Answer : The lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.
Explanation:
Given that the mean lifetime of light bulbs is 850 hours with a standard deviation of 44 hours and it is normally distributed. We need to test the hypothesis that 850 hours against the alternative.
Therefore, we need to use a hypothesis test for mean. Let us assume a null hypothesis and an alternative hypothesis for the given data.
Null Hypothesis : The null hypothesis H0 states that there is no significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours. Mathematically, it is expressed asH0: μ = 850
Alternative Hypothesis : The alternative hypothesis Ha states that there is a significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours. Mathematically, it is expressed asHa: μ ≠ 850Here, μ represents the population mean and is equal to 850. We know that Z-score is given as, Z = (x - μ)/σwhere x = Sample Mean, μ = Population Mean, σ = Standard Deviation
Now, we need to find the Z-score for the given data. Z = (x - μ)/σZ = (15 - 850)/44Z = -18.75As we know that the area under the curve at 5% level of significance on each tail is 0.025 and the Z-score corresponding to this is ±1.96. The rejection region is in the left tail of the curve and the right tail of the curve.
Hence the critical value of Z at 5% level of significance for a two-tailed test is ±1.96. Z critical value = ±1.96Since the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. Hence, we can conclude that the lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.
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It is important to understand that integral equations also arise from problems in differential equations. (a) For example, write the initial value problem dx = f(t, x), x(to) = xo dt as an integral equation and indicate what kind of equation it is. (b) Show that an initial value problem d²x dt² = f(t, x), x(to) = xo, x'(to) = x₁ involving a second order differential equation can be transformed into a Volterra integral equation
The Volterra integral equation:
x(t) - xo = ∫[to, t] y(s) ds
y(t) - x₁ = ∫[to, t] f(s, x(s)) ds
(a) To write the initial value problem dx = f(t, x), x(to) = xo dt as an integral equation, we can use the integral representation of the solution.
Let's consider the integral equation:
x(t) = xo + ∫[to, t] f(s, x(s)) ds
This integral equation is of the Volterra type, as it involves a definite integral and depends on the function x(s) evaluated over the interval [to, t].
(b) To transform the second-order initial value problem d²x/dt² = f(t, x), x(to) = xo, x'(to) = x₁ into a Volterra integral equation, we can introduce a new variable, y(t), defined as the derivative of x(t):
y(t) = dx/dt
Now, we can rewrite the second-order differential equation as a system of first-order differential equations:
dx/dt = y(t)
dy/dt = f(t, x)
To represent this system as an integral equation, we'll integrate both equations from to to t.
This yields:
x(t) - xo = ∫[to, t] y(s) ds
y(t) - x₁ = ∫[to, t] f(s, x(s)) ds
Combining these two equations, we obtain the Volterra integral equation:
x(t) - xo = ∫[to, t] y(s) ds
y(t) - x₁ = ∫[to, t] f(s, x(s)) ds
This integral equation is also of the Volterra type, involving definite integrals and depending on the functions x(s) and y(s) evaluated over the interval [to, t].
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Look at the number line below. Tyhe number 2 is between 1 and 4 since 1 =1 and 4=2, that means that 2 must be between what two integers?
Answer: i dont know
Step-by-step explanation:
The measures of two complementary angles are in the ratio of 2 : 7. Find the measurements of the two angles.
Answer: 20° & 70°
Step-by-step explanation:
We know complementary angles will add up to 90° and we also know we can divide the total by 9 parts because our ratio is 2 parts to every 7 parts.
To find each individual part size...
9x=90
x=10
so use our ratio...
2x10=20 for first angle
7x10=70 for second angle
The data from a survey of ages of people taking an exercise class was skewed to the left
Answer:
It is really hard to see the picture
Step-by-step explanation:
Could you also give the choices to the answers that are possible? It would help out a lot. Just lmk in the comments and then I will revise my answer :)
Answer:
Part A: The appropriate measure of center to describe the distribution of the data would be, median.
Part B: The appropriate measure of spread to describe the distribution of data would be, interquartile range.
Part C: The box plot represents the data. Calculate the appropriate measure of spread, IQR = 13
Got it right on math nation. Hope this helps!
if m < c = 147 , determine m < e
a) 147
b) 57
c) 33
d) 180
Answer:
c) 33
Step-by-step explanation:
We can calculate supplementary angles by subtracting the given angle from 180°. To find the other angle (in your case, ∠e), use the ∠y = 180° – ∠x where ∠x is the given angle.
