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3 years ago

14

In a particular class of 26 students, 16 are men. What fraction of the students in the class are women?

2 answers:

swat323 years ago

8 0

If there are 26 students and 16 are men then that means that there are 10 women.

Hoochie [10]3 years ago

6 0

10 are women and 16 are men

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(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l

lara31 [8.8K]

$f(x,y)=x^4+y^4-4xy+1$

has critical points wherever the partial derivatives vanish:

$f_x=4x^3-4y=0\implies x^3=y$

$f_y=4y^3-4x=0\implies y^3=x$

Then

$x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1$

If $x=0$ , then $y=0$ ; critical point at (0, 0)
If $x=1$ , then $y=1$ ; critical point at (1, 1)
If $x=-1$ , then $y=-1$ ; critical point at (-1, -1)

$f(x,y)$ has Hessian matrix

$H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}$

with determinant

$\det H(x,y)=144x^2y^2-16$

At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
At (1, 1), the determinant is 128, and $f_{xx}(1,1)=12$ , which indicates a local minimum.
At (-1, -1), the determinant is again 128, and $f_{xx}(-1,-1)=12$ , which indicates another local minimum.

4 0

3 years ago

In 1983, a can of house paint cost $16.35. In 2000, a can of house paint cost $28.94, and in 2005, a can of house paint cost $32

Readme [11.4K]

The Consumer Price Index is calculated through the equation,
CPI = (current period price/base period price) x 100
The base period is 1983. Solving the CPIs for 2000 and 2005
(2000)
CPI = ($28.94/$16.35) x 100 = 177
(2005)
CPI = ($32.54/$16.35) x 100 = 199
The difference between the CPIs of 2005 and 2000 is 199 - 177 = 22.

8 0

3 years ago

Read 2 more answers

Find the first four terms of the sequence<br> An=2a n-1,where a1=3

yKpoI14uk [10]

The first four terms of the sequence are 3 , 6 , 12 , 24

Step-by-step explanation:

We need to find the first four terms of the sequence $a_{n}=2a_{n-1}$

where $a_{1}=3$ to find them do that

Substitute n by 2 in the rule to find $a_{2}$
Substitute n by 3 in the rule to find $a_{3}$
Substitute n by 4 in the rule to find $a_{4}$

∵ $a_{n}=2a_{n-1}$

- Substitute n by 2 to find the 2nd term

∴ $a_{2}=2a_{2-1}$

∴ $a_{2}=2a_{1}$

∵ $a_{1}=3$

∴ $a_{2}=2(3)$

∴ $a_{2}=6$

- Substitute n by 3 to find the 3rd term

∴ $a_{3}=2a_{3-1}$

∴ $a_{3}=2a_{2}$

∵ $a_{2}=6$

∴ $a_{3}=2(6)$

∴ $a_{3}=12$

- Substitute n by 4 to find the 4th term

∴ $a_{4}=2a_{4-1}$

∴ $a_{4}=2a_{3}$

∵ $a_{3}=12$

∴ $a_{4}=2(12)$

∴ $a_{4}=24$

The first four terms of the sequence are 3 , 6 , 12 , 24

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

#LearnwithBrainly

3 0

3 years ago

Jeri's lawn service charges an initial fee of $4.50 plus $3 an hour. If she is asked to

STALIN [3.7K]

Answer:

5 hours 22 minutes

Step-by-step explanation:

Let us represent the number of hours that Jeri worked as: h

Jeri's lawn service charges an initial fee of $4.50 plus $3 an hour

= $4.50 + $3 × h

= $4.50 + 3h

If she is asked to start before 7 a.m. Jeri charges 1.5 times the regular amount.

= 1.5 × ($4.50 + 3h)

If she made $29.25 on a job that began at 5 am, how many hours did Jeri work?

Hence, we have the final equation;

= 1.5 × ($4.50 + 3h) = $29.25

= 6.75 + 4.5h = 29.25

Collect like terms

= 4.5h = 29.25 - 6.75

4.5h = 22.5

h = 22.5/4.5

h = 5.3571428571

Approximately= 5.36 hours

1 hour = 60 minutes

0.36 hour =

60 × 0.36

= 21.6 minutes

Approximately ≈ 22 minutes

Therefore, Jeri worked for 5 hours 22 minutes

7 0

3 years ago

Derek spends three dollars on breakfast and $5.50 on lunch every school day how much does he spend on breakfast and lunch in a s

maks197457 [2]

(3+5.50)5

8.50*5=42.5

Derek spends $42.50 each school week.

7 0

3 years ago

Read 2 more answers