A box of books has a mass of 4.10 kilograms for every meter of its height. Convert this ratio into pounds per foot.

The symbols x, y, and z are examples of variables in an instruction like z = x + y.

A variable is a term that signifies anything that can be varied or altered. In programming, variables are utilized to hold values that might be modified and used in later code.

A variable is a name that identifies a memory location where data is stored. It can be changed anytime. Variables are commonly used in mathematical expressions, such as those seen in algebra. For example, x + 150 = 300In this instance, x is the variable. 150 and 300 are constants.

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Answer:

Step-by-step explanation:

(-11) + 3

-8

Answer:

=−8

Step-by-step explanation:

=−11−(−3)

=−11+3

=−8

Answer:

zxczxcz

Step-by-step explanation:

zxczxczxc

The graph of the linear equation is on the image at the end,

Here we want to graph the linear equation:

y = k*x + 5

We know that this line passes through the point (-6, 14), replacing these values we will get:

To graph it, we need to find another point on the line, evaluating in x = 0 we will get:

y = k*0 + 5

y = 5

So we also have the point (0, 5)

Now you just need to graph the two points (-6, 14) and (0, 5) and draw a line that connects them.

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The enzyme that has a very similar reaction mechanism to 6-phosphogluconate dehydrogenase in glucose oxidation by the citric acid cycle is isocitrate dehydrogenase.

Isocitrate dehydrogenase is a key enzyme in the citric acid cycle, also known as the Krebs cycle  or TCA cycle. It catalyzes the conversion of isocitrate to alpha-ketoglutarate, while producing NADH and CO2 as byproducts. This reaction is an important step in the oxidation of glucose and the production of energy in the form of ATP. The reaction mechanism of isocitrate dehydrogenase involves the removal of a carboxyl group from isocitrate, resulting in the formation of an intermediate molecule called oxalosuccinate. This intermediate is then decarboxylated to produce alpha-ketoglutarate. The overall reaction is coupled with the reduction of NAD+ to NADH. 6-phosphogluconate dehydrogenase, on the other hand, is involved in the pentose phosphate pathway and plays a role in glucose metabolism. Although it operates in a different pathway, the reaction mechanism of 6-phosphogluconate dehydrogenase shares similarities with isocitrate dehydrogenase, particularly in the decarboxylation step and the involvement of NAD(P)+ as a cofactor.

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Answer:

A. y=6x

Step-by-step explanation:

A. y=6x that's all I know

Answer: A. y=6x

Step-by-step explanation:

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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The net operating income will be $ 5000.

The profitability of real estate assets that produce income is evaluated using a formula known as net operating income (NOI). NOI is the total revenue from the asset less all running costs that are deemed to be absolutely required.

Here we have  

A product has a selling price of $10 per unit, variable expenses of $6 per unit, and total fixed costs of $35,000.

In total 10,000 units are sold  

The net operating income will be computed by Subtracting all expenditures from all money collected on the product.    

Net operating income = ($10 - $6) × 10000 - $ 35000

= ($10 - $6) × 10000 - $ 35000  

=  $ 40000 - $ 35000

= $ 5000    

Therefore,

The net operating income will be $ 5000.

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Answer:

0.9168

Step-by-step explanation:

From the data given:

Mean = 110

standard deviation = 5

Let consider a random sample n =49 which have a mean between 109 and 112.

The test statistics can be computed as:

\(Z_1 = \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}\)

\(Z_1 = \dfrac{109- 110}{\dfrac{5}{\sqrt{49}}}\)

\(Z_1= \dfrac{-1}{\dfrac{5}{7}}\)

\(Z_1\)  = -1.4

\(Z_2= \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}\)

\(Z_2 = \dfrac{112- 110}{\dfrac{5}{\sqrt{49}}}\)

\(Z_2 = \dfrac{2}{\dfrac{5}{7}}\)

\(Z_2 =2.8\)

Thus; P(109  <  \(\overline x\)  <  112) = P( - 1.4 < Z < 2.8)

= P(Z < 2.8) - P( Z < -1.4)

= 0.9974 - 0.0806

= 0.9168

Answer:

x = - 5, y = - 6

Step-by-step explanation:

Given the 2 equations

7x - 4y = - 11 → (1)

7x + 4y = - 59 → (2)

Adding the 2 equations term by term will eliminate the term in y

14x = - 70 ( divide both sides by 14 )

x = - 5

Substitute x = - 5 into either of the 2 equations and solve for y

Substituting into (2)

7(- 5) + 4y = - 59

- 35 + 4y = - 59 ( add 35 to both sides )

4y = - 24 ( divide both sides by 4 )

y = - 6

Thus x = - 5 and y = - 6

Answer:

x = -5

y = -6

Step-by-step explanation:

Let's take the top equation.

