Domain and Range

Find the Domain and Range for each graph​

The cost of wrapping both boxes is $0.92.

In three-dimensional space, a prism is a polyhedron where two ends are similar.

Given:

Two boxes need to be wrapped in paper (with no overlap).

Both boxes are in the shape of right rectangular prisms.

Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide.

The surface area of the rectangular prism A,

= 2(1.2 × 0.8 + 1 × 0.8 + 1 × 1.2)

= 5.92 square feet.

Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.

The surface area of the rectangular prism A,

= 2(1.6 × 0.5 + 0.5 × 0.8 + 0.8 × 1.6)

= 4.96 square feet.

The wrapping paper costs $6.79 per 80 square feet.

That means,

unit rate = 6.79 / 80 = $0.08 per square feet.

The cost of wrapping both boxes,

= 5.92 x 0.08 + 4.96 x 0.08

= $0.92

Therefore, the cost is $0.92.

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By using the Pythagoras theorem, AC + AD = BC is proved.

The relationship between the sides of a triangle can be proven using the properties of triangles.

Let us denote the length of AC as a and the length of AD as b. Since the triangle is right angled at A, the lengths of its sides must adhere to the Pythagorean theorem, that is a² + b² = (AB)². Additionally, since the bisector of ∠ C intersects the side AB at D, the length of AC must equal the length of AD, that is a = b.

Using the two equations above, we can substitute b for a in the equation a² + b² = (AB)² and solve for a. This results in a = AB/2. Substituting a for AB/2, we get

=> (AB/2)² + b² = (AB)².

Finally, multiplying by 2, we can get AB + 2b² = 2(AB)², which can be simplified to AB + 2b² = 2a².

Since a = b, this can be simplified to

=> AB + 2b² = 4b²,

resulting in AB = 2b².

Therefore, AC + AD = AB = 2b² = 2(AC) = BC, proving that the statement AC + AD = BC holds true for any right triangle right angled at A such that AB = AC and the bisector of ∠ C intersects the side AB at D

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Complete Question:

△ ABC is a right triangle right angled at A such that AB = AC and bisector of ∠ C intersects the side AB at D. Prove that AC + AD = BC.

Answer:

It is 5 seconds     option C

Step-by-step explanation:

When the ball would hit the ground, h would reduce 0.

We can equate the R.H.S to 0.

∴ 0= -16t²+64t+80

0 = t² - 4t - 5              (dividing both sides by -16)

0 = t²+t - 5t -5  (by splitting the middle term)

0 = t ( t+1) -5 (t+1)

0= (t-5) * (t + 1)

when t-5=0   ;   when t+1=0

t =5           ;          t= -1                    time cannot be -ve

∴ t= 5 seconds

Hope this helps you.

Answer:

C)  5 seconds

Step-by-step explanation:

Given equation:

\(h=-16t^2+64t+80\)

where:

The ball hits the ground when the height is zero.  

Therefore, substitute h = 0 into the given equation and solve for t.

\(\begin{aligned}\implies -16t^2+64t+80 & = 0\\-16(t^2-4t-5) & = 0\\t^2-4t-5 & = 0\\t^2-5t+t-5&=0\\t(t-5)+1(t-5)&=0\\(t+1)(t-5)&=0\\\end{aligned}\)

Apply the zero-product property:

\(\implies t+1=0 \implies t=-1\)

\(\implies t-5=0 \implies t=5\)

As time cannot be negative, t = 5 only.  

Therefore, it takes 5 seconds for the ball to hit the ground.

Answer: 216.75 in^2

Step-by-step explanation: area = 8.5 x (8.5x3)

8.5 x25.5

The correct vector, vector called countdown to have newsize elements and populate it with integers {newsize, newsize - 1, ..., 1},

Check if the current size of the vector (countdown.size()) is already equal to newsize. If it is, then no resizing is needed, and you can skip to step 4.

