In her math class, carla used unit cubes to build a right rectangular prism with a volume of 24 cubic units. The height of the prism was two units. Which figure could be bottom layer of the prism

Answer:

BC = \(\frac{12}{13}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

BC² + AC² = AB²

BC² + (\(\frac{5}{13}\) )² = 1²

BC² + \(\frac{25}{169}\) = 1 ( subtract \(\frac{25}{169}\) from both sides )

BC² = \(\frac{169}{169}\) - \(\frac{25}{169}\) = \(\frac{144}{169}\) ( take square root of both sides )

BC = \(\sqrt{\frac{144}{169} }\) = \(\frac{12}{13}\)

the size of the wedge for aqua pencils is 43°

Given:

A table showing the pencil collection

To find:

the portion that represents the aqua pencils in degree

The total number of pencils = 23 + 106 + 62 + 47 + 32

The total number of pencils = 270

In degrees:

Total angle in a circle = 360°

Size of the wedge for aqua = number of aqua pencils/total pencils × 360°

To the nearest degree, the size of the wedge for aqua pencils is 43°

Profit fall in one year = 116.8$

What is profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are several profit metrics that are frequently used.

Let cost price = C

And selling price before reducing = S

Profit for 1 day = S-C

Now, After reducing selling price to = S-0.32

Profit= S - 0.32 - C for 1 day

Profit fall by = (S-C)-(S - 0.32 - C)

                     = S - C - S + 0.32 + C

Profit fall by = 0.32 for 1 day

Profit fall by one year = 0.32×365

                                    = 116.8$

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There are a total of 216 ways in which the waiter could serve the meal types.

Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.

Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.

If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.

If the two B people both get F's, the situation is identical to the above and three possibilities arise.

If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.

In total, we see there are 24 possibilities, so the answer is 9*24 = 216

Thus, there are a total of 216 ways in which the waiter could serve the meal types.

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Your question was incomplete. Check for missing part below-

Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.

If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.

This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.

The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.

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The number of vehicles stuck in the traffic is 1152 .

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

It is given that,

60% of the traffic consists of cars = 0.6

40% of the traffic consists of trucks = 0.7

average distance between vehicles is 3 feet

average length of a car is 13.5 feet

average length of a truck is 20 feet

There are 5280 feet in 1 mile

Let 'n' be the total number of vehicles stuck in the traffic jam.

So, according to question we get the following equation

0.6n*13.5 + 0.7n*20 + 6n - 3 = 6*5280

⇒ 8.1n + 14n + 6n -3 = 31680

⇒ 28.1n = 31680 + 3

⇒ 28.1n = 31683

or, n = 31683/28.1

or, n = 1127.50

or, n ≈ 1128

So the closest option is 1152 vehicles.

Hence,The number of vehicles stuck in the traffic is 1152 .

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Answer:

Step-by-step explanation:

$68

--------------- * 15 months = $85

12 months

15 months will cost $85.  Total cost (m) = ($5.67/mo)*m, where m represents the number of months of service purchased.

Answer:2000/180=11.11 p

Step-by-step explanation:

mark brainliest

The value of the investment multiplier is 5.

Given that:

Consumption function: C = c0 + c1(Y − T)

Investment function: I = I0 − m(r)

Government spending: G = G0

Tax revenue: T = t0 + t1Y

Where, C = Consumption

GDP = Y = C + I + G

Disposable income = Y − T

Private saving = Y − T − CG

= Government spending

I = Investment

t0 = autonomous tax component

t1 = endogenous tax component

m(r) = investment multiplier

Finding the equilibrium values of GDP, consumption, disposable income, and private saving

To find the equilibrium values, we need to set Y = GDP,

C = Consumption, T = Tax revenue and

S = Private Saving.

So, Y = C + I + GY = c0 + c1(Y − T) + I0 − m(r)GDP

= (c0 + I0 + G0 + t0) + (c1 − m(r))Y − t1Y.

