Answer:
419.25
Step-by-step explanation:
The calculation of the cost of materials for the cheapest such container is shown below:-
We assume
Width = x
Length = 2x
Height = h
where, length = [tex]2 \times width[/tex]
Base area = lb
= [tex]2x^2[/tex]
Side area = 2lh + 2bh
= 2(2x)h + 2(x)h
= 4xh + 2xh
Volume = 24 which is lbh = 24
[tex]h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}[/tex]
Now, cost is
[tex]= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}[/tex]
now we have to minimize C(x)
So, we need to compute the C'(x)
[tex]= 52x - \frac{648}{x^2}[/tex]
C"(x) [tex]= 52x - \frac{1,296}{x^3}[/tex]
now for the critical points, we will solve the equation C'(x) = 0
[tex]= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}[/tex]
[tex]C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0[/tex]
So, x is a point of minima that is
= [tex](\frac{648}{52} )^\frac{1}{3}[/tex]
Now, Base material cost is
[tex]= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}[/tex]
= 139.75
Side material cost is
[tex]= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }[/tex]
= 279.50
and finally
Total cost is
= 139.75 + 279.50
= 419.25
The cost of the side material is $279.50, the cost of the base material is $139.75 and the total cost is $419.25 and this can be determined by using the arithmetic operations.
Given :
A rectangular storage container with an open top is to have a volume of 24 cubic meters.The length of its base is twice the width.Material for the base costs 13 dollars per square meter.Material for the sides costs 9 dollars per square meter.Let the width of the rectangular storage container be 'x' then according to the given data the length is '2x' and let the height of the container be 'h'.
The base area of the rectangular storage container is given by:
Base Area = [tex]2x^2[/tex] ----- (1)
The side area of the rectangular storage container is given by:
Side Area = 2(2x)h + 2xh
= 6xh ---- (2)
Now, the volume of the rectangular storage container is given by:
Volume = lbh
Put the values of known terms in the above equation.
24 = [tex]2x^2h[/tex]
[tex]h = \dfrac{12}{x^2}[/tex]
Now, the cost is given by:
[tex]\rm C(x)=13(2x^2)+9(6xh)[/tex]
[tex]\rm C(x)= 26x^2 + \dfrac{648}{x}[/tex]
Now, to minimize C(x) differentiate the C(x) with respect to x.
[tex]\rm C'(x)=52x -\dfrac{648}{x^2}[/tex] ---- (3)
Now, equate the above equation to zero.
[tex]0 = 52x =\dfrac{648}{x^2}[/tex]
[tex]x = \sqrt[3]{\dfrac{648}{52}}[/tex]
Now, differentiate equation (3) with respect to x.
[tex]\rm C"(x) = 52+\dfrac{1296}{x^3}[/tex]
Now, put the value of x in the above equation.
[tex]\rm C"(x) = 52+\dfrac{1296}{\dfrac{648}{52}}[/tex]
[tex]\rm C"(x) = 52+104[/tex]
[tex]\rm C"(x) = 156 > 0[/tex]
Therefore, 'x' is the point of minima.
Now, the cost of the base material is:
[tex]= 13\times 2 \times (\dfrac{648}{52})^\frac{2}{3}[/tex]
= $139.75
Now, the cost of the side material is:
[tex]=\dfrac{648}{\sqrt[3]{\dfrac{648}{52}} }[/tex]
= $279.50
Therefore, the total cost is given by:
= 139.75 + 279.50
= $419.25
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A recipe for chili uses 213 cups of beans. Keith is making 112 times the recipe. Which equation helps Keith find how many cups of beans he needs?
Answer:
213 x 112
Step-by-step explanation:
You have to multiply the recipe with the amount of times it's made.
Answer:
213 cups of beans.Keith is making 112 times the recipe.
Step-by-step explanation:
Suppose x = 7 is a solution to the equation 4x − 2(x + a) = 8. Find the value of a that makes the equation true.
Answer:
a=6 x=1
Step-by-step explanation:
4x1=4 4-2=2
2+6=8
Answer:
a=3 i think, sorry if i'm wrong
Step-by-step explanation:
4x-2(x+a)=8 ~parenthesis first.
4*7-14-2a=8 ~4 times 7= 28 and just bring down the rest.
28-14-2a=8 ~ add 14 to negative 14 and 8, the positive and negative 14 would cancel out each other.
28-2a=22 ~ subtract 28 from both positive 28 and 22.
-2a=-6 ~ divide by 2 on both sides.
a=3 ~ The reason why it is 3 is because negative 2 times positive 3 equals negative 6.
