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2 years ago

The following table shows the number of hours a cleaning company spends cleaning apartments.

Mathematics

1 answer:

mart [117]2 years ago

7 0

First, plot the points in a graph to see the general trend. The independent variable is time. I used MS Excel to plot the points in a graph, as shown in the attached picture.

1. The relationship is linear as shown in the general trend.
2. The relationship presents that as time increases, the number of apartments cleaned also increases. The two variables are directly proportional.
3. The rate of change represents the slope of the line. Choose any two points and find the slope.

m = (6-3)/(2-1) = 3 apartments cleaned/hour

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A flu epidemic is spreading through a town of 48,000 people. It is found that if x and y denote the numbers of people sick and w

Liula [17]

Answer:

a) The simultaneous equation represented in matrix form, is

[1/3 1/4] [x] = [s]

[2/3 3/4] [y] = [w]

Ax = B

[1/3 1/4] = matrix A (matrix of coefficients)

[2/3 3/4]

[x] = matrix x (matrix of unknowns)

[y]

[s] = matrix B (matrix of answers)

[w]

b) Number of sick people the preceding week = 12005

Step-by-step explanation:

x = Number of sick people in a week

y = Number of people that are well in a week

s = Number of sick people the following week

w = Number of people that are well the following week.

The relationship between these is given as

(1/3)x + (1/4)y = s

(2/3)x + (3/4)y = w

In matrix form, this is simply presented as

[1/3 1/4] [x] = [s]

[2/3 3/4] [y] = [w]

which is more appropriately written as

Ax = B

where

[1/3 1/4] = matrix A (matrix of coefficients)

[2/3 3/4]

[x] = matrix x (matrix of unknowns)

[y]

[s] = matrix B (matrix of answers)

[w]

b) Taking the current conditions as s and w, then the preceding week will be x and y

The number of sick people in this week, s = 13000

The number of people well in this week, w = total population - Number of sick people.

w = 48000 - 13000 = 35000

So, the simultaneous equation becomes

(1/3)x + (1/4)y = 13000

(2/3)x + (3/4)y = 35000

Then we can solve for the number of sick and well people the preceding week.

We can solve normally or use matrix solution.

Ax = B

x, the matrix of unknowns is given by product of the inverse of A (inverse of the matrix of coefficients) and B (matrix of answers)

x = (A⁻¹)B

But, solving normally,

(1/3)x + (1/4)y = 13000

(2/3)x + (3/4)y = 35000

x = 12004.8 = 12005

y = 35995.2 = 35995

Number of sick people the preceding week = x = 12005

8 0

2 years ago

fill inbthe bubble next to all the double facts you could use to find the sum of 3+2? A 2+2 B 5+5 C 3+3 D 1+1

GarryVolchara [31]

Answer:

Option A , C and D are correct.

Step-by-step explanation:

Double Facts states that the additions in which a number is added to itself.

then; by definition of double facts

Use Double facts to find the sum of 3 + 2

3 + 2

=3 + (3 - 1)

= 3+ 3 - 1

= 6 - 1

= 5

similarly,

3+2 = (1+2) + 2 = 1 + 2+2 = 1 + 4 = 5

Also;

3 + 2 = 3 + (1+1) = 3 +1+1 = 5

therefore, the double facts that used to find the sum of 3+2 are; 2+2 , 3+3 and 1+ 1.

4 0

2 years ago

The rule for the dilation of quadrilateral QRST to the image Q'R'S'T' is DO,0.5(x, y) → (0.5x, 0.5y).

Harlamova29_29 [7]

Applying the rule for dilation, we will multiply the scale factor to its coordinates.
Having Q (0,2) and DO 0.5(x.y), the coordinates of Q' will be:

x = (.5)(0) = 0
y = (.5)(2) = 1

Therefore coordinates of Q' is (0,1)

*Having a scale factor of >1, the figure is said to be reduced.

8 0

2 years ago

Read 2 more answers

One factor of the function f(x) = x3 − 8x2 + 17x − 10 is (x − 5). Describe how to find the x-intercepts and the y-intercept of t

kozerog [31]

Answer:

x-intercepts: (1,0), (2,0), (5,0)

y-intercepts: (0,-10)

Step-by-step explanation:

One factor of the function $f(x) = x^3-8x^2 + 17x-10$ is $(x-5).$

Factor the polynomial in the following way:

$x^3-8x^2 + 17x-10\\ \\=x^3-5x^2-3x^2+15x+2x-10\\ \\=x^2(x-5)-3x(x-5)+2(x-5)\\ \\=(x-5)(x^2-3x+2)$

Now factor the quadratic in brackets:

$x^2-3x+2\\ \\=x^2-2x-x+2\\ \\=x(x-2)-(x-2)\\ \\=(x-2)(x-1)$

Hence,

$f(x)=(x-5)(x-2)(x-1)$

The x-intercepts are points at which y = 0, so

$(x-5)(x-2)(x-1)=0\\ \\x-5=0\ \text{or}\ x-2=0\ \text{or}\ x-1=0\\ \\x=5\ \text{or}\ x=2\ \text{or}\ x=1$

The y-intercepts are points at which x = 0, so

$y=0^3-8\cdot 0^2+17\cdot 0-10=-10$

4 0

2 years ago

Read 2 more answers

On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from

Anna007 [38]

Okay, so Sang is standing 20 yards away from one corner, and Jazmin is standing 99 yards away from the same corner. If this is a rectangle (I like visuals, so I'll use them to explain), then:

99ft
A ------------------------- B
   |    |
20 ft |    |
   |    |
C -------------------------- D

The question is asking you to solve for the diagonal line between points C and B. If you imagine a line there, you actually have the rectangle split into two triangles. So if you have triangle ABC, side CB would be the longest line, or the hypotenuse. That means you can use the Pythagorean Theorem to solve the problem.

A^2 + B^2 = C^2
99^2 + 20^2 = C^2
9,801 + 400 = C^2
10,201 = C^2

Now you solve for the square root of 10,201 to get C.

sqr (10,201) = C
C = 101 yards

3 0

2 years ago