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Citrus2011 [14]
3 years ago
7

A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited

the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. [You may find it useful to reference the t table.] a. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Mathematics
1 answer:
morpeh [17]3 years ago
5 0

Answer:

a: 28 < µ < 34

Step-by-step explanation:

We need the mean, var, and standard deviation for the data set.  See first attached photo for calculations for these...

We get a mean of 222/7 = 31.7143

and a sample standard deviation of: 4.3079

We can now construct our confidence interval.  See the second attached photo for the construction steps.

They want a 90% confidence interval.  Our sample size is 7, so since n < 30, we will use a t-score.  Look up the value under the 10% area in 2 tails column, and degree of freedom is 6 (degree of freedom is always 1 less than sample size for confidence intervals when n < 30)

The t-value is: 1.943

We rounded down to the nearest person in the interval because we don't want to over estimate.  It said 28.55, so more than 28 but not quite 29, so if we use 29 as the lower limit, we could over estimate.  It's better to use 28 and underestimate a little when considering customer flow.

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Architects make scale models of buildings to present their ideas to clients. If an
MaRussiya [10]

The area of the model is 80 square foot

Step-by-step explanation:

Let the area of the house model be 'a'

The scale = 1:50

The area of the house= 4000 square foot

Area of the model =4000/50

a = 80 square foot

The area of the model is 80 square foot

5 0
3 years ago
How many different perfect cubes are among the positive actors of 2021^2021
9966 [12]

Answer:

hope this helps :D

Step-by-step explanation:

Perfect cube factors:

If a number is a perfect cube, then the power of the prime factors should be divisible by 3.

Example 1:Find the number of factors of293655118 that are perfect cube?

Solution: If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube 4x3x2x3=72

Perfect square and perfect cube

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.

Example 2: How many factors of 293655118 are both perfect square and perfect cube?

Solution: If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are 2x2x1x2=8

Example 3: How many factors of293655118are either perfect squares or perfect cubes but not both?

Solution:

Let A denotes set of numbers, which are perfect squares.

If a number is a perfect square, then the power of the prime factors should be divisible by 2. Hence perfect square factors must have

2(0 or 2 or 4 or 6 or 8)—– 5 factors

3(0 or 2 or 4 or 6)  —– 4 factors

5(0 or 2or 4 )——- 3 factors

11(0 or 2or 4 or6 or 8 )— 5 factors

Hence, the total number of factors which are perfect square i.e. n(A)=5x4x3x5=300

Let B denotes set of numbers, which are perfect cubes

If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube i.e. n(B)=4x3x2x3=72

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are i.e.n(A∩B)=2x2x1x2=8

We are asked to calculate which are either perfect square or perfect cubes i.e.

n(A U B )= n(A) + n(B) – n(A∩B)

=300+72 – 8

=364

Hence required number of factors is 364.

8 0
3 years ago
Suppose a squad patio has an area of 441 square feet. Use the formula for the area of a square to find the length of each side o
Sonja [21]
For a square: A=s^{2}

Solve for the length of a side by taking the square root of both sides:
\sqrt{A}=\sqrt{s^{2}}
\sqrt{A}=s

Now we can substitute known values:
s=\sqrt{A}
s=\sqrt{441ft^{2}}
s=21ft

8 0
3 years ago
Rewrite the function in the form of g(x)=a/x-h+k<br> 1. g(x)=7x+17/x+2<br><br> 2. g(x)=5x-7/x-3
butalik [34]

Answer:

Step-by-step explanation:

hello :

the form :  g(x)=a/(x+h)+k

1 )  <u>g(x)=7x+17/x+2 :</u>

you can write : 7x+17 = 7(x+2)+3

so : g(x) =(7(x+2)+3)/(x+2) = 7(x+2)/(x+2) +3/(x+2)

g(x) = 7+ 3/(x+2)    or g(x) = 3/(x+2) +7 compare with g(x)=a/(x+h)+k

a=3  and k=7  and h=2

2)   <u>g(x)=5x-7/x-3 :</u>

you can write same method for 1   ..... here is other method :

g(x)=a/(x-h)+k = (a+k(x-h))/(x-h)

g(x) = (kx+a-kh)/(x-h)     h=3

so : k=5 and  a-kh = -7

a-(5)(3)=-7       a = 8

g(x) =8/(x-3) +5

7 0
2 years ago
There are 97 students in South High School. South High School offers only Chinese and Spanish. There are 5 more students in Chin
Viefleur [7K]

Answer:

5

Step-by-step explanation:

Spanish: 46

Chinese: 51

Both languages: 46 - 41 = 5

Hope this helps

8 0
1 year ago
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