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rjkz [21]
2 years ago
13

A home building company routinely orders standard interior doors with a height of 80 inches. Recently the installers have compla

ined that the doors are not the standard height. The quality control inspector for the home building company is concerned that the manufacturer is supplying doors that are not 80 inches in height. In an effort to test this, the inspector is going to gather a sample of the recently received doors and measure the height. The alternative hypothesis for the statistical test to determine if the doors are not 80 inches is
Mathematics
1 answer:
Helga [31]2 years ago
3 0

Answer: Alternative Hypothesis

Ha : u ≠ 80 inches ( mean not equal to 80 inches)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean.

While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above, the mean door height is 80 inches

H0 : u = 80 inches

Ha : u ≠ 80 inches ( mean not equal to 80 inches)

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Find any relative extrema of the function. (Round your answers to three decimal places.)
Strike441 [17]

(x) = arcsec(x) − 8x

f'(x) = d/dx( arcsec(x) − 8x )

<span> 1/xsqrt( x^2 - 1) - 8</span>

f'(x) = 0

1/xsqrt( x^2 - 1) - 8 = 0

8 x sqrt (x^2-1) = 1

<span> ( 8 x sqrt (x^2-1) )^2 = 1</span>

64 x^2 ( x^2 - 1) = 1

64 x^4 - 64 x^2 =1

64 x^4 - 64 x^2 - 1 = 0

x = 1.00766 , - 1.00766

<span> x =   - 1.00766</span>

f(- 1.00766) = arcsec(- 1.00766) − 8( - 1.00766)

f( - 1.00766 ) = 11.07949

x = 1.00766

f(1.00766) = arcsec(1.00766) − 8( 1.00766)

f(1.00766 ) = -7.93790

relative maximum (x, y) = (- 1.00766 , 11.07949 ) relative minimum (x, y) = ( 1.00766 , -7.93790  )


8 0
2 years ago
A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a
True [87]

Answer:

a) t(x)  = [ √ (4)² + (x)²]/ 4    +   7/5  - x/5

b) x = 0,97 miles

c) t (min)  = 1,24 hours

Step-by-step explanation: See Annex

Figure in annex shows a clear description of the situation

Let  x be distance in miles between point P and where boat lands

A woman has to row  a distance L

L = √ (4)² + (x)²

and the part to get to the town (which she has to walk)

d = ( 7 -  x)

But we are required to give time as a function of x

distance   =  speed * time     ⇒   t  = distance / speed

Therefore

t(x)  = [ √ (4)² + (x)²]/ 4   +   ( 7  -  x  ) / 5

t(x)  = [ √ (4)² + (x)²]/ 4    +   7/5  - x/5

Taking derivatives both sides of the equation

t¨(x)   = ( 2x)*4 / 16√ (4)² + (x)²]   -  5/25  

t¨(x)   = x/  2√ (4)² + (x)²]  - 1/5

t¨(x)   = 0      x/  2√ (4)² + (x)²]  - 1/5   =  0

[ 5 x  -  2√ (4)² + (x)²]  =  0       ⇒   5x    =  2√ (4)² + (x)²]   or

   25 x² =  4  (  4 +   x²)

   25 x² = 16  +   8x²

  17x²   =   16

  x²  =   16/17      

   x²   =  0,941

  x = 0,97 miles  

And the distance walking to get to town

d =  7  -  x       d =   7  -  0,97

d  = 6,03 miles

The least travel time  is   t(x)  = [ √ (4)² + (x)²]/ 4    +   7/5  - x/5  

t (min)  =  √ 16 +  0,94) /4   +  1,4  - 0,97/5

t (min)  = 1,03  +  1,4  - 0,194

t (min)  = 1,24 hours

7 0
2 years ago
ΔABC is dilated using a scale factor of 12 to produce ΔA'B'C'. Select all of the statements that apply to the transformation.
GalinKa [24]

Answer:

Options (3) and (6)

Step-by-step explanation:

ΔABC is a dilated using a scale factor of \frac{1}{2} to produce image triangle ΔA'B'C'.

Since, dilation is a rigid transformation,

Angles of both the triangles will be unchanged or congruent.

m∠A = m∠A' and m∠B = m∠B'

Since, sides of ΔA'B'C' = \frac{1}{2} of the sides of ΔABC

Area of ΔA'B'C' = \frac{1}{2}(\text{Area of triangle ABC})

Area of ΔABC > Area of ΔA'B'C'

Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.

ΔABC ~ ΔA'B'C'

Therefore, Option (3) and Option (6) are the correct options.

3 0
2 years ago
7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the account after 24 years, to t
Amanda [17]

Answer:

A = $18,326.00

(assuming simple interest)

Step-by-step explanation:

Assuming simple interest, the following formula applies:

final amount = (principal amount) x [1  + (annual rate)(time elapsed) ]

or

A = P (1 + rt)

in our case,

P = $7,700

r = 5.75% = 0.0575

t = 24 years

hence,

A = 7700 [ 1 + (0.0575)(24)]

A = 7700 ( 1 + 1.38)

A = 7700 x 2.38

A = $18,326.00  

4 0
2 years ago
Brandon bought 21 chicken wings for $39.90. How much would it cost for 15 wings?
Pachacha [2.7K]

Answer:

$28.50

Step-by-step explanation:

21 chicken wings= $39.90

1 chicken wing= 39.90÷21= $1.90

15 chicken wings= 15×1.90= $28.50

4 0
2 years ago
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