in building electronic circuitry, the breakdown voltage of diodes is an important quality characteristic. the breakdown voltage of 12 diodes was recorded as follows: 9.099, 9.174, 9.327, 9.377, 8.471, 9.575, 9.514, 8.928, 8.800, 8.920, 9.913, and 8.306. (a) check the normality assumption for the data. (b) test the claim that the mean breakdown voltage is less than 9 volts with a significance level of 0.05. (c) construct a 95% one-sided upper confidence bound on the mean breakdown voltage. suppose that the true breakdown voltage is 8.8 volts; it is important to detect this with a probability of at least 0.95. using the sample standard deviation to estimate the population standard deviation and a significance level of 0.05, determine the necessary sample size.
Answers
Therefore , the solution of the given problem of probability comes out to be breakdown voltage is no higher than 9.365 volts.
What precisely is probability?The main objective of any procedure's criteria-based techniques is to determine the likelihood of a statement being accurate or of a particular event happening. Any number in the range of 0 to 1, when 0 typically denotes probability and 1 typically denotes degree of certainty, can be used to denote chance. A probability illustration shows the likelihood that a particular occurrence will occur.
Here,
(a) The lines that appear to approximately connect the points on the normal probability plot do contain some outliers at the low end of the distribution. Overall, there are some issues with the normality premise.
(b) A one-sample t-test can be used to assess the hypothesis that the mean breakdown voltage is less than 9 volts at a significance level of 0.05.
The group mean and standard deviation can be calculated as follows:
=> x' = 9.084
=> s = 0.470
This is the exam statistic:
=> t = (x' - μ)/(s/√n)
where n is the sample size and is the hypothetical community mean. Using = 9, n = 12, and 0.05 as the significance threshold, we obtain:
=> t = (9.084 - 9)/(0.470/√12) ≈ -1.37
(c)
=> x' + t(1-α,n-1)(s/√n)
We have: Using the same numbers as in part (b)
=> t(1-α,n-1) = t(0.95,11) ≈ 1.796
The higher limit of confidence is:
=> x' + t(1-α,n-1)(s/√n) = 9.084 + 1.796(0.470/√12) ≈ 9.365
As a result, we can say with 95% certainty that the actual mean breakdown voltage is no higher than 9.365 volts.
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Related Questions
Rick deposited $1500 in a savings account that earns 6% interest for 4 years. How much money is in his account at the end of the 4 years?
Answers
Answer:
$5820
Step-by-step explanation:
1500*6%=90 per month
90*(48months=4yrs)=4320
1500+4320=5820
what is the markdown what was sebastains percent error on his prediction
Answers
Answer:
i need the answer
Step-by-step explanation:
Suppose you are offered an investment that will pay you $800 a month for 40 years. If your required return is 6% per year, compounded monthly, what would you be willing to pay for this investment?
Answers
If you have a required return of 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, you would be willing to pay approximately $206,595.71 for this investment.
To determine the value you would be willing to pay for this investment, we can use the concept of present value. The present value of an investment is the current worth of the future cash flows it will generate. In this case, the investment will pay you $800 a month for 40 years.
To calculate the present value, we can use the formula:
\(PV = CF / (1 + r)^n\)
Where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods.
In this case, the cash flow is $800 per month, the required return is 6% per year (or 0.06/12 = 0.005 per month), and the number of periods is 40 years * 12 months = 480 months.
Plugging these values into the formula, we have:
PV = $800 / \((1 + 0.005)^(480)\)
Calculating this expression, we find that the present value is approximately $206,595.71. Therefore, you would be willing to pay approximately $206,595.71 for this investment to achieve your required return of 6% per year, compounded monthly.
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find the exact values of the sine, cosine, and tangent of the angle. 255° = 300° − 45°
Answers
The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.
To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.
By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.
We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.
Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.
For 45°:
sin(45°) = cos(45°) = 1/√2
tan(45°) = 1
Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.
Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.
Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.
Therefore, for the angle 255°:
sin(255°) = -1/√2
cos(255°) = 1/√2
tan(255°) = -1
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Solve for x.
-18x + 21 > -15 OR 20x – 13 >27
Answers
Answer:
C
Step-by-step explanation:
-18x + 21 > -15 /// x = 2
20x – 13 >27 /// x = 2
The solution of inequality -18x + 21 > -15 OR 20x – 13 > 27 is x ∈ (- ∞, ∞), so option E is correct.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
-18x + 21 > -15 or 20x – 13 >27
Solve the first inequality as shown below,
-18x + 21 > -15
-18x + 21 - 21 > -15 - 21 (Subtract 21 from both sides)
-18x > -36
-18x / -18 > -36 / -18 (Divide by -18 into both sides, the inequality sign changes as the value will become positive)
x < 2
Similarly, solve the second inequality,
20x – 13 > 27
20x > 40
x > 2
Thus, the solution will be x < 2 ∪ x > 2 or x ∈ (- ∞, ∞)
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i need some help with this question please and thank you!.
Answers
The width of the walkway is 3 feet, If the area of the garden is 484 and the area covered by both the garden and the walkway (the entire square) is 784 .
The given is,
Area of the garden is 484
Area covered by both the garden and the walkway (the entire square) is 784 .
Let, x - Width of the walkway
Step:1
Formula to calculate area of square is,
A = a^2 ...........................(1)
Where, r - Radius of square
Step:2
For garden,
A = 484
Equation (1) becomes,
Take square root on both sides,
a= √484
a = 22 feet
For garden and the walkway (the entire square),
A = 784
Equation (1) becomes,
Take square root on both sides,
a = √784
a = 28 feet
Step:3
Side of garden and the walkway =
Side of garden + 2 (width of the walkaway)....(1)
28 = 22 + 2 ( x )
2 ( x ) = 28 - 22
= 6
x = 6/2
Width, x = 3 feet
Result:
The width of the walkway is 3 feet, If the area of the garden is 484 and the area covered by both the garden and the walkway (the entire square) is 784 .
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complete question:
A square garden is surrounded by a walkway of width X. If the area of the garden is 484 ft2 and the area covered by both the garden and the walkway (the entire square) is 784 ft2, what is the width of the walkway?
What is the endpoint of a segment with endpoint (−3, 5) and midpoint (2, 5)?
Answers
Answer:
You can use the midpoint formula, knowing the midpoint between two points (x1,y1) and (x2,y2) has the coordinates
[(x1 + x2)/2, (y1 + y2)/2]
Substituting what we are given, we get:
(2 + x2)/2 = 5 and (5 + y2)/2 = 1
so,
2 + x2 = 10 and 5 + y2 = 2
Solving for x2 and y2 puts the endpoint at (8,-3), which is in the 4th quadrant.
You could also graph the points to get the same result.
Step-by-step explanation:
The coordinate of the other endpoint is (7,5)
Using the mid point formula expressed as:
\(M(x, y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\)Get the coordinate of x2
X = x1+x2/2
2 = -3+x2/2
-3 + x2 = 4
x2 = 4+3
x2 = 7
Get the coordinate of y2
Y = y1+y2/2
5 = 5+y2/2
5 + y2 = 10
y2 =10 - 5
y2 = 5
Hence the coordinate of the other endpoint is (7,5)
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18 An artist makes $1,000 in profit after
renting a booth and selling 50 prints.
Another artist makes $550 after renting
a booth and selling 32 prints. Which
equation describes the relationship
between the number of prints sold, x, and
the profit, y?