PLEASE I NEED HELP ASAP PLEASE
Answer:
work is shown and pictured
Consider the formula for the slope between two coordinate points, m, shown below. Which of the following equations is equivalent to the slope formula?
Answer:
Answer is A
Step-by-step explanation:
[tex]m = y2 - y1 \div x2 - x1 \\ y2 = m(x2 - x1) + y1[/tex]
Help ASAP!!! Savings Account.Christine Chu borrowed $4500 from a bank at a simple interest rate of 2.5% for one year.
a) Determine how much interest Christine paid at the end of 1 year.
b) Determine the total amount Christine will repay the bank at the end of 1 year
Answer: $112.50 ; $4612.5
Step-by-step explanation:
a) Determine how much interest Christine paid at the end of 1 year.
This will be:
Simple interest = PRT/100
where
P = principal = $4500
R = rate = 2.5%
T = time = 1 year
Interest = (4500 × 2.5 × 1)/100
= 11250/100
= $112.50
b) Determine the total amount Christine will repay the bank at the end of 1 year.
Total amount = Principal + Interest
= $4500 + $112.50
= $4612.5
While making desserts for Fun Day, Methuki used 5/6 of a scoop of brown sugar as well as 1/2 of a scoop of white sugar. How much more brown sugar did she use?
Hey there! I'm happy to help!
We want to find how much more 5/6 is than 1/2. To do this, we simply subtract 1/2 from 5/6. This will show us how much more 5/6 is.
First, we multiply 1/2 by 3/3 so that the denominator is 6.
1/2×3/3=3/6
Now, we subtract this from 5/6.
5/6-3/6=2/6
We can simplify this to 1/3.
Therefore, Methuki used 1/3 scoop more of brown sugar than white sugar while making desserts for Fun Day.
Have a wonderful day! :D
write the decimal form of 1/5 + 1/4
Answer:
[tex]\Huge \boxed{\mathrm{0.45}}[/tex]
Step-by-step explanation:
1/5 in decimal form is 0.2
1/4 in decimal form is 0.25
1/5 + 1/4
0.2 + 0.25 = 0.45
Answer:
1/5 + 1/4 = 9/20.
9/20 = 0.45
Joey participated in a standardized reading test. He scored in the middle of the third stanine in a normal distribution. All of the following are incorrect except:_________. a. His score was the median for the group that participated in the test.b. His t-score is 40.c. His score fell at +2 standard deviationd. His score fell at a z-score of -3.
Answer:
b. His t-score is 40.
Step-by-step explanation:
The middle of the third stanine in a normal distribution means that the standard of nine that is applied has the middle of the third count.
It means that if we divide the normal distribution with the standard of nine we will find the score to be the middle of the third division.
So it will be (1/3*9=3) more than 3.
Which in normal distribution will be more than 30.
The t distribution is approximately normal when the number of degrees of freedom is greater than 30 .
So the best answer is that His t-score is 40 ( choice b).
4. Each small square in the graph paper represents 1 square unit. Find the area of each
figure. Explain your reasoning.
A
B
Answer: A = 6.5
B = 10.
Step-by-step explanation:
First, remember that when we have a triangle of height H and base B, the area of the triangle is:
Area = B*H/2.
A:
First, count the complete squares:
We have 6 complete squares.
Now the diagonal part:
The diagonal connects a section of 1 by 3 squares, and the shaded area is a right triangle
Then the shaded area will be half of 1 by 3.
this is 1.5 squares.
The total area of A is:
6 + 1.5 = 7.5 squares.
B:
This is more complicated.
At the beginning, we have 4 completed squares in the top right.
At the left, we have a 2 by 4 = 8 square region, where the shaded part is only a triangle rectangle.
Then the area of this triangle is half of 8 squares:
8/2 = 4 squares.
Last, at the bottom, we have two times a 2 by 1 = 2 square region, where the shaded part is a triangle rectangle.
Then the area of each triangle is 2/2 = 1 square.
And we have two of them, so there are 2 squares here.
Then the total area is:
A = 4 + 4 + 1 + 1 = 10 squares.
Each small square In the graph paper represents 1 square unit
Solve for xxx. Your answer must be simplified. \dfrac x{-6}\geq-20 −6 x ≥−20
Answer:
x ≤ - 27
Step-by-step explanation:
[tex]\frac{x}{-9}\ge \:3\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\frac{x\left(-1\right)}{-9}\le \:3\left(-1\right)\\\\Simplify\\\\\frac{x}{9}\le \:-3\\\\\mathrm{Multiply\:both\:sides\:by\:}9\\\\\frac{9x}{9}\le \:9\left(-3\right)\\\\\mathrm{Simplify}\\\\x\le \:-27[/tex]
The solution of the given inequality is x ≤ -27.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given inequality ( x / -9) ≥ 3 is solved as:-
( x / -9 ) ≥ 3
Multiply both sides by ( -1 ).
