Problem Statement: Create a function named tclip that determines the intersection of a line (solution of a given linear equation) with a clipping triangleT having vertices(0,0),(1,0)and(0,1).The function declaration should have the form function [count, list] =tclip(a,b,c)where the line in question is ordinarily the solution set of the linear equation ax+by=c.The value of the variable count returned should be −2 if the equation ax+by=c has no solutions(e.g.0x+0y=1). −1if the equation ax+by=c is solved by all values of x and y(0x+0y=0)0 if the solutions of ax+by=c do not intersectT(e.g.0x+1y=7)1 if the solutions of ax+by=cintersect T in one point (e.g.1x+1y=0)2 if the solutions of ax+by=c intersect T in more than one point(e.g.∣x−1y=0)The variable 1.st, which reports the distinct endpoints of the intersection, should be a2x0 empty array (empty list of 2-vectors) if count is−2,−1 or 0, 2×1 array (a single column vector)-the unique point of intersection-if count is 12×2 array (list of two column vectors)-the endpoints of the intersection- if count is 2.

Answers

Answer 1

The equation that determines the intersection of line with a clipping triangle is ax + by + c = 0 [1]. The solution has been obtained by using functions.

What is a function?

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input. A function is typically shown as y = f(x).

The equation ax + by + c = 0 [1] represents the line in question. A list of pairs of coordinates for each intersection point and the number of intersections (count) should be returned by the function (list).

A list of items can be sent to the function count list, which will return the total number of objects in the list. The function returns the number of objects in the specified list after accepting an array or list of objects.

Hence, the equation that determines the intersection of line with a clipping triangle is ax + by + c = 0 [1].

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Related Questions

if z is directly proportional to the product of x and y and if z is 15 when x is 5 and y is 6, then x, y, and z are related by the equation

Answers

Since z is directly proportional to the product of x and y, then x, y, and z are related by this equation: z = xy/2.

How to determine the equation?

Mathematically, a proportional relationship or direct variation can be represented by the following equation:

y = kx

Where:

k is the constant of proportionality. x, y, and z represents the variables of a proportional relationship.

Based on the information provided, we have the following:

z ∝ xy

z = kxy

In order to have a proportional relationship and equivalent ratios, the variables z, x, and y must have the same constant of proportionality:

Constant of proportionality (k) = z/xy

Constant of proportionality (k) = 15/(5 × 6)

Constant of proportionality (k) = 15/30

Constant of proportionality (k) = 1/2.

For the equation, we have:

z = kxy

z = 1/2 × xy

z = xy/2

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triangle abc is an equilateral triangle with side length 6. arcs are drawn centered at the vertices connecting midpoints of consecutive sides. find the area of the shaded region

Answers

The area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.

What is the area of triangle?

The area of a triangle can be found using the following formula:

Area = (base * height) / 2

The area of the shaded region can be found by subtracting the sum of the areas of three small equilateral triangles from the area of the original equilateral triangle.

Each of the small equilateral triangles has side length 3, since it is half the length of the original triangle's sides. The area of each small triangle is (3^2 * √3)/4 = (9 * √3)/4 square units.

The area of the original equilateral triangle is (6^2 * √3)/4 = (36 * √3)/4 square units.

Hence, the area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.

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I honestly don’t know what I’m doing please help

Answers

Answer:

6.5

Step-by-step explanation:

C = 2πr

40.841/2π = r

6.5 = r

Answer:

○ [tex]\displaystyle 6,5\:ft.[/tex]

Step-by-step explanation:

[tex]\displaystyle {\pi}d = C \\ 13,000094062…{\pi} = 40,841 \\ \\ \boxed{6,5000470308…} = \frac{13,000094062…}{2} \\ \\ \\ \boxed{\boxed{6,5 \approx r}}[/tex]

I am joyous to assist you at any time.

Graph the numbers that are the solution to both x + 1 < 9 and 4x ≤ 8.

Answers

The solution of the inequality are shown in figure.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequalities are,

⇒ x + 1 < 9

⇒ 4x ≤ 8

Now, We can simplify as;

⇒ x + 1 < 9

Subtract 1 both side;

⇒ x < 9 - 1

⇒ x < 8

⇒ 4x ≤ 8

Divide by 4;

⇒ x ≤ 4

Thus, The solution of the inequality are shown in figure.

