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3 years ago

14

The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is appointing. If there are 15

eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed

1 answer:

skad [1K]3 years ago

7 0

Answer: There are 360360 ways to appoint the members of the cabinet.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 15

Number of spots available = 5

We need to find the number of different ways the members can be appointed where rank matters

For this we will use "Permutations":

So, the required number of different ways in choosing the members for appointment is given by

$^{15}P_5=360360$

Hence, there are 360360 ways to appoint the members of the cabinet.

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The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batterie

Fittoniya [83]

Answer:

The confidence interval is $25.16 < \mu < 26.85$

Step-by-step explanation:

From the question we are given a data set

25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is

$\= x = \frac{\sum x_i}{n}$

where is the sample size with values n = 10

$\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}$

$\= x = 26$

The standard deviation is evaluated as

$\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }$

substituting values

$= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }$

$\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }$

$\sigma = 1.625$

The confidence level is given as 90% hence the level of significance is calculated as

$\alpha = 100 -90$

$\alpha =10$ %

$\alpha = 0.10$

Now the critical values of $\frac{\alpha }{2}$ is obtained from the normal distribution table as

$Z_{\frac{\alpha }{2} } = 1.645$

The reason we are obtaining the critical values of $\frac{\alpha }{2}$ instead of $\alpha$ is because we are considering two tails of the area under the normal curve

The margin of error is evaluated as

$MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

substituting values

$MOE = 1.645 * \frac{1.625 }{\sqrt{10} }$

$MOE = 0.845$

The 90%, two sided confidence interval is mathematically evaluated as

$\= x - MOE < \mu < \= x + MOE$

$26 - 0.845 < \mu < 26 + 0.845$

$25.16 < \mu < 26.85$

Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours

5 0

3 years ago

Solve for y 5x-10y=20

MakcuM [25]

5 (x-2y)=20
x-2y=20/5
x-2y =4
-2y=4-x
y=- 4-x/2
ans -4-x/2

3 0

4 years ago

Solve the equation for k.<br> 4k - 2z = 8

lozanna [386]

4k-2z=8

Move -2z to the other side. Sign changes from -2z to + 2z

4k-2z+2z= 8+2z

4k= 8+2z

Divide by 4 for 4k and 8+2z

4k/4= 8/4+ 2z/4

k= 2 +1/2z

Answer: k= 2 +1/2z

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3 years ago

Read 2 more answers

What is cos 45º?<br>See picture for more details

madreJ [45]

Answer:

C. 1/√2

Step-by-step explanation:

cos∅ is adjacent over hypotenuse:

cos45° = 1/√2

cos45° = √2/2

Alternatively, if you learned and memorized your unit circle, cos(π/2) = √2/2

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4 years ago

Read 2 more answers

katrin2010 [14]

Answer:

-45.211
210.77
₹262.94
124.44 kg

Step-by-step explanation:

Given:

89.9 from 44.689

789.03 from 999.8

₹ 789.56 from ₹ 1052. 5

15.56 kg from 28 kg

Computation:

89.9 from 44.689

44.689 - 89.9

-45.211

789.03 from 999.8

999.8 - 789.03

210.77

₹ 789.56 from ₹ 1052.5

₹ 1052.5 - ₹ 789.56

₹262.94

15.56 kg from 28 kg

28 kg - 15.56 kg

124.44 kg

7 0

3 years ago