You pick two marbles from a bag and record their color. How can you make your selections independent events? Dependent events?

A. Do not replace marbles after picking them; do replace marbles.
B. Replace marbles after picking them; do not replace marbles.

Answer:

The maximum value is 126 occurs at (9 , 9)

Step-by-step explanation:

* Lets remember that a function with 2 variables can written

 f(x , y) = ax + by + c

- We can find a maximum or minimum value that a function has for

 the points in the polygonal convex set

- Solve the inequalities to find the vertex of the polygon

- Use f(x , y) = ax + by + c to find the maximum value

∵ 8x + 2y = 36 ⇒ (1)

∵ -3x + 6y = 27 ⇒ (2)

- Multiply (1) by -3

∴ -24x - 6y = -108 ⇒ (3)

- Add (2) and (3)

∴ -27x = -81 ⇒ divide both sides by -27

∴ x = 3 ⇒ substitute this value in (1)

∴ 8(3) + 2y = 36

∴ 24 + 2y = 36 ⇒ subtract 24 from both sides

∴ 2y = 12 ⇒ ÷ 2

∴ y = 6

- One vertex is (3 , 6)

∵ 8x + 2y = 36 ⇒ (1)

∵ -7x + 5y = -18 ⇒ (2)

- Multiply (1) by 5 and (2) by -2

∴ 40x + 10y = 180 ⇒ (3)

∴ 14x - 10y = 36 ⇒ (4)

- Add (3) and (4)

∴ 54x = 216 ⇒ ÷ 54

∴ x = 4 ⇒ substitute this value in (1)

∴ 8(4) + 2y = 36

∴ 32 + 2y = 36 ⇒ subtract 32 from both sides

∴ 2y = 4 ⇒ ÷ 2

∴ y = 2

- Another vertex is (4 , 2)

∵ -3x + 6y = 27 ⇒ (1)

∵ -7x + 5y = -18 ⇒ (2)

- Multiply (1) by 7 and (2) by -3

∴ -21x + 42y = 189 ⇒ (3)

∴ 21x - 15y = 54 ⇒ (4)

- Add (3) and (4)

∴ 27y = 243 ⇒ ÷ 27

∴ y = 9 ⇒ substitute this value in (1)

∴ -3x + 6(9) = 27

∴ -3x + 54 = 27 ⇒ subtract 54 from both sides

∴ -3x = -27 ⇒ ÷ -3

∴ x = 9

- Another vertex is (9 , 9)

* Now lets substitute them in f(x , y) to find the maximum value

∵ f(x , y) = 9x + 5y

∴ f(3 , 6) = 9(3) + 5(6) = 27 + 30 = 57

∴ f(4 , 2) = 9(4) + 5(2) = 36 + 10 = 46

∴ f(1 , 5) = 9(9) + 5(9) = 81 + 45 = 126

- The maximum value is 126 occurs at (9 , 9)

The maximum value of the function for the polygonal convex set determined by a system of inequalities can be found using linear programming. The key steps are to plot the inequalities, find the vertices of the feasible region, and substitute these points into the function to find the maximum value.

This problem is related to linear programming, which is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. To find the maximum value of the function for the polygonal convex set determined by the given system of inequalities, you essentially need to apply the rules of linear programming.

Firstly, plot the system of inequalities on a coordinate system to determine the feasible region, which is the polygonal convex set. Then, find each vertex of this polygonal convex set. These vertices are points where boundaries of the system of inequalities intersect. Once you have these vertices, substitute each of them into the function you are maximizing. The largest output will be the maximum value of the function within the given polygonal convex set.

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Answer: 0.1(175-n)+0.05n=13.30

Step-by-step explanation: The question is asking you to make and simplify a system of equations.

The 2 equations are:

n+d=175

0.1d+0.05n=13.30.

d=175-n

Solve for n, then substitute into the second equation.

0.1(175-n)+0.05n=13.30

Hope this helps!

