The figure below shows a rectangular prism and a cube:

A rectangular prism and a cube are drawn side by side. The length of the rectangle prism is 4 inches, the width is 3 over 4 inch, and its height is 1 and 2 over 4 inches. The cube has a side length of 1 over 4 inch.

How many such cubes are required to completely pack the prism without any gap or overlap?
choices:
288
576
1,152
1,636

Answer:

The highest common factor (HCF) of 24 and 20 is 4.

Step-by-step explanation:

Answer:

x = 33

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180 for x

x = 180 - (90 + 57) = 180 - 147 = 33

Using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

A triangle having vertices A, B, and C is known as triangle ABC.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

The closed, two-dimensional shape known as a triangle has three sides, three angles, and three vertices.

A triangle is part of a polygon.

So, we know that:

We must ascertain the value of x in order to determine the triangle's perimeter, IJK.

Using the ratio of comparable triangles and the triangles above, we have:

HF/KI = FG/IJ

Where,

HF = 35, KI = 77, FG = 27 and IJ = x

By changing the values, we obtain:

35/77 = 27/x

Take the cross product of the aforementioned equation, and we have:

35x = 27*77

x = 27*77/35 = 27 * 11/5 = 59.4

The triangle's perimeter is thus equal to the sum of its sides:

△IJK = 44 + 77 + 59.4 = 180.4

Therefore, using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.

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Correct question:

Watch the help video on the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Answer:

Step-by-step explanation:

exponents raised to a - power  is an inverse function probably not the right word

       a^-b    =  1/(a^b)     example       4^-2   = 1/(4^2)     =  1/16

so   (7^-1)^-1  is a double inverse which is back to the original number  7

      inverted 7 twice

      (7^-1)^-1     = (1/7)^-1     =  1/(1/7)     =   7     trust me or use your calculator

since the coeffients are the same  just add the powers...  some exponent rule

     5^2 * 5^4 * 5^-3   = 5^(2+4-3)   = 5³

here is it written out

5^2 * 5^4 * 5^-3    = 5²  ×   5^4   ×  5^-3    =   (5×5) × (5×5×5×5)  × (1/5×1/5×1/5)

    5×5 × 5× (5×5×5  × 1/5×1/5×1/5)           (5×5×5  × 1/5×1/5×1/5)  = 1

    5×5×5    = 5³

   so

Answer:

I am the son of waterbut when I return to water I die

Ice

Answer:

1. False

2. False

3. True

4. False

Step-by-step explanation:

Answer:

I think yes because u will have 760 leftover

Answer:

x=16

Step-by-step explanation:

3*4=12

4*4=16

Answer:

The minimum number of different rooms for accommodating 390 classes if there are 10 different time periods is 39

Step-by-step explanation:

Number of time periods = 10

Number of Classes = 390

Now, if we have a single room, then we can accommodate 10 classes

if we have 2 rooms, we can accommodate (10)(2) = 20 classes

and so on

so we have the relation,

(number of rooms)(number of time periods) = (number of classes that can be accommodated)

We need to find the number of rooms for 390 classes, given that number of time periods is 10, so we get,

(number of rooms)(10) = 390

number of rooms = 390/10

number of rooms =39

Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn - one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins

The probability that, at the tip of the fourth round, each of the players has four coins is 5/192.

Given that game consists of 4 rounds and every round, four balls are placed in an urn one green, one red, and two white.

It amounts to filling in an exceedingly 4×4 matrix. Columns C₁-C₄ are random draws each round; row of every player.

Also, let \(\%R_{A}\) be the quantity of nonzero elements in \(R_{A}.\)

Let \(C_{1}=\left(\begin{array}{l}1\\ -1\\ 0\\ 0\end{array}\right)\).

Parity demands that \(\%R_{A}\) and\(\%R_{B}\) must equal 2 or 4.

Case 1: \(\%R_{A}\)=4 and \(\%R_B\)=4. There are \(\left(\begin{array}{l}3\\ 2\end{array}\right)\)=3 ways to put 2-1's in \(R_A\), so there are 3 ways.

Case 2: \(\%R_{A}\)=2 and \(\%R_B\)=4. There are 3 ways to position the -1 in \(R_A\), 2 ways to put the remaining -1 in \(R_B\) (just don't put it under the -1 on top of it!), and a pair of ways for one among the opposite two players to draw the green ball. (We know it's green because Bernardo drew the red one.) we are able to just double to hide the case of \(\%R_{A}=4,\%R_{B}=2\) for a complete of 24 ways.

