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Kruka [31]
2 years ago
13

An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before

they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values?a. 8.9 and 18.9
b. 12.2 and 14.2
c. 14.1 and 22.1
d. 16.6 and 21.4
Mathematics
1 answer:
joja [24]2 years ago
8 0

Answer:

option (d) 16.6 and 21.4

Step-by-step explanation:

Data provided in the question:

The mean life for a particular use before they failed = 19.0 hours

The distribution of the lives approximated a normal distribution

The standard deviation of the distribution = 1.2 hours

To find:

The values between which 95.44 percent of the batteries failed

Now,

In Normal distribution, the approximately 95% ( ≈ 95.44% of all values ) falls within 2 standard deviations of the mean

Therefore,

Upper limit = Mean + 2 × standard deviation

⇒ Upper limit = 19.0 + 2 × 1.2 = 21.4

Lower  limit = Mean - 2 × standard deviation

⇒ Lower  limit = 19 - 2 × 1.2 = 16.6

Hence,

the answer is option (d) 16.6 and 21.4

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BE/BC=BD/BA

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4 0
2 years ago
From a point 100 m from a building the angles of elevation of the top and bottom of a flagpole atop a building are 54.5 degrees
AnnZ [28]

Answer:60ft

Step-by-step explanation:The height of the flagpole is approximately  

60

feet.

Explanation:

Always try to draw a diagram.

enter image source here

We know that there is a right angle between the ground and the building. Therefore, we can use the 3 basic trig ratios instead of the sine or cosine law to solve this problem.

Since the angle in the corner of the larger right triangle measures  

42

˚

, the top angle in this triangle measures  

180

˚

−

90

˚

−

42

˚

=

48

˚

.

By basic trig ratios, we can find the height of the building with the flag pole on top, call it  

H

.

tan

42

˚

1

=

H

500

H

=

500

tan

42

˚

I would keep it in exact form until the last step.

We now devise an expression for the height of the building (without the flag pole). Call it  

a

tan

38

˚

1

=

a

500

a

=

500

tan

38

˚

We can now state that

h

=

H

−

a

h

=

500

tan

42

˚

−

500

tan

38

˚

h

≈

59.559

≈

60

feet

Hopefully this helps!

Answer link

EET-AP

Apr 10, 2017

The flagpole is  

60

f

t

in height to the nearest foot.

Explanation:

1) The flagpole is on top of a building.

2)Angles of elevation both measured from point  

500

f

t

from building

3) Angle of elevation to the top of building is  

38

d

e

g

4) Angle of elevation to the top of flagpole is  

42

d

e

g

The information above will provide us with two right angle triangles, one smaller one inside a larger one.

Both will have a base of  

500

f

t

.

The smaller triangle will have a base angle  

β

of  

38

deg opposite the  

90

deg, and the larger triangle will have a base angle  

β

of  

42

deg.

From this information we can find the heights of the building and the building + pole using the definition of the tangent of the two base angles  

β

:

tan

(

β

)

=

o

p

p

a

d

j

where the  

o

p

p

is the height and the  

a

d

j

is the  

500

f

t

o

p

p

(

b

u

i

l

d

)

=

tan

(

38

)

⋅

(

500

f

t

)

=

390.6

f

t

=

height of building

o

p

p

(

f

l

a

g

)

=

tan

(

42

)

⋅

(

500

f

t

)

=

450.2

f

t

=

height of building + pole

Then to the nearest foot the height of the flagpole is:

450.2

f

t

−

390.6

f

t

=

60

f

t

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