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Gennadij [26K]
2 years ago
13

An environmental agency studying the effects of drought on a lake found that the water level decreased at a constant rate during

the first few months of the drought. When the agency began its research, the depth of the lake was 346 feet. The table represents the agency’s susequent observations about the lake's depth.
Which equation represents the depth of the lake, y, based on the number of weeks passed, x?

y = -0.6x + 346

y = -1.2x + 346

y = -0.6x

y = -1.2x
Mathematics
2 answers:
Ad libitum [116K]2 years ago
6 0

Answer:

y = -0.6x + 346

Step-by-step explanation:

dybincka [34]2 years ago
5 0
"y = -0.6x + 346" is the one equation among the choices given in the question that <span>represents the depth of the lake, y, based on the number of weeks passed, x. The correct option among all the options that are given in the question is the first option. I hope that this is the answer that has helped you.</span>
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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
2 years ago
The height of 44 students (in centimeter) are presented in the frequency distribution below. Complete the table, and then find t
JulijaS [17]

Given:

The height of 44 students (in centimeter) are presented in the given frequency distribution.

To find:

The median of the given data.

Solution:

The given intervals are inclusive first make the intervals exclusive by adding 0.5 in upper limit and by subtracting 0.5 from the lower limit.

The complete frequency distribution table is shown below:

Height              Frequency           L                            <cf

182 - 188                  1                  181.5 - 188.5            44

175 - 181                   3                 174.5 - 181.5             43

168 - 174                  6                 167.5 - 174.5            40

161 - 167                 15               160.5 - 167.5            34   Median class

154 - 160                 12                153.5 - 160.5           19

147 - 153                   4                146.5 - 153.5             7

140 - 146                   3                139.5 - 146.5             3

We have, n=44.

\dfrac{n}{2}=\dfrac{44}{2}

\dfrac{n}{2}=22

The 22th term is include in the class 160.5 - 167.5 because is cf is greater than 22 but the cf of o preceding class is less than 22. So, it is the median class is 160.5 - 167.5.

Formula for median:

Median=l+\dfrac{\dfrac{n}{2}-cf}{f}\times h

Where, l is the lower limit of median class, cf is the cumulative frequency of preceding class, f is the frequency of median class and h is the size of the class.

Now, l=160.5,f=15,cf=19,h=7.

Median=160.5+\dfrac{22-19}{15}\times 7

Median=160.5+\dfrac{3}{15}\times 7

Median=160.5+1.4

Median=161.9

Therefore, the median of the given data table is 161.9.

3 0
3 years ago
What is the slope of the line that contains these points?
miskamm [114]

Answer:

-5/4

Step-by-step explanation:

change in y/change in x

3 0
2 years ago
Read 2 more answers
Take 56 and divide it by 4
Hunter-Best [27]
The answer will be 9 ok
3 0
2 years ago
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Marvin wants to purchase a rectangular rug. It has an area represented by the expression 4x^2+64x+256. what is the length and wi
jasenka [17]

Answer: the length and width are

(x + 8) and (x + 8)

Step-by-step explanation:

The rug has an area represented by the expression

Area = 4x² + 64x + 256.

The factors in the factored expressions represent the length and width of the rug.

Dividing the the equation by 4, it becomes

x² + 16x + 64 = 0

We would find two numbers such that their sum or difference is 16x and their product is 64x^2.

The two numbers are 8x and 8x. Therefore,

x² + 8x + 8x + 64 = 0

x(x + 8) + 8(x + 8) = 0

The factors are

(x + 8)(x + 8)

7 0
3 years ago
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