A chemist is weakening an 80% solution by adding a 40% solution. How much of each should he use to get 100 milliliters of a 50% solution? the chemist’s problem is modeled by the system: {0.80x+0.40y=0.50⋅100 (x+y=100 where x is the number of milliliters of 80% solution and y is the number of milliliters of 40% solution.
Answers
Answer: The chemist needs to mix 25 milliliters of the 80% solution with 75 milliliters of the 40% solution to get 100 milliliters of a 50% solution.
Step-by-step explanation:
Let x be the number of milliliters of 80% solution needed, and y be the number of milliliters of 40% solution needed.
From the first equation, we can write:
0.80x + 0.40y = 0.50(100)
Simplifying this equation, we get:
0.80x + 0.40y = 50
Dividing both sides by 0.20, we get:
4x + 2y = 250
From the second equation, we know that:
x + y = 100
Solving this equation for y, we get:
y = 100 - x
Substituting this expression for y into the first equation, we get:
4x + 2(100 - x) = 250
Simplifying this equation, we get:
2x + 200 = 250
Subtracting 200 from both sides, we get:
2x = 50
Dividing both sides by 2, we get:
x = 25
Substituting this value for x into the equation y = 100 - x, we get:
y = 75
Therefore, the chemist needs to mix 25 milliliters of the 80% solution with 75 milliliters of the 40% solution to get 100 milliliters of a 50% solution.
Related Questions
pls help again with these chapes
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Drag each expression to show whether it is equivalent to 36x+9
or 9(4x−1)
.
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In order to find out what 36x + 9 is equivalent to,, we must factor out 9 from the expression. Once we do this you will find that this expression is equivalent to 9(4x + 1),, or option E.
Next we will look at the expression 9(4x-1). In order for us to find out the equivalent to this expression,, we must first multiply each term in the parenthesis by 9.
9 × 4x - 9
Now calculate the product
36x - 9
This means that the equivalent for this expression is
36x - 9,, or option A.
Lastly,, we will look at the final expression given which is 4(9x + 2). The first step for finding the equivalent of this expression is to multiply the numbers in the first parenthesis together.
(36x) + (4 × 2)
Now multiply the numbers in the second parenthesis together.
(36x) + 8
Remove the parenthesis
36x + 8
Now factor out 4 from the expression to get your final answer.
4(9x + 2)
This means that the last expression is equivalent to 4(9x + 2),, or option C.
Let me know if you have any further questions
What is likely to have a mass close to 3 kilograms
A. 5-year-old-child
B. A Bowling ball
C. A lemon
D. A lion
Answers
B. A Bowling ball
3 kilograms is approximately 7 pounds, the weight of most Bowling balls
B. A Bowling ball
Step-by-step explanation:
Options A and D are most likely to weigh more than 3kg and option C will most likely weigh less but option B can weigh up to 3kg
What's the median for these set of numbers and do it step by step explanation. 3,2,3,4,3,5,7,5,4
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Solve the word problem below
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The distance is going by 30 and then u divide that by 60
Explanation
150+30=180 distance
180/60=3 hours
U go like this till u get till 4.5 hours
ANSWER? PLSSSSSSSSSSSSSSSSSSS
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Answer: I might be wrong, but I think its just $53.50
Honors Refresher Quiz #8 1. If a figure is dilated by a scale factor of 12, the area of the figure will change by a factor of
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Answer:144
Step-by-step explanation:
When area is dilated you have to multiply the dialation factor by itself, in this case (12 x 12)
Can someone help?- I will mark brainliest !!
Answers
HELPPPPPPPP
If f(x) = 2x - 5, then f(4) is _____.
17
3
4
5
If f(a) = 3a – a2, which of the following are not true statements?
Select all that apply.
f(-5) = -40
f(4) = -4
f(-1) = 2
f(0) = 3
f(3) = 0
Answers
Answer:
1st is 3, 2nd i didnt learn this sorry
Step-by-step explanation:
F(4)=2(4)-5
f(4)=8-5
So, f(4) =3
Question number 2 is a bit difficult I’m sorry.
Triangle ABC is a scale drawing of Triangle XYZ, as shown.
Based on the information shown in these triangles, which of the following is a true statement?
A) The length of side XZ is 11.5.
B) The length of side XZ is 28.
C) The measure of angle A is equal to the measure of angle Z.
D) The measure of angle A is not equal to any of the angle measures of Triangle XYZ.
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B) false
C) true
D) false
Could someone please help me
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Answer: Answer:
Step-by-step explanation: Step-by-step explanation:
A startup software company’s total investment for the first two years is $24,894. Write and solve an equation to find the investment for the second year if the first year’s investment is $12,955.
