Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation can he use to find n, the number of gallons of water he should remove?
Answer:
its c on edge babes, yw <3
Step-by-step explanation:
Grant should remove approximately 7.33 gallons of water to obtain a 24% ammonia solution from the initial 16% ammonia solution.
Let x be the number of gallons of water that Grant needs to remove.
The equation you can use to represent this situation is based on the principle of maintaining the amount of ammonia in the solution:
The amount of ammonia in the original solution = The amount of ammonia in the final solution
The amount of ammonia in the original solution is the product of the initial concentration (16%) and the initial volume (22 gallons).
The amount of ammonia in the final solution is the product of the desired concentration (24%) and the final volume (22 - x gallons, where x is the amount of water removed).
So, the equation becomes:
0.16 * 22 = 0.24 * (22 - x)
Now, you can solve this equation for "x" (the number of gallons of water to remove) to achieve the desired concentration:
0.16 * 22 = 0.24 * (22 - x)
3.52 = 5.28 - 0.24x
Now, isolate the variable "x" by subtracting 3.52 from both sides:
0.24x = 5.28 - 3.52
0.24x = 1.76
Now, divide both sides by 0.24 to solve for "x":
x = 1.76 / 0.24
x ≈ 7.33
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Given 4x-8y=8, transform the equation into slope intercept form
To the nearest tenth of a degree, what is the measure of the central angle that represents 46% in a circle graph?
a.
180.3
c.
156.5
b.
149.7
d.
165.6
WILL MARK BRAINLIEST Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18. A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2). The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2). The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1). The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).
Answer:
The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).
Step-by-step explanation:
To see if the answer to an equation is right, you just have to put the value of X and Y into the equation system, since we don´t have the equation system that the student used, we will make our own, so we will start by stating that Notebooks are represented by X and index cards are represented by Y.
Your equation would look like this:
3x+ 4y=34
The student said that the price of the notebook is $5 and the index card would be $1, now we put those values into the equation.
3(5)+4(1)=32
15+4=32
19=32
Since 19 is not equal to 32, the equation is wrong, therefore the student is wrong.
Now to solve it you get your other equation, since if he had bought 5 and 5 he would have needed 18 extra dollars that means that
5x+5y= 32 +18
5x+5y=50
With the two equations you just use elimination process to create a single equation:
(5x+5y=50)-3= -15x-15y=-150
(3x+4y=32)5 = 15x+20y= 160
You eliminate the x from the equation and are left with:
-15y+20y= -150+160
5y=10
y=[tex]\frac{10}{2}[/tex]
y=2
Now that you have the value of Y you just put it into the equation to know the value of x:
5x + 5(2) = 50
5x+10=50
You clear the x and the result would look like this:
x= [tex]\frac{50-10}{8}[/tex]
x=8
How much money would need to be deposited into an account earning 5.25% interest compounded annually in order for the accumulated value at the end of 25 years to be $75,000?
P = the principal
t = 25 years the time in years
r = 0.0525 or 5.25% annual rate
m = 1 compounding periods per year
i = 0.0525 or 5.25% interest rate per period
n = t*m = 25 total number of compounding periods
A = $75,000 future value
A = P(1 + i)^n
P(1 + i)^n = A
P(1 + 0.0525)^25 = 75000
by solving we find:
P = $20,869.34
Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.
The flow chart with missing statements and reasons proves that the measure of angle ECB is 62°.
Which statement and reason can be used to fill in the numbered blank spaces?
Base angle theorem
Corresponding angle are congruent
Measure of angle AED is 28°.
Alternate interior angles are congruent
Base angle theorem
Measure of angle AED is 62°.
Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 28°.>> my answer?
Corresponding angles are congruent
Triangle Sum Theorem
Measure of angle AED is 62°.
Answer:
(D)
Step-by-step explanation:
Given: Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.
To prove: The measure of angle ECB is 62°.
Proof:
Step1. Segment DE joins the mid points of segments AB and AC (GIVEN).
Step 2. Segment DE is parallel to segment BC (MIDSEGMENT THEOREM)
Step3. Angle ECB is congruent to angle AED (CORRESPONDING ANGLES ARE CONGRUENT) that is ∠AED≅∠ACB.
