A shopkeeper sold a book for $ 180.He made a profit of 20%.calculate the cost price of the book.

Please help!Am new to this chapter.

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's solve ~

Perimeter of square is :

\(\qquad \sf  \dashrightarrow \:4 \times side \: length\)

so, we can take side length as a, and solve for a ~

\(\qquad \sf  \dashrightarrow \:4a = 60\)

\(\qquad \sf  \dashrightarrow \:a = 60 \div 4\)

\(\qquad \sf  \dashrightarrow \:a = 15\)

Now, since we know the side length. let's find Area of square :

\(\qquad \sf  \dashrightarrow \: {15}^{2} \)

\(\qquad \sf  \dashrightarrow \:area = 225 \: m {}^{2} \)

The degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.31) to be less than 0.001 is 4.

To determine the degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.31) to be less than 0.001, we can use Taylor's theorem and the concept of Taylor series.

Taylor's theorem states that if a function f(x) has derivatives of all orders at x = a, then the function can be approximated by a polynomial (Taylor polynomial) centered at a.

In this case, we want to estimate f(0.31) using a Maclaurin polynomial. Since the Maclaurin series is a special case of the Taylor series centered at a = 0, we can use the Taylor polynomial centered at a = 0 to approximate f(0.31).

The error in the estimate of f(0.31) using a Taylor polynomial is given by the remainder term, which is related to the next term in the Taylor series. To ensure that the error is less than 0.001, we need to find the degree of the Maclaurin polynomial such that the absolute value of the next term is less than 0.001.

The given function f(x) = 2ln(x + 1) can be represented by its Maclaurin series expansion as:

f(x) = 2(x - x^2/2 + x^3/3 - x^4/4 + ...)

To find the degree of the Maclaurin polynomial necessary, we need to determine the term with the highest power of x that satisfies |x^(n+1)/(n+1)!| < 0.001.

By evaluating the terms, we find that the term with the highest power of x is x^4/4, which is the fifth term in the series (n = 4). Thus, to ensure the error is less than 0.001, we need a Maclaurin polynomial of degree 4 or higher.

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Answer:1.84

Step-by-step explanation: We can add this in a very easy way.

Step 1- We can put the 1 in the ones place as if there is no number before a decimal (which is the case for the first number) we can assume it is 0.

Step 2- We can then place the decimal point after the 1 and then put 0.8 since there are no more numbers that are at the tenths

Step 3- At the end we add the .04 (also known as 0.04) as there are no more places in both the numbers that are in the hundredths (and in 1.8, it can also be known as 1.80 as there are none!)

Hope this helps!

I would appreciate if you can mark me brainliest :)

Answer:

the answer is 3 or less dhevvshsbdvdd

Answer:

Answer is 18 degree as per the question

Answer: A. 18°

Step-by-step explanation:

Your formula is 108°+54°+X=180°
To find X, add 108° & 54°. The sum is 162°.
Next you need to subtract your sum from 180°.
180°-162°=18°
X=18°

The correct answer is d  is used to test the effect of the IV on the variability of the DV.

The correct answer is d. The "stand alone F test" is used to test the effect of the independent variable (IV) on the variability of the dependent variable (DV). It is an inferential test commonly used in analysis of variance (ANOVA) to determine if there is a significant difference among the means of three or more groups.

Option a is incorrect because the "stand alone F test" is an inferential test that involves making a conclusion about a population based on sample data.

Option b is incorrect because the "stand alone F test" is used to test the assumption of equal variances, not homogeneity of variance.

Option c is incorrect because the "stand alone F test" can be directional or non-directional, depending on the research question and hypothesis being tested.

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Real Life Problem:

A baseball field is shaped like a rhombus, with side lengths of 70 meters and one diagonal length of 120 meters. The outfield fence must be a continuous structure that connects all four corners of the rhombus. What is the minimum length of fence needed to enclose the entire field?

