Answer:
x=6.28 inches
y=191.08 inches
Step-by-step explanation:
Let the dimensions of the rectangle be x and y
Area of the rectangular sheet
x*y=1200 in^2}
x = circumference of the cylinder
This means x=2πr
Volume of a cylinder=πr^2h
h=y
Volume of the cylind=πr^2(y)=600 in^3
From x=2πr
r=x/2π
Substitute r=x/2π into Volume=πr^2(y)=600 in^3
We have,
Volume of the cylinder=πr^2(y)=600 in^3
π*(x/2π)^2(y)=600
(x^2/4π)y=600
Recall, x*y=1200
y=1200/x
Substitute y=1200/x into (x^2/4π)y=600
(x^2/4π)y=600
(x^2/4π)(1200/x)=600
1200x/4π=600
Multiply both sides by 4π
(x^2/4π)(1200/x)(4π)=600*4π
1200x=2400π
Divide both sides by 1200
1200x/1200 = 2400π/1200
x=2π
Substitute x=2π into y=1200/x
We have,
y=1200/2π
y=600/π
The dimensions are x=2π and y=600/π
Let π=3.14
x=2π
=2(3.14)
=6.28 inches
y=600/π
=600/3.14
=191.08 inches
helpppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
4
Step-by-step explanation:
Answer:
1/8 < 1/6
Step-by-step explanation:
The top is divided into 8 and 1 part is shaded so 1/8
The bottom is divided into 6 and 1 part is shaded so 1/6
Comparing
1/8 < 1/6
A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five. The study involved a large random sample of mothers and children and was conducted over several years. What is the population of interest in this survey
Answer: Parents and children ( till the age of 5) of Norway
Step-by-step explanation:
The population in a survey is the group of people sharing common features or characteristics as per the researcher point of view.Here, A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five.
Since the study involved a large random sample of mothers and children and was conducted over several years.
So, the population of interest in this survey is "Parents and children ( till the age of 5) of Norway".
Graph a line that contains the point (-7,-4)and has a slope of - 2/3
Hi there! :)
Answer:
Given the information, we can write an equation in slope-intercept form
(y = mx + b) to graph the line:
Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the
x-coordinate given for 'x':
-4 = -2/3(-7) + b
-4 = 14/3 + b
Solve for b:
-12/3 = 14/3 + b
-12/3 - 14/3 = b
-26/3 = b
Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)
Some points on the line include:
(-7, -4)
(-4, -6)
(0, -26/3)
(2, -10)
(5, -12)
A concert starts at 7:45pm and ends at 1:35 am. How long was the concert?
Answer:
The concert starts at 7:45 pm and ended at 1:35 am which mean the concert going on 5 hours and 50 minutes.
A factory manufactures chairs and tables, each requiring the use of three operations: cutting, assembly, and finishing. The first operation can use at most 40 hours; the second at most 42 hours; and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; a table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 for a table, what is the maximum revenue? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.
Answer:
z(max) = 650 $
x₁ = 10 units
x₂ = 15 units
Step-by-step explanation:
That is a linear programming problem, we will use a simplex method to solve it
Formulation:
Let´s call x₁ number of chairs and x₂ number of tables then :
Item (in hours) cutting assembly finishing Profit ($)
Chairs (x₁) 1 2 1 20
Tables (x₂) 2 1 1 30
Availability 40 42 25
Objective Function
z = 20*x₁ + 30x₂ ( to maximize) subject to:
x₁ + 2x₂ ≤ 40
2x₁ + x₂ ≤ 42
x₁ + x₂ ≤ 25
x₁ , x₂ >= 0
Using excel or any other software we find:
z(max) = 650
x₁ = 10
x₂ = 15
The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674
Let x represent chairs, and y represent tables
So, the given parameters are:
Cutting:
Chairs: 1 hourTable: 2 hoursHour available: 40So, the constraint is:
[tex]\mathbf{x + 2y \le 40}[/tex]
Assembly:
Chairs: 2 hoursTable: 1 hourHour available: 42So, the constraint is:
[tex]\mathbf{2x + y \le 42}[/tex]
Finishing:
Chairs: 1 hourTable: 1 hourHour available: 25So, the constraint is:
[tex]\mathbf{x + y \le 25}[/tex]
The unit profit on the items are:
Chairs: $20Table: $30So, the objective function to maximize is:
[tex]\mathbf{Max\ z = 20x + 30y}[/tex]
And the constraints are:
[tex]\mathbf{x + 2y \le 40}[/tex]
[tex]\mathbf{2x + y \le 42}[/tex]
[tex]\mathbf{x + y \le 25}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Using graphical method (see attachment for graph), we have the following feasible points:
[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]
Calculate the objective function using the feasible points.