Step 4. Measure of angle DAE is 90° (Definition of right angle)
Step 5. Measure of angle ADE is 28° (Given)
Step 6. Thus, by triangle sum theorem, we have
∠DAE+∠ADE+∠AED=180°
∠AED=180-118
∠AED=62°
Step 7. Thus, by substitution, we have
∠AED≅∠ACB that is ∠ECB=62°
Hence proved.
Which is the completely factored form of 12x^3 – 60x2 + 4x – 20?
4(3x^2 – 1)(x – 5)
4x(3x^2 + 1)(x – 5)
4x(3x^2 – 1)(x + 5)
4(3x^2 + 1)(x – 5)
The correct option is:
4(3x² + 1)(x – 5)
To find the completely factored form of the expression 12x³ – 60x² + 4x – 20, we can first factor out the greatest common factor, which is 4.
4(3x³ – 15x² + x – 5)
Next, we can factor the quadratic expression 3x³ – 15x² + x – 5 by grouping:
4[3x²(x – 5) + 1(x – 5)]
4(3x² + 1)(x – 5)
Therefore, the completely factored form of 12x³ – 60x² + 4x – 20 is:
4(3x² + 1)(x – 5
So, the correct option is:
4(3x² + 1)(x – 5)
imkim
What is 5 1/4 divided by 1 5/9 ?
Express the answer in simplest form.
What is x and y in 2x+4y=1 and 3x-5y=7
2/3, 3/4, 4/5, 5/6, 6/7
Which of the following represents the general term for the sequence given?
n/n+1
n-1/n
n+1/n+2
Answer:
Option C. (n + 1)/(n +2).
Step-by-step explanation:
The given sequence is 2/3, 3/4, 4/5, 5/6, 6/7.
and we have to find the general term of the given sequence.
Since first term of the sequence is 2/3
So numerator can be represented as (n + 1) and the denominator as (n + 2)
Therefore the general term will be (n + 1)/(n + 2)
Option C is the answer.
Which answer is the explicit rule for the sequence: 13, 10.5, 8, 5.5, 3, 0.5, ...
Answer: The explicit rule for the sequence will be
[tex]a_n=15.5-2.5n[/tex]
Step-by-step explanation:
Since we have given that
[tex]13,10.5,8,5.5,3,0.5.....[/tex]
Here,
a = first term = 13
d = common difference
[tex]a_2-a_1 = 10.5-13=-2.5[/tex]
Since it forms an A.P. ;
[tex]a_n=a+(n-1)d\\\\a_n=13+(n-1)(-2.5)\\\\a_n=13-2.5n+2.5\\\\a_n=15.5-2.5n[/tex]
Hence, the explicit rule for the sequence will be
[tex]a_n=15.5-2.5n[/tex]
Answer:
[tex]a_n[/tex] [tex]= 15.5-2.5n[/tex]
Step-by-step explanation:
What is cos 45
A.
B.
C. 1
D.
E.
F.
Based on the graph shown, which of the following statements is true?
median < mode
median = mode
median > mode
Answer:
Option 2 is correct.
Step-by-step explanation:
In the given graph x-axis represents the numbers and y-axis represent the frequency.
Number Frequency Cumulative frequency
100 14 14
200 6 20 (20<36)
300 18 38 (38>36)
400 12 50
500 2 52
600 12 64
700 8 72
Total 72
Mode is the number which has highest frequency. From the above table it is noticed that the highest frequency is 18 at 300. Therefore mode of the data is 300.
Sum of frequency is 72, which is an even number.
[tex]Median=\frac{n}{2}\text{th term}[/tex]
[tex]Median=\frac{72}{2}\text{th term}[/tex]
[tex]Median=36\text{th term}[/tex]
We have to find the number whose cumulative frequency is more than 36 but preceding cumulative frequency is less than 36.
Median of the graph is 300.
Since the value of median and mode are same, therefore
[tex]median=mode[/tex]
Option 2 is correct.
What is the value of the expression 30n when n = 2?
PLEASE HELP
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 24.5 m/s is
h = 2 + 24.5t − 4.9t2
after t seconds. (Round your answers to two decimal places.)
The question requires solving various problems involving projectile motion, a physics topic, using kinematic equations and algebraic techniques to determine height, flight time, and impact speeds.
