If 12 ft² of material is available to make a box with square base and open top, find the largest possible volume for the box. (Make sure to justify why your answer corresponds to an absolute maximum.)

result = 39 - 39 x 3% = 39 x 0,97 = 37,83

Answer:

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The ratio by mass of copper to zinc in the alloy is 3:1.

To find the ratio by mass of copper to zinc in the alloy, we need to first calculate the total mass of the alloy. We can do this by adding the mass of copper and zinc:

Total mass of alloy = 13.5 g + 4.5 g = 18 g

Now we can find the ratio of copper to zinc by dividing the mass of copper by the mass of zinc:

Ratio of copper to zinc = 13.5 g / 4.5 g = 3:1

Therefore, the ratio by mass of copper to zinc in the alloy is 3:1.

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Answer:

c

Step-by-step explanation:

Answer:

18c

= 18(36)

=648

Hope this helps you

Answer:

Part H

How many holes need to be drilled for 36 parts? Show your work.

Step-by-step explanation:

18c

= 18(36)

= 648

Cards are dealt from a standard shuffled deck of cards until the first ace is drawn. So the chance that the next card is a king is 0.05 percent.

            When drawing a card from a standard deck of 52 cards, the chance of drawing an ace is 4/52 or 1/13. After an ace has been drawn, there are 51 cards left in the deck, and 4 of them are kings.

           So, the probability of drawing an ace and then a king is

                     (1/13) × (4/51) = 4/663.

There are 4 different aces that could be drawn, each with the same probability of

                      (1/13) × (4/51) = 4/663,

So we multiply by 4 to account for all the possible aces that could be drawn.

Therefore, the total probability of drawing an ace and then a king is

                     (4/663) × 4 = 16/663.

         Once an ace has been drawn, there are 51 cards remaining in the deck, and only one of them is a king. Therefore, the probability of drawing a king after an ace has been drawn is 1/51.

         The probability that the next card is a king after the first ace is drawn is thus:

                    (16/663) × (1/51) = 16/33663

                                              = 1/2104.

      This simplifies to 0.0475 percent or approximately 0.05 percent.

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Answer:

x = 112°

Step-by-step explanation:

The missing two internal angles of the triangle measure:

\(180-126=54^{0}\)

\(180-58-54=68^{o}\)

then:

\(x=180-68=112^{o}\)

Hope this helps

Two processes are ,independent assortment and crossing over or recombination.

independent assortment

Independent assortment is the process where the chromosomes move randomly to separate poles during meiosis. A gamete will end up with 23 chromosomes after meiosis, but independent assortment means that each gamete will have 1 of many different combinations of chromosomes.

Crossing over or Recombination

Crossing over is a cellular process that happens during meiosis when chromosomes of the same type are lined up.

It refers to the exchange of genetic material between non-sister chromatids of homologous chromosomes. It occurs at the pachytene stage of prophase 1 in meiosis 1. It is the event that leads to recombination.

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The scale factor of the dilation of the triangles is 2

From the question, we have the following parameters that can be used in our computation:

The similar triangles

The scale factor of the dilation is the division of the corresponding sides

So, we have

Scale factor = 6/3

When evaluated, we have

scale factor = 2

Hence the scale factor is 2

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Answer:

\(9x - 7 \leq 38 \\ 9x \le 45x \\ x\le \frac{45}{9} \\ \therefore x \le5\)

Answer:By solving a system of equations, we will see that the function is continuous for all values of x

Step-by-step explanation:

Answer:

20 is.the net force act in object

Answer:

equation form: 12 + 2x = 18

x = 3

lets check the work see if its true

12 + 2(3) = 18

12 + 6 = 18

It Checks!

therefore your answer is 3. He can get 3 different toppings

Step-by-step explanation:

Answer:

hi,

Step-by-step explanation:

