Answer:
The cost function of manufacturing this box is:
[tex]C_{T} = 2.15\cdot x^{2}+30\cdot x[/tex], where [tex]x[/tex] is the length of the box, measured in US dollars.
Step-by-step explanation:
From the statement we know that:
1) The box has a square base ([tex]w = l = x[/tex]).
2) The box has a depth of 10 inches ([tex]h = 10\,in[/tex]).
3) The cost of manufacturing the top of the box is $ 1.20 per square inch.
4) The cost of manufacturing the bottom of the box is $ 0.95 per square inch.
5) The cost of manufacturing each side of the box is $ 0.75 per square inch.
The total cost of manufacturing the box is:
[tex]C_{T} =C_{bottom} + C_{top} + 4\cdot C_{side}[/tex]
Where:
[tex]C_{bottom}[/tex] - Cost of the bottom of the box, measured in US dollars.
[tex]C_{top}[/tex] - Cost of the top of the box, measured in US dollars.
[tex]C_{side}[/tex] - Cost of the side of the box, measured in US dollars.
Dimensionally, cost equals unit cost, measured in US dollars by square inch, multiplied by surface area, measured in square inches. Now, the expression is expanded:
[tex]C_{T} = c_{bottom}\cdot x^{2}+c_{top}\cdot x^{2}+4\cdot c_{side}\cdot h\cdot x[/tex]
[tex]C_{T} =(c_{bottom}+c_{top})\cdot x^{2}+4\cdot c_{side}\cdot h \cdot x[/tex]
If we know that [tex]c_{bottom} = \$\,0.95\,in^{-2}[/tex], [tex]c_{top} = \$\,1.20\,in^{-2}[/tex], [tex]c_{side} = \$\,0.75\,in^{-2}[/tex] and [tex]h = 10\,in[/tex], the cost function of manufacturing this box is:
[tex]C_{T} = 2.15\cdot x^{2}+30\cdot x[/tex], where [tex]x[/tex] is the length of the box, measured in US dollars.
Look at the incomplete multiplication problem below. 632x28
5600
+[?]
What value is missing?
A)11,376
B)12,540
C)12.640
D)18,328
how do you write five and nine tenths in standard form?
Answer:
5.9
Step-by-step explanation:
Answer:
5 9/10
Step-by-step explanation:
this is how you would write it in standard form
The door was 6ft 7 inches high. How many inches is that?
What the answer
Answer:
79 inches is how tall the door is
Step-by-step explanation:
Someone help me on thissss
Lina rolled a die.
What is the probability that she got 3?
Answer:
1/6
Step-by-step explanation:
So asuming that she didn't roll a biased die the probability of getting a three is 1/6
This is because the total outcomes are 6 and there is only one three thus the probability that she got 3 is 1/6.
HOPE THIS HELPED
Barbara's Catering Company makes the best fruit salad despite using only four ingredients. They use four apples for every mango, two pears for every apples, and one pineapple for every mango. If they use 8 pineapple in their most recent batch, how many recent batch l, how many total pieces of fruit did they use?
Answer:
2
Step-by-step explanation:
Find all values of k such that the graph of the inequality (x-2)(x-5)(x-k) >= 0 consists of a single interval on the number line.
(x - 2)(x - 5)(x - k) >= 0
Let's set each term equal to 0
x - 2= 0
Add 2 to both sides
x = 2.
x - 5 = 0
Add 5 to both sides
x = 5
x - k = 0
Add k to both sides
x = k
Since x = 2 and 5, k = 2, 5
Let's plug our numbers into the inequality.
(2 - 2)(2 - 5)(2 - 2) >= 0
(0)(-3)(0) >= 0
0>=0
(5 - 2)(5 - 5)(5 - 5) >= 0
(3)(0)(0) >= 0
0 >= 0
This proves that 2 and 5 are equal to k
For Jack's lemonade recipe, 12 lemons are required to make 18 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?
Which is the length of a student's textbook?
