What amounts of 30% pure silver and 45% pure silver should be mixed to obtain 14 grams of 43% pure silver? Please give exact answers, which are
fractions. If this isn't possible, give at least 5 decimal places
Answers
The amounts of 30% pure silver and 45% pure silver that should be mixed to obtain 14 grams of 43% pure silver are approximately 1.867 grams and 12.133 grams, respectively.
To determine the amounts of 30% pure silver and 45% pure silver that should be mixed to obtain 14 grams of 43% pure silver, we can set up a system of equations based on the given information.
Let's assume x represents the amount (in grams) of the 30% pure silver and y represents the amount (in grams) of the 45% pure silver.
Equations based on the amounts of silver:
x + y = 14 -- equation (1) (total amount of silver is 14 grams)
Equations based on the percentages of silver:
(0.30x + 0.45y) / (x + y) = 0.43 -- equation (2) (overall purity of the mixture is 43%)
To solve the system of equations, we can use substitution or elimination method. In this case, let's use the substitution method.
From equation (1), we can express x as 14 - y and substitute it into equation (2):
(0.30(14 - y) + 0.45y) / (14 - y + y) = 0.43
Simplifying the equation:
(4.2 - 0.3y + 0.45y) / 14 = 0.43
(4.2 + 0.15y) / 14 = 0.43
4.2 + 0.15y = 0.43 * 14
4.2 + 0.15y = 6.02
0.15y = 6.02 - 4.2
0.15y = 1.82
y = 1.82 / 0.15
y ≈ 12.133
Now, substitute the value of y back into equation (1) to find x:
x + 12.133 = 14
x = 14 - 12.133
x ≈ 1.867
Therefore, the amounts of 30% pure silver and 45% pure silver that should be mixed to obtain 14 grams of 43% pure silver are approximately 1.867 grams and 12.133 grams, respectively.
Please note that the answers have been rounded to three decimal places for convenience, but you can use the exact decimal values for more precise calculations if needed.
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Related Questions
3(4x-1) greater than or equal to 2(4-x)
Answers
Answer:
Greater than
Step-by-step explanation:
First, I solved the expressions.
3(4x-1)=12x-3
2(4-x)=8-2x
12x-3>8-2x
As we can see, 12x-3 is greater than 8-2x.
Step-by-step explanation:
12x - 3 (expand 3(4x-1))
8-2x (expand 2(4-x))
if you assume that x=1 then 12x-3 would be 12(1)-3 then it would be 9 for the first
for the second equation, 8-2x, it would be 8- 2(1) or 6
9>6 so, 3(4x-1) > 2(4-x)
2) Solve the system of linear equations using elimination by addition or
subtraction.
Sy=x-1
12. – y=0
O (1,2)
0 (-1,2)
O (-1, - 2)
O (1, - 2)
Answers
Answer:the answer is -1,-2
Step-by-step explanation:you add y to 2x-y and x-1 to 0, getting 2x=x-1. You go on from there, and the answer is x=-1, y=-2. Hope that helped
Could use some help
Answers
The quadrilateral FGHI is a parallelogram
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
F = (0, -6), G = (7, -4), H = (8, 4), I = (1, 2)
The lengths can be calculated as
Lengths = √[(x₂ - x₁)² + (y₂ - y₁)²]
Using the above as a guide, we have the following:
FG = √[(0 - 7)² + (-6 + 4)²] = √53
GH = √[(8 - 7)² + (4 + 4)²] = √65
HI = √[(8 - 1)² + (4 - 2)²] = √53
IF = √[(1 - 0)² + (2 + 6)²] = √65
For the slopes, we have
Slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
FG = (-6 + 4)/(0 - 7) = 2/7
GH = (4 + 4)/(8 - 7) = 8
HI = (4 - 2)/(8 - 1) = 2/7
IF = (2 + 6)/(1 - 0) = 8
Based on the above computations, we have
Opposite sides are equalOpposite sides are parallelHence, the shape is a parallelogram
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how to use the five number summary to give the smallest intervat that we know contains the 30th percentile
Answers
The five number summary is the minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and the maximum.
