A rectangular prism has a length of 12 feet, a height of 13 feet, and a width of 8 feet. What is its volume, in cubic feet?

The approximate positive value of x for the function f(x)=g(x) is 8.

The characteristic that the every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Now in order to get f(x)=g(x) the functions

put the value of f(x) and g(x)

3×2×x=4x+16

6x=4x+16

2x=16

On solving we get,

x=8

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solution of the inequality is r>4/3.

An inequality is a mathematical statement that compares two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are expressed using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequalities can also involve variables, and solutions to such inequalities are the sets of values of the variable that make the inequality true. For example, the inequality 2x + 3 < 7 states that 2x + 3 is less than 7, and solving for x gives the solution x < 2.

Given inequality

2>6-3r

Solving the inequality

2-6>-3r

-4>-3r

r>4/3

Hence, solution of the inequality is r>4/3

Image of the inequality is attached below.

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The expression is a polynomial, it is a binomial of degree 6.

We want to see if the given expression:

-5s⁴t² - 8t⁴

We know that as long as the exponents are positive whole numbers, then it will be a polynomial.

It is a bynomial, because it has two terms.

Now to identify the degree we need to find the maximum exponent in a single term.

If you look at the first term we have 2 exponents, the sum of these expoents will be teh degree, then we will get:

degree = 4 + 2 = 6

degree = 6

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The required length of the other leg is [tex]$\sqrt{5}$[/tex] cm. If we need to round to the nearest tenth, we get: [tex]$b \approx 2.2$[/tex] cm

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:

[tex]$c^2 = a^2 + b^2$[/tex]

where c is the length of the hypotenuse, a and b are the lengths of the legs.

We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:

[tex]$3^2 = 2^2 + b^2$[/tex]

[tex]$9 = 4 + b^2$[/tex]

[tex]$b^2 = 5$[/tex]

[tex]$b = \sqrt{5}$[/tex]

So the length of the other leg is [tex]$\sqrt{5}$[/tex] cm. If we need to round to the nearest tenth, we get: [tex]$b \approx 2.2$[/tex] cm (rounded to one decimal place).

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The differential equation xy" + xy' + 4y = 0 has ordinary points at x = 0 and x = ∞. The point x = 0 is a regular singular point, and the point x = ∞ is an irregular singular point.

To solve this differential equation using the power series method about x = 0, we first need to expand the solution as a power series:

y(x) = c0 + c1x + c2x2 + c3x3 + ...

Substituting this series into the differential equation and equating the coefficients of like powers of x to 0 gives us a set of equations for ci. Solving this set of equations gives us the coefficients of the power series, and hence the solution.

To solve the differential equation using the Frobenius method about x = 0, we first need to look for a solution of the form:

y(x) = xr(c0 + c1x + c2x2 + c3x3 + ... ).

Substituting this series into the differential equation and equating the coefficients of like powers of x to 0 gives us a set of equations for ci and r. Solving this set of equations gives us the coefficients of the power series, and hence the solution.

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The problem is "What is 5 divided by 4?". The answer is 1 more than the quotient, which is 1.25. To change the problem so that the answer is the quotient, we subtract 1 from the original problem.

The new problem is "What is 4 divided by 4?". The answer is the quotient, which is 1. We can calculate this by dividing 4 by 4 to get the answer of 1.The problem is "What is 5 divided by 4?" The answer is 1 more than the quotient, which is 1.25.To calculate, we set up the equation 5 / 4 = x. We then divide 5 by 4 to get the answer of 1.25, which is 1 more than the quotient.To change the problem so that the answer is the quotient, we need to subtract 1 from the original problem. So the new problem is "What is 4 divided by 4?" The answer is the quotient, which is 1. We can calculate this by setting up the equation 4 / 4 = x. We then divide 4 by 4 to get the answer of 1, which is the quotient.

