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3 years ago

What does the notation f prime of x mean?

1 answer:

8 0

F ' (x) represents the derivative of a function. Primarily used in calculus, the derivative is the rate of change on a nonlinear system.
If you recall from linear algebra, lines have a slope, as they have a constant rate of change (and the slope was defined as 'm' in y=mx+b).
Curved systems (like parabola and other complex functions) have varying rates of change, requiring the use of the derivative of a function.

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Is anyone here like rlly good at algebra bc im not and I kinda forgot What my teacher told me so-

raketka [301]

Answer:

The question is asking you to subtract 516 from 1,000 to find b.

$1,000 - 516 = 484$

Therefore, b = 484

5 0

2 years ago

Read 2 more answers

National data in the 1960's showed that about 44% of the adult population had never smoked cigarettes. In 1995 a national health

Marta_Voda [28]

Answer:

a) $0.52 - 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.487$

$0.52 + 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.553$

The 95% confidence interval would be given by (0.487;0.553)

b) After see the confidence interval we see that the lower limits 0.487>0.44 with 0.44 or 44% the estimated proportion for 1960, we can conclude that we have a significant increase in the adult proportion had never smoked cigarettes.

Step-by-step explanation:

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".

Solution to the problem

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.52 - 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.487$

$0.52 + 1.96\sqrt{\frac{0.52(1-0.52)}{881}}=0.553$

The 95% confidence interval would be given by (0.487;0.553)

Part b

After see the confidence interval we see that the lower limits 0.487>0.44 with 0.44 or 44% the estimated proportion for 1960, we can conclude that we have a significant increase in the adult proportion had never smoked cigarettes at 5% of significance.

4 0

4 years ago

Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }

NemiM [27]

Answer:

A, E

Step-by-step explanation:

There should be 2^8-1 proper subsets of A. Its every one besides { }

8 0

3 years ago

His new employer has offered Malcom Davis a choice of profit-sharing plans. For Plan A, he can receive 1/90 of the company’s gro

Strike441 [17]

Malcom Davis earnings is an illustration of equations and proportions.

The equation is: $\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}$
The gross income must be $300000, for Dave to earn the same amount with either plan.
His earning is $3333.33 when the plans are the same.

Let the profit be P, and the gross income be G.

So, we have:

$\mathbf{P= G - 100000}$

(a) The equations

For plan A, we have:

$\mathbf{A = \frac{1}{90}G}$ ----1/90 of the company's gross income

For plan B, we have:

$\mathbf{B = \frac{1}{60}P}$ ----1/90 of the company's profit

When both are the same, we have:

$\mathbf{A= B}$

This gives

$\mathbf{\frac{1}{90}G= \frac{1}{60}P}$

Substitute $\mathbf{P= G - 100000}$

$\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}$

Hence, the equation is: $\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}$

(b) Solve the equation in (a), and intepret

$\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}$

Cross multiply

$\mathbf{60G = 90G - 9000 000}$

Collect like terms

$\mathbf{90G - 60G = 9000 000}$

$\mathbf{30G = 9000 000}$

Divide both sides by 30

$\mathbf{G = 3000 00}$

The gross income must be $300000, for Dave to earn the same amount with either plan.

(c) His earnings based on (c)

We have:

$\mathbf{A = \frac{1}{90}G}$

Substitute $\mathbf{G = 3000 00}$

$\mathbf{A = \frac{1}{90} \times 300000}$

$\mathbf{A = 3333.33}$

His earning is $3333.33 when the plans are the same

(d) If the gross income in less than (b)

If the gross income is less than $300,000, then plan A would better for Malcom Davis, because his earnings in plan A would be greater than plan B