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What is the volume of a block of wood with a height of 3 inches, a length of 5 inches and a width of 10 inches?
30 inches cubed
15 inches
150 inches
150 inches cubed

help pls

Answers

5 inches x 3 inches x 10 inches
= 150
Therefore your answer is 150 inches cubed

Answer:

150 in cubed

Step-by-step explanation:

which of the follwoing is not one of the three privacy rights created by the supreme courtt through its interpretation of vasious constitutional amendments

Answers

The Supreme Court's interpretation of numerous constitutional amendments did not result in the creation of the right to privacy or any of the other three privacy rights. The average freedom against arbitrary searches and seizures, the right to due process, and the right to free speech are the three privacy rights.

The Supreme Court's interpretation of numerous constitutional amendments did not result in the creation of the right to privacy or any of the other three privacy rights. The freedom against arbitrary searches and seizures, the right to due process, and the right to free speech are the three privacy rights. The Fourth, Fifth, and First Amendments of the Constitution, respectively, gave rise to these rights. The right to privacy has been developed and is safeguarded by the Supreme Court through its interpretation of the various amendments, despite the fact that it is not expressly stated in the Constitution. Individuals are protected by the right to privacy from having their private information or activities revealed without their permission.  Additionally, it gives people the freedom to decide how they want to live their life, including the right to marry, the right to access contraception, and the right to help getting an abortion. Despite not being one of the three privacy rights established by the Supreme Court, the right to privacy is still a crucial kind of protection for people. It guarantees that people have control over the information they share, the choices they make, and the respect for their privacy.

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The complete question is

which of the following is not one of the three privacy rights created by the supreme court through its interpretation of various constitutional amendments right to privacy or any of the other three privacy rights.

The doctor has ordered baby Nathaniel to receive Gentamicin IM 1.3 mg/kg q 8 hours. Nathaniel weighs 8.1 pounds. How much gentamicin would you give baby Nathaniel? **Rounding rule: This is a dosage not a portion of ml, so round to the 100th place.
______ mg

Answers

We would give 4.78 mg of Gentamicin to baby Nathaniel.

What is unit conversion?

Unit conversion means the conversion between different units and measurements of the same quantity done by the process of multiplication or division.

Given,

Dosage of Gentamicin per kg = 1.3 mg/kg

Weight of the baby = 8.1pounds

1 pound = 0.4536 kg

8.1 pounds = 3.674 kg

Weight of the baby in kilograms = 3.674 kg

Then dosage to the baby = 3.674 × 1.3

                                          = 4.7762 ≈ 4.78mg

Hence, 4.78 mg of Gentamicin, baby Nathaniel would receive.

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using the priority list t2, t7, t6, t4, t10, t8, t9, t3, t1, t5, schedule the project below with two processors.

Answers

The average T2, T7, T6, T4, and T10 in Processor 1

T8, T9, T3, T1, and T5 on Processor 2.

Work on tasks t2, t7, t6, t4, and t10 will be done by processor 1. The first task to be finished is task t2, followed by tasks t7, t6, t4, and lastly t10. Work on tasks t8, t9, t3, t1, and t5 will be done by processor 2. The first work to be finished is task t8, followed by t9, t3, t1, and ultimately t5. In order to finish the job quickly, both processors will cooperate, with Processor 1 concentrating on the early tasks and Processor 2 concentrating on the later duties. This guarantees that the project is finished on schedule and that all the tasks are carried out in the proper order.

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A sine function has the following key features:

Period = 4

Amplitude = 4

Midline: y = 1

y-intercept: (0, 1)

The function is not a reflection of its parent function over the x-axis.
What will the graph look like?

Answers

The Sine Function is y =  4 sin(π /2 x ) + 1

What is Sine function?

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.

Given:

Period = 4

Amplitude = 4

Midline: y = 1

y-intercept: (0, 1)

We know that

y = Asin (Bx + C) + D

A = the amplitude = 4

So, B =  2pi / period

         = 2π / 4

         = π /2

and, C = phase shift  

C = 0

Also, D = midline  =  1

So, the sine Function is

y =  4 sin(π /2 x ) + 1

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carlos willl play today and tommorow. He plans to play. 15 minutes longer tomorrow, How should he expect his score to change?

Pls help asap

Answers

He should expected tomorrows's score to be about 75 points greater than today's score.