Answer:
c)33
Step-by-step explanation:
A restaurant used 231 eggs last week. 46 of them are colored white, w. The remaining eggs are colored brown. Write an equation that represents the situation. ( i will give you brainly)
Answer:
46 + W = 231
Step-by-step explanation:
Answer:
My guess: 231 = 46 + b
Step-by-step explanation: Because they didn't mention how many were colored brown, we would use a variable to represent them, in this case I use b. But we do know 46 of them were white. so the equation would simply be 231 = 46 + b. After you add 46 and b you will get the total to 231. You can find b from subtracting 231 to 46. Then add b to 46 and get the total of 231
gloria went to the mall and spent 50 minutes shopping
Answer:
11:00 AM+ 50 minutes= 11:50
11:50 AM+30 minutes= 12:20
Step-by-step explanation:
Gloria went to the mall and spent 50 minutes shopping. Then she had lunch for 30 minutes. If Gloria arrived at the mall at 11:00 A.M., at what time did she finish lunch?
it takes 6 hours to travel 372 miles. How long will it take to travel 279 miles?
Answer:
4 hours and a half. 4 hours and 30 minutes
Step-by-step explanation:
Answer:
4hrs 30 minutes
Step-by-step explanation:
6hrs = 372miles
372 ÷ 6 = 62
1hr = 62 miles
62 x 4hrs = 248 miles
You need to 279 miles. 0.5 = 30 minutes.
how to remove Dec in casio calculator?
0
Answer:
htgjyk
Step-by-step explanation:
Check for a significant change over first-time composite scores when a group of 30 high school seniors retake the Miller Analogies Test (MAT) after completing a Test Preparation Workshop; note that each student will have taken the MAT twice, once before and once following the workshop, and the scores are on a ratio scale.
The preparation workshop’s impact on first-time composite scores can be assessed by evaluating the scores of a group of 30 high school seniors who retake the Miller Analogies Test (MAT) after attending the workshop.
The MAT is taken twice by each student: once before the workshop and once after it. The scores are reported on a ratio scale.
To check if there has been a significant change in scores, the following steps can be followed:
Step 1: To determine the change in scores, subtract the scores obtained before the workshop from the scores obtained after the workshop.
Step 2: Calculate the average score change for the group of 30 students by dividing the sum of score changes by 30.
Step 3: Calculate the standard deviation of the score change by using the following formula:
SD = √[∑ (Xi - X)2 / (n - 1)]
where Xi is the individual score change, X is the average score change, and n is the number of students.
Step 4: Use a t-test to determine if the change in scores is statistically significant. If the t-value is greater than the critical value (using a 5% significance level and 29 degrees of freedom), then the change in scores is significant.
Thus, by following these steps, the impact of the preparation workshop on first-time composite scores of the MAT can be assessed.
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The paired t-test is the appropriate statistical analysis to use for this type of data.
The first step to check for a significant change over first-time composite scores when a group of 30 high school seniors retake the Miller Analogies Test (MAT) after completing a Test Preparation Workshop, note that each student will have taken the MAT twice, once before and once following the workshop, and the scores are on a ratio scale is to compute the ratio of the scores before and after the workshop for each student.
Then, calculate the mean and standard deviation of the ratios.
Finally, conduct a paired t-test to determine if the mean ratio is significantly different from 1 at the 0.05 level of significance.
The paired t-test is the appropriate statistical analysis to use for this type of data.
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You school plans to collect at least 1500 pairs of socks for the homeless shelter. So far they have collected 183 pairs of socks. There are 4 days left of the sock drive. Write an inequality and solve to represent the average number of pairs of socks to be collected each of the last 4 days.
Answer: the amount of socks they will collect in four days is less than the amount of socks they plant to collect, in other words 915<1500 socks.
Step-by-step explanation:
If they collect 183 pairs of socks in one day, and there are four days left, then 183 x 5 = 915 (pairs of socks) in five days. They need to collect 1,500 pairs.
Find the volume of a right circular cone that has a radius of 4 inches and a height of 12 inches. A. 36 in. B. 48 in. C. 52 in. D. 64 in.
Answer:
A) 36 inches
36 Incheon is the correct answer
Answer:
D.) 64pi in.³
Step-by-step explanation:
I got it right in quiz, trust me.
I hope this helps! ^^
i don’t know the answer please help
Make a bowl of Pho wit 3 ingredients that cost 14.50.