Answers
Answer:x=9689
Step-by-step explanation:based on given conitions,formulate:13205+x=22894
Answer:
12,955 + x = 24,894
x = 11,939
Marvin was in charge of ordering sodas for the class fundraiser. He made a circle graph to show the number of each size of soda. However, he accidently put his work in the graph showing the degree measures he used to make the chart instead of the number of sodas he needed and he threw away his original paper showing the number of each. Help him figure out how many of each size of soda he needs to order by answering the questions below. (Hint: There are 360 degrees total in a full circle.)
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Answer:
for a: small=17% medium=38% large=33% extra large=13%
Step-by-step explanation:
what is the surface area
Answers
Answer:
75 cm^3
Step-by-step explanation:
The small prism is 3x smaller than the large prism (look at lengths given).
Thus, as the surface area of the small prism is 25 cm^3 the larger prism will be 3x as much surface area.
25 x 3 = 75
Therefore, the surface area will be 75 cm^3.
Answer: 225
Step-by-step explanation:
9 x 25 I believe I’m so sorry if it’s wrong but the s2 should be the long side
What changes would you make to solve any problems you might have in your society?
Answers
What are the coordinates of the image of (1, 3), where R(−3, 5) is the center of dilation with scale factor 0.5?
PLS ANSWER QUICK
Answers
Answer:
the coordinates of the image D are (-1, 4)
Step-by-step explanation:
To find the coordinates of the image D, we need to apply the dilation transformation centered at R(-3, 5). Let the scale factor be k.
The x-coordinate of D will be shifted k times the distance between 1 and -3, which is 4 units, from the x-coordinate of R, which is -3. So we have:
0.5 = -3 + k(4)
Solving for k, we get:
k = 1.375
Similarly, the y-coordinate of D will be shifted k times the distance between 3 and 5, which is 2 units, from the y-coordinate of R, which is 5. So we have
R: (x, y) = (-3, 5)
D: (x, y) = (-3 + 1.375(1 - (-3)), 5 + 1.375(3 - 5))
D: (x, y) = (-1, 4)
Therefore, the coordinates of the image D are (-1, 4), which is option D.
Choose one point on the scatterplot. What does it represent?
What type of data is best for scatter plots? please don't give a short once sentence explanation
Answers
Answer:
decrease
Step-by-step explanation:
this graph is showing a decorative response to whatever content.
How can we use the distributive property to find an expression equivalent to 4(5−3x)
? Place the steps in order.
Answers
Answer:
Multiply 4 by 5 and 4 by 3x
Step-by-step explanation:
4 ( 5 -3x ) =
4 x 5 + (4)(-3x)
Answer:
4(5-3x)
4(5) -4(3x)
20-12x
Could someone help me fast
Answers
Answer:
A movie is $2.5
A video game is $6
Step-by-step explanation:
Pre-SolvingWe are given that Ann had rented 2 movies and 5 video games for a total of $35.
We also know that she also rented 8 movies and 3 video games for a total of $38.
We want to know how much a movie costs, and how much a video game costs.
If a movie costs x dollars, then a video game costs y dollars.
This means that costwise, 2 movies will cost 2x, and 5 video games will be 5y.
8 movies will cost 8x, and 3 video games will cost 3y.
So, we will have two equations:
2x + 5y = 35
8x + 3y = 38
We now have this system of equations, which we can solve.
Let's solve this by elimination.
To eliminate, we need to clear one of the variables, and solve for the other one.
To do this, we need to make sure that one variable has the same coefficient with opposite signs (e.g. -3x and 3x). We might need to multiply one equation by a number in order to achieve this.
We can multiply 2x + 5y = 35 by -4.
-4(2x + 5y) = -4(35)
-8x - 20y = -140
We can rewrite the equations:
-8x - 20y = -140
8x + 3y = 38
They can be added together. The result will be:
-17y = -102
Divide both sides by 017.
y = 6
We found y, but now we need to find x.
We can substitute 6 as y into 2x + 5y = 35 or 8x + 3y = 38 to find x.
Taking 2x + 5y = 35 for instance:
2x + 5(6) = 35
2x + 30 = 35
Subtract 30 from both sides.
2x = 5
Divide both sides by 2
x = 2.5
Recall that x = price of a movie, and y = price of a video game.
Therefore, a movie is 2.5 dollars, and a video game is 6 dollars.
and a snack is $6
Rita gets paid $16 per hour for the first 8 hours she works each day. She earns 1 1/2 times her hourly pay rate for time she works over 8 hours each day. Rita′s work day for Monday is described in the list. worked from 8:00 a.m. to 12:00 p.m. took a 30-minute lunch break worked until 6:00 p.m. Rita does not get paid for her lunch break. How much money did Rita earn for the time she worked on Monday? Show or explain all of the steps you used to determine your answer.]
