An alloy of tin is 15% tin and weighs 20 pounds. A second alloy is 10% tin. How many pounds of the second alloy must be added to the first to get a 12% mixture? 30 lb 40 lb 60 lb

Answers

Answer 1

so, they alloy is hmmm some piece of metal.

it has tin, among other metals, regardless of what other metals it may have, we know that for the first one, 15% is tin, the rest something else, and we also know that the alloy itself, weights 20 lbs.

now, how much is just the weight of the tin metal in it alone? well, is 15% of 20 lbs, or (15/100) * 20, or 3 lbs, so of all those 20 lbs, only 3 lbs or 15% is tin.

for the second alloy, let's say we'll add "x" lbs, we know the second alloy is 10% tin, how much of that weight is tin? well 10% of x, or (10/100) * x, or 0.10x lbs.

now, we're looking for a mixture, say the resulting lbs of mix will be "y" lbs, and we know the mixture will be 12% of tin, how much is 12% of y? (12/100) * y, or 0.12y.

now, regardless of what "x" and "y" is, we know that 20 + x = y, and that 3 + 0.10x = 0.12y, thus

[tex]\bf \begin{array}{lccclll} &\stackrel{lbs}{amount}&\stackrel{tin~\%}{quantity}&\stackrel{tin~lbs}{quantity}\\ &------&------&------\\ \textit{15\% alloy}&20&0.15&3\\ \textit{10\% alloy}&x&0.10&0.10x\\ ------&------&------&------\\ mixture&y&0.12&0.12y \end{array} \\\\\\ \begin{cases} 20+x=\boxed{y}\\ 3+0.10x=0.12y\\ ----------\\ 3+0.10x=0.12\left( \boxed{20+x} \right) \end{cases} \\\\\\ 3+0.10x=2.4+0.12x\implies 3-2.4=0.12x-0.10x \\\\\\ 0.6=0.02x\implies \cfrac{0.6}{0.02}=x\implies 30=x[/tex]

Related Questions

Important state labor laws and safety regulations came about as a result of the 1911 __________.
a. labor relations act
b. triangle shirtwaist factory fire
c. homestead strike
d. massachusetts child safety campaign

Answers

b. triangle shirtwaist factory fire

Answer:

Option B is correct.

Step-by-step explanation:

Important state labor laws and safety regulations came about as a result of the 1911 - Triangle shirtwaist factory fire

The Triangle shirtwaist factory fire was one of the worst industrial disasters during that time. Many people died due to a fire breakout in the factory. They could not escape the building and died due to smoke inhalation or burns.

After this incident, a Committee on Public Safety was formed that led to a legislation requiring labor laws and improved factory safety standards.

If $5000 is invested at 7.8% interest compounded monthly, how much would you have after 54 months?

Answers

5000 x (1+0.078/12)^54

5000 x (1.0065)^54

$7094.37

which graph shows the inequality y>-2

Answers

The answer for your question is b

What is the value of x in the parallelogram?

Answers

The value of x is (180-67) = 113 degrees.

Extra information:

In a parallelogram, the consecutive angles are supplementary (so in this case, that means that because the line from corner x to the corner of 67 degrees is 180 degrees in total, the value of x has to be 180-67 = 113 degrees).

Find the geometric mean of 6 and 7.

A. √42

B. 4√3

C. 7

D. 42

Please select the best answer from the choices provided.

Answers

First, it is important to understand the terms used in the problem.

The Arithmetic Mean: (this is the mean we are used to seeing)
[tex]m= \frac{a+b+c}{n} [/tex]
(n= number of variables, in this case n=3)

To Find the Geometric Mean of n #'s:
[tex]m_{geometric} = \sqrt[n]{a*b} [/tex]
(n= number of variables, in this case n=2)

So, using this information we can find the geometric mean of 6,7 by plugging them into the equation as "a" and "b". n=2 (when n=2 a square root can be used)[tex]m_{geometric} = \sqrt[n]{a*b}[/tex]
[tex]m_{geometric} = \sqrt{a*b} [/tex]
[tex]m_{geometric} = \sqrt{6*7} [/tex]
[tex]m_{geometric} = \sqrt{42} [/tex]

So the answer in this case is A.[tex] \sqrt{42} [/tex]

1. y and x have a proportional relationship, and y = 7 when x = 2. What is the value of x when y = 21?

2. y and x have a proportional relationship, and y = 9 when x = 2. What is the value of y when x = 3?

3.he table shows a proportional relationship.

x y

2 2.8

4 5.6

6 8.4

8 11.2

Complete the equation that represents the table.

Enter your answer as a decimal in the box. y = ____x

Answers

Attached solutions with steps.