To give the smallest interval that we know contains the 30th percentile, we would take the 25th percentile and the 30th percentile. So, the smallest interval that we know contains the 30th percentile would be [25th percentile, 30th percentile].
The smallest interval that contains the 30th percentile is [25th percentile, 30th percentile], which is found using the five number summary (minimum, first quartile, median, third quartile, and maximum).
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heyyy.... can someone pls help asap. Rearrange the formula to write r in terms of P and pi.
\(p = 2r + \pi \: r\)
Answers
Step-by-step explanation:
p = 2r + pi×r
p = r(2 + pi)
r = p/(2 + pi)
Answer:
r = \(\frac{p}{2+\pi }\)
Step-by-step explanation:
p = 2r + πr ← factor out r from each term
p = r(2 + π) ← divide both sides by (2 + π )
\(\frac{p}{2+\pi }\) = r
Margo mixed 24 ounces of blue paint and 16 ounces of red paint to create a new purple color. In order to create 72 more ounces of this exact purple color, how many ounces of red paint would she need?
Answers
Answer:
Step-by-step explanation:
Well, since 24+16 is 40, this would mean we get 40 ounces of purple paint. There is also a 150% difference between 24 and 16, so 2/3 times 24 = 16.
2/3 of the mixture is blue paint, while 1/3 of the mixture is red paint, so 1/3 of 72 is 24.
Thus, the answer is 24 ounces of red paint.
Solve the system using any method:
y = x - 3
y = 7x + 3
Answers
Answer:
x=-1, y=-4
Step-by-step explanation:
For this question, you can replace y in one equation with the second one.
This means x-3=7x+3.
From there, you subtract x from each side, giving -3=6x+3.
Subtracting 3 from each side makes it -6=6x.
Dividing both sides by 6 leaves x isolated, with a result of x=-1.
You can substitute the value of x into either equation to work out y. I'm using the first one, as it has smaller numbers.
This equation is now y=-1-3, which can be solved for y=-4.
**This content involves simultaneous equations, which you may wish to revise. I'm always happy to help!
Which of the following tables represents a linear relationship that is also proportional?
(A)
x −1 0 1
y 0 2 4
(B)
x −3 0 3
y −2 −1 0
(C)
x −2 0 2
y 1 0 −1
(D)
x −1 0 1
y −5 −2 1
Answers
Answer: 我不知道你好
Step-by-step explanation:
can someone help me ill mark you brainliest
Answers
Answer:
Equation: x+x+6=20
x=7
Andy completed 16 problems
Step-by-step explanation:
mark sweeney wants to receive a letter grade of a for this course, and he needs to earn at least 90 points to do so. based on the regression equation developed in part (b), what is the estimated minimum number of hours mark should study to receive a letter grade of a for this course? (round your answer to one decimal place.)
Answers
Mark needs to invest 5572.24 hours (rounded to one decimal place) of study time in order to achieve an A letter grade in this course.
To determine the estimated minimum number of hours Mark should study, we need to solve for the number of hours such that his predicted score, given by the regression equation from part (b), is at least 90.
The regression equation is as follows: Predicted score = 48.74 + 0.00726(number of hours studied)
Setting the predicted score equal to 90 and solving for the number of hours studied gives:90 = 48.74 + 0.00726 (number of hours studied)
Solving for the number of hours studied gives: number of hours studied = (90 - 48.74)/0.00726= 5572.24
Therefore, Mark should study for 5572.24 hours (rounded to one decimal place) to receive a letter grade of A for this course.
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The angle of elevation to the top of the
school is 37° from where you are standing
11.2 m from the wall of the school. Find
the height of the school.
Answers
Answer:
8.44 m
Step-by-step explanation:
SohCahToa is a good way to remember that Sin = opposite/hypotenuse, Cosine = adjacent/hypotenuse and Tangent = opposite/adjacent. In this case, we have to use tangent. So tan 37° = x/11.2. Multiply both sides by 11.2 and you get tan 37° × 11.2 = x; The height of the school is x so the height of the school is 8.44 m
So, the area is square units.
