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3 years ago

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Mathematics

1 answer:

BaLLatris [955]3 years ago

8 0

Answer:

a) t(n) = 200n -238

b) t(n) = 2.7n -4.3

Step-by-step explanation:

This is the same sort of problem as writing the equation of a line through two points. The slope (coefficient of n) is found using the slope formula:

m = (y2 -y1)/(x2 -x1)

And the constant term is found from one point and the slope:

b = y1 -m·x1

As always, if you have a number of these to do, you can save some trouble by putting the formulas in a spreadsheet. It will guarantee the formula is executed without mistakes.

In the attached, we have labeled the points (n1, t1), (n2, t2) instead of (x1, y1) and (x2, y2).

a) t(n) = 200n -238

b) t(n) = 2.7n -4.3

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At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students, and 28 chose social studies as their favorite. He us

Umnica [9.8K]

Answer:

No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20% of 90.

Step-by-step explanation:

At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students from each grade level for their favorite subject.

90 randomly selected students from each grade level for their favorite subject, and 28 chose social studies as their favorite.

so, the percent of students who love social studies is given by:

28/90 x 100=31.11%

He used this data to draw the inference that out of the 250 middle school students, about 20% prefer social studies.

No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20% of 90.

6 0

3 years ago

(2x+6) -(6x+1) please help me with this expression

a_sh-v [17]

Simplify

2x + 6 - (6x + 1)

Simplify brackets

2x + 6 - 6x - 1

Collect like terms

(2x - 6x) + (6 - 1)

Simplify

5 0

3 years ago

Read 2 more answers

(1 point) a tank contains 1060 l of pure water. a solution that contains 0.06 kg of sugar per liter enters the tank at the rate

kirill115 [55]

(a) There is 0 kg of sugar in the tank at the beginning since it contains pure water at the start. The sugar only comes from the solution.

(b)

$S' = f(t,S) = \left(0.06 \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) - \left(\dfrac{S}{1060} \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) \ \Rightarrow \\ \\ S' = 0.54 \text{ kg}/\text{min} - \dfrac{9S}{1060}$

So yes, you enter S' = 0.54 - (9S/1060)

(c)

$\displaystyle\frac{dS}{dt} = 0.54 - \frac{9S}{1060} \ \Rightarrow\ \frac{dS}{dt} = \frac{572.4 - 9S}{1060}\ \Rightarrow\ \dfrac{dS}{572.4 - 9S} = \frac{1}{1060} dt\ \Rightarrow \\ \\
\int \dfrac{dS}{572.4 - 9S} = \int \frac{1}{1060} dt\ \Rightarrow\textstyle\ -\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t + C \\ \\
S(0) = 0 \ \Rightarrow\ -\frac{1}{9}\ln|572.4 - 0| = \frac{1}{1060}(0) + C\ \Rightarrow\ C = -\frac{1}{9} \ln 572.4$

$-\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t -\frac{1}{9} \ln 572.4\ \Rightarrow \\ \\
\ln|572.4 - 9S| = \ln 572.4 - \frac{9}{1060}t \ \Rightarrow \\ \\
|572.4 - 9S| = e^{\ln 572.4 - 9t/1060}\ \Rightarrow \\ \\
572.4 - 9S= \pm 572.4 e^{-9t/1060}\ \Rightarrow \\ \\
S = \frac{-1}{9}\left(-572.4 \pm 572.4 e^{-9t/1060}\right)$

But only (+) satisfies $S(0) = 0$

$S= -\frac{1}{9}\left(-572.4 + 572.4 e^{-9t/1060}\right) \\ \\
S= 63.6 - 63.6 e^{-9t/1060}\text{ kg}$

Enter in S = 63.6 - 63.6 * e^(-9t/1060)

3 0

3 years ago

The interior angles formed by the sides of a hexagon have measures that sum to 720°.

navik [9.2K]

Answer:

Angle F = 140°

Step-by-step explanation:

Add up all the angles and set it equal to 720°

x-20+x-40+x-60+130+120+110=

720

Add the x's together. And the numbers together.

3x - 120 + 360 =720

3x + 240 = 720

Subtract 240.

3x = 480

Divide by 3.

x = 160

Now find Angle F.

F = 160 - 20

F = 140°

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2 years ago

Which of the following solutions solves the system?

gavmur [86]

Answer:

i think its

Step-by-step explanation:

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3 years ago