The volume of a rectangular prism is 5058
50
5
8
cubic inches.
The dimensions are given below.
What is the missing value in the table?

number one take the second

The function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3).

In mathematics, a function is a relation between two sets that associates each element of the first set, called the domain, with a unique element of the second set, called the range. In other words, a function maps each input value to a unique output value.

The notation used to represent a function is f(x), where f is the name of the function and x is the input value. The output value is then given by the expression f(x).

Functions can be represented in various ways, such as tables, graphs, equations, and verbal descriptions. They are used to model real-world phenomena, analyze data, and solve problems in various fields, including science, engineering, economics, and finance.

To find the intercepts of the rational function, we set the numerator equal to zero and solve for x:

2/(2x² - x - 3) = 0

2 = 0 (there is no solution for x that makes the numerator zero)

Therefore, the rational function has no x-intercepts.

To find the y-intercept, we set x = 0:

f(0) = 2/(2(0)² - 0 - 3) = -2/3

Therefore, the y-intercept is (0, -2/3).

To find the vertical asymptotes, we set the denominator equal to zero and solve for x:

2x² - x - 3 = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 24))/4

x = (1 ± 5)/4

x = -3/2, 1

Therefore, the rational function has vertical asymptotes at x = -3/2 and x = 1.

To describe the behavior at the vertical asymptotes, we can use limits. Let's consider the vertical asymptote at x = -3/2:

lim x → -3/2+ f(x) = 2/(2(-3/2)² - (-3/2) - 3) = -∞

lim x → -3/2- f(x) = 2/(2(-3/2)² - (-3/2) - 3) = +∞

This means that as x approaches -3/2 from the right, the function approaches negative infinity, and as x approaches -3/2 from the left, the function approaches positive infinity. Therefore, the function has a vertical asymptote at x = -3/2 with a vertical (or infinite) discontinuity.

Let's now consider the vertical asymptote at x = 1:

lim x → 1+ f(x) = 2/(2(1)² - (1) - 3) = +∞

lim x → 1- f(x) = 2/(2(1)² - (1) - 3) = -∞

This means that as x approaches 1 from the right, the function approaches positive infinity, and as x approaches 1 from the left, the function approaches negative infinity. Therefore, the function has a vertical asymptote at x = 1 with a vertical (or infinite) discontinuity.

To analyze and draw the graph of the rational function, we can use the intercepts, asymptotes, and behavior at the vertical asymptotes that we found earlier. We can also find the horizontal asymptote by looking at the degree of the numerator and denominator:

Degree of numerator = 0

Degree of denominator = 2

Therefore, the horizontal asymptote is y =0

As we can see from the graph, the function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3). The behavior at the vertical asymptotes is a vertical (or infinite) discontinuity.

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The complete question is:

The possible rule of the polynomial function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

From the question, we have the following zeros and multiplicities that can be used to derive the rule of the function

The possible rule of the function is represented as

f(x) = a(x - zero)^multiplicity

So, we have

f(x) = a(x + 2)(x + 1)²(x - 1)²

The graph passes through (0, 1)

So, we have

a(0 + 2)(0 + 1)²(0 - 1)² = 1

This gives

2a = 1

Divide

a = 1/2

Recall that

f(x) = a(x + 2)(x + 1)²(x - 1)²

So, we have

f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

Hence, the function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

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The length of the tank should be approximately 150.4 inches in order to hold 450 gallons of water, with a width of 21 inches and a height of 33 inches.

To find the length of the tank, we first need to convert the volume of water from gallons to cubic inches, using the given conversion factor:

1 gallon = 231 cubic inches

Therefore, the volume of water in the tank is:

450 gallons * 231 cubic inches/gallon = 103950 cubic inches

We can then use the formula for the volume of a rectangular prism to find the length of the tank:

Volume = length * width * height

Substituting the given dimensions, and solving for the length, we get:

103950 cubic inches = length * 21 inches * 33 inches

length = 103950 cubic inches / (21 inches * 33 inches)

length ≈ 150.4 inches

Therefore, the length of the tank should be approximately 150.4 inches in order to hold 450 gallons of water, with a width of 21 inches and a height of 33 inches.

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Thus, the total surface area of the given right triangular prism is found as : 96 sq. in.

The bases of a prism, which can have up to n sides, are joined to one another by parallel lines that create planes. These bases plus planes would create right angles with one another in a right prism if they were perpendicular to one another.

surface area of right triangular prism S:

surface area of right triangular prism  = base area + 2*triangle area + 2* rectangle area

surface area of right triangular prism  = 4*8 + 2*(1/2*8*3) + 2*4*5

surface area of right triangular prism   = 32 + 24 + 40

surface area of right triangular prism  = 96

Thus, the total surface area of the given  right triangular prism is found as : 96 sq. in.