How to model the linear function?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope, representing the rate of change.b is the y-intercept, representing the value of y when x = 0.

The input and output variables for this problem are given as follows:

Input: time in minutes.Output: score.

The slope is given as follows:

m = 5.

Meaning that when the input increases by one, the output increases by 5, hence the expected score's increase with an increase in the input of 15 is given as follows:

15 x 5 = 75.

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The equation
V
=
23900
(
0.91
)
t
V
=
23900
(
0.91
)
t
represents the value (in dollars) of a car
t
t
years after its purchase. Use this equation to complete the statements below.
The value of this car is at a rate of

The purchase price of the car was .

Answers

Answer: The equation represents the value (in dollars) of a car t years after its purchase, so the purchase price of the car would have been the value of the car when t = 0. Plugging in t = 0 into the equation, we get:

V = 23900 * (0.91)^0

V = 23900

So the purchase price of the car was $23,900.

Regarding the rate of decrease in the value of the car, we can observe that the value decreases at a rate proportional to (0.91)^t, so the rate of decrease is proportional to 0.91.

Step-by-step explanation:

please help answer this:

Answers

The monomial is 6² completes it and makes it (6p - 7q)².

What is a polynomial?

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

We know a monomial is a polynomial that consists of a single term.

Given, __ - 42pq + 49q².

= ___ - 42pq + 7²q².

Now, 6×7 = 42,

Therefore,  ___ - 42pq + 7²q²,

= 6²p² - 42pq + 7²q².

= (6p)² - 42pq + (7q)².

= (6p - 7q)².

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5. Six differently colored balls (red, blue, green, orange, purple, and white) are placed in a basket. Without looking, three balls are removed. What is the total number of combinations that include a red ball?
a. 3
b. 10
c. 20
d. 60
e. 80

Answers

I think it is a. 3 because there 6x5x4=120 total combinations. Then you have a choice of red for one place out of the three balls that are taken so the answer is three

Evaluate the expression 5+(-3x) for the given x-values. a) x=3 b) x=1/3 c( x= -3

Answers

Answer:

-4

4

14

Step-by-step explanation:

A:

5 + (-3)(3) = 5 -9 = -4

B:

5+ (-3)(1/3) = 5 - 1 - 4

C:

5 + (-3)(-3) = 5 + 9 = 14

Use the associative law of
the expression 22 x (12 x 9).
O 12 × 9 × 22
O (12 x 9) x 22
O
O
(22 × 12) × 9
multiplication to rewrite
(22 x 9) x 12

Answers

(22 x 12) x 9 or 22 x 12 x 9. In both cases, the product is obtained by multiplying 22 by 12, and then multiplying that result by 9, which gives us 3024.

How the associative law words?

The associative law of multiplication states that the way in which the numbers are grouped within an expression does not change the product. In other words, you can change the grouping of the factors and still obtain the same result. For example, the expression 22 x (12 x 9) can be rewritten as (22 x 12) x 9 or 22 x 12 x 9, and the product will be the same in all cases.

According to question:

In the expression 22 x (12 x 9),

the associative law can be used to rearrange the factors into

(22 x 12) x 9 or

22 x 12 x 9.

In both cases, the product is obtained by multiplying 22 by 12, and then multiplying that result by 9, which gives us 3024.

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Which binomial below is a factor of the polynomial 3a^2+6a-2a-4 A. (a – 2) B. (a + 4) C. (3a – 2) D. (3a + 2)

Answers

The solution is Option C.

The value of the quadratic equation is A = 3a² + 4a - 4 , where the factor of a is given by a = 2/3

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

A = 3a² + 6a - 2a - 4   be equation (1)

On simplifying the equation , we get

A = 3a² + 4a - 4

Now , when the factor of the equation is ( 3a - 2 ) = 0

Adding 2 on both sides of the equation , we get

3a = 2

Divide by 3 on both sides , we get

a = 2/3

Substitute the value of a in the equation , we get

A = 3 ( 2/3 )² + 4 ( 2/3 ) - 4

On simplifying the equation , we get

A = 3 ( 4/9 ) + 8/3 - 4

A = ( 4/3 + 8/3 ) - 4

A = ( 12/3 ) - 4

A = 4 - 4

A = 0

Hence , the binomial ( 3a - 2 ) is a factor of the equation

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Jenny uses half of a garden space to
plant roses. She uses 1/4 of that space
to plant pink roses. What fraction of
the entire space does Jenny use for
pink roses?

Answers

The fraction of the entire space jenny use for pink roses is 1/8 of the whole garden

What is word problem?

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.

These word problem are translated into mathematical equations.

Represent the total garden by x

Jenny uses 1/2 of the garden to plant roses

= 1/2×x = x/2

She uses 1/4 of the space to plant pink roses

= 1/4 × ×/2

= x/8

Therefore she uses 1/8 of the whole garden to plant pink roses.

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Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 78.7 Mbps. The complete list of 50 data speeds has a mean of x=16.44 Mbps and a standard deviation of s=39.37Mbps.

a. What is the difference between​ carrier's highest data speed and the mean of all 50 data​ speeds?

b. How many standard deviations is that​ [the difference found in part​ (a)]?

c. Convert the​ carrier's highest data speed to a z score.

d. If we consider data speeds that convert to z scores between - 2
and 2 to be neither significantly low nor significantly​ high, is the​ carrier's highest data speed​ significant?

Answers

(a). There is a 57.16 Mbps difference. (b). There is a 2.74 standard deviation difference. (c). 2.74 is the z-score (d). The maximum data rate offered by the carrier is more than 2.

What is an appropriate response?

When something is careful and purposeful, you use the word measured to describe it. The men's voices were measured and quiet. Voters will be attracted to her more considered reaction. These are a couple of those illustrations. using a thermometer to measure body temperature using a measuring cylinder to determine the weight of produce in a store. Measuring the stature of an infant to retain his/her growth record.

(a). (74.5 - 17.34) = 57.16

(b). 57.16/20.79

= 2.74

(c). z = (X - μ)/sd

= (74.5 - 17.34)/20.79

= 2.74

(d). Because it is higher than 2, the carrier's greatest data speed is noteworthy.

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find the expansion of (x y)5 a) using combinatorial reasoning
b) using the binomial theorem.

Answers

Using combinatorial reasoning, the expression of[tex](x y)5 is x^5y^5 + 5x^4y^6 + 10x^3y^7 + 10x^2y^8 + 5xy^9 + y^10[/tex]. Using the binomial theorem, it is[tex]1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex].

a) Combinatorial reasoning involves breaking the expression down into different combinations of x and y, and then multiplying each combination. In this case, (x y)5 can be broken down into

[tex]x^5y^0 + x^4y^1 + x^3y^2 + x^2y^3 + x^1y^4 + x^0y^5[/tex],

and the coefficient of each term is the number of ways that combination can be derived from the expression. For example, there are 5 ways to arrange the combination [tex]x^4y^1[/tex], so its coefficient is 5. When the coefficients are multiplied with the combinations, they become

[tex]5x^4y^1 + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex],

which is the expansion of (x y)5.

b) The binomial theorem states that for any expression of the form [tex](x + y)^n[/tex], the expansion can be found by multiplying the term[tex]x^n[/tex]with the coefficient of each term in Pascal’s triangle. For example, for[tex](x + y)^5[/tex], the coefficient of[tex]x^5[/tex] is 1, the coefficient of[tex]x^4y[/tex]is 5, the coefficient of[tex]x^3y^2[/tex]is 10, the coefficient of [tex]x^2y^3[/tex]is 10, the coefficient of[tex]x^1y^4 is 5[/tex], and the coefficient of[tex]y^5[/tex]is 1. Thus, the expansion of [tex](x + y)^5 is 1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5.[/tex]

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The number of chirps that crickets make is closely related to the temperature in after environment. When the temperatures between 12 and 38°C ,we can tell the temperature by counting the number of chirps.

Answers

Answer:

a)  32° Celsius

b)  C = m/3 + 4

c) 30 chirps

d) m = 3C - 12

This would be the equation needed to find the number of chirps as a function of temperature

Step-by-step explanation:

Part a.

Since there are 84 chirps in 25 seconds
we get temperature, C = 84/3 + 4 = 28 + 4 = 32° Celsius

part b.
Equation is
C = m/3 + 4

Part c.

We have C = 14

Therefore

14 = m/3 + 4

Multiply throughout by 3

==> 3 x 14 = 3 x m/3 + 3 x 4

==> 42 = m + 12

Subtract 12:

42 - 12 = m30 = m

or m = 30 chirps

part d.

Inverse of the function C = m/3 + 4 is m expresses as a function of C

C = m/3 + 4

Multiply by 3 both sides:
3C = m + 12

3C - 12 = m

or m = 3C - 12

This would be the equation needed to find the number of chirps as a function of temperature

How do I find the solution

Answers

Answer: maybe look up the answer and ask ur teacher what to do

Step-by-step explanation:

The sum of two three-digit number b67 and aa5 is a four-digit number 1a12. What is the value of (a + b)?

Answers

Answer: 13

Step-by-step explanation: The two numbers are 967 and 445 making a=4 and b=9. We know a+b= 9+4 which is 13. For starters, you add the last digits of b67 and aa5 so 7+5=12 which is why the four digit number ends in two. When adding, the one from 12 would carry so the second to last digit on the four digit number would have to be 11. To get eleven you would add 7 and 4. The seven comes from the second digit in the b67 number including the one that came from 7+5=12. Now we know a=4. Knowing this now aa5= 445 and 1a12= 1412. We can now substract 445 from 1412 to get 967. b67= 967. To check 967+445=1412.  

What is the discriminant of the quadratic equation 9x^2-2x-9=09x
2
−2x−9=0?

Answers

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-2)^2-4(9)(-9)\implies \text{\LARGE 328}[/tex]

Mary buys a pack of sugar paste to cover her cakes. the pack is in the shape of a cuboid measuring 5cm by 8cm by 9cm a) she rolls out her sugar paste into rectangular sheet of pasty of uniform thickness measuring 30cm by 60cm. Work out the thickness of this rectangular sheet. B) Mary cuts out two circular pieces of pastry, each of diameter 25cm from her rectangular sheet of pastry. What volume of pastry remains when she removes these two circular pieces of pastry?

Answers

A. The thickness of the rectangular sheet of sugar paste is 1/5 cm.

B. The volume of the remaining pastry can be expressed as approximately 45.84 cm³.

What is the volume of the cuboid?

The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.

The volume of a cuboid is length × breadth× height

A) The volume of the cuboid pack of sugar paste is 5 cm x 8 cm x 9 cm = 360 cm³.

To find the thickness of the rolled-out rectangular sheet, we need to divide the volume of the pack by the area of the rectangular sheet:

thickness = volume/area

thickness = 360 cm³ / (30 cm x 60 cm)

thickness = 360 cm³ / 1800 cm²

thickness = 1/5 cm

So the thickness of the rectangular sheet of sugar paste is 1/5 cm.

B) The two circular pieces of pastry each have a diameter of 25 cm and thus a radius of 25/2 = 12.5 cm.

The volume of each circular piece of pastry can be calculated as:

V = π × (radius)² × thickness

V = π × (12.5 cm)² × 1/5 cm

V = π × 156.25 × 1/5 cm³

V = 50 × π cm³

Since Mary cuts out two circular pieces, the total volume of pastry that she removes is 2 x 50 x π cm³. The remaining volume of pastry is the original volume of the pack minus the volume of the two circular pieces:

Volume remaining = 360 cm³ - 2 × 50 × π cm³ = 45.84 cm³

The volume of the remaining pastry can be expressed as approximately 45.84 cm³.

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What is the area of the parallelogram?
(-6.6)
(-9,-3)*
(-5-3)
(-2,6)

Answers

Answer:

  36 square units

Step-by-step explanation:

You want the area of the parallelogram with vertex coordinates (-6, 6), (-9, -3), (-5, -3), (-2, 6).

Area

The area of a parallelogram is the product of the base length and the height perpendicular to that base.

Here, the base is a horizontal line, so its length is the difference of the x-coordinates of the end points:

  -5 -(-9) = 4 . . . . base

The height is the difference of y-coordinates between the top edge and the bottom edge:

  6 -(-3) = 9 . . . . height

Then the area is ...

  A = bh = 4·9 = 36 . . . . square units

If I took 480 minutes a day in school (that would be 8 hours a day in school), and there is 4 weeks in a month, and all together we spend time in 10 months in school, if 1 hours is 60 minutes, then how much time and days to we spend in school.

Answers

You spend 480 minutes per day at school. We will assume that you go to school for 5 days per week.

480 minutes × 5 days = 2,400 minutes per week

There are 4 weeks in a month, so we will multiply the minutes per week by 4 weeks to get the monthly time spent in school.

2,400 minutes per week × 4 weeks = 9,600 minutes per month

You are in school for 10 months, so we will multiply the minutes per month by 10.

9,600 minutes per month × 10 months = 96,000 minutes in school

Now, we will divide the time in school by the number of minutes in school per day.

96,000 minutes in school ÷ 480 minutes per day = 200 days in school

Answer: 96,000 hours or 200 days

5. Use the slope formula to calculate the slope of the path you selected in question 4. Round your answer to the nearest hundredth. Show your work. Use the coordinates from question 1 and the pair in question 3 that matches the path you chose. Then use the Compass Tool to confirm your answer by dragging the point on the line that goes through the boat. (5 points: 3 points for a correctly written equation and work, 2 points for the slope)

Answers

The equation for the given scenario is y=50/57x-3.16.

What is slope of a line?

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 formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

From the given figure, the coordinate points are (129, 110) and (300, 260).

Substitute (x₁, y₁)=(129, 110) and (x₂, y₂=(300, 260) is slope formula, we get

Slope (m) =(260-110)/(300-129)

= 150/171

= 50/57

Substitute, m=50/57 and (x, y)=(129, 110) in y=mx+c, we get

110=50/57 (129)+c

110=113.16+c

c= -3.16

Substitute, m=50/57 and c= -3.16 in y=mx+c, we get

y=50/57x-3.16

Therefore, the equation for the given scenario is y=50/57x-3.16.

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In one hour, John can produce 20 loaves of bread or 18 cakes. In one hour, Phyllis can produce 30 loaves of bread or 15 cakes. Which of the following statements is true?
a. John has a comparative advantage in producing cakes.
b. Phyllis has an absolute advantage in both goods.
c. Phyllis has a comparative advantage in producing cakes.
d. John has an absolute advantage in both goods.

Answers

Correct Answer is c. Phyllis has a comparative advantage in producing cakes.

What is comparative advantage?

Comparative advantage is an economic concept that refers to the ability of an individual, firm, or country to produce a particular good or service more efficiently compared to others.

The opportunity cost of producing one cake for John is (20 loaves of bread) / (18 cakes) = 1.11 loaves of bread per cake.

The opportunity cost of producing one cake for Phyllis is (30 loaves of bread) / (15 cakes) = 2 loaves of bread per cake.

Since Phyllis has a lower opportunity cost of producing cakes (2 loaves of bread per cake) compared to John (1.11 loaves of bread per cake), Hence, Phyllis has a comparative advantage in producing cakes.

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On Monday it took 5 people 3 and half hours to build a wall. An identical wall needs to be built on Tuesday but only 2 people are available. Each person is paid £9.30 for each hour or part of an hour they work. Work out how much each builder will be paid for the work completed on Tuesday.

Answers

Each builder will be paid £32.55 for work on tuesday.

What are algebraic expressions?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that on Monday it took 5 people, three and half hours to build a wall. An identical wall needs to be built on Tuesday but only 2 people are available. Each person is paid £9.30 for each hour or part of an hour they work.

5 people take 3.5 hours to build a wall.

1 person will take (3.5/5) hours to build a wall.

2 persons will take (3.5/5 x 2) hours to build a wall.

1 person is paid £9.30 for each hour. So 2 persons will get -

£{9.30 x 3.5/5 x 2}

£32.55

Therefore, each builder will be paid £32.55 for work on tuesday.

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State the coordinate of the image of the given point B (4,9) under a dilation with center
at the origin with the given scale factor of 2.

Answers

As a result, the coordinate of the picture of point B (4, 9) under dilation with the origin as the center and a scale factor of 2 is (8, 18).

What is coordinate?

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate. Point (3, 2), for example, is three units distant from the positive y-axis and two units away from the positive x-axis.

Here,

A dilation with center at the origin and scale factor of 2 will stretch or shrink the distances from the origin by a factor of 2. If the given point B is (4,9), its image under the dilation will be:

(2 * 4, 2 * 9) = (8, 18)

So the coordinate of the image of point B (4, 9) under the dilation with center at the origin and scale factor of 2 is (8, 18).

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