Find the value of x which optimises the total surface area of the box, and showthat it minimises the total surface area.
Answers
Solution:
Given data:
Let the width of the box be
[tex]=x[/tex]The volume of the box is
[tex]V_{\text{box}}=400\operatorname{cm}[/tex]The height of the box is
[tex]=h[/tex]Let the length of the box be
[tex]=l[/tex]The length is four times the width of the base, this can be represented below as
[tex]\begin{gathered} l=4\times x \\ l=4x\ldots\ldots\ldots\text{.}(1) \end{gathered}[/tex]Part A:
Show that the height h of the box is given by
[tex]\frac{400}{x^2}[/tex]Concept:
To show that the height is given as above, we will use the volume of the box which is given below as
[tex]\begin{gathered} V_{\text{box}}=\text{length}\times width\times height \\ V_{\text{box}}=l\times x\times h \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V_{\text{box}}=l\times x\times h \\ \text{Substituite equation (1) in the formuka above,} \\ 400=4x\times x\times h \\ 400=4x^2h \\ \text{divide both sides by 4x}^2 \\ \frac{4x^2h}{4x^2}=\frac{400}{4x^2} \\ h=\frac{100}{x^2}(\text{PROVED)} \end{gathered}[/tex]Part B:
Show that the total surface area A of the box is given by
[tex]A=4x^2+\frac{1000}{x}[/tex]Concept:
To prove the above relation, we will use the formula of the area of the box below
[tex]\begin{gathered} A_{\text{box}}=2(lw+lh+wh) \\ \text{where,} \\ l=\text{length}=4x \\ w=\text{width}=x \\ h=\text{height}=\frac{100}{x^2} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{box}}=2(lw+lh+wh) \\ A_{\text{box}}=2(4x\times x+4x\times\frac{100}{x^2}+x\times\frac{100}{x^2}) \end{gathered}[/tex]By simplifying the relation above, we will have
[tex]\begin{gathered} A_{\text{box}}=2(4x\times x+4x\times\frac{100}{x^2}+x\times\frac{100}{x^2}) \\ A_{\text{box}}=2(4x^2+\frac{400}{x}+\frac{100}{x}) \\ A_{\text{box}}=2(4x^2+\frac{500}{x}) \\ A_{\text{box}}=8x^2+\frac{1000}{x} \end{gathered}[/tex]Hence,
The Total surface area of the box will be given below as
[tex]A_{\text{box}}=8x^2+\frac{1000}{x}[/tex]To determine the value of x which optimizes the total surface area of the box, and show
that it minimizes the total surface area, we will have to look for the first derivative of the function above
[tex]\begin{gathered} A_{\text{box}}=8x^2+\frac{1000}{x} \\ \frac{dA}{dx}=\frac{d}{dx}(8x^2+\frac{1000}{x}) \\ \frac{dA}{dx}=16x-\frac{1000}{x^2} \end{gathered}[/tex]To find the value of x, we will substitute the value of dA/dx to be = 0
[tex]\begin{gathered} \frac{dA}{dx}=0 \\ 16x-\frac{1000}{x^2}=0 \\ 16x=\frac{1000}{x^2} \\ \frac{16x^3}{16}=\frac{1000}{16} \\ x^3=62.5 \\ x=\sqrt[3]{62.5} \end{gathered}[/tex]To show the minimum value of x, we will have to look for the second derivative
[tex]\frac{d^2A^{}}{dx^2}[/tex][tex]undefined[/tex]Related Questions
Shannon's bicycle travels 50 feet for every 3 pedal turn. How many pedal turns are needed to travel one mile (1 mile=5280 feet)?
Answers
Shannon's bicycle travels 50 feet for 3 pedal turn
He travels
[tex]50ft=3\text{ pedal turn}[/tex]Converting 1 mile to feet
[tex]1\text{mile}=5280ft[/tex]The number of pedal turns needed to travel a mile is
[tex]\begin{gathered} 50ft=3\text{ pedal turn} \\ For\text{ 1mile (5280ft)=}\frac{5280\times3}{50}=3168\text{ pedal turns} \end{gathered}[/tex]Hence, the answer is 3168 pedal turns
create a non linear function that has a solution at (-2,6). Include a calculation that shows why this is a solution to your function.
