The volume of a box is the amount of space in the box
The dimensions that minimize the cost of the box is 4 in by 4 in by 4 in
How to determine the dimensions that minimize the costThe dimensions of the box are:
Width = x
Depth = y
So, the volume (V) is:
[tex]V = x^2y[/tex]
The volume is given as 64 cubic inches.
So, we have:
[tex]x^2y = 64[/tex]
Make y the subject
[tex]y = \frac{64}{x^2}[/tex]
The surface area of the box is calculated as:
[tex]A =x^2 + 4xy[/tex]
The cost is:
[tex]C = 2x^2 + 4xy[/tex] --- the base is twice as expensive as the sides
Substitute [tex]y = \frac{64}{x^2}[/tex]
[tex]C = 2x^2 + 4x * \frac{64}{x^2}[/tex]
[tex]C =2x^2 + \frac{256}{x}[/tex]
Differentiate
[tex]C' =4x - \frac{256}{x^2}[/tex]
Set to 0
[tex]4x - \frac{256}{x^2} = 0[/tex]
Multiply through by x^2
[tex]4x^3 - 256= 0[/tex]
Divide through by 4
[tex]x^3 - 64= 0[/tex]
Add 64 to both sides
[tex]x^3 = 64[/tex]
Take the cube roots of both sides
[tex]x = 4[/tex]
Recall that:
[tex]y = \frac{64}{x^2}[/tex]
So, we have:
[tex]y = \frac{64}{4^2}[/tex]
[tex]y = 4[/tex]
Hence, the dimensions that minimize the cost of the box is 4 in by 4 in by 4 in
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4
3
С
2
1
In the similarity
transformation of AABC
to ADEF, AABC was dilated by
a scale factor of [?], reflected
across the [ ], and moved
through the translation [ ].
B.
A
-7
-6
-5
-4
-2
-1 0
1
2
3
+
E
D
-2
-3
F
A. 2
B. 1/2
C. 3
D. 1/3
Answer: A
Step-by-step explanation:
Since DE=4 and AB=2, we know the scale factor of the dilation was 4/2 = 2.
Which is a better deal? Three packs of gum for 5 dollars or 9 packs of gum for 14 dollars? HOW DO YOU KNOW?
Answer:
9 for 14 is slightly less expensive, but for convenience 3 for 5 is better
Step-by-step explanation:
5/3=1.(6)
14/9=1.(5)
Answer the following
Answer:
14
sorry if i need any.
Step-by-step explanation:
9-8=1 + 13 = 14
3.
What is the value of the expression below when a = 3 and b = 5?
8a^2– 6b + 10
Answer: 52
Step-by-step explanation:
We can plug in the values for a and b.
= 8*3^2 - 6*5 + 10
= 72 - 30 + 10
= 42 + 10
= 52
Answer:
52
Step-by-step explanation:
Start by substituting the given values into the expression:
[tex]8a^2-6b+10\\8(3^2)-6(5)+10\\\text{Solve the expression}\\8(9)-30+10\\72-30+10\\42+10\\52[/tex]
Remember Order of Operations:
Parentheses
Exponents
Multiplication/Division (Whichever comes first)
Addition/Subtraction (Whichever comes first)
There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.How many kids own their own instruments?
Answer:
18 kids
Step-by-step explanation:
because you multiply 0.2 by 90 and it equals 18
Decreasing 3/4 times a number by 18 is equal to increasing 1/2 times the number by 5 give an equation and solution to the situation.
Please help me out on this problem thank you!!!!!!
Answer:
solved below.Explanation:
[tex]\sf \frac{3}{4} x-18 = \frac{1}{2} x +5[/tex]collect variables:
[tex]\sf \frac{3}{4} x - \frac{1}{2} x = + \ 5 + 18[/tex]simplify:
[tex]\sf \frac{1}{4} x = 23[/tex]final answer:
[tex]\sf x = 92[/tex]simplify 2 2/5 x 1 2/5
A. 8/25
B. 84/25
C. 2 4/25
D. 3 9/25
please hurry due in 11 min!!!
Answer:
84/25
Step-by-step explanation:
An employee works as a teacher at an online school making $38,900 per year. However, the school is hiring a principal at a salary of $59,500 per year.
The employee went back to school to become a principal.
How much more money could the employee make working as a principal instead of a teacher over 5 years?
Enter your answer in the box
Answer:
$103,000
Step-by-step explanation:
teacher : 38,900 x 5 = 194,500
principal : 59,500 x 5 = 297,500
$297,500 - $194,500 = $103,000 more
1. what is the y-intercept of this line?
