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A rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
Basic
4.07 Quiz: Finding the Volume of a Prism
7.

The series [tex]\lim_{n \to \infty} sin(n)[/tex] does not converge, because the function [tex]sin(n)[/tex] oscillates infinitely between -1 and 1 as n approaches infinity.

More formally, for any positive integer [tex]k[/tex], we can find an integer [tex]n[/tex] such that [tex]n\pi[/tex] is very close to [tex]\pi[/tex], which implies that [tex]sin(n)\approx(-1)^k[/tex]. Therefore, the sequence [tex]{sin(n)}[/tex] does not converge to any limit as [tex]n[/tex] approaches infinity.

Alternatively, we can also prove that [tex]\lim_{n \to \infty} sin(n)[/tex] does not exist using the epsilon-delta definition of a limit. Suppose there exists a limit [tex]L[/tex], then for any [tex]\epsilon > 0[/tex], there exists a positive integer [tex]N[/tex] such that for all [tex]n > N[/tex], we have [tex]|sin(n) - L| < \epsilon[/tex].

However, we can choose [tex]\epsilon = 1/2[/tex] and find two subsequences [tex]{a_n}[/tex] and [tex]{b_n}[/tex] such that [tex]|sin(a_n) - sin(b_n)| = 1[/tex]. Therefore, for any possible limit [tex]L[/tex], we can always find two subsequences that converge to different values, contradicting the assumption that the limit exists.

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[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

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Answer:

90 feet

Step-by-step explanation:

To find the perimeter of the classroom, we need to calculate the distance between each pair of adjacent corners and add them up.

Using the distance formula, the distance between the first two corners is:

√[(-12 - (-12))^2 + (15 - (-9))^2] = √(0^2 + 24^2) = 24 feet

The distance between the second and third corners is:

√[(-12 - 9)^2 + (-9 - 15)^2] = √(21^2 + 24^2) ≈ 31.8 feet

The distance between the third and fourth corners is:

√[(9 - 9)^2 + (15 - (-9))^2] = √(0^2 + 24^2) = 24 feet

Finally, the distance between the fourth and first corners is:

√[(9 - (-12))^2 + (-9 - 15)^2] = √(21^2 + 24^2) ≈ 31.8 feet

Therefore, the perimeter of the classroom is:

24 + 31.8 + 24 + 31.8 = 111.6 feet ≈ 112 feet (rounded to the nearest foot)

So the closest option to this answer is 90 feet.

Answer: 12 years

Step-by-step explanation:

     We will substitute the given amount after the investment period and then solve for t, the number of years the period was.

     Given:

A = 10,000(1 + 0.043t)

     Substitue:

15,160 = 10,000(1 + 0.043t)

     Distribute:

15,160 = 10,000 + 430t

     Subtract 10,000 from both sides of the equation:

5,160 = 430t

     Divide both sides of the equation by 430:

t = 12 years

Answer: 3237 photos

Step-by-step explanation:

Let the number of photos of size 3R that the school ordered be 'x', and the number of photos of size 6R be 'y'.

We know that the school ordered 308 photos of size 3R, so:

x = 308

We also know that the total amount spent on photos was Rs 18500, so:

3x + 6y = 18500

Substituting the value of x from the first equation:

3(308) + 6y = 18500

924 + 6y = 18500

6y = 17576

y = 2929.33 (rounded off to the nearest whole number)

Since the number of photos must be a whole number, we can assume that the school ordered 2929 photos of size 6R.

Therefore, the total number of photos that the school ordered together is:

x + y = 308 + 2929 = 3237

Hence, the school ordered a total of 3237 photos.

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Answer:

90° clockwise rotation.

Step-by-step explanation:

The values of midline, amplitude and period are 2, 5 and 4.

What is midline, period and amplitude?

The amplitude is the separation between the midline and either the greatest or minimum. The period is defined as the separation between the midline points before the maximum value and points after the minimum value. From one peak to the next, or from any point to the following corresponding point, is the Period The height between the center line and the peak is known as the amplitude (or to the trough).

Midline = (Highest value + Lowest value)/2

y = (7 - 3)/2

y = 4/2

y = 2

Amplitude =  (Highest value - Lowest value)/2

= (7 - (-3)) / 2

= (7 + 3) /2

= 10/2

= 5

Period = difference between the two highest values

= 4.

