Save Submit Assignment for Grading Exercise 10.04 (Inferences About the Difference Between Two Population Means: Sigmas Known) Question 2 of 13. Hint(s) Condé Nast Traveler conducts an annual survey

The volume of the rectangular prism is 428,544 cubic cm.

To find the volume of the rectangular prism, we can start by determining the dimensions of the prism.

Let's assume the length, width, and height of the prism are L, W, and H, respectively.

Given that the rectangular prism is filled exactly with 248 cubes, we can express the total number of cubes as the product of the length, width, and height of the rectangular prism:

\(L \times W \times H = 248\)

Since each cube has an edge length of 12 cm, the volume of one cube can be calculated as follows:

Volume of one cube \(= (12 cm) \times (12 cm) \times(12 cm)\)

Volume of one cube \(= 1728 cm^3\)

Now, we can set up the equation based on the given information:

\(L \times W \times H = 248 \times Volume of one cube\)

\(L \times W \times H = 248 \times 1728 cm^3\)

To find the volume of the rectangular prism, we need to calculate the right side of the equation:

\(248 \times1728 = 428,544 cm^3\)

Therefore, the volume of the rectangular prism is \(428,544 cm^3\).

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Answer:

67 1/2 cm

Step-by-step explanation:

v=lxwxh

v=4 1/2x 6x 2 1/2

v=67 1/2 cm^3

Volume of rectangular prism is given by:

‎ㅤ‎ㅤ‎ㅤ➙ V = l × b × h

Here, we have :

Therefore, volume:

\( \implies\quad \tt {V =l\times b\times h }\)

\( \implies\quad \tt { V =6\times 2\dfrac{1}{2}\times 4\dfrac{1}{2}}\)

\( \implies\quad \small{\tt { V = 6\times \dfrac{(2\times 2)+1}{2}\times \dfrac{(4\times 2)+1}{2}}}\)

\( \implies\quad \tt {V = 6\times \dfrac{4+1}{2}\times \dfrac{8+1}{2} }\)

\( \implies\quad \tt {V =6\times \dfrac{5}{2}\times\dfrac{9}{2} }\)

\( \implies\quad \tt {V =\dfrac{6\times 5\times 9}{2\times 2} }\)

\( \implies\quad \tt { V =\cancel{\dfrac{270}{4}}}\)

\( \implies\quad \tt { V = \dfrac{135}{2}}\)

\( \implies\quad \underline{\underline{\pmb{\tt { V = 67\dfrac{1}{2}\:cm^2}}}}\)

Answer:

2

Hopefully that's the answer you wanted XD

Answer:

2

Step-by-step explanation:

The relation R is not reflexive, but it is symmetric and transitive.

A homogeneous relation R over the set A, which comprises the elements x, y, and z, is known as a transitive relation. If R relates x to y and y to z, then R likewise relates x to z.

For x, y ∈ Z, xRy if and only if (x+y)² ≡ ±1.

(a) Reflexivity: For x ∈ Z, we have (x + x)² = 4x² ≡ 0 (mod 1), which is not equal to ±1. Therefore, xRx does not hold for any x ∈ Z, and R is not reflexive.

(b) Symmetry: For x, y ∈ Z, if xRy, then (x + y)² ≡ ±1. This implies that (y + x)^2 ≡ (x + y)² ≡ ±1. Therefore, yRx also holds, and R is symmetric.

(c) Transitivity: For x, y, z ∈ Z, if xRy and yRz, then (x + y)² ≡ ±1 and (y + z)² ≡ ±1. Expanding these expressions, we get:

(x + y)² ≡ ±1  =>  x² + 2xy + y² ≡ ±1

(y + z)² ≡ ±1  =>  y² + 2yz + z² ≡ ±1

Adding these two equations, we get:

x² + 2xy + y² + y² + 2yz + z² ≡ ±2

Simplifying, we get:

x² + 2xy + 2yz + z² ≡ ±2 - 2y²

Now, we need to show that (x + z)² ≡ ±1. Expanding (x + z)², we get:

(x + z)² = x² + 2xz + z²

Substituting x² + 2xy + 2yz + z² ≡ ±2 - 2y², we get:

(x + z)² ≡ 2 - 2y² + 2xz

To complete the proof, we need to show that there exists some integer k such that 2 - 2y² + 2xz - k² ≡ ±1. We can rewrite this expression as:

2xz - k² ≡ 2y² - 3 (mod 4)

Since the left-hand side is even, the right-hand side must also be even. Therefore, y² ≡ 1 (mod 4), which implies that y is odd.

Now, we can substitute y = 2m + 1 for some integer m, and simplify:

2xz - k² ≡ 8m² + 8m - 1 (mod 4)

We can rewrite the right-hand side as 4(2m² + 2m) - 1, which is congruent to -1 (mod 4). Therefore, there exists some integer k such that 2xz - k² ≡ ±1, which implies that (x + z)² ≡ ±1. Hence, xRz holds, and R is transitive.