\(\left\{\begin{array}{ccc}a&=&3*\vec{i}-4\vec{j}\\b&=&2*\vec{i}-5\vec{j}\\c&=&\lambda*\vec{i}+\mu*\vec{j}\\\end{array}\right.\\\\\\\lambda*c=2a+3b\\=2*(3*\vec{i}-4\vec{j})+3*(2*\vec{i}-5\vec{j})\\=12*\vec{i}-23\vec{j}\\=\lambda*(\lambda*\vec{i}+\mu*\vec{j})\\\\\\\left\{\begin{array}{ccc}\lambda^2&=&12\\\lambda*\mu&=&-23\end{array}\right.\\\\\\\left\{\begin{array}{ccc}\lambda&=&2\sqrt{3}\\\mu&=&\dfrac{-23*\sqrt{3} }{6} \\\end{array}\right.\\\)

Answer:

x = 8

y = 36

Step-by-step explanation:

The triangle shown in the image is an isosceles triangle.

We can find the value of x using the above mentioned information:

∠B = ∠A

5x = 40 divide both sides by 5

x = 8

The sum of interior angles in a triangle is equal to 180°.

Since ∠B and ∠C are both 40°:

40 + 40 + 3y - 8 = 180 add/subtract like terms

72 + 3y = 180 subtract 73 from both sides

3y = 108 divide both sides by 3

y = 36

Answer:

8) x = 3

9) x = 10

Step-by-step explanation:

8) 45° ≅ 15x, therefore, the equation would look like: \(45 = 15x\)

☆Let's solve it!

\( \frac{45}{15} = \frac{15x}{15} \\ 3 = x\)

9) 12x - 10 is supplementary to 8x - 10. So the equation would be: \(12 x- 10 + 8x - 10 = 180\)

☆Let's solve it!

\(12x - 10 + 8x - 10 = 180 \\ 20x - 20 = 180 \\ \frac{ \: \: \: \: \: \: \: \: \: \: + 20 = + 20}{ \frac{20x}{20} = \frac{200}{20} } \\ x = 10\)

You mean like graph? Yeah.

Write in Function form

\(\frac{y-3}{x-6}=2\\y-3=2(x-6)\\y=2(x-6)+3\\y=2x-12+3\\y=2x-9\)

So (y-3/x-6)=2 does represent "line"

\(\frac{y-6}{x-4}=5\)

multiply x-4 all side.

\(y-6=5(x-4)\)

Notice how the equation is similar to "Tangent" so it's clearly a line.

About reasoning, No idea how to explain but this might help...

Whenever you get rid of the fraction part, it'll leave only y-f(a)=f'(a)(x-a) which is a Tangent Line (It explains it.)

And when you simplify in Function Form, you'll get an exact linear function  "\(y=mx+b\)"

Answer:

(\(\frac{5}{2}\)), \(-\frac{1}{2}\)

Step-by-step explanation:

Formula:

Add both "x" coordinates, divide by 2

Add both "y" coordinates, divide by 2

~I hope I helped you! :)~

\(\frac{-3 - (-4)}{1 - (-5)}\)

= \(\frac{-3 + 4}{1 + 5}\)

= 1/6

The values obtained in part (a), we have: ∫∫xy dσ = ∫∫(ρsin(φ)cos(π/4))(ρsin(φ)sin(π/4))ρ^2sin(φ)dφdθ. Simplifying and evaluating the integral, we can calculate the value of ∫∫xy dσ over surface S.

(a) To find a parametrization of the surface S, we can use spherical coordinates. In spherical coordinates, the equations for x, y, and z are given by:
x = ρsin(φ)cos(θ)
y = ρsin(φ)sin(θ)
z = ρcos(φ)
Given that x = y, we can substitute this into the equations above: ρsin(φ)cos(θ) = ρsin(φ)sin(θ)
Simplifying the equation, we have: cos(θ) = sin(θ)
This equation holds true when θ = π/4. Substituting this value into the equations above, we get:
x = ρsin(φ)cos(π/4)
y = ρsin(φ)sin(π/4)
z = ρcos(φ)

So, a parametrization of the surface S in spherical coordinates is:
ρ = √2
φ ∈ [0, π]
θ = π/4
(b) To calculate the integral ∫∫xy dσ over surface S, we can use the parametrization obtained in part (a). The surface element dσ can be expressed in spherical coordinates as:
dσ = ρ^2sin(φ)dφdθ
Substituting the values obtained in part (a), we have:

∫∫xy dσ = ∫∫(ρsin(φ)cos(π/4))(ρsin(φ)sin(π/4))ρ^2sin(φ)dφdθ
Simplifying and evaluating the integral, we can calculate the value of ∫∫xy dσ over surface S.