Will choose brainliest
Answer: $8 bowl, noodles, bean sprouts, beef
Step-by-step explanation:
Charlotte started soccer practice at 5:30 pm. Practice lasted for 1 hour and 45 minutes. What time was practice over?
Answer:
7: 15
Step-by-step explanation:
What is the value of f(x) = 4x -9
Answer:
F= 1 /4 y+ 9 /4
Step-by-step explanation:
brainliest?
Please answer correctly! I will mark you Brainliest!
20-10=10
10-3=7
7cm
Then the volume is 7cm
Step-by-step explanation:
volume of cuboid=lbh =10*3*20 =600cm3HELPPPPPPPPPPPPPPPPPPPP
An item is priced at $13.75. If the sales tax is 7%, what does the item cost including sales tax?
Answer:
divide 7/100 which is 0.07
multiply that by 13.75, and you get 0.96
13.75+0.96= $13.20
(this is including sales tax)
Answer:
$12.78
Step-by-step explanation:
I THINK you are supposed to multiply the original price (13.75) by the sales tax as a decimal (0.07) and then subtract that answer from, the original, amount.
consider the following function and express the relationship between a small change in x and the corresponding change in y in the from dy = f^1 (x) dx.
f(x) = 2x^3-4x
dy= dx
For a small change in x (dx), the corresponding change in y (dy) is given by the equation dy = (6x² - 4)dx.
To find the relationship between a small change in x (dx) and the corresponding change in y (dy) for the function f(x) = 2x³ - 4x, we can differentiate the function with respect to x.
f(x) = 2x³ - 4x
Differentiating both sides with respect to x:
f'(x) = d/dx (2x³ - 4x)
f'(x) = 6x² - 4
Now, we can express the relationship between dx and dy in the form of dy = f'(x)dx:
dy = (6x² - 4)dx
Therefore, for a small change in x (dx), the corresponding change in y (dy) is given by the equation dy = (6x² - 4)dx.
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In a data set with a, b, c, d, e, and f numeric variables, given there are strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as:
Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e
Given two predictor variables with correlation at 0.32879, we should expect there is multicollinearity between them.
Given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.
In a data set with a, b, c, d, e, and f numeric variables, given there is a strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as
Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e.
Given two predictor variables with a correlation of 0.32879, we should expect there is multicollinearity between them.
The statement that is true regarding the given two predictor variables with a correlation of 0.32879 is:
we should expect there to be multicollinearity between them.
Multicollinearity is a situation in which two or more predictor variables in a multiple regression model are highly correlated with one another. Multicollinearity complicates the understanding of which predictor variables are significant in the regression model's estimation.
Therefore, given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.
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What is x abc def
A. 45
B. 60
C. 75
D. 30
Answer:
C
Step-by-step explanation:
What is the height of the models sail in centimeters?
Step-by-step explanation:
the the height should be 16 cm I used the Pythagoras theory thank you.
Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
Answer:
x ≈ 9.6
Step-by-step explanation:
Using Pythagoras' identity in the right triangle, that is
x² + 14² = 17²
x² + 196 = 289 ( subtract 196 from both sides )
x² = 93 ( take the square root of both sides )
x = [tex]\sqrt{93}[/tex] ≈ 9.6 (to the nearest tenth )
25
119 degrees
13
Find the value of
X. Round to the
nearest 10th.
Answer:
30.5
Step-by-step explanation:
The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter.
Let's denote the lengths of the legs of the right triangle as a and b, and the length of the hypotenuse as c. We are given that the altitude perpendicular to the hypotenuse is 12 cm.
Using the Pythagorean theorem, we have:
[tex]a^2 + b^2 = c^2[/tex]
The perimeter of the right triangle is given by:
Perimeter = a + b + c
We want to express the length of the hypotenuse (c) as a function of the perimeter.