Solution:

To find the length of the fence needed to enclose the entire field, we need to find the length of the other diagonal of the rhombus. We can use the formula for the area of a rhombus to find this length:

Area of rhombus = (d1 * d2)/2

where d1 and d2 are the lengths of the diagonals.

We know that one diagonal (d1) has a length of 120 meters and the side lengths are all equal to 70 meters. To find the other diagonal (d2), we can use the Pythagorean theorem:

d2 = sqrt((2 * area)/sin(theta))

where area is the area of the rhombus and theta is the angle between the two diagonals.

Since the diagonals of a rhombus bisect each other at right angles, the angle between them is 90 degrees. Therefore, we can simplify the formula to:

d2 = sqrt(2 * area)

We can substitute the values we know into this formula:

Area of rhombus = (120 * 70)/2 = 4200 square meters

d2 = sqrt(2 * 4200) = 91.5 meters

Now that we know the length of both diagonals, we can use the formula for the perimeter of a rhombus to find the length of the fence:

Perimeter of rhombus = 4 * side length

= 4 * 70 = 280 meters

Therefore, the minimum length of fence needed to enclose the entire field is 280 meters.

Answer: The minimum length of fence needed to enclose the entire field is 280 meters.

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Answer:

90 degrees

Step-by-step explanation:

90 degrees hhgffdfkgdf

Answer:

90 degrees clockwise rotation

Step-by-step explanation:

Because

Answer:

boy:girls

5:4

64/4= 16

5 X 16 =80

there are 80 boys

Answer:

Step-by-step explanation:

318 / 40 = 7.95

each store got 7 boxes of milk

40 x 7 = 280

318 - 280 = 38

38 boxes got stored

so

true

false

false

true

When the current mortgage rates are high and expected to drop in the near future, the loans that will be gotten is one that has C. variable rate.

It should be noted that a mortgage simply means a loan that's made by a bank to purchase a house.

In this case, the current mortgage rates are high and expected to drop in the near future, the loans that will be gotten is one that has a variable rate. This is because once the mortgage rate decreases, one will pay a lesser amount.

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The linearization of the function f(x) = cos x at point a = 5/2 is L(x) = cos(5/2) - sin(5/2)(x - 5/2).The word count of the answer is 41.

Given function:f(x)

= cos x Linearization is given by:L(x)

= f(a) + f'(a)(x - a)where f(a) is the value of the function at point a and f'(a) is the derivative of the function at point a.In the given problem, the value of point a is 5/2.Thus, the first derivative of the given function is:f'(x)

= -sin x Applying the value of x in the above function, we get:f'(5/2)

= -sin(5/2)L(x)

= f(a) + f'(a)(x - a)L(x)

= cos(5/2) - sin(5/2)(x - 5/2).The linearization of the function f(x)

= cos x at point a

= 5/2 is L(x)

= cos(5/2) - sin(5/2)(x - 5/2).The word count of the answer is 41.

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When the particle attains zero acceleration, its velocity will be equal to the coefficient of the linear term in the position function, which is 'a'.

To understand this, let's consider the given position function: x(t) = at + bt^2 - ct^3.

The velocity of the particle is the derivative of the position function with respect to time:

v(t) = d(x(t))/dt.

Taking the derivative of x(t), we have:

v(t) = a + 2bt - 3ct^2.

To find the velocity when the particle attains zero acceleration, we set the acceleration equal to zero:

a(t) = d(v(t))/dt = 2b - 6ct.

Setting 2b - 6ct = 0 and solving for t, we get:

t = (2b)/(6c) = b/(3c).

Substituting this value of t back into the velocity function, we find:

v(t) = a + 2b(b/(3c)) - 3c(b/(3c))^2

    = a + 2b^2/(3c) - b^2/c

    = a + (2b^2 - 3b^2)/(3c)

    = a - b^2/(3c).

Therefore, when the particle attains zero acceleration, its velocity will be equal to 'a', which is the coefficient of the linear term in the position function.