Answer:

1.67%

Step-by-step explanation:

With the given information that the computer depreciates 20% a year, we have our basis for making the calculation. What is asked for is how much of a depreciation the computer has monthly. One year has 12 months, so in order to get to the result we just simply need to divided the 20% with the number of months in a year to get the result:

20 / 12 = 1.67

The result is 1.67%, thus the computer depreciates 1.67% on a monthly basis.

ANSWER

b=1, c=81, and d=9.

EXPLANATION

The given function is:

[tex]y={x}^{2}-18x[/tex]

This function is the same as:

[tex]y={(x - 9)}^{2}-81[/tex]

To find the inverse of this function, we interchange x and y.

[tex]x={(y-9)}^{2}-81[/tex]

Solve for y:

[tex]x+81={(y- 9)}^{2}[/tex]

Take square root of both sides:

[tex]\pm \sqrt{x + 81}=y-9[/tex]

[tex]y=\pm \sqrt{x + 81}+9[/tex]

Hence,

b=1, c=81, and d=9.

Answer: b=1, c=81, d=9

Step-by-step explanation:

The diagonal (d) of the rectangular solid with dimensions l=8, w=4, h=2 is found using the Pythagorean theorem in three dimensions. Plugging in the values, d is approximately 9.17 units.

To find the diagonal (d) of a rectangular solid with length (l), width (w), and height (h), you can use the Pythagorean theorem in three dimensions. The formula for the diagonal of a rectangular solid is given by:

d = √(l² + w² + h²)

Given that l = 8, w = 4, and h = 2, we can substitute these values into the formula to find d:

d = √(8² + 4² + 2²) = √(64 + 16 + 4) = √84 ≈ 9.17

So the diagonal of the rectangular solid is approximately 9.17 units.

Answer:

13.86 units to the nearest hundredth.

Step-by-step explanation:

By Pythagoras:

16^2 = x^2 + 8^2

x^2 = 16^2 - 8^2

x^2  (16 + 8)(16 - 8) = 192

x = √192

= 13.86 (answer).

Answer:

x = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Since the triangle is right use Pythagoras' theorem to solve for x

The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides, thus

x² + 8² = 16²

x² + 64 = 256 ( subtract 64 from both sides )

x² = 192 ( take the square root of both sides )

x = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]

[tex]\dfrac1{x(x-1)}=\dfrac ax+\dfrac b{x-1}[/tex]

[tex]1=a(x-1)+bx[/tex]

If [tex]x=0[/tex], then

[tex]1=-a\implies a=-1[/tex]

If [tex]x=1[/tex], then

[tex]1=b[/tex]

So we have

[tex]\dfrac1{x(x-1)}=\dfrac1{x-1}-\dfrac1x[/tex]

Answer:

A. 12.4

Step-by-step explanation:

To find a, we'll use the Law of Sines that says:

[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]

And we'll isolate a to get:

[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]

We first need to find A, which is easy.  The sum of the interior angles of a triangle is 180 degrees... and we already have 2 of them, so:

A = 180 - 90 - 16.75 = 73.25

(converted 16°45' to 16.75)

Then we will plug-in the information we already have

[tex]c = \frac{sin(73.25) * 13}{sin(90)} = 12.45[/tex]

So, let's round it to 12.4 to match the answer A.

Answer:

The length of side marked a is 12.4 units.

Step-by-step explanation:

In ΔABC

∠B = 16°45’ = 16.75°

1 min arc = [tex]\frac{1}{60} degrees [/tex]

c = 13 units

a = ?

[tex]\cos \theta=\frac{Base}{Hypotenuse}[/tex]

[tex]\cos B=\frac{a}{13}[/tex]

[tex]0.95757=\frac{a}{13}[/tex]

[tex]a=0.95757\times 13=12.4484\approx 12.4 units[/tex]

The length of side marked a is 12.4 units.

For this case we have that by definition:

1 pound is equivalent to 16 ounces.