Answers
The area of a triangle is 4 square units.
Given that, the coordinates of the triangle ABC are A(4, 3), B(5, 1) and C(1, 1).
We need to find the area of a triangle ABC.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The base of the triangle = |5-1|=4
From vertices, A(4, 3) to the base the distance is 2 units at the vertice (4, 1)
So, the height of the triangle = 2 units
Now, the area of a triangle ABC = 1/2 × 4 × 2 = 4 square units.
In the given solution the height of a triangle is wrongly calculated.
Therefore, the area of a triangle is 4 square units.
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for each ordered pair, determine whether it is a solution to 7x+3y=2
the ordered pairs:
0, -8
-1, 3
2, -4
5, 2
Answers
Answer:
Step-by-step explanation: i thimk 5,2
Consider the following NLP: min s.t. 2x12+2x1x2+x22−10x1−10x2
x12+x22≤5
3x1+x2≤6
x1,x2≥0 (a) Aside from regularity and the given constraints, what are the first order necessary conditions for this problem? (Be as specific as possible.) (b) Find a solution by assuming the first Lagrangian multiplier constraint is active and the second one is inactive. (c) Does this satisfy the first order necessary conditions? Explain.
Answers
The first-order necessary conditions for the given NLP problem involve the KKT conditions, and a specific solution satisfying these conditions needs further analysis.
(a) The first-order necessary conditions for constrained optimization problems are defined by the KKT conditions. These conditions require that the gradient of the objective function be orthogonal to the feasible region, the constraints be satisfied, and the Lagrange multipliers be non-negative.
(b) Assuming the first Lagrangian multiplier constraint is active means that it holds with equality, while the second one is inactive implies that it does not affect the solution. By incorporating these assumptions into the KKT conditions and solving the resulting equations along with the given constraints, a solution can be obtained.
(c) To determine if the solution satisfies the first-order necessary conditions, one needs to verify if the obtained values satisfy the KKT conditions. This involves checking if the gradient of the objective function is orthogonal to the feasible region, if the constraints are satisfied, and if the Lagrange multipliers are non-negative. Only by performing this analysis can it be determined if the solution satisfies the first-order necessary conditions.
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Please help solve this, my last two brain cells aren't working rn
Answers
Answer:
dude my brain cells are perishing
-2/3 is your answer my guy
have fun
Step-by-step explanation:
Obtuse triangle. Step 1: Suppose angle A is the largest angle of an obtuse triangle. Why is cosA negative? Step 2: Consider the law of cosines expression for a 2and show that a 2>b2+c2Step 3: Use Step 2 to show that a>b and a>c Step 4: Use Step 3 to explain what triangle ABC satisfies A=103 ∘,a=25, and c=30
Answers
CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.
Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.
Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.
Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.
Therefore, the largest angle of an obtuse triangle is opposite the longest side.
Step 4: In triangle ABC, A=103°, a=25, and c=30.
a² = b² + c² - 2bccos(A),
a² = b² + 900 - 900 cos(103),
a² = b² + 900 + 900 cos(77),
a² > b² + 900, so a > b.
Similarly, a² > c² + 900, so a > c.
Therefore, triangle ABC satisfies a>b and a>c.
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Question
What is the slope of this graph?
Responses
1 fourth
negative 4
negative 1 fourth
4
Answers
Answer: The slope of the graph is negative 4.
Donnie, Karim, and Shawn run on the cross-country team. At yesterday’s practice, Donnie ran 200% as far as Karim. The ratio of the distance that Karim ran to the distance that Shawn ran is 4 : 3.
If you add the distance that all three boys ran, you get a sum of 45 miles. How far did each boy run individually?
this is ratio problem
Answers
The distance that each boy ran is as follows:
Donnie = 24 miles
Karim = 12miles
Shawn = 9 mile.
What is ratio?Ratio is defined as an expression that is used to represent the part of a whole entity or structure.
The total distance covered by the three boys = 46miles.
