A The null and alternative hypotheses in this case are:
Null hypothesis: H_o: μ ≥ 11
Alternative hypothesis: H_A: μ < 11
B We have statistically significant evidence to conclude that the setting results in less than 11% kernels unpopped.
C The t-statistic is -2.94.
d) The p-value is 0.004.
How to explain the informationa) In this case, the company has made a Type I error. This is when the null hypothesis is rejected, even though it is true. In this case, the company would be rejecting the hypothesis that the setting results in less than 11% kernels unpopped, even though it is actually true. The consequence of this would be that the company would be losing money on refunds for popcorn that is not actually defective.
b) In order to answer this question, we need to calculate the t-statistic and the p-value.
The t-statistic is calculated as follows:
t = (x - μ) / (s / √n)
Substituting these values into the formula for the t-statistic, we get:
t = (6.7 - 11) / (3.5 / √8)
= -2.94
The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.
c) The t-statistic is -2.94.
d) The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.The p-value is 0.004.
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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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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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i don’t know the answer please help
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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(-1 1/4 divided by (-0.2)
Answer:
6.25
Step-by-step explanation:
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?
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!
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.
25
119 degrees
13
Find the value of
X. Round to the
nearest 10th.
Answer:
30.5
Step-by-step explanation:
how to remove Dec in casio calculator?
0
Answer:
htgjyk
Step-by-step explanation:
Find the indicated margin of error. In a survey of 1485 adults from one town, 744 said they had tried some form of alternative medicine. Find the margin of error for the 97% confidence interval used to estimate the population proportion. Round your answer to three decimal places.
The margin of error for the 97% confidence interval is approximately 0.021
The margin of error for the 97% confidence interval used to estimate the population proportion can be calculated using the formula: margin of error = z * √((p * (1 - p)) / n), where z is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.
To calculate the margin of error, we need to determine the sample proportion, which is the ratio of the number of adults who said they had tried alternative medicine to the total sample size: p = 744/1485 = 0.5017.
The z-score for a 97% confidence level is approximately 1.8808 (obtained from the standard normal distribution table).
Plugging in the values:
margin of error = 1.8808 * √((0.5017 * (1 - 0.5017)) / 1485) ≈ 0.021
Therefore, the margin of error for the 97% confidence interval is approximately 0.021, rounded to three decimal places.
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Help me plsssssssss I need help
Answer:
432 each.
Step-by-step explanation:
You make 20% .2%
What is the value of f(x) = 4x -9
Answer:
F= 1 /4 y+ 9 /4
Step-by-step explanation:
brainliest?
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:
What is x abc def
A. 45
B. 60
C. 75
D. 30
Answer:
C
Step-by-step explanation:
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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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 =600cm3Find 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 )
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°
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
(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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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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Find the measure of the indicated angle to the nearest degree.
Answer:
37 degrees
Step-by-step explanation:
Cos x = 48/60
Cos x = 0.8
x = cos^-1 0.8
x = 36.8699
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! ^^
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
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:
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.
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.
1. Determine the truth values for each of the following statements. (a) The sum of 4 and 6 is prime if and only if either 4 or 6 is prime. (b) If 3 divides 20, then 6 divides 20.
(a) The statement "The sum of 4 and 6 is prime if and only if either 4 or 6 is prime" is false.
(b) The statement "If 3 divides 20, then 6 divides 20" is true.
(a) The sum of 4 and 6 is prime if and only if either 4 or 6 is prime.
To determine the truth value of this statement, we need to evaluate both directions separately.
Direction 1: If the sum of 4 and 6 is prime, then either 4 or 6 is prime.
This direction is true because the sum of 4 and 6 is 10, which is not a prime number. Therefore, the statement is true.
Direction 2: If either 4 or 6 is prime, then the sum of 4 and 6 is prime.
This direction is false because neither 4 nor 6 is a prime number, but their sum is 10, which is not a prime number. Therefore, the statement is false.
Since the statement is not true in both directions, the overall statement is false.
(b) If 3 divides 20, then 6 divides 20.
To determine the truth value of this statement, we need to evaluate the implication.
If 3 divides 20, then 6 divides 20.
This statement is true because 3 divides 20 (3 is a factor of 20), and 6 also divides 20 (6 is a factor of 20). Therefore, the statement is true.
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The linear graph shows the possible combinations of cakes and pies a club must sell to meet their fundraising goal. What is the domain of the graph? A) {x: 0 < x < 40} B) {x: 0 ≤ x ≤ 40} C) {x: 0 < x < 20} D) {x: 0 ≤ x ≤ 20}
Answer:
[tex]\{x: 0 \le x \le 40 \}[/tex]
Step-by-step explanation:
Given
See attachment for graph
Required
The domain of the graph
To do this, we simply write out the range of value of the x-coordinate.
From the attached graph, the x values are:
[tex]x = [0,40][/tex] i.e. from 0 to 40 (both inclusive)
So, the domain is:
[tex]\{x: 0 \le x \le 40 \}[/tex]