GDP = \([c0 + I0 + G0 + t0] / [1 − (c1 − m(r) + t1)]\)

Now, we need to calculate the value of consumption and private saving

Disposable income = Y − T

Disposable income = Y − (t0 + t1Y)

Disposable income = (1 − t1)Y − t0

Consumption = c0 + c1(Y − T)

\(= c0 + c1(1 − t1)Y − c1t0\)

Private saving = \((1 − t1)Y − (t0 + c0 + c1(1 − t1)Y − c1t0)\)

Private saving = \((1 − c1)(1 − t1)Y + (c0 − c1t0)\)

The expression of the investment multiplier in terms of c0 and/or c1 is:

\(ΔY / ΔI = 1 / [1 − c1 + m'(r)]\)

The values of c0 and c1 are 48 and 0.6, respectively.

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The value of x in the figure is 18

The angle with the measure 9x -12 and the angle with the measure 30 degrees are internal angles of a transversal

This means that

9x -12 + 30 = 180

Evaluate the like terms

9x = 162

Divide by 9

x = 18

Hence, the value of x in the figure is 18

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When s = 0, it will take 20 units of time for the account to double to 2X.

(a) When s = 0, it means the deposit is made at time t = 0. We want to find the time it takes for the account to double to 2X.

To find this time, we need to solve the equation a(t) = 2, where a(t) is the accumulation function.

1 - 0.05t = 2

Simplifying the equation, we have:

-0.05t = 1

Dividing both sides by -0.05, we get:

t = -1 / (-0.05)

t = 20

Therefore, when s = 0, it will take 20 units of time for the account to double to 2X.

(b) When s = 5, it means the deposit is made at time t = 5. We want to find the time it takes for the account to double to 2X.

Using the same equation a(t) = 2 and substituting t = 5, we have:

1 - 0.05(5) = 2

1 - 0.25 = 2

0.75 = 2

This equation is not satisfied, which means the account will not double to 2X when the deposit is made at time t = 5.

(c) The answer in (a) is greater than the answer in (b) because when the deposit is made at time t = 0, the account has more time to accumulate interest and grow compared to when the deposit is made at time t = 5. As time progresses, the effect of compounding becomes more significant, and starting earlier allows for more growth and a shorter time to double the account.

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Answer:

b i did this a week ago

Step-by-step explanation:

The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.

To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.

Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.

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Answer:

3.15 for 10 is the better deal

Step-by-step explanation:

This is because $3.15 for 10 apples is worth 32 cents per apple. On the other hand, $4.10 for 11 apples is worth 37 cents per apple. And even though you're getting more apples it is costing you more per apple.

The door would have been 3 inches high in Alice's normal world.

If Alice's height changed from about 50 inches to 10 inches, we can find the ratio of her height change:

Height change ratio = (Final height) / (Initial height)

Height change ratio = 10 inches / 50 inches

Height change ratio = 1/5

Now, let's apply this height change ratio to the height of the door in Wonderland. If the door in Wonderland was 15 inches high, we can calculate its height in Alice's normal world using the height change ratio:

Door height in Alice's normal world = (Door height in Wonderland) * (Height change ratio)

Door height in Alice's normal world = 15 inches * (1/5)

Door height in Alice's normal world = 3 inches

Therefore, the door would have been 3 inches high in Alice's normal world.

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There are two stiff transforms to use:

The fact that the real domain is the domain of quadratic functions makes it possible to identify the solution set.

Thus, we must decide which rigid transformations to apply to f(x) in order to produce g(x). Rigid transformations are transformations applied to geometric loci in the field of Euclidean geometry so that Euclidean distances within the latter are conserved (x).

Following thorough consideration, we come to the conclusion that the two stiff transformations listed below must be used:

Vertical translation 7 units to the plus side.

reflection along the y = 5 line.