Answers
Answer: $158
Step-by-step explanation:
$16(8) + $24(1 ¼) = $128 + $30 = $158
Rita earned a Total of $196 for the time she worked on Monday.
To determine how much money Rita earned for the time she worked on Monday, we need to calculate her earnings for each portion of the day separately.
1. From 8:00 a.m. to 12:00 p.m. (4 hours):
Rita worked for 4 hours within the first 8 hours, so she earns her regular rate of $16 per hour for this time:
Earnings = 4 hours * $16/hour = $64.
2. From 12:30 p.m. to 6:00 p.m. (5.5 hours):
Rita worked for 5.5 hours beyond the initial 8 hours, so she earns 1.5 times her regular rate for each of these hours:
Earnings = 5.5 hours * ($16/hour * 1.5) = $132.
Now, we can sum up Rita's earnings for both periods:
Total earnings = Earnings from the first period + Earnings from the second period
Total earnings = $64 + $132
Total earnings = $196.
Therefore, Rita earned a total of $196 for the time she worked on Monday.
For more questions on Total .
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80 points ★ plsss answer these worded problems !!
★ / mrs . green has 8.25 cups of flour for her cooking class. Hector uses 3.75 cups of flour to bake cookies . how much flour is left ?
★ / mr . trang bought 15.5 ft of rope to make a swing . after making the swing , 3.375 ft of rope are left . how much rope did mr . trang use in the swing ?
★ / a street sign is attached to a 92.75 in long pole . the pole is buried 24.25 inches below ground . whats the length of the pole above ground ?
★ / kim lip ( haha ) filled a pitcher with 259/12 [fraction] ounces of water . She
spilled 0.25 ounce when she placed the pitcher on the
table . how much water is left in the pitcher ?
★ / travis is swimming 3.25 feet below the surface of the
water . connor is swimming 5.75 feet below the surface
of the water. how far apart are travis and connor ?
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Answer:
1: 4.5 cups of flour
2: 12.125 ft of rope
3: 68.5 inches above ground
4: 21.3333..... ounces of water
5: 2.5 ft below the surface
Step-by-step explanation:
1: 8.25-3.75=4.5
2: 15.5-3.375=12.125
3: 92.75-24.25=68.5
4: (259÷12)-.25=21.33333.....
5: 5.75-3.25=2.5
Help asap!!! Easy math!!! Offering brainiest!!!
Answers
Answer:
64
27
6
15
Step-by-step explanation:
64 is a cube and is even,
27 is a cube and not even,
6 is not a cube and is even,
and finally 15 is a not a cube and is not even,
he number line shows the solution set of which inequality?
A horizontal number line is labeled from 51 to 52. There is a closed circle at 51.52, and the number line is shaded to the right of 51.52.
A. j/4.6 > 11.2
B. j/1.5 > 16.3
C. j/12.7 > 19.6
D. j/1.4 > 1.1
Answers
Mrs. Irons places the names of each of her four children in a hat at one time. She randomly draws a name, places it back in the hat, and draws again. The results are shown in the table below.
What is the experimental probability of selecting the name Alex?
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Answer:
As a Fraction : 4/10
As a Decimal : 0.4
Four swimmers are training for a relay race. Each day they practice by swimming at least 1,600 yards total. The friends evenly divide the number of yards they swim.
Write and solve an inequality to determine how many yards each friend will swim. Show all your work.
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Step-by-step explanation:
Saturn's moon, Titan, has a radius of 2575 kilometers, which is covered by a 600-kilometer atmosphere. How much of the moon's volume is atmospheric haze?
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Answer:
approximately 4.57 × 10^10 km^3 of Titan's moon is atmospheric haze.
Step-by-step explanation:
The answer is about [tex]4.57[/tex] × [tex]10^1^0[/tex] [tex]km^3[/tex] of the titan moons atmospheric haze.
Step-by-step explanation:
I did the test and got it right
hope this helps :)
Use equivalent fractions to order these fractions from least to greatest: 2 over 3 , 1 over 2, 4 over 12, 5 over 6 . Explain the steps you took to find your answer.
Answers
Answer:
so u take 4/12 and do it to 1/3 then try to do lest to greatest
Step-by-step expla
2/3 5/6 1/2 1/3 try
Solve for x.
A) 30
B) 45
C) 60
D) 90
Answers
2x+x=90
3x=90
X=30
A
Solve the word problem below
Answers
Answer:
View the image above
Step-by-step explanation:
Distance = 60 miles per hour
Time = ?
Distance = 150
Time = 2/120 × 150 = 2.5
Solve the rest!
Have a nice day!!!
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