What number must be added to both sides of this equation in order to "complete the square"?

A middle schooler took all the 6th grader on a field trip to see ballet. The students filled up 570 seats, which was 95% of the

Musya8 [376]

The total number of seats in the theater is 600 seats, if the students filled up 570 seats, which was 95% of the total number of seats in the theater.

Step-by-step explanation:

The given is,

Seats filled by students are 570 seats

Which is 95% of the total number of seats in the theater

Step: 1

Let, x - Total number of seats available in theater

Percentage of seats filled, y= 95%

Seats filled by students = 570

Formula to calculate total number of seats in theater,

95% of seats $= \frac{95}{100}( x)$

570 = $0.95 (x)$

x = $\frac{570}{0.95}$

= 600

x = 600 seats

Step: 2

Check for solution,

5% of seats $= \frac{5}{100} (600)$

= (0.05 × 600)

= 30 seats

Total no. of seats = 5% of seats + 95% of seats

= 30 + 570

600 = 600

Result:

The total number of seats in the theater is 600 seats.

7 0

3 years ago

A researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic

Delvig [45]

Answer:

90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

Step-by-step explanation:

We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.

Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean iron concentration = 0.802 cc/cubic meter

s = sample standard deviation = 0.093

n = number of water samples = 27

$\mu$ = population mean

Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.706 < $t_2_6$ < 1.706) = 0.90 {As the critical value of t at 26 degree of

freedom are -1.706 & 1.706 with P = 5%}

P(-1.706 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.706) = 0.90

P( $-1.706 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.706 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ]

= [ $0.802 -1.706 \times {\frac{0.093}{\sqrt{27} }$ , $0.802 +1.706 \times {\frac{0.093}{\sqrt{27} }$ ]

= [0.771 , 0.832]

Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

4 0

3 years ago

Help Nxhxhxhdhdhdbsbsbdhdhd

Annette [7]

Your answer is number 2 it is 38.2 because 26 out of 68 is a percentage of 38.24

3 0

2 years ago

IL 8x-9 5x-3 What’s x

shepuryov [24]

Step-by-step explanation:

8x-9=5x-3

Move any equation to the opposite side. I'll use the left this time

$8x - 8x - 9 + 9 = 5x - 8x - 3 + 9$

$0 = - 3x + 6$

move 6 to opp side

$- 3x = - 6$

$\frac{ - 6 = - 3x}{ - 3}$

$x = 2$

3 0

3 years ago

When solving a system of equations by substitution, what is meant by a useless result (12=12)?. a.. parallel lines. c.. inconsis

Montano1993 [528]

When solving a system of equations by substitution, meant by a useless result of (12=12) is no solution. The answer is letter B, the equation has no solution because it can have infinite solution. I hope the answer helps, thank you for posting your question here.

4 0

3 years ago

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