Answer: 6

Step-by-step explanation:

Let p: The shape is a rhombus. Let q: The diagonals are perpendicular. Let r: The sides are congruent. Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

Answers

Given that p represents "The shape is a rhombus", q represents "The diagonals are perpendicular", and r represents "The sides are congruent".

"if and only if" is represented using the biconditional logic operator (↔) and "and" is represented using the logical conjuction operator (∧).

Therefore, "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent” is represented by "p ↔ (q ∧ r)"

Answer:

C.)p ↔ (q ∧ r)

Step-by-step explanation:

I scored a 100 on my quiz

[02.05]
Solve for x: 4 − (x + 2) < −3(x + 4) (1 point)

x < −7

x > −7

x < −9

x > −9

Answers

first, get rid of the paranthesis:
4-x-2<-3x-12 => 2-x<-3x-12
next, eliminate x on one side. here I'll eliminate -3x by adding 3x on both side:
2+2x<-12
2x<-14
x<-7

Option A

x<-7

Given :

[tex]4 - (x + 2) < -3(x + 4)[/tex]

Explanation :

Solve the given inequality for x by applying algebraic properties

We use order of operation to simplify the left and right side of inequality

[tex]4- (x + 2) < -3(x + 4)\\4-x-2<-3x-12\\-x+2 < -3x -12\\Add\; 3x \; on \; both \; sides\\2x+2<-12\\Subtract\; 2\; from \; both \; sides\\2x<-14\\Divide \; both \; sides \; by 2\\x<-7[/tex]

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What is the equation of the line shown in this graph?
pls help

Answers

the line of the graph is vertical since both x coordinates are the same ( both are -2)

so the equation would be x = -2

Find the quotient of 3 2/5 and 3 2/6. Express your answer in simplest form.

Answers

32/5÷32/6=32/5×6/32=6/5

You give up a full time salary of 45,000 a year to go to school for 2 years the total cost of going to school is 30,000, if want to be able to recover your investment in 5 years or less what is the minimum salary you would need to earn upon earning your degree?

Answers

I would say that this person has lost out on 2 years salary while in school plus 5 year repayment period. Total amount divided over 5 years is:

( (2+5)(45,000) + 30,000 ) / 5 =

(7(45,000)+30,00)/5 = 69,000 salary

Answer:

69,000

Step-by-step explanation:

Given,

There is loss of 45,000 per year for two years,

So, the total lost = 2 × 45000 = 90,000

Also, the cost of school going = 30,000

∴ the total recovering amount = 90,000 + 30,000 = 120,000

If this amount must recover in 5 years or less than 5,

Then, the minimum recovering amount per year = [tex]\frac{120000}{5}[/tex] = 24,000

Now, the original salary per year = 45,000

Hence, the new salary per year = original salary + recovering amount

= 45,000 + 24,000

= 69,000

Find the area of the shaded region. Thanks!

Answers

check the picture below.

now, let's rationalize the denominator for "r" first.

also notice, that section is just 1/4 of the area of that circle, so, let's just find the area of the whole circle with that "r", get one-quarter of it, and subtract it from the half of the area of the square.

[tex]\bf r=\cfrac{8}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies r=\cfrac{8\sqrt{2}}{2}\implies \boxed{r=4\sqrt{2}} \\\\\\ \stackrel{\textit{area of that circle}}{A=\pi (4\sqrt{2})^2}\implies A=\pi (16\cdot 2)\implies A=32\pi \\\\\\ \textit{how much is one-quarter of that?}\quad \cfrac{32\pi }{4}\implies \boxed{8\pi }\\\\ -------------------------------\\\\[/tex]

[tex]\bf \stackrel{\textit{area of the square}}{A=8\cdot 8}\implies A=64\qquad \stackrel{\textit{half of that square's area}}{32}\\\\ -------------------------------\\\\ \textit{shaded region}\implies \stackrel{\stackrel{\textit{half of that square}}{area}}{32}~~-~~\stackrel{\stackrel{\textit{one-quarter of the circle}}{area}}{8\pi }[/tex]

Answer:

-8π + 32

6.8675

Step-by-step explanation:

So we know that the are of the square is 64, and we know that the equation for the are of the shaded region is Area of square - 1/4 area of circle with a radius of 4√2 - area of 90/45/45 triangle with side lengths of 8 and 8.

s = square area

c = circle area

t = triangle area

∆ = shaded region area

∆ = s - 1/4c - t

input the numbers that we have for those variables:

∆ = 64 - 1/4(100.53) - 32

∆ = 64 - 25.1325 - 32

∆ = 32 - 25.1325

shade region approximate ≈ 6.8675

or to get an exact answer in terms of pi

∆ = 64 - 1/4(32π) - 32

∆ = 32 - 8π

shaded region = -8π + 32

just added this because it is hard to pick out the actual answer in the other person's answer.