Thus, the values of midline, amplitude and period are 2, 5 and 4.

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the coefficient of the squared term in the equation of this parabola is -1/9.

what is parabola ?

A parabola is a type of symmetrical curve that is defined by a set of points in a plane. It is a conic section, meaning it is formed by the intersection of a plane and a cone. A parabola has a U-shape and can be either upward-facing or downward-facing, depending on its equation.

In the given question,

If the vertex of a parabola is at (h,k), then the equation of the parabola can be written in vertex form as y = a(x - h)² + k, where "a" is the coefficient of the squared term.

We are given that the vertex of the parabola is at (1,-4), so we can write:

y = a(x - 1)² - 4

We are also given that when the y-value is -5, the x-value is 4. Substituting these values into the equation, we get:

-5 = a(4 - 1)² - 4

Simplifying this equation, we get:

-5 = 9a - 4

9a = -1

a = -1/9

Therefore, the coefficient of the squared term in the equation of this parabola is -1/9.

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The area of the regular polygon, or equilateral triangle, is determined as  27.71 mm².

The area of a regular polygon can be calculated using the formula:

Area = (perimeter * apothem) / 2

where;

Assuming the regular polygon is an equilateral triangle, the following formula will be used to find the area of the triangle.

A = a² × √3/4

where;

a is the side length of the  equilateral triangle = 8 mm

The area of the equilateral triangle is calculated as follows;

A = ( 8² ) x √ ( 3 ) / 4

A = 27.71 mm²

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The diameter of the circle is 4 inches.

The diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circumference of the circle.

The area of the circle is 12.6 inches square. Let's find the diameter of the circle as follows:

area of a circle = πr²

area of a circle = π(d / 2)²

where

Therefore,

12.6 = 3.14 × d² / 4

12.6 = 0.785d²

divide both sides by 0.785

d² = 12.6 / 0.785

d = √16.050955414

d = 4.00635744786

Therefore,

diameter = 4 inches

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Since the y-intercept of f(x)=4(3)ˣ is (0,4) and the y-intercept for the  table whose function is g(x) = 3²⁻ˣ is (0,9). See the attached graph. Hence, the function with the larger y-intercept is g(x) = 3²⁻ˣ.

In analytic geometry, a point where the graph of a given function or relation intersects with the y-axis of its coordinate system is known as the vertical intercept.

It obeys one standard convention: That all horizontals correspond to values on x and all verticals correspond to those on y. At these points, metrics assessing intersection require that x must always equal zero.

Hence, on the basis of the points at which the curve meets the y axis in  both graphs, we can correctly state that: the function with larger y-intercept is g(x) = 3²⁻ˣ.

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Answer:

Danielle will need 27 gallons of blue paint.

Step-by-step explanation:

If the shade of green paint requires 2 parts yellow and 3 parts blue, that means for every 2 gallons of yellow paint, we need 3 gallons of blue paint.

So to find how many gallons of blue paint Danielle will need, we can set up a proportion:

2/3 = 18/x

where x is the number of gallons of blue paint.

To solve for x, we can cross-multiply:

2x = 54

x = 27

Therefore, Danielle will need 27 gallons of blue paint.

Answer:  To make the special shade of green paint, Danielle needs 2 parts yellow and 3 parts blue. This means that for every 2 gallons of yellow paint, she needs 3 gallons of blue paint.

If Danielle uses 18 gallons of yellow paint, we can set up a proportion to find how many gallons of blue paint she needs:

2/3 = 18/x

where x is the number of gallons of blue paint she needs.

To solve for x, we can cross-multiply and simplify:

2x = 3 * 18

2x = 54

x = 27

Therefore, Danielle will need 27 gallons of blue paint to make the special shade of green paint.

Step-by-step explanation: Would really apreciate brainliest :D

Since the point (-4, a) is on the graph of y = x², the value of a is equal to 16.

In Mathematics and Geometry, a quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Where:

When x = -4, the value of y or a can be calculated as follows;

y = x²

y = a = (-4)²

y = a = 16.

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Using trigonometry we know that the measure for θ is 25.747121° respectively.

The branch of mathematics is concerned with the computation of certain angles and their functions.

There are six widely used angles-related trigonometric functions.

Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

So, 14.5 meters is the hypotenuse.