-1 ( x / -9 ) ≥ -3
x / 9 ≤ -3
x ≤ -27
Hence, the solution is x ≤ -27.
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You are playing monopoly with your friends. You just landed on a site
where your friend owns four houses. The rent for each house is 20 coins.
You have 50 coins. How many coins will you have after paying the total
rent?
Answer:
You wont have any coins left. You will have a negative number of coins because 20 x 4 = 80. 80 - 50 = 30. You will need to owe 30 coins
A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get 7/12. What is the number?
Answer:A rational number is such that when you multiply it by 5/2 and add 2/3 to the product you get -7/12 . What is the number.
Step-by-step explanation:Let p/q (q ≠ 0) denote the rational number. Multiplying it by 5/2 gives (p/q)(5/2). Add 2/3 to the product and we get (p/q)(5/2) + 2/3 . The result is given to be -7/12.
∴ (p/q)(5/2) + 2/3 = -7/12 …………………………..……………………………………..(1)
Transposing 2/3 to right-hand-side and changing the sign to negative,
(p/q)(5/2) = -2/3 -7/12 = -(2/3 + 7/12) =- (2 x 4 + 7)/12 (Taking L.C.M.)
Or, (p/q)(5/2) = -(8+7)/12 = - 15/12
Multiplying both sides by 2/5,
(p/q)(5/2) x (2/5) = -15/12 . 2/5 = -(3x5)/(3x4) . 2/5 =- 5/4 .2/5
Since 2/5 is the multiplicative inverse of 5/2, 5/2 x 2/5 = 1 and we obtain
(p/q).1 = -1/4 . 2/1 = -1/2
⇒ p/q = -1/2 which is a negative rational number in which p = 1 and q = 2 ≠ 0 .
∴ the rational number = -1/2
Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$.
Complete the squares to get
[tex]x^2+y^2=2x-6y+6[/tex]
[tex]\implies(x^2-2x+1)+(y^2+6y+9)=16[/tex]
[tex]\implies(x-1)^2+(y+3)^2=4^2[/tex]
which is the equation of a circle centered at (1, -3) with radius 4, and thus with area 16π.
The area of the region enclosed in the graph x²+y² =2x-6y+6 is 50.26 square units.
What is the area of the circle?The area of the circle can be calculated by the product of π times square of the radius or the product of π/4 times square of diameter.
Area of the circle= A= πr²= πd²/4
where r is radius of the circle and d is diameter of the circle.
Here given that
the equation of circle is given by
x²+y² =2x-6y+6
⇒ x²+y² -2x-6y = 6
⇒ x²-2x+y²-6y = 6
Adding 1 on both sides
⇒ x²-2x+1+y²-6y = 6+1
Adding 9 on both sides
⇒ x²-2x+1+ y²-6y+9 = 6+1+9
⇒x²-2x+1+ y²-6y+9 = 16
⇒ (x-1)² + (y-3)²= 4²
which is similar to equation of the circle
(x-a)² + (y-b)²= r²
This is the equation of the circle in center and radius form where (a,b) is the center of the circle and r is the radius of the circle.
here in the equation of the circle the center of the circle is (1,3)
radius is 4 units.
then the area of the circle is = πr²= π4²= 16π= 50.26 square units.
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Two trains leave stations 468 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet?
Answer:
2.6 hours
2 hours 36 minutes.
Step-by-step explanation:
Let the time be x hours
we know
distance = speed*time
speed of one train = 85 miles/hour
time = x hours
distance traveled by one train = 85*x = 85x miles
speed of one train = 95 miles/hour
time = x hours
distance traveled by other train = 95*x = 95x miles
__________________________________________________
Given that
Two trains leave stations 468 miles apart at the same time and travel toward each other
Thus, together cover 468 miles.
distance traveled by one train + distance traveled by other train = 468
85x+95x = 468
=> 180x = 468
=> x = 468/180 = 2.6
Thus, it will take 2.6 hours to meet each other
we know 1 hour = 60 minutes
0.6 hour = 60*0.6 minutes = 36 minutes
Thus, we can also say that it took 2 hours 36 minutes to meet each other.
if x -1 = 2y/3,then y=
Answer:
The answer is
[tex]y = \frac{3x - 3}{2} [/tex]Step-by-step explanation:
[tex]x - 1 = \frac{2y}{3} [/tex]To solve for y cross multiply
That's
3( x - 1) = 2y
2y = 3x - 3
Divide both sides by 2 to make y stand alone
That's
[tex] \frac{2y}{2} = \frac{3x - 3}{2} [/tex]We have the final answer as
[tex]y = \frac{3x - 3}{2} [/tex]Hope this helps you
Answer:
[tex]\Large \boxed{{y = \frac{3}{2}(x-1)}}[/tex]
Step-by-step explanation:
We have to solve for the y variable.
