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Tasya [4]
2 years ago
6

In a regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample points in the sample space

S for the number of possible orders at the conclusion of the contest fora. all 8 finialist.b. the first 3 positions.
Mathematics
1 answer:
posledela2 years ago
5 0

Answer: a.) 40320

b.) 336

Step-by-step explanation:

since we have 8 possible positions, with 8 different candidates, then there are 8 possible ways of arranging the first position, 7 possible ways of arranging the Second position, 6 ways of arranging the 3rd position, 5 possible ways od arranging the 4th position, 4 possible ways of arranging the 5th position, 3 possible ways of arranging the 6th position, 2 possible ways of arranging the 7th position and just one way of arranging the 8th position since we have only one person left.

Hence, the Number of possible sample space for different 8 positions is by multiplying all the number of ways we have in our sample space which becomes:

8*7*6*5*4*3*2*1 = 40320.

b.) By the sample space we have, since we've been asked ti arrange for only the firat 3 positions, then we multiply just for the first 3ways of choosing the positions, this becomes:

8*7*6 = 336

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Employees in the marketing department of a large regional restaurant chain are researching the amount of money that households i
kap26 [50]

Answer:

The <em>z</em>-score for the group "25 to 34" is 0.37 and the <em>z</em>-score for the group "45 to 54" is 0.25.

Step-by-step explanation:

The data provided is as follows:

25 to 34              45 to 54

  1329                    2268

  1906                    1965

 2426                     1149

  1826                     1591

  1239                    1682

   1514                     1851

  1937                     1367

  1454                    2158

Compute the mean and standard deviation for the group "25 to 34" as follows:

\bar x=\frac{1}{n}\sum x=\frac{1}{8}\times [1329+1906+...+1454]=\frac{13631}{8}=1703.875\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 1086710.875}=394.01

Compute the <em>z</em>-score for the group "25 to 34" as follows:

z=\frac{x-\bar x}{s}=\frac{1851-1703.875}{394.01}=0.3734\approx 0.37

Compute the mean and standard deviation for the group "45 to 54" as follows:

\bar x=\frac{1}{n}\sum x=\frac{1}{8}\times [2268+1965+...+2158]=\frac{14031}{8}=1753.875\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 1028888.875}=383.39

Compute the <em>z</em>-score for the group "45 to 54" as follows:

z=\frac{x-\bar x}{s}=\frac{1851-1753.875}{383.39}=0.25333\approx 0.25

Thus, the <em>z</em>-score for the group "25 to 34" is 0.37 and the <em>z</em>-score for the group "45 to 54" is 0.25.

8 0
2 years ago
The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a f
d1i1m1o1n [39]

Answer:

Yes, the relationship between x and y is a non-linear function.

Step-by-step explanation:

Given the table

Edge Length, x            Surface Area, y

1                                             6

2                                            24

3                                            54

4                                             96

  • The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

  • Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

4 0
2 years ago
Mr Thomson wants to protect his garage by installing a flood barrier.He connects two barriers side by side.Each barrier is 9 fee
disa [49]

Answer:

  36 square feet

Step-by-step explanation:

The area of one barrier is the product of the given dimensions:

  (9 ft)(2 ft) = 18 ft²

Two such barriers will have twice the area: 36 ft².

4 0
2 years ago
Find c, yenvelope(x,t), and ycarrier(x,t). express your answer in terms of a, k1, k2, x, t, ω1, and ω2. separate the three parts
steposvetlana [31]

Answer:

C,Y_{envelope}(x,t), Y_{carrier}(x,t)=2A, \cos ((k_1-k_2)x/2-(\omega_1 -\omega_2)t / 2 ) , \sin ((k_1+k_2)x / 2 - (\omega_1 +\omega_2)t / 2 )

Step-by-step explanation:

Given

Y_1(x,t)=A \sin(K_1x- \omega _1 t)\\\\Y_2(x,t)=A \sin(K_2x- \omega _2 t)

using a trigonometrical identity

sin p + sin q = 2 sin ( p+q/2) cos ( p-q/2)

and here the condition is

the choice is in between sinax and cosax

where a > b

so we get using above equation

C,Y_{envelope}(x,t), Y_{carrier}(x,t)=2A, \cos ((k_1-k_2)x/2-(\omega_1 -\omega_2)t / 2 ) , \sin ((k_1+k_2)x / 2 - (\omega_1 +\omega_2)t / 2 )

4 0
2 years ago
The physician orders 1500 flu injections. There were 300 shots given in September, 450 shots given in October, and 665 shots giv
GalinKa [24]

Answer:

94.33

Step-by-step explanation:

add up all numbers then input into a percentage calculator

7 0
2 years ago
Read 2 more answers
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