If the current size is greater than newsize, you need to remove elements from the end of the vector until its size matches newsize. You can use the resize() function to accomplish this:

countdown.resize(newsize);

If the current size is less than newsize, you need to add elements to the vector until its size reaches newsize. You can use a loop to populate the vector in reverse order, starting from newsize and decrementing by 1:

while (countdown.size() < newsize) {

 countdown.push_back(newsize);

 newsize--;

}

At this point, the vector countdown has been resized to have newsize elements and populated with integers {newsize, newsize - 1, ..., 1}.

Here's the complete code snippet:

#include <iostream>

#include <vector>

void resizeCountdown(std::vector<int>& countdown, int newsize) {

 if (countdown.size() == newsize) {

   // Vector already has the desired size

   return;

 }

 if (countdown.size() > newsize) {

   // Resize by removing elements

   countdown.resize(newsize);

 } else {

   // Resize by adding elements

   while (countdown.size() < newsize) {

     countdown.push_back(newsize);

     newsize--;

   }

 }

}

int main() {

 std::vector<int> countdown = {5, 4, 3, 2, 1};

 int newsize = 8;

 resizeCountdown(countdown, newsize);

 // Print the resized countdown vector

 for (int num : countdown) {

   std::cout << num << " ";

 }

 std::cout << std::endl;

 return 0;

}

In this example, the initial vector countdown has elements {5, 4, 3, 2, 1}, and we resize it to have newsize = 8 elements. The output will be: 8 7 6 5 4 3 2 1.

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Assumptions: For the purpose of this exercise, let's assume that we are analyzing defects in a manufacturing process. We will invent data for five different categories of defects and their corresponding frequencies. the cumulative percentage for each category, we find that the top 20% category of defects is Category A.

a. Based on the invented data, the histogram analysis reveals the following distribution of defects and their frequencies:

Category A: 50 defects

Category B: 30 defects

Category C: 20 defects

Category D: 15 defects

Category E: 10 defects

To identify the top 20% of the category of defects contributing to 80% of the total volume, we calculate the cumulative frequency. Starting with the category with the highest frequency, we add up the frequencies until we reach 80% of the total. In this case, Category A contributes the highest frequency, and its cumulative frequency is 50. The total number of defects is 125 (50 + 30 + 20 + 15 + 10). By calculating the cumulative percentage for each category, we find that the top 20% category of defects is Category A.

b. Performing a Root Cause Analysis for the Top Contributing Factor (Category A) using the 5-Why method or Fishbone diagram helps determine the underlying causes. We identify potential factors such as equipment malfunction, operator error, insufficient training, or process variability. By asking "why" repeatedly, we dig deeper into each cause to uncover the root cause.

c. Based on the analysis, we develop a corrective action plan and preventive action plan. For example:

Corrective Action Plan: Assign qualified technicians to regularly inspect and maintain the equipment, conduct additional training for operators to enhance their skills, and implement process control measures to reduce variability.

Preventive Action Plan: Establish a preventive maintenance schedule for equipment, implement a comprehensive training program for all operators, and conduct regular process audits to identify and address potential issues proactively.

The corrective and preventive action plans should clearly define the tasks, responsibilities, and timelines. The maintenance department may be responsible for equipment maintenance, the training department for operator training, and the quality department for process audits. Regular monitoring and evaluation of the action plans should be conducted to ensure effectiveness and make any necessary adjustments.

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The records that determines the lost of different crops grown on the farm during the whole year with an annual profitability of the farm is farm income statement.

Others are:

The kinds of farms sales records are:

Cash flow statement is known to be the records that shows flows of sales intake and out of any enterprise. In terms of farming one can say farm Diary record.

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a) the depth of the neutral axis is approximately 112.03 mm.

b) the strain at the tension bars is approximately 0.00123.