The variable must be isolated on one side of the equation.
x - 1 = [tex]\frac{2y}{3}[/tex]
Multiply both sides of the equation by 3.
3(x - 1) = 2y
Divide both sides of the equation by 2.
[tex]\frac{3}{2}[/tex] (x - 1) = y
Can someone please help solve this? Could you also show the formula as to how it is solved?
Step-by-step explanation:
the opposite side is AC
Calculate the distance between the points N=(-2, 4) and H=(6, -1) in the coordinate plane. Give an exact answer (not a decimal approximation).
Answer:
√89
Step-by-step explanation:
The distance formula is good for this.
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = ((6 -(-2))^2 +(-1-4)^2) = √(64 +25)
d = √89
The distance between the point is √89 units.
Given fx ( ) = 2x 2 + 4 f 2 , determine ( ) f −1 and () .
Answer:
12 and 6Step-by-step explanation:
The equation is not properly formatted presumably here is the format.
Given
[tex]f(x) = 2x^2 + 4[/tex]
determine f(2) , and f(−1).
So we are expect to perform substitution operation and return an answers for values of x= 2 and x= -1
1. When x= 2 we have
[tex]f(2) = 2*2^2 + 4\\\\f(2)= 2*4+4\\\\f(2)= 8+4\\\\f(2)= 12[/tex]
2. When x= -1 we have
[tex]f(-1) = 2*-1^2 + 4\\\\ f(-1)= 2*1+4\\\\ f(-1)= 2+4\\\\ f(-1)= 6[/tex]
23h Sam will be going shopping on Dec 26. He currently has $150. He wants to buy pants for $90 and
t-shirts for $12.50 each. He expects to get at most $150 for Christmas. How many t-shirts can he expect to
purchase?
Answer:
4 t shirts.
Step-by-step explanation:
Given that money available with Sam = $150
Price for pants = $90
Price of each t shirt = $12.50
To find:
How many t shirts can he expect to purchase?
Solution:
Price for 2 pants = $180 which is more than $150.
Therefore, he can not buy more than 1 pants.
The remaining amount after buying pants = $150 - $90 = $60
This amount will be used for buying t-shirts.
Number of t-shirts that can be bought:
[tex]\dfrac{60}{12.5} \approx 4.8[/tex]
But answer in decimal points for number of t shirts is not possible and he does not have more money.
It means, he can buy at most 4 t-shirts.
please pick out of ABCDE :) please help :) Kiran records the height of each plant―those with a colored filter and those without. A. asking a question B. performing an investigation C. collecting data D. providing explanations E. communicating results
Answer:
c
Step-by-step explanation:
you have to collect the data to record the height of each plant.
Amelia rented a DVD and it was due to be returned on 26 November. She actually returned it to the shop on 12 December. The rental shop applies a fine of 9p for every day the DVD is overdue. Work out the total fine paid by Amelia, give your answer in £.
Answer:
1.53 £
Step-by-step explanation:
9×17 = 153p
we know this because there are 5 days left in November and 12 days in December (hence the 17).
Answer:
The correct answer would be No fine is paid if the DVD is returned by the due date, because the first 0 means it is 0 days overdue, so it is returned on time, and the second 0 means the fine would be $0
Step-by-step explanation:
Is x(x-6)=20 a quadratic equation
We can distribute the outer x to each term inside
x(x-6) = x^2-6x
So the original equation turns into
x^2-6x = 20
Then you could subtract 20 from both sides to get everything to the same side
x^2-6x-20 = 20-20
x^2-6x-20 = 0
This quadratic equation is in the form ax^2+bx+c = 0 with a = 1, b = -6, c = -20.
The presence of the x^2 term, and having it be the largest exponent, is what makes this a quadratic.
please help with the question asked
Answer:
C, None of the above
Step-by-step explanation:
Step 1: Expand the brackets
-7 - 3(-4e-3)
-7 + 12e + 9
Step 2: Collect like terms
12e + 2
Because the answer is not a or b the answer is 'None of the Above'
Hey there! I'm happy to help!
