a copper alloy that is 40% copper is to be combined with a copper alloy that is 80% copper to produce 120 kilograms of an alloy that is 70% copper. how many kilograms of each alloy must be used? please work it out
Answers
1. note, that in such tasks mass of pure copper before merging and after merging is the same (this is the base);
2. If the mass of pure copper in alloy with 40% solution is 'x' and the mass of pure copper in alloy with 80% solution is 'y', then It means before merging was x/0.4 and y/0.8, after merging was (x+y)/0.7. It is one equation of the future system.
3. Using 120 kg. of 70% solution, it is possible to define mass of pure copper after merging, 120*0.7(=84 kg.). And before merging it was 'x+y' kg. of pure copper. It is the second equation of the future system.
4. according to the items no.2&3 (to make up the system of two equations and solve it). All the details are in the attached picture.
5. pure copper in 40% solution is 12 kg., pure copper in 80% solution is 72 kg. It means, that the copper alloy with 40% solution is x:0.4=12/0.4=30 kg., and the copper alloy with 80% solution is y:0.8=72/0.8=90 kg.
After setting up and correcting a system of equations, the student needs to use 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy to create 120 kg of a 70% copper alloy.
To solve this problem, we need to set up a system of equations. Let x be the amount of 40% copper alloy needed, and y be the amount of 80% copper alloy needed.
First, we have the total weight equation:
x + y = 120 kg (the final alloy's total weight)
Next, we have the copper content equation:
0.40x + 0.80y = 0.70 × 120 kg (the final alloy's copper content)
Now, let's solve this system of equations:
Address the second equation: 40x + 80y = 8400
Express x in terms of y: 40x = 8400 - 80y
Divide by 40: x = 210 - 2y
Substitute x in the first equation: (210 - 2y) + y = 120
Solve: 210 - y = 120, y = 90 kg
Finally, substitute the value of y back into x = 210 - 2y: x = 210 - 2 imes 90 = 210 - 180 = 30 kg
So, we need 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy.
Related Questions
a bag contains 1p 2p and 5p coins .3/8 of the bag are 1p coins.there are as many 5p coins than 1p coins in the bag . there are 640 cois in total. work out the number of 2p coins in the bag
Answers
The number of 2p coins in the bag is 160
How to get the number of 2p coins
Assuming:
the number of 1p coins is xthe number of 2p coins is y and the number of 5p coins is z.According to the given information:
x = 3/8 * 640 = 240
z = x = 240
total number of coins is 640.
x + y + z = 640
plugging in the values
240 + y + 240 = 640
y + 480 = 640
y = 160
what are the points of intersection of the lines below 2x-y=10 y=-4x+2
Answers
2x-y=10
y=-4x+2
Use substitution method:
2x-(-4x+2)=10
y=-4x+2
2x+4x-2=10
y=-4x+2
6x-2=10
y=-4x+2
6x=12
y=-4x+2
x=2
y=-4(2)+2
The points of intersection are: x=2 and y=-6.
The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?"
Answers
INITIAL CASH AMOUNT IN THE BANK: USD3,000
ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%
YEARS THE CASH STAYED IN THE BANK: 2 years.
AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206
AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206
First, we need to solve for YEAR 1:
FOR YEAR 1:
Initial Deposit * Annual Increase Rate = Annual Increase
3,000 * 0.10 = Year 1's Annual Increase
Year 1's Annual Increase = USD300
∴The YEAR 1'S ANNUAL INCREASE IS USD300.
∴The NEW AMOUNT is now USD3,300.
BUT NOT SO FAST! After the year, you took out USD1,206.
New Amount - USD1,206 = Year 1 Amount
3,300 - 1,206 = Year 1 Amount
Year 1 Amount = USD2094
∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.
Now, let us solve for the REMAINING BALANCE.
FOR YEAR 2's Annual Increase:
YEAR 1 AMOUNT * Annual Increase = Year 2's Annual Increase
2094*0.10 = Year 2's Annual Increase
Year 2's Annual Increase = USD209.4
∴The YEAR 1'S ANNUAL INCREASE IS USD209.4.
∴The NEW AMOUNT is now USD2,303.4.
But you took out USD1,206
USD2,303.4 - USD1,206 = Remaining Balance
Remaining Balance = USD1097.4
∴The Answer is: USD1097.4
"The amount remaining in the account after the withdrawals at the end of years 1 and 2 is $1,818.
To solve this problem, we will calculate the amount in the account at the end of each year, taking into account the interest earned and the withdrawals made.