Answers
In order to find a nonlinear function that has a solution at (-2,6) we need to choose first a parent function that is no linear in this case, we will use
[tex]y=x^2[/tex]in order to know that the solution is (-2, 6) so if I introduce the value of x coordinate which is -2 in the function we need to have as result 6
In this case, taken the parent function above and in order to have the desired result we have the next calculations
[tex]\begin{gathered} 6=(-2)^2+2 \\ 6=4+2 \\ 6=6 \end{gathered}[/tex]so the function that has a solution (-2,6) and is no linear is
[tex]y=x^2+2[/tex]I do not know how to find the information from a word question and would love some help
Answers
Explanation
Given
From the question, we can see that the bottom of the ferris wheel is 30 feet about the ground and also while rotating, it can move to a height of 550 feet off the ground. In essence the actual height the ferris wheel can attain is
[tex]h=550-30=520[/tex]The amplitude then becomes half of the height which is
[tex]A=\frac{h}{2}=\frac{520}{2}=260[/tex]The vertical shift the Ferris wheel undergoes becomes the sum of the amplitude and its distance above the ground.
[tex]D=260+30=290[/tex]Since it takes the Ferris wheel 15 minutes to move from bottom to top, it will take it twice that to complete one revolution which will be its period.
[tex]T=2\times15mins=30[/tex]Therefore, the frequency B, becomes;
[tex]B=\frac{2\pi}{T}=\frac{2\pi}{30}=\frac{\pi}{15}[/tex]We can then place in the above parameters to form the equation.
[tex]y=Acos(B(t+C))+D\Rightarrow260cos(\frac{\pi}{15}(t+C)+290[/tex]The last missing parameter is the phase shift C. At time t =0, the function (y) has a position at 30. Therefore,
[tex]\begin{gathered} 30=260cos(\frac{\pi}{15}C)+290 \\ 260cos(\frac{\pi}{15}C)=-290+30 \\ 260cos(\frac{\pi}{15}C)=-260 \\ divide\text{ both sides by 260} \\ \frac{\begin{equation*}260cos(\frac{\pi}{15}C)\end{equation*}}{260}=\frac{-260}{260} \\ cos(\frac{\pi}{15}C)=-1 \\ \frac{\pi}{15}C=cos^{-1}(-1) \\ \frac{\pi}{15}C=\pi \\ C=\frac{15\pi}{\pi} \\ C=15 \end{gathered}[/tex]Therefore, the function y becomes
Answer:
[tex]y=260cos(\frac{\pi}{15}(t+15)+290[/tex]P(x) = x3 + 3x2 − 16x − 48, c = −3 Show that the given value of c is a zero of P(x)
Answers
The value of c is a true zero of the polynomial function P(x)
How to show that c is a zero of the polynomial?The polynomial function is given as
P(x) = x³ + 3x² - 16x - 48
Also, we have the value of c to be
c = -3
If truly, the variable c is a zero of the polynomial, then the following must be true
P(c) = 0
Start by substituting -3 for c in the equation P(x) = x³ + 3x² - 16x - 48
So, we have
P(-3) = (-3)³ + 3(-3)² - 16(-3) - 48
Evaluate the exponents
P(-3) = -27 + 3(9) - 16(-3) - 48
Evaluate the products
P(-3) = -27 + 27 + 48 - 48
Evaluate the sum and the difference
P(-3) = 0
Recall that
c = -3
So, we have
P(c) = 0
Hence, c is a zero of the polynomial because P(c) = 0
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Find the value of x in the figure below. (7x + 17) (8.x + 2)(please be kind)
Answers
The angles shown are vertically opposite, then they are equal:
[tex]7x+17=8x+2[/tex]Solving for x, we have:
[tex]\begin{gathered} 7x+17=8x+2 \\ 7x-8x=2-17 \\ -x=-15 \\ x=15 \end{gathered}[/tex]Therefore, x=15.
