the ratio of fiction and non-fiction books in a library is 5 : 2. total books are 1421, how many more fiction books than non fiction books are in library, please explain in simple terms complicated answers are hard to understand ​

Answer:t= 1/4

Step-by-step explanation:

Divide both sides by -2/3, and simplify which would leave u with 1/4.

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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Answer: Length = 7 and Width = 2

Step-by-step explanation:

Perimeter = 2(length + width)  
18 = 2(L+W)
[tex]\frac{18}{2}[/tex] = (L+W)  
9 = L+W  
Make width the subject.
w = 9-L ------Equation 1

  Area = Length × Width
⇒14 = L×(9-L)   | Substitute Eq.1 in place of Width
⇒14 = 9L - L²
⇒L² - 9L + 14 = 0
⇒L² -7L - 2L + 14 = 0
⇒L×(L-7) -2×(L-7) = 0
⇒(L-7)(L-2) = 0
∴ L=7(Answer) or L=2(Not Applicable since length can't be larger than width)

Substitute the value into eq.1
when L=7
W=9-7      
  =2      

Lenth=7
Width=2

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Answer:

Step-by-step explanation:

Let the length of the plank be "l" and the width be "w".

The perimeter of the plank is the sum of the lengths of all four sides, which is:

2(l + w) = 18

Simplifying the equation, we get:

l + w = 9

The area of the plank is given by:

lw = 14

We can solve for one of the variables in terms of the other by rearranging the equation:

l = 14/w

Substituting this expression for "l" into the equation for the perimeter, we get:

(14/w) + w = 9

Multiplying both sides by "w", we get:

14 + w^2 = 9w

Rearranging the terms, we get:

w^2 - 9w + 14 = 0

This is a quadratic equation that can be factored as:

(w - 7)(w - 2) = 0

Therefore, the possible values of "w" are 7 and 2.

If we take "w = 7", then using the equation l = 14/w, we get:

l = 14/7 = 2

Therefore, the length and width of the plank are 2 feet and 7 feet, respectively.

If we take "w = 2", then using the equation l = 14/w, we get:

l = 14/2 = 7

Therefore, the length and width of the plank are 7 feet and 2 feet, respectively.

In summary, the plank could have a length of 2 feet and a width of 7 feet, or a length of 7 feet and a width of 2 feet, given its perimeter of 18 feet and area of 14 square feet.

Using translation the graph of y = (x - 2)² - 5 is the graph of y = x² shifted 2 units to the right and 5 units down.

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To translate the graph of y = x² to y = (x - 2)² - 5, apply the following transformations -

Shift the graph to the right by 2 units.

This means that we replace x with x - 2, which moves the graph 2 units to the right.

Shift the graph down by 5 units.

This means that we subtract 5 from the entire function, which moves the graph 5 units down.

So the transformed function is -

y = (x - 2)² - 5

To see how this transformation changes the graph, compare the original function y = x² to the transformed function y = (x - 2)² - 5.

The vertex of the parabola has moved from the origin (0,0) to the point (2,-5).

Therefore, the graph is shifted using translation.

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The coordinates of the point on the directed line segment is (- 6, 4).

A line segment is a subset of a line that has two endpoints.

We know, When a line segment is divides another line segment in the ratio of m : n at (x, y), The coordinate of the intersecting points is,

x = (nx₁ + mx₂)/(m + n) and y = (ny₁ + my₂)/2.

Therefore, The coordinates of the point directed on the line segment is,

x = (1×2 + 2×- 10)/(1 + 2).

x = (2 - 20)/3.

x = - 18/3.

x = - 6.

And,

y = (- 8×1 + 10×2)/(1 + 2).

y = 12/3.

y = 4.

So, The coordinates are (- 6, 4).

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Answer:

Step-by-step explanation:

x inter for line a = 1

x inter for line B = -4

Line A is greater then Line B

Part A: You can decompose Figure ABCDE into two triangles and two rectangles. The two triangles are triangle ABC and triangle AED. The two rectangles are rectangle BCD and rectangle AEB.

Part B: The length of Side AB is 4 units and the length of Side AE is 5 units.