6.3 meters on the opposite side

Using trigonometry now:

sin θ = Opposite side / Hypotenuse

Using the provided values, we obtain:

sin θ = 6.3 / 14.5

sin θ = 63/145

sin θ = 0.4344

θ =25.747121°

Therefore, using trigonometry we know that the measure for θ is 25.747121° respectively.

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Solve the trigonometric equation to find a particular solution: [tex]\theta=\text{arccos} \ (0.9659)[/tex] or [tex]\theta=2\pi -\text{arccos} \ (0.9659)[/tex]

Solve the trigonometric equation to find a general solution: [tex]\theta=\text{arccos} \ (0.9659)+2n\pi[/tex] or [tex]\theta=2\pi -\text{arccos} \ (0.9659)+2n\pi[/tex], [tex]n \ \in Z[/tex]

Approximate the inverse trigonometric value: [tex]\theta\thickapprox0.261899+2n\pi[/tex] or [tex]\theta\thickapprox2\pi +-0.261899+2n\pi[/tex], [tex]n \ \in Z[/tex]

Calculate: [tex]\theta\thickapprox6.021286+2n\pi[/tex], [tex]n \ \in Z[/tex]

Find the union of solution sets: [tex]\theta\thickapprox0.261899+2n\pi[/tex] or [tex]\theta\thickapprox6.021286+2n\pi[/tex], [tex]n \ \in Z,n \ \in Z[/tex]

Answer: [tex]\bold{\theta\thickapprox0.261899+2n\pi}[/tex] or [tex]\bold{\theta\thickapprox6.021286+2n\pi}[/tex]

The value of A is approximately 19.318 units.

We can now find the value of side A using the formula for a right-angled triangle:

Cos θ = A / H

where A is the length of the adjacent side, and H is the length of the hypotenuse.

Let's substitute the given values:

0.9659 = A / 20

To find the value of A, we can multiply both sides of the equation by 20:

A = 0.9659 * 20

A ≈ 19.318

So, the value of A is approximately 19.318 units.

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Should it be necessary, round your response to the nearest whole number. Your credit card debt increases by a factor of three in just nine months, going from $800 to $2400. It would take 34.9 months for the balance to increase by $7000 if it grows linearly.

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The 99.7% confidence interval for the mean of the population is (112.82, 125.18).

The degree of variance or dispersion in a collection of data is measured by standard deviation. It is a statistic that gauges how much values deviate from the dataset's mean (average).

To calculate the 99.7% confidence interval for the mean of the population, we need to use the formula:

Confidence Interval = X ± Z(α/2) * (σ/√n)

where:

X is the sample mean

Z(α/2) is the critical value of the standard normal distribution at α/2 level of significance (α is the level of significance)

σ is the population standard deviation (unknown)

n is the sample size

In this case, X = 119, σ = 16, n = 64, and α = 0.003 (because 99.7% corresponds to the area under the curve outside the range of ±3 standard deviations from the mean, and the standard normal distribution is symmetric around the mean, so we need to split the area of 0.003 equally between the two tails).

Using a standard normal distribution table or calculator, we find that Z(α/2) = Z(0.0015) = 3.090.

Plugging in the values, we get:

Confidence Interval = 119 ± 3.090 * (16/√64)

Confidence Interval = 119 ± 6.18

Therefore, the 99.7% confidence interval for the mean of the population is (112.82, 125.18).

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]

[tex]1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P[/tex]

Answer: 58.72 degrees Celsius.

Step-by-step explanation:

We can use the following formula to estimate the temperature of the coffee when t = 10:

T(t) = T(room) + [T(initial) - T(room)] * e^(-r(t) * t)

where T(t) is the temperature of the coffee at time t, T(room) is the temperature of the room, T(initial) is the initial temperature of the coffee, and r(t) is the rate of change of the coffee's temperature.

Substituting the given values, we get:

T(10) = 20 + [90 - 20] * e^(-(-7 e^(-0.1 * 10)) * 10)

T(10) = 20 + 70 * e^(0.7)

T(10) ≈ 58.72 degrees Celsius (rounded to two decimal places)

Therefore, the estimated temperature of the coffee when t = 10 is 58.72 degrees Celsius.

Answer:

degree is 4

Step-by-step explanation:

The degree is the largest exponent on the variable, which is 4.

