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frosja888 [35]
1 year ago
14

The spring has a stiffness k=200n/m and is unstretched when the 25 kg block is at

Mathematics
1 answer:
g100num [7]1 year ago
7 0
To solve this we are going to use the formula fro the force applied to a spring: F=ks
where
k is the spring constant 
s is the extension 

Since we know the F=ma, we can replace that in our formula and solve for a :
ma=ks
a= \frac{ks}{m}
where
a is the acceleration 
k is the spring constant
s is the extension 
m is the mass

We know for our problem that k=200, s=0.4, and m=25. So lets replace those values in our formula to find a:
a= \frac{ks}{m}
a= \frac{(200)(0.4)}{25}
a=3.5 \frac{m}{s^2}

We can conclude that the acceleration of the block when s=0.4m is 3.5 \frac{m}{s^2}.
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A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times
WARRIOR [948]

Answer:

We conclude that the new procedure will not decrease the population mean amount of time required to produce the part.

Step-by-step explanation:

We are given that a large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ = 45 hours.

A random sample of 25 parts will be selected and the average amount of time required to produce them will be determined. The sample mean amount of time is = 43.118 hours with the sample standard deviation s = 5.5 hours

<em>Let </em>\mu<em> = population mean amount of time required to produce an electrical part using new procedure</em>

SO, <u>Null Hypothesis</u>, H_0 : \mu \geq  45 hours   {means that the new procedure will remain same or increase the population mean amount of time required to produce the part}

<u>Alternate Hypothesis,</u> H_a : \mu < 45 hours   {means that the new procedure will decrease the population mean amount of time required to produce the part}

The test statistics that will be used here is <u>One-sample t test statistics </u>because we don't know about the population standard deviation;

              T.S.  = \frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }  ~ t_n_-_1

where,  \mu = sample mean amount of time = 43.118 hours

             s = sample standard deviation = 5.5 hours

             n = sample of parts = 25

So, <u><em>test statistics</em></u>  =  \frac{43.118-45}{{\frac{5.5}{\sqrt{25} } } }  ~ t_2_4

                               =  -1.711

<em>Now at 0.025 significance level, the t table gives critical value of -2.064 at 24 degree of freedom for left-tailed test. Since our test statistics is more than the critical value of t so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.</em>

Therefore, we conclude that the new procedure will remain same or increase the population mean amount of time required to produce the part.

4 0
1 year ago
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data in
Alex_Xolod [135]

Answer: B. 89

Step-by-step explanation:

-29.202x7= -204.414

-204.414+293.5= 89.086

So the answer is B. 89

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1 year ago
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