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Amanda [17]
3 years ago
9

Jack is performing an experiment in a laboratory. The resulting rise in temperature, t(x), of the chemical under observation, ov

er time x, in hours, for the first ten hours can be modeled by a cubic function. Each of the following functions is a different form of the cubic model for the situation given above. Which form would be most helpful if attempting to determine the time at which the temperature is approximately constant?
t(x) = 0.05x(x2 - 15x + 75) + 43.75

t(x) = 0.05(x - 5)3 + 50

t(x) = 0.05(x3 - 15x2 + 75x + 875)

t(x) = 0.05x3 - 0.75x2 + 3.75x + 43.75
Mathematics
2 answers:
Scorpion4ik [409]3 years ago
7 0
I'd say option D because you can just tell right off the bat that if x = 0, then f(x) = 43.75.
k0ka [10]3 years ago
7 0

Answer:

t(x)= 0.05(x-5)^3+50

Step-by-step explanation:

Since the balance point in a cubic function appears on the line of symmetry, it is the vertex itself.  A translation h units to the right and k units up of a cubic function, which has the vertex at the origin, can be represented by the function in the following form, where (h,k) is the vertex of the function.

 

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Solve for d.<br> d + 67 = 87<br> р<br> Submit
Vsevolod [243]

Answer:

d=20

Step-by-step explanation:

d+67=87

Subtract 67 from both sides

d=20

Hope this is helpful

7 0
3 years ago
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What are the roots of the polynomial equation x^2+8x-48=0
____ [38]

<span> Given polynomial x^2+8x-48 = 0</span>

<span>x^2+12x-4x-48 = 0</span>

<span>x(x+12)-4(x+12) = 0</span>

<span>(x+12)(x-4) = 0</span>

<span>x+12 = 0</span>

Subtract 12 from each side.

<span>x+12-12 = 0-12</span>

<span>x = -12</span>

<span>and x-4 = 0</span>

Add 4 to each side.

<span>x-4+4 = 0+4</span>

<span>x = 4</span>

<span>Roots are -12,4.</span>

4 0
3 years ago
The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.
dybincka [34]

Answer:

Critical values:t_{\alpha/2}=-2.201 t_{1-\alpha/2}=2.201

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is \bar X= 4.059

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df=n-1=12-1=11

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,11)" for t_{\alpha/2}=-2.201

"=T.INV(1-0.025,11)" for t_{1-\alpha/2}=2.201

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}  

And we can use Excel to calculate the limits for the interval

Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646

Upper interval :  "=4.059 +2.201*(0.6503/SQRT(12))" =4.472

So the 95% confidence interval would be given by (3.646;4.472)

8 0
3 years ago
4 Gears A and B turn together. Gear A turns 20 times when
aleksandr82 [10.1K]

Answer:

  • 90 turns

Step-by-step explanation:

<u>Ratio of turns</u>

  • A/B = 20/30 = 2/3

<u>If A = 60 then the ratio is</u>

  • 60/B = 2/3 ⇒ B = 60*3/2 = 90
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3 years ago
The model represents an equation. What value of x makes the equation true?
Cerrena [4.2K]

Answer:

C

Step-by-step explanation:

(-3) x 4 = (-12) + 6 = -6

3 + 3 = 6 + (-12) = -6

(-6) = (-6)

Because adding positive to negative is like subtracting the negative if that makes sense.

Hope this helps!

Have a great day!

Plz mark brainliest

6 0
3 years ago
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