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The chance of getting a number that is either a multiple of 2 or a multiple of 3 when tossing a fair dice once is 0.50.

When a fair dice is tossed once, there are six possible outcomes, which are the numbers 1 to 6. To determine the chance of getting a number that is either a multiple of 2 or a multiple of 3, we need to identify the favorable outcomes.

The numbers that are multiples of 2 are 2, 4, and 6, while the numbers that are multiples of 3 are 3 and 6. However, we need to be careful not to count 6 twice since it is both a multiple of 2 and a multiple of 3.

Thus, we have three favorable outcomes: 2, 4, and 6. Since there are six possible outcomes, the probability of getting a number that is either a multiple of 2 or a multiple of 3 is calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 3 / 6 = 0.50

Therefore, the chance of getting a number that is either a multiple of 2 or a multiple of 3 when tossing a fair dice once is 0.50, indicating a 50% probability.

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Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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The length of the kite and the tail are \(4\frac{2}{3}\) and \(10\frac{5}{6}\) ft respectively.

The tail of the kite is 1.5 feet plus twice the length of the kite.  Together, the kite and tail are 15.5 ft long.  

The length of the tail and the kite can be found as follows:'

let

length of kite = x

Therefore,

length of the tail = 1.5 + 2x

Together the length of kite and tail is 15.5 ft

Hence,

1.5 + 2x + x  = 15.5

1.5 + 3x = 15.5

3x = 15.5 - 1.5

3x = 14

x = 14  /3

x = \(4\frac{2}{3}\) ft

length of the tail =  1.5 + 2(14 / 3)

length of the tail = 1.5 + 28 / 3

length of the tail = 65 / 6 = \(10\frac{5}{6}\) ft

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The equation of the tangent plane to the surface x²/4 + y²/9 - z²/5 = 0 at the point (1, 2, 5/6) is 2x + 4y - 5z + 17/6 = 0.

To find the equation of the tangent plane, we first calculate the partial derivatives of the given surface equation with respect to x, y, and z. The partial derivatives are ∂f/∂x = x/2, ∂f/∂y = 2y/9, and ∂f/∂z = -z/5.

Next, we substitute the coordinates of the given point (1, 2, 5/6) into these partial derivatives to find their respective values at that point.

Plugging these values into the equation of a plane (Ax + By + Cz + D = 0) and simplifying, we obtain 2x + 4y - 5z + 17/6 = 0 as the equation of the tangent plane to the surface at the given point.


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Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing.  I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

y = -(2/3) -(4/3)

y = -(6/3) or -2

The solution is (2,-2)

===============

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

Answer:

I believe it's  (5.7, 2.2)

I hope it's correct :)

c

Step-by-step explanation:

for the lazy people like me its c

The number of cups sold at the first game is 55.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of each souvenir = $2.25

The total amount collected from the souvenir cups sales = $123.75

The number of cups sold at the first game.

= 123.75/2.25

= 55

Thus,

The number of cups sold is 55.

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Yes, there is a correlation between these measures. The higher the placement exam score, the higher the student's score on their first exam tends to be. For example, students with placement exam scores of 11 and 49 had first exam scores of 27 and 71 respectively, indicating that the higher the placement exam score, the higher the first exam score.

A measure in mathematics is a generalization of the ideas of length, area, and volume. Measures are sometimes referred to as "mass distributions" informally. A measure, in more exact terms, is a function that gives numbers to particular subsets of a given set. This quantity is described as the set's measure.

To measure length or distance, this system employs inches, feet, yards, and miles. Volume or capacity are expressed in fluid ounces, cups, pints, quarts, or gallons. In ounces, pounds, and tons, weight or mass is expressed.

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