Distance covered by Donnie = 200% of Karim (ratio 4)
That is;
200/100×4 = 8
Now the ratio of the three boys = 8:4:3
To calculate the distance of each boy is by finding the total ratio of the whole boys such as:
= 8+4+3 = 15
For Donnie = 8/15×45 = 24 miles
For Karim = 4/15×45 = 12 miles
For Shawn = 3/15 × 45 = 9 miles
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write the equation of the graphed line
Answers
Answer:
Y=-1/4x+2
Step-by-step explanation:
.
Nerissa has 5 pink bows, 1 blue bow, and 4 purple bows in a box. She will randomly choose 1 bow from the box.
What is the probability Nerissa will choose a purple bow?
Answers
Answer:
the answer would be 4/10 but the simplified version would be 2/5.
Step-by-step explanation:
add up how many bows you have, that will be the denominator. Then, the numerator is the number of purple bows. and if your going to simplify it divide the numerator and denominator by 2.
Answer:
fraction wise(4/10 chance)
percent wise:(40% chance)
Step-by-step explanation:
(There are 2 options) First add all of the bows then see how many purple bows there are. Since there are 4 bows it would be 4/10 or 40%.
eval calculates an expression and puts the resulting ____ into a new or existing field.
Answers
Eval is a function that evaluates an expression and puts the resulting value into a new or existing field.
To calculate the value of an expression using Eval, you must use the correct syntax. The syntax for Eval is Eval(expression, optional_parameter). The expression can take the form of a mathematical equation or a logical expression. For example, if you wanted to calculate the sum of two numbers, you would use the following expression: Eval(A + B). The optional parameter allows you to specify a range of values to evaluate the expression against.
For example, if you wanted to calculate the sum of two numbers within a given range, you would use the following expression: Eval(A + B, range). The range parameter can be used to specify the starting and ending values that the expression should be evaluated against.
Using Eval to calculate an expression is a useful tool for quickly getting the desired value. It is also useful for quickly testing the accuracy of a complex expression before implementing it in your code.
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please help asap :) i will give brainliest, too!
A group of students is investigating whether aluminum is a better thermal conductor than steel. The students take an aluminum wire and a steel wire of the same length and diameter. They put equal lengths of wax on one end of each wire and dip the other end into a beaker of hot water. The length of wax left on the wires after 10 minutes is shown.
Which step should the students take next?
a. Make a hypothesis
b. Analyze the data
c. Test another variable
d. Share their conclusion
Answers
Answer:
They should do B analyze the data.
Step-by-step explanation: hope it helps
Answer:
it is B
Step-by-step explanation:
sorry if it is not right
Pls. Help find these answers?!
Answers
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
can someone help? I'll give brainlest !
Answers
Answer:
B
Step-by-step explanation:
I actually only when based on the y-intercept so you see where the y-intercept is, that would be your last number of your equation, in this case it’s 5
Answer:
B y = - 5/2x +2
Step-by-step explanation:
I want to be friends with you
SOMEONE PLZ HELP?!!!
Answers
Answer:
\(-\frac{11}{3}\)
Jermain plans to pay back the loan in full after 5 years. He estimates that he should save $5500 in that time in order to pay off the loan completely. Is Jermain's estimate correct?
Answers
No, the estimate is not correct. He will need to save more than $5500 to pay off the loan in full after 5 years.
Let's assume that Jermain took out a loan of $5000 at an interest rate of 6% per year, compounded annually. Using the formula for future value of a single sum, we can calculate the future value of the loan after 5 years:
FV = PV x (1 + r)n
where PV is the present value, r is the interest rate, and n is the number of compounding periods.
In this case, PV = $5000, r = 0.06, and n = 5 (since the interest is compounded annually and Jermain plans to pay off the loan in 5 years).
Plugging in these values, we get:
FV = $5000 x (1 + 0.06)^5 = $6715.10
So the future value of Jermain's loan after 5 years is $6715.10. This means that he would need to save at least $6715.10 in order to pay off the loan completely.
