Answer:
1. They help you with estimation
2. It makes numbers simpler and easier to do
3. Makes mental maths much quicker
A chemist has three different acid solutions,
The first solution contains 20 % acid, the second contains 35 % acid, and the third contains 55%
acid.
She created 108 liters of a 40 % acid mixture, using all three solutions. The number of liters of
55 % solution used is 3 times the number of liters of 35 % solution used.
How many liters of each solution was used?
The chemist used
liters of 20% solution,
liters of 35 % solution, and
liters of 55 % solution.
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Answer:
36 liters of 20%18 liters of 35%54 liters of 55%Step-by-step explanation:
Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...
a + b + c = 108 . . . . . total number of liters
.20a +.35b +.55c = 0.40·108 . . . . . liters of acid
0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution
__
Solving these three equations by your favorite method gives ...
(a, b, c) = (36, 18, 54)
The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.
_____
Comment on alternate approach
Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...
(3(.55) +1(.35))/4 = 0.50 = 50%
So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.
Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.
__
* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...
x(50%) +(1 -x)(20%) = 40%
x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x
x = (40% -20%)/(50% -20%)
The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.
CAN SOMEONE PLZ HELP ME:))))))))
Hey guys can you help me?
Answer:
850
Step-by-step explanation:
2×400=800
2×20=40
2×5=10
800+40+10=850
8x=-1/2 Whats the answer
Solve for h: A = (1/2)*b*h*
O h = 2*A*b
O h = A *(b/2)
O h = (2*A)/b
0 h = (2+b)/A
Step-by-step explanation:
The answer is the third option
Kaiwan sold 40 tickets for Young Baby Durk NBA for the Howard Homecoming concert. He sold general admission tickets for twenty dollars each and VIP tickets for thirty dollars each. He collected eight hundred and eighty dollars. How many of each kind of ticket did Kaiwan sell?
Answer:
number of general admission tickets sold = 32
Number of VIP tickets sold = 8
Step-by-step explanation:
Total Number of tickets = 40
Cost of general admission tickets = $20
Cost of VIP tickets = $30
Total revenue = $880
Let
x = number of general admission tickets sold
y = number of VIP tickets sold
The equations are:
x + y = 40 (1)
20x + 30y = 880 (2)
From (1)
x = 40 - y
Substitute x = 40 - y into (2)
20x + 30y = 880
20(40 - y) + 30y = 880
800 - 20y + 30y = 880
10y = 880 - 800
10y = 80
y = 80 / 10
= 8
y = 8
Substitute y = 8 into (1)
x + y = 40
x + 8 = 40
x = 40 - 8
= 32
x = 32
number of general admission tickets sold = 32
Number of VIP tickets sold = 8
3 (4x - 2) - 30 = -6 (6 - 2x) - 20
A.Infinite Solutions/Identity
B.No Solution
C.x = 0
D.x = 1
show work please
Answer:
B.
Step-by-step explanation:
3(4x-2)-30=-6(6-2x)-20
12x-6-30=-36+12x-20
12x-36=12x-56
Which number line shows the solution to -6 -(-2)
Answer:
2nd one
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
-6 -(-2) can also mean -6+2 because the (-) in that equation can also mean -1, so a negative time a negative is a positive.
so, there is -6 and ur adding 2 to it, which is -4
Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
А
V = 7(3)h
B
V = *(3h)
CV = +(1.5)h
DV = +(1.5h)
Any help and this please ??
Help ASAP
Write the fraction [tex]\frac{45}{81}[/tex] in simplest form.
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Given
[tex]\frac{45}{81}[/tex] ( divide numerator and denominator by HCF of 9 )
= [tex]\frac{5}{9}[/tex] ← in simplest form
Which statement correctly identifies a local minimum of the graphed function?
Over the interval [–3, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 2.2.
Over the interval [–1, 0.5], the local minimum is 1.
Over the interval [0.5, 2], the local minimum is 4.
Statement which is correctly identifies the local minimum of the graphed function is given by over the interval [tex][-1,0.5],[/tex] the local minimum is [tex]1[/tex].
What is graph?
" Graph is defined as the pictorial representation of the relation between the given variables on the coordinate plane along x-axis and y-axis."
According to the question,
Form the given graph of the function local minimum is given by
a. Over the interval [tex][-3, -2][/tex], the local minimum is [tex]0[/tex]:
From the graph value of y coordinate at [tex]x= -3[/tex] is closest to [tex]-6[/tex]. As per given statement local minimum is zero . [tex]-6 < 0[/tex]
At [tex]-2[/tex] closest to [tex]1[/tex] , [tex]1 > 0[/tex]
Therefore , local minimum [tex]=0[/tex] is not a correct option.
b. Over the interval[tex][-2, -1][/tex], the local minimum is [tex]2.2.[/tex]
From the graph at [tex]-2[/tex] closest to [tex]1[/tex] , [tex]1 \neq 2.2[/tex].