F. y = -25x
- 250
G. y = 25x + 250
H. y = 25x – 250
J. y = -25x - 250
Answers
Answer:
y = 25x - 250
2. Multiply each coordinate by 3 in (4, 9).
Answers
We just multiply each part of the coordinate
\(\begin{gathered} 3\cdot(4,9)=(3\cdot4,3\cdot9) \\ =(12,27) \end{gathered}\)Answer: (12, 27)
what is m if 9/7m= 1/7
Answers
M=1/7*7/9=1/9
Answer: \(m=\frac{1}{9}\)
Step-by-step explanation:
\(\frac{9}{7}m=\frac{1}{7}\)
Multiply by the reciprocal to isolate m.
\((\frac{7}{9} )\frac{9}{7}m=\frac{1}{7}(\frac{7}{9} )\)
\(m=\frac{1}{9}\)
Perform the indicated operations and simplify.
(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)
Answers
Let's simplify the expression step by step: Expand the squared term:
(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²
Expand the second term:
3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)
Expand the third term:
x(3x + 4y + 3) = 3x² + 4xy + 3x
Now, let's combine all the expanded terms:
(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)
= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x
Combining like terms:
= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x
= 7x² - 5xy + 5y² + 3x
The simplified form of the expression is 7x² - 5xy + 5y² + 3x.
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what is the answer to -2(-4x-3)-5x+3=-3
Answers
Answer:
X= -4
Step-by-step explanation:
Answer:
x = -4
Step-by-step explanation:
Distribute the -2 to the parentheses:
-2(-4x - 3) -5x + 3 = -3
8x + 6 - 5x + 3 = -3
Add like terms:
3x + 9 = -3
Solve for x:
3x = -12
x = -4
So, the answer is x = -4
Which expression is equivalent to 5/6c + 76c, if c+ 0?
Answers
Answer:
0
Step-by-step explanation:
If c=0
that expression also equals 0
x-5+x-11=100 what is the reason for this statement for geometry?
Answers
Answer:
because when the value of x is replaced in the factorisation it Will be equivalent to 100
najib brought a handheld game console for $289 after a 15% discount how much was the discount .. and what was the usual price of the handheld game console
Answers
Answer:
340
Step-by-step explanation:
289=85%*x
289=.85*x
289/.85=x
x=340
the proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is:
Answers
The proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.
What is square of correlation coefficient?
A helpful number in linear regression is the square of the correlation coefficient, or r2.
The percentage of the variance in one variable that can be partially explained by another variable is represented by this value.
The summary table in the Regression output contains the "R" value, which is the coefficient of correlation.
Coefficient of determination is another name for R square. To calculate R squared, multiply R by R.
The square of the correlation coefficient is what is meant by the term "coefficient of determination."
Hence, the proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.
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can you please help me
Answers
The parent factors are the colours white or gray
Below is an image to represent the Tree diagram
It shows that for a white shirt Marcus can buy either a white medium and white large sizes
It also shows that for a gray shirt Marcus can also buy a gray medium and a gray large shirt
With this information, we can conclude that the possible answer to the question is the last OPTION D
You need to build a model that predicts the volume of sales (Y) as a function of advertising (X). You believe that sales increase as advertising increase, but at a decreasing rate. Which of the following would be the general form of such model? (note: X^2 means X Square)
A. Y ^ = b0 + b1 X1 + b2 X2^2
B. Y ^ = b0 + b1 X + b2 X / X^2
C. Y ^ = b0 + b1 X + b2 X^2
D. Y ^ = b0 + b1 X
E. Y ^ = b0 + b1 X1 + b2 X2
Answers
The general form of such a model that predicts the volume of sales (Y) as a function of advertising (X) in which sales increase as advertising increases, but at a decreasing rate is given by Y^ = b0 + b1X + b2X². Option C.
The general form of the model that fits the description of the sales model that is given in the problem is C. Y^ = b0 + b1X + b2X². Where Y^ represents the predicted or estimated value of Y. b0, b1, and b2 are the coefficients of the model, and they represent the intercept, the slope, and the curvature of the relationship between X and Y, respectively.