In other words, the velocity of the particle when it has zero acceleration does not depend on the constants 'b' and 'c' in the position function. It is solely determined by the constant 'a'.

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Complete question:

The position of a particle as a function of time t, is given by x(t)=at+bt

2

−ct

3

 where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be?

Alright! Let's go step by step. We want to understand how the house size relates to the number of residents. In other words, as the number of residents changes, how does the size of the house change? This relationship can be represented by a linear regression equation. The general form of a linear regression equation is:

y = m*x + b

Here:

- y is the dependent variable (in our case, the house size).

- x is the independent variable (in our case, the number of residents).

- m is the slope of the line (how much y changes for a unit change in x).

- b is the y-intercept (the value of y when x is 0).

We'll use the data you provided to calculate 'm' and 'b'. There are different ways to calculate these values, but I'll use a method that is relatively simple to understand:

m = (N * Σ(xy) - Σx * Σy) / (N * Σ(x^2) - (Σx)^2)

b = (Σy - m * Σx) / N

Where:

- N is the number of data points (in our case, 15).

- Σ stands for summation (sum of all values).

Now, let's calculate 'm' and 'b' using the data you provided:

Number of Residents(x) | House size (Sq. ft)(y) | xy | x^2

------------------------|------------------------|----|-----

3                      | 1992                   |5976|9

3                      | 1754                   |5262|9

3                      | 1766                   |5298|9

5                      | 2060                   |10300|25

6                      | 2293                   |13758|36

6                      | 2139                   |12834|36

3                      | 1836                   |5508|9

4                      | 1924                   |7696|16

6                      | 2321                   |13926|36

4                      | 2060                   |8240|16

3                      | 1769                   |5307|9

4                      | 1955                   |7820|16

5                      | 2309                   |11545|25

4                      | 1857                   |7428|16

4                      | 1972                   |7888|16

Σx = 66

Σy = 30999

Σxy = 120978

Σ(x^2) = 282

Plug these values into our formulas:

m = (15 * 120978 - 66 * 30999) / (15 * 282 - 66^2)

  ≈ 305.91

b = (30999 - 305.91 * 66) / 15

  ≈ 905.27

So our linear regression equation is:

House size = 305.91 * (Number of Residents) + 905.27

Now, let's predict the house size for a family of 5 residents:

House size = 305.91 * 5 + 905.27

           ≈ 2444.82 Sq. ft

This means that, according to our linear regression model, a family of 5 residents would need a house size of approximately 2445 square feet.

We are given the 95% confidence interval for the population mean of the change in AHE between 1992 and 2008 as [4.393, 9227].

This means that if we were to take multiple random samples and compute the confidence intervals for the change in AHE using the same method, approximately 95% of those intervals would contain the true population mean.

CI = X ± z* (s/√n)

where X is the sample mean, s is the sample standard deviation, n is the sample size, and z* is the critical value of the standard normal distribution for the desired confidence level.

However, we can conclude that the confidence interval has a lower bound of 4.393 and an upper bound of 9227, which means that we are 95% confident that the population mean of the change in AHE between 1992 and 2008 falls between these two values.

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A quadratic equation graph is a graph depicting the values of all the roots of the quadratic equation.

The value of b and c is zero.

A quadratic equation is said to be any polynomial equation of degree 2 or an equation that is in the form;

\(\rm ax^ 2 + bx + c = 0\)

A quadratic equation graph is a graph depicting the values of all the roots of the quadratic equation.

Let us have a quadratic equation which is;

\(\rm x^2+5x+6\)

On comparing with the standard equation of quadratic formula;

a = 1, b = 5, and c = 6

The equation is;

\(\rm y=x^2\\\\\)

In this case the value of a = 1, b = 0, and c =0.

Hence, the value of b and c is zero.

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The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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Based on the given information, it is difficult to determine if the errors would be heteroskedastic in this case.