Determine whether the variable is qualitative or quantitative.Favorite basketball playerIs the variable qualitative or quantitative?A. The variable is quantitative because it is an attribute characteristic.B. The variable is qualitative because it is a numerical measure.C. The variable is quantitative because it is a numerical measure.D. The variable is qualitative because it is an attribute characteristic.
Answers
We have that favorite is a characteristic. It is a qualitative data. We cannot measure it at the weight, length, and other similar variables.
Therefore, the correct option is D:
Gravel is piled in the shape of a cone. The circumference of the base is 221 ft. The slant height is 43 ft. Find the volume of gravel
Answers
Answer:
Step-by-step explanation:
What is the equation for the translation of x2 + y² = 64 three units to the left and two units down
(x - 3)² + (y-2)² = 64
(x+3)2 + (y + 2)2 = 64
(x-3)² + (y + 2)² = 64
(x+3)² + (y-2)² = 64
Answers
The equation for the translation of [tex]x^{2} +y^{2}=64[/tex], three units to the left and two units down is option (b) [tex](x+3)^2+(y+2)^2=25[/tex]
The equation is [tex]x^{2} +y^{2}=64[/tex]
The standard form of the circle
[tex](x-h)^2+(y-k)^2=r^{2}[/tex]
Where r is the radius of the circle
(h,k) are the coordinates of the center of the circle.
The equation is [tex]x^{2} +y^{2}=64[/tex]
The center is (0,0)
Here the circle translated three units to the left
Therefore h = -3
The circle is translated two units down
k = -2
Substitute the values in the standard form of the circle
[tex](x--3)^{2}+(y--2)^{2}=25[/tex]
[tex](x+3)^2+(y+2)^2=25[/tex]
Hence, the equation for the translation of [tex]x^{2} +y^{2}=64[/tex], three units to the left and two units down is option (b) [tex](x+3)^2+(y+2)^2=25[/tex]
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Suppose that there are two types of tickets to a show: Advanced and same day. Advanced tickets cost $40 and same-day tickets cost $25. For one performance there are 65 tickets sold in all, and the total amount paid for them was $2225. How many tickets of each type were sold?
Answers
Solution:
Given:
Two types of tickets; advanced and same-day tickets.
Let a represent advanced tickets
Let s represent same-day tickets.
Developing the word problem (statements) into mathematical expressions, we have;
[tex]\begin{gathered} \text{Advanced tickets cost \$40. This means;} \\ a=\text{ \$40} \\ \\ \text{Same}-\text{day tickets cost \$25. This means;} \\ s=\text{ \$25} \end{gathered}[/tex][tex]\begin{gathered} \text{Total tickets sold in all is 65. This means;} \\ a+s=65\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ \\ \text{Total amount paid for advanced tickets = \$40a} \\ \text{Total amount paid for same-day tickets = \$25s} \\ \\ \text{Total amount paid for all tickets = \$2225.} \\ \text{Hence,} \\ 40a+25s=2225\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Solving equations (1) and (2) simultaneously to get the values of a and s;
[tex]\begin{gathered} \text{From equation (1)},\text{ } \\ a+s=65 \\ a=65-s\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(3) \\ \\ \text{Substituting equation (3) in equation (2),} \\ 40a+25s=2225 \\ 40(65-s)+25s=2225 \\ 2600-40s+25s=2225 \\ 2600-15s=2225 \\ \text{Collecting the like terms;} \\ 2600-2225=15s \\ 375=15s \\ 15s=375 \\ \text{Dividing both sides by 15 to get s,} \\ s=\frac{375}{15} \\ s=25 \\ \text{Thus, same-day tickets sold were 25 tickets} \end{gathered}[/tex]Substituting the value of s in equation (3) to get the value of a.
[tex]\begin{gathered} a=65-s \\ a=65-25 \\ a=40 \\ \text{Thus, advanced tickets sold were 40 tickets} \end{gathered}[/tex]Therefore, advanced tickets sold were 40 tickets and same-day tickets sold were 25 tickets.
I NEED HELP ASP!! Which expression is equivalent to −2(5x + 3y)?