Case 3: \(\%R_A=\%R_B=2\). There are 3 ways to put the -1 in \(R_{A}\). Now, there are two cases on what happens next.

Hence, there are 3(2+2×2)=18 ways for this case. There's a grand total of 45 ways for this to happen, together with 12³ total cases. The probability we're soliciting for is thus 45/(12³)=5/192

Hence, at the top of the fourth round, each of the players has four coins probability is 5/192.

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Answer:

y=1/5x-1

Step-by-step explanation:

SI form is Y=mx+b

In a triangle, The value of x is, 40°

And, The value of y is, 50°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The triangle is show in figure.

We know that;

In a triangle, the pair of two opposite sides are equal then there corresponding angles are also equal.

Now, By figure we can formulate;

⇒ x + x + 100 = 180

Solve for x;

⇒ 2x + 100 = 180

⇒ 2x = 180 - 100

⇒ 2x = 80

⇒ x = 40

Thus, The value of x = 40°

And, We get;

⇒ x° + y° + 90° = 180°

⇒ 40 + y + 90 = 180

⇒ y + 130 = 180

⇒ y = 180 - 130

⇒ y = 50°

Thus, The value of y = 50°

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Answer:

$18 :)

Step-by-step explanation:

10% of 180 is 18

Answer:

A. x=20

Step-by-step explanation:

Answer: Probability cannot be greater than 1

so it would be D 1.1

Step-by-step explanation:

Answer:

D. 1.1

Step-by-step explanation: Hello

The second derivative, inflation point and slope of differential equation are explained below.

differential equation states how a pace of progress (a "differential") in one variable is connected with different factors. For example, when the position is zero (ie. the spring is neither extended nor compacted) then the  velocity isn't evolving.

We have,

dy/dx = 2x-y

Suppose f'(x) = 2x - y

d^2y/dx^2 = d(2x - y)/dx

⇒ 2

(b) To find the inflection points, equate f(x) to zero and solve for x.

f"(0) =0

f" (x)=2

So, the function defined on the interval (- ∞, 2) (2,  ∞)

In the interval (- ∞, 2), when x-1

f"(1)=2>0

So, the concave up wards on this interval.

In the interval (2,∞) when x=2

f"(2)=2>0

the concave up wards on this interval

Now, the slope of the function,

f(2)=3

here x-2y=3

Then, x = 2, y = 3

\(\frac{dy}{dx}|_{2, 3}\) = 2(2) - 3 = 1

Thus, the slope of the function is 1.

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The first five terms of the geometric sequence are:

So, the first five terms of the given geometric sequence:

Sequence is: a₁ = 20, r = 1/2

Now, get the terms as follows:

1st term: 20

2nd term: 20 × 1/2 = 10

3rd term: 10 × 1/2 = 5

4th term: 5 × 1/2 = 2.5

5th term: 2.5 × 1/2 = 1.25

Therefore, the first five terms of the geometric sequence are:

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Vince bought six boxes of worms to use as bait while fishing what his friends if each person uses exactly 3/8 of a box of worms, the number of people who can share the boxes of worms is 16.

The number of people who exactly share the boxes is determined through division of total number of boxes by fraction of box used by each person exactly.

The given information to compute the required information is:

The total number of boxes = 6

Box used by each person = 3/8

Therefore,

Number of people = Number of Boxes/Part of Box Used by One Person = 6÷ 3/8 = 6 x 8/3 = 16

Hence, the number of people who can share the six boxes exactly are 16 people.

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To determine whether the given sequence converges or diverges, we will examine each of the provided sequences and find their respective limits as n approaches infinity.

1. an = (-1)^n

The sequence alternates between -1 and 1 as n increases. Since it does not approach a specific value, the sequence diverges. Your answer for this sequence is NONE.

2. an = n^2 * e^(-n)

To find the limit as n approaches infinity, we can apply L'Hopital's Rule:

lim (n^2) / (e^n) as n approaches infinity.

Applying L'Hopital's Rule twice, we get:

lim (2n) / (e^n) and then lim (2) / (e^n).

As n approaches infinity, the denominator (e^n) increases without bound, so the limit becomes 0. The sequence converges to 0.