Explanation:The question involves calculating various aspects of projectile motion, which is a topic in physics. In these problems, equations of motion are used to determine the maximum height, time of flight, and speed at impact of objects thrown or released from certain heights.
Example Calculations
To calculate the maximum height, you can use the equation h = 2 + 24.5t − 4.9t2 and look for the time t when the velocity is zero.The time it takes for an object to reach the ground can be calculated by setting the height equation to zero and solving for t.To find the speed at impact, you use the conservation of energy or the kinematic equations to relate the initial velocity, acceleration due to gravity, and the distance fallen.Each of these problems requires an understanding of the kinematic equations for vertical projectile motion and the ability to apply algebraic and calculus techniques.
2. A chemist wants to make 4 liters of a 7% acid solution by mixing a 10% acid solution and a 4% acid solution. How many liters of each solution should the chemist use? Write your answer as a complete sentence. Be sure to: • Define your variable and expressions for the quantities. • Write an equation that models the problem. • Solve the equation. • State the answer in a complete sentence.
Part A
Ling and $44 each week for six weeks mowing lawns in his neighborhood. His weekly expenses for supplies are d. Write an expression to show the amount of money ling have after paying his expenses.
Part B
If Ling's expenses are $13 each week, how much money will ling have?
If 80 is 80 percent of a value what is that value
write the equation in standard form. 8−5y=−2x8−5y=−2x the equation in standard form is .
Keana’s piggy bank contains $4.30 in nickels and dimes only. If she has 59 coins in her bank, then what is the sum of the digits in the number of nickels in Keana’s bank? Write a system of equations for this situation and find its solution.
Final answer:
The question is about solving a system of equations to find the number of nickels and dimes in a piggy bank, given a total amount and quantity of coins. The solution involves using either the substitution or elimination method to find the values of the two variables representing nickels and dimes.
Explanation:
The question involves solving a system of equations to find the number of nickels and dimes in Keana’s piggy bank. Given the total amount is $4.30 and there are 59 coins in total, we can set up the following equations:
Let N represent the number of nickels and D the number of dimes.
The value equation is 0.05N + 0.10D = 4.30 or 5N + 10D = 430
The quantity equation is N + D = 59.
To solve these equations, we will use the substitution or elimination method. First, solve the quantity equation for one variable, for example, N = 59 - D. Then, substitute this expression for N in the value equation and solve for D. After finding D, substitute its value back into any of the original equations to find N. The sum of the digits in the number of nickels in Keana's bank is then found by adding together the digits of N.
we get, 5(59 - D) + 10D= 430
295 - 5D + 10D = 430
5D = 135 , Therefore D = 27
and N = 59 - D = 59 - 27 = 32.
To find the sum of the digits in the number of nickels (n=32), we add the digits 3+2=5
Therefore, the sum of the digits in the number of nickels in Keana’s bank is 5.
combine like terms 9x-5y-8y 10x 3=
Laplace Transform of t ^{2}sin(2t)? ...?
Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.
The Laplace transform of the given function is,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
What is Laplace transformation?Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.
Given information-
The function given in the problem is,
[tex]t^{2}\sin(2t)[/tex]
By the Laplace transform we can write that,
[tex]L[t^{2}\sin(2t)]=(-1)^2\dfrac{d^2}{ds^2}L(\sin 2t)\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\;\dfrac{d}{ds}\dfrac{2}{s^2+4}\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\left [\dfrac{-4s}{(s^2+4)^2} \right ]\\[/tex]
Solve further to get the final result,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{(s^2+4)^2(-4)+4s(s^2+4)\times2s}{(s^2+4)^2} \right ]\\[/tex]
Simplify the above equation as,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
Hence, the Laplace transform of the given function is,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
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HELP PYTHAGORAS THEOREM
Answer:
Step-by-step explanation:
Yes
When this polynomial is simplified, what is the coefficient of x: 10x^2+8x-6x^3+4x^2+12x^3-x+20
...?
By applying the PEMDAS rule, the coefficient of x is equal to 7.
In Mathematics and Euclidean Geometry, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
Based on the information provided, we have the following mathematical expression:
[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20\\\\12x^3-6x^3+10x^2+4x^2+8x-x+20\\\\6x^3+14x^2+7x+20[/tex]
In this context, we can reasonably and logically deduce that the coefficient of x is 7.
Complete Question:
When this polynomial is simplified, what is the coefficient of x?
