 0 False
0 to 4
+( -) (+) < 0 True
x>4
+( +) (+) < 0 False
The regions this is valid is
x< -3 and 0 < x < 4
A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?
Answer:
The survey result doesn't indicate the change
Step-by-step explanation:
Previous study result is 50%
Survey result:
483/1002 = 0.482 = 48.2%Comparing with previous result:
50% - 48.2% = 1.8% < 5%Since this result is within 5% level of significance, it can be concluded that the survey result doesn't indicate the change
The quotient of 3 and the cube
of y+2
Answer:
[tex]\dfrac{3}{(y+2)^3}[/tex]
Step-by-step explanation:
Maybe you want this written using math symbols. It will be ...
[tex]\boxed{\dfrac{3}{(y+2)^3}}[/tex]
Answer the question :)
Answer:
A. -11
Step-by-step explanation:
In the function, replace x with -2
R(x) = x^2 - 3x - 1 ➡ R(-2) = (-2)^2 - 3 × 2 -1 = -11
Kenji earned the test scores below in English class.
79, 91, 93, 85, 86, and 88
What are the mean and median of his test scores?
Answer:
mean=87
median=87
Step-by-step explanation:
mean=sum of test score/number of subject
mean=79+91+93+85+86+88/6
mean=522/6
mean=87
Literal meaning of median is medium.
To find the number which lies in the medium, we must rearrange the number in ascending.
79, 91, 93, 85, 86, 88
79, 85, 86, 88, 91, 93
86+88/2=87
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
How is a reflection different than a rotation
Answer:
different
Step-by-step explanation:
reflection is basically like a mirror where it reflects you. rotation is when an object spins/rotates.
PLEASE HELP ASAP THANKS IN ADVANCE
Answer:
the answer to the question is "C"
What's the solution of the following linear system? 5x + 2y = 9 –5x – 2y = 3
━━━━━━━☆☆━━━━━━━
▹ Answer
(-39/35, 9/7)
▹ Step-by-Step Explanation
5y + 2y = 9
-5x - 2y = 3
Solve the equation:
y = 9/7
-5x - 2y = 3
Substitute the value of y:
-5x - 2 * 9/7 = 3
x = -39/35
(x, y) = (-39/35, 9/7)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
To solve this system by addition, we start by adding both of our equations together but notice that the x terms and the y terms cancel out.
This leaves us with 0 on the left side and on the right side,
9 + 13 = 12 so we are left with the equation 0 = 12.
Since 0 = 12 is a false statement, this means that
there is no solution to our system of equations.
Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet. A rectangle labeled 2 x squared + x minus 6 Which expressions can represent the length and width of the garden? length = x2 – 3 feet; width = 2 feet length = 2x + 3 feet; width = x – 2 feet length = 2x + 2 feet; width = x – 3 feet length = 2x – 3 feet; width = x + 2 feet
Answer:
2x^2 + x - 6 = rectangular garden: length = 2x – 3 feet; width = x + 2 feet
Step-by-step explanation:
(2x - 3)(x + 2) = 2x^2 + x - 6 =
2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 =
2x^2 + x - 6
You get the original equation from the two sides multiplied. :)
Hope this helps, have a good day.
The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area is 2x² + x – 6 square feet. Then the factor of the equation is given as,
A = 2x² + x – 6
A = 2x² + 4x – 3x – 6
A = 2x(x + 2) – 3(x + 2)
L × W = (2x – 3)(x + 2)
The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
#SPJ6
domain and range A) D: (–7, –2], (–1, 3] R: (–10, 9.2] B) D: [–7, –2], [–1, 3] R: [–10, 9.2] C) D: (–7, 3] R: (–10, 9.2] D) D: (–7, –2), (–1, 3) R: (–10, 9.2)
Answer:
[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]
Step-by-step explanation:
The domain is the set of all possible x values.
The range is the set of all possible y values.
For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.
[tex]\mathrm{D= (-7,3] }[/tex]
For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.
[tex]\mathrm{R= (-10,9.2] }[/tex]
Consider various ways of ordering the letters in the word TENNESSEE. TENENESES, EESSENNET, TNNEESSEE, and so on. (a) How many distinguishable orderings are there
Answer:
3780.
