a nursery owner buys 9 panes of glass to fix some damage to his greenhouse the 9 panes cost 19.35 unfortunately he breaks 4 more panes while repairing the garage. what is the cost of another 4 panes?

The constant of proportionality from the proportional relationship is 3/2

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.

To determine the constant of proportionality, we need to use the proportional relationship given.

y = kx

k = constant of proportionality

3/8 = k(1/4)

Solve for k

k = [(3/8) / (1/4)]

k = 3/2

k = 1.5

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_(_)+_(+)_so

2-3-3

=1-3

=2

If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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The coordinates of K is (-1, 2).

The section formula for the point (x, y) that the point divides the line with end points (x₁, y₁) and (x₂, y₂) internally in the ratio m : n is,

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

Here given that the internal ratio of division is 1 : 6.

The endpoints of the line segment given are J(-13, 20) and L(1, -1).

Let the coordinates of K be (x, y).

Using the section formula,

x = [(1 × -13) + (6 × 1)] / (1 + 6) = -7/7 = -1

y = [(1 × 20) + (6 × -1)] / (1 + 6) = 14/7 = 2

Hence the coordinates of the dividing point K is (-1, 2).

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Answer:

y=3x+3

Step-by-step explanation:

First find put the intersect point at the end then find slope.

easy

The correct answer is option D which is the function is even because of its symmetry about the y-axis.

The function which remains unchanged when the negative value of the variable is filled in the function is called an even function and this function is symmetric about the y-axis.

Given function:-

f(x) = 3x⁴+2x²

Now put the value x = -x in the function

f(-x) = 3( -x⁴)+2(-x²)

f(-x) = 3x⁴ + 2x²

f(-x) = f(x)

here we can see that when we put the value of negative x the function remains unchanged.

Therefore the correct answer is option D which is the function is even because of its symmetry about the y-axis.

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Answer:

A 5,2

Step-by-step explanation:

Answer:

400 Liters increased by 20 percent is 480 Liters.

The statement "you will be expected to know the antiderivatives of the six trigonometric functions for the final" is false because it is subjective and dependent on the specific requirements and expectations of your course or exam.

While it is true that knowledge of the antiderivatives of the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) can be beneficial in calculus and integration.

Whether or not you will be specifically expected to know them for your final exam depends on your course syllabus and the instructions provided by your instructor.

It is important to consult your course materials, syllabus, or instructor to determine the specific content that will be covered on your final exam.

This will ensure that you allocate your study time and focus on the relevant topics that will be assessed.

Therefore, the correct option is (b) false, as the expectation of knowing specific antiderivatives of trigonometric functions for the final exam is not universally applicable and may vary depending on the course and instructor.

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Answer:

$128

Step-by-step explanation:

Answer:

x  =  2

Step-by-step explanation:

Answer:

x = .61

Step-by-step explanation:

Don't really know how to explain other than use a graphing calculator. Desmos is quite helpful.

Hope that this helps!

Answer:

x = 1.13504161 … , − 1.46837494 …

Step-by-step explanation:

hope this helps(::

i: 1

ii: 6

iii: 3

iv: 2

v: 4.5

vi: 2.5

Answer:

the answer is A

Step-by-step explanation:

Answer:

8a - 7

Step-by-step explanation:

First, subtract 12a from 20a

20a - 12a

= 8a

Now, subtract -3 from -10.

Subtracting a negative number is the same as adding a positive number, so add 3 to -10.

-10 + 3

= -7

Put together 8a and -7

8a - 7

So, the simplified expression is 8a - 7

Answer:

replace rhombus with square, or rectangle

Step-by-step explanation:

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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The statement that is true among the given options is that both false position and secant methods are in the open method category.

The methods mentioned in the options are numerical methods used for finding roots of equations. Let's evaluate each statement to determine which one is true:

1. Method of false position always converges to the root faster than the bisection method: This statement is not true. The convergence rate of the method of false position and the bisection method depends on the specific equation being solved. In some cases, the false position method may converge faster, while in others, the bisection method may converge faster. The convergence rate can vary depending on the behavior of the function and the initial interval.

2. Method of false position always converges to the root: This statement is not true. The method of false position may not always converge to the root. There can be cases where the method fails to converge, such as when the function is highly nonlinear or has multiple roots within the initial interval.

3. Both false position and secant methods are in the open method category: This statement is true. The false position method and the secant method are both categorized as open methods because they do not require a bracketed interval to start the iteration. They can be applied with a single initial guess and iteratively approach the root.