Let's use the distributive property to undo the parentheses. We multiply the number next to the parentheses by each number inside of the parentheses.
-7+3(-4e-3)
-7-12e-9
We combine like terms.
-16-12e
This means that Answer B is incorrect. Answer A could still be correct though as it could have equal value to -16-12e.
-4(3e+4)
We use distributive property.
-12e-16
We see that these have the same value, so the correct answer is A.
Have a wonderful day! :D
If g(x) = -3x^2 +4x+5 find g(3)
Answer:
-10
Step-by-step explanation:
g(x) = -3x^2 +4x+5
Let x = 3
g(3) = -3*(3)^2 +4*3+5
= -3*9 +12+5
= -27+12+5
= -10
Answer:
g(3) = -10
Step-by-step explanation:
g(x) = -3x^2 + 4x + 5
g(3) = -3(3^2) + 4(3) + 5
g(3) = -3(9) + 12 + 5
g(3) = -27 + 12 + 5
g(3) = -15 + 5
g(3) = -10
Write (x - 3) (x + 2)^2 in standard form. Answer choices in picture attached.
Greetings from Brasil...
Let us solve by parts. Power first
(X + 2)² = X² + 2.2.X + 2² = X² + 4X + 4
Rewriting
(X - 3).(X² + 4X + 4) applying distributive property
X³ + 4X² + 4X - 3X² - 12X - 12
X² + X² - 8X - 12can someone please understand how to add and subtract negative numbers? such as 2 - (-3)= or -7 + 4=
Answer:
2-(-3)=2+3=5
-7+4=-3
Step-by-step explanation:
Answer:
2 - (-3) is 5 because (-) × (-) is (+)
And for -7 + 4 is 3 because (-) × (+) is (-).
An arithmetic progression has the 3rd term of 13 and the last term of 148. If the common difference is 5, find the number of terms of the progression.
Answer:
30 terms
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here d = 5 and a₃ = 13, thus
a₁ + 2d = 13
a₁ + 2(5) = 13
a₁ + 10 = 13 ( subtract 10 from both sides )
a₁ = 3
Thus
[tex]a_{n}[/tex] = 3 + 5(n - 1) = 148 ( subtract 3 from both sides )
5(n - 1) = 145 ( divide both sides by 5 )
n - 1 = 29 ( add 1 to both sides )
n = 30
The progression has 30 terms
Graph -7x+5y=35. khan acadmy forms of linear equations question. pls show work (10 points)
Answer:
Below
Step-by-step explanation:
● -7x + 5y = 35
Add 7x to both sides
● -7x +7x + 5y = 35+7x
● 5y = 7x + 35
Divide both sides by 5
● 5y/5 = (7x+35)/5
● y = 1.4x + 7
The graph of the function:
Answer:
Step-by-step explanation:
-7x+5y=35
write the equation in the form : y=mx+b
5y=35+7x ( divide both sides by 5)
y=7/5 x +35/5
y=7/5 x +7
if y=0 then 7/5 x+7=0 ⇒7/5 x=-7 ⇒x=-35/7 ⇒x=-5
x=0 then y=7
two points (0,7) and (-5,0)
Which of the following choices will simplify 1 - 5(3+2 x 3)?
A. -44
B. -60
C. -36
D. None of these choices are correct.
Answer:
(A.) -44Step-by-step explanation:
[tex]1-5\left(3+2\cdot \:3\right)=-44\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3+2\cdot \:3\right)\::\quad 9\\\\=1-5\cdot \:9\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:5\cdot \:9\::\quad 45\\\\=1-45\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:1-45\:\\\\:\quad -44[/tex]
Answer:
-36
Step-by-step explanation:
1-5(3+2x3)
-4(3+2x3)
-4(3+6)
-12-24
-36
Hope this helps ;) ❤❤❤
Write the rule that transforms p(x) into q(x), where q(x)=2p(x+3)−6
Answer:
The graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).
Step-by-step explanation:
It is given that p(x) and q(x) are two functions such that
[tex]q(x)=2p(x+3)-6[/tex] ...(1)
The translation is defined as
[tex]q(x)=kp(x+a)+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2) we get
k=2>1, so the graph of p(x) stretch vertically by factor 2.
a=3>0, so the graph of p(x) shifts 3 units left.
b=-6<0, so the graph of p(x) shifts 6 units down.
Therefore, the graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).