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frosja888 [35]
2 years 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]2 years 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 company receives shipments of a component used in the manufacture of a component for a high-end acoustic speaker system. When
Tanya [424]

Answer:

ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434

Step-by-step explanation:

For this case we have a sample size of n = 250 units and in this sample they found that 24 units failed one or more of the tests.

We are interested in the proportion of units that fail to meet the company's specifications, and we can estimate this with:

\hat p = \frac{24}{250}= 0.096

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The confidence interval for a proportion is given by this formula  

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}  

For the 98% confidence interval the value of \alpha=1-0.98=0.02 and \alpha/2=0.01, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=2.33  

And the margin of error would be:

ME= 2.33*\sqrt{\frac{0.096*(1-0.096)}{250}}= 0.0434

4 0
2 years ago
Based on an online poll, 35% of motorists routinely use their cell phone while driving. Tree people are chosen at random from a
mart [117]

Answer:

The anwerss to the question are

(A) P(No less than two people use their phones while driving) =  0.1225

(B) P(The probability that no more than one person of the three people use their cell phone while driving) = 0.147875

Step-by-step explanation:

The given relations are

Percentage of motorists that routinely drive while sing their phone = 35 %

The probaboloty that if a peerson is random;ty  selected from a group of hudred person routinely uses their phone wjile friving P(phone) = 35

The probability that a  motorist randomly selected fron a set of 100 do not routinely use thir phones while driving = P(No celll phone)  = 65

Then the probability that when three people are selected at random at least two people of the three people use their cell phone while driving is

P(phone)  = 35/100m = 0.35

P(No celll phone)  = 65/100 = 0.65

(A) Probability of at least two of three use their phones whle driving is

0.35×0.35×0.65 +0.35×0.35×0.35 = 0.1225

(B) The probability of only one person out of three seted use their phones while driving is

(0.35)(0.65)(0.65) = 0.147875

7 0
2 years ago
Sandra Leatherwood invested money received from a game show for 10 months at 9% interest.
taurus [48]
P=i/rt
P=1687.5/(0.09*10/12)
P=22500
4 0
2 years ago
The number of people, n, who know a rumor can be modeled using the equation n(*)=20(2)*, where * is the number of days since Mon
galben [10]
U need n = 2 6 hope this help u nedd 62626wnesslln
6 0
2 years ago
In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all resi
Alborosie

Answer:

80.67 hours

Step-by-step explanation:

Data provided in the question:

The number of weekly hours worked :

78 85 82 79 77 82 81 82 81 81 82 78

total number of observations = 12

Now,

Mean = (Sum of all the data values) ÷ (Total number of data values)

or

Mean = ( 78 + 85 + 82 + 79 + 77 + 82 + 81 + 82 + 81 + 81 + 82 + 78 ) ÷ 12

or

Mean = 968 ÷ 12

or Mean = 80.67 hours

8 0
2 years ago
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