1. At the end of the first year, the account earns 10% interest on the initial $3,000 deposit. The calculation is as follows:
[tex]\[ \text{Amount at the end of year 1}[/tex] = 3000 \times (1 + 0.10) = 3000 \times 1.10 = 3300 \]
2. At this point, $1,206 is withdrawn from the account, leaving:
[tex]\[ \text{Amount after withdrawal at the end of year 1}[/tex]= 3300 - 1206 = 2094 \]
3. This remaining amount then earns 10% interest for the second year:
[tex]\[ \text{Amount at the end of year 2} = 2094 \times (1 + 0.10) = 2094 \times 1.10 \][/tex]
4. At the end of the second year, another $1,206 is withdrawn:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
5. To find the exact amount, we calculate the interest earned in the second year and then subtract the withdrawal:
[tex]\[ \text{Interest earned in year 2} = 2094 \times 0.10 = 209.4 \][/tex]
[tex]\[ \text{Amount after interest in year 2} = 2094 + 209.4 = 2303.4 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 = 1097.4 \][/tex]
However, there seems to be an error in the calculation. Let's correct it:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2094 \times 1.10 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]
This is not the correct final amount. We need to correctly calculate the amount after the second withdrawal:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
\[tex][ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]
Upon re-evaluating the calculation, we find that the correct amount after the second withdrawal is:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2294.4 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 1} = 3300 - 1206 = 2094 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 = 2294.4 \][/tex]
A student athlete run 3 1/3 miles in 30 minutes A professional runner can run 1 1/4 times as far in 30 minutes . how far can the professional runner run in 30 minutes
Answers
Since the professional can run 1 1/4 times as far in 30 minutes, we multiply 3 1/3 by 1 1/4:
(3 1/3)(1 1/4)
Convert each to an improper fraction (multiply the whole number by the denominator and add the numerator):
10/3(5/4) = 50/12 = 25/6 = 4 1/6.
Suppose that Bangladesh, India, Pakistan, and Nepal are economically interdependent. The following table shows the exports and imports of each country, with all monetary values given in millions of equivalent US dollars. Country of Origin Exporting to... Amount ($ 2007-13-04-00-00_files/i0260000.jpg 1,000,000) Bangladesh India 2,817 Bangladesh Pakistan 2,369 Bangladesh Nepal 3,039 India Bangladesh 2,023 India Pakistan 3,462 India Nepal 2,184 Pakistan Bangladesh 3,201 Pakistan India 2,336 Pakistan Nepal 2,338 Nepal Bangladesh 2,707 Nepal India 3,363 Nepal Pakistan 2,332 Based on the information in the table, assuming that these four countries trade strictly within the group, what is the value of the greatest trade balance in this group? a. $841 million b. $847 million c. $8,402 million d. $8,516 million
Answers
1. Total trade between Bangladesh and other three nations which are India , Pakistan, Nepal= 2,817 + 2,369 + 3,039=$ 8,225
2. Total trade between India and other three nations which are Bangladesh , Pakistan, Nepal= 2,023 +3,462 + 2,184=$7669
3. Total trade between Pakistan and other three nations which are Bangladesh,India, Nepal=3,201 + 2,336 +2,338= $7875
4. Total trade between Nepal and other three nations which are Bangladesh,India, Pakistan=2,707 +3,363+2,332 = $ 8402
The greatest trade is between Nepal and other three nations which are Bangladesh,India, Pakistan=2,707 +3,363+2,332 = $ 8402→→Option (C)
Which of the following is an odd function?
g(x) = x2
g(x) = 5x – 1
g(x) = 3
g(x) = 4x
Answers
The 4th selection is appropriate.
Answer:
g(x) = 4x is an odd function.
Step-by-step explanation:
A function g(x) is odd if it satisfies that, for all x we have g(-x) = -g(x). Then,
[tex]g(x) =x^2[/tex] is not an odd function beacuse only give positive values, then for example if x= 2
[tex]g(-2) =(-2)^2 = 4 \neq -4 = -g(2)[/tex].
g(x) = 5x-1 is not an odd function. I'll also give you a counterexample: for x=1 we have
g(-1) = 5(-1)-1 = -6 ≠ -4 = -(5-1) = -g(1).
g(x) = 3 is not an odd function. I'll also give you a counterexample: for x=1 we have
g(-1) = 3 ≠ -3 = -g(1).
Finally, g(x) = 4x is an odd function because for all x we have g(-x) = -g(x):
g(-x) = 4(-x) = -4x = -g(x).
at a certain time of day a person 6 ft tall cast a 4 ft shadow how long is the shadow cast by ba 21 ft tree at the same time?
