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MA_775_DIABLO [31]

3 years ago

5

The schoool has budgeted $2,000 for an end of the year party at the local park. The cost to rent the park shelter is $150. How m

uch can the student council spend per student on food if each of the 225 students receives a $3.50 gift?

1 answer:

Alekssandra [29.7K]3 years ago

4 0

Well if each student got a gift of $3.50, then that would be $787.05... And $2,000 - $787.05= $1,212.95. So they could spend $1,212.95, BUT, if they rented a park shelter, then they would have $1,062.95 dollars left over to spend.

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Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360

Natasha2012 [34]

$\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]$

$\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]$

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

$\rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]$

5 0

3 years ago

Exercise 6.13 presents the results of a poll evaluating support for the health care public option in 2009, reporting that 52% of

sleet_krkn [62]

Answer:

A sample size of 6755 or higher would be appropriate.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error M is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

52% of Independents in the sample opposed the public option.

This means that $p = 0.52$

If we wanted to estimate this number to within 1% with 90% confidence, what would be an appropriate sample size?

Sample size of size n or higher when $M = 0.01$ . So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.01 = 1.645\sqrt{\frac{0.52*0.48}{n}}$

$0.01\sqrt{n} = 0.8218$

$\sqrt{n} = \frac{0.8218}{0.01}$

$\sqrt{n} = 82.18$

$\sqrt{n}^{2} = (82.18)^{2}$

$n = 6754.2$

A sample size of 6755 or higher would be appropriate.

3 0

3 years ago

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

AnnZ [28]

Answer:

The answer to your question is below

Step-by-step explanation:

Formula

Triangle's Area = 1/2 bh/2

Trapezoid's area = 1/2 (b1 + b2)h

Parallelogram's area = bh

Rectangle's area = bh

Considering the formulas, we can conclude that:

a) The first choice is true, both formulas have 1/2 in.

b) The second choice is also true, both equations are the same

c) The third choice is incorrect

d) This choice is correct, the bases are added,

e) This choice is incorrect, the sides are not added.

4 0

3 years ago

Read 2 more answers

Please help i dont understand this problem

DaniilM [7]

y=x+5

Step-by-step explanation:

The opposite of y is x axis

7 0

3 years ago

The ages of three siblings are all consecutive

ankoles [38]

Answer:

12 year old is the youngest sibling

Step-by-step explanation:

Given: The ages of three siblings are all consecutive integers.

The sum of sibling´s age is 39.

Now, finding the age of youngest sibling.

Lets assume the age of youngest sibling be "x"

As given, The ages of three siblings are all consecutive integers.

∴ Age of 2nd sibling will be $(x+1)$

Age of 3rd sibling will be $(x+2)$

next, forming an equation for the sum of sibling´s age.

⇒ $x+(x+1)+(x+2)= 39$

Opening the parenthesis

⇒ $x+x+1+x+2= 39$

⇒ $3x+3= 39$

Subtracting both side by 3

⇒ $3x= 39-3$

⇒ $3x= 36$

Dividing both side by 3

⇒ $x= \frac{36}{3}$

∴ x= 12

Subtituting the value of x to find the age of other sibling

∴Youngest sibling age= 12 years

2nd sibling age= 13 years

3rd sibling age= 14 years

Hence, The youngest sibling is 12 years old.

3 0

3 years ago