[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]
[tex]\mathbf{z = 650}[/tex]
[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]
[tex]\mathbf{z = 580}[/tex]
[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]
[tex]\mathbf{z = 673.5}[/tex]
Approximate
[tex]\mathbf{z = 674}[/tex]
Hence, the maximum revenue is 674
Read more about linear programming at:
https://brainly.com/question/14225202
In a class full of men and women, 5 9 of the class are women. What is the ratio of men to women in its simplest form?
6th grade math, help me please
Answer:
1. 2/5
Step-by-step explanation:
When it says the ratio is 5 to 2, that means 5 is always first:
5 : 2 is correct
5/2 is correct
10 : 4 is correct (multiplied 2 on both sides)
2/5 is incorrect because 2 is first. That means that this ratio would be 2 to 5, not 5 to 2.
Answer:
2/5
Step-by-step explanation:
because you are not supposed to flip the two numbers. You need to keep them in the same order.
Sorry, if this isn't the greatest answer. Its my first time.
Please show step by step working out of stationary points and points of inflection with the y coordinates (and sketch graph) for the equation y=x^4-36x^2
Answer:
See picture attached
Step-by-step explanation:
Consider the Equation y > 3x + 1 (a) Find an ordered pair that satifies the equation (b) Is the equation a Releation? explain (c) Is the equation a Function? explain
Answer:
(a) (1,5)
(b) Every subset of a cartesian product is a relation, therefore this is a relation.
(c) The relation IS NOT a function.
Step-by-step explanation:
(a)
(1,5)
Notice that 3(1) +1 = 4 < 5 therefore (1,5) is an order pair that satisfies the equation.
(b)
Every subset of a cartesian product is a relation, therefore this is a relation.
(b)
A relation is a function of the following condition holds
if (a,b) and (c,b) belong to the relation then (a=c)
In this case, (1,5), (0,5) belong to the relation but 0 is different than 5, therefore the relation IS NOT a function.
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model. The silver model requires 1 minute in a grinder and 3 minutes in a bonder. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder. Because of maintenance procedures, the grinder can be operated no more than 30 hours per week and the bonder no more than 50 hours per week. The company makes $5 on each silver pen and $7 on each gold pen. How many of each type of pen should be produced and sold each week to maximize profits?
Answer:
Optimal production = 600 gold pens
Revenue = 600*7 = $4200 gold pens
Step-by-step explanation:
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.
A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.
B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.
Because of maintenance procedures,
C. the grinder can be operated no more than 30 hours per week and
D. the bonder no more than 50 hours per week.
The company makes
E. $5 on each silver pen and
F. $7 on each gold pen.
How many of each type of pen should be produced and sold each week to maximize profits?
Solution:
We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.
1. From A and C, the maximum number of silver pens
x <= 30*60 / 1 = 1800 and
x <= 50*60 /3 = 1000 ....................(1) bonder governs
2. from A & D, the maximum number of gold pens
y <= 30*60 / 3 = 600 .....................(2) grinder governs
y <= 50*60 / 4 = 750
3. From D,
x + 3y <= 30*60 = 1800 ...................(limit of grinder) ..... (3)
3x + 4y <= 50*60 = 3000 .................(limit of bonder) .......(4)
Need to maximize profit,
Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.