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Answer:

p=9h

Step-by-step explanation:

Answer:

9 * h =p

Step-by-step explanation:

You multiply 9 by the number of hours (h) and you get the product or her total pay (p).
Example- 9 * 8 = 72
8 is the number of hours Diane works and 72 is how much she is payed after.

The volume of a parallelepiped is equal to the product of the magnitudes of its three adjacent edges. In this case, the three adjacent edges are given by the vectors <6,-9>, <5,-2,9> and <7,6,-2>.

Therefore, the volume of the parallelepiped is equal to |<6,-9>| x |<5,-2,9>| x |<7,6,-2>|

We can find the magnitudes of each vector using the formula for the magnitude of a vector, which is the square root of the sum of the squares of its components.

|<6,-9>| = sqrt(6^2 + (-9)^2) = sqrt(36 + 81) = sqrt(117)
|<5,-2,9>| = sqrt(5^2 + (-2)^2 + 9^2) = sqrt(25 + 4 + 81) = sqrt(110)
|<7,6,-2>| = sqrt(7^2 + 6^2 + (-2)^2) = sqrt(49 + 36 + 4) = sqrt(89)

Therefore, the volume of the parallelepiped is sqrt(117) x sqrt(110) x sqrt(89) = 834.45.

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The volume of the parallelepiped whose adjacent sides are the vectors =6 −9, =5−2 9, and =7 6−2 is 387.

To find the volume of a parallelepiped given three adjacent vectors, we can take the scalar triple product of the three vectors.

The scalar triple product of three vectors a, b, and c is given by:   a · (b x c)

where · represents the dot product and x represents the cross product.

In other words, the scalar triple product is the dot product of the first vector with the cross product of the second and third vectors.

So in this case, we can find the volume of the parallelepiped whose adjacent sides are the vectors a=6−9, b=5−2 9, and c=7 6−2 by computing:

V = a · (b x c)

To compute the cross product b x c, we can use the following determinant:

i   j   k

5 -2 9

7 6 -2

Expanding this determinant, we get:

(−2×9−6×7)i−(5×−2−7×9)j+(5×6−−2×5)k

= −60i − 83j + 40k

So b x c = -60i - 83j + 40k, and:

a · (b x c) = (6)(-60) + (-9)(-83) + (0)(40) = 387

Therefore, the volume of the parallelepiped is 387 cubic units.

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Answer:

3/4, 4/5, 5/6, 6/7...... ect.

The equation of the circle that passes through the point (-4,-3) and has a center at (-8, -6) is [tex](x + 8)^2 + (y + 6)^2 = 25[/tex]. The equation is in standard form, where the center and radius of the circle is (-8, -6), 5 units.

The equation of a circle with center (a, b) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this problem, we are given that the center of the circle is (-8, -6), so we can substitute these values for a and b in the equation:

[tex](x - (-8))^2 + (y - (-6))^2 = r^2[/tex]

[tex](x + 8)^2 + (y + 6)^2 = r^2[/tex]

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

[tex]d = sqrt((4)^2 + (3)^2)[/tex]

d = 5

Therefore, the radius of the circle is 5.

[tex](x + 8)^2 + (y + 6)^2 = 5^2[/tex]

[tex](x + 8)^2 + (y + 6)^2 = 25[/tex]

So the equation of the circle that passes through the point (-4, -3) and has a center at (-8, -6) is: [tex](x + 8)^2 + (y + 6)^2 = 25[/tex]

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The given function is f(x) = -3x^2 + 2x + 3.

The interval(s) over which the function f(x) = -3x^2 + 2x + 3 is continuous is: x ∈ (-∞, ∞)

Steps to find the interval notation of continuous function:

For a given function, check if it has any discontinuities such as a vertical asymptote, a jump discontinuity, or a removable discontinuity.

If the function does not have any such discontinuities, then the function is continuous for all real values of x.

Write the answer using interval notation.

