Given :
[tex]F(x)=3(x^2-1)[/tex]
To Find :
the absolute minimum and absolute maximum values of f on the given interval
[-1,2] .
Solution :
Now , getting first order differential equation and equating its equal to zero.
[tex]\dfrac{d(3x^2-3)}{dx}=0\\\\6x=0\\x=0[/tex]
So , x=0 is critical point .
Now , coefficient of [tex]x^2[/tex] is positive .
Therefore , it is increasing function after x=0 .
So , min value will be at , x=0.
[tex]Min = (0^2-1)\times 3=-3[/tex]
And maximum value will be the maximum at the x=2 because it is increasing function .
[tex]Max=(2^2-1)\times 3=9[/tex]
Therefore , max and min value is 9 and -3 respectively .
Hence , this is the required solution .
8 limes/$2.00 You have $5. How much change would you receive after purchasing 12 limes?
Answer:
2 dollars
Step-by-step explanation:
if 8 limes costs 2 dollars, then 4 limes cost 1 dollar
you purchased 12 limes so since you already know what 8 limes coms, you could subtract that
12-8=4
now you need to find out how much for 4 limes which would be half the price of 8 limes.. which should be 1 dollar
so $2.00+$1.00= $3.00
finally 5 dollars minus 3 would result in a change of 2 dollars
The sum of the measures of the angles is 180. The sum of the measures of the second and third angles is two times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
(60,47,73)
Step-by-step explanation:
Write an equation for the description: Tanmayi wants to raise $175 for a school fundraiser. She has raised $120 so far. How much more does she need to reach her goal?
WRITE AN EQUATION......
DONT SOLVE IT.....I REPEATE, DONT SOVLE IT.......
JUST WRITE AN EQUATION
Thx y'all for helping for real. :)
At the north campus of a performing arts school, 20% of the students are music majors. At the south campus, 70% of the students are music majors. The campuses are merged into one east campus. If 30% of the 1000 students at the east campus are music majors, how many students did the north and south campuses have before the merger?
Answer:
The north campus had [tex]800[/tex] while the south campus had [tex]200[/tex].
Step-by-step explanation:
The question stated that there are [tex]1000[/tex] students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.
Let [tex]x[/tex] denote the number of students in the north campus before the merger. The other [tex](1000 -x)[/tex] students would all belong to the south campus before the merger.
Before the merger, [tex]20\%[/tex] of the students of the north campus are of music majors. In terms of [tex]x[/tex], that's [tex](20\%)\cdot x = 0.20\,x[/tex] students.
On the other hand, [tex]70\%[/tex] of the students of the south campus are of music majors. That corresponds to [tex](70\%)\cdot (1000 - x) = 0.70\cdot (1000 - x) = 700 - 0.70\, x[/tex] students.
With a similar logic, the number of music students in the merged east campus will be [tex]30\% \times 1000 = 300[/tex].
The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:
[tex]0.20\, x+ (700 - 0.70\, x) = 300[/tex].
Solve for [tex]x[/tex]:
[tex]x = 800[/tex].
In other words, there are [tex]800[/tex] students in the north campus and [tex](1000 - 800) = 200[/tex] students in the south campus before the merger.
Twice the difference of a number and 5 is equal to 9.
Use the variable w for the unknown number.
Answer:
n = 19/5
Step-by-step explanation:
2(n - 5) represents "twice the difference of a number n and 5" and is equal to 9:
2(n - 5) = 9.
Performing the multiplication:
2n - 10 = 9, and so
2n = 19, or n = 19/5
Answer:28 hope this helps
Step-by-step explanation:
Help me 20 points FOR HELPING
Answer:
Twins in Family History Twins not in Family History
Twins Born 0.06 0.03
Single child born 0.94 0.97
Any one can help with this Venn Diagram question?.Please note that there is an another language, ignore except if you can understand it.