To test for heteroskedasticity in this regression, we can use the White test or the Breusch-Pagan test. These tests involve regressing the squared residuals on the independent variables and checking for significant coefficients. If the coefficients are significant, it indicates the presence of heteroskedasticity.

Heteroskedasticity in this case can lead to inefficient and biased parameter estimates. The standard errors will be incorrect, affecting the hypothesis tests and confidence intervals. One potential consequence is that the estimated coefficients may appear more significant than they actually are. To address heteroskedasticity, we can use robust standard errors or apply heteroskedasticity-consistent covariance matrix estimators, such as the White estimator, to obtain reliable inference.

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The area of a rectangle with base of 3x+1 in and a height of 2x-3 in is given as follows:

D. A = 6x² - 7x - 3 in².

The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:

A = lw.

The dimensions for this problem are given as follows:

Hence the expression for the area of the rectangle is given as follows:

A = (3x + 1)(2x - 3)

A = 6x² - 9x + 2x - 3

A = 6x² - 7x - 3 in².

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Answer:

the bottom right

Step-by-step explanation:

6/8= 75%

The reference angle for a rotation of 334° is 26°.

A reference angle is the smallest acute angle between the terminal side of an angle and the x-axis. To find the reference angle of a given angle, you need to subtract the nearest multiple of 360° from the given angle until the resulting angle is between 0° and 360°.

In this case, 334° is greater than 360°, so you can subtract 360° from it once to get 334° - 360° = -26°. Since the reference angle is always positive, you can take the absolute value of -26° to get 26°. Therefore, the reference angle for a rotation of 334° is 26°.

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Answer:

(0,0) and (3,2)

(1,5) and (4,7)

(-2, -2) and (4, 2)

Step-by-step explanation:

The first option will have a slope of 3-0 over 2-0, which is 1.5, which is incorrect.

The second option will have a slope of 2-0 over 3-0, which is 2/3, and is correct.

The third option will have a slope of 7-5 over 4-1 which is 2/3, and is also correct.

The fourth option has a slope of 2+2 over 4+2, which is 2/3, and is correct.

The fifth option has a slope of -30-30 over -20-20, which is also 1.5, and is incorrect.

Therefore, the middle three options are correct.

Pairs of points have lines passing through them with a slope of 2/3 are (0,0) and (3,2), (1,5) and (4,7) , and (-2,-2) and (4,2)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find pairs of points have lines passing through them with a slope of 2/3

(0,0) and (2,3)

m=3/2 which is not equal to 2/3

Hence it is not passing through these points.

(0,0) and (3,2)

m=2/3 which is equal to 2/3

it is  passing through (0,0) and (3,2)

(1,5) and (4,7)

m=7-5/4-1=2/3 which is equal to 2/3

it is  passing through (1,5) and (4,7)

(-2,-2) and (4,2)

m=2+2/4+2=4/6=2/3 which is equal to 2/3

it is  passing through (-2,-2) and (4,2)

(20,30) and (-20, -30)

m=-30-30/-20-20=-60/-40=3/2

Hence pairs of points have lines passing through them with a slope of 2/3 are (0,0) and (3,2), (1,5) and (4,7) , and (-2,-2) and (4,2)

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Answer:

i believe the awnser is 0.5

Answer:

I think it is 0.5

Step-by-step explanation:

0.5

i cant understand your question define briefly

Answer:

1/12

Step-by-step explanation:

The probability of rolling a two is

P(2) = number of twos/ total

        =1/6

The probability of landing on tails

P(tails) = tails/total

             =1/2

P(2, tails) = P(2)  *  P(tails)  since they are independent events

               = 1/6 * 1/2

                 =1/12

In the equation 12x+33=93, the value of x is 5.

The given equation is 12x+33=93.

Twelve times of x plus thirty three equal to ninety three.

x is the variable in the equation.

We need to solve for x:

Subtract 33 from both sides of the equation:

12x=93-33

12x=60

Divide both sides of the equation by 12:

x=60/12

x=5

Hence, the value of x in the equation is 5.

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