The given function is a polynomial function and does not have any vertical asymptotes, jump discontinuities, or removable discontinuities. Therefore, the function is continuous for all real values of x, and the interval notation for the continuous function is x ∈ (-∞, ∞).

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And The Answer is:

..........a)12

Answer:

56.65 miles

Step-by-step explanation:

[tex]C=\pi D[/tex]

[tex]C=\pi (18)[/tex]

[tex]C=18\pi =56.55[/tex]

Hope this helps.

If you account for 64% of the variability for one variable with another variable, the correlation coefficient found is 0.8, indicating a strong positive linear relationship between the two variables. So, the correct answer is B).

The correlation coefficient measures the strength and direction of the linear relationship between two variables, and it ranges from -1 to +1. If you conducted a study where you could account for 64% of the variability for one variable with another variable, you have found a correlation coefficient of the square root of 0.64, which is:

r = sqrt(0.64) = 0.8

Therefore, a correlation coefficient of 0.8 indicates a strong positive linear relationship between the two variables, and it suggests that there is a high degree of predictability in the relationship between them. So, the correct option is: B) 0.80.

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The area of the rhombus is found to be  238 sq.in.

A flattened object with four equal-length straight sides. In addition, opposing sides and angles are parallel and equal.

Features of the rhombus

Base =  17 inches

Height =  14 inches.

Area of the rhombus = base*height'

Area of the rhombus = 17*14

Area of the rhombus = 238 sq.in.

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Therefore , the solution of the given problem of function comes out to be the rocket returns to the earth in 8.3 seconds (rounded to the nearest tenth).

The math lesson includes a wide range of topics, such as mathematics, integers, as well as one's divisions, architecture, and both actual mostly and fictitious geographic locations. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is composed of numerous unique elements that work together to produce unique outcomes for each input.

Here,

The rocket's height will be zero when it touches down. Therefore, we can enter H = 0 into the algorithm and find t:

=> 0 = -1/12 (32) t² + 66t + 0

When we simplify this solution, we obtain:

=> 0 = -8t² + 66t

When we factor the solution, we obtain:

=> 0 = 2t(33 - 4t) (33 - 4t)

So, either 2t = 0 or 33 - 4t = 0.

The rocket is launched at this moment, so t = 0 if 2t = 0 is not the solution we are looking for.

If 4t = 33 and 33 - 4t = 0, then t = 8.25 seconds.

Because of this, the rocket returns to the earth in 8.3 seconds (rounded to the nearest tenth).

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The given statement " We also use the three properties of equality: For all objects A, B, and C, (1)A=A, (2) if A=B then B=A, and (3) if A=B and B=C, then A=C. • In addition, we assume that there is no integer between 0 and 1 and that the set of all integers is closed under addition, subtraction, and multiplication. This means that sums, differences, and products of integers are integers." is true and proved by using induction method.

Let n be an odd integer. By definition, an odd integer can be expressed as 2k+1 for some integer k. Therefore, we have:

n = 2k + 1

Squaring both sides of the equation, we get:

n^2 = (2k + 1)^2

Expanding the right-hand side, we get:

n^2 = 4k^2 + 4k + 1

Factoring out 2 from the first two terms on the right-hand side, we get:

n^2 = 2(2k^2 + 2k) + 1

Let m = 2k^2 + 2k. Since k is an integer, so is m. Therefore, we can rewrite the equation as:

n^2 = 2m + 1

Since m is an integer, 2m is even. Therefore, 2m + 1 is odd. This shows that n^2 is odd, which completes the proof.

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The area οf the square piece οf gοld is 9 square millimeters.

Area is a measure οf the amοunt οf twο-dimensiοnal space enclοsed by a shape οr surface. It is typically measured in square units such as square meters, square feet, οr square centimeters

The area οf a square is given by the fοrmula A = side x side. In this case, the side length is 3 millimeters, sο we can substitute this value intο the fοrmula tο find the area:

A = 3 mm x 3 mm

A = 9 mm²

Therefοre, the area οf the square piece οf gοld is 9 square millimetres.

