Final answer:
To achieve a 15 percent saline solution by mixing a 10 percent solution with a 25 percent solution, we calculate that we need to add 1.5 liters of the 25 percent saline solution to the initial 3 liters of the 10 percent solution.
Explanation:
To solve the problem, we need to calculate how much of a 25 percent saline solution should be added to 3 liters of a 10 percent saline solution to get a 15 percent saline solution. We'll use the concept of the conservation of mass of the solute (NaCl) and set up an equation to find the required volume of the 25 percent solution.
Let V be the volume of the 25 percent solution we need to add. The amount of NaCl in the 10 percent solution is (0.10)(3 L), and the amount of NaCl in the 25 percent solution is (0.25)(V). The resulting solution has a concentration of 15 percent, so the amount of NaCl in the final solution will be (0.15)(3 L + V).
Now we set up our equation based on the mass of NaCl being equal before and after the addition of the 25 percent solution:
(0.10)(3 L) + (0.25)(V) = (0.15)(3 L + V)
Solving this equation:
0.30 + 0.25V = 0.45 + 0.15V
0.25V - 0.15V = 0.45 - 0.30
0.10V = 0.15
V = 0.15 / 0.10
V = 1.5 L
Therefore, 1.5 liters of a 25 percent saline solution must be added to the initial 3 liters of a 10 percent solution to obtain a 15 percent saline solution.
Work out problem in picture
for x multiply 6 by sin(45) = 3sqrt(2) = 4.2426
for y since it is a right triangle with 45 degree angle both legs are equal
so y = x
Given the points (2,k) and (0,−6) for which values of k would the distance between the points be square root of 5
?
Given the points (2,k) and (0,−6) for which values of k would the distance between the points be √5 ?
We will find that there are two possible values of k;
k = -5 and k = -7.
We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Here we have the points (2,k) and (0,−6), then the distance will be given by:
[tex]d = \sqrt{(2 - 0)^2 + (k - (-6))^2} = \sqrt{4 + (k + 6)^2}[/tex]
Now we want to find the value of k such that the distance is equal to √5, then we need to solve:
[tex]\sqrt{5} = \sqrt{4 + (k + 6)^2}[/tex]
removing the square root in both sides we get:
[tex]5 = 4 + (k + 6)^2\\\\5 - 4 = (k + 6)^2\\\\1 = (k + 6)^2[/tex]
Then we can see that (k + 6) = ± 1, solving these two equations (one for each sign) we get:
k + 6 = 1
k = 1 - 6 = -5
and
k + 6 = -1
k = -1 - 6 = -7
Then we found two possible values of k:
k = -5
k = -7
Below you can see the graph of the points A = (2, -5), B = (0, -6) and C = (2, -7)
If you want to learn more about distances, you can read:
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what is the domain and range of each function graohed below?
The scale on a map indicates that 1 in = 2.5mi. How far apart are two cities that measure 2.5 ft apart on the map? A. 60 miles B. 6.25 miles C. 75 miles D. 90 miles
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
2x+9y=-30;(-8,0
Use the discriminant of x^2+4x-32=0 to describe the roots
The formula for discriminant is:
discriminant = sqrt (b^2 – 4 a c)
Where,
a = 1
b = 4
c = -32
Therefore:
discriminant = sqrt (4^2 – 4 (1) (-32))
discriminant = sqrt 144
discriminant = 12
Since the discriminant is a positive real integer, then there are 2 unequal roots or 2 distinct real roots.
Find the height of the figure below if the volume is 480.66^3 cm.
volume = PI x r^2 x H
you know the volume and the radius ( 12/2 = 6)
480.66 =3.14 x 6^2 x H
480.66 = 113.04 x h
h = 480.66/113.04 = 4.252
round off as needed.
Simplify the product using the distributive property. (-4h +2)(3h +7)
A.
-12h 2 - 22h + 14
B.
-12h 2 - 34h - 14
C.
-12h 2 + 34h - 14
D.
-12h 2 + 22h + 14
please help
Answer:
A. -12h² - 22h + 14
Step-by-step explanation:
(-4h +2)(3h +7) = -4h(3h +7) +2(3h +7) . . . . . . . (a +b)c = ac +bc
= (-4h)(3h) + (-4h)(7) + (2)(3h) + (2)(7) . . . . . . . a(b +c) = ab +ac . . . (twice)
= -12h² -28h +6h +14
= -12h² -22h +14 . . . . . . . . collect terms
88 is the product of
8
and Jenny's score
product means multiplication
88 is the product of 8 multiplied by a number
so 88/8 =11
jenny's score is 11
why is it useful to factor out the gcf first when factoring
Factoring out the Greatest Common Factor (GCF) simplifies the expression, making further manipulation and factoring simpler. It reduces complexity, much like simplifying fractions in arithmetic, and aids in revealing patterns for easier factoring. This step also minimizes calculation errors and assists in proper unit analysis during problem-solving.
Factoring out the Greatest Common Factor (GCF) is a critical step in the process of factoring algebraic expressions. This is important because it simplifies the remaining expression, making it easier to manipulate and factor further if necessary. It is similar to simplifying fractions before performing operations with them; the process becomes cleaner and more straightforward.
For example, when you have an equation with multiple terms, each with a common factor, factoring out this GCF reduces the complexity of the terms, possibly revealing a more obvious pattern or structure that can then be factored more easily. Additionally, removing the GCF early in the process can prevent calculation errors and make other factoring techniques, like the difference of squares or trinomial factoring, more apparent and easier to apply.
