To minimize production cost, we need to find the dimensions of the package that will satisfy the volume equation and minimize the cost equation. Taking the partial derivatives of the cost equation with respect to the variables 'r' and 'h', and setting them equal to zero, we can find the critical points. Solving these equations, we find that the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
Explanation:To find the dimensions of the package that will minimize production cost, we need to consider the cost of the sides and bottom made of styrofoam and the cost of the top made of glued paper. Let's denote the radius of the base of the cylinder as 'r' and the height of the cylinder as 'h'.
The volume of a cylinder is given by the formula V = πr²h. We know that the volume of the package needs to be 350 cubic centimeters, so we can write the equation as πr²h = 350.
The cost of the sides and bottom of the container is given by the formula C1 = 0.03 * (2πrh + πr²), and the cost of the top is given by the formula C2 = 0.08 * πr².
To minimize the cost, we need to find the values of 'r' and 'h' that satisfy the volume equation and minimize the cost equation.
Since this is a calculus problem, we will differentiate the cost equation with respect to 'r' and 'h', and set the derivatives equal to zero to find the critical points.
Taking the partial derivatives of C1 and C2 with respect to 'r' and 'h', we get:
∂C1/∂r = 0.03 * (2πh + 2πr) = 0∂C1/∂h = 0.03 * (2πr) = 0∂C2/∂r = 0.08 * (2πr) = 0∂C2/∂h = 0Solving these equations, we find that h = 7 cm and r = 2.5 cm. Therefore, the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
A pair of standard dice is rolled find the probability that the sum of the two dice is greater than 12
Answer:
Probability that the sum of the two dice is greater than 12 is ZERO.
Step-by-step explanation:
Here, when two dices are rolled together, the sample space is given as:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4),(6,5), (6,6) = Total 36 outcomes
Now, E : Event of getting a sum greater than 12.
So here, number of possible outcomes = 0
So, the probability that the sum of the two dice is greater than 12 = 0/36 = 0
So, it is an IMPOSSIBLE EVENT.
It is impossible to roll a sum greater than 12 with two standard six-sided dice, as the maximum sum possible is 12. Therefore, the probability of rolling a sum greater than 12 is zero.
Explanation:The student asked about the probability that the sum of two standard six-sided dice is greater than 12. Since the highest sum one can achieve with two six-sided dice is 12 (when both dice show a 6), it is impossible to roll a sum greater than 12. Therefore, the probability of this event is zero.
When considering every outcome of rolling a die, we must include all possible individual results, which range from 1 to 6 for each die. The sum of two dice ranges from a minimum of 2 (both dice showing 1) to a maximum of 12 (both dice showing 6). Consequently, there are no combinations of dice that can result in a sum that exceeds 12.
The highest sum achievable on two six-sided dice is 6 + 6 which equals 12. This makes sums greater than 12 unattainable, and highlights the importance of considering the specified number of sides on dice when calculating probabilities related to their sums.
Please help having trouble!
Answer:
Option C is the correct choice that is [tex]y<-\frac{5}{2}x-2[/tex]
Step-by-step explanation:
As this is a multiple choice question we will reduce the options and work on it with the given points [tex](0,-2),(-2,-3)[/tex]
Note:We know that [tex]\leq ,\geq[/tex] where there is [tex]=[/tex] sign associated with it have a straight line graph there is no breaking in the line.
And when there is simply [tex]<,>[/tex] we have a dashed line when we plot it on a graph.
So option B and D are discarded.
Now one-by one we will put the values [tex](x,y)\ (-2,3)[/tex] to know which equation it satisfies.
If we put [tex]y=3[/tex] then [tex]x=-2[/tex].
So working with option A.
[tex]y<-\frac{2}{5}x-2[/tex]
Plugging the values.
[tex]3<-\frac{2}{5}x-2\ ,3<\frac{-2x-10}{5}\ ,15<-2x-10\ ,15+10< -2x\ ,x=\frac{25}{-2}=-12.5[/tex]
And we know that [tex]x[/tex] must be equal to [tex]-2[/tex] so this is not the right answer.
We are left with only one choice that is C .
So option C is the correct option of the above inequality.
What is 6% of 24.77?
Answer: 1.4862
Step-by-step explanation: To find 6% of 24.77, first write 6% as a decimal by moving the decimal point two places to the left to get 0.06.
Next, the word "of" means multiply so we will multiply 0.06 by 24.77.
(0.06) (24.77) = 1.4682
Therefore, 6% of 24,77 is 1.4862.
Deon split 4/5 pounds of candy among 5 people.
What is the unit rate in pounds per person?
Write your Anwser in simplest form.