Part C: To find the area of Figure ABCDE, we can simply add the areas of the two triangles and two rectangles. The area of triangle ABC is 3 units2, the area of triangle AED is 6 units2, the area of rectangle BCD is 10 units2, and the area of rectangle AEB is 3 units2. Thus, the area of Figure ABCDE is 3 + 6 + 10 + 3 = 22 units2.

Answer:

2x + h - 5

Step-by-step explanation:

To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.

[tex]f(x) = x^{2} -5x+9\\f(x+h) = (x+h)^{2}-5(x+h)+9[/tex]

Now we can plug them into the fraction:

[tex]\frac{((x+h)^{2}-5(x+h)+9)-(x^{2} -5x+9)}{h}[/tex]

Expanding all of the terms, we get:

[tex]\frac{(x^{2} +2hx + h^{2} -5x-5h+9)-(x^{2} -5x+9)}{h}[/tex]

Distributing the negative we get:

[tex]\frac{x^{2} +2hx + h^{2} -5x-5h+9-x^{2} +5x-9}{h}[/tex]

Now we see that [tex]x^{2} -x^{2} ,-5x+5x,[/tex] and [tex]9-9[/tex] all cancel, leaving us with:

[tex]\frac{2hx + h^{2}-5h}{h}[/tex] (Notice the only terms left are those with h in them)

As every term contains an h, we can remove an h from every term, giving us:

2x + h - 5

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Answer:

Area = 380 square inch

Volume = 697 cubic inch

Step-by-step explanation:

Diameter = 11

=> radius = 11/2 = 5.5

A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch

V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch

Therefore, the value of the expression -2f(-6) - 7g(-7) is equal to -99.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

Using the function notations given in the problem, the statement can be read as follows:

-2 times the value of the function f evaluated at x = -6, minus 7 times the value of the function g evaluated at x = -7, is equal to:

-2f(-6) - 7g(-7) =

Substituting the expressions for f(x) and g(x) given in the problem, we get:

-2*(3*(-6)+1) - 7*(-2*(-7)+5) =

Simplifying this expression, we get:

-2*(-17) - 7*(19) = 34 - 133 = -99

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Answer:

Step-by-step explanation:

18.) 19 - 3x = 14 + 2x

To solve for x, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side:

19 - 3x = 14 + 2x

19 - 14 = 2x + 3x

5 = 5x

x = 1

To check our solution, we can substitute x = 1 back into the original equation and see if it holds true:

19 - 3(1) = 14 + 2(1)

19 - 3 = 14 + 2

16 = 16

Since both sides of the equation are equal when x = 1, we have verified that x = 1 is the correct solution.

19.) 2(7 + 5y) - 3y = -35

We can start by simplifying the left-hand side of the equation by using the distributive property:

2(7 + 5y) - 3y = 14 + 10y - 3y = 14 + 7y

Now, we can solve for y by moving the constant term to the other side:

14 + 7y = -35

7y = -49

y = -7

To check our solution, we can substitute y = -7 back into the original equation and see if it holds true:

2(7 + 5(-7)) - 3(-7) = -35

2(7 - 35) + 21 = -35

-56 + 21 = -35

-35 = -35

Since both sides of the equation are equal when y = -7, we have verified that y = -7 is the correct solution

20.) 14 + 4(x - 5) = 6 - 2x

We can start by simplifying the left-hand side of the equation by using the distributive property:

14 + 4(x - 5) = 14 + 4x - 20 = 4x - 6

Now, we can solve for x by moving the constant term to the other side:

4x - 6 = 6 - 2x

6x = 12

x = 2

To check our solution, we can substitute x = 2 back into the original equation and see if it holds true:

14 + 4(2 - 5) = 6 - 2(2)

14 - 12 = 6 - 4

2 = 2

Since both sides of the equation are equal when x = 2, we have verified that x = 2 is the correct solution.

Answer:

B

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To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:

6x²2 - 4xy = 2x(3x - 2y)

What is factorization?

Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.

For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):

x²2 - 4x - 21 = (x - 7)(x + 3)

This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.

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Applying the law of sines, the value of c is calculated as: c ≈ 11.8.

The Law of Sines, also known as the Sine Rule, is a theorem in trigonometry that relates the side lengths of a triangle to the sine of its angles.