Answer:
(i) 30
(ii) 8
Step-by-step explanation:
Start by drawing 3 rings for the Venn diagram. Each ring represents either Audi, BMW, or Citroën.
Next, add the information provided in the problem statement. We know that 20 choose BMW only. Another 20 choose Citroën only.
We know the number who choose all 3 is the same as the number that choose BMW and Citroën, but not Audi. We'll call this number x.
Similarly, we know that the number who choose all 3 is half of those choose Audi and BMW, but not Citroën. So we'll say that number is 2x.
We know the total number of Audi votes is 48, the total number of BMW votes is 36, and the total number of Citroën votes is 34.
Finally, we know the total number of voters is 100, including those who voted for no favorites (we'll call that number n).
We know that BMW got 36 votes, so:
20 + x + x + 2x = 36
20 + 4x = 36
4x = 16
x = 4
We know that Citroën got 34 votes, so:
20 + x + x + z = 34
20 + 4 + 4 + z = 34
28 + z = 34
z = 6
We know that Audi got 48 votes:
y + 2x + x + z = 48
y + 2(4) + 4 + 6 = 48
y + 18 = 48
y = 30
Finally, we know that the total number of voters is 100.
20 + 20 + x + x + 2x + y + z + n = 100
20 + 20 + 4 + 4 + 2(4) + 30 + 6 + n = 100
92 + n = 100
n = 8
which of the binomials below is a factor of this trinomial
x^2-13+42
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{(x - 7)(x - 6)}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ {x}^{2} - 13x + 42 }[/tex]
Here, we have to find the two numbers that adds to 13 and multiplies to 42.
The numbers are 7 and 6
[tex] \sf{ {x}^{2} - (7 + 6)x + 42}[/tex]
⇒[tex] \sf{ {x}^{2} - 7x - 6x + 42}[/tex]
Factor out x from the expression
⇒[tex] \sf{x(x - 7) - 6x + 42}[/tex]
Factor out 6 from the expression
⇒[tex] \sf{x(x - 7) - 6(x - 7)}[/tex]
Factor out x - 7 from the expression
⇒[tex] \sf{(x - 7)(x - 6)}[/tex]
Hope I helped!
Best regards!!
Answer:
x-7 For AP EX peeps
Step-by-step explanation:
Show that 551 is a rational by writing it in the form a/b, where a and b are integers
Answer:
551/1
Step-by-step explanation:
[tex]551 = \dfrac{551}{1}[/tex]
__
Any integer can be written as a rational number with a denominator of 1.
help please I don't understand
Answer:
x = 8AM = 64 cmBM = 64 cmM is the midpointStep-by-step explanation:
Part A. The total length of a line segment is the sum of the lengths of its parts.
AM +MB = AB
Substituting the given information, this equation becomes ...
(7x +8) cm + (9x -8) cm = 128 cm
16x = 128 . . . . . . . . . collect terms, divide by cm
x = 128/16 . . . . . divide by the coefficient of x
x = 8
__
Part B. Then the length of AM is ...
AM = (7x +8) cm = (7(8) +8) cm = (56 +8) cm
AM = 64 cm
__
Part C. The length of BM is ...
BM = (9x -8) cm = (9(8) -8) cm = (72 -8) cm
BM = 64 cm
__
Part D. AM = BM = 64 cm, so point M is the midpoint of AB. Point M divides the segment into two equal parts.
Determine whether the function is continuous or discontinuous. Justify your reasoning. If discontinuous, identify points of discontinuity.
Please I am in need of urgent help.
Brainliest to the first answer
[tex]f (x)=\left \{ {{(2-x^2) if x\leq1 } \atop {(x) if x\ \textgreater \ 1}} \right.[/tex]
17. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth
$2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include
in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
Answer:
E
Step-by-step explanation:
Let's let c denote the amount of cashews and let's let p denote the amount of peanuts.
So, the owner wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound.
