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3 years ago

7

the angle of elevation of a jet plane from a point P on the ground is 60 degree after a flight of 15 seconds the angle of elevat

ion changes to 30 degree if the jet plane is flying at a constant height of 1500 root 3 metre find the speed of the jet plane

1 answer:

Nana76 [90]3 years ago

5 0

Answer:

200m/s

Step-by-step explanation:

Please see the attached pictures for full solution.

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The tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm2 and a stand

Elanso [62]

Answer:

95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

Yes, this data suggest that the tensile strength was changed after the adjustment.

Step-by-step explanation:

We are given that the tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm 2 and a standard deviation of 2.15.

A machine was recently adjusted and a sample of 50 items were taken to determine if the mean tensile strength has changed. The mean of this sample is 74.28. Assume that the standard deviation did not change because of the adjustment to the machine.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean strength of 50 items = 74.28

$\sigma$ = population standard deviation = 2.15

n = sample of items = 50

$\mu$ = population mean tensile strength after machine was adjusted

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level of

significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

<u><em>95% confidence interval for</em></u> $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $74.28-1.96 \times {\frac{2.15}{\sqrt{50} } }$ , $74.28+1.96 \times {\frac{2.15}{\sqrt{50} } }$ ]

= [73.68 kg/mm2 , 74.88 kg/mm2]

Therefore, 95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

<em>Yes, this data suggest that the tensile strength was changed after the adjustment as earlier the mean tensile strength was 72 kg/mm2 and now the mean strength lies between 73.68 kg/mm2 and 74.88 kg/mm2 after adjustment.</em>

8 0

3 years ago

Answer the following.

Assoli18 [71]

Answer:

40000

Step-by-step explanation:

Simple interest (I) is calculated as

I = $\frac{PRT}{100}$

P is the amount borrowed , R is the interest and T the time in years

Here I = 2000 , R = 5 and T = 1 with P to be found , then

2000 = $\frac{P(5)(1)}{100}$ ( multiply both sides by 100 )

5P = 200000 ( divide both sides by 5 )

P = 40000

5 0

2 years ago

Read 2 more answers

Gnom [1K]

Problem 3: Let x = price of bag of pretzels Let y = price of box of granola bars
We have Lesley's purchase: 4x+2y=13.50
And Landon's: 1x+5y=17.55
We can use the elimination method. Let's negate Landon's purchase by multiplying by -1. -1x-5y=-17.55
We add this four times to Lesley's purchase to eliminate the x variable.
2y-20y=13.50-70.2
-18y=-56.7
y = $3.15 = Price of box of granola bars

Plug back into Landon's purchase to solve for pretzels.
x+5*3.15=17.55
x+15.75=17.55
x = $1.80 = price of bag of pretzels

Problem 4.
Let w = number of wood bats sold
Let m = number of metal bats sold

From sales information we have: w + m = 23
24w+30m=606
Substitution works well here. Solve for w in the first equation, w = 23 - m, and plug this into the second.
24*(23-m)+30m=606
552-24m+30m=606
6m=54
m=9 = number of metal bats sold
Therefore since w = 23-m, w = 23-9 = 14. 14 wooden bats were sold.

6 0

3 years ago

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A+b=77,a-b=13 care sun nr

STALIN [3.7K]

It's a simultaneous equation:
Steps:
1.Number the equations..

a+b=77 -1
a-b=13 -2

2. Choose what variable you want to use. In this case I would use the "b". Since the signs in front of the "b's" are different, add the two equations together

a + b = 77
+ + +
a (-b) = 13

Which gives;
2a = 90

Then solve to find a:
2a=90
a= 90/2
a=45

3.Then plug the "a" value into any of the original equations to find the "b" value. I would use equation 1 since the all the variables are positive.

a + b = 77
(45) + b = 77
b=77-45
b=32

4.Solution

a=45
b=32

3 0

3 years ago

HELP PLEASE! Thanks :)

Alex Ar [27]

Pi. I don't know what the square root is doing there because it has no number under it.

7 0

3 years ago

Read 2 more answers