In summary, the relation R is not reflexive, but it is symmetric and transitive.

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Answer:

Let x be the length of the base of the triangle, then the height h is given by h = 2x - 3 (since the height is 3 inches less than twice the length of the base).

The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. We are given that the total area of the triangle is 7 square inches, so we can write:

(1/2)(x)(2x - 3) = 7

Multiplying both sides by 2 to eliminate the fraction, we get:

x(2x - 3) = 14

Expanding the left side, we get:

2x^2 - 3x = 14

Subtracting 14 from both sides, we get:

2x^2 - 3x - 14 = 0

We can now use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac))/(2a)

where a = 2, b = -3, and c = -14. Plugging in these values, we get:

x = (-(-3) ± sqrt((-3)^2 - 4(2)(-14)))/(2(2))

= (3 ± sqrt(169))/4

= (3 ± 13)/4

Taking the positive value for x (since the length of the base must be positive), we get:

x = (3 + 13)/4

= 4

Therefore, the length of the base is 4 inches. To find the height h, we can use the formula h = 2x - 3:

h = 2(4) - 3

= 5

So the height of the triangle is 5 inches.

Incomplete question.  

Answer:

x -2.

Step-by-step explanation:

Given  : (x + 5) and (2x + 3).

To find : Find the difference between .

Solution : We have given   (x + 5) and (2x + 3).

According to question :

Difference of (x + 5) and (2x + 3).

(2x + 3) - (x +5).

2x + 3 - x - 5 .

On combine like terms.

2x -x +3 -5.

x -2.

Therefore, x -2.

The difference between (x + 5) and (2x + 3) is -x + 2

Difference is the result of subtracting one number from another. Therefore,

the difference between (x + 5) and (2x + 3) can be calculated below:

Open the bracket with the minus sign

Therefore,

x + 5 - 2x - 3

combine like terms

x - 2x + 5 - 3

-x + 2

Therefore, the difference between  (x + 5) and (2x + 3) is -x + 2

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Answer:

Elena = 3 1/2 yards

Nailah = 1 2/3 yards

Yu = 4/5 yards

Step-by-step explanation:

Pieces of ribbon purchased :

Yu - 3 pieces

Nailah - 5 pieces

Elena - 6 pieces

We could infer that ;

Elena who bought 6 pieces or ribbon bought the highest amount of ribbon followed by Nailah, then Yu

Given that the number of yards each of Yu, Elena and Nailah could have bought :

1 2/3yd ; 4/5yd ; 3 1/2yd

Elena bought the highest number of prices and hence would possibly have the highest number of yards = 3 1/2

Nailah bought next, with 5 pieces, which is greater than Number of pieces bought by Yu but less than Elena ; hence, she could have bought 1 2/3 yards

Then Yu who has the least could have 4/5 yards

Answer:

66°

Step-by-step explanation:

Draw the figure to left on a piece of paper and rotate in to fit. I think ∠C = ∠M.

the figures are ≅ so corresponding sizes and angles are ≅.

Answer:

\(8 \div \frac{1}{2} = 8 \times \frac{2}{1} = 8 \times 2 = 16\)

The length of each side of the box is 10 centimeter.

Volume is the amount of space occupied by a three-dimensional figure as measured in cubic units.

Given,

The volume of the cubic box = 1 liter

We know 1 liter= 1000 cubic centimeter

Volume of the cubic box= \(x^3}\)

Then,

\(x^{3}=1000\\ x=\sqrt[3]{1000}\)

x=10 centimeter

Hence, the length of each side of the box is 10 centimeter.

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Answer:10

Step-by-step explanation:

For real and distinct roots of a quadratic a₁v² + a₂v + a₃ = 0, with v the unknown, then the discriminant D > 0 which makes option C correct

Suppose a₁p² + a₂p + a₃ = 0, where a₁, a₂ and a₃ are constants, then the discriminant D = (a₂)² - 4a₁a₃ which makes option C correct.

The quadratic equation is of the general form ax² + bx + c = 0 where x is the unknown, a, b and c are constants and the discriminant D = b² - 4ac. The nature of its roots are:

For the equation a₁v² + a₂v + a₃ = 0 with real and distinct roots, the discriminant D > 0

For the equation a₁p² + a₂p + a₃ = 0, where a₁, a₂ and a₃ are constants, the discriminant D = (a₂)² - 4a₁a₃.

Therefore, the discriminant D > 0 for the real and distinct roots of the equation a₁v² + a₂v + a₃ = 0. And the discriminant D = (a₂)² - 4a₁a₃ for the quadratic equation a₁p² + a₂p + a₃ = 0

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To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:

∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du  

= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C

Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.

In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.

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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

What is intergration?

Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.

To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.