4. Secant and Newton's methods both require the actual derivative in the iterative process: This statement is not true. While Newton's method requires the derivative of the function, the secant method approximates the derivative using two function evaluations without explicitly requiring the actual derivative.

Based on the explanations provided, the statement that is true is that both false position and secant methods are in the open method category.

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We are told to the write the given expression in standard form ;

\({:\implies \quad \sf \dfrac{6.6\times 10^{-2}}{3.3\times 10^{-4}}}\)

Rewrite as ;

\({:\implies \quad \sf \dfrac{66\times 10\times 10^{-2}}{33\times 10\times 10^{-4}}}\)

\({:\implies \quad \sf \dfrac{2\times 10^{-2}}{10^{-4}}}\)

\({:\implies \quad \sf 2\times \dfrac{10^{-2}}{10^{-4}}}\)

\({:\implies \quad \sf 2\times 10^{-2-(4)}\quad \qquad \bigg\{\because \dfrac{a^m}{a^n}=a^{m-n}\bigg\}}\)

\({:\implies \quad \sf 2\times 10^{-2+4}}\)

\({:\implies \quad \boxed{\bf{2\times 10^{2}}}}\)

This is the required answer

Answer:

there will be 20 dollars

Step-by-step explanation:

500 multiplied by .12 and then timesed by 8 then subtracted by 500

2% of 800 is 16 so you need to do 800-16 and that = 784

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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Answer:

option B : Upen

Step-by-step explanation:

To find who saves the greatest. Find who spent the least.

That is find the smallest of these fractions.

To find the smallest among the fraction:

Step 1 : make the denominators the same.

Step 2 : to make denominators same find LCM of 8, 4, 3, 6

Step 3: LCM = 24

\(\frac{7}{8}\ , \frac{3}{4} \ , \frac{2}{3} \ , \frac{5}{6}\)

\(\frac{7 \times 3}{8 \times 3}, \ \frac{3 \times 6}{4 \times 6} , \ \frac{2 \times 8 }{ 3 \times 8} ,\ \frac{5 \times 4}{6 \times 4}\\\\\frac{21}{24}, \ \frac{18}{24}, \ \frac{16}{24}, \ \frac{20}{24}\\\\Arranging\ the \ fractions \ in \ ascending \ order \ to \ find \ the \ least \ spent .\\\\\\frac{16}{24} , \ \frac{18}{24} , \ \frac{20}{24}, \frac{21}{24}\)

So 2/3 is the smallest fraction,  which means 2/3 spent the least amount from the salary.

Therefore, Upen saves the greatest amount every month.

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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"An inaccurate assumption often made in statistics is that variable relationships are linear". The statement is true.

In statistics, it is indeed an inaccurate assumption to assume that variable relationships are always linear. While linear relationships are commonly encountered in statistical analysis, many real-world phenomena exhibit nonlinear relationships. Nonlinear relationships can take various forms, such as quadratic, exponential, logarithmic, or sinusoidal patterns.

By assuming that variable relationships are linear when they are not, we risk making incorrect interpretations or predictions. It is essential to assess the data and explore different types of relationships using techniques like scatter plots, correlation analysis, or regression modeling. These methods allow us to identify and account for nonlinear relationships, providing more accurate insights into the data.

Therefore, recognizing the possibility of nonlinear relationships and employing appropriate statistical techniques is crucial for obtaining valid results and making informed decisions based on the data.

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The slope of the ramp is 1/3 and the ramp should rest approximately 8.57 feet from the van to maintain a slope of 1.4 inches per foot or less.

a) To determine the slope of the ramp, we can use the formula:

Slope = Vertical rise / Horizontal run

In this case, the vertical rise is the height of the van door, which is given as 16 inches. The horizontal run is the distance from the bottom of the ramp to the van, which is 4 feet or 48 inches.

Slope = 16 inches / 48 inches = 1/3

Therefore, the slope of the ramp is 1/3.

b) If the ramp cannot have a slope of more than 1.4 inches per foot, we can set up a proportion to find the appropriate distance from the van for the ramp to rest.

Let x be the distance from the van that the ramp should rest (in feet).

According to the given condition, the maximum slope allowed is 1.4 inches per foot. This can be written as:

1.4 inches / 12 inches = x feet / x

Simplifying the proportion:

1.4 / 12 = x / x

1.4x = 12

x = 12 / 1.4

x ≈ 8.57 feet

Therefore, the ramp should rest approximately 8.57 feet from the van to maintain a slope of 1.4 inches per foot or less.

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Answer:

they are called periods