Answers
Answer:
-10x - 6y
Step-by-step explanation:
simplify - 2(5x + 3y): - 10x - 6y
-2(5x + 3y)
Apply the distributive law: a(b + c) = ab + ac
-2(5x + 3y) = -2 · 5x - 2· 3y
simplify -2 · 5x - 2· 3y : - 10x - 6y
therefore the answer is: = -10x - 6y
Graphthe line with slope 2/5 and y-intercept -3.
Answers
1) As the line has a slope m=2/5 and a y-intercept = -3
Then we can write y=2/5x -3
2) Now let's plot that, setting a table with at least 3 values for that
x | y
0 -3
-1 -3.4
2 -2.2
With these points, we can trace a line.
Which of the following quadratic functions has a graph that opens downward? Check all that apply. A v=Bx2- 8x– 13 B. v= - (3+x? e. v=zx2 - 13x+5 O d. v=2r-
Answers
Ok, so
Remember that:
For any quadratic equation of the form:
[tex]y=ax^2+bx+c[/tex]- If the leading coefficient is greater than zero, the parabola opens upward, and
- If the leading coefficient is less than zero, the parabola opens downward.
So, here we have the following functions:
[tex]v=\frac{1}{3}x^2-8x-13[/tex]The leading coefficient is greater than zero, so this parabola opens upward.
Option B:
[tex]\begin{gathered} v=-(3+x^2) \\ v=-x^2-3 \end{gathered}[/tex]The leading coefficient is less than zero, so this parabola opens downward.
Option C:
[tex]v=\frac{2}{3}x^2-13x+5[/tex]The leading coefficient is greater than zero, so this parabola opens upward.
Option D:
[tex]v=2x-x^2[/tex]The leading coefficient is less than zero, so this parabola opens downward.
Therefore, the correct options are B and D.
find the volume specified. use 3.14 as the approximate value of pi, and round your answer to the nearest tenth.find the volume of a feed bin having the shape of a right circular cylinder of radius 5 ft and height 5 ft topped by a right circular cone of the same radius and height 3 ft Draw a picture to get started.
Answers
ANSWER
The volume of the bin is 471 cubic feet
EXPLANATION;
Given that;
The radius of the cylinder is 5ft
The height of the cylinderis 5 ft]
The height of the cone s 3ft]
To find the total volume of the bin, follow the steps below
Firstly, draw the structure of the bin
Secondly, Write the formula for calculating the volume of a cone and a cylinder
[tex]\begin{gathered} \text{ The volume of a cone = }\frac{1}{3}\pi r^2h \\ \text{ The volume of a cylinder = }\pi r^2h \end{gathered}[/tex][tex]\begin{gathered} \text{ The volume of the cone = }\frac{1}{3}\pi r^2h \\ \text{ where }\pi\text{ = 3.14} \\ \text{ The volume of the cone = }\frac{1}{3}\times\text{ 3.14 }\times\text{ 5}^2\text{ }\times\text{ 3} \\ \text{ The volume of the cone = }\frac{1}{3}\times\text{ 3.14 }\times\text{ 25 }\times\text{ 3} \\ \text{ The volume of the cone }=3.14\text{ }\times\text{ 25} \\ \text{ The volume of the cone = 78.5 ft}^3 \end{gathered}[/tex][tex]\begin{gathered} \text{ The volume of the cylinder = }\pi r^2h \\ \text{ }\pi\text{ = 3.14} \\ \text{ The volume of the cylinder = 3.14 }\times\text{ 5}^2\text{ }\times\text{ 5} \\ \text{ The volume of the cylinder = 3.14 }\times\text{ 25 }\times\text{ 5} \\ \text{ The volume of the cylinder = 392.5 ft}^3 \end{gathered}[/tex]Find the volume of the bin
[tex]\begin{gathered} \text{ Volume of the bin = volume of the cone + volume of cylinder} \\ \text{ Volume of the bin = 78.5 + 392.5} \\ \text{ Volume of the bin = 471 ft}^3 \end{gathered}[/tex]Hence, the volume of the bin is 471 cubic feet
What is the ratio of the areas of ΔABC to ΔA'B'C' ?