Answers
If 20% of a class takes a car to school and 48% takes the bus and 8% ride their bikes to school and there are 825 in the school what percent of students use another method to travel to school
Answers
Add up the percentages for car, bus and bike travel. Subtract that total from 100%.
x= percent that uses another method
x= 100% - (20% + 48% + 8%)
x= 100% - 76%
x= 24%
This doesn't say, but if you needed to find the number of students that use another method, multiply the total number of students by the percent that use another method of travel:
= 825 * 24%
= 198 students use another method
ANSWER: 24% of students use another method of travel to school. (And in case you needed it, 24% is 198 students).
Hope this helps! :)
What is 0.0371 × 10000?
Answers
Your answer would then be: 367
Hope that helps explain a little bit better! Good luck. :)
What is the overtime rate for a mail carrier who regularly earns $9.80 an hour?
Answers
The overtime rate for a mail carrier earning $9.80 per hour is calculated as one and a half times the regular rate, resulting in an overtime pay of $14.70 per hour.
The question is asking for the overtime rate for a mail carrier earning a regular hourly wage of $9.80. In the United States, the standard overtime rate is typically one and a half times the employee's regular hourly pay for any hours worked beyond 40 in a workweek. Therefore, to calculate the overtime rate for a mail carrier earning $9.80 per hour, the following calculation is performed:
Regular hourly wage times 1.5 = Overtime rate
$9.80 times 1.5 = $14.70 per hour
the longest side of an acute isosceles triangle is 8 centimeters . rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
Answers
Explanation:
1) The acute angle is restricted to an upper bound of to 90°, i.e. the greatest value of an acute angle must be less than 90°.
2) the smaller the acute angle the longer the two congruent sides of the isosceles triangle, the greater the acute angle the shorter the two congruent sides.
3) Find the lower bound of the two congruent sides by using the upper bound of the acute angle.
4) when the angle is 90°, you can use the Pytagorean theorem
c^2 = a^2 + b^2
c = 8 cm, a = b
c^2 = 2a^2
8^2 = 2a^2
2a^2 = 64
a^2 = 64/2
a^2 = 32
a = √32
a = 5.7 cm
5.7 cm is the lower bound of the length of the two small sides, therefore, the length of the two small sides has to be greater than 5.7 cm
Answer:5.7 cm
Step-by-step explanation:
Just took the test.
What is the order of 5x10^4 , 7x10^-5 , 3x10^-9 , 8x10^4 from least to greatest?
Answers
Answer:
[tex]3\times10^{-9},7\times 10^{-5},5\times 10^4,8\times10^4[/tex]
Step-by-step explanation:
We want to order ; [tex]5\times 10^4,7\times 10^{-5},3\times10^{-9},8\times10^4[/tex] from least to greatest.
Observe that all these numbers are in standard form.
We can order them based on the exponents.
[tex]-9<\:-5<\:4[/tex]
Since two numbers have the same exponent of 4, we need to use the multiplier to order the last two(5<8).
From least to greatest we have;
[tex]3\times10^{-9}\:<\:7\times 10^{-5}\:<\:5\times 10^4\:<\:8\times10^4[/tex]
The numbers in ascending order from least to greatest are 3x10²-9, 7x10²-5, 5x10²4, 8x10²4
To order the numbers from least to greatest, to compare the values of the numbers without the powers of 10 first and then consider the powers of 10.
Given numbers:
5x10²
7x10²-5
3x10²-9
8x10²4
Step 1: Compare the numbers without the powers of 10:
The numbers without the powers of 10 are: 5, 7, 3, and 8.
Step 2: Arrange the numbers in ascending order based on their values:
3, 5, 7, 8
Step 3: Now, consider the powers of 10:
The powers of 10 are: 10²4, 10²-5, 10²-9, and 10²4.
Since all the powers of 10 are positive, larger powers of 10 indicate larger numbers.
Step 4: Combine the results from Steps 2 and 3 to get the final order:
3x10²-9, 7x10²-5, 5x10²4, 8x10²4
To know more about ascending here
https://brainly.com/question/30325384
#SPJ6
Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long.
Answers
the Area of a circle=pi*r²
the length of a radius of circle circumscribed about an equilateral triangle is
r=b*(√3)/3
where
b---------> length of a side equilateral triangle-------> 18 in
then
r=18*(√3)/3=10.39 in
A=pi*(10.39)²=108*pi=339.29 in²
the answer is 339.29 in²
a population of 140000 grows 4% per year for 16 years. How much will the population be after 16 years?
Answers
.
.
.
.