The vertex of the graph of a quadratic function is (–2, –9) and the y-intercept is (0, –5). Which of the following is the equation of the function? A. y = x2 +10x + 2 B. y = x2 +10x – 2 C. y = x2 – 2x – 5 D. y = x2 + 4x – 5

Answers

using up extra characters

Which pair of triangles are congruent by ASA ?

Answers

the answer for this question is D because it has an angle then a side measurement then it has another angle measurement

The pair of triangles that are congruent by ASA is figure C

The ASA theorem

Two triangles can be judged to be congruent using the ASA (Angle-Side-Angle) criterion. For triangles to satisfy ASA congruency:

Angle: The triangles' two matching angles have to coincide.Side: There must also be congruence on the included side that lies between the congruent angles.

Put otherwise, the ASA criterion determines that two triangles are congruent if two of their angles and the included side are congruent, respectively. For this criterion, the angles and sides' order matters.

Based on the explanations, hence the pair of triangles that are congruent by ASA is figure C

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The table below represents the atmospheric temperature at a location as a function of the altitude:

Altitude
(in thousand feet)
x
15
20
25
30

Temperature
(in °C)
f (x)

4
−6
−16
−26

The average rate of change of the function between x = 15 to x = 25 is ___degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

Answers

from x15 to x 25 is 4 - -16 = -20 degree change

25 -15 = 10000 feet

-20/10 = -2 degrees every 1000 feet

Answer: The average rate of change of the function between x = 15 to x = 25 is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

Step-by-step explanation:

The average rate of change of a function y=f(x) from [tex]x_1\ to\ x_2[/tex]is given by :-

[tex]k=\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{-6-4}{20-15}[/tex]

Now, by the given table the average rate of change of the function between x = 15 to x = 25 will be :_

[tex]k=\frac{-16-4}{25-15}=\frac{-20}{10}=-2[/tex]

Hence, the average rate of change of the function between x = 15 to x = 25 is -2 degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet.

For what values of x and y must each figure be a parallelogram?

Answers

(5x - 180)° +x° = 180°

(6x - 180)° = 180°

6x = 360°

x = 60°

5(60)-180= 300-180=120°

Can someone how to get the answer? Thanks! PLEASE HELPpppppppppppppppppppppppp

Answers

[tex]\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right) \ \textgreater \ \ln \left(6^x\right)=\ln \left(21\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\ \log _a\left(x^b\right)=b\cdot \log _a\left(x\right) \ \textgreater \ \ln \left(6^x\right)=x\ln \left(6\right) [/tex]

[tex]x\ln \left(6\right)=\ln \left(21\right) \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}\ln \left(6\right) \ \textgreater \ \frac{x\ln \left(6\right)}{\ln \left(6\right)}=\frac{\ln \left(21\right)}{\ln \left(6\right)} [/tex]

[tex]Therefore \: x=\frac{\ln \left(21\right)}{\ln \left(6\right)}[/tex]

In your case ln means [tex] \frac{log 21}{log 6} [/tex]

in your graphing calculator you have to press the button (2nd) then (catalog) which is the number (0).
after that you press (ALPHA) (L) which iOS the button for the parenthesis (. ). )
find LOG and then plug in the number you want.
repeat this until you get the equation you want.

How do I simplify ((3x^2+12x+12)/(2x^2+x-6))/((4x^2-9)/(3x^3+x^2-10))

Answers

[tex] \dfrac{ \frac{3x^2+12x+12}{2x^2+x-6} }{ \frac{4x^2-9 }{3x^3+x^2-10} } =[/tex]

[tex]= \dfrac{3(x + 2)^2}{(2x - 3)(x + 2)} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} } [/tex]

[tex]= \dfrac{3(x + 2)}{2x - 3} \times \dfrac {3x^3+x^2-10} {(2x + 3)(2x - 3)} } [/tex]

[tex]= \dfrac{3(x + 2)(3x^3+x^2-10) }{(2x - 3)^2(2x + 3)} [/tex]

The table below represents ordered pairs of a function. Which change could be made so that the relation in the table is no longer a function

Answers

in order to be a function we need one x-value corresponding to one y-value which is shown in the table. if we can have the same x value corresponding to multiple y values then it is no longer a function it is a relation.

What theorem or postulate can prove a triangle to be an isosceles?

Answers

Final answer:

The Converse of the Base Angles Theorem states that if two angles of a triangle are congruent, then the triangle is isosceles.

Explanation:

In geometry, the theorem that can prove a triangle to be isosceles is the Converse of the Base Angles Theorem. It states that if two angles of a triangle are congruent, then the triangle is isosceles. In other words, if the two base angles of a triangle are equal, then the triangle is isosceles. For example, if angles A and B in triangle ABC are congruent (angle A = angle B), then triangle ABC is isosceles.

Which is harder linear algebra or abstract algebra?