In other words, the total pounds as an equation is:
[tex]c+p=0.5[/tex]
Also, the price would be:
[tex]5.5c+2.3p=(p+c)2.8[/tex]
Since we mixed the peanuts and cashews, our sum would be 2.8(p+c).
And we already determined that p+c is 0.5. Thus, substitute:
[tex]5.5c+2.3p=(0.5)(2.8)[/tex]
Simplify:
[tex]5.5c+2.3p=1.4[/tex]
Now, we can solve the system of equations. Isolate a variable from the very first equation:
[tex]c+p=0.5[/tex]
Subtract p from both sides:
[tex]c=0.5-p[/tex]
Now, substitute this into the equation earlier:
[tex]5.5c+2.3p=1.4\\5.5(0.5-p)+2.3p=1.4[/tex]
Distribute:
[tex]2.75-5.5p+2.3p=1.4[/tex]
Combine like terms:
[tex]2.75-3.2p=1.4[/tex]
Subtract both sides by 2.75:
[tex]-3.2p=-1.35[/tex]
Divide everything by -3.2:
[tex]p=0.412875[/tex]
Now, find c:
[tex]p+c=.5[/tex]
Substitute:
[tex]c+0.421875=.5[/tex]
Subtract:
[tex]c=0.078125[/tex]
Thus, the owner would need 0.08 pounds of cashews and 0.42 pounds of peanuts.
Our answer is E.
What is the y-intercept of the line that passes through the points (-3,8) and (1,6)? Convert the answer to a decimal, if necessary.
Answer:
6.5
Step-by-step explanation:
The midpoint of the line is (-1,7). If you draw a line between that and (1.6), you’ll pass through the y-axis at 6.5.
Answer:
y-intercept =6.5
Step-by-step explanation:
First , lets find the slope
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-3,\:8\right),\:\left(x_2,\:y_2\right)=\left(1,\:6\right)\\m=\frac{6-8}{1-\left(-3\right)}\\\\Refine\\m=-\frac{1}{2}[/tex]
[tex](-3,8) =(x_1,y_1)\\m =-\frac{1}{2} \\\\[/tex]
Plug in values point point slope form
[tex]y-y_1=m(x-x_1)\\\\y -8=-\frac{1}{2} (x-(-3))\\\\y - 8 =-\frac{1}{2} (x+3)\\\\y -8= -\frac{1}{2} x -\frac{3}{2} \\\\y =-\frac{1}{2} x - \frac{3}{2} +8\\\\y = -\frac{1}{2}x +\frac{13}{2} \\y =\:mx\:+\:b[/tex]
Where b = y-intercept
y-intercept =[tex]\frac{13}{2}[/tex]
Cynthia typed 372 words in 6 minutes what's her typing rate in words per minute
Answer:
x = 62 words
Explanation:
→ We write the data problems.
372 words .............6 minutes
→ We must find: What's Cynthia typing rate in words per minute?
372 words .............6 minutes
x words ..................1 minute
x = 372 words * 1 minute/ 6 minutes
x = 62 words
The length of a rectangle is 10m greater than the width. The area is 24m^2
Answer:
length: 12m
width: 2m
Step-by-step explanation:
24 = a*w
a = w+10
then:
24 = (w+10)w
24 = w*w + 10*w
24 = w² + 10w
0 = w² + 10 - 24
w = {-10±√((10²)-(4*1*-24))} / (2*1)
w = {-10±√(100+96)} / 2
w = {-10±√196} / 2
w = {-10±14} / 2
only positive numbers:
w = {-10+14}/2
w = 4/2
w = 2m
a = w+10
a = 2 + 10
a = 12m
Check:
24 = 12*2
Suson caves 5% of her allowance cach week.
This week her allowance was $10
How much money did she save?
Write it in an algebraic expression and evaluate
Answer:
(10 - .05)w
w= weeks she saves
Find the product: 377(10, 000).
