Peter is painting his bedroom. His bedroom has four walls. Yesterday, he painted 1 2/5 walls. What fraction of the walls is left to paint?

Answer:

5

Step-by-step explanation:

Given that 3 is a root of the equation x²-px+6=0

To find the value of p, substitute 3 into the equation for x

Hence x²-px+6=0

becomes

3^2 - 3p + 6 = 0

9 -3p + 6 = 0

collect like terms

-3p = -9 - 6

-3p = -15

Divide both sides by -3

p = -15/-3

p = 5

The area of region R2 is (sqrt(13)-1)/8 square units. To find the area of region R1, we need to integrate the difference between the two curves with respect to x. The curves intersect when 2x2 = 3 - x, which simplifies to 2x2 + x - 3 = 0. Solving for x, we get x = \((sqrt(13)-1)/4\)or x = (-sqrt(13)-1)/4. Since we only care about the positive value, the intersection point is x =\((sqrt(13)-1)/4.\)

So, the area of region R1 is given by:

∫[0,(sqrt(13)-1)/4] (3-x - \(2x^2\)) dx

Using the power rule and evaluating at the limits of integration, we get:

(3(sqrt(13)-1)/4) - (2(sqrt(13)-\(1)^3\)/48) = (3sqrt(13)-11)/12

Therefore, the area of region R1 is (3sqrt(13)-11)/12 square units.

B) To find the area of region R2, we can see that it is a triangle with height equal to the y-coordinate of the intersection point between y=\(2x^2\) and y=3-x (which we found in part A) and base equal to the x-coordinate of the intersection point. So, the area of region R2 is:

(1/2) [(sqrt(13)-1)/4] [2(sqrt(13)-1)/4] = (sqrt(13)-1)/8

Therefore, the area of region R2 is (sqrt(13)-1)/8 square units.

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Jon and Jim together painted 2/3 of the fence.

To find the total amount of the fence that Jon and Jim painted, we need to add the fractions representing the portions they each painted.

Jon painted one quarter of the fence, which can be written as 1/4.

Jim painted five twelfths of the fence, which can be written as 5/12.

To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 4 and 12. In this case, the LCM is 12.

Now, let's rewrite the fractions with a common denominator of 12:

Jon's portion: (1/4) × (3/3) = 3/12

Jim's portion: (5/12)

Adding these fractions together:

Total portion = Jon's portion + Jim's portion = 3/12 + 5/12 = 8/12

The fraction 8/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:

Total portion = (8/4) / (12/4) = 2/3

Therefore, Jon and Jim together painted 2/3 of the fence.

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Answer:

268 cm

Step-by-step explanation:

A P E X

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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There are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x

where a is a constant and a>1

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two equations:

y = –2x – 1 and

\(\rm y = 3^{-x-1}\)

From the graph, we can see:

There are two intersection points:

(-1, 1) and (-2, 3)

The x coordinates are -1 and -2

x = -1, y = 1

x = -2, y = 3

Thus, there are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

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The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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Answer:

Equation of line perpendicular to given graph is:

\(y = -\frac{1}{2}x+4\)

Step-by-step explanation:

Given equation of line is:

14x-7y=8

First of all, we have to convert the given equation into slope-intercept form to find the slope of the line

The slope-intercept form is:

\(y = mx+b\)

Now

\(14x-7y=8\\14x-8 = 7y\\\frac{7y}{7} = \frac{14x-8}{7}\\y = \frac{14}{7}x - \frac{8}{7}\\y = 2x - \frac{8}{7}\)

The co-efficient of x is 2 so the slope of given line is 2

Let m1 be the slope of line perpendicular to given line

The product of slopes of two perpendicular lines is -1

\(m.m_1 = -1\\2.m_1 = -1\\m_1 = -\frac{1}{2}\)

The equation for line perpendicular line to given line will be:

\(y = m_1x+b\\y = -\frac{1}{2}x+b\)

To find the value of b, putting (-2,5) in the equation

\(5 = -\frac{1}{2}(-2) + b\\5 = 1+b\\b = 5-1\\b = 4\)

The final equation is:

\(y = -\frac{1}{2}x+4\)

Hence,

Equation of line perpendicular to given graph is:

\(y = -\frac{1}{2}x+4\)

The x-intercept of the line 3x - 5y = 7 is at point ( 7/3, 0 ).

Given the function;

X-intercept occurs on the graph when y=0. Hence, to determine x-intercept, we substitute in 0 for y and solve for x.

3x - 5y = 7

3x - 5(0) = 7

3x - 0 = 7

3x = 7

x = 7/3

Hence, we have a point ( 7/3, 0 ).

The x-intercept of the line 3x - 5y = 7 is at point ( 7/3, 0 ).

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Answer:

Step-by-step explanation:

(

7/3,0)

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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Answer - 25.761-17.49=?

