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zzz [600]
3 years ago
9

A rectangular auditorium seats 1302 people. The number of seats in each row exceeds the number of rows by 11. Find the number of

seats in each row
Mathematics
1 answer:
sveticcg [70]3 years ago
8 0
Number of seats = 42

Seats per row x row = 1302
s x r = 1302

rows + 11 = seats per row
r + 11 = s

s x r = 1302
(r + 11) x r = 1302
r^2 + 11r = 1302
r^2 + 11r - 1302 = 0
(r + 42) x (r - 31) = 0
r = -43 or 31

Cannot have negative rows so the number of rows is 31, and the number of seats per row is 31 + 11 = 42

Check: 31 x 42 = 1302 :)
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There are 4 red balls, 6 white balls, and 3 green balls in a bag. If one ball is drawn from the bag at random, what is the proba
Yuri [45]

Answer:

D.7/13

Step-by-step explanation:

Hope this helps :))

3 0
3 years ago
Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random
Katyanochek1 [597]

Answer:

a) Null hypothesis: \mu_A =\mu_B =\mu C

Alternative hypothesis: \mu_i \neq \mu_j, i,j=A,B,C

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5  

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=df_{within}=k-1=3-1=2 where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=3*6-3=15.

And the total degrees of freedom would be df=N-1=3*6 -1 =15

The mean squares between groups are given by:

MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166

And the mean squares within are:

MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544

And the F statistic is given by:

F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326

And the p value is given by:

p_v= P(F_{2,15} >11.326) = 0.00105

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

b) (\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}

The degrees of freedom are given by:

df = n_B +n_C -2= 6+6-2=10

The confidence level is 99% so then \alpha=1-0.99=0.01 and \alpha/2 =0.005 and the critical value would be: t_{\alpha/2}=3.169

The confidence interval would be given by:

(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321

(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part a  

Null hypothesis: \mu_A =\mu_B =\mu C

Alternative hypothesis: \mu_i \neq \mu_j, i,j=A,B,C

If we assume that we have 3 groups and on each group from j=1,\dots,6 we have 6 individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5  

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=df_{within}=k-1=3-1=2 where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=3*6-3=15.

And the total degrees of freedom would be df=N-1=3*6 -1 =15

The mean squares between groups are given by:

MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166

And the mean squares within are:

MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544

And the F statistic is given by:

F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326

And the p value is given by:

p_v= P(F_{2,15} >11.326) = 0.00105

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

Part b

For this case the confidence interval for the difference woud be given by:

(\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}

The degrees of freedom are given by:

df = n_B +n_C -2= 6+6-2=10

The confidence level is 99% so then \alpha=1-0.99=0.01 and \alpha/2 =0.005 and the critical value would be: t_{\alpha/2}=3.169

The confidence interval would be given by:

(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321

(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345

7 0
3 years ago
Which expression has a positive quotient?
svp [43]

Answer:

Only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.

Option A is correct.

Step-by-step explanation:

We will solve to find out Which expression has a positive quotient.

We know the division rule: \frac{-a}{-b}=\frac{a}{b} and \frac{-a}{b}=\frac{-a}{b}

We will use these rules

1) Negative three-fourths divided by Negative two-thirds

=\frac{-\frac{3}{4} }{-\frac{2}{3} }\\=-\frac{3}{4}\times -\frac{3}{2}\\=\frac{9}{8}

The quotient is positive.

2) Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth

\frac{-\frac{1}{8} }{3\frac{1}{5} }\\=\frac{-\frac{1}{8} }{\frac{16}{5} }\\=-\frac{1}{18} \times \frac{5}{16}\\=-\frac{5}{288}

The quotient is negative.

3) 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth

\frac{2\frac{2}{7} }{-\frac{1}{5} }\\= \frac{\frac{16}{7} }{-\frac{1}{5} }\\=\frac{16}{7} \times -5\\=-\frac{80}{7}

The quotient is negative.

4) Negative 6 divided by Five-thirds

\frac{-6}{\frac{5}{3} }\\=-6 \times \frac{3}{5}\\=-\frac{18}{5}

The quotient is negative.

So, only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.

Option A is correct.

4 0
3 years ago
Read 2 more answers
Your friend has a bag of 20 marbles. Seven
Elis [28]

Answer:

20%

Step-by-step explanation:

First, I added them up. From the things we know, blue, red, green, yellow combined equals 16 marbles. 20-16 equals 4. So there are 4 white marbles. 4/20 times 5 equals 20/100. So the percent of the marbles that are white is 20%.

6 0
3 years ago
Read 2 more answers
Pls help will give Brainlyist
kvasek [131]

Answer:

B

Step-by-step explanation:

7 0
3 years ago
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