Answer:
4/25 pounds of candy per person.
Step-by-step explanation:
(4/5)/5=(4/5)(1/5)=4/25
To find the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). Therefore, each person received 4/25 pound of candy.
Explanation:The unit rate is found by dividing the total quantity by the total number of units. In this problem, Deon divided 4/5 pounds of candy among 5 people.
To find the amount of candy per person which is the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). So, 4/5 divided by 5 equals 4/25. Thus, each person received 4/25 pound of candy.
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Sandwiches
Veggiburger....... .........03.25
Roast BeetWrap............ $4.50
Ham and Cheese..............$3.75
Side Orders
Steak Fries.....
..$1.50
Salad........
...$2.50
Soup.
$2.25
Beverages
Cola
Ice Tea.
Coffee......
Water...
..$1.50
..$1.75
...$0.90
$1.00
If you and a friend order 2 veggiburgers, one salad, one fries and 2 coffees, what is the total bill
with 4% tax and 15% tip?
$13.70
0
$16.43
$15.67
•
$14.64
Thing
The total bill is $14.64 ⇒ last answer
Step-by-step explanation:
The given is;
Sandwiches
Veggieburger................$3.25Roast Beet Wrap.............$4.50Ham and Cheese....... ....$3.75Side Orders
Steak Fries.......$1.50Salad..................$2.50Soup...................$2.25Beverages
Cola...................$1.50Ice Tea..............$1.75Coffee...............$0.90Water.................$1.00∵ You order 2 veggieburgers, one salad, one fries and 2 coffees
∵ The price of the 1 veggieburgers = $3.25
∵ The price of the 1 salad = $2.5
∵ The price of the 1 fries = $1.5
∵ The price of the 1 of one coffee = $0.9
∴ The cost of the order = 2(3.25) + 1(2.5) + 1(1.5) + 2(0.9)
∴ The cost of the order = 6.5 + 2.5 + 1.5 + 1.8 = $12.3
∵ There is a tax 4%
∴ The tax = 4% × 12.3 = [tex]\frac{4}{100}[/tex] × 12.3 = $0.492
∵ There is a tip 15%
∴ The tip = 15% × 12.3 = [tex]\frac{15}{100}[/tex] × 12.3 = $1.845
To find the total bill add the cost of the order, the tax and the tip
∵ The total bill = cost of the order + tax + bill
∴ The total bill = 12.3 + 0.492 + 1.845
∴ The total bill = $14.637 ≅ $14.64
The total bill is $14.64
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Miami and Orlando are 205 miles apart. If a map shows them as 5 inches apart, give the scale.
Answer:
1 inch = 41 miles
Step-by-step explanation:
205 / 5 = 41
1 inch = 41 miles
Answer:
41 miles per inch
could be answered as 41/1 or 41:1
Step-by-step explanation:
Use a ratio to find the scale.
205/5
Divide the numerator and denominator by 5 to simplify.
41/1
Let x represent one number and let y represent the other number. The sum of two numbers is -11 if one number is subtracted from the other their difference is -3 use the given conditions to write of the equation and solve the system find the numbers
Answer:
look at above image for answer. thank you for the question
Using the given conditions, we formed two equations: x + y = -11 and x - y = -3. We then solved these simultaneous equations to find that the two numbers are -7 and -4.
We have been given two conditions to find the values of two numbers, represented by x and y. The first condition can be expressed as the equation x + y = -11. The second condition gives us the second equation x - y = -3.
adding the first and second equation:
(x + y) + (x - y) = -11 + (-3)
2x = -14
x = -7
We can then substitute the value of x back into one of the original equations to solve for y:
-7 + y = -11
y = -11 + 7
y = -4
Thus, the two numbers are -7 and -4.
Simplify (x − 4)(3x2 − 6x + 2). 3x3 + 6x2 − 22x + 8 3x3 − 18x2 + 26x − 8 3x3 − 18x2 − 22x − 8 3x3 + 6x2 + 22x + 8
Answer:
3x^3-18x^2+26x-8
Step-by-step explanation:
(x-4)(3x^2-6x+2)
3x^3-6x^2+2x-12x^2+24x-8
3x^3-6x^2-12x^2+2x+24x-8
3x^3-18x^2+26x-8
A survey showed that 35% of the students prefer plain white milk over chocolate milk. If the school has 1200 students. How many students prefer chocolate milk?
Answer:
The number of students who prefer chocolate milk is 780 .
