A company needs to determine the optimum power and time settings for their new licorice-flavored microwaveable popcorn. They want to find a combination of power and time that delivers high-quality popcorn with less than 11% of the kernels left unpopped, on average-a value that their market research says is demanded by their customers. Their research department experiments with several settings and determines that power 9 at 4 minutes is optimum. Their tests confirm that this setting meets the less than 11% requirement. They change the instructions on the box and promote a new money back guarantee of less than 11% unpopped kernels. Complete parts a) and b) below.
a) If, in fact, the setting results in more than 11% kernels unpopped, what kind of error have they made? What will the consequence be for the company? What are the null and alternative hypotheses in this case?
A. H_o: μ< 11 vs. H_A: μ = 11
B. H_o: μ= 11 vs. H_A: μ> 11
C. H_o: μ= 11 vs. H_A: μ< 11
D. H_o: μ> 11 vs. H_A: μ = 11
b) To be sure that the method was successful, the research department popped 8 more bags of popcorn (selected at random) at this setting. All were of high quality, with the percentages of unpopped kernels being 6.7,12.9, 10.6, 7, 7.1, 3.1, 2.0, and 4.8. Does this provide evidence that they met their goal of an average of fewer than 11% unpopped kernels? Assume α=0.05.
c) Find T
d) Find P

Step-by-step explanation:

the the height should be 16 cm I used the Pythagoras theory thank you.

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!

Answer:

htgjyk

Step-by-step explanation:

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! ^^

Answer:

F= 1 /4 y+ 9 /4

Step-by-step explanation:

brainliest?

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 )

Answer:

7: 15

Step-by-step explanation:

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

Answer:

30.5

Step-by-step explanation:

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

(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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Answer: i dont know

Step-by-step explanation:

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]

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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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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Answer:

C

Step-by-step explanation:

20-10=10

10-3=7

7cm

Then the volume is 7cm

Step-by-step explanation:

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 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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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 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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Answer:

6.25

Step-by-step explanation:

Answer:

37 degrees

Step-by-step explanation:

Cos x = 48/60

Cos x = 0.8

x = cos^-1 0.8

x = 36.8699

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.

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.

Answer:

432 each.

Step-by-step explanation:

You make 20% .2%

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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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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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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