Step-by-step explanation:
To solve this we will start by just considering the number of ways to arrange 9 objects. We can do this in 9! ways.
However since we have 3 reoccurring letters in Tennessee namely n,s and e we need to remove the times these form the same arrangement. Let me give an example to show what this means. Lets say we have the arrangement:
ennetssee
Now what happens if we exchange the places of the letters n for example? Of course we get the same arrangement of letters. We don’t want to count these as 2 different arrangements since for our interests they are the same. We therefore divide 9! by the number of times this type of double counting occurs.
Since the word has the letter n occurring twice we will start by diving by 2! .
The letter s occurs 2 times as well so we will have to divide by 2! again.
Finally the letter e occurs 4 times and so we will have to divide by 4! here.
Now we get the following result:
9/(2 x 2 x 4)=3780.
So in conclusion there are 3780 different ways to arrange the letters in Tennessee.
You run a souvenir store that sells key rings. You can get 50 key rings from your first supplier for $.50 cents each. You can get the same 50 key rings from your second supplier for $30 total, or you can get them from your third supplier for $27.50. How much will you pay if you get the best deal?
Answer:
$25
Step-by-step explanation:
.5 * 50 = 25
25<27.5<30
The cheapest supplier is the first one.
Need help please! what is the total length of a 20 mm steel coiled like a spring with a 16 turns and an outer diameter of 600 mm. pitch is 300 mm. Show your solution please coz i don't really know how to do it! thanks
Answer:
L = 29,550 mm
Step-by-step explanation:
i think i've done this before.. but anyway Lets make it simple and easy.
Let A = 600mm
Let B = 300mm
Let C = 16 as number turns
Let d = 20mm
L = sqrt ((3.14 * (600 - 20))² + 300³) * 16
L = 29,550 mm
What is the domain of f(x)=2/5x+6
Answer:
Look at that picture
Step-by-step explanation:
i will give brainliest and 5 stars if you help ASAP
Answer:
BC = 13.4
Step-by-step explanation:
its a law of cosines S-A-S
a² = b² + c² - 2bc cosA
a² = 12.6² + 4.6² - ( 2 * 12.6 * 4.6 * cos 90 )
a² = 179.92
a = sqrt (179.92)
a = 13.4
The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.
Answer:
Yes it can be concluded that state employees earn on average less than federal employees
The critical value is [tex]Z_{\alpha } = - 2.33[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 59593[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$ 58800[/tex]
The standard deviation is [tex]\sigma = \$ 1500[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 59593[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 59593[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_{\alpha } = - 2.33[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]
=> [tex]t = -2.896[/tex]
The p-value is obtained from the z-table
[tex]p-value = P(t < -2.896) = 0.0018898[/tex]
Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees
Will mark Brainliest! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
Given there are 26 alphabets in the English language, how many possible three-letter words are there?
We have 26 letters and 3 slots to fill. We can reuse a letter if it has been picked, so we have 26^3 = 26*26*26 = 17,576 different three letter "words". I put that in quotes because a lot of the words aren't actual words, but more just a sequence of letters.
A man saves 4% of his monthly
income of $19,540, the percentage
Savings is increased in the ratio
3:2 Calculate the savings from
the monthly
income.
Answer:
Although the question is not clear, It most likely looks like you were asking for the calculation of the savings for the month after increase.
savings for the month after increase = $1172.4
Step-by-step explanation:
First, let us calculate how much was saved before the increase in savings:
monthly income = $19,540
Percentage saved = 4% of monthly income
= 4/100 × 19,540 = 0.04 × 19,540 = $781.6
Next, we are given the ratio of increase in savings as 3:2
Let the new savings amount be x
3 : 2 = x : 781.6
[tex]\frac{3}{2} = \frac{x}{781.6} \\781.6\ \times 3\ =2x\\2344.8 = 2x\\x =\frac{2344.8}{2} \\x = \$1172.4[/tex]
therefore savings for the month after increase = $1172.4
Just incase you were looking for the savings before the increase, the answer is $781.6 (as calculated above)
a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?
volume of a cone
.
.
.
volume of sphere
.
.
number of spheres that can be made......
.
.
hence a hemisphere can be formed
Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent
The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]
where T is the set
[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]
(a) I've attached an image of the integration region.
[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]
(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]
[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]
Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.
