If p varies jointly as q and the cube of r, when
p=270 when q=6 and r=3, find the constant of
variation. Write your answer as a fraction.
y=kxz
Answers
The value of constant of variation is, 5.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
⇒ p varies jointly as q and the cube of r.
Since, p varies jointly as q and the cube of r.
Hence, We can formulate;
⇒ p = k × q × r²
Where, k is constant of variation.
Here, p = 270 when q = 6 and r = 3.
Substitute all the values, we get;
⇒ p = k × q × r²
⇒ 270 = k × 6 × 3²
⇒ 270 = 54k
⇒ k = 270 / 54
⇒ k = 5
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A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses salad dressings is working properly when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared. Is there evidence that the machine should be stopped and production wait for repairs? The lost production from a shutdown is potentially so great that management feels that the level of significance in the analysis should be 99%.
Answers
Answer:
Step-by-step explanation:
From the given information:
The null hypothesis is:
[tex]H_o: \mu = 8[/tex]
The alternative hypothesis is:
[tex]H_1 : \mu \ne 8[/tex]
The sample size n = 35
Sample mean = 7.91
variance = 0.03
Standard deviation = [tex]\sqrt{0.03} = 0.173[/tex]
The t-test statistics is computed as:
[tex]t = \dfrac{\bar x - \mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{7.91 -8}{\dfrac{0.1732}{\sqrt{35}}}[/tex]
[tex]t = \dfrac{-0.09}{\dfrac{0.1732}{5.916}}[/tex]
t = - 3.0741
Degree of freedom:
df = n - 1
df = 35 - 1
df = 34
Level of significance = 1 - C.I
= 1 - 0.99
= 0.01
The t_{critical} value for the two-tailed test at 0.01 is within the rejection region:
[tex]t_{critical} = -2.728 \ and \ 2.728[/tex]
Decision rule: To reject [tex]H_o[/tex] if [tex]t< -2.728 \ or \ t > 2.728[/tex]
As [tex]t_{statistics}[/tex] fails the rejection region, we reject [tex]H_o[/tex]
Conclusion: There is sufficient evidence to believe that the machine will not dispense 8 ounces & and it must be stopped for repairs.
You can use hypothesis testing with t test to know if there is enough evidence that he machine should be stopped and production wait for repairs.
There is enough evidence that the machine should be stopped and production wait for repairs.
Given information about taken sample are:Sample mean [tex] \overline{x} = 7.91[/tex]Sample size n = 35Sample standard deviation [tex]s = \sqrt{variance} = \sqrt{0.03} = 0.1732[/tex]Confidence should be of 99%.Let the population mean be denoted by [tex]\mu[/tex]
Forming hypotheses:Null hypothesis: [tex]\mu = 8[/tex] (that is, machine needs no repair and working fine)
Alternate hypothesis: [tex]\mu \neq 8[/tex] (that is, machine is not dispensing right amount and need repairs)
Using t test:
[tex]t = \dfrac{\overline{x} - \mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{7.91- 8}{\dfrac{0.1732}{\sqrt{35}}} = -0.30821[/tex]
Degree of freedom = sample size - 1 = 34
Level of significance = [tex]\alpha = 1 -0.99 = 0.01[/tex]
From t tables we have:
[tex]t_{critical} = t_{0.01} = \pm 0.278[/tex] (two tailed test) (at 34 degree of freedom)
Since obtained value of t -0.30821 is less than the minimum value of range [tex](-0.278, 0.278)[/tex], thus lying outside the range and thus, we cannot accept the null hypothesis and end up accepting the alternate hypothesis.
Thus, there is enough evidence that the machine should be stopped and production wait for repairs.
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Answer:
B is the answer.
Step-by-step explanation:
Answer:
The second one
Step-by-step explanation:
-2 and 1/4 is the same as -9/4 bec -9/4 is just in the improper form.
(can i get brainliest now)
trapped in a cell that contains 3 doors. The first door leads to a tunnel that returns her to back tothe cell after 2 days of travel. The second door leads to a tunnel that returns her back to the cell after 4days of travel. The third door leads her freedom after 1 day of travel. If it is assumed that Ally will alwaysselect doors 1, 2, and 3 with probabilities 0.5, 0.3, and 0.2 (respectively), what is the expected number ofdays until she reaches freedom
Answers
Answer:
The expected number of days until prisoner reaches freedom is 12 days
Step-by-step explanation:
From the given information:
Let X be the random variable that denotes the number of days until the prisoner reaches freedom.