In cryptography, algorithms rely on the principle that multiplying large numbers is computationally simple, whereas factoring a large number into its prime factors is difficult. Similarly, in algebra, starting by factoring out the GCF simplifies the entire problem, making the next steps more manageable. In physics equations, where units are involved, ensuring that all factors are in proper form before solving can prevent unit conversion errors, thus factoring out can play a useful role in unit analysis as well.
Calvin and hobbes are making snowballs to throw at suzi calvin made 3/7 of the snowballs and hobbes made 8/14 of the snowballs who mae more snowballs in fractions
recalculate 3/7 to have the same denominator as 8/14 ( 14)
so multiply both top and bottom by 2. 3/7 becomes 6/14
8/14 - 6/14 = 2/14 reduces to 1/7
Hobbes made more snowballs by 1/7
recalculate 3/7 to have the same denominator as 8/14 ( 14)
so multiply both top and bottom by 2. 3/7 becomes 6/14
8/14 - 6/14 = 2/14 reduces to 1/7
Hobbes made more snowballs by 1/7
What is the negative square root of 361?
the square root of 361 = 19
so the negative square root would be -19
The negative square root of 361 is -19.
The negative square root of 361 is -19. This is because the square root of a number gives both a positive and negative result. In this case, the square root of 361 is 19, so the negative square root is -19.
Select the inequality that corresponds to the given graph. graph of an inequality with a solid line through the points negative 8 comma 0 and 0 comma negative 4 and shading above the line A 4x − 3y > − 12 B x + 4y > 4 C 4x − 2y < − 8 D 2x + 4y ≥ − 16
Step-by-step explanation: In the given graph x-intercept is -8 and y-intercept is -4.
Also the graph is shaded up of the line for greater values of y's.
On the option 2x+4y ≥ -16 has x-intercept at -8 and y-intercept at -4.
Also all other inequalities has only less than or greater than sign.
In the given graph we have a solid line.
So, there should be greater than or equal to inequality sign for the inequality.
Only option 4 has greater than with equal to sign.
Therefore, correct option is 2x+4y ≥ -16
If x-5=2 then find the value of 6x-20
Please help me and show work so I can understand worth 20 points!!!
1. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.
2. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.
Solve 4r2 – 7 = 29.
a. +-6
b. +-3
c. +-4
d. +-5
How do I find ac in this problem
7 / x+4 = 5/x+1 =
5x+20 = 7x+7 =
20=2x+7
13=2x
x=13/2 = 6.5
6.5+4 = 10.5
6.5+1 =7.5
10.5+7.5 = 18
length of AC = 18
which is enough information to prove that s||t
One half of a number decreased by 16
(06.01 LC)
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
b
im taking the same test 4 years later
There were n balloons at the beginning of the party. By the end of the party, 5 of them had popped. Using n, write an expression for the number of balloons that were left
Answer:
The expression for the number of balloons that were left is [tex]n-5[/tex].
Step-by-step explanation:
There were n balloons at the beginning of the party.
By the end of the party, 5 of them had popped.
Let the remaining balloons be represented by x
So, x = total balloons minus 5
This gives: [tex]x=n-5[/tex]
Therefore, the expression for the number of balloons that were left is [tex]n-5[/tex].
If 300 cm^2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
A local carpet company has been hired to carpet a planetarium which is in the shape of a circle. If the radius of the planetarium is six yards, and the cost of the carpet is $14 per square yard, find the total cost to carpet the planetarium. (use 3.14 for π )
Line p contains points A(–7, –9) and B(4, 0). Line q is parallel to line p. Line r is perpendicular to line q. What is the
slope of line r? Explain.
If k pencils cost c cents what is the cost in cents of p pencils
If k pencils cost c cents. Then the cost in cents of p pencils will be cp / k.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If k pencils cost c cents. Then the cost of each pencil is given as,
⇒ c / k
Then the cost in cents of p pencils is given as,
⇒ (c / k) x p
⇒ (cp) / k
If k pencils cost c cents. Then the cost in cents of p pencils will be cp / k.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
Which of these is NOT a part of formal proof? A.Reasons
b.statements
c. given
d. diagram
e.none of the above
The sum of three consecutive even integers is 288. find the three integers.
288/3 =96
96-2 = 94
96+2 = 98
94 +96 +98 = 288
Answer:
94, 96, 98
Step-by-step explanation:
Let the smallest integer is x,
So, second larger integer = x + 2 (Because integer are even and consecutive),
And, largest integer = x + 2 + 2 = x + 4,
So, the sum of these integers = x + x + 2 + x + 4 = 3x + 6
According to the question,
3x + 6 = 288
3x = 282
⇒ x = 94
Hence, the integers are,
94, 94+2, 94+4
= 94, 96, 98
An expression is shown below:
square root of 32 plus square root of 2
Which statement is true about the expression?
please help 25 points
A. It is rational and equal to 4
B. It is rational and equal to 5
C. It is rational and equal to 5√2
D. It is rational and equal to 4√2
Triangle ABC is similar to triangle XYZ. Which of the following proportions is correct?
1) AB/XY = AC/YZ
2) AC/XY=BC/XZ
3) AB/XY=AC/XZ
4) BC/XY=AB/YX
Answer:
The correct option is 3.
Step-by-step explanation:
It is given that triangle ABC is similar to triangle XYZ.
The corresponding sides of similar triangles are proportional.
Since it is given that the triangle ABC is similar to triangle XYZ, so by using the definition of similarity triangles
[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]
From first and third term, we get
[tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]
Therefore the correct option is 3.