In June, Mr. Chen's students read 40 books. In July they read 30 books.

What is the percent increase or decrease of the books they read?

Answer:

Step-by-step explanation:

y = 6X

so this is a direct variation , b/c as X goes up, so does Y

The equation that models the data is y = 6x

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To determine whether the data in the table represents a direct or inverse variation, we need to check whether the ratio of x to y is constant.

When we divide each y-value by its corresponding x-value, we get the ratios:

6/1 = 6

12/2 = 6

30/5 = 6

60/10 = 6

We see that the ratio of y to x is constant, which means that the data represents a direct variation.

To write an equation to model the data in the table, we can use the formula for direct variation, which is:

y = kx

where k is the constant of variation.

To find k, we can use any of the given data pairs.

For example, we can use the first pair (x = 1, y = 6):

6 = k(1)

Solving for k, we get:

k = 6/1 = 6

Thus,

The equation that models the data is y = 6x

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To determine the minimum thickness of the iron, we need to calculate the diffusion flux of hydrogen through the iron and equate it to the maximum allowed hydrogen loss.

The diffusion flux (J) of hydrogen through a material can be calculated using Fick's first law of diffusion:

J = -D * (∆C/∆x)

Where:

J is the diffusion flux

D is the diffusion coefficient of hydrogen in iron

∆C is the difference in hydrogen concentration across the thickness (∆C = C1 - C2)

∆x is the thickness of the iron

We are given:

Maximum allowed hydrogen loss = 50 g/cm²/year

Temperature (T) = 400 °C (673 K)

Hydrogen concentration at surface 1 (C1) = 0.05 H atom per unit cell

Hydrogen concentration at surface 2 (C2) = 0.001 H atom per unit cell

First, we need to convert the hydrogen concentrations into a common unit. The atomic mass of hydrogen (H) is approximately 1 g/mol. The number of atoms in a unit cell for BCC iron is 2.

Concentration in g/cm³:

C1 = (0.05 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.025 g/cm³

C2 = (0.001 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.0005 g/cm³

Now, we can calculate the difference in hydrogen concentration across the thickness:

∆C = C1 - C2 = 0.025 g/cm³ - 0.0005 g/cm³ = 0.0245 g/cm³

Next, we need to determine the diffusion coefficient of hydrogen in iron at 400 °C. The diffusion coefficient can be estimated using the following equation:

D = D0 * exp(-Q/RT)

Where:

D0 is the pre-exponential factor

Q is the activation energy for diffusion

R is the gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

For hydrogen diffusion in iron, typical values are:

D0 = 5 x 10^-7 cm²/s

Q = 40,000 J/mol

Plugging in the values:

D = (5 x 10^-7 cm²/s) * exp(-40000 J/mol / (8.314 J/(mol·K) * 673 K))

D ≈ 2.70 x 10^-12 cm²/s

Now, we can substitute the values into Fick's first law of diffusion and solve for the thickness (∆x):

J = -D * (∆C/∆x)

Rearranging the equation:

∆x = -D * (∆C/J)

Substituting the given values:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year))

Converting the year unit to seconds:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year)) * (1 year / 3.1536 x 10^7 s)

Calculating:

∆x ≈ -0.000347 cm ≈ 3.47 μm

The negative sign indicates that the thickness (∆x) is measured in the opposite direction of the hydrogen diffusion. Thus, the minimum thickness of the iron required to limit the hydrogen loss to no more than 50 g per year through each square cent.

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Answer:

-25 is the correct answer

Step-by-step explanation:

hope this helps:)

The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y \(+\) 6| \(=\) 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

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Absolute minimum value is -4/81 and the Absolute maximum value is 72 at x = 9.

