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3 years ago

What’s 1 and what’s 2 ?

Mathematics

1 answer:

katrin2010 [14]3 years ago

3 0

Answer:

For question 1:

The length of hypotenuse expression =√(8^2+9^2)

For question 2:

The expression for length a is

a=√(15^2-4^2)

Step-by-step explanation:

For question 1:

The length of hypotenuse expression =√(8^2+9^2)

For question 2:

Then expression for length a is

a=√(15^2-4^2)

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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

4 years ago

On a number line, where is the sum (-2) + (-3) located?

Ede4ka [16]

Answer: -5

Step-by-step explanation: -2 -3 = -5

4 0

3 years ago

Read 2 more answers

Find the distance between the points (1, 0) and (0, 2). √3 √5 1

GalinKa [24]

For this case we have that by definition, the distance between two points is given by:

$d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}$

We have the following points:

$(x_ {1}, y_ {1}): (1,0)\\(x_ {2}, y_ {2}): (0,2)$

Substituting we have:

$d = \sqrt {(0-1) ^ 2 + (2-0) ^ 2}\\d = \sqrt {(- 1) ^ 2 + (2) ^ 2}\\d = \sqrt {1 + 4}\\d = \sqrt {5}$

Thus, the distance between the points is $\sqrt {5}$

Answer:

$d = \sqrt {5}$

4 0

3 years ago

2{3[a-4(1-a)]-(5-a)} help me simplify the operation

AveGali [126]

Using order of operations, I simplified this down to -24+22a.

I hope this helps, and let me know if you need more explanation!

4 0

4 years ago

I need help and thank u

kogti [31]

Hello! I can help you!

12. Okay. 16 1/5 is 16.2 in decimal form. Let’s subtract both numbers. 19.8 - 16.2 = 3.6. Paloma is 3.6 seconds faster than Savannah in the 100m dash.

13. Two lengths that are within the given span of 0.08 and 0.4 are 0.22 and 0.17. 0.22 as a fraction in simplest form is 11/50 and 0.17 as a fraction in simplest form is 17/100.

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4 years ago