Step-by-step explanation:
Given as :
The total number of students in the school = 1200
The percentage of students who prefer plain white milk = 35 %
Let the number of students who prefer chocolate milk = x
Now, ∵ The percentage of students who prefer plain white milk = 35 %
∴ The percentage of students who prefer chocolate milk = 100 % - 35 % = 65%
So , As The number of students who prefer chocolate milk = x
Or, 65 % of total number of students in school = x
So, x = [tex]\frac{65}{100}[/tex] × 1200
or, x = [tex]\frac{65\times 1200 }{100}[/tex]
∴ x = 780
So, the number of students who prefer chocolate milk = x = 780
And students who prefer plain white milk = 1200 - x = 1200 - 780 = 420
Hence, The number of students who prefer chocolate milk is 780 . Answer
Find the equation of a line (5,-2) (-3, -2)
Answer:
y=-2
Step-by-step explanation:
y-y1=m(x-x1)
m=slope & (x1, y1) is a point on the line
m=(y2-y1)/(x2-x1)
m=(-2-(-2))/(-3-5)
m=(-2+2)/(-8)
m=0
y-(-2)=0(x-5)
y+2=0
y=0-2
y=-2
Answer each question and explain your reasoning. How long is 50% of 60 minutes? How long is 10% of 60 minutes? How long is 75% of 60 minutes?
Answer:
Step-by-step explanation:
50% of 60? 0.5*60=30
10% of 60? 0.1*60=6
75% of 60? 0.75*60=45
50percent of 60 minutes is 30 minutes, 10percent of 60 minutes is 6 minutes, and 75percent of 60 minutes is 45 minutes.
50percent of 60 minutes: 50percent of 60 minutes is half of 60, which equals 30 minutes.
10percent of 60 minutes: 10percent of 60 minutes is 6 minutes (10percent of 60 is 6).
75percent of 60 minutes: 75percent of 60 minutes is 45 minutes (75percent of 60 is 0.75 * 60 = 45).
M=x1+x2/2 solve for x1
After solving for x1, we get
[tex]x_1 = 2M-x_2[/tex]
Step-by-step explanation:
Given formula is:
[tex]M = \frac{x_1+x_2}{2}[/tex]
In order to solve for x1, we have to isolate x1 on one side of the equation
So,
Multiplying the whole equation by 2:
[tex]2M = \frac{x_1+x_2}{2} * 2\\2M = x_1+x_2[/tex]
Subtracting x2 from both sides
[tex]2M-x_2 = x_1+x_2-x_2\\2M-x_2 = x_1[/tex]
so,
After solving for x1, we get
[tex]x_1 = 2M-x_2[/tex]
Keywords: Formulas, Solving for a variable
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A triangle has two sides of length 40 cm and an angle of 110°.
a) Determine the length of the third side. Then find the perimeter of the triangle.
47
b) Determine the area of the triangle
Answer:
a) c = 65.532 cm
P = 145.532 cm
b) A = 751.754 cm²
Step-by-step explanation:
This is an isosceles triangle. The given angle is obtuse, so it must be the vertex angle.
a) One way to find the length of the third side is law of cosine:
c² = a² + b² − 2ab cos C
c² = 40² + 40² − 2(40)(40) cos 110°
c = 65.532
Another way is to cut the triangle in half and use sine.
sin (110°/2) = (c/2) / 40
c = 80 sin 55°
c = 65.532
The perimeter is the sum of the sides:
P = 40 + 40 + 65.532
P = 145.532
b) You can find the area using the SAS equation:
A = ½ ab sin C
A = ½ (40)(40) sin 110°
A = 800 sin 110°
A = 751.754
Another way is to split the triangle in half, find the height using cosine, then use half the base times height.
cos (110°/2) = h / 40
h = 40 cos 55°
h = 22.943
A = ½ ch
A = ½ (65.532) (22.943)
A = 751.754
A Shark Weighs 405 kilograms and 68 grams a second shark weighs 324 kilograms and 75 grams how much more does the first shark weigh in grams than the second shark
Answer:
7 grams
Step-by-step explanation:
If you're asking me grams specifically, and not kilograms, subtract 68 from 75 to get your answer. If it's only kilograms subtract 324 from 405. If it's both of them added together subtract 399 from 473, you're welcome!
Answer:
7 grams
Step-by-step explanation:
A total of 814 tickets were sold for the school play. They were either adult tickets or student tickets. There were 64 more student tickets sold than adult tickets. How many adult tickets
Answer:
STUDENT TICKETS SOLD = 439ADULT TICKETS SOLD = 375814 - 64 = 750
750 ÷ 2 = 375
375 + 64 = 439
The problem can be solved by setting up two equations based on the given information, substituting one equation into the other, and then solving for the variable. In this case, 375 adult tickets were sold.