To find the absolute maximum and absolute minimum values of the function f(x) = x(x² - x)/9 on the interval [0, 9], we need to follow these steps:

1. Find the critical points by taking the derivative of f(x) and setting it to zero.

2. Evaluate the function at the critical points and endpoints of the interval.

3. Compare the values obtained to determine the absolute maximum and minimum.

1. f'(x) = (3x² - 2x)/9

Set f'(x) to 0: (3x² - 2x)/9 = 0

Solve for x: 3x² - 2x = 0 -> x(3x - 2) = 0

Critical points: x = 0, x = 2/3

2. Evaluate f(x) at critical points and endpoints: - f(0) = 0(0² - 0)/9 = 0 - f(2/3) = (2/3)((2/3)² - (2/3))/9 = -4/81 - f(9) = 9(9²- 9)/9 = 72

3. Comparing the values:

- Absolute minimum value: -4/81 at x = 2/3

- Absolute maximum value: 72 at x = 9

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Answer:

0.0312

Step-by-step explanation:

You subtract 29.12 by 26 which equals 3.12

Then you divide by 100 which equals 0.0312

Answer:

12

Step-by-step explanation:

Answer:

x>−2

Step-by-step explanation:

−3x+12−12<18−12

−3x<6

Step 2: Divide both sides by -3.

−3x

−3

<

6

−3

Answer:

Here is your answer

((3 * 6) ^ 8) ^ 7 =

(18 ^ 8) ^ 7 =

11019960576 ^ 7 = 19736052228807988194997231645899399052500495522364054175325333567307776

Step-by-step explanation:

Diego's mistake was that he forgot to distribute the 1/3 across the parentheses, so he should have solved the equation like this:  1/3x + 5 = 3, which can be rearranged to x = 14.

Given equation is 1/3(x+15)=3. For solving this equation we have to simplify this equation as follows:

Multiplying both sides by 3 to eliminate the fraction; we get(x + 15) = 9. Distributing the number 1/3 to both terms inside the parenthesis we get (x/3) + 5

Combining like terms we get(x/3) = -2. Multiplying both sides by 3 we get x = -6.

the solution to the given equation is x = -6.So, Diego's mistake was that he didn't eliminate the fraction first.

An equation is a mathematical statement that asserts the equality of two expressions. Equations typically involve variables, which are symbols that represent numbers or other mathematical objects whose specific value or identity is unknown or unspecified.

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Answer: $659.40

Step-by-step explanation: You start with 471.00 X 0.4 which equals $188.40. So then you add $471.00 and $188.40 and you get $659.40!

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

80% = $471

100% = $588.75

The original cost of the sofa is $588.75

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Original cost in percentage = 100% ____(1)

Cost after 40% discount = $471

This can be written as,

80% = $471 _____(2)

From (1) and (2) we get,

80% = 471

Multiply 100/80 on both sides,

100/80 x 80% = 100/80 x 471

100% = $588.75

Thus,

80% = $471

100% = $588.75

The original cost of the sofa is $588.75

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The standard normal curve can be described as a bell-shaped curve or Gaussian distribution. It is used to model a variety of phenomena in many fields, including physics, finance, and engineering. Its mean is zero, and its standard deviation is one.

The standard normal curve is symmetrical about the mean and is characterized by the empirical rule. The majority of the population is distributed within one, two, and three standard deviations from the mean (68%, 95%, and 99.7%, respectively).

Part a)13th percentile can be calculated using the standard normal distribution tables. From the tables, the value of z when the area under the curve to the left of z is 0.13 is -1.04. Therefore, the 13th percentile is -1.04. 80th percentile can be calculated in the same way as 13th percentile.

The value of z when the area under the curve to the left of z is 0.8 is 0.84. Therefore, the 80th percentile is 0.84.Part b)The values of Q and Q3 cannot be obtained from the standard normal curve since the standard normal curve is not used to study a particular set of data.

It is used to model phenomena with a normal distribution with a mean of zero and a standard deviation of one. Instead, the quartiles can be calculated using the empirical rule in conjunction with the normal distribution tables.

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The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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Answer:

The mean will increase, and the median will stay the same.

Step-by-step explanation:

We know that the mean of scores is the average value of the scores of  the score obtained by 4 friends.

i.e. it is the ratio of sum of scores of 4 friends to the total number of person i.e. 4.

