To make 30 liters of a 60% solution from 40% and 70% solutions, set up two simultaneous linear equations representing volume and concentration; solve them to find the required volumes.
Explanation:To solve the question posed by Gabe, a nuclear physicist, we will need to use the concept of mixtures in Mathematics. The total volume he needs is 30 liters of a 60% acid solution, and he has available 40% and a 70% acid solutions.
The solution to this problem involves setting up two equations, one for the total volume and second for the amount of acid.
Let's denote the volume of the 40% solution by x and the volume of the 70% solution by y. Our first equation based on volume is: x + y = 30 (because total volume needed is 30 liters).
Our second equation represents the fact that the volume times the percentage of acid present (converted to a decimal) for each solution should match up to the total volume times the overall percentage of acid (also converted to a decimal) in the final 60% solution. This gives us: 0.4x + 0.7y = 30*0.6.
Solving these two linear equations simultaneously using methods such as substitution or elimination will give us the value of x and y, which are the required liters of 40% solution and 70% solution respectively.
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name the property of real numbers illustrated by the equation (2+ √5) + 3=2 + (√5+3)
please help
Answer:
it's associatively property of addition
(a+b)+c= a+(b+c)
The height of a triangle is twice it's base. If the area of the triangle is 40 cm squared, what is the measure of it's height
What is the volume of this rectangular prism?
Answer:
The answer is B. 54 cm
Step-by-step explanation:
When you find the volume of a rectangle you have to multiply the length, width, and height. The length is 9, width 3, and height 2. When you multiply them together you'll get 54
what is the coefficient of determination for this data set.....the answer is 0.91
The coefficient of determination for this data set would be 0.91
What is Correlation Coefficient ?A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables. In other words, it reflects how similar the measurements of two or more variables are across a dataset.
The correlation coefficient for this data set will be positive, since the dependent variable increases as the independent variable decreases.
Since the data appears to be fairly linear, the correlation coefficient will be close to 1 which means 0.91 is our best choice.
Hence, The coefficient of determination for this data set would be 0.91
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Which of the two real numbers are greater? The square root of 3 or 1/3
Answer:
√3 is greater than 1/3:
√3 = about 1.7
1/3 = about .3
The square root of 3 is greater than 1/3.
To determine which of the two real numbers is greater, we can compare their values directly. The square root of 3 is a well-known irrational number, and its approximate value is 1.732. On the other hand, 1/3 is a rational number with a value of approximately 0.333.
Let's compare the two:
- The square root of 3: [tex]\sqrt(3)[/tex] = 1.732
- One third: 1/3 = 0.333
It is clear that 1.732 (the approximate value of √3) is greater than 0.333 (the approximate value of 1/3). Therefore, the square root of 3 is greater than 1/3.
if g is the midpoint of FH and FH =6y-2 find y
Answer:8
Step-by-step explanation: trust me
The relationship between y and x, given that g is the midpoint of FH is y = (1/3)x + (1/3).
If g is the midpoint of FH, it means that FH is divided into two equal segments, FG and GH, such that FG = GH.
Given that FH = 6y - 2, set up an equation to represent this:
FH = FG + GH
Substituting the values we know:
6y - 2 = FG + GH
Since FG = GH then
6y - 2 = x + x
Now, combine like terms:
6y - 2 = 2x
To find the value of y, isolate it on one side of the equation:
6y = 2x + 2
Now, divide both sides by 6 to solve for y:
y = (2x + 2) / 6
y = (2/6)x + (2/6)
y = (1/3)x + (1/3)
So, y is equal to (1/3)x + (1/3).
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What is the solution set of 4x2 - 36 = 0?
4x^2 - 36 = 0
4x^2 = 36
x^2 = 36/4
x^2 = 9
sqrt{x^2} = sqrt{9}
x = - 3 and x = 3
What is the volume of the right square pyramid shown?
Answer:
C. 32 cm³
Step-by-step explanation:
[tex] {a}^{2}\frac{h}{3} = V[/tex]
[tex]({4})^{2}( \frac{6}{3}) = (16)(2) = 32[/tex]
a → length\base edge
I am joyous to assist you anytime.
