The left and right page numbers on an

The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation σ = 25 hours. A random sam

irina [24]

Answer: a) (1008.34,1019.658) b) (1009.24,1018.76)

Step-by-step explanation:

Since we have given that

n = 75

mean = 1014 hours

Standard deviation = 25 hours

At 95% two sided , z = 1.96

So, confidence interval would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.96\dfrac{25}{\sqrt{75}}\\\\=1014\pm 5.658\\\\=(1014-5.658,1014+5.658)\\\\=(1008.34,1019.658)$

(b) Construct a 95% lower confidence bound on the mean life.

z = 1.65

So, confidence interval would be

$\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.65\times \dfrac{25}{\sqrt{75}}\\\\=1014\pm 4.76\\\\=(1014-4.76,1014+4.76)\\\\=(1009.24,1018.76)$

Hence, a) (1008.34,1019.658) b) (1009.24,1018.76)

4 0

3 years ago

6:20=9:x=x:10=x:60=16:x=12:x

ivolga24 [154]

6:20=9:30=3:10=18:60=16:160/3=12:40

Step-by-step explanation:

The question requires you to find value of x in the ratios given;

Start with the first pair

6:20 = 9:x

6/20 =9/x

6x=20*9

6x=180

x=180/6=30 ⇒⇒ 6:20 = 9:30

The second pair after replacing the value of x=30 will be

9:30 = x:10

9/30=x/10

90=30x

90/30 =x

3=x⇒⇒ 9:30 = 3:10

The third pair after replacing value of x=3 will be

3:10 =x:60

3/10 =x/60

180=10x

180/10 =x

18=x ⇒⇒ 3:10 = 18:60

The fourth pair after replacing value of x=18 will be;

18:60 = 16:x

18/60 = 16/x

18x=16*60

x= (16*60)/18 =160/3

x= 160/3 ⇒⇒⇒ 18:60 = 16: 160/3

The firth pair after replacing value of x=160/3 will be;

16: 160/3 =12:x

16x= 160/3 *12

16x = 160 * 4

x= (160 *4 )/16

x=40

⇒⇒ 16: 160/3 = 12: 40

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Ratios and proportions :brainly.com/question/9512748

Keywords : ratio, value of x, proportion

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6 0

3 years ago

What is the shaded portion of the circle

blagie [28]

Answer:

$(5\pi-11.6)\ ft^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector minus the area of the triangle

step 1

Find the area of the circle

the area of the circle is equal to

$A=\pi r^{2}$

we have

$r=5\ ft$

substitute

$A=\pi (5)^{2}$

$A=25\pi\ ft^{2}$

step 2

Find the area of the sector

we know that

The area of the circle subtends a central angle of 360 degrees

so

by proportion find out the area of a sector by a central angle of 72 degrees

$\frac{25\pi}{360}=\frac{x}{72}\\ \\x=72*25\pi /360\\ \\x=5\pi\ ft^{2}$

step 3

Find the area of triangle

The area of the triangle is equal to

$A=\frac{1}{2}(2.9+2.9)(4)= 11.6\ ft^{2}$

step 4

Find the area of the shaded region

Subtract the area of the triangle from the area of the sector

$(5\pi-11.6)\ ft^{2}$

8 0

3 years ago

What is the value of f(5) ?

qwelly [4]

Answer:

243

Step-by-step explanation:

6 0

2 years ago

Which expression represents h(x)?

blsea [12.9K]

Answer:

(g-f)x is the answers for the question

Step-by-step explanation:

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3 0

3 years ago