We can evaluate E(X) by calculating the doors selected, If Y be the event that the prisoner selects a door, Then;
E(X) = E( E[X|Y] )
E(X) = E [X|Y =1 ] P{Y =1} + E [X|Y =2 ] P{Y =2} + E [X|Y =3 ] P{Y =3}
[tex]E(X) = (2 + E[X])\dfrac{1}{2}+ (4 + E[X])\dfrac{3}{10}+ 1 (\dfrac{2}{10})[/tex]
[tex]E(X) = (2 + E[X])0.5+ (4 + E[X])0.3+ 0.2[/tex]
Solving for E[X]; we get
E[X] = 12
Each of four test scores in Connie’s class is to be weighted equally. On the first three tests, Connie scored 80%, 90% and 95%. What percent must she score on her fourth test to have an overall average of exactly 90%?
Answers
Answer:
95%is the answer
Step-by-step explanation:
Answer:
95%
Step-by-step explanation:
We can use the balancing method to do this.. first what is the total below 90?
The total is 10% because 90-80 which was the only percentage below 90 is 10%. Then, what is the total above 90?
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Now we use the balancing method to get from 5-10.
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Answer:
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Step-by-step explanation:
Answer:
20% is 4.70
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
if that is what u are asking. simplist form is 2 3/4 and 2 11/12.
Hope that helps and good luck :)
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Answers
Answer:
7/9
Step-by-step explanation:
7/9 = 0.777777777777777777...
0.7 repeated can be written as a fraction [tex]\frac{7}{9}[/tex].
What are Fractions?Fractions are defined as a part or portion in a whole. There are two parts for a fraction, numerator which is the upper part and the denominator, which is the lower part.
Fractions are generally written in the form [tex]\frac{p}{q}[/tex], where p and q are real numbers. Here, the number p is called the numerator and the number q is called the denominator.
Fractions can be simplified as decimals.
We have to find the fraction representing the number 0.7 repeated.
0.7 repeated is actually the number 0.77777.....
The quotient of 5/8 = 0.625
The quotient of 6/7 = 0.857...
The quotient of 7/9 = 0.777.......
The quotient of 7/100 = 0.07
So, the quotient of 7/9 is the required number.
Hence the fraction which on simplification gives 0.7 repeated is 7/9.
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20
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if you were to solve it
x would be 24
[ x = 24 ]
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ok
Step-by-step explanation:
The original cost of a sofa was $600. If it was discounted 40% and sales tax is 8%, what is the final cost of the sofa
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Answer:
$312
Step-by-step explanation:
10% of $600 is $60
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0.25
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Step-by-step explanation:
12/5+(7x5)
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x < 15
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
how many men have a waist measurement of more than 85cm
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A meteorologist predicted that there would be 1.0 inches of rainfall from a storm. Instead, there were 2.2 inches of rainfall. Which statements are true?
a
The prediction was off 35%
b
The percent error of the prediction was about 55%.
c
If the percent error should be less than 20%, the prediction was acceptable.
d
The difference between the predicted and the actual rainfall was 1.2 inches
Answers
Answer:
pls write the question clearly
Step-by-step explanation:
hxhdhdudjfjfjfjfjjfucjdjshshsshsh
The statements that is true: B. The percent error of the prediction was about 55%.
D. Difference between the predicted and actual rainfall was 1.2 inches.
What is the percentage error?Percentage error can be calculated using this formula;
Percentage error = Actual value observed - Expected value /Expected value
The Percentage error is;
= 2.2 - 1.0 / 2.2
Percentage error = 1.2 /2.2
Percentage error = 0.545 × 100
Percentage error = 55% (Approximately)
Since Difference between the predicted and actual rainfall;
Difference = Actual rainfall - Predicted rainfall
Difference = 2.2 -1.2
Difference = 1.2 inches.
Hence the correct statement is option B and D.
Learn more about percentage error;
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Plz answer the question attached
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Answer:
y = -2x + 5
Step-by-step explanation:
To find the slope, you need to pick two points and put into the slope formula. It doesn't matter which ones, you will get the right answer regardless. I used (-3, 11) and (2, 1).
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{11 -1 }{-3 -2 } \\m=\frac{10 }{-5 } \\m=-2[/tex]
Now that you have the slope, you can plug it into point-slope form to find the equation in slope-intercept form. You will also need to plug one of the given points. Again, it doesn't matter which one.
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