Explanation:The subject of this problem is mathematics, particularly a class of problems known as linear equations. Let's assign variables to each type of ticket: A for the number of adult tickets and S for the number of student tickets.
According to the problem, S = A + 64 (because there were 64 more student tickets sold) and S + A = 814 (because a total of 814 tickets were sold).
With these two equations, you can substitute the value of S from the first equation into the second equation. Therefore, (A + 64) + A = 814. Simplify this to get 2A + 64 = 814.
To find the number of adult tickets, solve the simplified equation for A. Subtract 64 from both sides to get 2A = 750, and then divide by 2 to find that A = 375.
So, 375 adult tickets were sold.
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868 divided by 4 equals
Answer:
217
Step-by-step explanation:
868/4=217
Answer:
217
Step-by-step explanation:
help me with this geometry question with proofs
Answer:
m ∠ AMC = 75°
Step-by-step explanation:
Given:
In Δ ABC, m ∠C=90°
m∠ B =30°
CM is angle bisector
We need to find m ∠AMC
In Δ ABC Sum of all angle is 180° so we get,
[tex]m\angle A+m\angle B+m\angle C =180\\m\angle A+90+30 =180\\m\angle A+120 =180\\m\angle A=180-120\\m\angle A=60[/tex]
Now we know that CM is angle bisector of ∠C
∴ [tex]m\angle ACM +m\angle BCM =90\\m\angle ACM +m\angle ACM =90\\2m\angle ACM =90\\m\angle ACM =\frac{90}{2}=45[/tex]
Now in Δ ACM we know that Sum of all angles is 180
[tex]m\angle ACM + m\angle AMC + m\angle A=180\\45 + m\angle AMC + 60 =180\\105 + m\angle AMC =180\\m\angle AMC =180 -105 =75[/tex]
Hence m ∠ AMC = 75°
Sin 60 is what? Exact value please
Answer: 0.8660254038
The school principal determined that 1/4 of the original student school desks would need to be replaced this year. 50 teachers would also receive new, improved desks. A total of 295 student and teacher desks were purchased.
How many original student desks were there before the
purchase was made?
There were 980 student desks originally before the purchase was made.
Step-by-step explanation:
Total desks purchased = 295
As 50 new desks are for teachers, therefore, we will subtract this amount from total;
Desks purchased for students = 295-50 = 245
Let,
x be the number of original student desks, therefore,
[tex]\frac{1}{4}\ of\ x=245\\\frac{x}{4}=245[/tex]
Multiplying both sides by 4
[tex]4*\frac{x}{4}=245*4\\x=980[/tex]
There were 980 student desks originally before the purchase was made.
Keywords: subtraction, fractions
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value of the expression below on the horizontal span of 0 to 10. (Round your answer to two decimal places.)
x2 + 19x + 2
Answer:
The value of expression increases from [tex]2[/tex] to [tex]292[/tex] on spanning [tex]x[/tex] from [tex]0[/tex] to [tex]10[/tex].Step-by-step explanation:
The expression given here is
[tex]x^2+19x+2[/tex]
Now if we differentiate this expression we can find the portions in its graph where it is increasing and decreasing or neither both.
If the differentiated expression is less than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is decreasing.
If the differentiated expression is greater than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is increasing.
[tex]\frac{d}{dx}(x^2+19x+2)[/tex]
⇒[tex]2x+19[/tex]
For [tex]2x+19>0[/tex] ⇔[tex]x>\frac{-19}{2}[/tex]
For [tex]2x+19<0[/tex] ⇔[tex]x<\frac{-19}{2}[/tex]
Now for us the horizontal span is asked from 0 to 10 for the expression which is from [tex]x=0[/tex] to [tex]x=10[/tex] ,in which portion the value of the expression is strictly increasing so the vlaue increases from [tex]0+0+2=2[/tex] to [tex]10^2+190+2=292[/tex].
If five times a number is increased by four, the result is at least 19. Find the least possible number that satisfies these conditions
3 is the least possible number that satisfied these conditions
The solution set is: x≥3
Step-by-step explanation:
Let x be the number
Then according to given statement
If five times a number is increased by four
[tex]5x+4[/tex]
At least 19 means that the result will be equal to or greater than 19
so,
[tex]5x+4\geq 19[/tex]
subtracting 4 from both sides
[tex]5x+4-4 \geq 19-4\\5x \geq 15[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5} \geq \frac{15}{5}\\x\geq 3[/tex]
3 is the least possible number that satisfied these conditions
The solution set is: x≥3
Keywords: Inequality, Variables
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A bookcase has 3 shelves with a total of 24 books. The top shelf has 8 mystery books. The middle shelf has 10 math books. The bottom shelf has 6 science books. Two books are now taken off each shelf. What fraction of the books remaining on the three shelves are math books? Express your answer as a common fraction.