7x - 4y = -11

and solve it for x.

7x - 4y = -11

7x = 4y - 11

x = \(\frac{4y - 11}{7}\)

Now we can substitute it in to the other equation.

7x + 4y = -59

7(\(\frac{4y-11}{7}\)) + 4y = -59

Now solve this equation.

4y - 11 + 4y = -59

8y - 11 = -59

8y = -48

y = -6

Then substitute negative 6 into the first equation.

7x - 4(-6) = -11

7x -(-24) = -11

7x = 35

x = -5

Answer:

The volume of the regular polyhedron whose vertices are the midpoints of the edges of the original tetrahedron is 45/√2.

Step-by-step explanation:

Given that the volume of a tetrahedron is 120.

Therefore, let's first calculate the length of each edge of the regular tetrahedron using the formula of regular tetrahedron volume.

Volume of a regular tetrahedron = `(a³)/(6√2)`

Here, given that the volume of the tetrahedron is 120.

So, 120 = `(a³)/(6√2)`

On solving this equation, we get the length of an edge,

a = `(120×6√2)^(1/3)`

Now, let's find out the length of the diagonal of the cube whose vertices are at the midpoints of the edges of the tetrahedron.

We can do this by using Pythagorean theorem.

Diagonal of a cube = `√(a²+a²+a²)` = `√3a`

So, the length of the diagonal of the cube is, `√3a` = `√3(120×6√2)^(1/3)`

Now, let's calculate the length of each side of the cube. Since each vertex of the other polyhedron is located at the midpoint of an edge of the tetrahedron, the length of the side of the cube is half the length of the edge of the tetrahedron.

So, the length of each side of the cube is, `a/2` = `(120×6√2)^(1/3)/2`

Now, let's calculate the volume of the cube whose vertices are at the midpoints of the edges of the tetrahedron.

The volume of the cube is `s³` = `[(120×6√2)^(1/3)/2]³` = `(120×6√2)/8` = `(45√2)`

Therefore, the volume of the other regular polyhedron is `(45√2)`.

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Answer:

B) 5

Step-by-step explanation:

$6000 × 0.03 = $180 - this means that every year, $180 is added to the invested amount.

We can now do $900 ÷ $180 to find out the number of years the money was invested for: $900 ÷ $180 = 5

The money was invested for 5 years

Hope this helps!

Given:

The first 10 GB of data costs $3 per GB.

After exceeds 10 GB, the company charges $15 for each GB.

Required:

We need to find the function for the given situation.

Explanation:

Let x be the number of GB that "Demetrius' used.

Let f(x) be the cost.

The first 10 GB of data costs $3 per GB.

After exceeding 10 GB, the company charges $15 for each GB

Final answer:

4/20 ×100

20 % of eggs are broken tho

20 % of the eggs broke then died and is now haunting you

SOLUTION

Given the question in the question tab, the following are the solution steps to prove the theorem

STEP 1: Write the theorem

Theorem: Vertical Angles are congruent

Step 2: Define Vertical Angles

When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles. In the image given below, (∠1, ∠3) and (∠2, ∠4) are two vertical angle pairs.

STEP 3: State the Vertical angles theorem

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

STEP 4: Prove the theorem

The proof is based on straight angles. We already know that angles on a straight line add up to 180°.

The expressions for Y(t) and X(t) obtained by applying inverse Laplace transforms to the given equations are :

For Y(t):

Y(t) = 2 + 2e^(-t) + 1/4 + 1/4 * sin(2t)

For X(t):

X(t) = 1/12 + e^(-0.5t) - e^(-4t) - e^(-3t)

To find Y(t) using Laplace transforms for the equation Y(s) = 2(s + 1) / (s(s^2 + 4)), we need to apply the inverse Laplace transform to the given expression.

Decompose the fraction using partial fraction decomposition:

1/(s(s^2 + 4)) = A/s + (Bs + C)/(s^2 + 4)

Multiplying through by s(s^2 + 4), we get:

1 = A(s^2 + 4) + (Bs + C)s

Expanding the equation, we have:

1 = As^2 + 4A + Bs^2 + Cs

Equating the coefficients of like powers of s, we get the following system of equations:

A + B = 0 (for s^2 term)

4A + C = 0 (for constant term)

0s = 1 (for s term)

Solving the system of equations, we find:

A = 0

B = 0

C = 1/4

Therefore, the decomposition becomes:

1/(s(s^2 + 4)) = 1/4(s^2 + 4)/(s^2 + 4) = 1/4(1/s + s/(s^2 + 4))

Taking the Laplace transform of the decomposed terms:

L^(-1){Y(s)} = L^(-1){2(s + 1)/s} + L^(-1){1/4(1/s + s/(s^2 + 4))}

The inverse Laplace transform of 2(s + 1)/s is 2 + 2e^(-t).

For the second term, we have two inverse Laplace transforms to find:

L^(-1){1/4(1/s)} = 1/4

L^(-1){1/4(s^2 + 4)} = 1/4 * sin(2t)

Combining all the terms, we get:

Y(t) = 2 + 2e^(-t) + 1/4 + 1/4 * sin(2t)

Thus, Y(t) = 2 + 2e^(-t) + 1/4 + 1/4 * sin(2t).

Now, let's find X(t) using Laplace transforms for the equation X(s) = (s + 1 * e^(-0.5s))/(s(s + 4)(s + 3)).

Apply the inverse Laplace transform to X(s).

X(t) = L^(-1){(s + 1 * e^(-0.5s))/(s(s + 4)(s + 3))}

Decompose the fraction using partial fraction decomposition:

1/(s(s + 4)(s + 3)) = A/s + B/(s + 4) + C/(s + 3)

Multiplying through by s(s + 4)(s + 3), we get:

1 = A(s + 4)(s + 3) + Bs(s + 3) + C(s)(s + 4)

Expanding the equation, we have:

1 = A(s^2 + 7s + 12) + Bs^2 + 3Bs + Cs^2 + 4Cs

Equating the coefficients of like powers of s, we get the following system of equations:

A + C = 0 (for s^2 term)

7A + 3B + 4C = 0 (for s term)

12A = 1 (for constant term)

Solving the system of equations, we find:

A = 1/12

B = -1/3

C = -1/12

Therefore, the decomposition becomes:

1/(s(s + 4)(s + 3)) = 1/12(1/s - 1/(s + 4) - 1/(s + 3))

Taking the Laplace transform of the decomposed terms:

L^(-1){X(s)} = L^(-1){(1/12)(1/s - 1/(s + 4) - 1/(s + 3))}

The inverse Laplace transform of 1/s is 1.

The inverse Laplace transform of 1/(s + 4) is e^(-4t).

The inverse Laplace transform of 1/(s + 3) is e^(-3t).

Combining all the terms, we get:

X(t) = 1/12 + 1 * e^(-0.5t) - 1 * e^(-4t) - 1 * e^(-3t)

Thus, X(t) = 1/12 + e^(-0.5t) - e^(-4t) - e^(-3t).

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Answer:

Step-by-step explanation:

121 is an outlier.  it's a data point that lies outside of the rest.  All the other numbers are clumped around 70-79 and 121 is so far off

The decimal number 3.16 in the form of the simplest fraction is 79/25.

The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

Consider the decimal number,

Let x = 3.16

Then,

x = 3.16 = 316/100

The fraction then can be simplified as,

x = ( 158 × 2)/ (50 × 2)

x = 158/50

x = ( 79 × 2)/ ( 25 × 2 )

x = 79/25

Hence, the number 3.16 in the simplest fraction is 79/25.

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Answer:

A

Step-by-step explanation:

1. 10 + 5x = 20

2. 5 + 10x = 20

3. 20 - 5x = 10

4. x/5 + 10 = 20

The simplest form is 15z+ 15x²

In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.

Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.

Given,

(5z+5 x²)3

15z+15x² by simplifying,

3(5z+5 x²)

apply the distributive formula :a (b + c) =ab + ac

3(5z+5 x²) = 5x+3 * 5x²

By simplifying 3 5z+3 , 5x², 15z+15x²

we get

15z+ 15x²

Therefore the simplest form is 15z+ 15x² .

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Answer:

7 or 8 days

Step-by-step explanation:

The answers is correct ⬆️

Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

Answer:

on which days did it rain less then one-fifth of an inch

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A 90 degree rotation would be a rotation of 90° about the origin. Knowing this, we can eliminate C since it is a 180° rotation. We can also eliminate A, as it would be a 0° or 360° rotation. This leaves us with B and C.

A counterclockwise rotation would be one that goes the opposite direction of the rotation of the hands of a clock. A 90° counterclockwise rotation would yield triangle B, making that our answer.

I hope you find my answer and explanation to be helpful. Happy studying.