Moving from [tex]-2[/tex] to [tex]-1[/tex] graph is increasing . At [tex]-1[/tex] y - coordinate is equals to [tex]2[/tex].
Again [tex]2\neq 2.2[/tex]
Therefore, it is not a correct option.
c. Over the interval[tex][-1, 0.5][/tex], the local minimum is [tex]1[/tex]
From the graph at [tex]-1[/tex] closest to [tex]2[/tex] ,and keep on decreasing till [tex]x=0[/tex] .
From [tex]0[/tex] to [tex]0.5[/tex] graph keep on increasing.
At [tex]x= 0[/tex] value of y-coordinate is equals to [tex]1[/tex] , which represents the local minimum at [tex]x= 0[/tex] which is in the interval [tex][ -1, 0.5][/tex]
At [tex]x= -1[/tex] y- coordinate is equals to [tex]2[/tex]
At [tex]x= 0.5[/tex] y- coordinate is equals to [tex]2[/tex]
Local minimum [tex]= 1[/tex] at [tex]x=0[/tex]
Therefore, it is a correct option.
d. Over the interval [tex][0.5, 2],[/tex] the local minimum is [tex]4.[/tex]
In the given interval graph keeps on increasing [tex]1[/tex] to [tex]4[/tex] and so on.
It is not a correct option.
Hence, statement which is correctly identifies the local minimum of the graphed function is given by over the interval [tex][-1,0.5],[/tex] the local minimum is [tex]1[/tex].
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PLEEEEEEEEEEEEASE HELP ME WITH THIS! IT IS DUE TOMORROW!!!
Perform the indicated operation.
(-7) · (-5)
-12
-35
12
35
Answer:
35
Step-by-step explanation:
A negative number multiplied by a negative number is positive. Multiplication is repeditive addition.
(-7) * (-5) = -(-7 + -7 + -7 + -7 + -7) or -( -5 + -5 + -5 + -5 + -5 + -5 + -5 ) = 35.
Answer:
35 is the answer I remember my brother telling me that two negitives always makes a positive no matter the symbol
Step-by-step explanation: 7 x 5 = 35 that is really all you have to do. but this is a random tip always remember that two negitives equal a positve also when you add positve to negitive it goes right so say you have -5 + 5 that would equal zero. when you add negitive and negitve numbers it will have a negitive sum
Karen works at a car dealership. She makes only $5 an hour, but for every car she sells, she makes $1,000 in commission. If Karen worked 200 hours this month and made a total of $6,000, how many cars did Karen sell this month?
Answer:
4
Step-by-step explanation:
Which expression represents the area of this figure in square feet
Answer: A im positive its A
Step-by-step explanation: 3 times 2 equals 6 and add that to 3 times 4 which is 12 and you get 18
In efforts of improving their orofit margins, a company is considering creating their own manufacturing plant for their product. It had a start-up cost of 25,000 to build the plant. This plant will drop the production cost down to $15 per item. If each item sells for $50, then how many items would it take to get an overall profit of $100,000 for the year?
Answer:
To get an overall profit of $100,000, then 3,571 items is needed to be produced
Step-by-step explanation:
Mathematically;
Profit = Revenue - Production cost
In the question, we are told that the profit we are expecting is $100,000
Let the number of items to be produced for sales be x items
Now let’s look at the production cost ;
The production cost will be number of items for sale * production cost = 15 * x = $15x
Now, we need to add the start-up cost to the production cost to get the total amount spent on production;
Mathematically the total amount would be = $25,000 + $15x
Let’s look at the revenue;
The revenue will be selling price of each item * price of each item;
Mathematically, that would be 50 * x = $50x
So therefore;
50x - (25,000 + 15x) = 100,000
50x -25,000 -15x = 100,000
35x = 100,000 + 25,000
35x = 125,000
x = 125,000/35 = 3571.42 which is approximately 3,571 items
someone please help me ASAP
Answer:
Step-by-step explanation:
1. 9.6x10^4
2. 7.2x10^8
3. 1.19x10^-7
4. 9.48x10^-3
5. 2.04x10^8
Vance wants to determine if an old photo frame is still rectangular. The height of the frame is
8 inches, the base is 6 inches and the diagonal is 10 inches long. Is the old photo frame still
rectangular? How do you know?
Answer:
The old photo frame is still rectangular
Step-by-step explanation:
Rectangles
The rectangle shape can be identified because it has 4 internal angles of 90° each. The diagonal forms with two adjacent sides a right triangle where the Pythagora's Theorem must stand. Being a and b the length of the sides of the rectangle and d the diagonal, then:
[tex]d^2=a^2+b^2[/tex]
Vince's photo frame has dimensions of 8 inches and 6 inches, with a diagonal of 10 inches. If the above condition is met, then the frame is still rectangular.