We make a rule of three to determine the ounces of butter:

1lb ------------------------> 16onzas

[tex]\frac {1} {12}[/tex]----------> x

Where "x" represents the ounces of butter

[tex]x = \frac {\frac {1} {12} * 16} {1}\\x = \frac {16} {12}\\x = \frac {8} {6}\\x = \frac {4} {3}[/tex]

Thus, there are [tex]\frac {4} {3}[/tex]ounces of butter.

Now we must find the amount of eggs that remain:

[tex]92- (43+ \frac {1} {5}) =\\92 - (\frac {43 * 5 + 1} {5}) =\\92 - (\frac {215 + 1} {5}) =\\92 - (\frac {216} {5}) =\\92-43.2 =\\48.8[/tex]

Round down. There are 48 eggs left.

Answer:

There are [tex]\frac {4} {3}[/tex] ounces of butter.

48 eggs left

The overall change in surface area when the height of a rectangular prism is increased by 0.2 cm can be calculated with the formula 0.4w + 0.4l.

In this question, we are looking at the surface area of a box that is a rectangular prism and how it will change if the height of the box is increased by 0.2 cm. The surface area of a prism is given by the formula 2lw + 2lh + 2wh, where l, w and h are the length, width and height respectively.

Now, if the height is increased by 0.2 cm, the difference in the surface area will be 2lw (because there are two ends with area lw that do not change) plus the change in the area of the sides. The sides' areas will increase by 2w x 0.2 and 2l x 0.2 respectively (since we have two opposing sides that both increase by 0.2 cm in height).

Therefore, the overall change in surface area when the height is increased by 0.2 cm is simply the sum of these two parts, which is 2w x 0.2 + 2l x 0.2. This can also be simplified to 0.4w + 0.4l.

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9514 1404 393

Answer:

Step-by-step explanation:

If y = f(x) then x = f^-1(y) is true if and only if f(x) is a one-to-one function.

__

1. False. Trig functions are periodic, so are not one-to-one.

2. True. The f(x) is specified as being one-to-one.

Answer:

1. True
2. True

Step-by-step explanation:

1. Since a capital letter (F) is used to show that the inverse equation is indeed a function, the question is true. If the inverse (second equation) was written as x=f-1(y), it would be false.

2. For one-to-one functions, all you need to do to reverse them is switch the x and y variables, and the [tex]f^-1[/tex] signifies that it is an inverse function.

so she saved $20 and that was 40% of the regular price, let's say the regular price is "x".

if 20 is 40%, what is "x" or namely the 100%?

[tex]\bf \begin{array}{ccll} amount0&\%\\ \cline{1-2} 20&40\\ x&100 \end{array}\implies \cfrac{20}{x}=\cfrac{40}{100}\implies \cfrac{20}{x}=\cfrac{2}{5}\implies 100=2x \\\\\\ \cfrac{100}{2}=x\implies 50=x[/tex]

Answer:This is an equation! Solutions: x=1.

Step-by-step

-5 cause it is 32-42 and the anserw is -5

Answer:

Option d.

±π/2 ; ±3π/2

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)= 3*cos (x)

We can see from the graph that the zeros are

±π/2 ; ±3π/2

Correct option is d.

Answer:

D

Step-by-step explanation:

If you made a table and filled in the values,  the rate column it would look like this:  

                   d     =      r             t

truck                         80

car                            90

So far so good.  If we want the car to catch up with the truck, that means that in the end they travel the exact same amount of miles.  So let's fill in the d:

               d     =     r             t

truck       d           80

car          d           90

Again, not too bad.  If the car leaves 20 minutes later than the truck, that means that the time the truck is traveling is 20 minutes more than the car's time.  So the car's time is t and the truck's time is t + 20:

             d     =     r         t

truck      d           80     t+20

car         d           90        t

Now because the distances are equal, we can set the rate times time for each vehicle equal to each other:

80(t + 20) = 90t

That is choice D

Answer:

7.5 weeks

Step-by-step explanation:

If you want to find out how long it take for the plant to reach a foot you set up the equation like so:

12=1.2w+3

and solve from there.