-30 millimeters
-30 centimeters
-30 decimeters
-30 hecometers
20.
19. passes through (-2, 19), parallel to the x-axis
Answer:
yah
Step-by-step explanation:
x + 4 = 13 simple equations
Answer:
9
Step-by-step explanation:
13-4=9
9+4=13
Hey there!☺
[tex]Answer:\boxed{x=9}[/tex]
[tex]Explanation:[/tex]
[tex]x+4=13[/tex]
To find x, subtract 13 by 4.
[tex]13-4=9[/tex]
Let's try substituting 9 for x to see if we get 13.
[tex]x+4=13\\9+4=13[/tex]
[tex]x=9[/tex]
Hope this helps!
Simplify the radical /1829.
Answer:
Step-by-step explanation:
Let's find
1/2+3/7
First write the addition with a common denominator.
Then add.
1/2+3/7=
Answer:
7/14+6/14=13/14
Step-by-step explanation:
find the common denominator(14)
change both fractions
1/2*7/7(2*7=14)=7/14
3/7*2/2(7*2=14)6/14
then add.
What is 6x^3 - z ?
x= -8
and
z= 9
FYI the 3 is an exponent on 6x
Answer:
-110601
Step-by-step explanation:
All you have to do is replace the variables with their value. So the equation would look like this,
6(-8)³ - 9
Always solve the parenthesis first ending up with
-48³ - 9
Now the exponents,
-110592 -9
Here we just subtracting getting the answer of...
-110601
Hope that helps and have a great day!
There are 7 fewer cups than plates. There are 4 cups. How many plates are there?
Answer:
-3 plates
Step-by-step explanation:
Subtract 7 - 4 = 3. Since there are 7 FEWER plates then you add a negative sign in front of it.
if there are 91 seats in 7 rows how many seats are in 4 rows
Answer:
It would be 52
Step-by-step explanation:
You divide 91 by 7 and u get 13 so u multiply that by 4 and u get your answer
Use the slope formula to find the missing coordinate.
m= 3, P(3, 2) and Q(8,_)
O-1
1
05
Let the missing value = x
Slope is the change in y over the change in x:
3 = (x-2)/ (8-3)
3 = (x-2) / 5
Multiply both sides by 5:
15 = x-2
Add 2 to both sides:
X = 17
The missing coordinate is 17
please help i have been doing homework for ages
Answer:
Give the full question
ruger has a dartboard with an area of 1600 cm^2. The dartborad has a circular bullseye centered at (0 cm, 0 cm). The point ( square root 3cm, square root 7cm) is on the circumference of the bullseye.
A percentage is given by dividing a given value by a total and multiplying the result by 100
The percentage of the dartboard occupied by the bullseye is approximately 1.963 %
Reason:
The given parameters are;
The area of the dartboard, A = 1,600 cm²
The location of the center of the bullseye = (0 cm, 0 cm)
The coordinates of a point on the circumference = (√3 cm, √7 cm)
Question: Possible question with regards to the given parameter; The percentage of the dartboard covered by the bullseye
Solution;
The radius of the bullseye, r = [tex]\sqrt{(\sqrt{3})^2 + (\sqrt{9})^2} = \sqrt{10}[/tex]
The area of the bullseye, [tex]A_b[/tex] = π· r² = π × [tex](\sqrt{10})^2[/tex] = 10·π
∴ The area of the bullseye, [tex]A_b[/tex] = 10·π cm²
The percentage area is given as follows;
[tex]Percentage \ area = \dfrac{A_b}{A} \times 100[/tex]
Therefore;
[tex]Percentage \ area \ occupies \ by \ bulleseye = \dfrac{10 \cdot \pi}{1,600} \times 100 \approx 1.963 \%[/tex]
The percentage of the dartboard occupied by the bullseye ≈ 1.963 %
Learn more about percentage area here:
https://brainly.com/question/11642822
Answer:
2%
Step-by-step explanation:
Should be Choice B
Which equation represents the data shown in the table below? x y 2 9 3 12 4 15 5 18 A. y = 2x + 9 B. y = 3x + 3 C. y = 3x + 12 D. y = 4x + 1
Answer:
Step-by-step explanation:
The answer is B. Because 3 multiplied by x and add it by 3 equates to y. example: (x=2) 3x2+3= y. y=9 .