By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:

\(dx = a sec(\theta) tan(\theta) d(\theta)\)

Now, let's substitute these values into the integral:

\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)

Simplifying the expression, we have:

\(= \int \sec(\theta) d(\theta)\)

The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):

\(= \ln|\sec(\theta) + \tan(\theta)| + C\)

Finally, substituting back \(x = a sec(\theta)\), we get:

\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)

Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

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Answer:

x = 11.3125

Step-by-step explanation:

0.25 + 13 = 4(x - 8)

Distribute the 4 across the parentheses.

0.25 + 13 = 4x - 32

Combine the constants on the left side of the equal sign.

13.25 = 4x - 32

Combine all the constants by adding 32 to both sides.

45.25 = 4x

Divide by 4 to isolate the x.

45.25/4 = x

11.3125 = x

Check.

0.25 + 13 = 4(x - 8)

0.25 + 13 = 4(11.3125 - 8)

0.25 + 13 = 4(3.3125)

0.25 + 13 = 13.25

13.25 = 13.25

Answer:

well i cant really tell so much though

Step-by-step explanation:

To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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A polynomial is represented as \(\mathbf{ax^n + bx^{n-1} + cx^{n-2} + .... + d}\)

The leading coefficient of the polynomial is "a"

The leading coefficient of a polynomial is simply the coefficient of the variable with the highest power.

Take for instance:

\(\mathbf{2x^3 + 4x^2 + 5x - 6}\)

In the above polynomial,

This means that, the leading coefficient is 2

Another instance:

\(\mathbf{-6y^5 + 2y^4 + 19y^3 - y^2 -17y + 1}\)

In the above polynomial,

This means that, the leading coefficient is -6

In general,

The leading coefficient of the polynomial \(\mathbf{ax^n + bx^{n-1} + cx^{n-2} + .... + d}\) is "a"

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Answer:

The answer to this is B. y=32.55

The surface area and volume of the trianglular prism are 179.2m² and 492.8m³ respectively.

area of one trianglular face = 1/2 × 8m × 11.2m

area of one trianglular face = 44.8m²

surface area of the trianglular prism = 4 × 44.8m²

surface area of the trianglular prism = 179.2m²

Volume of triangular prism = base area × height

base area of prism = 1/2 × 8m × 11.2m

base area of prism = 44.8m²

volume of the trianglular prism = 44.8m² × 11m

volume of the trianglular prism = 492.8m³

Therefore, the surface area and volume of the trianglular prism are 179.2m² and 492.8m³ respectively.

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Answer:

-100

Step-by-step explanation:

-10×-10 =-100.

Because square means twice

Answer:

\(\huge\boxed{\sf{100c^2}}\)

Step-by-step explanation:

Hello.

(-10c) squared can be written as

(-10c)²

Now simplify.

First, -10 times -10 is equal to 100.

So we have

100 times c²

or

100c²

And we're done!

I hope it helps & have an outstanding day!

~ST2710 :)

The shortest distance (d) between the point P0 and the line L, as well as the closest point Q on L to P0, need to be found.

o find the shortest distance (d) between the point P0 and the line L, we can use the formula that involves the projection of the vector connecting P0 to any point on L onto the direction vector of L.

Find the vector connecting P0 to a point on L: →v = →P0 - →P = [-2 - (-2), -1 - 2, 5 - (-5)] = [0, -3, 10].

Calculate the projection of →v onto the direction vector →d: proj_→d →v = (→v · →d) / ||→d||^2 * →d = (-6 - 3 + 30) / (9 + 1 + 9) * [-3, -1, -3] = [3, 1, 3].

The shortest distance d is the magnitude of the vector →v - proj_→d →v: d = ||→v - proj_→d →v|| = ||[0, -3, 10] - [3, 1, 3]|| = ||[-3, -4, 7]|| = sqrt(74).

The point Q on L that is closest to P0 is found by adding the projection vector to point P: Q = P + proj_→d →v = [-2, 2, -5] + [3, 1, 3] = [1, 3, -2].

Therefore, the shortest distance d from P0 to L is sqrt(74), and the closest point Q on L to P0 is (1, 3, -2).


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Answer:

Step-by-step explanation:

Let's call the number x. The statement "...2 times a number" if the number is x looks like this:

2x

"8 less than" that looks like this:

... - 8

Putting the whole thing together:

2x - 8

Answer:

-10

Step-by-step explanation:

70= -7k

70 -7k

-- --

-7 -7

-10=k

Have a great day

Answer:

k= -10

Step-by-step explanation:

70= -7k

Divide both sides by -7

-7k/-7 = 70/7

Simplify

k=-10

a least squares linear trend line is just a simple regression line with the years recoded  then it is a true statement

The simple linear regression model is;

y = mx + c

Where,

y = dependent variable

m is the slope

x is the independent variable

c is the y- intercept

The long-term trend only Least-Squares Regression Model also follows the same format except y becomes Yt and x becomes t.

The long-term trend only Least-Squares Regression Model is therefore the same as a simple linear regression only with different variable terms.

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To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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