3. an = (3n - 1)! / (3n + 1)!

To find the limit as n approaches infinity, let's rewrite the sequence as:

an = 1 / [(3n)(3n + 1)]

As n approaches infinity, the denominator (3n)(3n + 1) increases without bound, and the sequence converges to 0.

In summary:
1. The sequence (-1)^n diverges (NONE).
2. The sequence n^2 * e^(-n) converges to 0.
3. The sequence (3n - 1)! / (3n + 1)! converges to 0.

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The foundational concepts of algebra include variables, equations, and operations. These concepts provide a basis for understanding and manipulating mathematical expressions and solving problems.



Variables are symbols that represent unknown quantities in algebraic expressions and equations. They allow us to generalize problems and find solutions that work for different scenarios. Equations are statements that express the equality of two algebraic expressions, providing a framework for solving problems. By setting up and solving equations, we can find values for variables and determine the relationships between different quantities.

Operations such as addition, subtraction, multiplication, and division are fundamental in algebra. They allow us to combine and manipulate expressions and equations, enabling us to simplify and solve complex problems. Operations also follow certain rules, such as the order of operations (PEMDAS/BODMAS), which ensure consistent and accurate computations.

Understanding these foundational concepts of variables, equations, and operations forms the basis of algebraic thinking. They provide the tools needed to analyze and solve problems in mathematics and real-world situations, allowing for the extension of algebra to more complex scenarios, such as systems of equations, inequalities, and functions.

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Replace x with any number and solve for Y.

Do this at least twice to get 2 points.

Place these points on the graph and draw a line through them.

See attached graph.

Let x = 2

y = 1.4(2)

y = 2.8

First point = (2,2.8)

Let x = 5

y = 1.4(5)

y = 7

Second point = (5,7)

The y-intercept is zero, that means the line is passing through origin.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The equation is given below.

y = 1.4x

In the above equation, y-intercept is not there, which means the line is passing through origin.

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Answer:

point C ad B located on the x axis

Missing values: 2 cups, 4 cups, 9 cups,Equivalent ratios: 34:13, 23:3, 1:6, 2:4, 13:9

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A quadratic equation is an equation whose leading coefficient is of second degree. The time can not be negative, therefore, the time in which the athlete complete the jump is 0.75 seconds.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The  jump is represented by the equation h(x)= -16x²+4x+6. The time is represented by x, now the height of the athlete will be zero when the jump will be completed therefore, we can write,

0 = - 16x² + 4x + 6

0 =  - 16x² + 12x - 8x + 6

0 = -4x(4x-3) -2(4x-3)

0 = (-4x-2)(4x-3)

x = -0.50, 0.75

Since the time can not be negative, therefore, the time in which the athlete complete the jump is 0.75 seconds.

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Answer:

l + w = 25 and lw = 136

w(25 - w) = 136

25w - w² = 36

w² - 25w - 136 = 0

(w - 17)(w - 8) = 0

w = 8, so l = 17

The dimensions of the bookmark are 8 cm by 17 cm.

it would take approximately 1,192,850 joules of energy to heat 0.5 kg of water from 70°C to steam at 100°C.

To calculate the energy required to heat 0.5 kg of water from 70°C to 100°C and then to convert it to steam at 100°C, we need to consider two separate processes: heating the water and then vaporizing it. The energy required for each process can be calculated using the specific heat capacity and latent heat of vaporization of water.

First, we need to calculate the energy required to heat the water from 70°C to 100°C. This can be done using the formula:

Q = m * c * ΔT

where Q is the energy required, m is the mass of water, c is the specific heat capacity of water (which is 4186 J/(kg°C)), and ΔT is the change in temperature. So:

Q1 = 0.5 * 4186 * (100 - 70) = 62850 J

Next, we need to calculate the energy required to vaporize the water at 100°C. This can be done using the formula:

Q = m * L

where Q is the energy required, m is the mass of water, and L is the latent heat of vaporization of water (which is 2260 kJ/kg). So:

Q2 = 0.5 * 2260 * 1000 = 1130000 J

The total energy required to heat 0.5 kg of water from 70°C to steam at 100°C is the sum of Q1 and Q2: Qtotal = Q1 + Q2 = 1130000 + 62850 = 1192850 J

Therefore, it would take approximately 1,192,850 joules of energy to heat 0.5 kg of water from 70°C to steam at 100°C.

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