Answers
The first step is to find the scale factor relating ABC to A'B'C'. Since they are dilated, ABC is similar to A'B'C'. This means that the ratios of their corresponding sides are equal. Thus,
AB/A'B' = BC/B'C' = AC/A'C'
From the information given,
AB = 7
A'B' = 28
Thus,
ratio of ABC to A'B'C' = 7/28 = 1/4
Ratio of area of ABC to A'B'C' = (1/4)^2
Ratio of area of ABC to A'B'C' = 1/16
Find the slope of the line that passes through the following points . Simplify your answer .
(-10, 10) and (-9, -10)
Answers
Answer:
-20 is the slope
Step-by-step explanation:
Using the slope formula y1-y2/x2-x1,
you get the slope of -20
Answer: -20/1
Step-by-step explanation:
1) Use the slope formula
y1-y
--------
x1-x
2) Substitute the numbers
-10-10
------
-9-(-10)
3) Solve
-20
------
1
-20/1
If the same number is added to the nunerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?
Answers
Answer:
x = 3
Step-by-step explanation:
If the same number is added to the numerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?
[tex]\frac{12+x}{13-x} =\frac{3}{2}[/tex]
multiply both sides by 13-x:
[tex](13-x)\frac{12+x}{13-x} =\frac{3}{2}(13-x)\\\\12+x = \frac{3(13-x)}{2} \\\\12+x = \frac{39-3x}{2} \\[/tex]
multiply both sides by 2:
[tex]2(12+x) = (\frac{39-3x}{2})\\\\24+2x = 39-3x[/tex]
subtract 24 from both sides:
24 + 2x - 24 = 39 - 3x - 24
2x = 15 - 3x
add 3 x to both sides:
2x + 3x = 15 - 3x + 3x
5x = 15
divide both sides by 5:
5x/5 = 15/5
x = 3
check:
[tex]\frac{12+x}{13-x} =\frac{3}{2}\\\\\frac{12+3}{13-3} =\frac{3}{2}\\\\\frac{15}{10} =\frac{3}{2}\\\\\frac{3}{2} =\frac{3}{2}[/tex]
For a card trick, Barry is using 14 cards from a deck if each suit he uses had 5 numbered cards and c face cards, which expression shows how many suits he is using.
A. 14 x 5 + c
B 14 divided by (5+c)
C 14 divided by 5+ C
D 14 x (5+c)
Answers
Answer:
b
Step-by-step explanation:
8) Type your answers in the boxes.
A sequence is given by the equation an= 1/4n where a1 = 512 and n > 1 and is a
whole number.
What are the first 4 terms of the series?
Series:
Answers
The first 4 terms of the sequence are 512 , 128 , 32 and 8 .
In mathematics, a sequence is a named collection of elements where repeats are allowed and order matters.
It has pieces, much like a set (also called elements, or terms). The number of items determines how long the series is (potentially infinite). The same elements could appear in a sequence more than once at different places in contrast to a set, where the order is crucial. Formally, a sequence can be defined as a relationship between the items at each of the positions in the sequence and natural numbers (the positions of the sequence's constituents). It is possible to think of an indexed family, which is a function from any index set, as a generalization of the concept of a sequence.The formula for the sequence is given by aₙ = 1/4 aₙ₋₁
It is given that a₁ = 512
Hence a₂ = 1/4 a₁ = 1/4 × 512 = 128
a₃ = 1/4 a₂ = 32
a₄ = 1/4 a₃ = 8
Therefore the first 4 terms of the sequence are 512 , 128 , 32 and 8 .
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help meeeeeeeeeeeeeeeeeee please
Answers
Answer:c
Step-by-step explanation:
In a company, %90 of the workers are men . If 500 people work for the company who aren't , how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answers
90%=500x9=4500
4500+500=5000
or
90:10
9:1
4500:500=5000
5000 people
Mark and Nina own different flower shops, which both open at the same time in the morning.
Function m models the number of roses Mark has at his flower shop, and function n models the number of roses in Nina's flower shop, x hours after
the shops open.
m(x)=616-24x
n(x)=552-36x
Which function correctly represents how many more roses Mark has at his flower shop than Nina has at hers, x hours after the shops open?