2. what is the slope of this line?
3. what is the equation for this line?
Step-by-step explanation:
1. The y-intercept is the value for y when x = 0.
When x = 0, y equals 7.
Represented as:
(0, 7)
2. How to find the Slope?
Find 2 points on the graph then use the slope formula.
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
m = slope
2 points:
(0, 7)
(2, 3)
Substitute the points into the formula:
[tex] \frac{3}{2} - \frac{7}{0} = m[/tex]
Subtract:
[tex] \frac{ - 4}{2} = m[/tex]
[tex] \frac{ - 4}{2} = m[/tex]Simplify:
[tex] \frac{ - 4 \div 2}{2 \div 2} = - \frac{2}{1} [/tex]
The slope is -2.
Forming an equation:
Use the slope-intercept format.
[tex]y = mx + b[/tex]
m = slope
b = y-intercept
Substitute 7 for b, and -2 for m.
[tex]y = - 2x + 7[/tex]
Repost of the last question.. Sorry it wasn't full.
someobe please help me here
Answer:
[tex]y < -\frac{4}{5} x+4[/tex]
Step-by-step explanation:
To graph the equation, draw the line [tex]y = -\frac{4}{5} x+4[/tex] and shade in the lower left part of the graph under the line to illustrate the inequality
Then pick two points to test
Hank is painting houses this summer. He can paint 7 houses in 5 weeks. At this rate, how many houses did he paint in 18 weeks?
[tex]\begin{array}{ccll} houses&weeks\\ \cline{1-2} 7&5\\ x&18 \end{array}\implies \cfrac{7}{x}=\cfrac{5}{18}\implies 126=5x \\\\\\ \cfrac{126}{5}=x\implies 25\frac{1}{5}=x[/tex]
Write and solve a word problem that requires multiplying two mixed numbers.
Answer:
Jack ate two and a half pieces of a pie. Amy ate one and three fourth pieces of a pie. How much pie did they eat altogether?
Step-by-step explanation:
Jack ate 2 1/2 pie
Amy ate 1 3/4 pie
2 1/2 + 1 3/4 = 4 1/4
They ate four and one-fourth pieces of pie altogether.
new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.
a Find the probability that the employee is idle.
The probability that the employee is idle in the shopping mall based on the information given will be 0.33.
How to calculate probability?From the information given, it is believed that people will arrive at the desk at a rate of 20 per hour and that it takes an average of 2 minutes to answer a question.
Therefore, the probability that the employee is idle will be:
= 1 - (20/30)
= 1 - 0.67
= 0.33
Therefore, probability that the employee is idle is 0.33.
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Only 12 people can ride a trolley at one time. This is 20% of the people waiting to ride. How many people are waiting to ride?
Answer:
2 people are waiting if you want a whole number
What is the surface area?
32 cm
11 cm
15 cm
Answer:
(rectangular prism) Opposite sides are equal;
Area of bottom base:-
11 x 15 = 165
Above base, (165 x 2) = 330
Area of front:-
15 x 32 = 480
Area of back, (480 x 2) = 960
Area of left side:-
11 x 32 = 352
Area of right side, (352 x 2 ) = 704
Add the sums of all the areas;
330 + 960 + 704 = 1,994 square cm
As an apprentice to a chef you are preparing a recipe that says to bake the dish for 3/4 of a hour how many minutes should you bake the dish?
What is the missing numbers in the synthetic division problem below?
Answer:
A. 9
Explanation:
2×4=8 and 8+1=9 so that's it.
How many solutions does the nonlinear system of equations graphed below
have?
A. Two
B. Zero
C. One
D. Four
The solutions of a system of equations is also the intersection of the two lines. In this case the red parabola and the blue linear equation intersects at One point and there fore the answer is C.) One
I hope it helped, if you need more explanation just comment and I will try to explain better!
Find the probability of a couple having at least one boy when a couple has three children
Answer:
7/8
Step-by-step explanation:
assuming the probability of getting a boy and girl is 50 50,
(1/2)^3=1/8
1-1/8=7/8
The sum of two numbers is 16. One number is 2 less than the other. Find the numbers
Answer:
9+7=16
Step-by-step explanation:
Which equation has the same solution as x^2 - 6x - 14 = 0?