12=1.2w+3                       Subrtact 3 from both sides

9=1.2w                             Divide by 1.2 to isolate w

7.5=w                              Answer is 7.5 weeks

The [tex]7.5[/tex] weeks it will take the plant to reach one foot.

What is height?

In math, height is the vertical distance from the top to the base of the object and it is measured in cm, inches, meters, etc.

It is given that the height [tex]h[/tex] of the plant (in inches) [tex]w[/tex] weeks.

The equation is,

[tex]h=1.2w+3[/tex]

As we know that,

[tex]$12\,\text{inches}=1\,\text{foot}$[/tex]

The number of weeks that it will take the plant to reach one foot will be:

[tex]h=1.2w+3[/tex]

[tex]12=1.2w+3[/tex]

[tex]1.2w=12-3[/tex]

So,

[tex]w=\frac{9}{1.2}[/tex]

[tex]$\therefore w=7.5$[/tex]

Hence, it will take [tex]7.5[/tex] weeks.

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ANSWER

A. 8x=16

EXPLANATION

The given equations are:

1st equation: y=2x

2nd equation: 2x+3y=16

We substitute the first equation into the second equation to get:

2x+3(2x)=16

This implies that:

2x+6x=16

We combine like terms to get:

8x=16

The correct choice is A. 8x=16

Answer:

C

Step-by-step explanation:

The formula for effective annual interest rate is:

[tex]r=(1+\frac{i}{n})^{n}-1[/tex]

where

r is the effective annual interest rate

i is the stated interest rate (here, it is 1.55%, or 0.0155)

n is the number of compounding periods (here, compounded monthly, so it means 12 times a year, so n = 12)

plugging these info into the formula, we get:

[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.0155}{12})^{12}-1\\r=0.0156[/tex]

0.0156 * 100 = 1.56%

correct answer is C

Answer:

The answer is C

Step-by-step explanation:

i got it right on Plato : ) Brainliest?

Answer:

x + 6 =

Step-by-step explanation:

In math sum means addition, difference is subtraction, product is multiplication, and quotient is division

ANSWER

x+6

EXPLANATION

An algebraic expression contains letters and numbers that are connected with mathematical operators or symbols.

The sum of x and 6 as an algebraic up expression is:

x+6

This expression contains a variable , a mathematical symbol and a number.

Answer:

(2x+3)(2x+3)

Step-by-step explanation:

a^2+2ab+b^2

Simplify for -5/8*2/3= -5/12

-0.416 as a mixed number

To find the volume, you need to do length times width times height

SO you have to do 5 times 5 times 6

The volume is 150 cubic feet

Since 150 cubic feet of this rectangular prism is 15 tons

you can do 15 divided by 150

so one cubic feet of this stone sculpture weight 0.1 tons

Btw, a pyramid is  a triangular structure, not rectangular

ANSWER

I) 5:11

ii) 5:11

iii) 125:1331

EXPLANATION

Let the side lengths be in the ratio:

x:y

This implies that the area will be in the ratio:

[tex] \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121} [/tex]

Take positive square root.

[tex] \frac{x}{y} = \sqrt{ \frac{25}{121} } [/tex]

[tex] \frac{x}{y} = \frac{5}{11} [/tex]

Hence the sides are in the ratio:

x:y=5:11

The perimeter of the smaller hexagon is 6×5=30

The perimeter of the larger hexagon is 6×11=66

The ratio of the perimeter is

30:66=5:11

The volume will be in the ratio

5³:11³

125:1331

Answer:

a=25.km

Step-by-step explanation:

A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km

The concluding part could be the following:

On the path to the traveler's left, a sign reads "Turtle Lake: 17km." The traveler also observes that the angle between the paths is 1.3 radians. Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake? km Round your answer to the nearest kilometer

since the angle between them is actually 1.3 rad

lets convert to degrees

74.48 degrees

using cosine of angle we can find the distance  between the two destinations

[tex]a^{2} =b^{2} +c^{2} -2bcCos\alpha[/tex]