The data best fit the line y = 3x+3, the correct option is B.
What is an Equation?The equation is a statement that equates two algebraic expressions with an equal sign.
The data is given
x y
2 9
3 12
4 15
5 18
The equation that represents the data can be found by substituting the data and checking if they satisfy the equation.
The first equation is
y = 2x +9
Substitute ( 2,9)
9 = 2 *2 +9
9 ≠ 13
The second equation is
y = 3x +3
Substitute ( 2,9)
y = 3 *2 +3
9 = 9
Substitute ( 3,12)
12 = 3 *3 +3
12 = 12
Therefore, the data best fit the line y = 3x+3, the correct option is B.
To know more about Equation
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Help I’m stupid and don’t know how to do this
Answer:
y = x/w
Step-by-step explanation:
1) We have to isolate y
2) An easy way to do this is to switch the places of y and w since we are just solving for y
3) Therefore, the answer is y = x/w
Hope this helps!
Solve the following equation for the unknown quantity: 12x-8=3x+10. a. x=4 b. =2 c =12 d. x=1/2
Answer:
b. x=2
Step-by-step explanation:
Step 1- Move the variable to one side.
12x-8= 3x+10
-3x -3x
9x-8= 10
Step 2- Add 8 to both sides.
9x-8= 10
+8 +8
9x= 18
Step 3- Divide to both sides.
9x= 18
9 9
x= 2
How to be good at ratios
Answer:to be good at ratios you must simply look at the numbers and count them in the order that the question asks for
Step-by-step explanation:example 4:2 :::: ;; there are 4 : and 2 ;
How is adding and subtracting decimals similar to and different from adding and subtracting whole numbers?
Answer:
it is the answer here copy and paste
Step-by-step explanation:
adding and subtracting decimals are different from adding and subtracting whole number because of the values are not going to be the same any more.
extra; example 40.04 has hundredths and 4004 has hundreds.
Answer:
The answer is:
In both types of problems you rewrite the problem vertically, line up the decimals, and add zeros or rename where needed.
Step-by-step explanation:
Edge 2021
Please help me
I need to submit it now!!
Answer:
Alicia is correct because....
Step-by-step explanation:
12 - 4 = 8 + 3 = 11
What is the sum of the first 10 even multiples of 8?
A map is made of a park. The scale from the park to the map is 36 mi to 6 cm. The length of great oaks trail is 4.5 cm on this map. The scale from the same park to a different map is 24 mi to 3 cm. The length of salamander trail is 3.5 cm on that map. Which is the longer trail, great oaks trail or salamander trail?
Answer:
Salamander trail is longer than great oaks trail.
Step-by-step explanation:
We have the data from two different maps of the same park.
In the first map the length of great oaks trail is 4.5 cm
The scale from the park to the map is 36 mi to 6 cm ⇒
We can find the real length of great oaks trail writing the following equivalence :
[tex]\frac{36mi}{6cm}=\frac{x}{4.5cm}[/tex]
Where x is the real length of great oaks trail ⇒
[tex]x=\frac{(36mi).(4.5cm)}{6cm}=27mi[/tex]
We find that the real length of great oaks trail is 27 mi
In the second map the length of salamander trail is 3.5 cm
The scale from the park in the second map is 24 mi to 3 cm.
Again we can find the real length of salamander trail writing the equivalence :
[tex]\frac{24mi}{3cm}=\frac{y}{3.5cm}[/tex]
Where y is the real length of salamander trail ⇒
[tex]y=\frac{(24mi).(3.5cm)}{3cm}=28mi[/tex]
We find that the real length of salamander trail is 28 mi.