In this model, the variable X has a quadratic relationship with the variable Y because of the presence of the squared term X². This indicates that the effect of X on Y is not linear but curvilinear, which means that the effect of X on Y changes as X increases. Specifically, the effect of X on Y increases initially but then levels off or diminishes as X becomes larger. Answer option C.
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Alonzo buys a roast that weighs 2.5 pounds and costs 4.36 a pound. Find the amount he pays.
Answers
Answer:
$10.90
Step-by-step explanation:
Hmm... this question can be tricky. Don't get caught up! The formula is simple once you know what you're doing. Let's figure it out!
So, from the word problem we can determine that the weight is 2.5 pounds with a price of 4.36 a pound.
The formula we will be using for this question is \(2.5(4.36)\). This may seem complicated, but all its saying is 2.5x4.36. You may be wondering, why are we using this formula? Well, for every pound of roast he buys, he pays 4.36 dollars. He is buying 2.5 pounds of roast, so we can do 4.36 2 times and 4.36 .5 times, which translates into 2.5 times 4.36. You with me so far? I hope so, because here comes the tricky part. Let's multiply:
4.36
x 2.5
--------
10.9
And there you have it! $10.90.
Please consider giving this response a brainliest. It took plenty of effort and time
There were 25 vocabulary words on the quiz. Megan got 60% correct. How many did she get correct?
Answers
Answer:
15
Step-by-step explanation:
25=100º
x=60
\(\frac{25}{x}=\frac{100}{60}\)
\(\frac{x}{25}=\frac{60}{100}\)
x=15
In ΔOPQ, q = 110 inches, o = 970 inches and ∠P=167°. Find the area of ΔOPQ, to the nearest square inch.
Answers
Answer:
\(Area = 12004\) square inches
Step-by-step explanation:
Given
\(q = 110\)
\(o = 970\)
\(\angle P =167\)
Required
The area of the triangle
To do this, we use:
\(Area = \frac{1}{2} * o * q * sin(P)\)
So, we have:
\(Area = \frac{1}{2} * 970 * 110 * sin(167^\circ)\)
\(Area = \frac{1}{2} * 970 * 110 * 0.2250\)
\(Area = 12003.75\)
Approximate
\(Area = 12004\)
Answer:
12001
Step-by-step explanation:
Please help with this SAT question. A solution gets Brainliest!
Answers
Answer:
i think Chope its help
C is my answer
another EASY question for y’all mathy people, easy points! Question in photo.
Answers
Answer:
the answer is c
Step-by-step explanation:
Solve the system by elimination.
{y= 16x+44
{y= -x^2 +8x+28
Answers
Answer:
x= -4, y= -20
Step-by-step explanation:
y= 16x+44
(y= -x²+8x+28) * (-1)
multiply both sides by -1
y= 16x+44
-y= x²-8x-28
add the equations to eliminate y
y-y= x²+16x-8x+44-28
0= x² +8x +16 this is the same with (x+4)²=0 so x= -4
go back to the first equation and substitute x with -4 and solve for y
y= 16*(-4) +44 = -64+44 = -20
Help, pls this is urgent
9/3 - 1/6
Answers
\( \frac{9}{3} - \frac{1}{6} = \frac{9 \times 2}{3 \times 2} - \frac{1}{6} = \frac{18}{6} - \frac{1}{6} \\ \\ \frac{18 - 1}{6} = \frac{17}{6} = 2 \frac{5}{6} \)
Answer: 2 5/6
Step-by-step explanation:
9/3-1/6 is 2 5/6 what you do is cross multiply 9/3 and 1/6 to get 18/6 and 1/6 then you subtract across
One positive number is 6 times another number. The difference between the two numbers is 205. Find the numbers. (Enter your answers as a comma-separated list.)