[tex]\alpha[/tex]=74.48 deg

a^2=17^2+24^2-(2*17*24)cos74.48

a^2=646.65

find the square root of both sides

a=25.42km

approximately=25Km

Answer:

Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

[tex]x\leq 7.5\ pounds[/tex]

Part 2) [tex]m+n=(0.76x-0.28)[/tex]

Step-by-step explanation:

Part 1)

Let

x-----> the number of pounds of regular coffee

we know that

The inequality that represent the situation is

[tex]2x\leq 15[/tex]

Solve for x

Divide by 2 both sides

[tex]x\leq 15/2[/tex]

[tex]x\leq 7.5\ pounds[/tex]

The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

The solution of the inequality is the interval ------> (-∞,7.5]

but the number of pounds cannot be a negative number

therefore

The solution is the interval -----> [0,7.5]

see the attached figure

Part 2) we have

[tex]m=0.56x-0.25[/tex]

[tex]m=0.20x-0.03[/tex]

Adds m and n

[tex]m+n=(0.56x-0.25)+(0.20x-0.03)[/tex]

Group terms that contain the same variable

[tex]m+n=(0.56x+0.20x)+(-0.25-0.03)[/tex]

Combine like terms

[tex]m+n=(0.76x-0.28)[/tex]

ANSWER

C(2,-6)

EXPLANATION

The solution set to given inequality is the shaded region.

The points are also located in the graph above.

The only point that falls in the solution region is C(2,-6)

The ordered pair that is in the solution set is C(2,-6)

The third option is correct.

Answer:

[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]

Step-by-step explanation:

1. Calculate the slope of Line f

y - 3 = -⁹/₄(x – 6)

The coefficient of x is -⁹/₄, so

The slope m₁ = -⁹/₄.

2. Calculate the slope of the perpendicular line

m₂ = -1/m₁

m₂ =  ⁴/₉

3. Calculate the y-intercept of line g

y = mx + b

4 = 6(⁴/₉) + b

4 = ⁸/₃ + b

Subtract ⁸/₃ from each side:     b = 4 - ⁸/₃ = ⁴/₃

The y-intercept is b = ⁴/₃.

Step 4. Write the equation for line g

[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]

The Figure below shows the graph of line f in red, and the graph of its perpendicular line g in black.

Answer:

[tex]\frac{38}{7}[/tex]

Step-by-step explanation:

Using the properties of logarithms,

[tex]\log(7)+\log(x-4)=1\\\log(7(x-4))=1\\\log(7x-28)[/tex]

Now think about what this is asking. The log function say 10 to the power of whats on the other side of the equals sign, equals whats in the parenthesis. So, this means whats is the parenthesis is equal to [tex]10^1[/tex] or just 10.

We can now solve to x.

[tex]7x-28 = 10\\7x=38\\x=\frac{38}{7}[/tex]

Answer:

x=38/7

Step-by-step explanation:

Just took the test

Answer:

a. 1/150.

b. 14.

Step-by-step explanation:

a.  That would be 2/300 = 1/150.

b.  So we expect 1 out of every 150  bikes will have 1 with defective brakes so out of 2,100 it is (1/150) * 2,100

= 14.

Step-by-step explanation:

Answer:

The area of the hexagon is [tex]96\sqrt{3}\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the hexagon is equal to

[tex]A=\frac{1}{2}Pa[/tex]

where

P is the perimeter of the hexagon

a is the apothem

Find the Perimeter P

[tex]P=6(8)=48\ cm[/tex]

Find the apothem a

[tex]a=(8)sin(60\°)[/tex]

[tex]a=8(\frac{\sqrt{3}}{2})=4\sqrt{3}\ cm[/tex]

Find the area of the hexagon

[tex]A=\frac{1}{2}(48)(4\sqrt{3})=96\sqrt{3}\ cm^{2}[/tex]