Answer:22/24 or 11/12
Step-by-step explanation:
Answer:
Six books are removed from the shelves, so $24-6=18$ books remain. Of these, $10-2=8$ are math books. Therefore, $8/18=\boxed{4/9}$ of the books remaining are math books.
Step-by-step explanation:
4/9
The sum of two numbers is 48, and their difference is 14. What are the two numbers?
Answer: 17 and 31
Step-by-step explanation:
first number = x
second number = y
x+y=48
-(x-y=14)
---------------
2y=34
y=17
x=31
Answer:
17 and 31
Step-by-step explanation:
17 + 31 = 48, I basically just plugged in random numbers until I got the answer.
subtract 3x squared +7x-4 from 8x squared-6+2 your answer should be polynomial in standard form
Answer:
5x² - 13x + 6
Step-by-step explanation:
8x² - 6x + 2 - (3x² +7x -4)
Simplify the expression:
8x² - 6x + 2 - 3x² -7x + 4
Combine like terms:
5x² - 13x + 6
20 POINTS PLEASE HELP!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x)= e^x
What is the equation of the line that passes through the point (-2, 7) and has a slope of zero
Answer:
y = 7 is the equation of the line that passes through the point ( -2, 7 ) and has a slope of zero.
Step-by-step explanation:
Given:
Let,
A ≡ ( x1 , y1 ) ≡ ( -2, 7 )
Slope = m = 0
To Find :
Equation of Line:
Solution:
Formula for , equation of a line passing through a point ( x1 , y1 ) and having a slope m is given by
[tex](y - y_{1})=m(x-x_{1})[/tex]
Now substituting the values of x1 = -2 and y1 = 7 and slope m = 0 we get,
[tex]y-7=0\times(x--2) \\y-7=0\times (x+2)\\y-7=0\\\therefore y=7[/tex]
Which is the required equation of a line passing through the point ( -2, 7 ) and slope zero
The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.
The equation of the line that passes through the point (-2, 7) and has a slope of zero is written as: y = 7
The equation of the line through a point (x1, y1) can be represented by the algebraic equation:
y = mx + c
where:
m = slope
c = y - intercept
From the question,
(x1, y1) = (-2, 7)
m = slope = 0
Substituting these values into the algebraic equation,
7 = (0 x -2) + c
7 = 0
Hence, y = 7
The equation of the line that passes through the point (-2, 7) and has a slope of zero is y = 7
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Is -9 2/7 bigger equal or less than -9.3
Answer:
-9 2/7 is bigger than -9.3.
Step-by-step explanation:
Imagine these two integers on a number line. On the negative side of the line, these two lie. The way I think of it is that the smaller the value is on the positive side, the bigger it is on the negative side. For example, -1 is bigger than -5. -0.5 is bigger than -1. -13.5 is bigger than -13.7.
The given fraction - 9 2/7 is bigger than the given number - 9.3.
Given the fraction is - 9 2/7
-9 2/7 = - (9 + 2/7)
Now, 2/7 is equal to approximately 0.286.
So, - 9 2/7 = - ( 9 + 2/7 ) = - ( 9 + 0.286) = - 9.286
Thus, 9.286 < 9.3
When negative quantity multiplied then inequality sign changes so,
( -1 ) ( 9.286 ) > ( -1 ) ( 9.3 )
- 9.286 > - 9.3
Therefore the given fraction - 9 2/7 is bigger than the given number - 9.3.
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please graph these dont have time to finish
Mr Anderson has a 10 foot metal pipe that he cut into 4 equal length pieces. What is the length of each piece
Answer:
The length of each piece is 2.5.
Step-by-step explanation:
10/4=2.5
Answer:
2.5 ft
The drawing will help
Suppose mr reeds class has 3 hours for presentations how many projects can be presented show your solution by writing both a division equation and a multiplication equation
Number of projects that can be presented is 15.
What is Multiplication and Division?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that
Time alloted for each team = 1/5
Total time for the presentation = 3 hours
Division equation can be written as :
Number of projects = 3 / (1/5), where 3 hours is divided into 1/5 equal parts.
Number of projects = 15
Multiplication equation can be written as :
Number of projects = 3 × 5 = 15
Hence 15 projects can be presented.
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The complete question is as follows:
Teams of students in Mr. Reed’s classroom are presenting Social Studies projects. Each team has 1/5 hour for their presentation.
Suppose Mr Reeds class has 3 hours for presentations. How many projects can be presented show your solution by writing both a division equation and a multiplication equation.