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Step2247 [10]
3 years ago
8

Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. Wh

en he starts his shift, the water level shows 8 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
150 minutes
160 minutes
170 minutes
180 minutes
Mathematics
2 answers:
lilavasa [31]3 years ago
5 0
that should be 150
Tatiana [17]3 years ago
4 0

Answer:

160

Step-by-step explanation:

You might be interested in
(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y
a_sh-v [17]

Answer:

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n       (1)

where:

m is the slope of the line and m is the intercept with the axis of the dependent variable, y in this case.

In order to obtain the value of the slope (m) we can use the corresponding slope formula:

m=\frac{y_{2}-y_1 }{t_2-t_1}         (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

t_1=0\\t_2=4\\y_1=545\\y_2=726\\

Substituting these values in equation (2) we obtain:

m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25

Hence, the line equation is now:

y=45.25t+n     (3)

Now to obtain the value of n you can follow two options:

  1. You can substitute one of your points, A or B, in equation (3). In this way, you will obtain an equation where the variable is n

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0. Hence, substituting point A in equation (3):

45.25*0+n=545\\n=545

Therefore, the line equation is: y=45.25t+545

The second option to find n is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that n is equal to 545.

See the attachment for a plot of the line.

7 0
3 years ago
Factoring a polynomial is essentially dividing.
joja [24]

<span>yes, in the sense that factoring is the process of breaking apart things that are multiplied</span>
4 0
3 years ago
Read 2 more answers
Given the function f(x)=3x+5a / x^2-a^2 find the value of a for which f'(12) = 0
maria [59]
The function, as presented here, is ambiguous in terms of what's being deivded by what.  For the sake of example, I will assume that you meant

           3x+5a
<span> f(x)= ------------
</span>          x^2-a^2

You are saying that the derivative of this function is 0 when x=12.  Let's differentiate f(x) with respect to x and then let x = 12:

             (x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
                [x^2-a^2]^2

(144-a^2)(3) - (36+5a)(24)
------------------------------------  =  0
               [   ]^2

Simplifying,

(144-a^2) - 8(36+5a) = 0

144 - a^2 - 288 - 40a = 0

This can be rewritten as a quadratic in standard form:

-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.

Solve for a by completing the square:

a^2 + 40a + 20^2 - 20^2 + 144 = 0
        (a+20)^2    = 400 - 144 = 156

        Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)

         Finally, a = -20 plus or minus 2sqrt(39)

You must check both answers by subst. into the original equation.  Only if the result(s) is(are) true is your solution (value of a) correct.
6 0
3 years ago
4/5,3/10 =. Please help
KengaRu [80]

Answer:

The answer would be 0,0754716981

5 0
3 years ago
Graph the linear equation in three plots: -x+2y=11
MariettaO [177]

Answer:

<h2>In the attachment.</h2>

Step-by-step explanation:

Convert the given equation to the form y = mx + b:

-x+2y=11          <em>add x to both sides</em>

2y=x+11          <em>divide both sides by 2</em>

y=\dfrac{1}{2}x+\dfrac{11}{2}

It's a linear function.

We need only two points to plot the graph. Select any two x values, insert into the equation and calculate y values.

for x = 1

y=\dfrac{1}{2}(1)+\dfrac{11}{2}=\dfrac{1}{2}+\dfrac{11}{2}=\dfrac{12}{2}=6\to(1,\ 6)

for x = -5

y=\dfrac{1}{2}(-5)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to(-5,\ 3)

3 0
3 years ago
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