To calculate the depth of the neutral axis and the strain at the tension bars in a reinforced beam, we can use the principles of reinforced concrete design and stress-strain relationships. Here's how you can calculate them:

1)  Calculation of the depth of the neutral axis:

The depth of the neutral axis (x) can be determined using the formula:

x = (0.87 * fy * Ast) / (0.36 * fc' * b)

Where:

x is the depth of the neutral axis

fy is the yield strength of the reinforcement bars (415 MPa in this case)

Ast is the total area of tension reinforcement bars (3 bars with a diameter of 32 mm each)

fc' is the compressive strength of concrete (32 MPa in this case)

b is the width of the beam (200 mm)

First, let's calculate the total area of tension reinforcement bars (Ast):

Ast = (π * d^2 * N) / 4

Where:

d is the diameter of the reinforcement bars (32 mm in this case)

N is the number of reinforcement bars (3 bars in this case)

Ast = (π * 32^2 * 3) / 4

= 2409.56 mm^2

Now, substitute the values into the equation for x:

x = (0.87 * 415 MPa * 2409.56 mm^2) / (0.36 * 32 MPa * 200 mm)

x = 112.03 mm

Therefore, the depth of the neutral axis is approximately 112.03 mm.

2)  Calculation of the strain at the tension bars:

The strain at the tension bars can be calculated using the formula:

ε = (0.0035 * d) / (x - 0.42 * d)

Where:

ε is the strain at the tension bars

d is the diameter of the reinforcement bars (32 mm in this case)

x is the depth of the neutral axis

Substitute the values into the equation for ε:

ε = (0.0035 * 32 mm) / (112.03 mm - 0.42 * 32 mm)

ε = 0.00123

Therefore, the strain at the tension bars is approximately 0.00123.

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A continuous function is a function where small changes in the input result in small changes in the output, with no abrupt jumps or breaks in the function's graph.

Since f(x,y) is independent of x, we can write it as f(x,y) = g(y). We are given that the integral of g(x) from 0.3 to 10 is 1, so we can write:

∫0.3^10 g(x) dx = 1

Using this information, we can find g(y) by integrating g(x) with respect to x:

g(y) = ∫0.3^10 g(x) dx / ∫0^10 dx
g(y) = 1 / 9.7

Now, we can find f(x,y) by substituting g(y) into f(x,y) = g(y):

f(x,y) = g(y) = 1 / 9.7

We need to find the integral of f(x,y) over the rectangle R, which is:

∫0^3 ∫0^10 f(x,y) dy dx
∫0^3 ∫0^10 1 / 9.7 dy dx
(1 / 9.7) ∫0^3 ∫0^10 dy dx
(1 / 9.7) * 3 * 10
= 3.0928

Therefore, the value of the integral of f(x,y) over the rectangle R is 3.0928.

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Answer:

-0.5x\(x^{2}\)+3x=0

Step-by-step explanation:

Answer:

y = 3

Step-by-step explanation:

We move all terms to the left:

26y-4-(68+2y)=0

We add all the numbers together, and all the variables

26y-(2y+68)-4=0

We get rid of parentheses

26y-2y-68-4=0

We add all the numbers together, and all the variables

24y-72=0

We move all terms containing y to the left, all other terms to the right

24y=72

y=72/24

y=3

Answer:

I believe it's 1 because of the variable 1/1 = 1

The conditional density function of x given y is fx|y(x|y) = y^6x^1e^(-x(y^5)).

To find the conditional density functions of x given y and y given x, we need to use the definition of conditional probability and Bayes' theorem.

(a) To find fx|y(x|y):

fx|y(x|y) = f(x,y) / fy(y)

where fy(y) is the marginal density function of y. To find fy(y), we integrate the joint density function over all possible values of x:

fy(y) = ∫f(x,y)dx from x=0 to infinity

fy(y) = ∫(5xe^(-x(y^5)))dx from x=0 to infinity

fy(y) = 5/y^6

Now, we can find fx|y(x|y) as follows:

fx|y(x|y) = f(x,y) / fy(y)

fx|y(x|y) = (5xe^(-x(y^5))) / (5/y^6)

fx|y(x|y) = y^6x^1e^(-x(y^5))

So, the conditional density function of x given y is fx|y(x|y) = y^6x^1e^(-x(y^5)).