Answers
Answer:
Hence the positive numbers are 246, and 41
(246, 41)
Step-by-step explanation:
From the question,
One positive number is 6 times another numberLet the first positve number be \(x\)
and the other number be \(y\)
Hence,
\(x = 6y\) ....... (1)
Also,
The difference between the two numbers is 205That is,
\(x - y =205\) ........(2).
To solve for the two unknowns, substitute the value of \(x\) in equation (1) into equation (2).
Since,
\(x = 6y\)
Then
\(x - y =205\) becomes
\((6y) - y =205\\\)
Then,
\(6y - y = 205\\5y = 205\\\)
Divide both sides by 5
\(\frac{5y}{5} = \frac{205}{5} \\ y = 41\\\)
∴ the value of \(y\) is 41
Now, substitute the value of y into equation (1) to find \(x\)
Then,
\(x = 6y\) becomes
\(x = 6(41)\\x = 246\\\)
∴ the value of \(x\) is 246
Hence the positive numbers are 246, and 41
(246, 41)
Suppose a 95% confidence interval for the average amount of weight loss on a diet program for males is between 13. 4 and 18. 3 pounds. These results were based on a sample of 42 male participants who were deemed to be overweight at the start of the 4-month study. What is the standard error of the sample mean?.
Answers
The standard error of the sample mean is 1.21.
Given;
Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.
A 95% confidence interval for a population mean is (13.4, 18.3)
Upper limit = 18.3
Lower limit = 13.4
Since population SD is unknown, this interval is constructed using the t distribution.
n = 42
c = 0.95
∴ α = 1 - c = 1 - 0.95 = 0.05
α/2 = 0.025
Also, d.f = n - 1 = 42 - 1 = 41
∴ ta/2.d.f = ta/2.n-1 = t0.025,41 = 2.02 . . . . use t table
Now,
The margin of error = (Upper limit - Lower limit)/2
= (18.3 - 13.4)/2
= 2.45
But,
Margin of error = ta/2.d.f- * (s / \sqrt{} n)
Margin of error = ta/2.d.f- * Standard error
2.45 = 2.02 * Standard error
Standard error = 1.2129
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(PLEASE HURRY! EXTRA POINTS!)
Two students created models of the same building. One student used a scale factor of 3 centimeters (cm) = 15 meters (m). The
second student used a scale factor of 4.5 = 15 m. The height of the original building is 20 meters. What is the difference between the heights of the two students’ models?
A. 1.5 cm
B. 6.5 cm
C. 33 cm
D. 2 cm
Answers
Answer:
im pretty sure its A. 1.5cm
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Lets find the rate of centimeters to meters.
3 / 15 = 0.2cm per m
4.5 / 15 = 0.3cm per m
Multiply to find the height in cm of the model.
0.2 * 20 = 4cm
0.3 * 20 = 6cm
Subtract to find the distance.
6 - 4 = 2cm
Best of Luck!
A manager at a shopping mall counts 244 males and n females as they enter the mall. The manager realizes that 25% of all males and 25% of all females are children. She writes the expression 0.25n + 61 to represent the number of children who enter the mall. Is the manager correct?
Answers
Answer:
Step-by-step explanation:
The manager is not correct in her calculation.
Step-by-step explanation:
There are 244 males and n females who entered the mall as the manager at the shopping mall counts.
If 25% of all males are children, then the number of male children are .
Again, the 25% of all female are children, then the number of female chilfren are .
Therefore, the total number of children will be (60 + 0.25n).
But the manager gives the number of children to be 0.25n + 61 who entered the mall.
So, the manager is not correct in that calculation. (Answer)
Somebody please help me with this
Answers
The resulting shape after the reflection is added as an attachment
How to reflect the shape across the line y = x
From the question, we have the following parameters that can be used in our computation:
The shape A
To reflect the shape across the line y = x, we swap the coordinates of x with y
This means that the rule of transformation is
(x, y) = (y, x)
Next, we reflect the shape across the line y = x using the above rule
The resulting shape is added as an attachment
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