Expand: log 4(x/ y^5z)

Answer: Check whether the given ratios are equal? The given ratios 3: 5 and 15: 25 are equal. Because when you divide the ratio 15: 25 by 5 on both numerator and denominator, the first ratio 3: 5 can be obtained. Similarly, when you multiply the first ratio 3: 5 by 5, the ratio 15: 25 can be obtained.

Step-by-step explanation:

Hope this helps!

Answer:

We have sin² x + cos² x =1 for all real x.

Therefore, sin² x = 1 – cos² x = 1 – (8/17)² = 1 – 64/289 = 225/289 = (15/17)².

However, remember that if x² = a², then x can be +a or –a.

Therefore, sin x can be either –15/17 or +15/17.

Everyone but Anirban so far has forgotten the negative solution.

Step-by-step explanation:

Given that sinθ=817 and cosθ<0 , we have: cosθ=−√1−sin2θ. cosθ=−√1−(817)2. cosθ=−√1−64289.

Answer:

$394.38

Step-by-step explanation:

the formula is I=PRT the trick here is converting the rate from 7% to a decimal. its 0.07. so you have I=(939)(.07)(6)=394.38

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

Answer:

32.50

Step-by-step explanation:

I took the test

Answer:32.50

Step-by-step explanation: I Have taken the test

using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).

To approximate the value of e^(-2.5) using the fifth partial sum of the exponential series, we can use the formula:

e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + (x^4 / 4!) + ... + (x^n / n!)

In this case, we have x = -2.5. Let's calculate the fifth partial sum:

e^(-2.5) ≈ 1 + (-2.5) + (-2.5^2 / 2!) + (-2.5^3 / 3!) + (-2.5^4 / 4!)

Using a calculator or performing the calculations step by step:

e^(-2.5) ≈ 1 + (-2.5) + (6.25 / 2) + (-15.625 / 6) + (39.0625 / 24)

e^(-2.5) ≈ 1 - 2.5 + 3.125 - 2.60417 + 1.6276

e^(-2.5) ≈ 1.64893

Therefore, using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).

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When salt is added to water, the boiling point of water is increased. The boiling point elevation depends on the concentration of salt added. The addition of salt increases the boiling point of water.

The extent of the increase in boiling point is directly proportional to the amount of salt added. Boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the pressure exerted on it by the surrounding atmosphere.

In layman's terms, this means that a liquid boils when its vapor pressure equals atmospheric pressure. Boiling point of a liquid can be increased or decreased by the addition of solutes such as salt.When a solute such as salt is added to water, the boiling point of water increases due to the phenomenon of boiling point elevation.

This is because the solute particles in the water interfere with the formation of water vapor molecules at the surface of the liquid. As a result, more energy is required to boil the water, which means that the boiling point is elevated.

The amount of elevation is directly proportional to the concentration of salt added. In short, the addition of salt to water increases the boiling point of water.

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Answer: 432

Step-by-step explanation:

540 x 0.8

Answer:

760

Step-by-step explanation:

5 times 6 is 30 and 30 + 8 = 38. 38 times 20 = 760

Hope this helps

Answer:

8

Step-by-step explanation:

Billy started with 15 apples.

Lost 2, and another 5, In total 7 apples were taken.

" Lost " Indicates subtraction.

The equation would look like this: 15 - 7.

Subtract.

Hence, your answer should be 8.

Hopes this helps!

Have a good day :).

Answer: 8

Step-by-step explanation: 15 - 2 = 13 and 13 - 5 = 8.

Answer:

11 and 4

Step-by-step explanation:

Given:

11(7+4)=

11·7+11·4

Hope this helps! :)

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer:

3-> 10

60<-200

Step-by-step explanation:

X times something = Y

6 times something= 20

something= 20/6= 10/3

3 times 10/3 = 10

200 / 10/3 = 200 times 3/10 =60

y=10

x=60

Answer:

2040

Step-by-step explanation:

We know Appleville is predicted to double its population every 10 years, while Brigdetown simply adds 1000. Doing the math, the 2040 Census will be the first one where Appleville's population (8,000) will be larger than Bridgetown's (7,000).

Appleville: 1,000 * 2³ = 1,000 * 8 = 8,000 people in 2040

Bridgetown: 4,000 + 3(1,000) = 4,000 + 3,000 = 7,000 people in 2040

8,000 > 7,000, so 2040 will be first census year where Appleville is larger than Bridgetown. (I know this is extra, but if this was asking for first year overall, then it would be 2037. 6,800 > 6,600)

Answer:

2040

Step-by-step explanation:

i got it right

Answer:

Step-by-step explanation:

No, the number of students at the school is not proportional to the number of teachers. In a proportional relationship, two quantities have a constant ratio. However, in this case, the number of teachers is not directly proportional to the number of students because there is a fixed number of teachers regardless of the number of students. Even if the number of students changes, the number of teachers remains the same.

A more appropriate way to describe the relationship between the number of teachers and students at the school is to say that there are 2 teachers for every 48 students, or that the ratio of teachers to students is 2:48, which simplifies to 1:24.

Answer:

x = -3    b no answer is 1/27000

Step-by-step explanation:

Answer:

ether:

y= 1/3 = 0.333

OR

y= 3/2 = 1.500

A one-to-one relationship between two tables is indicated by a primary key in one table being used as a foreign key in the other table. It means each record in one table corresponds to exactly one record in the other table.

In a one-to-one relationship between two tables, a primary key in one table is used as a foreign key in the other table. This relationship is established to ensure that each record in one table corresponds to only one record in the other table.

For example, in the "Customers" and "Orders" tables, each customer can have only one order, and each order can belong to only one customer. The primary key "CustomerID" in the "Customers" table would be used as the foreign key in the "Orders" table.

This indicates that each record in the "Orders" table is associated with a specific customer in the "Customers" table, creating a one-to-one relationship. For example, in the "Customers" and "Orders" tables, each customer can have only one order, and each order can belong to only one customer.

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Answer:

D

Step-by-step explanation:

you mean the formula is 4×pi×r² (not 4×pi/r²), right ?

then the correct answer is the sphere (ball).

the surface area of a cylinder is

top and bottom circle area = pi×r² each = 2×pi×r² both

and the mantle is 2×pi×r×height

the surface area of a block has nothing to do with pi.

it is the sum of 6 rectangles.

the surface area of a cone is

A = πr(r + sqrt(h² + r²))

again, also depending on "hight"

Answer:

Solution : Let Tn=0. Then,21+(n-1)×(-3)=0⇒n=8. So, 8th term is zero.

Step-by-step explanation:

Answer:

\(\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}\)

Step-by-step explanation:

\(\sqrt{(\frac{5}{4})^7 }\)

Apply rule : \(\sqrt{a} =a^{\frac{1}{2} }\)

\(((\frac{5}{4})^7 )^{\frac{1}{2} }\)

Apply rule : \((a^b)^c=a^{bc}\)

\((\frac{5}{4} )^{7 \times \frac{1}{2} }\)

\((\frac{5}{4} )^{\frac{7}{2}\)

The value of 'x' or the length of the base of the triangle is \(\sqrt{141}\) units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, In right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

The given triangle has a hypotenuse of 25 units and a height of 22 units.

Therefore,

Hypotenuse² = Base² + Height².

Base² = Hypotenuse² -  Height².

Base = \(\sqrt{Hypotenuse^2 - Height^2}\).

Base = \(\sqrt{25^2 - 22^2}\).

Base = \(\sqrt{625 - 484}\).

Base = \(\sqrt{141}\).

So, The length of the base is \(\sqrt{141}\) units.

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the controllable cost variance is $9,400.

To calculate the controllable cost variance, we need to compare the actual variable overhead costs with the flexible budgeted variable overhead costs based on the actual production level.

The flexible budgeted variable overhead cost per unit is:

$50,400 ÷ 42,000 = $1.20 per unit

The flexible budgeted variable overhead cost for 34,000 units is:

$1.20 × 34,000 = $40,800

The difference between the actual variable overhead costs and the flexible budgeted variable overhead costs is:

$50,200 - $40,800 = $9,400

what is variable?

In mathematics, a variable is a symbol or letter that represents a value or quantity in a mathematical expression or equation. Variables can take on different values or quantities, which can be manipulated and solved for using mathematical operations. In algebra, variables are often used to represent unknown values that need to be solved for, while in calculus, variables can represent rates of change or infinitesimally small quantities.

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That's possible when function tends to zero

\(\\ \rm\hookrightarrow 0.25x^2-x+9.5=0\)

\(\\ \rm\hookrightarrow 1/4x^2-x+19/2=0\)

\(\\ \rm\hookrightarrow x^2-x+38=0\)

\(\\ \rm\hookrightarrow x=\dfrac{1\pm\sqrt{1-152}}{2}\)

\(\\ \rm\hookrightarrow x=\dfrac{1\pm\sqrt{151}i}{2}\)

Answer:

8.5 ft

Step-by-step explanation:

\(f(x) = 0.25x^2 - x + 9.5\)

To find the minimum point of the function, differentiate:

\(f'(x) = 0.5x - 1\)

set to zero and solve for x:

\(f'(x) =0\\ \implies0.5x - 1=0\\\implies x=2\)

Substitute found value of x into function to find y (height):

\(f(2) = 0.25(2)^2 - 2 + 9.5=8.5\)

Therefore, the lowest point on the bottom edge of the banner is 8.5 ft above the floor.

We cannot compute P(B complement given A) without knowing the conditional probability P(B|A).

To compute P(B complement given A), we need to use the conditional probability formula: P(B complement | A) = P(A and B complement) / P(A).

Since we don't have any information about the probability of A and B occurring together, we cannot use the formula directly. However, we can use the fact that P(B) = P(A and B) + P(A and B complement), which implies that P(A and B complement) = P(B) - P(A and B).

Substituting the given probabilities, we have:

P(A and B complement) = P(B) - P(A and B) = 0.6 - (0.2 x P(B|A))

We don't know the value of P(B|A), but we can use the fact that P(A and B) = P(A) x P(B|A) to rewrite the equation:

P(A and B complement) = 0.6 - (0.2 x P(A) x P(B|A))

Substituting the given probabilities, we have:

P(A and B complement) = 0.6 - (0.2 x 0.2 x P(B|A)) = 0.56 - 0.04 x P(B|A)

Therefore, we cannot compute P(B complement given A) without knowing the conditional probability P(B|A).

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Step-by-step explanation:

-5 - 2x < - 4

Bringing like terms on one side

-2x < - 4 + 5

-2x < 1

x < - 1/2

Option none is the correct answer

False, The eigenvalues of a matrix A are not same as the eigenvalues of the reduced row echelon form of A.

A matrix's eigenvalues are not the same as those of the matrix's reduced row echelon form, contrary to what is claimed.

This is due to the fact that when a matrix is reduced to its echelon form via row operations, its eigenvalues may not always stay the same. The eigenvalues of a matrix may be different in the reduced row echelon form than they are in the original matrix as a result.

Think about these matrices as an illustration:

Likewise, B's reduced row echelon form is B, and B's eigenvalues are both 1.

A = [1 2; 2 1]

and

B = [1 0; 0 1].

The eigenvalues of a matrix and its reduced row echelon form are thus typically not the same.

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FALSE. The eigenvalues of a matrix A are NOT the same as the eigenvalues of the reduced row echelon form of A.

Explanation:

Eigenvalues are scalar values that, when multiplied by an eigenvector, produce the same effect as the original matrix A on that eigenvector. Mathematically, for a matrix A and its eigenvector v, Av = λv, where λ is the eigenvalue.

Row echelon form is a matrix transformation using elementary row operations to obtain a triangular form. The reduced row echelon form (RREF) is a further simplified version of the row echelon form.

However, transforming a matrix A to its RREF changes the properties of the matrix, and therefore the eigenvalues of matrix A and its RREF are generally not the same. The eigenvalues are preserved only under specific matrix transformations, such as similarity transformations, which row echelon form is not one of them.

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Let's calculate the total cost of all the items purchased by the computer club:

Cost of 14 portfolios = 14 * $24.59

Cost of 14 binders = 14 * $12.92

Cost of 14 school sweatshirts = 14 * $14.00

Cost of 14 music cases = 14 * $1.25

Cost of 14 phone cases = 14 * $1.99

Cost of 14 mouse pads = 14 * $2.14

Total cost of all items = Cost of 14 portfolios + Cost of 14 binders + Cost of 14 school sweatshirts + Cost of 14 music cases + Cost of 14 phone cases + Cost of 14 mouse pads

Plugging in the given values:

Total cost of all items = (14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14)

Now, the computer club will pay for 40% of the total cost. To calculate this, we can multiply the total cost by 40% (or 0.40):

Club's payment = 0.40 * Total cost of all items

The remaining cost will be divided equally among the 14 members:

Remaining cost per member = (Total cost of all items - Club's payment) / 14

Plugging in the values and calculating:

Club's payment = 0.40 * ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14))

Remaining cost per member = ((14 * $24.59) + (14 * $12.92) + (14 * $14.00) + (14 * $1.25) + (14 * $1.99) + (14 * $2.14) - Club's payment) / 14

So, each member of the computer club will owe the calculated value for "Remaining cost per member".

Hope this is good

The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)

To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.

From the given information, we can observe that Lindsey's scores are increasing at the same rate.

This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.

Let's denote the first term as a₁ = 67 and the common ratio as r.

Recursive Formula:

In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:

aₙ = aₙ₋₁ \(\times\) r

For Lindsey's scores, the recursive formula would be:

aₙ = aₙ₋₁ \(\times\) r

Explicit Formula:

The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.

The explicit formula for a geometric sequence is:

aₙ = a₁ \(\times r^{(n-1)\)

For Lindsey's scores, the explicit formula would be:

aₙ \(= 67 \times r^{(n-1)\)

In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.

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