A painting contractor determined the average amount of time needed to paint a house.

- When 2 painters are used, it takes 15 hours to paint

- When 6 painters are used, it takes 5 hours to paint.

If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?

F. The time required to paint a house varies directly with

the number of painters because h = 30p.

G. The time required to paint a house varies directly with

the number of painters because ph = 30.

H. The time required to paint a house varies inversely

with the number of painters because h = 30p.

J. The time required to paint a house varies inversely

with the number of painters because ph = 30.

The domain and range of y = Q(-t) are [-3,-1] and [-4,7], respectively.

The domain and range of y = -Q(t) are [1,3] and [-7,4], respectively.

The domain and range of y = -Q(-t) are [-3,-1] and [-4,7], respectively.

a) In the domain of Q(t), we must replace t with -t for the transformation y = Q(-t). The domain of y = Q(-t) will be [-3,-1] because the domain of Q(t) is [1,3]. The range of Q(t), which is [-4,7], will not change.

As a result, the domain and range of y = Q(-t) are [-3,-1] and [-4,7], respectively.

b) For the transformation y = -Q(t), we must take the negative of Q(t)'s range. Because Q(t) has a range of [-4,7], y = -Q(t) has a range of [-7,4]. The domain of Q(t), [1,3], will remain unchanged.

As a result, the domain and range of y = -Q(t) are [1,3] and [-7,4], respectively.

c) We must take the negative for the transformation y = -Q(-t). in the domain of Q(t) and replace t with -t in the range of Q(-t). Because Q(t) has the domain [1,3], Q(-t) has the domain [-3,-1]. Reflecting the range of Q(t) about the y-axis yields the range of Q(-t). As a result, the range of Q(-t) is [-7,4]. Taking the inverse of the range, we get [-4,7] for y = -Q(-t).

As a result, the domain and range of y = -Q(-t) are [-3,-1] and [-4,7], respectively.

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The speed of P when t = 3 seconds is  95.00 m/s

We can find the speed by finding the net force acting on the particle P. Let F_net be the net force acting on P, then we have:

F_net = F₁ + F₂

where:

F₁ = (-i + 2j)N

F₂ = the direction of the vector (i + j).

Let's find the magnitude and direction of F₂. We know that F_net is in the direction of the vector (i + 3j), so we can write:

F_net = F₂ + k(i + 3j)

where:

k = some constant. Since F₂ is in the direction of (i + j), we can write:

F₂ = a(i + j)

where:

a = constant.

Substituting the into the equation for F_net:

F_net = a(i + j) + k(i + 3j)

To find the values of a and k, we use the acceleration of P which is (31 + 9j) m/s². The net force on P is:

F_net = m*a

where m = the mass of P.

Equating the two expressions for F_net:

a(i + j) + k(i + 3j) = m(31 + 9j)

Expanding both sides:

(ai + aj) + (ki + 3kj) = 31m + 9mj

Equating the coefficients of i and j, we get two equations:

a + k = 31m (1)

a + 3k = 9m (2)

Solving these equations:

a = 9m

k = 22m

Substituting these values back into the expression for F_net, we have:

F_net = 9m(i + j) + 22m(i + 3j) = 31mi + 69mj

Now, we can use the equation for acceleration to find the mass of P:

F_net = m*a

31mi + 69mj = m(31 + 9j)

m = 31 / (31 + 9j) = 31 / (31 - 9i)

Next, we shall use the initial velocity and acceleration to find the velocity of P after 3 seconds.

Let v(t) be the velocity of P at time t, then:

v(t) = v(0) + a*t

where v(0) = 3i - 22j and

a = (31 + 9j) m/s²

Substituting t = 3 seconds:

v(3) = (3i - 22j) + (31 + 9j)(3)

= 96i - 1j

Therefore, the speed of P at t = 3 seconds is the magnitude of v(3):

v(3)| = ([tex]\sqrt{96^{2} }[/tex] + (-1)²) = [tex]\sqrt9217[/tex] = 95.00 m/s

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Step-by-step explanation:

to find the percentage you have to take 5 as 100% so to find the percentage of 4 you have to divide 100 by 5 making 20%. then do 20 multiplied by 4 which is 80%. so the answer is 80^

The least common multiple of 47 and 45 is 2,115. Therefore, at 2,115 minutes, both patients receive their medication at the same time. 

we need to find the least common multiple of 47 and 45, the smallest number that is divisible by both 47 and 45.