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Answer:

(C) {-3, 2} is the correct answer.

The mean low temperature in Ketchikan from Monday to Friday is given as follows:

b. -5.4 ºF.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The five observations in the data-set are given as follows:

-10, -20, 5, 3 and -5.

Hence the mean of the data-set is given as follows:

(-10 - 20 + 5 + 3 - 5)/5 = -5.4 ºF.

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Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.

Here,

Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.

The standard error of the mean (SE) can be calculated as:

SE = σ / √(n)

where σ is the standard deviation of the population, n is the sample size.

Substituting the given values, we get:

SE = 1150 / √(600)

≈ 47.03

The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:

z = (x - μ) / SE

z = ($90) / 47.03

≈ 1.915

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.

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The requried,  3025 bacteria are present after 12 hours.

To find the number of bacteria present after 12 hours, we simply need to substitute t=12 in the given equation:

[tex]n(12) = 500e^{(0.15*12)}[/tex]

[tex]n(12) = 500e^{1.8}[/tex]

n(12) ≈ 3024.82

Rounding this to the nearest whole number, we get:

n(12) ≈ 47,416 ≈ 3025

Therefore, there are approximately 3025 bacteria present after 12 hours.

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Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

To find the multiplicative inverse of a fraction, we need to find another fraction that, when multiplied by the original fraction, results in a product of 1.

Let's start by finding the multiplicative inverse of the fraction (4/3) - (2/9):

(4/3) - (2/9) = (12/9) - (2/9) = (10/9)

The multiplicative inverse of (10/9) would be a fraction (a/b) such that:

(10/9) x (a/b) = 1

Multiplying both sides by (9/10) (the reciprocal of 10/9), we get:

(a/b) = (9/10) x (1/(10/9))

Simplifying the expression on the right-hand side, we get:

(a/b) = (9/10) x (9/10) = 81/100

So the multiplicative inverse of (4/3) - (2/9) is 81/100.

Next, we need to find what we should subtract from (7/12) + (7/8) to obtain 81/100.

We can first find a common denominator between (7/12) and (7/8), which is 24:

(7/12) = (7/12) x (2/2) = 14/24

(7/8) = (7/8) x (3/3) = 21/24

So, we can rewrite (7/12) + (7/8) as:

(14/24) + (21/24) = 35/24

To obtain the difference between 35/24 and 81/100, we subtract the smaller fraction from the larger one:

81/100 - 35/24 = (81/100) x (6/6) - (35/24) x (25/25)

= 486/600 - 875/600 = -389/600

Therefore, we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

Final answer:

(7/12) + (7/8) - (389/600) = 1.0158 (rounded to four decimal places)

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Answer:

The distance between (3, 4.1) and (3, 1.2) is approximately 2.9 units.

Step-by-step explanation:

You're welcome.

The power function that models the data is 0.117t^1.585.

In 1985, the average cost of natural gas was estimated to be $7.24 per 1000 ft³.

a. To model the data with a power function, use general form of a power function:

C = ktⁿ,

where C = average cost of natural gas, t = time in years, k = a constant, and n = power.

Take the logarithm of both sides to linearize the equation:

log(C) = log(k) + n × log(t)

Use a linear regression to find the slope and y-intercept of the line, which will give us the values of k and n:

n ≈ 1.585

log(k) ≈ -0.921

k ≈ 0.117

Therefore, the power function that models the data is:

C = 0.117t^1.585

b. To estimate the average cost of natural gas in 1985, we can substitute t = 11 (since 1985 is 11 years after 1974) into the power function:

C = 0.117(11)^1.585 ≈ 7.24

Therefore, estimate the average cost of natural gas in 1985 to be $7.24 per 1000 ft³.

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The original numbers multiplied by 10² are:

968

0.002

3.33

When a number is multiplied by 10², the position of the decimal point will move to the right by 2 steps. If the number does not have decimal point, two zeros is added to the back of the number .

6 * 10³  = 6,000

968 * 10² = 96,800

0.002 * 10² = 0.2

70,000 ÷ 10² = 700

3.33 * 10² = 333

Thus, the original numbers multiplied by 10² are 968, 0.002 and 3.33

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The median the most useful measure of central tendency for these

times: is A) The median is not affected by an outlier.

The median is the middle value in a set of data when the values are arranged in order. In this case, the median of Brandon's climbing times would be 16, because it is the fourth value when the times are arranged in order:

13, 13, 14, 16, 17, 18, 35

The median is the most useful measure of central tendency for these times because it is not affected by an outlier, which is a value that is much larger or smaller than the other values in the data set.