A (x + 3)^2 = 23
B (x - 3)^2 = 23
C(x + 3)^2 = 5
D (x-3)^2 = 5
Answer: B
Step-by-step explanation:
[tex]x^{2}-6x-14=(x-3)^{2}-14-9=(x-3)^{2}-23[/tex]
What is the exact volume of the cone
Answer:
V = [tex]\frac{400}{3}[/tex][tex]\pi[/tex]
Step-by-step explanation:
Volume of a cone is:
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
Substitute values given:
[tex]V = \pi (5^{2} )(\frac{16}{3})[/tex]
[tex]V = \pi (25)(\frac{16}{3} )[/tex]
V = [tex]\pi \frac{400}{3}[/tex]
V = [tex]\frac{400}{3}[/tex][tex]\pi[/tex]
Tony needs to buy hotdogs and hotdog buns for his cookout
Answer:
then what happened next so I can answer your questions
Answer:
Do you have any more information on this question so we can answer it for you?
Solve the follow inequality. ∣3x−4∣≥8
Hello.
Let's solve the absolute value inequality.
In order to do that, let's imagine that |3x-4| is positive.
Since the absolute value of |3x-4| is 3x-4, we write 3x-4 and solve:
[tex]\mathrm{3x-4\geq 8}[/tex]
Now, move -4 to the right, using the opposite operation:
[tex]\mathrm{3x\geq 8+4}[/tex]
Add:
[tex]\mathrm{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\mathrm{x\geq 4}[/tex]
However, this is only 1 solution.
Let's imagine that |3x-4| is a negative number.
So, the inequality looks like so:
[tex]\mathrm{-3x+4\geq 8}[/tex]
Move 4 to the right:
[tex]\mathrm{-3x\geq 8-4}[/tex]
[tex]\mathrm{-3x\geq 4}[/tex]
Divide both sides by -3:
[tex]\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
Therefore, the solutions are
[tex]\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
[tex]\bigstar[/tex] Note:
If we divide both sides of an inequality by a negative number, we flip the inequality sign.
I hope this helps you.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Ms. Ashley planned to stay at a hotel that charges $88 per night for a room and $20 per night in fees and taxes. She used this expression to calculate the total cost of staying in the hotel for n nights. 88n 20n
Step-by-step explanation:
Since 88 is for one night and 20 per night in fees and taxes.
Step 1 : Calculate for $88
[tex] \frac{88n}{88} \\ [/tex]make N the subject of formula
[tex]n = \frac{88}{88} \\ [/tex]
N= 1
Step 2: Calculate for $20
[tex] \frac{20n}{20} \\ [/tex]
make N the subject of formula
[tex]n = \frac{20}{20} [/tex]
N = 1
3x - 2 + x + 8 = -(9x + 7
=
- 2(9x + 7 - x + 5)
1 (8x + 12)
4x + 6 =
2
4x + 6 = 4x + 6
4x + 6 = 4x - 6 = 4x + 6 - 4x - 6
0=0
Is this correct?
Answer:
no
Step-by-step explanation:
3x−2+x+8=−9x−7
4x+6=−9x−7
4x+6+9x=−7
13x+6=−7
13x=−13
x=−1
Finding Circumference The radius is cm. v cm OZ The circumference in terms of ais Using 3.14 for A, the approximate circumference of the circle is cm. d=2cm
Answer:7picm Circumference = pi x d Diameter = 7 C = pi x 7 C = 7pi cm.
Step-by-step explanation:
The circumference of the circle with diameter 2 cm is 6.28 cm.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given that a circle has a diameter of 2 cm we need to find its circumference,
The circumference of a circle is given by, π × diameter
Therefore, the circumference of the circle with diameter 2 cm =
= π × diameter
= π × 2
= 3.14 × 2
= 6.28 cm
Hence, the circumference of the circle with diameter 2 cm is 6.28 cm
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what is the Estimate 26% of 84.
Answer: 26% of 84 is 21.84
Step-by-step explanation:
0.26 * 84 = 21.84
Answer:
26%
of
84
=
21
Step-by-step explanation:
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Madison is buying a laptop for $586. He paid for the laptop
using four $100 bills, fifteen $10 bills and forty-six $1 bills. How
much did Madison pay?
Pls help me and thanks rounding
Answer:
Step-by-step explanation:
1399 rounds to 1400 so A is not the answer
1449 rounds to 1400 so B is not the answer
1589 rounds to 1600 so D is not the answer
The hundreds place is second from the left. Third from the left determines what happens to second from the left. 5 and over round up. Less than 5 just use the first 2 digits left and 2 zeros.
The answer is C
1457 rounds to 1500
1547 rounds to 1500