Since Jermain's estimate of $5500 is less than the actual future value of his loan, his estimate is not correct. He will need to save more than $5500 to pay off the loan in full after 5 years.
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Let A(0,4,2), B(2,22,9), C(3,-2,0) and D(0,1,2) be 4 points in
R'3. Find the plane such that both AB and BC lying on it. Hence,
Find the distance between the plane r and the point D(0,1,2).
Answers
-6x+25y+66z=232 is the equation of the plane and distance between the point D and the plane is 157/70.
lets find the equation of the line AB and BC and equations of the lines will be of the form
\( \text{ $\frac{x-a}{l}$ = $\frac{y-b}{m}$ = $\frac{z-c}{n}$ } \)
So, the equation of AB is
\( \text{ $\frac{x}{2}$ = $\frac{y-4}{18}$ = $\frac{z-2}{7}$ } \)
So, the equation of AB is
\( \text{ $\frac{x-3}{-1}$ = $\frac{y+2}{24}$ = $\frac{z}{9}$ } \)
let b1 andb2 are the direction vectors of the two above lines.
b1= 2i + 18j + 7k
b2= -1i + 24j + 9k
now n= Det( i j k)
2 18 7
-1 24 9
or, n= -6i + 25j + 66k
the point (0,4,2) lies on the plane. the equation of the plane passing through (0,4,2) and perpendicular to a line with a direction ratio (-6, 25, 66) is
-6x+25(y-4)+66(z-2)=0
or, -6x+25y+66z=232.
now formula of distance between the point (x0,y0,z0) and the plane is
\( \frac{Ax0+By0+Cz0+D}{√A^2+B^2+C^2} \)
so for the point D and the plane is
( -6*0 + 25*1 + 66*2 - 132)/√5017 = 157/70.
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Use the confidence interval to find the margin of error and the sample mean:
(0.256,0.380)
a.The margin of error is: _____
b.The sample mea is: _____
Answers
The confidence interval to find the margin of error and the sample mean:
(0.256,0.380) The sample mean is the average value obtained from the sample data.
To find the margin of error and the sample mean, we need more information.
The confidence interval (0.256, 0.380) provides the range of possible values for the true population mean.
However, without knowing the sample size or the level of confidence associated with the interval, we cannot calculate the margin of error or the sample mean.
The margin of error is typically calculated by multiplying the standard error by the appropriate critical value, based on the desired level of confidence. The sample mean is the average value obtained from the sample data.
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⚠️6TH GRADE MATH⚠️
Six percent of the sale price of a home
goes to the real estate agents as their
commission. The buyer's agent and
the seller's agent split the commission
evenly. How much commission does
each agent get when they complete
the sale of a $340,000 house?
Answers
Answer:
10200
Step-by-step explanation:
0.06*340,000=20400
20400÷2=10200
need help to find x. with the equation 9/x^2-9=3/6x-18
Answers
Answer:
x = 15
Step-by-step explanation:
Pre-SolvingWe are given the following equation:
\(\frac{9}{x^2-9} = \frac{3}{6x-18}\)
We want to find the value of x of it.
SolvingEquationWe can start by cross multiplying to get:
9(6x-18) = 3(x²-9)
Distribute the 9 and 3.
54x - 162 = 3x² - 27
Subtract 54x from both sides
-162 = 3x² - 54x - 27
Add 162 to both sides.
3x² - 54x + 135 = 0
We can divide each term by 3. We'll end up with:
x² - 18x + 45 = 0
This can be factored to become:
(x -15)(x-3) = 0
Applying zero product property,
x - 15 = 0
x = 15
And:
x-3 = 0
x = 3
DomainWe aren't done yet though; we need to find the domain of this equation, because we have variables in the denominator.
x² - 9 and 6x - 18 both cannot be zero. Because of that:
x² - 9 ≠ 0
x² ≠ 9
x ≠ ±3
and:
6x - 18 ≠ 0
6x ≠ 18
x ≠ 3
The value of x cannot be 3 or -3. This means that our only answer is x = 15.