Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.
Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.
The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.
When both machines are working together, they can make 10,000 cans in 9 hours.
Now, we can set up an equation based on the work rates of the two machines:
Work rate of the older machine + Work rate of the new machine = Combined work rate
The work rate is the amount of work (number of cans made) per unit of time (hours).
For the older machine:
Work rate of the older machine = 10,000 cans / t hours
For the new machine:
Work rate of the new machine = 10,000 cans / (t/3) hours
Combined work rate when both machines work together:
Combined work rate = 10,000 cans / 9 hours
Now, the equation becomes:
10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours
To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:
t/3 is the same as (1/3)t. So the equation becomes:
10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours
Now, to combine the fractions, we find the common denominator, which is 3t:
(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours
(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours
Combine the terms on the left side of the equation:
40,000t / (3t^2 hours) = 10,000 cans / 9 hours
Now, cross-multiply to solve for "t":
40,000t * 9 hours = 10,000 cans * 3t^2 hours
360,000t hours = 30,000t^2 hours
Now, rearrange the equation:
30,000t^2 - 360,000t hours = 0
Divide by 30,000t to simplify the equation:
t - 12 = 0
Now, solve for "t":
t = 12 hours
Therefore, it takes the older machine 12 hours to make 10,000 cans.
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Ryan flew from Wiley Post to Ponca City and back. Ryan maintained an average rate of 450 mph going to Ponca City and an average rate of 400 mph returning to Wiley Post. If the actual flying time for the round trip was one hour, about how far is it from Wiley Post to Ponca City? Round to nearest mile.
A.
0.47 miles
B.
212 miles
C.
239 miles
D.
3,600 miles
Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1.
Which table represents the second piece of the function f(x)
Answer:
Third table represents the second piece of the function f(x)
Step-by-step explanation:
The second piece of the function f(x) is [tex]f(x)=8-2x[/tex]
Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.
For x = 1
[tex]f(1)=8-2(1)\\f(1)=6[/tex]
For x = 2
[tex]f(2)=8-2(2)\\f(2)=4[/tex]
For x = 3
[tex]f(3)=8-2(3)\\f(3)=6[/tex]
Among the given tables, third tables contains these values.
Third table represents the second piece of the function f(x)
A mouse spots an owl flying 10.1 feet over a nearby bush. The mouse is 30 feet away from the bush, and it sees the owl at a certain angle of elevation.
Which trigonometric equation can be used to solve for x, the angle of elevation from the mouse to the owl?
Hey rectangular pan has a link that is for third the with the total area of the pan is 432 in.² what is the width of the cake pan
If y varies inversely as the square of x and y=4 when x=5, find y when x is 2
need to kind K
Y=k x 1/x^2 = k/x^2
Find K when y=4 & x=5
Y=k/x^2 =
4=k/5^2=
4=k/25
K=4*25 =100
When x = 2
Y=100/2^2
Y=100/4
Y=25
I need some assistance in figuring this out
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expression?
The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4
What is the simplification of an algebraic expression?The simplification of algebraic expressions follows an approach where we aim to solve for the unknown variables of the algebraic expression.
From the given algebraic expression, we have:
0.3(4x – 8) – 0.5(–2.4x + 4)
Open brackets1.2x - 2.4 + 1.2x - 2
Collect like terms1.2x + 1.2x = 2.4 + 2
2.4x = 4.4
2.4x - 4.4
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Answer:
simply d
Step-by-step explanation:
The equation =+y3115
is solved in several steps below.
For each step, choose the reason that best justifies it.
Which equation would best help solve the following problem? Rennie kicks a field goal with an initial vertical velocity of 31 m/s. How long will it take the football to hit the ground?
–4.9t2 + 31t = 0
–4.9t2 – 31t = 0
16t2 + 31t = 0
–16t2+ 31t = 0
A man paid the bank $4,080 at the end of three years. This was the amount borrowed plus 12% interest for three years. How much money had he borrowed?
Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16
A local university accepted 2300 students out of 4500 applicants for admission. What was the acceptance rate expressed as a percent
Can someone help me with this math question?
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.
Answer:
x^2/25 + y^2/81 =1
Step-by-step explanation:
solved it
Question 1(Multiple Choice Worth 5 points) (07.05 HC)
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step?
Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7
Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5 A. (–10, 3) B. (–3, 10) C. (0,0) D. Infinitely many solutions
Provide the reasons for the proof:
Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N
how do you solve this system of linear equation by substitution
x-3y=-12
y=2x+9
Find the value of 'y' in the equation 3/y-3 =8
A.) y= -2 3/8
B.) y= -1 5/8
C.) y= 1 5/8
D.) y= 2 3/8
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
f(x)= 3x^2+9x+12
Answer with explanation:
Equation of the Parabola is
[tex]f(x)= y=3x^2+9x+12\\\\y=3[x^2+3 x+4]\\\\y=3[(x+\frac{3}{2})^2+4-(\frac{3}{2})^2]\\\\y=3[(x+\frac{3}{2})^2+(\frac{\sqrt 7}{2})^2]\\\\y-\frac{21}{4}=3[(x+\frac{3}{2})^2][/tex]
Vertex of the parabola can be obtained by
[tex]x+\frac{3}{2}=0\\\\ x=\frac{-3}{2}\\\\ y-\frac{21}{4}=0\\\\y=\frac{21}{4}\\\\ Vertex(\frac{-3}{2},\frac{21}{4})[/tex]
Axis is that line of parabola which divides the parabola into two equal halves.
[tex]x+\frac{3}{2}=0\\\\x=-\frac{3}{2}[/tex]
What are radians, how do I solve for the measurement of radians in the angle of BAC
ANSWER PLEASE
In the figure, sin ∠MQP =
a. cos N and sin R
b. sin R and sin N
c. cos N and sin M
d. cos R and sin N
An 800 gallon swimming pool is being drained. After five hours, 500 gallons have been drained. If the rate of drainage continues, how long will it take to drain the pool?
A) 0.125 hours
B) 5 hours
C) 8 hours
D) 9 hours
The length of the rectangle is 4 times the height. the area of the triangle is 63 cm2. Find the width. Round to the nearest tenth of an inch
area = l x h
l=4h
area = 4h x h = 4h^2
4h^2 =63
63/4 = 15.75
h^2 = 15.75
sqrt(15.75)=h
h = 3.968cm
rounded to nearest tenth would be 4.0cm
check L=4(4) = 16 x 4 = 64 ( since it was round 64 is pretty close to 63)
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows: First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0 Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2 Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3 Which is the best measure of center for second period and why?
A) Mean, because there are no outliers that affect the center.
B) Median, because there is 1 outlier that affects the center.
C) Interquartile range, because there is 1 outlier that affects the center.
D) Standard deviation, because there are no outliers that affect the center
I believe the answer is D.
Answer:
B) Median, because there is one outlier that affects the center
If the ratio between the radii of the two spheres is 5:8, what is the ratio of their volumes?
Answer: The required ratio of the volumes of two spheres is 125 : 512.
Step-by-step explanation: Given that the ratio between the radii of the two spheres is 5 : 8.
We are to find the ratio of the volumes of the two spheres.
Let, 'r' and 'R' represents the radii of the two spheres, so
r : R = 5 : 8.
The volume of a sphere with radius 'r' units is given by the formula:
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Let, V and V' be the volumes of the spheres with radius r and R units respectively.
Then, the ratio of the volumes of the two spheres will be
[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]
Thus, the required ratio of the volumes of two spheres is 125 : 512.
Answer: 125:512
Step-by-step explanation:
a p e x
Help!!!!ASAP PLEASE
Given a polynomial f(x), if (x + 7) is a factor, what else must be true? Help plzzz im running out of time
f(0) = 7
f(0) = −7
f(−7) = 0
f(7) = 0
Eight people enter a race. If there are no ties, in how many ways can the first two places come out
The number of ways the first two places can come out is 56.
Permutation and CombinationPermutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nP_r = \dfrac{n!}{(n-r)!},\ \ ^nC_r = \dfrac{n!}{(n-r)!\times r!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given to us,Eight people enter a race, n = 8,
There are no ties, r = 2,
As there is an equal chance of everyone being first and second, but also there will be cases where the first and second positions can be exchanged between the same two people. therefore, there is a particular order in which these 8 people can win. Thus, we will use permutation.
Permutation[tex]^8P_2 = \dfrac{8!}{(8-2)!}=\dfrac{8!}{(6)!} = \dfrac{8\times 7\times 6!}{6!} = 8\times 7 = 56[/tex]
Hence, the number of ways the first two places can come out is 56.
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