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horrorfan [7]
2 years ago
13

Chang made $156 for 13 hours of work at the same rate, how many hours would he have to work to make $108?

Mathematics
1 answer:
sdas [7]2 years ago
8 0

Answer:

  9 hours

Step-by-step explanation:

"At the same rate" means time and wages are proportional.

  time/wages = t/$108 = (13 h)/$156

  t = 108(13 h)/156 . . . . . . . . . . . . . . . units of dollars cancel

  t = 9 h

Chang would have to work 9 hours to make $108.

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An area is approximated to be 14 in 2 using a left-endpoint rectangle approximation method. A right- endpoint approximation of t
USPshnik [31]
The trapezoidal approximation will be the average of the left- and right-endpoint approximations.

Let's consider a simple example of estimating the value of a general definite integral,

\displaystyle\int_a^bf(x)\,\mathrm dx

Split up the interval [a,b] into n equal subintervals,

[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]

where a=x_0 and b=x_n. Each subinterval has measure (width) \dfrac{a-b}n.

Now denote the left- and right-endpoint approximations by L and R, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are \{x_0,x_1,\cdots,x_{n-1}\}. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints, \{x_1,x_2,\cdots,x_n\}.

So, you have

L=\dfrac{b-a}n\left(f(x_0)+f(x_1)+\cdots+f(x_{n-2})+f(x_{n-1})\right)
R=\dfrac{b-a}n\left(f(x_1)+f(x_2)+\cdots+f(x_{n-1})+f(x_n)\right)

Now let T denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

T=\dfrac{b-a}n\left(\dfrac{f(x_0)+f(x_1)}2+\dfrac{f(x_1)+f(x_2)}2+\cdots+\dfrac{f(x_{n-2})+f(x_{n-1})}2+\dfrac{f(x_{n-1})+f(x_n)}2\right)

Factoring out \dfrac12 and regrouping the terms, you have

T=\dfrac{b-a}{2n}\left((f(x_0)+f(x_1)+\cdots+f(x_{n-2})+f(x_{n-1}))+(f(x_1)+f(x_2)+\cdots+f(x_{n-1})+f(x_n))\right)

which is equivalent to

T=\dfrac12\left(L+R)

and is the average of L and R.

So the trapezoidal approximation for your problem should be \dfrac{14+21}2=\dfrac{35}2=17.5\text{ in}^2
4 0
3 years ago
Select from the drop-down menus to correctly complete each statement.
tino4ka555 [31]

Answer:

Right of -7 and left of -1

Step-by-step explanation:

-7 is in the left and -4 is in the right

-7<4

-4 in the left and -1 in the right

-4<-1

just use directions

4 0
3 years ago
In one jar, I have two balls labelled 1 and 2 respectively. In a second jar, I have three balls labelled 0, 1 and 2 respectively
PolarNik [594]

Step-by-step explanation:

this is a kind of trick question, actually.

with whatever we draw, we produce X values as power of 3.

to be precise, we can have only

3⁰ = 1

3¹ = 3

3² = 9

3⁴ = 81

due to the possible combinations of drawn numbers (e.g. 3 cannot be created by a multiplication of 0s, 1s and 2s).

so, mostly, these results cannot be exact factors of 1024.

1024 cannot be divided by 3, nor by 9 nor by 81.

but 1024 is a multiple of 1 (as is every number).

so, we are looking at the probability to get 0 as multiplication result of the numbers on the 2 drawn balls.

the only possibilities are

1 and 0

2 and 0

out of in total 6 (2×3) different outcomes

1 and 0

1 and 1

1 and 2

2 and 0

2 and 1

2 and 2

the probability of this "0" event is again

number of desired outcomes / number of possible outcomes = 2/6 = 1/3

6 0
2 years ago
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In pre
Juliette [100K]

Answer:

The test statistic is t = 2.79

Step-by-step explanation:

From the question we are told that

    The population mean is \mu   = 59.3

    The sample size is  n  =  79

    The  sample mean is  \= x  = 62.4

    The  standard deviation is  \sigma  =  9.86

Generally the test statistics is mathematically represented as

            t =  \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }

substituting values

          t =  \frac{ 62.2 -  59.3 }{ \frac{  9.86}{ \sqrt{ 79} } }

          t = 2.79

4 0
3 years ago
The graph of Line M has a slope of -7 and passes through the point (4,
Soloha48 [4]
Centralizándolos situationist beneficioso punto
4 0
3 years ago
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