Start by listing the multiples of each number until you find a common multiple.

Multiples of 47:

47, 94, 141, 188, 235, 282, 329, 376, 423, 470, 517, 564, 611, 658, 705, 752, 799, 846, 893, 940, 987, 1034, 1081, 1128, 1175, 1222, 1269, 1316, 1363, 1410, 1457, 1551, 1598, 1645, 1692, 1739, 1786, 1833, 1880, 1927, 1974, 2021, 2068, 2115, 2162, 2206, 2206, 2309

Multiples of 45:

45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990, 1035, 1080, 1125, 1170 1215 1260 1305 1350 1395 1440 1485 1530 1575 1620 1665 1710 1755 1800 1845 1890 1935 1980 2025 232070

We can see that the least common multiple of 47 and 45 is 2,115. Therefore, at 2,115 minutes, both patients will receive their medication at the same time.

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For the augmented matrix,

1. Row 1 multiplied by -5 is

[tex]\left[\begin{array}{cccc}20&-30&25&15\\-2&4&0&-3\\2&-6&1&-1\end{array}\right][/tex]

2. Row 1 interchanged with row 3

[tex]\left[\begin{array}{cccc}2&-6&1&-1\\-2&4&0&-3\\20&-30&25&15\end{array}\right][/tex]

3. Row 1 multiplied by -2 and added to row 3

[tex]\left[\begin{array}{cccc}2&-6&1&-1\\-2&4&0&-3\\16&42&23&17\end{array}\right][/tex]

An augmented matrix can be described as a rectangular shaped array of numbers that represents a system of linear equations. These numbers are arranged in rows and colums. They can differ  in sizes depending on the array of numbers in the matrix.

The above answer is in response to the questions below as seen in the picture.

Perform the indicated row operation on the given augmented matrix.

[-4 6 -5 -3, -2 4 0 -3, 2 -6  1  -1]

a. Multiply row 1 by -5

[_ _ _ _, _ _ _ _, _ _ _ _]

b. interchange row 1 and row 3

[_ _ _ _, _ _ _ _, _ _ _ _]

c. Multiply row 1 by -2 and add to row 3

[_ _ _ _, _ _ _ _, _ _ _ _]

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If the given integer is positive, then it is plotted to the right of zero on the number line. If the given integer negative, then it is plotted to the left of zero on the number line.

The equation of the oblique asymptote of g(x) = x²+x+4/x-1 is y=x+1.

Synthetic division is a shorthand method for dividing polynomials. It is similar to long division, but simplified by removing all the steps except for the division, such as a linear factor with a leading coefficient of one.

To find the equation of the oblique asymptote, we need to divide the numerator (x²+x+4) by the denominator (x-1) using synthetic division.

To do this, we must first create a synthetic division setup, as shown above. The first number in the setup is the number that is being divided by the polynomial in the denominator.

In this case, it is 1. The other numbers in the setup are the coefficients of the polynomial in the numerator.

The synthetic division setup has 1 as the number being divided and 1, 1, and 4 as the coefficients of the numerator.

After dividing, the quotient is x+1 and the remainder is 0. Since the remainder is 0, the equation of the oblique asymptote is y = x+1.

This means that the line with the equation y = x+1 is the oblique asymptote of g(x) = x²+x+4/x-1.

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Answer:

y= 1+x+2

Step-by-step explanation:

Answer:

(7-2√6)/10

Step-by-step explanation:

I assumed the fraction in the question was:

(√6 - 1) / (2√6 + 2)

Working is attached below.

The value of the percentage 64% of 35 is 22.4

To find 64% of 35, we can use the following formula:

percent × whole = part

where percent is the percentage we want to find, whole is the total value, and part is the result we are looking for.

In this case, we want to find 64% of 35, which means that percent = 64 and whole = 35.

Let's substitute these values into the formula:

64% × 35 = part

To calculate the product of 64% and 35, we can convert 64% to a decimal by dividing it by 100:

64% ÷ 100 = 0.64

Substituting this value into the formula, we get:

0.64 × 35 = part

Multiplying 0.64 by 35, we get:

22.4 = part

Therefore, 64% of 35 is 22.4.

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