Hence, if the score of any of the person will increase then the mean will also increase

( Since, the denominator remains the same and the numerator is increasing so , the resultant value will increase )

Also, we know that the median of the score lie between the data set, i.e. the change in the score of the last score won't affect the median :

Since, here we have  4 data points and the median lie between the 2nd and 3rd data point so change in the 4th data point won't affect the median.

Hence, increasing Adam's high score affect the mean and median as:

Mean will increase and Median remains the same.

Answer:

The area of the new triangle will be 90cm

How to find the area of a triangle

Given that the area of a triangle is expressed as:

A = 0.5bh

36 = 0.5bh

bh = 18

If the base and height are scaled by a factor of 5, then the area will be:

5(bh) = 5(18)

5(bh) = 90cm²

Hence the area of the new triangle will be 90cm²

Step-by-step explanation:

Answer:

Remember, a positive and a negative while being added is always a negative outcome, so when you add -29.03 + 26.5, you get -2.53

(a) The probability that a 1 is received is 4/9.

(b) The (unconditional) probability that an error occurs is 1/6.

(c)  The probability that a 1 was sent, given that a 1 was received, is 7/8.

To solve this problem, we can use Bayes' theorem and conditional probability.

(a) The probability that a 1 is received can be found using the law of total probability. We can calculate it by considering the probabilities of two mutually exclusive events: receiving a 1 when a 1 is sent and receiving a 1 when a 0 is sent.

Let P(1) be the probability that a 1 is sent and P(0) be the probability that a 0 is sent. Both probabilities are equal to 1/2 since they are equally likely.

The probability of receiving a 1 when a 1 is sent is 1 minus the probability of an error when a 1 is sent, which is 1 - (2/9) = 7/9.

The probability of receiving a 1 when a 0 is sent is the probability of an error when a 0 is sent, which is 1/9.

Using the law of total probability:

P(1 received) = P(1 sent) x P(1 received | 1 sent) + P(0 sent) x P(1 received | 0 sent)

P(1 received) = (1/2) x (7/9) + (1/2) x (1/9)

P(1 received) = 7/18 + 1/18

P(1 received) = 8/18

P(1 received) = 4/9

Therefore, the probability that a 1 is received is 4/9.

(b) The (unconditional) probability that an error occurs can be calculated by considering the probabilities of two mutually exclusive events: an error occurs when a 1 is sent and an error occurs when a 0 is sent.

Using the law of total probability:

P(Error) = P(1 sent) x P(Error | 1 sent) + P(0 sent) x P(Error | 0 sent)

P(Error) = (1/2) x (2/9) + (1/2) x (1/9)

P(Error) = 2/18 + 1/18

P(Error) = 3/18

P(Error) = 1/6

Therefore, the (unconditional) probability that an error occurs is 1/6.

(c) The probability that a 1 was sent, given that a 1 was received, can be calculated using Bayes' theorem:

P(1 sent | 1 received) = (P(1 sent) x P(1 received | 1 sent)) / P(1 received)

P(1 sent | 1 received )= (1/2) x (7/9) / (4/9)

P(1 sent | 1 received) = (1/2) x (7/9) * (9/4)

P(1 sent | 1 received) = 7/8

Therefore, the probability that a 1 was sent, given that a 1 was received, is 7/8.

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The simplest form of the radical expression (√2+√5) over (√2-√5) is  

(- 7 - 2√10 )  /  3.

A radical expression is reduced to its simplest form when all its cubes, perfect squares, etc. are removed from inside the radical.