The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4). Using slope intercept form,
(y-480) = -(5/7)(x-360)
or y=-(5/7)x + (737+1/7) [the purple line] which violates the red line, so not a solution.
Next try the point (0,600)
(y-600) = -(5/7)(x-0), or
y = 600 - (5/7)x [the black line]
As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of
Revenue = 600*7 = 4200 gold pens
Find the standard divisor to two decimal places (hundredth) for the given population and number of representative seats.
Population : 140,000
# seats : 9
A) 15,555.56
B) 17,055.56
C) 13,056
D) 14,055.56
E) 16,055
Answer:
A
Step-by-step explanation:
A divisor refers to a number by which another number is to be divided.
So what this question is practically asking us is that which of the values in the options to 2 decimal places is the result dividing the population by the number of seats
Thus we have;
140,000/9 = 15,555.55555 which to 2 decimal places is 15,555.56
how could you correctly rewrite the equation 4(5+3)=2(22-6) using the distributive property?
We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.
4(5+3) = 2(22-6)
4(8) = 2(16)
32 = 32
Once you finish distributing each side, you can check to see if it is equal on both sides.
In our case it is since they both equal 32 after distributing the terms.
Solve 2x2 – 6x + 10 = 0 by completing the square.
Answer: x = 6.32 or -0.32
Step-by-step explanation:
2x² - 6x + 10 = 0
No we divide the expression by 2 to make the coefficient of x² equals 1
We now have
x² - 3x + 5 = 0
Now we remove 5 to the other side of the equation
x² - 3x = -5
we add to both side square of half the coefficient of x which is 3
x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²
(x - ³/₂)² = -5 + ⁹/₄
Resolve into fraction
(x - ³/₂)² = ⁻¹¹/4
Take the roots of the equation
x - ³/₂ = √¹¹/₄
x - ³/₂ = √11/₂
x = ³/₂ ± 3.32/₂
= 3+ 3.32 or 3 - 3.32
= 6.32 or - 0.32
Type the correct answer in the box. Use numerals instead of words. What is the missing value in the inverse variation given in the table?
Answer:
48
Step-by-step explanation:
If x varies inversely as y, we have:
[tex]x \propto \frac{1}{y} \\\implies x = \frac{k}{y}[/tex]
When x=2, y=96
[tex]2 = \frac{k}{96}\\k=192[/tex]
When x=8, y=24
[tex]8 = \frac{k}{24}\\k=192[/tex]
Therefore, the constant of proportionality, k=192.
The equation connecting x and y is:
[tex]x = \frac{192}{y}[/tex]
When x=4
[tex]4 = \frac{192}{y}\\4y=192\\y=48[/tex]
The missing value in the inverse variation given in the table is 48.
The average flight time from Seattle (SEA) to New York (JFK) is 4.3 hours. The distance between them is 2421 miles. The average flight time going the other way, JFK to SEA is 5.5 hours. The difference is due to the jet stream. Translate this situation to a system of equations and find the average speed of the jet and the average speed of the jet stream.