Specifically, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be expressed as:

a / sin A = b / sin B = c / sin C

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Applying the law of sines, we have:

c/sin 105 = 7/sin 35

Cross multiply:

c * sin 35 = 7 * sin 105

c = 7*sin 105/sin 35

c ≈ 11.8

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The linear equation for coordinate points (-2,8) and (5,-6) is option B: y = -2x + 4.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Since there are two points on the graph, use the slope-intercept form of a linear equation to find the equation that matches the graph.

The slope-intercept form is -

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, we use the two given points -

m = (y2 - y1) / (x2 - x1)

m = (-6 - 8) / (5 - (-2))

m = -14 / 7 = -2

To find the y-intercept, we can use one of the points and the slope -

y = mx + b

8 = (-2) × (-2) + b

8 = 4 + b

b = 4

So the equation that matches the graph is -

y = -2x + 4

Therefore, the equation is -2x + 4.

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The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.

Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.

To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:

Assets                                    2017        2018        Change   % Change

Cash                                     $2,500 $3,900  $1,400  56%

Accounts receivable, net    $35,000 $40,000  $5,000     14%

Inventory                               $85,000 $122,000  $37,000   44%

Other current assets            $3,400      $4,110       $710        21%

Total current assets              $125,900  $170,010   $44,110    35%

PPE, net                                 $180,000  $230,000  $50,000  28%

Other assets                         $15,000    $26,000   $11,000    73%

Total assets                          $320,900   $426,010  $105,110 33%

Interpretation

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Answer:

The equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.

Step-by-step explanation:

Inverse variation is a type of relationship between two variables, in which the product of the variables is constant. The equation that represents inverse variation is:

y = k/x

where y and x are the variables, and k is the constant of proportionality.

To find the equation that represents inverse variation for the given values of x=6 and y=1/2, we can first substitute these values into the equation:

1/2 = k/6

To solve for k, we can multiply both sides by 6:

k = 6 * (1/2)

k = 3

Now that we know the value of k, we can substitute it back into the equation to get the final equation for the inverse variation:

y = 3/x

Therefore, the equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.

The solution is, x = 39. Since we have a 102 degree angle it is a obtuse triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

given that,

its angles , x, 102, x

now, we know,

The sum of the angles in a triangle add to 180

i.e.

x+ 102+x = 180

Combine like terms

so, we get,

102 + 2x = 180

Subtract 102 from each side

2x = 78

divide by 2, both sides,

x =39

Since we have a 102 degree angle it is a obtuse triangle.

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Answer: -1/2

Step-by-step explanation: The formula is y=mx+b where m is your slope and b is your y-intercept. Therefore, your b or y-intercept is -1/2

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

In the equation [tex]y=mx+b[/tex], m is the slope and b is the y intercept. In this equation, we are given the slope is 4 and the y intercept as [tex]-\frac{1}{2}[/tex] because the equation can be simplified to [tex]y=4x+-\frac{1}{2}[/tex]

Therefore, the parameters of the binomial distribution in this scenario are:

p = 0.404

n = 21

Probability, or the probability that an event will occur, is calculated by dividing the number of favourable outcomes by the total number of potential possibilities. Indeed, a coin flip is the most simple illustration. When you flip a coin, only one of two outcomes—heads or tails—is possible.

A binomial distribution with p and n parameters is present in this situation.

The likelihood of making a free throw, p (a success).

The quantity n represents the attempted free throws.

p = 0.404, which is the probability of making a free throw.

1 - p = 0.596, which is the probability of missing a free throw.

n = 21, which is the total number of free throws attempted.

the probability that the player makes no more than 6 of the 21 free throws. This can be represented as P(X ≤ 6), where X is the number of successful free throws (or made free throws).

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Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.

What is the least common multiple (LCM)?

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them

To solve this problem, we need to find the least common multiple (LCM) of the numbers 2, 3, and 5. The LCM is the smallest number that is a multiple of all three numbers.

Prime factorizing the numbers, we have:

2 = 2

3 = 3

5 = 5

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers, and multiply them together. Therefore, the LCM of 2, 3, and 5 is:

LCM = [tex]2^1 * 3^1 * 5^1 = 30[/tex]

Hence, Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.

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the expected value of the random variable with this probability distribution is 7.

Why it is?

To find the expected value of a discrete random variable with a probability distribution, you multiply each possible value of the random variable by its corresponding probability and then add up all of the products.