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The allowance for sampling risk is included in the computed upper deviation rate of 7.8 is 3.8%.

The substantial percentage variation identified in the audit samples that the auditing expert would approve by adhering to the particular internal controls is known as the tolerable deviation rate. The auditor won't rely on those internal controls if the deviation rate is higher than the predetermined limit.

a) Tolerable = Allowance for sampling risk + Expected Deviation

Upper Deviation = Allowance for sampling risk + Actual Deviation

Sample deviation rate = No. of deviation/Sample size

= 6/150

= 4%

Allowance for sampling rate = Upper deviation rate - sample deviation

= 7.8% - 4%

= 3.8%

allowance for sampling risk is 3.8%.

b) 1.) In order to assure effective controls, Mr. M may increase the sample size because the tolerated deviation level is lower than the estimated deviation level.

2.) Because the computed maximum deviation is more than the anticipated and acceptable deviation rates, Mr. M may raise the initial control risk assessment.

3.) As the sample deviation rate is lower than the allowable deviation rate, Mr. M may continue his consideration in addition to creating the first risk assessment. The tolerance rate, nevertheless, is less than the estimated deviation rate. The auditor must, however, use professional discretion.

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Complete question;

Nathan Matthews conducted a test of controls where the tolerable deviation rate was set at 6 percent and the expected population deviation rate was 3 percent. Using a sample size of 150, Matthews performed the planned test of controls. He found six deviations in the sample, and he calculated the computed upper deviation rate to be 7.8 percent.

Required:

a. Based on the sample results, what allowance for sampling risk is included in the computed upper deviation rate of 7.8?

b. Assume that Matthews preliminarily assessed control risk as “low.” Given the results above, the auditor could decide to do one of three things: (1) increase the sample size, (2) increase the preliminary assessment of control risk, or (3) not adjust the preliminary assessment of control risk. Describe how Matthews could justify each of those three actions

The probability of throwing a number greater than 2 with a fair dice is 2/3 or 0.67, because there are 4 favorable outcomes out of the total 6 possible outcomes.

A fair dice has six equally likely outcomes, which are the numbers 1 through 6. The probability of throwing a number greater than 2 with a fair dice can be calculated by finding the number of favorable outcomes (throwing a 3, 4, 5, or 6) and dividing by the total number of possible outcomes (throwing any number from 1 through 6). Therefore, the probability of throwing a number greater than 2 with a fair dice is:

Number of favorable outcomes = 4 (throwing 3, 4, 5, or 6)

Total number of possible outcomes = 6 (throwing any number from 1 through 6)

So, the probability of throwing a number greater than 2 with a fair dice is:

Probability = Number of favorable outcomes / Total number of possible outcomes = 4/6 = 2/3 = 0.67 (rounded to two decimal places)

Therefore, the probability of throwing a number greater than 2 with a fair dice is 0.67 or 67%.

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The probability of throwing a number greater than 2 with a fair dice is?

Answer:

6 bucks

Step-by-step explanation:

10+6=16 bucks

The rectangular coordinates of the point are (5, 0, 4e).

When working with points in three-dimensional space, it is often useful to describe them using different coordinate systems such as cylindrical, spherical, or rectangular.

In order to convert cylindrical coordinates to rectangular coordinates, we use a set of equations that relate the distance from the origin, the angle in the xy-plane, and the height to the corresponding x, y, and z values.

x = r*cos(theta)

y = r*sin(theta)

z = z

Where r is the radius, theta is the angle, and z is the height.

Given the cylindrical coordinates (5, , 4e), we can plug in the values into the equations to find the rectangular coordinates.

x = 5*cos() = 5*cos(0) = 5*1 = 5

y = 5*sin() = 5*sin(0) = 5*0 = 0

z = 4e

Therefore, the rectangular coordinates of the point are (5, 0, 4e).