Answer:
Speed of the jet is 563.02 miles/hr
Speed of the jet stream is 122.83 miles/hr
Step-by-step explanation:
The average time for going from Seattle to New York is 4.3 hours
The distance between these places is 2421 miles
The average time for going back (impaired by jet stream) is 5.5 hours
If we designate the speed of the jet = v
and the speed of the jet stream = u
then on the return trip, the relative speed of the jet = v - u
Also, recall that distance = speed x time
For the going trip, the distance covered by the jet = 4.3 x v = 2421 miles
For the return trip, the distance covered by the jet = 5.5 x (v - u) = 2421 miles
= 5.5(v - u)
these translate into the following equation written below
4.3v = 2421 ....equation 1
5.5(v - u) = 2421 ....equation 2
solving, equation 1, we'll have
4.3v = 2421
v = 2421/4.3 = 563.02 miles/hr this is the speed of the jet
substituting the value of v into equation 2, we'll have
5.5(v - u) = 2421
5.5(563.02 - u) = 2421
3096.61 - 5.5u = 2421
3096.61 - 2421 = 5.5u
675.61 = 5.5u
u = 675.61/5.5
u = 122.83 miles/hr this is the speed of the jet stream
In the figure below, YZA and YZX are right angles, XYZ and AYZ are congruent, and XZ = 10. What is the length of ?
A.
25
B.
20
C.
10
D.
5
Answer:
C. 10
Step-by-step explanation:
The given information tells you that triangles YZX and YZA are congruent, so ZA = ZX = 10.
Suppose that you have $100. You have two options for investing your money.
Option 1: Increase by $10 each year
Year
Amount
1
100
110
Type:
a =
b =
Answer:
Option One:
type : linear growth
a : 120
b : 130
Option 2:
type: linear growth
d : 121
e : 133
Step-by-step explanation:
its right on EDG 2020
Option One:
type: linear growth
a: 120
b: 130
Option 2:
type: linear growth
d: 121
e: 133
What is linear and exponential growth?Linear growth occurs with the aid of including an equal amount in each unit of time. An exponential increase happens while a preliminary population will increase by the same percent or issue over the same time increments or generations.
What is the distinction between linear and exponential?Linear and exponential relationships vary within the way the y-values change whilst the x-values increase with the aid of a steady quantity: In linear dating, the y-values have identical variations. In an exponential relationship, the y-values have identical ratios.
Learn more about Linear growth here: brainly.com/question/4025726
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F(n)=6.5n+4.5 find the 5th term of the sequence defined by the given rule
Answer:
37
Step-by-step explanation:
To find the fifth term , we have to take the value of n as 5
So, F(5)= 6.5 (5) +4.5
= 32.5 + 4.5
= 37
Helpppp asapppppp....
Answer:
C.
Step-by-step explanation:
So, here's what you need to remember:
If we have a function f(x) and a factor k:
k(f(x)) will be a vertical stretch if k is greater than 1, and a vertical compression if k is greater than zero but less than 1.
f(kx) will be a horizontal compression if k is greater than 1, and a horizontal stretch if k is greater than zero but less than 1.
We are multiplying 0.5 to the function. In other words: 0.5f(x).
This is outside the function, so it's vertical.
0.5 is less than 1, so this would be a vertical compression
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
Examine today’s stock listing for SFT Legal, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 74.80 44.61 SFT 8.94 56.11 5.74 What was the price of SFT Legal yesterday? a. $47.17 b. $56.11 c. $50.37 d. $61.85
Answer:
c. $50.37
Step-by-step explanation:
Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.
Answer:
c.50.37
Step-by-step explanation:
Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Determine the probability that at least one contain regular soda.
Answer:
161/184 or 0.875
Step-by-step explanation:
Total number of cans = 24 cans
Total number of diet soda = 3 cans
Total number of regular soda = 21 cans
We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly
We have two ways for this happening
a) two of the cans are regular soda
b) one of the cans is regular , while one is diet
Hence,
Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)
Probability(that two of the cans are regular soda) = 21/24 × 20/23
= 35/46
Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23
= 21/184
Probability (that at least one contain regular soda) = 35/46 + 21/184
We find the Lowest common multiple of the denominators = 184
= 35/46 + 21/184
= (35 × 4) + (21 × 1)/184
= 140 + 21/184
= 161/184
= 0.875
Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the Algebraic equation by replacing the tens digit with x.
Let a be the number in the 10s place and b in the 1s place. Then the original two-digit number is 10a + b.