For example, for the probability distribution given:

X P(X)

2 1/36

3 1/18

4 1/12

5 1/9

6 5/36

7 1/9

8 1/12

9 1/18

10 1/36

The expected value, denoted by E(X), can be calculated as follows:

E(X) = (2)(1/36) + (3)(1/18) + (4)(1/12) + (5)(1/9) + (6)(5/36) + (7)(1/9) + (8)(1/12) + (9)(1/18) + (10)(1/36)

E(X) = 7

Therefore, the expected value of the random variable with this probability distribution is 7.

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Answer: |x + 4| = 3

Step-by-step explanation:

This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

This is a binomial distribution problem, where the probability of success (a household tuned to Pretty Betty) is p = 0.26 and the number of trials is n = 14.

The probability that none of the households are tuned to Pretty Betty is:

P(none) = (1 - p)ⁿ = (1 - 0.26)¹⁴≈ 0.031

The probability that at least one household is tuned to Pretty Betty is:

P(at least one) = 1 - P(none) = 1 - 0.031 ≈ 0.969

The probability that at most one household is tuned to Pretty Betty is:

P(at most one) = [tex]P(0) + P(1) = (1 - p)^n + np(1 - p)^{(n-1)[/tex] ≈ 0.500

However, if more than one household is tuned to Pretty Betty, it may indicate that the share value is inaccurate.

Therefore, This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

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The mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The number of patients experiencing side effects in a sample of 100 patients as a binomial distribution with n = 100 and p = 0.20.

The mean of a binomial distribution is given by:

μ = np

Substituting n = 100 and p = 0.20, we get:

μ = 100 × 0.20 = 20

Therefore, the mean is 20.

The variance of a binomial distribution is given by:

σ²= np(1 - p)

Substituting n = 100 and p = 0.20, we get:

σ² = 100 × 0.20 × (1 - 0.20) = 16

Therefore, the variance of the number of patients experiencing side effects in a sample of 100 patients is 16.

The standard deviation of a binomial distribution is the square root of its variance:

σ =√Variance

=√16

= 4

Hence, the mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.

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The area of the isosceles trapezoid is 281.25 square cm.

Let's denote the length of the base of the trapezoid as "b".

According to the problem statement, the length of each of the equal sides is one-half the length of the base, which means each equal side has length b/2.

The height of the trapezoid is given as one-fourth the length of the base, so we can write it as h = b/4.

To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

The two parallel sides of length b each contribute b to the perimeter, while the other two sides of length b/2 contribute a total of b to the perimeter.

Therefore, we can write:

Perimeter = 2b + 2(b/2) = 3b

We know that the perimeter of the trapezoid is 45 cm, so we can set up an equation:

3b = 45

Solving for b, we get:

b = 15

Now we can use the formula for the area of a trapezoid to find the area of this isosceles trapezoid. The formula is:

Area = (1/2)h(b1 + b2)

where h is the height, b1 and b2 are the lengths of the two parallel sides. In this case, b1 and b2 are both equal to b (since it's an isosceles trapezoid), and h = b/4.

Substituting these values, we get:

Area = (1/2)(b/4)(b + b) = (1/2)(b/4)(2b) = b^2/8

Substituting b = 15, we get:

Area = 15^2/8 = 281.25 sq cm

Therefore, the area of the isosceles trapezoid is 281.25 square cm.

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In an isosceles trapezoid, the length of the equal sides is one-half the length of the base, while the height is one-fourth the length of the base. If the perimeter of the trapezoid is 45 cm.

Find the areae

The loan's future value A, or the total amount due at time t is equal to $3,720.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 3,000 × 6/100 × 5

S.I = 3,000 × 0.06 × 4

S.I = $720.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = $720 + $3,000

Future value, A = $3,720.

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The standard equation of a hyperbola centered at the origin and a vertical transverse axis values of a=8 and b=9 is  y²/64 - x²/81 = 1.

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The standard equation of a hyperbola centered at the origin and a vertical transverse axis is given by

y²/a² - x²/b² = 1

We are given that;

a = 8

b = 9

Now, putting the values of the variables into the equation;

y²/a² - x²/b² = 1

y²/8² - x²/9² = 1

y²/64 - x²/81 = 1

Therefore, the standard equation will be  y²/64 - x²/81 = 1.

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