Answer:
37, 700, 000
Step-by-step explanation:
377(10,000) = 377 x 10,000
= 37, 700, 000
an easy way to see it is to just add the number of zeros from 10,000 to 377. since there are four zeros, you put four zeros behind 377.
[it's not mathematical but it helps u see the answer better. and it only works with numbers that start with 1]
8.01 + 24.192 need answer please
Answer: 32.202
or 32.20
or 32.2
Your bedroom wall is 138 inches inches inches wide. You want to hang two posters, each 36 inches inches across, with an equal space between each poster and the wall edges. How many inches of space should you leave between the wall edge and each poster?
Answer:
Space in inches= 22 inches
Step-by-step explanation:
bedroom wall is 138 inches inches inches wide.
want to hang two posters, each 36 inches inches across, with an equal space between each poster and the wall edges
Total space remaining= 138-(36*2)
Total space remaining=138-72
Total space remaining= 66
To hang the posters to have equal spacing from the egde and between each other, let's bear in mind that we have 3 partions..
Space in inches= 66/3
Space in inches= 22 inches
A corporate team-building event costs $32, plus an additional $1 per attendee. If there are 66 attendees, how much will the corporate team-building event cost?
Answer:
corporate team-building event cost will cost $98
Step-by-step explanation:
A corporate team-building event costs $32, plus an additional $1 per attendee.
Let cost be C
The expression for the above statement
C($)= 32+n(1)
Where n is the number of attendees
So a situation where there are 66 attendees, the total cost will be
C($) = 32 +66(1)
C($) = 32+66
C($)= 98
Three spherical balls with radius r are contained in a rectangular box. two of the balls are each touching 5 sides of the rectangular box and the middle ball. the middle ball also touches four sides of the rectangular box. What is the volume of the space between the balls and the rectangular box? This is a SAT question and is no calculator. Show all the work Answer is 4r^3(6-pi)
Answer:
The volume of the space between the balls and the rectangular box is [tex]4r^{3}(6 - \pi)[/tex]
Step-by-step explanation:
The attachment below shows the description of the rectangular bow and the three spherical balls.
From the description,
Two of the balls are each touching 5 sides of the rectangular box, say the 5 sides touched by one of the balls are sides 1,2,3,4, and 5; then the other ball will touch sides 2,3,4,5, and 6). The middle ball also touches four sides of the rectangular box, These four sides touched by the middle ball will be sides 2,3,4, and 5.This means the balls are tightly fitted into the rectangular box.
Each of the balls has a radius r
Hence, The volume of one of the balls is given by the volume of a sphere
[tex]Volume of a sphere = \frac{4}{3} \pi r^{3} \\[/tex]
The volume occupied by one of the balls is [tex]\frac{4}{3} \pi r^{3} \\[/tex]
∴ The volume occupied by the three spherical balls will be
3 × [tex]\frac{4}{3} \pi r^{3} \\[/tex]
= [tex]4\pi r^{3}[/tex]
The volume occupied by the three spherical balls [tex]4\pi r^{3}[/tex]
For the rectangular box,
The volume of a rectangular box = [tex]l w h[/tex]
Where [tex]l\\[/tex] is the length
[tex]w[/tex] is the width and
[tex]h[/tex] is the height
Since the balls are tightly packed,
The width of the rectangular box will be the diameter of the balls
diameter of the balls = 2r
∴ [tex]w[/tex] = 2r
The height of the rectangular box will also be the diameter of the balls
∴ [tex]h[/tex] = 2r
The length of the rectangular box will be 3 times the diameter of the balls
∴[tex]l[/tex] = 3 × 2r = 6r
Hence,
The volume of a rectangular box = 6r × 2r × 2r
= 24r³
The volume of the space between the balls and the rectangular box is given by
Volume of the space between the balls and the rectangular box =
volume of the rectangular box - volume occupied by the three spherical balls
Volume of the space between the balls and the rectangular box= 24r³ - 4πr³
= 24r³ - 4πr³
= 4r³(6 - π)
1620( 1 + 0.08/365 )^1825
Answer:
2.416,65
Step-by-step explanation:
1620( 1 + 0.08/365 )¹⁸²⁵
1620( 1 + 8/100 / 365 )¹⁸²⁵
1620( 1 + 8/36500 )¹⁸²⁵
1620(9127 / 9125 )¹⁸²⁵
2.416,65
please help quickly.