Answer:
Step-by-step explanation: To find the area of the pyramid shown, we can first start by finding the area of the base. To find the area of the base, we can multiply the length by the width. Notice that both the length and the width of a square are equal so the area of a square will be equal to the length of a side multiplied by the length of a side.
Area = Length x Width = (side) (side)
Area = Side²
(4 cm²) = 16 cm².
Therefore, the area of the bases is 16 cm².
Now, let's finish the problem.
Image provided.
The graph shows the relationship between the late fines the library charges and the number of days late
Answer:
[tex]y=0.25x[/tex]
Step-by-step explanation:
We are given that a graph which shows the relationship between the late fines the library charges and the number of days late.
From given graph we can see that
The graph passes through the points (2,0.5) and (10,2.5).
We have to find the equation for the relationship.
Slope formula:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
By using the formula
Slope of graph=[tex]m=\frac{2.5-0.5}{10-2}[/tex]
Slope of graph=m=[tex]\frac{2}{8}=\frac{1}{4}[/tex]
Point slope- form:[tex]y-y_1=m(x-x_1)[/tex]
We have [tex]y_1=2.5,x_1=10[/tex]
Substitute the values then we get
The equation of for the relationship
[tex]y-2.5=\frac{1}{4}(x-10)[/tex]
[tex]y-2.5=0.25x-2.5[/tex]
[tex]y=0.25x-2.5+2.5=0.25x[/tex]
Hence, the equation for the relationship is given by
[tex]y=0.25x[/tex]
today my i am twice my daughters age. in 20 years i will be 1.5 times her age how old is she
Good morning ☕️
______
Answer:
She is 20 years old
____________________
Step-by-step explanation:
Let x be the age of the daughter.
Let y be the age of the mother.
then , we have to solve the system:
y=2x (1)
y+20=1.5(x+20) (2)
If we substitute y by 2x in the second equation we get :
(2) 2x+20=1.5(x+20) ⇔ 2x+20=1.5x+30 ⇔ 2x-1.5x=30-20
⇔ 0.5x=10 ⇔ x=20.
By the way the mother’s s age = 40 years.
:)
A trust fund worth $25,000 is invested in two different portfolios, this year, one portfolio is expected to earn 5.25% interest and the other is expected to earn 4%. Plans are for the total interest on the fund to be $1,150 in one year. How much money should be invested at each rate
Answer:
The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x ------> the amount of money that should be invested at the rate of 5.25%
25,000-x -----> the amount money that should be invested at the rate of 4%
in this problem we have
[tex]t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150[/tex]
substitute in the formula above
[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]
[tex]1,150=x(0.0525*1)+(25,000-x)(0.04*1)[/tex]
Solve for x
[tex]1,150=0.0525x+1,000-0.04x[/tex]
[tex]0.0525x-0.04x=1,150-1,000[/tex]
[tex]0.0125x=150[/tex]
[tex]x=\$12,000[/tex]
[tex]|$25,000-x=\$13,000[/tex]
therefore
The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000
Answer:
Step-by-step explanation:
Let x be the investment at 5.25% and y at 4%
Then we have
[tex]x+y =25000\\5.25x+4y = 115000[/tex]
We have to solve this system to get x and y
Multiply I equation by 4
[tex]100000=4x+4y\\115000=5.25x+4y\\-----------------------------\\15000 = 1.25x\\x = 12000\\y =25000-12000 = 13000[/tex]
12000 should be invested in 5.25% and 13000 in 4% interest.
The diameter of a basketball is 9.47 inches. What is the length of 12 basketballs lined up next to each other?
A) 112.92 inches B) 21.47 inches
B) 116.88 inches C) 108 inches
Answer:
B) 116.88 inches
Step-by-step explanation:
we know that
To find out the length of 12 basketballs lined up next to each other, multiply the diameter of one basketball by 12
[tex]12(9.47)=113.64\ in[/tex]
therefore
The logical answer between the options is 116.88 inches, because the length cannot be less than 113.64 in
Let find x=3x+1 and g x=1-5x
The corresponding composite function for (f∘g)(x) include the following: (f∘g)(x) = 4 - 15x.