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Answer: 2

Step-by-step explanation:

to have a proportional relationship they must have a constant ratio such as 2 which as a 1:4 ratio so for every rider it costs 4 dollars

The final answer is:

sin2(x)cos2(x) = cos2(x) - cos4(x

To express sin2(x)cos2(x) as a sum of powers of cos(x) using the appropriate Pythagorean trigonometric identity, we can use the identity sin2(x) = 1 - cos2(x).

First, we will substitute this identity into the original expression:

sin2(x)cos2(x) = (1 - cos2(x))cos2(x)

Next, we will distribute the cos2(x) term:

= cos2(x) - cos4(x)

Now we have expressed sin2(x)cos2(x) as a sum of powers of cos(x).

Therefore, the final answer is:

sin2(x)cos2(x) = cos2(x) - cos4(x)

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Answer:

ten

Step-by-step explanation:

It is not true that for every positive integer, there exists a circle which contains exactly lattice points in its interior.

A lattice point is a point with integer coordinates. For example, the point (2, 3) is a lattice point because both 2 and 3 are integers.

A circle is a set of points that are a fixed distance from a center point. The equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

It is possible to find a circle with a certain number of lattice points in its interior, but it is not guaranteed for every positive integer. For example, there is no circle with exactly 2 lattice points in its interior. This is because if a circle contains 2 lattice points, it must also contain the line segment connecting those two points, which would include additional lattice points.

Therefore, it is not true that for every positive integer, there exists a circle which contains exactly lattice points in its interior.

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Graphical Solution:

Step 1: Draw V1 and V2

Step 2: Find the magnitude

Step 3: Draw the vector

Step 4: Measure the magnitude

Step 5: Measure the angle

Algebraic Solution:

Step 1: Write the vector

Step 2: Find the magnitude

Step 3: Find the angle

Graphical Solution:

Step 1: Draw V1 and V2 on the same graph with the origin (0, 0).

Step 2: Find the magnitude of each vector, V1 and V2.

Step 3: Draw the vector sum V, by beginning at the origin and following the direction of V1 and then V2.

Step 4: Measure the magnitude of V by using a ruler.

Step 5: Measure the angle θx which V makes with the positive x-axis by using a protractor.


Algebraic Solution:

Step 1: Write the vector sum V = V1 + V2 as an ordered pair (x, y).

Step 2: Find the magnitude of V using the Pythagorean theorem, |V| = √(x2 + y2).

Step 3: Find the angle θx which V makes with the positive x-axis using the arctangent, θx = arctan(y/x).

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Let Z1, Z2, ... be i.i.d with distribution Uniform[-20,10] use the central limit theorem and a tabel to esitmatep(900 i=1 zi ≥ −4470) is essentially zero.


The central limit theorem helps us to estimate the distribution of the sum of the independent variables. According to this theorem, if the sample size is sufficiently large, the sampling distribution of the sum is approximately normal.

The probability that 900 i.i.d values drawn from Uniform[-20, 10] will have a sum greater than or equal to -4470 can be calculated as follows: The mean value of each sample is 10-20/2=-5/2. The standard deviation is calculated using the formula:  σ = sqrt((b-a)²/12) where a=-20 and b=10. The variance of the sample is σ²= 625/3.

The sample size is n=900, so the distribution of the sum of random variables will be normally distributed with mean = -5/2*900=-2250 and standard deviation = sqrt(n*σ²) = sqrt(900*(625/3))=50*sqrt(3).  We want to find the probability that the sum is greater than or equal to -4470. We convert this value to a z-score using the formula z = (x - μ)/σ. z = (-4470 - (-2250))/(50sqrt(3)) = -37.4

Using a standard normal distribution table, we find that the probability of a standard normal variable being less than or equal to -37.4 is extremely small, approximately zero. Therefore, the probability of the sum of 900 i.i.d values drawn from Uniform[-20,10] being greater than or equal to -4470 is essentially zero.

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