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3 years ago

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Mathematics

1 answer:

Artyom0805 [142]3 years ago

6 0

The expression is not simplified, because both the numerator and the denominator can be divided evenly

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Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the ca

KatRina [158]

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

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

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean breaking weight = 768.2 lb

s = sample standard deviation = 15.1 lb

n = sample of cables = 45

$\mu$ = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

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

P(-2.02 < $t_4_4$ < 2.02) = 0.95 {As the critical value of t at 44 degree

of freedom are -2.02 & 2.02 with P = 2.5%}

P(-2.02 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.02) = 0.95

P( $-2.02 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }$ , $768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }$ ]

= [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

3 0

3 years ago

Please can help me with this problem.Thanks.

ElenaW [278]

The answer is c. 8m tell me if I did something wrong

8 0

4 years ago

Read 2 more answers

Please help I’m struggling on this question.

timofeeve [1]

Answer: $\frac{2(y^2-4y+40)}{(y-8)(y+4)}$

Step-by-step explanation:

To solve this problem, we want to make sure the denominators are the same on both fractions. Once they are equal, we can dd them together.

$\frac{y+4}{y-8} +\frac{y-8}{y+4}$ [multiply first fraction by y+4 and second by y-8]

$\frac{(y+4)(y+4)}{(y-8)(y+4)} +\frac{(y-8)(y-8)}{(y-8)(y+4)}$ [distribute by FOIL]

$\frac{y^2+8y+16}{(y-8)(y+4)} +\frac{y^2-16y+64}{(y-8)(y+4)}$ [add numerator]

$\frac{y^2+8y+16+y^2-16y+64}{(y-8)(y+4)}$ [combine like terms]

$\frac{2y^2-8y+80}{(y-8)(y+4)}$ [factor out 2 from numerator]

$\frac{2(y^2-4y+40)}{(y-8)(y+4)}$

Now we know that $\frac{2(y^2-4y+40)}{(y-8)(y+4)}$ is the factored form after adding.

5 0

3 years ago

5 + (-3) is units from 5 in which direction

kakasveta [241]

Answer:

Step-by-step explanation:

That would be "3 units to the left of x = 5."

5 0

3 years ago

Read 2 more answers

Solve the following equation for x: 2x – 3y = 6.

frez [133]

Answer:

x = 3/2 y + 3

Step-by-step explanation:

2x – 3y = 6.

Add 3y to each side

2x – 3y+3y = 3y+6.

2x = 3y+6

Divide each side by 2

2x/2 = 3y/2 + 6/2

x = 3/2 y + 3

4 0

3 years ago

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