[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20[/tex]
In the diagram, transversal t cuts parallel lines a and b. Which angles form a pair of alternate exterior angles?
∠1 and ∠7
∠1 and ∠8
∠2 and ∠8
∠2 and ∠5
In the diagram, the pair of angles ∠1 and ∠7 form a pair of alternate exterior angles.
Here is the reason:
A transversal is a line where two parallel lines meet. In the diagram, line t is the transversal.Parallel lines: Parallel lines are two lines that never meet, no matter how distant they are amplified. Within the graph, lines a and b are parallel.Interchange exterior angles: When a transversal crosses two parallel lines, it makes eight points. The combination of points that are on the inverse sides of the transversal and exterior of the parallel lines are called substitute outside points.Within the graph, ∠1 and ∠7 are on the inverse sides of transversal t and exterior lines a and b. Subsequently, they are a combination of substitute outside points.
The other answer choices are not correct since:
∠1 and ∠8 are not on inverse sides of the transversal.∠2 and ∠8 are not both exterior parallel lines.∠2 and ∠5 are comparing points, not substituting outside points.If events A and B are independent, and the probability that event A occurs is 83%, what must be true?
c The probability that event A occurs, given that event B occurs, is 83%.
How do you write 175% as a fraction, mixed number, or whole number in simplest form?
In fraction,
175% = 35/20
In mixed fraction,
175% = [tex]1\frac{15}{20}[/tex]
In simplest form,
175% = 1.75
The given percentage is,
175%
Now to write it into fraction,
Divide it by 100 we get
175% = 175/100
= 35/20
Thus,
175% = 35/20
Now divide 35 by 20 to write it into mixed fraction
20 ) 35 ( 1
- 20
___
15
Hence in simple fraction
175% = [tex]1\frac{15}{20}[/tex]
Now again proceed the division,
20 ) 35 ( 1.75
- 20
___
15 0
- 14 0
_____
10 0
- 10 0
____
x
Hence in simplest form,
175% = 1.75
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19 Julia is allowed to watch no more than 5 hours of television a week. So far this week, she has watched 1.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week.
20 You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 2 advantage points. When you earn 100 points, you get a free movie pass. Currently, you have 40 advantage points.
Write an equation to model the number of movies m you have to watch before you earn a free movie pass.
Solve the equation. Show your work. 21 Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
My answers: 19 T<5 T - 1.5 < 5 - 1.5 T = 3.5 20 40 + 2m = 100 40 + 2m - 40 = 100 - 40 2m = 60 2m ÷ 2 = 60 ÷ 2 m = 30 21. ????????
The solution to the first problem is that Julia can watch up to 3.5 more hours of TV this week. The solution to the second problem is that you need to watch 30 more movies to earn a free movie pass. An example of an equation with infinitely many solutions is x = x.
Explanation:19. To represent this scenario as an inequality, we let T be the amount of television Julia can still watch this week. Since she can watch no more than 5 hours per week and she has already watched 1.5 hours, we subtract 1.5 from 5. So we have the inequality T + 1.5 <= 5. Subtracting 1.5 from both sides gives us the inequality T <= 3.5. So Julia can watch 3.5 more hours of TV this week.
20. Let m be the number of movies you need to watch to get a free movie pass. Each movie gives you 2 advantage points and you currently have 40 points. The equation to model this situation is 2m + 40 = 100. Subtracting 40 from both sides gives 2m = 60. Dividing by 2 gives m = 30. So you need to watch 30 more movies to get a free movie pass.
21. An equation with infinitely many solutions is one where all the terms on one side can be made identical to all the terms on the other side. A simple example is x = x. For every value of x, the equation holds, meaning it has an infinite number of solutions.
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what number multiplied by itself 4 times equals 81
Final answer:
The number that, when multiplied by itself 4 times equals 81, is 3, as 3 to the fourth power (3^4) is 81.
Explanation:
To find what number multiplied by itself 4 times equals 81, we need to find the fourth root of 81. The fourth root is the same as raising a number to the 0.25 power. To calculate manually, we may take two square roots in succession, since the square root of a number squared is the original number. The square root of 81 is 9, and the square root of 9 is 3, thus the fourth root of 81 is 3. Indeed, 34 = 3 × 3 × 3 × 3 = 81.