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At the end of the Year n the population , Px=n+nrx+(x-1)r2n+(x-2)r3n+...........+(x-x+2)r(x-1)x+(x-x+1)rxn=n(1+r)x.....At the end of the Year 16 the population , P16= n+16rn+15r2n+14r3n+.............+3r14n+2r15n+r16n=n(1+r)16 Thus under given condition of rate of growth, the Population P(x) at xth year will be P(x)=n(1+r)x Therefore, a population of 110,000 growing at 4% per year, in 16 years will be= 110,000(1+4/100)16= 110,000(1.04)16=206027.93702999115428132473599427≈206028
I hope this is helpful. I found the solution on the internet. Hope you have a good day and bye.
Assume the method dosomething has been defined as follows: public static void dosomething (int[] values, int p1, int p2) { int temp = values[p1]; values[p1] = values[p2]; values[p2] = temp; } what does the method do?3
Answers
ANALYSIS:"int temp = values[p1]"this line creates variable "temp" which is integer. then this line goes to the list "values" and takes value that is at position "p1" and stores it into variable "temp"
"values[p1] = values[p2]"this line goes to the list "values" and takes value that is at position "p2" and stores it into variable that is at position "p1"
"values[p2] = temp"this line takes value of the variable "temp" and stores it into list values at position "p2"
Short explanation:this code replaces values of the list at between positions p1 and p2
witch one of these is correct
Answers
Exlanation For A: 42 divided by 6 is 7, and 105 divided by 15 is 7. That is equivalent
Explanation For C: 36 divided by 6 is 6, and 90 divided by 15 is 6. That is also equivalent.
Why Not B: B does not work because 6 does not go into 8 evenly, so it is already out of the picture.
~Deceptiøn
Rosalie earns extra money by working as a babysitter over the weekend. She charges $10 to drive to the home and an additional $8 per hour.
Answers
2 hour =26
3 hour =34
4 hour=42
Hope this helps ;)
So by babysitting 48 hours she would earn 394 dollars i guess
What are the intercepts of the line?
A.
x-intercept:-8 ; y-intercept:0
B.
x-intercept:0 ; y-intercept:
C.
x-intercept:-8 ; no y-intercept:
D.
no x-intercept: ; y-intercept:-8
Answers
Answer:
D cause it crosses at -8
Step-by-step explanation:
NEED HELP ASAP!!!!!!!!
Answers
C = 2 x 3 x 2
C = 12 units
answer
A. 12 units
C= 2(3.14)(2)
C= 12.56
ANSWER: the best estimate is A) 12
Hope this helps! :)
Using the graph below, find the missing value to complete the t-chart.
the chart:
x y
-3 5
0 -1
2 ?
A. -3
B. 5
C. 3
D. -5
Answers
Answer:
I THINK THE ANSWER IS A
Step-by-step explanation:
BECAUSE IF YOU SEE THEN IT WILL NOT BE B BECAUSE IT WENT DOWN AND IF YOU LOOK IT UP IT WILL BE A
Answer: you answer would be -5
Step-by-step explanation:
Go to the origin and count to the right to places. Then count downwards towards the line and count the number. In this case you move down 5 so it is -5. So count down (or up) towards the line and however many you went that’s your answer (remember up and right are both positive, and down and left are both negative.)
What are two pair fractions with common denominators for 3/5 and 3/4
Answers
[tex]\bf \cfrac{3}{5}\cdot \cfrac{4}{4}\implies \cfrac{12}{20}\qquad \qquad \qquad \qquad \qquad \cfrac{3}{4}\cdot \cfrac{5}{5}\implies \cfrac{15}{20}[/tex]
Kareem lives 4/10 of mile from the mall.Write two equivalent fraction that show what fraction of mile Kareem lives from the mall
Answers
1) We can simplify 4/10 by dividing both #s by 2.
4/10 ÷ 2/2= 2/5
2) We can increase both #s by multiplying each by both by the same number. I choose the number 2 (bit this works with any number as long as you increase both numerator and denominator by the same amount).
=4/10 * 2/2
=(4*2)/(10*2)
=8/20
Two equivalent fractions are 2/5 and 8/20.
Hope this helps! :)
Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –x + 9 y = –x + 5 y = –3x – 11y y = –3x + 25
Answers
Step [tex]1[/tex]
Find the slope of the line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
Let
[tex]A(-6,7)\\B(-3,6)[/tex]
substitute the values
[tex]m=\frac{(6-7)}{(-3+6)}[/tex]
[tex]m=\frac{(-1)}{(3)}[/tex]
[tex]m=-1/3[/tex]
Step [tex]2[/tex]
with the slope m and the point [tex]A(-6,7)[/tex] find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex]y-y1=m*(x-x1)[/tex]
substitute the values
[tex]y-7=(-1/3)*(x+6)[/tex]
[tex]y=(-1/3)x-2+7[/tex]
[tex]y=(-1/3)x+5[/tex]
therefore
the answer is
[tex]y=(-1/3)x+5[/tex]
Emma is going camping. Each side triangle on her tent is 5 feet tall. The square base is 4 feet wide. What is the surface area of her tent?