Rearranging the equation for the perimeter, we have:
c = Perimeter - (a + b)
Substituting the equation for c into the Pythagorean theorem equation, we get:
[tex]a^2 + b^2[/tex] = (Perimeter - [tex](a + b))^2[/tex]
Expanding and simplifying, we have:
[tex]a^2 + b^2[/tex]= [tex]Perimeter^2[/tex] - 2Perimeter(a + b) +[tex](a + b)^2[/tex]
Simplifying further:
[tex]a^2 + b^2[/tex]= [tex]Perimeter^2[/tex]- 2Perimeter(a + b) + a^2 + 2ab + b^2
The terms with [tex]a^2[/tex] and [tex]b^2[/tex]cancel out, giving:
[tex]2ab = Perimeter^2 - 2Perimeter(a + b)[/tex]
Dividing both sides by 2, we have:
[tex]ab = (Perimeter^2 - 2Perimeter(a + b))/2[/tex]
[tex]ab = (Perimeter^2 - 2Perimeter(a + b))/2[/tex]
Now, since we are given that the altitude perpendicular to the hypotenuse is 12 cm, we know that:
ab = [tex]12^2 = 144[/tex]
We can solve this equation for either a or b, and then substitute the value into the expression for the hypotenuse (c):
For example, let's solve for a:
a = 144/b
Substituting this into the expression for c
c = Perimeter - (a + b)
c = Perimeter - (144/b + b)
Therefore, the length of the hypotenuse (c) can be expressed as a function of the perimeter.
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Internet Viewing A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How large a sample must she select if she wishes to be 90% confident that the population mean is within 13 minutes of the sample mean? Assume the population standard deviation is 46 minutes. Round your final answer up to the next whole number. The researcher needs a sample of at least people. Work Time Lost due to Accidents At a large company, the Director of Research found that the average work time lost by employees due to accidents was 98 hours per year. She used a random sample of 18 employees. The standard deviation of the sample was 5.2 hours. Estimate the population mean for the number of hours lost due to accidents for the company, using a 99% confidence interval. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number. Doctoral Student Salaries Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find the probabilities. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places. Part: 0/2 Part 1 of 2 (a) The student makes more than $17,000. P(X>17,000)-
Using the z-distribution, as we have the population standard deviation, it is found that a sample of 83 people must be taken.
Given,
Estimation of number of minutes per day a person spends on the internet .
Margin of error in Z distribution,
M = z σ/[tex]\sqrt{n}[/tex]
In which:
z is the critical value.
σ is the population standard deviation.
n is the sample size.
Here,
We have 90% confidence level ,
Thus ,
[tex]\alpha[/tex] = 0.9
z is the value of Z that has a p-value
(1+0.9) / 2
= 0.95
so the critical value is z = 2.575
Also we have
standard deviation = 46 minutes
Population mean = 13 minutes
To find minimum sample size solve for n
M = z σ/[tex]\sqrt{n}[/tex]
13 = 2.575 (46/[tex]\sqrt{n}[/tex])
n = 83 .30
Rounding up, a sample of 83 people must be taken.
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(1 point) Find the square root of 8-2i so that the real part of your answer is positive. The square root is
The square root of 8 - 2i, with the real part of the answer being positive, is approximately 2.34 + 0.52i.
To find the square root of 8 - 2i, we can represent the complex number in its polar form and then apply the square root operation.
First, we calculate the magnitude (r) and argument (θ) of the complex number 8 - 2i:
Magnitude: |8 - 2i| = √([tex]8^2[/tex] + (-2[tex])^2[/tex]) = √(64 + 4) = √68 = 2√17
Argument: θ = arctan(-2/8) = arctan(-1/4) ≈ -0.24498 radians
Next, we express the complex number in polar form:
8 - 2i = 2√17 * (cos(-0.24498) + isin(-0.24498))
To find the square root, we take the square root of the magnitude and divide the argument by 2:
√(8 - 2i) ≈ √(2√17) * (cos(-0.24498/2) + isin(-0.24498/2))
Simplifying the expression:
√(8 - 2i) ≈ √(2√17) * (cos(-0.12249) + isin(-0.12249))
≈ 2.34 + 0.52i
Therefore, the square root of 8 - 2i, with the real part of the answer being positive, is approximately 2.34 + 0.52i.
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(-1 1/4 divided by (-0.2)
Answer:
6.25
Step-by-step explanation:
SOCCER PRACTICE BEGAN AT 2:30 P.M 3:30 P.M THROUGH WHAT FRACTION OF A CIRCLE DID THE MINUTE HAND TURN HOW MANY DEGREES DID THE MINUTE HAND TURN
Answer:
1 /1 ; 360°
Step-by-step explanation:
Start time = 2:30 pm
Stop time = 3:30 pm
Minute hand makes a complete revolution per hour ;
This means that the minutes hand revolves round the whole circle in one hour, hence fraction of the circle covered by the minute hand between 2:30 pm - 3:30 pm is 1/1 = 1
The angle turned by the minutes hand :
1 complete revolution = 360°
A circle covers 360°
1 /1 fraction of a circle = 1/1 * 360° = 360°
Hence, angle turned by the minute hand = 360°