Answers

They both relatively easy depending on how much time you put into understanding but. But if I have to pick which is harder I’d say linear.

Linear algebra

I've always had trouble with graphs and it's much better if the algebra is similar to arthemetic

Difference of two numbers is 8. find the smallest possible product.

Answers

The smallest possible product would be 8. The two numbers used are 0 and 8. If you subtract 0 from 8 you get the difference of 8. If you add 8 plus 0, you get the product of 8.

The sum of two integers is 28, and their product is 192. what are the two integers?

Answers

The two integers are 12 and 16.

The product of 12 and 16 is 192, and the sum is 28.

Which graph represents the solution set of the system of inequalities?

Answers

Answer:
(see image)
bottom right image

Explanation:
First try the origin (0,0) to rule out two of the graphs.
3y ≥ x - 9
3(0) ≥ (0) - 9
3 ≥ - 9 yes
3x + y > - 3
3(0) + (0) > - 3
3 > - 3 yes
so the origin should be in the shaded area of the graph, which rules out the top right and bottom left graphs.
Now try a coordinate that is in the shaded area of one of the remaining graphs, but not in the other one. If it works, the graph is the one that has that point in the shaded region, and vice versa.
Try point (4, 2)
3y ≥ x - 9
3(2) ≥ (4) - 9
6 ≥ - 5 yes
3x + y > - 3
3(4) + (2) > - 3
12 + 2 > - 3
14 > - 3 yes
So the graph is the bottom right one since (4, 2) is included in that shaded region.

I have a graphing question

Answers

The point slope form of the equation of a straight line is given by

[tex](y-y_1)=m(x-x_1)[/tex]

where [tex](x_1,\ y_1)[/tex] is a point on the line.

Given

[tex]y-3=\frac{3}{4}(x+2) \\ \\ y-3=\frac{3}{4}(x-(-2))[/tex]

Thus the line has a slope of 3/4 and passes through the point (-2, 3), we can obtain another point on the line by substituting an arbitrary value for x.

Consider x = 2, then

[tex]y-3= \frac{3}{4} (2+2)= \frac{3}{4} (4)=3 \\ \\ \Rightarrow y=3+3=6[/tex]

Thus another point on the line is (2, 6).

The line can then be graphed by joining the two points.

Please help thank you.

30 points.

Answers

Question 1:

The sum of all angles with a polygon with n sides is
180(n-2)

We have 20 sides.

180(20 -2) = 180 * 18
= 3240

Thus, the sum of all angles is 3240 degrees.
The second choice is your answer.

Question 2:

First, let's calculate the sum of all the angles.

180(12 - 2) = 1800

Now, divide that by the number of sides to get the measure of one angle.

1800/12 = 150

Your answer is the last choice.

Question 3:

Do the same as we did in question 2, but instead of 12 sides, there are 6 sides.
A regular hexagon has an interior angle measure of 120 degrees.
(Note: you should remember that for future reference).

Now, let's form the following equation

3x = 120

Divide both sides by 3

x = 40

The first choice is your answer.

Have an awesome day! :)

Hey there!

1. 3240. 20 gon is called an isogon
2.150 because the formula for the interior angle or regular polynomials is [tex] \frac{180(n-2)}{n}[/tex]
3.3x = 120
Divide both sides by 3
x = 40

A triangle has base 6 cm and area 42 cm^2 what is the height of the triangle

Answers

To find the area of a triangle, the formula is
A=bh/2
42=6h/2
Divide both sides by 6 giving you
h/2=7
Then, multiply by 2 on both sides giving you
h=14
The height then is 14 cm.

Final answer:

The height of the triangle is 14 cm.

Explanation:

To find the height of the triangle, we can use the formula for the area of a triangle: Area = 1/2 * base * height. In this case, the base is 6 cm and the area is 42 cm^2. By rearranging the formula, we can solve for the height: Height = 2 * Area / Base. Plugging in the values, we get Height = 2 * 42 cm^2 / 6 cm = 14 cm.

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What is the value of cos 45 degrees?
(answers in picture)

Answers

The answer will be b

Help please! I need to show my work

Answers

The centroid of a triangle is 2/3 of the way from the vertex to the opposite side. The centroid is the intersection of the medians. Each median has as endpoints a vertex and the midpoint of the opposite side.
a.
PC is 2/3 of PY, and CY is 1/3 of PY.
If CY = 10, then PC = 20, and PY = 30

b.
If QC = 10, then ZC = 5, a nd ZQ = 15.

c.
X is the midpoint of side PQ.
PX = XQ = 1/2(PQ)
If PX = 20, PQ = 40

a line that passes through two sides of triangles divides the sides proportionally

A. always
B. sometimes
C. never

Answers

The answer is B: Sometimes

The possible answer is B: sometimes so good luck

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