Answers
A=2bs+b²
"A" is the surface area of the square pyramid.
"b" is the side length of the square base (b=4 feet).
"s" is the slant of the face (s=5 feet).
2. When you substitute these values into the formula for calculate the area of the square pyramid (A=2bs+b²), you obtain:
A=2bs+b²
A=2(4 feet)(5 feet)+(4 feet)²
A=2(20 feet²)+16 feet²
A=40 feet²+16 feet²
A=56 feet²
What is the surface area of her tent?
The answer is: The surface area of her tent s 56 feet².
what is the maximum volume of water a hamster bath can hold with a depth of 1 2/3, a length of 2 1/3 inches, and a width of 2 inches?
Answers
=========================================
[tex] \frac{5}{3} \times \frac{7}{3} \times \frac{2}{1} = \frac{70}{9} [/tex]
[tex] \frac{70}{9} = 7 \frac{7}{9}[/tex]
[tex]l \times w \times h = v[/tex]
Answer:
[tex]V=7\frac{7}{9} cubic inches[/tex]
Step-by-step explanation:
Given: The length of the hamster bath is [tex]2\frac{1}{3}[/tex] inches, width is 2 inches and the depth is [tex]1\frac{2}{3}[/tex] inches.
To find: The maximum volume of water a hamster bath can hold.
Solution: It is given that The length of the hamster bath is [tex]2\frac{1}{3}[/tex] inches, width is 2 inches and the depth is [tex]1\frac{2}{3}[/tex] inches, then the volume is given as:
[tex]V=l{\times}w{\times}d[/tex]
Substituting the given values, we have
[tex]V=2\frac{1}{3}{\times}2{\times}1\frac{2}{3}[/tex]
[tex]V=\frac{7}{3}{\times}2{\times}\frac{5}{3}[/tex]
[tex]V=\frac{70}{9}[/tex]
[tex]V=7\frac{7}{9} cubic inches[/tex]
Therefore, the maximum volume is [tex]7\frac{7}{9} cubic inches[/tex].
Tom and Arnold both leave the internet cafe at the same time, but in opposite directions. If Tom travels 9mph and Arnold travels 16mph, how long until they are 200 miles apart?
Answers
9x + 16x = 200
25x = 200
x = 8 hours
Work:
First, we create our equation right so its...
9x + 16x = 200
25x = 200
Then, we can just divide 25/200
Which is 8
Answer:
x= 8 h or hours.
Hoping this helps you!
-Arianna
How do I calculate the volume of a circle?
Answers
_____
The volume of a sphere is given by the formula
[tex] V = \frac{4 \pi}{3} r^{3} [/tex]
Fill in the value for the radius and evaluate the expression.
A circle, being 2-dimensional, does not have volume.
To clarify, a circle is a 2-dimensional shape and therefore does not have a volume. However, if you intended to calculate the volume of a 3-dimensional shape such as a sphere or a cylinder that has a circular base, here are the steps:
Volume of a Cylinder
The formula for the volume of a cylinder is:
V = πr²h
Volume of a Sphere
The formula for the volume of a sphere is:
V = 4/3 πr³
What is the value of y?
Answers
Answer:
57
Step-by-step explanation:
Ap3x
Which triangle is it ?
Answers
1. All the triangles are rigth triangles, because they have an angle of 90°. So, let's calculate the others angles of the first one:
Tan(α)^-1= opposite leg/adjacent leg
Opposite leg=5
Adjacent leg=5√3
Tan(α)^-1= 5/5√3
Tan(α)^-1=30°
2. Let's calculate the other angle:
Tan(α)^-1= opposite leg/adjacent leg
Now, the opposite leg will be 5√3 and the adjacent leg will be 5. Then:
Tan(α)^-1= 5√3/5
Tan(α)^-1=60°
As you can see, the angles of first triangle are: 30°,60° and 90°.
on a map, each centimeter represents 45 kilometers. two towns are 135 kilometers apart. what is the distance between the towns on the map
Answers
x cm = 135 km
135/45 = 3 cm
distance between the towns on the map is 3 cm.
i hope this helps :)