In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.
In this exercise, we would determine the corresponding output values for the given composite function by using the substitution method as follows;
f(x) = 3x + 1
g(x) = 1 - 5x
(f∘g)(x) = 3(1 - 5x) + 1
(f∘g)(x) = 3 - 15x + 1
(f∘g)(x) = 4 - 15x.
Complete Question:
Let f(x)=3x+1 and g(x)=1-5x. Find (f∘g)(x).
How do I solve the rest of this problem?
Answer:
Step-by-step explanation:
continuing from the 3rd line....
10x - 1 = 10x + 8 (subtract 10x from both sides)
10x - 10x - 1 = 10x -10x + 8
-1 = + 8 (this last line is not part of the solution but i'm showing it here so you can see what is going on, obviously -1 cannot be 8)
Since -1 ≠ 8, the equation has no (i.e zero) solutions
Help! I need help with this math problem. Only need to to D! (Will mark brainliest if you do all of them, though. :])
Answer:
Answer to D: 3/5
Step-by-step explanation:
There are 5 songs.
And 3 of them have the word "Mama" in the title.
Make 5 the total amount of songs and 3 songs are how many times the word "Mama" appears once in each song.
Hong traveled 37.9 miles each day for the past 6 days. How many miles did he travel in all?
Answer:
227.4 miles
Step-by-step explanation:
If Hong travelled 37.9 each day, then in 6 days :
37.9 × 6 = 227.4 miles
Answer:
227.4 miles hope this helps :3
What fraction represents 0.1875 ft?
Answer:
There is not much that can be done to figure out how to write 0.1875 as a fraction, except to literally use what the decimal portion of your number, the .1875 , means. Since there are 5 digits in 1875 , the very last digit is the "100000th" decimal place. So we can just say that .1875 is the same as 1875/100000.
Step-by-step explanation:
Answer:
fraction decimal
3/16 0.1875
hope this helps :3 & sorry if its wrong
If the two spinners below are spun, what is the probability that the numbers will match
Answer:
Yes, you are correct :)
Answer:
1/4
Step-by-step explanation:
Please answer this correctly
Answer:
Step-by-step explanation:
41:2
41:43
This is because the question wants the number of burgers with onions to the total amount of burgers. The question already states 41 have onions. It also states the total amount of burgers is 43. Therefore, your answer is 41:43.
use equivalent ratios to find unknown value plz halp!!!!
Answer:
21
Step-by-step explanation:
It might be 21/30 , hope it helps though :)
Answer:
21 is the un known value.
Step-by-step explanation:
10 times 3=30
7 times 3 = 21
so 21/30 is your answer.
The table shows the revenue for four companies in 2013.
What is the difference in revenue between the company with the greatest revenue and the one with the least revenue?
A. 2.2 × 10 (to the power of) -3
B. 2.2 × 10 (to the power of) 3
C. 6.79 × 10 (to the power of) 6
D. 6.79 × 10 (to the power of) 7
NEED HELP ASAP!
Greatest revenue = Company D with 6.8 x 10^7
Least revenue = Company C with 9.0 x 10^4
Difference = 6.8 x 10^ 7 - 9.0 x 10^4
= 68000000 - 90000
= 6.79 x 10^7
Answer is D
The difference in revenue between the company with the greatest revenue and the one with the least revenue is 6.79 x [tex]10^7[/tex]
Option D is the correct answer.
We have,
From the table,
D has the greatest revenue.
C has the lowest revenue.
Now,
D revenue = 6.8 x [tex]10^7[/tex]
C revenue = 9 x [tex]10^4[/tex]
The difference in revenue between the company with the greatest revenue and the one with the least revenue.
= 6.8 x [tex]10^7[/tex] - 9 x [tex]10^4[/tex]
= 67910000
= 6791 x [tex]10^4[/tex]
= 6.79 x [tex]10^7[/tex]
Thus,
The difference in revenue between the company with the greatest revenue and the one with the least revenue is D. 6.79 x [tex]10^7[/tex]
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Name the vertex and sides of each angle
Answer: 7) vertex = ∠H sides = HG and HI
8) ∠H, ∠IHG, ∠GHI, ∠4
9) ∠HVI, ∠HVJ, ∠IJV
NOTES:
1) The vertex is the point where the two segments, rays, or lines connect.