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Answer:

5i + 2

Step-by-step explanation:

(5-2i)(i)

5i - 2i^2

i^2= -1

5i -2(-1)

= 5i + 2

Answer:

736 trout in the lake in total

Answer:

Step-by-step explanation:

d = 4 cm   ⇒  r = 2 cm

so:

\(V=\frac13\pi r^2\cdot H=\frac13\pi\cdot 2^2\cdot8\approx\frac13\cdot3.1415926...\cdot32=33.51032...\approx33.5\ cm^3\)

Answer:

the ordered pair (0, 1/6)

Step-by-step explanation:

To reflect a function across the y-axis, we replace every occurrence of x with -x. Therefore, the function g(x) is given by:

g(x) = f(-x) = 1/6(2/5)^(-x)

To find an ordered pair on g(x), we need to choose a value of x and evaluate g(x). For example, if we choose x = 0, then:

g(0) = 1/6(2/5)^(-0) = 1/6

Therefore, the ordered pair (0, 1/6) is on the graph of g(x).

The equation of the line that meets the following conditions are as follows;

5. y + 2 = 3(x - 4).

6. y - 7 = -3/2(x + 5)

7. y + 8 = -20/7(x - 4).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (4, -2) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 3(x - 4)

Part 6.

At data point (-5, 7) and a slope of -3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = -3/2(x + 5)

Part 7.

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (12 + 8)/(-3 - 4)

Slope (m) = -20/7

At data point (4, -8) and a slope of -20/7, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 8 = -20/7(x - 4).

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Answer:

1.71

Step-by-step explanation:

x/4 = 3/7

4 * 3 = 12

12/7 = 1.714285714285714

Rounded to the nearest hundreths, the answer is  1.71

Answer:

The equation is \(199+49+79m=880\)

Kyle has had cable for 8 months.

Step-by-step explanation:

Let m denotes number of months cable services have been used.

Initial charge for the cable box = $199

Setup fee = $49

Monthly charges for cable services = $79

Also,

Total bill over a certain number of months, m = $880

Therefore,

\(199+49+79m=880\)

Now solve the equation.

\(199+49+79m=880\\248+79m=880\\79m=632\\m=\frac{632}{79}\\ m=8\)

That is Kyle has had cable for 8 months.

Answer:

The converse is true

Step-by-step explanation:

The converse of a statement is obtained by interchanging the conclusion for the hypothesis

The given statement is presented as follows;

If a pair of angles is linear, then the angles are supplementary

Therefore, the converse statement is;

If a pair of angles are supplementary, then the angles are a linear pair

A linear pair of angles angles are the adjacent angles formed by the intersection of two lines

Supplementary angles are two angles that sum up to 180° such that the angles sum is that of the angles forming a straight line

Therefore, the converse statement, 'If a pair of angles are supplementary, then the angles are a linear pair', is true

hope this helped buddy

Peace

Answer:

nope

Step-by-step explanation:

nope

Answer:

the exterior angle of the vertex: 60 degrees

the interior base angles: 30 degrees

the exterior angles of the bases: 150 degrees

Step-by-step explanation:

every straight angle is equal to 180 degrees and all the angles of the inside of a triangle is 180 degrees

There are 8 small boxes and 3 larges boxes.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the number of small box be x and large be y.

Each small box can hold 20 books and each large box can hold 40 books.

So, the system of equation

x+ y = 13.............(1)

20x + 40y = 360................(2)

Solving equation (1) and (2) we get

20x + 40(13 - x) = 360

20x + 520 - 40x = 360

-20x = -160

x= 8

and, y= 13-8 = 3

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Answer:

1: 7.5x10¹²

2: 1.6x10⁻⁵

3: 2x10¹²

4: 6x10⁻²

Step-by-step explanation: