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cricket20 [7]
3 years ago
13

Miss Ferguson recorded 17 absences the first 30 days of school. During the last 60 days of school, she recorded 42 absences. Are

the rates equivalent?
Mathematics
1 answer:
Sloan [31]3 years ago
5 0

Answer:

No, they are not

Step-by-step explanation:

The rate can be described in terms of absences per day.

Now in the first 30 days, they were 17 absences. The rate would thus be number of absences divided by number of days and that is 17/30

In the second run, there were 42 absences in the recent 60 days, rate here would be 42/60 and that is 21/30

Thus, the rates are not equivalent

You might be interested in
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o
Kruka [31]

For \fbox{\begin \\\math{x}=6\\\end{minispace}} the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 has same value.

Step by step explanation:  

The given functions are,

f(x)=-x^{2}+4x+12

g(x)=-x+6

Step 1:  

Substitute x=1 in f(x)=-x^{2} +4x+12 to obtain the value of f(1).

f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15

Substitute x=1 in g(x)=-x+6 to obtain the value of g(1) .

g(1)=-1+6\\g(1)=5

Step 2:

Substitute x=2 in f(x)=-x^{2} +4x+12 to obtain the value of f(2).

f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16

Substitute x=2 in g(x)=-x+6 to obtain the value of g(2) .

g(2)=-2+6\\g(2)=4

Step 3:

Substitute x=3 in f(x)=-x^{2} +4x+12 to obtain the value of f(3).

f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15

Substitute x=3 in g(x)=-x+6 to obtain the value of g(3) .

g(3)=-3+6\\g(3)=3

Step 4:

Substitute x=4 in f(x)=-x^{2} +4x+12 to obtain the value of f(4).

f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12

Substitute x=4 in g(x)=-x+6 to obtain the value of g(4) .

g(4)=-4+6\\g(4)=2

Step 5:

Substitute x=5 in f(x)=-x^{2} +4x+12 to obtain the value of f(5).

f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7

Substitute x=5 in g(x)=-x+6 to obtain the value of g(5) .

g(5)=-5+6\\g(5)=1

Step 6:

Substitute x=6 in f(x)=-x^{2} +4x+12 to obtain the value of f(6).

f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0

Substitute x=6 in g(x)=-x+6 to obtain the value of g(6) .

g(6)=-6+6\\g(6)=0

Step 7:

As per the given condition f(x)=g(x).

(a). Substitute f(x)=-x^{2} +4x+12 and g(x)=-x+6 in above equation.

-x^{2} +4x+12=-x+6

(b). Multiply with -1 on both sides.

x^{2} -4x-12=x-6

(c). Shift the term x-6 to left hand side.

x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0

(d). Split the middle term in such a way that its sum is 5 and multiplication is 6.

x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1 ,6

It is observed from the above solution that for x=6 both the functions f(x) and g(x) has same value.

Direct method:

f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1

The table for the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 is attached below.

Learn more:  

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0) brainly.com/question/1332667

2. which is the graph of f(x) = (x – 1)(x + 4)?  brainly.com/question/2334270  

Answer details:  

Grade: Middle school.  

Subjects: Mathematics.  

Chapter: Function.

Keywords: Function, Middle term split method, Binomial,Quadratic, Polynomial, Factorized, Perfect square, Zeros, Zeros of a function, Expression, Equation, x, x^2, x^3, -x^2+4x+12, -x+6, roots of equation.

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Over a period of years, a certain town observed that the correlation between x, the number of people attending churches, and y,
Alla [95]
No, it is a correlation not a causation.
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3 years ago
9.12*10 by the power of seven/3.2*10 by the power of 4
ivanzaharov [21]

Answer:

2.9184x10 to the power of 12

Step-by-step explanation:

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Which statement describes the graph of function g?
marta [7]

Answer:

a

Step-by-step explanation:

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On avarage kayla drinks 3/4 of an 6 ounce glass of water 1/6 of an hour.How much water does she drink, in glasses per hour?
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Answer:

4.5 ounces

Step-by-step explanation:

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