The collection of x-values necessary for the function to exist is represented by the solution set.  Due to the fact that both functions are quadratic equations, the entire real domain is described by their solutions.

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Answer:

300

Step-by-step explanation:

multiply 25 by 12

\(\begin{array}{| c | c |}\boxed{ \bf{Equations} }&\boxed{ \bf{YES \: OR \: NO}} \\ \\ \tt{1. \: \:y = {x}^{2} + 2} & \tt{YES} \\\tt{2. \: \:y = 2x - 10}& \tt{NO} \\ \tt{3. \: \:y = 9 - {2x}^{2}} & \tt{YES} \\ \tt{ 4. \: \:y = {2}^{x} + 2}& \tt{ NO} \\ \tt{5. \: \:y = {3x}^{2} + {x}^{3} + 2}& \tt{NO} \\ \tt{ 6. \: \:y = {2}^{x} + 3x + 2}& \tt{NO} \\ \tt{ 7. \: \:y = {2x}^{2}} & \tt{ YES} \\ \tt{ 8. \: \:y = (x - 2)(x + 4)}& \tt{YES} \\ \tt{9. \: \:0 = (x - 3)(x + 3) + {x}^{2} - y}& \tt{YES} \\ \tt{10. \: \:{3x}^{3} + y - 2x = 0}& \tt{NO}\end{array}\)

First of all we can solved the function

We using the identity,

(x + a)(x + b) = x² + (a + b)x + ab

(x - 2)(x + 4)

= x² + (-2 + 4)x + (-2)(4)

= x² + 2x - 8

First of all we can solved the function

We using the identity,

(a + b)(a - b) = a² - b²

(x - 3)(x + 3) + x² - y

= x² - 3² + x² - y

= x² - 9 + x² - y

= x² + x² - y - 9

= 2x² - y - 9

The classical probability density for a particle in an infinite square well is uniform within the well and zero outside. The classical averages for position and momentum are proportional to the size of the well.

(a) The classical probability density describing a particle in an infinite square well can be derived by considering the time the particle spends in each interval. In the classical framework, the probability for finding a particle in a particular interval is proportional to the time it spends in that interval.

For an infinite square well of dimension L, the particle is confined to the region between 0 and L. Assuming the particle has a constant velocity, the time it takes to travel from 0 to L is given by L/v, where v is the velocity. Therefore, the probability of finding the particle in the interval [a, b] is proportional to the time it spends in that interval, which is (b - a)/v.

Since the probability density is defined as the probability per unit length, we can express it as follows:

ρ(x) = k, if 0 ≤ x ≤ L,

      = 0, otherwise,

where k is a constant. This implies that the probability density is constant within the well and zero outside of it. Thus, the classical probability density for a particle in an infinite square well is uniform within the well and zero outside.

(b) Using the classical probability density derived in part (a), we can determine the classical averages and for a particle confined to the well. The classical average position is given by:

<x> = ∫ xρ(x) dx,

and the classical average momentum is given by:

<p> = ∫ pρ(x) dx.

Since the classical probability density is uniform within the well, the integrals become:

<x> = k ∫ x dx, from 0 to L,

<p> = k ∫ p dx, from 0 to L.

Evaluating these integrals yields:

<x> = k(L²/2),

<p> = k(Lp/2),

where Lp is the linear momentum. These results indicate that the classical averages for position and momentum are proportional to the size of the well. Comparing these classical results with the quantum results obtained from Example, we observe that the quantum averages are not proportional to the size of the well. s, especially in systems with confinement and discreteness. When compared to the quantum results, we observe deviations from the classical predictions, indicating the limitations of classical mechanics in describing confined quantum systems. This deviation is in line with the correspondence principle, which states that classical mechanics is a limiting case of quantum mechanics for large quantum numbers or systems.

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Answer:

-2/-3.

Step-by-step explanation:

Oh, this is easy!!

You need to find a point on the graph where it hits perfectly, for example, (2,-4), then use (-1,2).

Then use slope formula (y^2 - y^1/x^2 - x^1).

Plug in the X's and Y's.

Then, do  2 - (-4), and -1 - 2.

You'd get -2/-3 :)

(im not sure if im right, but i hope this helped!)

Answer:

Step-by-step explanation:

Answer:

3¹⁴

Step-by-step explanation:

Answer:

10% probability that the number is greater than 2, then P

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Event A: Number greater than 2.

Event B: Letter P.

These events are independent, so:

\(P(A \cap B) = P(A) \times P(B)\)

P(A)

There are 5 numbers.

3, 4 or 5, that is, 3 numbers greater than 2.

3/5 = 0.6. So P(A) = 0.6.

P(B)

6 letters, one of which is P. So

P(B) = 1/6 = 0.1667.

What is the probability the number is greater than 2, then P?

\(P(A \cap B) = P(A) \times P(B) = 0.6 \times 0.1667 = 0.1\)

10% probability that the number is greater than 2, then P

if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.

The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.

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Answer:

The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Step-by-step explanation:

The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2

Which gives;

3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0

3.1·x³ - 6.4·x²+ 3·x  - 5 = 0

Factorizing online, we get;

3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0

Therefore, the possible solutions are;

x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0

The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;

x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.

As a result, 4/9 participants choose vanilla ice cream with hot fudge topping.

A fraction is a number that symbolises a portion of a whole. It is written as two integers: the numerator, which is written above a line, and the denominator, which is written below the line. The denominator is the total number of equal parts in the whole, while the numerator is the number of equal parts that are being taken into account.

given

The chart indicates that a total of 20 partygoers selected ice cream and toppings. We must examine the intersection of the row for vanilla ice cream and the column for hot fudge topping in order to determine the percentage of persons who selected it. Four persons choose vanilla ice cream with hot fudge topping, according to the table.

The percentage of those who choose vanilla ice cream with hot fudge topping is as follows:

4 (consumers who selected vanilla ice cream with hot fudge topping) / 9 (consumers who did not) = 4/9

As a result, 4/9 participants choose vanilla ice cream with hot fudge topping.

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The given expression is

First, we solve the powers and the root

We solve the products on each side of the fraction

Now, we divide whole numbers each other and powers each other

Answer:

Options (2), (3) and (5)

Step-by-step explanation:

This question is incomplete; here is the complete question.

Which products result in a perfect square trinomial? Select three options.

1). (-x + 9)(-x - 9)

2). (xy + x)(xy + x)

3). (2x - 3)(-3 + 2x)

4). (16 - x²)(x²+ 16)

5). (4y² + 25)(25 + 4y²)

Option (1),

(-x + 9)(-x - 9) = -(-x + 9)(x + 9)

Therefore, product is not a perfect square.

Option (2)

(xy + x)(xy + x) = (xy + x)²

So the product is a perfect square trinomial.

Option (3)

(2x - 3)(-3 + 2x) = (2x - 3)²

Therefore, product is a perfect square trinomial.

Option (4)

(16 - x²)(x²+ 16) = (-x⁴+ 256)

Therefore, product is not a trinomial.

Option (5)

(4y² + 25)(25 + 4y²) = (4y² + 25)²

                                = 16y⁴ + 200y² + 625

Therefore, product is a perfect square trinomial.

Options (2), (3) and (5) are the correct options.

Answer:

Options (2), (3) and (5) are the correct options.

Answer: You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,

⇒ what you buy should be ≥ 20

Input the price to the inequality above

⇒ what you buy should be ≥ 20

⇒ paperback price + hardcover price ≥ 20

⇒ 10x + 17y ≥ 20

Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms

⇒ x ≥ 0

⇒ y ≥ 0

So this is the summary

10x + 17y ≥ 20

x ≥ 0

y ≥ 0

Step-by-step explanation: