Show different ways you can group two factors in 3 x 2 x 7

The engine torque y (in foot-pounds) of one model of car is given by y=−3.75x2+23.2x+38.8, where x is the speed (in thousands of

Stels [109]

Answer:

Step-by-step explanation:

If the engine torque y (in foot-pounds) of one model of car is given by y=−3.75x^2+23.2x+38.8

The engine speed is at maximum if dy/dx = 0

dy/dx = -2(3.75)x+23.2

dy/dx = -7.5x + 23.2

since dy/dx = 0

0 = -7.5x + 23.2

7.5x = 23.2

x = 23.2/7.5

x = 3.093

Hence the maximum torque is 3.09 rev/min

8 0

2 years ago

A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection

svet-max [94.6K]

Answer:

x = 2 cm

y = 2 cm

A(max) = 4 cm²

Step-by-step explanation: See Annex

The right isosceles triangle has two 45° angles and the right angle.

tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x

A(r) = x* y

Area of the rectangle as a function of x

A(x) = x * ( 4 - x ) A(x) = 4*x - x²

Tacking derivatives on both sides of the equation:

A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0

2*x = 4

x = 2 cm

And y = 4 - 2 = 2 cm

The rectangle of maximum area result to be a square of side 2 cm

A(max) = 2*2 = 4 cm²

To find out if A(x) has a maximum in the point x = 2

We get the second derivative

A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2

5 0

2 years ago

18.88 divided by 1.6

dybincka [34]

18.88 divided by 1.6 is 11.8.

3 0

3 years ago

Read 2 more answers

Select the correct answer

Zepler [3.9K]

Answer:

number 3

Step-by-step explanation:

thats my calcue

7 0

2 years ago

Read 2 more answers

According to the U.S. Bureau of Labor Statistics, 20% of all people 16 years of age or older do volunteer work. In this age grou

Murljashka [212]

Answer:

1. P(X≥35) = 0.0183

2. P(X≤21) = 0.0183

3. P(0.18<p<0.25) = 0.7915

Step-by-step explanation:

We have the proportion for women: pw=0.22, and the proportion for men: pm=0.19.

1. We have a sample of 140 woman and we have to calculate the probability of getting 35 or more who do volunteer work.

This is equivalent to a proportion of

$p=X/n=35/140=0.25$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.22*0.78}{300}}\\\\\\ \sigma_p=\sqrt{0.0006}=0.0239$

We calculate the z-score as:

$z=\dfrac{p-p_w}{\sigma_p}=\dfrac{0.25-0.22}{0.0239}=\dfrac{0.03}{0.0239}=0.8198$

Then, the probability of having 35 women or more who do volunteer work in this sample of 140 women is:

$P(X>35)=P(p>0.25)=P(z>2.0906)=0.0183$

2. We have to calculate the probability of having 21 or fewer women in the group who do volunteer work.

The proportion is now:

$p=X/n=21/140=0.15$

We can calculate then the z-score as:

$z=\dfrac{p-p_w}{\sigma_p}=\dfrac{0.15-0.2}{0.0239}=\dfrac{-0.05}{0.0239}=-2.0906$

Then, the probability of having 21 women or less who do volunteer work in this sample of 140 women is:

$P(X$

3. For the sample with men and women, we use the proportion for both, which is π=0.2.

The sample size is n=300.

Then, the standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.2*0.8}{300}}\\\\\\ \sigma_p=\sqrt{0.0005}=0.0231$

We can calculate the z-scores for p1=0.18 and p2=0.25:

$z_1=\dfrac{p_1-\pi}{\sigma_p}=\dfrac{0.18-0.2}{0.0231}=\dfrac{-0.02}{0.0231}=-0.8660\\\\\\z_2=\dfrac{p_2-\pi}{\sigma_p}=\dfrac{0.25-0.2}{0.0231}=\dfrac{0.05}{0.0231}=2.1651$

We can now calculate the probabilty of having a proportion within 0.18 and 0.25 as:

$P=P(0.18$

5 0

3 years ago