Calculating:
[tex]10^2=6^2+8^2[/tex]
[tex]100=36+64[/tex]
[tex]100=100[/tex]
Since the condition is met, the old photo frame is still rectangular
I need help a-sap! Please and thank you!!
Answer:
x = 80 degrees
Step-by-step explanation:
A straight line forms 180 degrees in total. It is given that the first angle is 100 degrees. 180 - 100 = 80, therefore x = 80 degrees
Which statement is false A the inequality sign alwats opens up to the largers number. B the greater number in the equality is always above the number on the vertical number line. C the smaller number is inequality is always located to the left of the other number on the horizontal number line. D inequality sign always open up to a smaller number
Answer:
D inequality sign always open up to a smaller number
Step-by-step explanation:
four times a number p is more than 22
Answer:
[tex]4p\: > 22[/tex]
[tex]four \: times \: a \: number \: p \: is \: \\ more \: than \: 22[/tex]
The expression of inequality four times a number p is more than 22 is
4p > 22.
What is inequality?Inequality compares two non-equal terms of both sides of the inequality sign. There are four types of inequality.
Given statement four times a number p is more than 22.
As it is stated more than we have to form an inequality strictly greater than 22 which is,
4p > 22.
p > 22/4.
p > 5.5.
This number p can also be represented on a real number line with an open circle at 5.5 and extended to infinity.
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2. Rena mixes i cup of blue paint for every cup of red paint to make purple paint.
Enter the number of cups of red paint Rena mixes with 1 cup of blue paint.
Rewrite x5/6 divided by x1/6 in simplest radical form
Ms. Rivera's class hoped to raise $135. They missed heir goal by $8.62. How ip much money did Ms. Rivera's class raise?
1. 144.42
2. 135
3. 126.38
4 127.28
Answer:
126.38
Step-by-step explanation:
$135.00-$8.62=$126.38
Tickets to an amusement park cost $35 for adults and $20 for children. The equation 35x+20y=140 shows how many adults x and children y can visit the amusement park with $140. If no children go, how many adults can go to the amusement park with $140?
A)7
B)5
C)4
D)2
Answer: Four adults
Step-by-step explanation: 4 x 35 = 140. There are no children, so you can just ignore 20y (I hope this helps!)
If no children will go to the amusement park then a total of 4 adults can go to the amusement park for $140. Hence, option C is correct.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.
You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement.
The given equation is :
35x + 20y = 140
Cost of adults to go to the amusement park, (x) = $35 and,
Cost of children going to the amusement park, (y) = $20.
If no children are going to the amusement park, then the number of adults who can go to the park is :
35x + 20(0) = 140
35x = 140
x = 140/35
x = 4.
Hence, this concludes that option C is correct.
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To quickly find the product of a whole number time 1000, add *Blank* Zeroes to the number
Answer:
Add three zeros to the end.
Step-by-step explanation:
When you add three zeros, the result is equivalent to when multiplying by 1000. For example, 20 times 1000 is 20,000.
Hi! I believe your answer is 3 zeros. For example, 7 × 1,000 = 7,000 (add 3 zeros). I hope this helps you! Good luck and have a great day/night. ❤️✨
what's the value for x makes this equation true 3/5 X-0.5=19
Answer:
what's the value for x makes this equation true 3/5 X-0.5=19 HERE YOU GO!!
Step-by-step explanation:
-5x - (-7 - 4x) = -2(3x - 4)
-5x + 7+ 4x = -6x + 8
-x + 7= -6x + 8
5x = 8 - 7
5x = 1
x = 1/5
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of x that makes the equation 3/5x - 0.5 = 19 true is 32.5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
3x = 6 + 5 is an equation.
We have,
3/5x - 0.5 = 19
Add 0.5 on both sides.
3/5x = 19 + 0.5
3/5x = 19.5
Multiply 5/3 on both sides.
x = 19.5 x 5/3
x = 32.5
Thus,
The value of x that makes the equation 3/5x - 0.5 = 19 true is 32.5.
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Rachel is a veterinarian. She charges $20 as a base and $10 for each animal that she vaccinates.
Let x be the number of animals vaccinated and y be the total amount charged. Write the equation.
Answer:
Step-by-step explanation:
y = total number charged.
x = number of animals vaccinated.
If she charges $20 as a base, this means it is a constant value.
She also charges $10 for each animal vaccinated, this can be written as 10x.
Therefore the equation for the total number charged (y) can be written as:
Total amount charged = $20 + $10 for every animal vaccinated.
y = 20 + 10x
2 3/8x3 3/7 please answer
Answer:
171/56
Step-by-step explanation:
convert the mix number to an improper fraction then calculate your income
Answer:
I think it would be 8 1/7 if im wrong im srry!
Step-by-step explanation: