-12 = 6+ 2/3 y


Pleaseeeee help me ❤️

Answer:  NO/MN   =     QR/PQ

Answer:

\(\frac{NO}{MN}\) = \(\frac{QR}{FQ}\)

Step-by-step explanation:

∠ 0 ≅ ∠ R and ∠ M ≅∠ F

thus Δ NOM ≅ ∠ QRF ( by the AA postulate )

the ratios of corresponding sides are in proportion, so

\(\frac{NO}{MN}\) = \(\frac{QR}{FQ}\)

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

x = \(\frac{7}{2}\) ± \(\frac{\sqrt{13} }{2}\)

Step-by-step explanation:

Given

x² - 7x + 9 = 0 ( subtract 9 from both sides )

x² - 7x = - 9

Solve using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2( - \(\frac{7}{2}\) )x + \(\frac{49}{4}\) = - 9 +

(x - \(\frac{7}{2}\) )² = \(\frac{13}{4}\) ( take the square root of both sides )

x - \(\frac{7}{2}\) = ± \(\sqrt{\frac{13}{4} }\) = ± \(\frac{\sqrt{13} }{2}\) ( add

x = \(\frac{7}{2}\) ± \(\frac{\sqrt{13} }{2}\) = \(\frac{7+/-\sqrt{13} }{2}\)

Answer:

Using quadratic formula again :)

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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We would need to know the distribution of the revenues, such as whether it follows a normal distribution or some other distribution. Additionally, we would need the specific values of the mean, standard deviation, UCL, and LCL.

To calculate the probability that the true average revenues per hour will be either greater than the Upper Control Limit (UCL) or lower than the Lower Control Limit (LCL), we need more information about the data distribution and the control limits themselves.

Control limits are typically used in statistical process control (SPC) to determine whether a process is stable and within the acceptable range of variation. They are derived from the process data and define the boundaries within which the process is expected to perform.

If we have a normal distribution assumption for the data and know the mean (μ) and standard deviation (σ), we can calculate the probability using the z-score and the standard normal distribution.

Let's assume we have the following information:

- Mean (μ) of the data.

- Standard deviation (σ) of the data.

- UCL and LCL values.

To calculate the probability of the true average revenues per hour being outside the control limits, we can use the z-score formula:

z = (x - μ) / (σ / sqrt(n))

Where:

- x is the value we are interested in (UCL or LCL).

- μ is the mean of the data.

- σ is the standard deviation of the data.

- n is the sample size.

Once we have the z-score, we can consult a standard normal distribution table or use statistical software to find the corresponding probability.

Please provide the necessary information (mean, standard deviation, UCL, LCL, and sample size) so that I can help you calculate the probability.

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After subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

So, we have:

(x+7) and (3x+4)

We have to subtract as:

(3x+4) - (x+7)

Now, subtract as follows:

(3x+4) - (x+7)

3x+4 - x-7

2x-3

Therefore, after subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

1,688 items

Step-by-step explanation:

So they had at total of 2,150 items at the start of the year. They had 400 sweatshirts, now they have 96(a decrease of 304), 650 T-shirts now they have 139(a decrease of 511), and 1100 notebooks to 227(a decrease of 873). They now have 462 items left. This means that they sold 1,688 items.

Hope this helps.

The estimated volume of the larger balloon is approximately 1.02 x 10⁵ cm³.

If two objects are similar, it means they have the same shape but different sizes. In this case, we have two spherical balloons that are similar. We can use the fact that the volumes of two similar objects are proportional to the cubes of their corresponding dimensions.

Let's denote the volume of the smaller balloon as V1 and its radius as r1. Similarly, let V2 and r2 be the volume and radius of the larger balloon. We are given that V1 = 817 cm³ and r1 = 5.8 cm.

We can set up a proportion between the volumes of the two balloons:

V1/V2 = (r1/r2)³

Solving for V2, we get:

V2 = V1 / (r1/r2)³

Substituting the given values, we get:

V2 = 817 cm³ / (5.8 cm / 29 cm)³

V2 ≈ 1.02 x 10⁵ cm³

Therefore, the estimated volume of the larger balloon is approximately 1.02 x 10⁵ cm³.

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Answer:what grade is this?

Step-by-step explanation:

Yes, Dr. Lawrence is collecting a representative sample.

The term representative sample is a term that is used to describe a group of individuals who are selected from a population and that are meant to represent the population as a whole. The sample that Dr. Lawrence is collecting is representative because she is selecting 55 women and 45 men from the university. This means that the sample is reflective of the proportion of men and women in the university as a whole.

Dr. Lawrence is the director of counseling services at her university. She is planning to conduct a survey of 100 students at the university to see how aware they are of the counseling services that are offered at the university. She wants the proportion of men and women in her sample to reflect the proportion in the university as a whole (55% women and 45% men).

To increase the probability of a representative sample, Dr. Lawrence could use a different sampling method, such as random sampling or stratified sampling, that ensures that all members of the population have an equal chance of being selected for the sample.

Dr. Lawrence plans to stand in the student union and ask people to participate until she has given the survey to 55 women and 45 men. Thus, Dr. Lawrence is collecting a representative sample.

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The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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Answer:

y = -7

Step-by-step explanation:

A horizontal line has an equation of the form

y = b,

where b = y-intercept

The y-intercept is -7, so the equation is

y = -7

Answer:

Y=-7

Step-by-step explanation:

No matter what x equals, y has to be equal to negative 7. For example i chose 3 to by X, the equation would still be (3,-7).

Step-by-step explanation:

Volume of 100chocolates:

((12^2 x 15)/3) x 100 =72000

volume of cylinder:

base area x height

base area= πr^2= 5625π

height=volume/base area

height=72000/5625π=4.07 (3sf)

ans: 4.07mm

Answer:

$305.9022863 or $305.90 (rounded to 2 decimal places)

Step-by-step explanation:

It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula  

A= P(1+R)^n

A= the total amount P=Initial amount       R= rate  n=time period

P=$100 R=15% or 0.15(decimal)  n=8 (years)  

A= 100 (1.15)^8

A= 100(3.059022863)

A=305.9022863

The amount you will have after 8 years is $220

The formula for calculating simple interest is expressed as:

SI =PRT

P is the principal = $100

T is the time = 8 years

R is the rate. = 15%

SI = 100 * 8 * 0.15
SI = $120

Amount after 8years = $100 + $120
Amount after 8years = $220

Hence the amount you will have after 8 years is $220

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The positive constant b is 0. This is obtained by setting the coefficient of the xy^2 term to zero in the equation derived from equating the integral of the joint probability density function to 1.

To compute the positive constant b, we need to calculate the integral of the joint probability density function (pdf) over the entire probability space and set it equal to 1 since it represents a valid probability density.

∫∫ f(x, y) dx dy = 1

Since the joint pdf is defined as:

f(x, y) = 5 - bcx * cb - bzycb

And it is zero otherwise, we can set up the integral as follows:

∫∫ (5 - bcx * cb - bzycb) dx dy = 1

To solve this integral, we need to determine the limits of integration. Since the joint pdf is not specified outside of the equation, we assume it is defined for all real values of x and y.

∫∫ (5 - bcx * cb - bzycb) dx dy = ∫∫ 5 - bcx * cb - bzycb dx dy

Integrating with respect to x first:

∫ (5x - bcx^2/2 * cb - bzy * cb) ∣∣ dy = 1

Now integrating with respect to y:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) ∣∣ dy = 1

Since this equation holds for all real values of x and y, we can ignore the limits of integration.

Next, we can solve for b by equating the integral to 1 and simplifying:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) = 1

Simplifying further:

5xy - bcxy^2/2 - bzy^2/2 = 1

Now, we can compare the coefficients of the terms on both sides of the equation:

- bc/2 = 0 (since there is no xy^2 term on the right-hand side)

Solving for b:

bc = 0

Since we are looking for a positive constant b, we can conclude that b = 0.

Therefore, the positive constant b is 0.

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Answer:

200

Step-by-step explanation:

Answer:

3/20

Step-by-step explanation:

By question it's given that ,

\(\implies \dfrac{a}{b}=\dfrac{2}{5}\)

\(\implies \dfrac{b}{c}=\dfrac{3}{8}\)

And we need to find out the value of a/c .For that Multiply both of them , we have ;

\(\implies \dfrac{a}{b} \times\dfrac{b}{c}=\dfrac{2}{5}\times \dfrac{3}{8} \\\\\implies \dfrac{a}{c}= \dfrac{3}{20}\)

Hence the required answer is 3/20 .

The mean of the given fuel prices data set is $4.61 with a standard deviation of $1.62.

To calculate the mean and standard deviation in Excel, you can use the following functions:

Mean: The AVERAGE function calculates the mean of a range of values. In this case, enter "=AVERAGE(A1:A30)" in an Excel cell, assuming the data is in cells A1 to A30.

Standard Deviation: The STDEV.S function calculates the standard deviation of a range of values. Enter "=STDEV.S(A1:A30)" in an Excel cell to calculate the standard deviation of the data set.

Using the mean ($4.61) and standard deviation ($1.62), we can now proceed to calculate the Confidence Interval.

The Confidence Interval can be determined using the formula: E = Z * (σ / √n)

In the formula, Z is the z-score corresponding to the desired level of confidence (e.g., 95% confidence corresponds to a z-score of approximately 1.96), σ is the population standard deviation (which can be estimated using the sample standard deviation in this case), and n is the sample size.

Let's assume we want a 95% confidence interval for the data set with a sample size of 30. We can use the formula "=CONFIDENCE.NORM(0.05, STDEV, 30)" in an Excel cell to calculate the E value.

Substituting the values into the formula, we get E = 1.96 * (1.62 / √30) ≈ 0.595.

Now, we can set up the confidence interval using the mean and E value:

Confidence Interval = (mean - E, mean + E)

Confidence Interval = ($4.61 - $0.595, $4.61 + $0.595)

Confidence Interval = ($4.015, $5.205)

Therefore, the 95% Confidence Interval for the given fuel prices data set is approximately $4.015 to $5.205.

In summary, the mean of the fuel prices data set is $4.61 with a standard deviation of $1.62. The 95% Confidence Interval for the data is approximately $4.015 to $5.205.

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Answer:

x = 2.37056012

Step-by-step explanation:

The marginal revenue in the interval between six and seven jet skis is $300.

Here we are given that total revenue from six jet skis is $2,400

and total revenue from seven jet skis is $2,700

Now, marginal revenue is defined as the revenue gained or lost by producing one more additional unit of a good.

Here, the total revenue increases from $2,400 to $2,700 as we go from producing 6 jet skis to 7 jet skis.

Thus, the change in total revenue will be-

2700 - 2400

= 300

This means that the gain in revenue is $300.

Thus, the marginal revenue in the interval between six and seven jet skis is $300.

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Answer:

9/16

Step-by-step explanation:

Answer:

The answer is 9/16

Step-by-step explanation:

Im doing the same work

Answer:

-1600

Step-by-step explanation:

−4^3(5^2)

5 × 5 = 25

-4 × -4 × -4

   -16 × -4

       -64

64 × 25 = -1600

The answer is -1600

Hope this helped.

Answer: 960 crayons

Step-by-step explanation:

From the question, we are informed that Mr Andrew bought 15 boxes of crayons at the store to share with his students and that each box contains 64 crayons.

The equation that represents ​c​, the total number of crayons that Mr. Andrew bought will be:

C = 15 × 64

= 960 crayons

The solution for s in the equation is s = √[(R - 3)/t]

The equation is given as:

R = ts^2 + 3

Subtract 3 from both sides

ts^2  =R - 3

Divide both sides by t

s^2 = (R - 3)/t

Evaluate the square root of both sides

s = √[(R - 3)/t]

Hence, the solution for s in the equation is s = √[(R - 3)/t]

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The linear system corresponding to [a1​a2​a3​b] has a solution when b can be written as a linear combination of a1​, a2​, and a3​. This is equivalent to saying that b is in Span{a1​, a2​, a3​}.

The given statement "The linear system corresponding to [a1​a2​a3​b] has a solution when b can be written as a linear combination of a1​, a2​, and a3​. This is equivalent to saying that b is in Span{a1​, a2​, a3​}." is true.

Let's prove why the above statement is true-If there are 'n' number of equations and 'n' unknowns, then the system of linear equations is said to be consistent if there exists at least one solution for the system of equations; otherwise, it is inconsistent.

To solve the system of equations, we express the coefficients of the variables in a matrix. If the determinant of the coefficient matrix is not equal to zero, the system of equations is consistent and has a unique solution if we apply the Gaussian elimination method or Cramer's rule or matrix inversion method.

If the determinant is equal to zero, the system of equations is consistent and has infinite solutions . Suppose we have a system of equations that are equivalent to the matrix equation: AX=B. Here, A is an m×n matrix, X is an n×1 column matrix, and B is an m×1 column matrix.

This system of equations is consistent if and only if B is a linear combination of the columns of A. Mathematically, it can be represented as B=a1A1+a2A2+...+anAn, where A1, A2,..., An are the columns of matrix A, and a1, a2, ..., an are constants. In other words, B is in the span of A1, A2, ..., An.

Therefore, The linear system corresponding to [a1​a2​a3​b] has a solution when b can be written as a linear combination of a1​, a2​, and a3​. This is equivalent to saying that b is in Span{a1​, a2​, a3​}. So, option (A) is the correct choice.

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