2) When naming an angle, the vertex is ALWAYS written in the middle with the sides on the left and right.
401,378 in word form
Answer:
Step-by-step explanation:
four hundred one thousand, three hundred seventy-eight
7. Triangle RPQ is similar to triangle WPV. Find the missing length PW.
Answer:
PW = 11
Step-by-step explanation:
Given that the triangles are similar then the ratio of corresponding sides are equal, that is
[tex]\frac{RQ}{WV}[/tex] = [tex]\frac{RP}{PW}[/tex] ← substitute values
[tex]\frac{12}{6}[/tex] = [tex]\frac{22}{PW}[/tex] ( cross- multiply )
12PW = 132 ( divide both sides by 12 )
PW = 11
4. Mimi has 15 cousins. All but 3 of her cousins live in Texas what percent of her cousins live in Texas?
Write a proportion and solve Show your work
It’s Not sure on the right answer
Answer:
20%
Step-by-step explanation:
15= 100%
3/15 = 1/5
100% divided by 5 is 20%
proportion: 1/5
Mimi has 15 cousins, and after subtracting the 3 who do not live in Texas, 12 of her cousins live there. By setting up a proportion, we calculate that 80% of Mimi's cousins live in Texas.
Mimi has 15 cousins, and all but 3 live in Texas. To find the percentage of her cousins that live in Texas, we first need to calculate the number of cousins who live in Texas. We do this by subtracting the 3 that do not live in Texas from the total number of cousins, which is 15.
Number of cousins living in Texas = Total cousins - Cousins not living in Texas
Number of cousins living in Texas = 15 - 3 = 12
Next, we set up a proportion to find the percentage. The proportion is based on the number of cousins in Texas over the total number of cousins:
Proportion = (Number of cousins in Texas / Total number of cousins) ×100%
Percentage = (12 / 15)× 100%
Percentage = 0.80 × 100%
Percentage = 80%
Therefore, 80% of Mimi's cousins live in Texas.
Simplify 6^4 x 6^3 divided by
6^-1
Answer:
6^6
Step-by-step explanation:
6^4 x 6^3 / 6^-1
exponent rule add exponents 4+3=7 so 6^7
exponent rule subtract exponents 7-(-1) so
Answer= 6^8
Answer:
1644624
At least that's what i got on my calculator
585,156.22 nearest thousand
Find the value that makes the ratios equal. 51/18=x/6
4x + 6 over 2 equals 3x - 15 over 3
Answer:
x = -8Step-by-step explanation:
[tex]\dfrac{4x+6}{2}=\dfrac{3x-15}{3}\qquad\text{cross multiply}\\\\3(4x+6)=2(3x-15)\qquad\text{use the distributive property}\\\\(3)(4x)+(3)(6)=(2)(3x)+(2)(-15)\\\\12x+18=6x-30\qquad\text{subtract 18 from both isdes}\\\\12x=6x-48\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x=-48\qquad\text{divide both sides by 6}\\\\x=-8[/tex]
x=-8
Given equation is (4x+6)/2=(3x-15)/3, we need to find x
What is cross multiplication method?Multiply the numerator of one fraction to the denominator of other and denominator of the first term to the numerator of another term is called Cross Multiplication Method.
Given, (4x+6)/2=(3x-15)/3
Apply cross multiplication method
3(4x+6)=2(3x-15)
12x+18=6x-30
12x-6x=-30-18
6x=-48
Divide both sides by 6
x=-8
Therefore value of x in (4x+6)/2=(3x-15)/3 is '-8'.
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Andy ran the 100-meter dash in 13.4 seconds. Below is a table showing Andy's heart rate during the race. What parent function does Andy's data best represent? Time (in seconds) Heart Rate 0 61.1 5 85.6 9 105.2 11 115 13.5 122.3 A. a linear function B. a cubic function C. a square root function D. an absolute value function