In this case, the value 35 is an outlier, because it is much larger than the other values. If we were to use the mean as the measure of central tendency, the outlier would greatly influence the result. However, the median is not influenced by outliers, and therefore provides a better representation of the typical climbing time for Brandon.

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Answer:

b

Step-by-step explanation:

b

The angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer.

From the information, the following can be deduced:

-√3 csc(2θ) = 2

csc(2θ) = -2/√3

sin(2θ) = -√3/2

We know that sin(2θ) = 2sin(θ)cos(θ) by the double-angle identity for sine,

2sin(θ)cos(θ) = -√3/2

2sin(θ)cos(θ) = -√3/2

sin(θ)cos(θ) = -√3/4

sin(θ)cos(θ) = sin(π/3)sin(θ)

cos(θ) = sin(π/3)

θ = π/6 + 2πn, 5π/6 + 2πn

Therefore, the angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer

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Answer:

a. 1.95 cm.

b. 3920 cm^2.

Step-by-step explanation:

(a) To find the length of the arc that subtends the central angle theta on a circle of diameter d, we can use the formula:

Arc Length = (theta / 360°) x (pi x d)

Substituting the given values, we get:

Arc Length = (1.6 / 360°) x (pi x 140 cm)

Arc Length ≈ 1.95 cm

Therefore, the length of the arc that subtends the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 1.95 cm.

(b) To find the area of the sector determined by the central angle theta, we can use the formula:

Area of Sector = (theta / 2π) x pi x (r^2)

where r is the radius of the circle.

Since the diameter of the circle is given as 140 cm, the radius is half of that, which is 70 cm.

Substituting the given values, we get:

Area of Sector = (1.6 / (2 x pi)) x pi x (70 cm)^2

Area of Sector ≈ 3920 cm^2

Therefore, the area of the sector determined by the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 3920 cm^2.

5/6 can be rewritten with a least common denominator of 6 as 10/12.

Fracture is  part of the whole. A fraction consists of two parts, the numerator and the denominator. Numerator: The numerator represents the number  above the fraction bar. For example, for 6/7, 6 is the numerator. Denominator: The denominator shows the number  placed under the fraction bar.  

We can write 5/6 in the lowest common denominator, we need to find the common multiple of 6. The smallest multiple  is 2. So we can write 5/6 with the lowest denominator  6 as follows:

5/6 = (5/6) x (2/2) = 10/12

Therefore, 5/6 can be rewritten as 10/12 with a lowest common denominator of 6.

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The missing step in the two column proof is

Statement              Reason

Δ DAC ≅ ΔBCA    ASA congruence theorem

The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).

The angle side angle theorem states uses the side two parameters which includes:

The parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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Answer:

The molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound.

unit of measurement: g/mol.

A mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.

Avogadro's number= 6.02*10^23 particles.

Answer:

Step-by-step explanation:

6x + 15 = x - 10

5x + 15 = -10

5x = -25

x = -5

The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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Answer:

The answer to (m+3)(m-3) is m^2-9.

Step-by-step explanation:

We will use distributive law to solve this question.

m(m-3)+3(m-3)

= m^2-3m+3m-9

= m^2-9 (since, 3m-3m=0)

As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.

so, here a=m and b=3.

(m+3)(m-3)

=m^2-3^2

=m^2-9

To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

To find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.

If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:

(Volume of A) / (Volume of B) = (a^3) / (b^3) = k

We can then solve for the ratio of edge lengths:

a / b = (k)^(1/3)

Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.

This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.

For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.

If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:

a / b = sqrt(Area of first triangle / Area of second triangle)

So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

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Answer:300

Step-by-step explanation:

We can find the answer the simple way.

There are 10 triangles in a regular pentagon

We used pythagorean theorm to find side b, 12

12*5*0.5 is 30

30*10 is 300

The woman invested $4,000 at 5% and $3,000 at 12%.

Let x be the amount invested at 5% and y be the amount invested at 12%. Then we have:

x + y = 7,000 (equation 1)

0.05x + 0.12y = 560 (equation 2)

To solve for x and y, we can use substitution method :

From equation 1, we have y = 7,000 - x. Substituting this into equation 2, we get:

0.05x + 0.12(7,000 - x) = 560

Simplifying and solving for x, we get:

0.05x + 840 - 0.12x = 560

-0.07x = -280

x = 4,000

Substituting x = 4,000 into equation 1, we get:

4,000 + y = 7,000

y = 3,000

Therefore, the woman invested $4,000 at 5% and $3,000 at 12%.

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