Then,

the answer is 8.271

Some additional context would be helpful in providing a complete answer. But the basic idea is this:

• Object ABC has a price X set on it.

• Hey, ABC is on sale! Let's say there's a 20% discount. That means 20% of the price X is subtracted from X.

• Boo, there's a 15% sales tax! This means whatever you would pay for ABC, discount included, you will ultimately have to pay an additional 15% of, or 0.15 times, that amount in tax.

Suppose you're looking to buy a T-shirt. The price tag on says it costs $25, but there's a 20% discount and a 15% sales tax.

• The discount has a value of 0.2 ($25) = $5. Subtract this from the original price, and its discounted price is $20.

• The sales tax is applied to this discounted price, and comes out to 0.15 ($20) = $3. This gets added to the discounted price, so you end up paying $23.

We find that there are 19 integers n for which x^2 x - n factors into the product of two linear factors with integer coefficients.

To find how many integers n between 1 and 100 make x^2 x - n factor into the product of two linear factors with integer coefficients, we can follow these steps:
Rewrite the expression as x(x^2 - n).
Since we want the expression to factor into two linear factors with integer coefficients, we need to find the pairs of integers (a, b) such that a * b = x^2 - n and a + b = x.
We know that x(x^2 - n) = (x - a)(x - b). So, x^2 - n = (x - a)(x - b) = x^2 - (a + b)x + ab.
Comparing the coefficients, we have ab = n and a + b = x.
Since n is between 1 and 100, we can check each n to see if it can be expressed as the product of two integers, a and b, with a + b = x.
After checking all values of n between 1 and 100, we find that there are 19 integers n for which x^2 x - n factors into the product of two linear factors with integer coefficients.

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Answer:

24 square meters of wallpaper

Step-by-step explanation:

Hope this helps.

The correct answer is a. The mean of the sampling distribution is always equal to the population mean.

This is known as the central limit theorem, which states that as the sample size increases, the sampling distribution will approach a normal distribution with a mean equal to the population mean. However, the standard deviation of the sampling distribution (option b) is not always equal to the population standard deviation and the shape of the sampling distribution (option c) is not always approximately normal, as it depends on the sample size and the underlying population distribution. Therefore, option d is incorrect. The correct is (a). The mean of the sampling distribution is always equal to the population mean. This is due to the fact that a sampling distribution is created by taking multiple random samples from the population, and as the number of samples increases, their mean tends to converge to the population mean. Options (b) and (c) are not always true, as the standard deviation and shape of the sampling distribution depend on the sample size and the underlying population distribution.

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Answer:

consecutive interior angles equal 180 not equal to each other

Step-by-step explanation:

Answer:

6x− 1 0 = 4 + 4 0

6x-10=4x+40

6x−10=4x+40

Solve

1

Add  

1 0

10

10

to both sides of the equation

6 − 1 0 = 4 + 4 0

6x-10=4x+40

6x−10=4x+40

6 − 1 0 + 1 0 = 4 + 4 0 + 1 0

6x-10+{\color{#c92786}{10}}=4x+40+{\color{#c92786}{10}}

6x−10+10=4x+40+10

2

Simplify

Add the numbers

Add the numbers

6 = 4 + 5 0

6x=4x+50

6x=4x+50

3

Subtract  

4 4x 4x

from both sides of the equation

6 = 4 + 5 0

6x=4x+50

6x=4x+50

6 − 4 = 4 + 5 0 − 4

6x{\color{#c92786}{-4x}}=4x+50{\color{#c92786}{-4x}}

6x−4x=4x+50−4x

4

Simplify

Combine like terms

Combine like terms

2x=50

5

Divide both sides of the equation by the same term

2x=50

2 /2 = 5 0 /2

\frac{2x}{{\color{#c92786}{2}}}=\frac{50}{{\color{#c92786}{2}}}

22x​=250​

6

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

= 2 5

Solution

= 2 5

Step-by-step explanation:

I'm sorry my stuff is coming off weird

Answer:

The approximate percent increase when the population of a town increases from 12,089 to 15,025 is 24.3%.

Step-by-step explanation:

First, we need to find the difference between the two numbers. That's 15,025 - 12,089 = 2,936.

Next, we need to find what percent that difference is of the original population. To do that, we divide the difference (2,936) by the original population (12,089) and multiply by 100.                                                           So:

2,936 / 12,089 = 0.2422

0.2422 * 100 = 24.22%

Rounding to one decimal place, we get 24.3%.

Answer:

x = 1/3

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

4x + 1 = 3 - 2x

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

Here we see that 7/3 does indeed equal 7/3.

∴ x = 1/3 is a solution of the equation.