Therefore salamander trail is longer than great oaks trail.
which expression is the simplest form of 5(x-3)-3(2x+4)/9?
Answer:
-x - 27/ 9 this is it djdjdj
The simplest form of the expression [tex]\frac{5(x-3)-3(2x+4)}{9}[/tex] is [tex]\frac{-x-27}{9}[/tex] .
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given the expression
[tex]\frac{5(x-3)-3(2x+4)}{9}[/tex]
⇒ (5x - 15 - 6x - 12) ÷ 9
⇒ (-x - 27)/9
⇒ [tex]\frac{-x-27}{9}[/tex]
Hence "The simplest form of the expression [tex]\frac{5(x-3)-3(2x+4)}{9}[/tex] is [tex]\frac{-x-27}{9}[/tex] .
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Solve this equation and show your work! (1 point for the correct answer and 1 point for showing how to solve the equation) x³ = -2,197
Here we are given with a equation:
[tex] {x}^{3} = - 2197[/tex]
And we have to solve it with appropriate steps.
So, let's start solving.
Add 2197 to both sides of the equation,
[tex] {x}^{3} + 2197 = - 2197 + 2197[/tex]
[tex] {x}^{ 3} + 2197 = 0[/tex]
Now, using the identity:
a³ + b³ = (a + b)(a² - ab + b²)Let's proceed further.
x³ is the cube of x and 2197 is the cube of 13
[tex](x) {}^{3} + (13) {}^{3} = 0[/tex]
[tex](x + 13)( {x}^{2} - x \times 13 + {13}^{2} ) = 0[/tex]
[tex](x + 13)( {x}^{2} - 13x + 13) = 0[/tex]
Now,
x + 13 = 0x² - 13x + 13 = 0So, x = -13
And, for the second let's use the discriminate formula,
➝ D = b² - 4ac
➝ D = (-13)² - 4(1)(13)
➝ D = 169 - 52
➝ D = 117
Now, using the D. formula,
[tex]x = \dfrac{ - b \pm \sqrt{ D} }{2a} [/tex]
[tex]x = \dfrac{13 \pm \sqrt{117} }{2} [/tex]
[tex]x = \dfrac{13 \pm 3 \sqrt{13} }{2} [/tex]
So the roots of the equation are:
[tex]{ \boxed{ \bf{x = - 1 ,\: \frac{13 + 3 \sqrt{13} }{2} and \: \frac{13 - 3 \sqrt{13} }{2} }}}[/tex]
And we are done !!
#CarryOnLearning
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Mateo scored in the 55th percentile of his class on the latest math exam. What does this mean in relation to the data set, and what did he score on the exam?
Answer:
d. Mateo scored as well as or better than 55% of his classmates, with a score of 82.Step-by-step explanation:
Mateo scored in the 55th percentile of his class on the latest math exam. What does this mean in relation to the data set and what did he score on the exam?{35, 42, 55, 68, 69, 72, 72, 77, 78, 78, 82, 85, 87, 88, 90, 93, 94, 96, 96, 99)
a. Mateo scored a 55% on his exam. b. Mateo scored as well as or better than 55% of his classmates, with a score of 78. c. Mateo scored worse than 55% of his classmates, with a score of 78. d. Mateo scored as well as or better than 55% of his classmates, with a score of 82. e. Mateo scored worse than 55% of his classmates, with a score of 82. SolutionThere are scores of 20 students. Each score is equivalent of 100%/20 = 5%
The easy way to understand Mateo' s place is to compare scores against 5% slots.
See attached.
We can also get the average score
Sum
∑ {35, 42, 55, 68, 69, 72, 72, 77, 78, 78, 82, 85, 87, 88, 90, 93, 94, 96, 96, 99) = 1556Average or mean score:
1556/20 = 77.8This is matching the 50% score.
As we see Mateo scored 82 which is matching 55%.
Correct option is d.