A. (m-n)(x)=64 + 12x
B. (m-n)(x)=64-16x
C. (m-n)(x)=64-12x
D. (m-n)(x) = 64-60x
Answers
Correct option is A. The equation representing the how many more roses Mark has at his flower shop than Nina has at hers is (m-n)(x)=64 + 12x
What constitutes a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
From the given equations,
Subtracting both of the functions,
m(x) - n(x) = (616-24x) - (552-36x)
⇒ (m - n) (x) = 64 - 12x
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what is the median? -95, -94, -93, 95, 91, -92, -89, -92, -98
Answers
Given the set of the data:
[tex]-95,-94,-93,95,91,-92,-89,-92,-98[/tex]Arranging the data in order from the least to the greatest:
[tex]-98,-95,-94,-93,-92,-92,-89,91,95[/tex]The number of the data = 9
so, the median is the number which is in the middle
It will be number (9+1)/2 = 10/2 = 5
so, the median = -92
GI = 6, HI = 8, DT = 12, what is IE?a.12b.16c.8d.4
Answers
Since both chords passes through the point I the should be equal.
Now we know that GI=6 and HI=8, then GH=14; hence DE have to be equal to 14 too.
From this we conclude that IE should be 4.
Marco is driving to the Grand Canyon his distance from the Grand Canyon decreases 150 miles every three hours after four hours his distance from the Grand Canyon is 200 Mi Marcos distance from the Grand Canyon in Miles Y is a function of the numbers of the hours he drives what is the initial value fine markers distance from the Grand Canyon when he starts to drive
Answers
Answer:
-50
Step-by-step explanation:
The Rate of change is -50 and not 50. Don't get mixed.
Lacey’s bank account shows a balance of –$45.10. The next day, she deposits $65.00 and uses her debit card for a purchase of $23.75. What is her new balance?
Answers
Lacey's new balance in the account is -$3.85.
What is account balance?
The amount of funds held in a financial institution, for example, a savings or checks account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.In order for a company's accounts to balance, debits and credits must be employed in the bookkeeping process. Credits raise liability, revenue, or equity accounts while decreasing asset or expenditure accounts. Credits operate in reverse.Lacey’s bank account balance = –$45.10
she deposits = $65.00
Debit card for a purchase = $23.75
Updated balance = –$45.10+$65.00-$23.75= -$3.85
Lacey's new balance in the account is -$3.85.
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Golfer Tiger Woods drives a golf ball with a vertical speed of 144 ft/sec at the time when he hits the ball with his club. The height function of one of his drives is H=-161 +1441, where t is the time in seconds and H is the height in feet. Find the maximum height of a drive. (hint: where does the maximum occur on a parabola?)
Answers
The given quadratic function
[tex]H=-16t^2+144t[/tex]Describes the height, in feet, of one of Tiger Woods's drives with respect to the time, t, measure in seconds.
The function is a parabola, to determine its maximum point, the first step is to determine if the parabola opens up or down, to do so you have to look at the sign of the coefficient of the quadratic term (a).
-If a>0, the parabola opens up, and its vertex will indicate the minimum value of the funtion.
-Id
For this function, the coefficient is a= -16, the coefficient "a" is negative, which
The stemplot below displays the grades (out of 30) that 26 students received on a quiz.
A stemplot titled quiz grades has values 12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30.
Which of the following boxplots correctly displays the distribution of quiz grades?
Answers
If a stemplot as shown in the attachments attached alongside the question statement, display the grades (out of 30) that 26 students received on a quiz, and has values [12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30], then the boxplot (A) correctly displays the distribution of quiz grades.
As per the question statement, a stemplot as shown in the attachments attached alongside the question statement, display the grades (out of 30) that 26 students received on a quiz, and has values [12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30].
We are required to determine which one of the four boxplots provided in the attachments correctly displays the distribution of quiz grades.
To solve this question, first let us observe the distribution of the grades, where the grade 13, 17, 18, 19, 20 and 21 are missing. Hence, the set is a discontinuous one.