The sum of the digits is 5:
a + b = 5
Subtract 9 from the original number, and we get the same number with its digits reversed:
(10a + b) - 9 = 10b + a
Simplifying this equation gives
9a - 9b = 9
or
a - b = 1
Add this to the first equation above:
(a + b) + (a - b) = 5 + 1
2a = 6
a = 3
Then
3 - b = 1
b = 2
So the original number is 32. Just to check, we have 3 + 2 = 5, and 32 - 9 = 23.
Can someone Give me the answer?
Answer:
(0,5)
Step-by-step explanation:
The solution to the system is where the two graphs intersect
From the graph, the graphs intersect at x = 0 and y =5
Step-by-step explanation:
I have trouble with these types of questions as well, but hopefully this might help.
Find x and y, please solve with steps and leave answers in fraction form, THANK YOU
Answer:
Below
Step-by-step explanation:
Using the proprtionality relation:
● 8/10 =5/x
● (4*2)/(5*2) = 5/x
Simplify using 2
● 4/5 = 5/x
Multiply both sides by 5
● (4/5)*5 = (5/x)*5
● 4 = 25/x
Switch x and 4
● x= 25/4
■■■■■■■■■■■■■■■■■■■■■■■■■
Again use the proportionality relation but this time with y.
● 8/10 =7/y
8/10 = 4/5
● 4/5 = 7/y
Multiply both sides by 5
● (4/5)*5 =(7/y)*5
● 4 = 35/y
Switch 4 and y
● y = 35/4
What is the image of the point by (-5,3) under a 270 rotation about the point (-7,-3)
Step-by-step explanation:
here, the given point is (-7,-3)
now, by the formula,
p(x,y)= p-1 (-y+a+b,x-a+b) ( p-1 is p das)
p(-5,3)= p-1 (-13,-1) is answer.
hope it helps..
Aiden is trying to pick up some lawn mowing jobs over the weekend to make extra money for a school trip. Each lawn in his neighborhood takes an average of 40 minutes to mow, and Aiden has no more than 11 hours, or 660 minutes, of available time to mow lawns. If Aiden mows his grandparents' farm which takes him 110 minutes, and x represents the number of lawns he mows in his neighborhood, which inequality represents this situation?
A.
40x + 110 ≤ 660
B.
110x + 40 ≤ 660
C.
110x + 40 ≥ 660
D.
40x + 110 ≥ 660
Answer:
A.
Step-by-step explanation:
40x is the number of lawns he can do, less the time to do his grandparents time (added to other law time) and he has 660 mins of less to complete them.
Answer:
a. 40x + 110 ≤ 660
Step-by-step explanation:
Find the left critical value for 95% confidence interval for σ with n = 41. 26.509 24.433 55.758 59.342
Answer: 59.342
Step-by-step explanation:
The chi-square critical values are used to find the confidence interval for σ.
Left critical value = [tex]\chi^2_{\alpha/2, n-1}[/tex] [i.e. chi-square value from chi-square table corresponding to degree of freedom n-1 and significance level of [tex]\alpha/2[/tex]]
To find : left critical value for 95% confidence interval for σ with n = 41.
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
degree of freedom = 41-1=40
Now, the left critical value for 95% confidence interval for σ with n = 41 is the chi-square value corresponding to degree of freedom n-1 and [tex]\alpha/2=0.025[/tex]
=59.342 [from chi-square table ]
According to medical data, the ages at which patients have their first knee replacement surgery
follows a normal distribution. The average age for a first knee replacement is 58 years of age, with a
standard deviation of 8.25 years. Therefore, doctors can expect the middle 68% of their knee
replacement surgery patients to be between what ages?
Answer:
The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
Step-by-step explanation:
68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years
So, the ages lies between x₀ + σ and x₀ - σ
So, the ages lie between 58 - 8.25 = 49.75 years
and 58 + 8.25 = 66.25 years
So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...