Answer:

x=1/3

Step-by-step explanation:

4x+1=3-2x

Add 2x to both sides

6x+1=3

Subtract 1 on both sides

6x=2

x=2/6

what's the question ? is there something you don't understand

Answer:

-8

Step-by-step explanation:

Following Order of Operations rules, we evaluate anything within parentheses first:

8-[12-(-4)] = 8 - 16 = -8

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

In mathematics, the y-intercept is the point where the graph of a function intersects the y-axis. It is the value of the function when the input variable (x) is zero. Here, the y-intercept for this table of data is 2.436 cm.

Finding the y-intercept can provide important information about the function, such as its starting point or the value of the function when the input is zero.

To find the y-intercept from a table of data, you need to identify the point where the x-value is zero or where the input variable is not present. In this case, we do not have an x-value of zero in the table, so we cannot directly determine the y-intercept from the given data.

However, we can use the data to find an equation that represents the relationship between the x-values and y-values in the table. One common method to find this equation is to use linear regression, which involves finding the line of best fit that passes through the data points.

Using linear regression on the given data, we obtain the equation: y = 0.103x + 2.436 where x represents the force in Newtons, and y represents the length in centimeters. This equation represents a linear relationship between force and length, where the y-intercept is 2.436 cm.

Therefore, the y-intercept for this table of data is 2.436 cm. It represents the value of the length when the force is zero or when there is no applied force.

In summary, the y-intercept is the point where the graph of a function intersects the y-axis, which can provide important information about the function. To find the y-intercept from a table of data, you need to identify the point where the input variable is not present and use regression analysis to find the equation that represents the relationship between the x-values and y-values in the table.

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Answer:

6.  162

7. c

Step-by-step explanation:

Answer:

6. 162

7. C

Step-by-step explanation:

6. Replace the values of a and b into the expression:

8a + 6b = 8(12) + 6(11)

             = 96 + 66

             = 162

7. The distributive property states that whatever is outside a bracket must be multiplied to ALL terms in the brackets:

5(2f+4) = (5 × 2f) + (5 × 4)

            = 10f + 20

Answer: NOT D have a good day!

Step-by-step explanation:

Answer:

C. 9%

Step-by-step explanation:

That's it

The volume of the solid the region defined by the given curves must be rotated about the x-axis is V = \(\frac{384\pi }{5}\).

Given that,

The region defined by the given curves must be rotated about the x-axis to determine the solid's volume, which is y =6 -x², y =2.

We know that,

Take the equation of the curves about the x- axis

y =6 -x², y =2.

Substitute y = 2 in equation y = 6 - x²

2 = 6 - x²

-x² = 2-6

x² = 4

Taking square root on both sides

x = ±2

Now, volume formula is define by using washer method

V =  \(\pi \int\limits^a_b {[f(x)]^2 - [g(x)]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {[6-x^2]^2 - [2]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {(36 + x^4 - 12x^2 - 4}) \, dx\)

V = \(\pi \int\limits^2_{-2} {(x^4 - 12x^2 - 32)} \, dx\)

V = \(\pi( [\frac{x^5}{5}] - 12\times\frac{x^3}{3} -32x)^2_{-2}\)

V = \(\pi[( [\frac{2^5}{5}] - 12\times\frac{2^3}{3} -32(2))-([\frac{-2^5}{5}] - 12\times\frac{-2^3}{3} -32(-2))]\)

V = \(\pi[( [\frac{32}{5}] - 4 \times 8 -64)-( [\frac{-32}{5}] - 4\times(-8) +64)]\)

V = \(\pi[( [\frac{32}{5}] - 32 -64)-( [\frac{-32}{5}] +32 +64)]\)

V = \(\pi( [\frac{384}{5}] )\)

V = \(\frac{384\pi }{5}\)

Therefore, The volume of the solid is V = \(\frac{384\pi }{5}\)

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The domain and range of the function is (-∞, ∞),  (-∞, 18]

A function is a rule that gives each element from the domain set to a single element from the range set. The range is the set of values that the function can take, whereas the domain is the set of values for which the function is defined.

Consider the function f(x) = x^2, for instance. As the function may be defined for any value of x, the domain of this function includes all real numbers. Nevertheless, as the function may only accept values larger than or equal to zero, the range is limited to non-negative real numbers.

a. The domain and range of the function f(x) = -2x² + 8x + 10 are;

domain = (-∞, ∞)

range = (-∞, 18]

b. The domain and range of the function is;

domain = [0, 12]

range = [0, 18]

c. The domain and range of the function are;

domain = (-∞, ∞)

range = [-7, ∞)

d. The domain and range of the function are;

domain = (-∞, ∞)

range = [1, ∞)

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As per the given dice, the probability of the total being equal to 8 is 1/9 or 11.11%.

Probability:

In statistics, probability refers the possibility of the particular event.

Given,

Here we need to find the probability of the total (when you sum up the dice) being equal to 8.

In order to calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8.

Hence both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6).

So, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.

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