Now, solving

= (√2 + √5 ) /  (√2 - √5 )

multiplying and dividing it by (√2 + √5 )

= [(√2 + √5 ) /  (√2 - √5 )]  x [(√2 + √5 ) /  (√2 + √5 )]

= [ (√2 + √5 )^2 ] / [ (√2)^2 - (√5 )^2 ) ]

= ( 2 + 2√10  + 5 ) / ( 2 - 5 )

= ( 7 + 2√10 ) /  - 3

= (- 7 - 2√10 ) /   3

Therefore, the simplest form of the given radical expression is as follows:

     (√2+√5) over (√2-√5) =   (- 7 - 2√10)  /   3

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To solve for x in the equation 2.5x + 1.5(x + 10) = 4x, we first need to simplify both sides of the equation.  First, we can distribute the 1.5 to the expression in parentheses:  2.5x + 1.5x + 15 = 4x

Then we can combine like terms:  4x + 15 = 4x , At this point, we can see that the variable x has cancelled out on both sides of the equation, leaving us with 15 = 0. This is not a true statement, and so there is no solution for x in this equation. Therefore, the value of x cannot be determined from the given equation.                                                                                    To find the value of x in the equation 2.5x + 1.5(x + 10) = 4x, we first need to simplify the equation by distributing the 1.5 to both terms within the parentheses: 2.5x + 1.5x + 15 = 4x
Next, combine like terms: 4x + 15 = 4x
Now, subtract 4x from both sides of the equation: 15 = 0
Since this statement is false, there is no solution for the value of x in this equation.

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Answer:

The length of the piggy bank is 6 cubic inches long, and the height of the piggy bank is 8 cubic inches high. So next, you multiply 6 and 8 together, which is 48. Therefore, the volume of the piggy bank is 48 cubic inches^3.

Step-by-step explanation:

The minimum number of masthead lights for the given vessel is 2.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
A towing vessel 35 meters in length, with a tow 100 meters astern,

Masthead lights = total length of the tow / total length of the vessel
                        = 100 / 35 = 2.85

So, the Number of Masthead lights for the given vessel is 2 ≤ x ≤ 3.
And a minimum number of masthead lights is 2.

Thus, the minimum number of masthead lights for the given vessel is 2.

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Answer:

y = (1/12)x^2

Step-by-step explanation:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus.  Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

Have  a good day!

-Millie

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Answer:

It is ten times the value of the seven in 7.835

Step-by-step explanation:

7.825 x 1/10 = .7825

3.7 x 10 = 37

The seven shifted to the right in place value.

I hope this helps.

Answer:

10 times

Step-by-step explanation:

7 divided 0.7=10

Answer:30.57 cm squared

Step-by-step explanation:

Step-by-step explanation:

42

=21+21

=42

OR

10+32

=42

Answer: x= 25.36

Step-by-step explanation:

Solve for x:
  Given: Acute Angle=29°
             Hypotenuse=29
             Adjacent - x=?

Relation: cosine

cos29°=\frac{x}{29}

\frac{cos29°}{1}=\frac{x}{29}

29(cos29°)=x
25.36=x

Answer:

Simple interest is calculated by multiplying the principal (the initial amount of money deposited), the interest rate, and the number of years the money is on deposit.

To find out how much interest Diane will be paid in the first 2 years, we need to calculate the total interest earned over that time period.

First, we find the interest rate by multiplying the annual interest rate of 5% by .01 (to convert the percentage to decimal form)

0.05 * .01 = 0.05

Next, we find the total interest earned by multiplying the principal (400), the interest rate (0.05), and the number of years (2)

400 x 0.05 x 2 = 40

So, in the first 2 years, Diane will be paid $40 in interest on her deposit of $400.

Answer:

in total, Diane will be paid $20 + $40 = $60 in interest over the first 2 years.

Step-by-step explanation:

Simple interest is calculated as:

I = Prt

where:

I = Interest

P = Principal (initial amount deposited)

r = Interest rate (expressed as a decimal)

t = Time (in years)

So in this case, with a principal of $400 and an interest rate of 5% (or 0.05 as a decimal), the interest paid in the first year would be:

I = $400 * 0.05 * 1 = $20

And in the second year, it would be:

I = $400 * 0.05 * 2 = $40

So in total, Diane will be paid $20 + $40 = $60 in interest over the first 2 years.

Answer:

Step-by-step explanation: I think this is the answer

Tina planted 75 plants and only 48 grow

To know how much is lost we subtract 75 from 48 which gives us 27

75-48=27