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Katyanochek1 [597]
3 years ago
15

Upon completion of an experiment a student realizes that the technique used for measuring the length and width of a rectangle ha

s a systematic error of 3.8 cm. (The measured length is always more than the actual length.) If the student found the most probable values of the width and length to be 85.7 cm and 123.5 cm, respectively; what is the systematic error of the area of the board
Mathematics
1 answer:
eduard3 years ago
6 0

Answer:

809.4cm²

Step-by-step explanation:

Given the following :

Systematic error = 3.8cm (The measured length is always more than the actual length.)

Most probable dimension :

Width = 85.7 cm

Length = 123.5 cm

Hence most probable area of Rectangle :

Area = Length × Width

Area = 85.7cm × 123.5cm = 10583.95 cm²

Dimension due to Systematic error :

Length = (85.7cm + 3.8cm) = 89.5cm

Width = (123.5cm + 3.8cm) = 127.3cm

Area = Length × width

Area = ( 89.5cm × 127.3) = 11393.35cm²

Systematic error of the area :

value of area with Systematic error - Probable value of area :

11393.35cm² - 10583.95 cm² = 809.4cm²

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Consider a chemical company that wishes to determine whether a new catalyst, catalyst XA-100, changes the mean hourly yield of i
kolezko [41]

Answer:

Null hypothesis:\mu = 750  

Alternative hypothesis:\mu \neq 750  

t=\frac{811-750}{\frac{19.647}{\sqrt{5}}}=6.943  

p_v =2*P(t_{4}>6.943)=0.00226  

If we compare the p value and a significance level assumed \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the actual true mean is significantly different from 750 pounds per hour.  

Step-by-step explanation:

Data given and notation

Data:    801, 814, 784, 836,820

We can calculate the sample mean and sample deviation with the following formulas:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X=811 represent the sample mean  

s=19.647 represent the standard deviation for the sample

n=5 sample size  

\mu_o =750 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the mean is different from 750 pounds per hour, the system of hypothesis would be:  

Null hypothesis:\mu = 750  

Alternative hypothesis:\mu \neq 750  

Compute the test statistic  

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

t=\frac{811-750}{\frac{19.647}{\sqrt{5}}}=6.943  

Now we need to find the degrees of freedom for the t distirbution given by:

df=n-1=5-1=4

What do you conclude?  

Compute the p-value  

Since is a two tailed test the p value would be:  

p_v =2*P(t_{4}>6.943)=0.00226  

If we compare the p value and a significance level assumed \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the actual true mean is significantly different from 750 pounds per hour.  

4 0
3 years ago
Is this right answer??
Lyrx [107]
Yes that is correct
7 0
3 years ago
110 as a product of prime numbers
sweet [91]
110 = 11 \times 10

110 = 11 \times \ 5 \times 2

So it is the product of 5 \times 2 \times 11

And 2,5 and 11 are prime numbers, so there you go :)
8 0
3 years ago
Layla played sports for 3 3/4 hours. Punish time playing sports was 3/8 as long. About how many hours did puno play sports
Nostrana [21]
I would say 13 3/4 but dont take me for my word
4 0
3 years ago
A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angled turn into a narrower hall
Rudiy27

Answer:

21.62m

Step-by-step explanation:

first draw the the pipe

second you need know wich is the angle between the pipe and the corner

β=Tan^-1(6/9)=33.7

find the components using tow triangles

a=9/cos(33.7)=10.81m

b=6/sen(33.7)=10.81m

finally sum the leghts

L=10.81+10.81=21.62mm

attached procedure

8 0
3 years ago
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