A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm.

The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.

tatuchka [14]

Answer:

a)Null hypothesis:- H₀: μ> 500

Alternative hypothesis:-H₁ : μ< 500

b) (5211.05 , 5411.7)

95% lower confidence bound on the mean.

c) The test of hypothesis t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Step-by-step explanation:

Step :-1

Given a random sample of 15 devices is selected in the laboratory.

size of the small sample 'n' = 15

An average life of 5311.4 hours and a sample standard deviation of 220.7 hours.

Average of sample mean (x⁻) = 5311.4 hours

sample standard deviation (S) = 220.7 hours.

Step :- 2

a) Null hypothesis:- H₀: μ> 500

Alternative hypothesis:-H₁ : μ< 500

Level of significance :- α = 0.95 or 0.05

b) The test statistic

$t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n-1} } }$

$t = \frac{5311.4 - 500}{\frac{220.7}{\sqrt{15-1} } }$

t = 5.826

The degrees of freedom γ= n-1 = 15-1 =14

tabulated value t =1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

calculated value t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Null hypothesis is rejected at 95% confidence on the mean.

C) The 95% of confidence limits

$(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } ,x^{-} + t_{0.05}\frac{S}{\sqrt{n} } )$

substitute values and simplification , we get

$(5311.4 - 1.761 \frac{220.7}{\sqrt{15} } ,5311.4 +1.761\frac{220.7}{\sqrt{15} } )$

(5211.05 , 5411.7)

95% lower confidence bound on the mean.

5 0

2 years ago

Is 1/3 more than 2/6

nevsk [136]

No they are equal, reduce 2/6 to get 1/3

5 0

3 years ago

Read 2 more answers

I really suck at math plz help me

inysia [295]

You would have to have common demoniators to add.
8/10 can be turn into 80/100 by multiplying the denominator and nominator by ten
75/100+80/100, you add the nominators ONLY, dont change the denominator.
75+80=155

so your answer would be 155/100

4 0

3 years ago

Read 2 more answers

Every that is fully readable

n200080 [17]

10)
60in=60in × (1ft/12in) = 5ft
30in= 30in × (1ft/12in) = 2.5ft
12in = 12in × (1ft/12in) = 1ft
answer is = 5ft × 2.5ft× 1ft =12.5 ft^3 = a

11)
dozen = 12 hammers
12 hammers = 20 pounds
therefore 1 hammer= 20/12 = 1.6666 lb

21 hammers ×1.666 = 35 = c

12)
convert qt to gal
600 gal × 4 qt/gal = 2400 qt

2400 qt ÷ 120 qt/min
=20 min = d

13)
Carla is 12
rob is 12+5= 17
cousin is 12-7 = 5

12+17+5= 34 =a

15)
convert 60ft into yards
60 ft × 0.333 yd/ft =20 yd

diameter = 20 yd

area of circle = (pi/4)×d^2
(pi/4)×20^2= 314.16 = b

8 0

3 years ago

Write an equation of a line that is parallel to y=2x-5 that passes through the point (2,6).

inessss [21]

Answer: Parallel lines have the same slope

y = 2x +b

Use the given point (2, 5)

5 = 2(2) +b

b = 5 -4 = 1

The equation of the line is

y = 2x +1

Note general form of the slope-intercept form of a line is y = mx +b, where m is the slope and b is the y-axis intercept

Step-by-step explanation:

3 0

2 years ago