Looking at options (B) and (D), these boxplots have a straight continuous line from 12 upto 30, which means that the grades 13, 17, 18, 19, 20 and 21 are also included in the set. This is false, and hence, options (B) and (D) cannot be the correct answers.
Coming to Option (C), it has a continuous line from 15 to 30, which means, the grades [17, 18, 19, 20 and 21] are also included in the set, and this is also not true. Hence, option (C) is also not our correct answer.
Finally coming to option (A), It has four individual dots over 12, 14, 15 and 16, and then, a gap, and a continuous line from 20 to 30 after the gap. From our set, we can observe that, 12, 14, 15 and 16 are in-fact present in the set, each of them having occurrence once only, and thus the four individual dots over 12, 14, 15 and 16 correctly addresses this situation. Also, every number between 22 and 30 are present in the set, and the numbers of (23, 24, 25, 26 and 27) have the most occurrences, which the boxes on top of (23 - 27) again correctly address.
Hence, our correct answer is option (A).
Stemplot: In Statistics, a stem and leaf plot, or a stem plot, is a technique used to classify discrete or continuous variables, and used to organize data as they are collected. Since it looks something like a bar graph, and each number in the data is broken down into a stem and a leaf, it gets the name of Stemplot.Boxplot: In Statistics, a boxplot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum of a set of observations, and the name "box plot" comes from the fact that the graph looks like a rectangle with lines extending from the top and bottom.To learn more about Stemplots and Boxplots, click on the link below.
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Use equation below to find v, if u = 18, a=6, and t = 4. v=utat
Answers
The given equation is
[tex]v=u\cdot t\cdot a\cdot t[/tex]Where, u=18, a=6, and t=4. Replacing these values, we have
[tex]v=18\cdot4\cdot6\cdot4=1,728[/tex]Therefore, the answer is 1,728.What is the degree of the polynomial, 105y75+125x5-100x10?
Answers
The degree of the polynomial is the largest of these three values, which is 75
What is polynomial ?Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
Simply locate the highest exponent in the formula to determine the degree of the polynomial. The degree of the polynomial is seven because it is the highest exponent above.
There are multiple variables in the polynomial. The biggest sum of ALL of the exponents for ALL of the variables in a term is the polynomial's degree.
Given that := 105[tex]y^{75} + 125^{5} - 100x^{10}[/tex]
= 105[tex]y^{75} + 125^{5} - 100x^{10}[/tex]
To find the degree of a polynomial, simply find the highest exponent in the expression. As seven is the highest exponent above, it is also the degree of the polynomial.
The polynomial has more than one variable. The degree of the polynomial is the largest sum of the exponents of ALL variables in a term.
The first term is 105[tex]y^{75}[/tex]
The degree of this term is 75
The second term is 125[tex]x^{5}[/tex]
The degree of this term is 5.
The third term is 100[tex]x^{10}[/tex]
The degree of this term is 10.
The degree of the polynomial is the largest of these three values, which is 75
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eWhat are the zeros of the function f(x) = (2x+6)(x-4)?OA. x = 6 and x = -4OB. x=-6 and x = -4OC. x=3 and x = -4OD. x=-3 and x = 4
Answers
Hello there. To solve this question, we have to remember some properties about roots of polynomials.
Given the following function:
[tex]f(x)=(2x+6)\cdot(x-4)[/tex]We want to determine its roots.
For this, we want to determine the values of x such that
[tex]f(x)=0[/tex]Then we have that
[tex](2x+6)\cdot(x-4)=0[/tex]We know that a product of two values is equal to zero if and only if one of them is equal to zero.
So we have that
[tex]2x+6=0\text{ or }x-4=0[/tex]Subtract 6 on both sides of the first equation, we get
[tex]2x=-6[/tex]Divide both sides of the equation by a factor of 2
[tex]x=-3[/tex]Now for the second equation, add 4 on both sides of the equation
[tex]x=4[/tex]Hence we say that the roots of this function are
[tex]x=-3\text{ and }x=4[/tex]This is the answer contained in the last option.