Answer:
Is the letter c
Step-by-step explanation:
What fraction of students are boys if 5 of the 8 students are boys
Answer:
Step-by-step explanation:
5/8
Answer: 5/8
Step-by-step explanation:
Well if 5 of the 8 students in total are boys then the fraction will be 5/8 because is the number of boys out of the total people.
Draw a two-card hand from a well-shuffled standard deck of cards. Given that the first card is a King, what is the chance the second card is NOT a King
Answer:
P ≈ 0,94
Step-by-step explanation:
The normal deck of cards consists of 52 cards, (with 4 kings )
If we take a king a deck will have 51 cards ( three kings )
The probability to get a non-king card is
Probability of non-king card (P) = 1 - Probability of getting a king card (P₁)
Probability of getting a king card P₁= 3/51 ≈ 0,059
Then P = 1 - 0,059
P ≈ 0,94
What is the difference between -3 and -12? -15 15 -9 9
Answer:
positive 9 hope this helped and a brainliest would be appreciated
Step-by-step explanation:
What is 5 minus the square of a number.
Answer:
5 - n^2
Step-by-step explanation:
Represent the unknown number by n. Then the desired expression is:
5 - n^2
Expressing the problem as a mathematical equation, the required expression ls n² - 5
Let the number = n ;
The square of the number, n = n²
Subtracting 5 from the squared Value of the number n² ;
The expression becomes ; n² - 5
Therefore, the required expression which expresses 5 minus the square of a number is n² - 5
Learn more : https://brainly.com/question/15165519
Is GPA qualitative or quantitative? Also, is it nominal, ordinal, interval or ratio?
While the letter grade to numerical contribution for a single subject is ordinal, the moment you compute a grade point average you already treated it as interval at that moment (otherwise you have no basis on which to assert that A+C = B+B).
Answer:
General rule of thumb: if you can add it, it's quantitative. For example, a G.P.A. of 3.3 and a G.P.A. of 4.0 can be added together (3.3 + 4.0 = 7.3), so that means it's quantitative. While the letter grade to numerical contribution for a single subject is ordinal, the moment you compute a grade point average you already treated it as interval at that moment
Please find the perimeter of both shapes if x = 4.5
Answer:
Rectangle: 27
Triangle: 39
Step-by-step explanation:
To find the perimeter of a rectangle use the expression P = 2(l + w)
Before substituting 4.5 for x simplify the equation
2((-3 + x) + 1/2(4x + 6)) = P
First simplify in the parenthesis
2(-3 + x + 2x + 3) = P
Now combine like terms, then multiply 2 and 3x
2(3x) = P
P = 6x
Lastly substitute 4.5 for x to find the perimeter
P = 6(4.5)
P = 27
Now do the same thing that we did with the rectangle but with a triangle
P = a + b + c
(3x - 4) + (3x - 4) + 2/3(6x + 3) = P
10x - 6 = P
10(4.5) - 6 = P
P = 39
Different Question. Please explain your answer
Answer:
(x-6)^2 + (y+8)^2 = 25
Step-by-step explanation:
The equation for a circle can be written as
(x-h)^2 + (y- k)^2 = r^2
where (h,k) is the center and r is the radius
The diameter is 10 so the radius is 10/2 =5
the center is 6,-8
(x-6)^2 + (y- -8)^2 = 5^2
(x-6)^2 + (y+8)^2 = 5^2
(x-6)^2 + (y+8)^2 = 25