A researcher wants to conduct a significance test for the correlation between extraversion and happiness. What is the null hypothesis in this analysis

Answer: θ≈48,81°.

Step-by-step explanation:

\(sin\theta=\frac{8}{\sqrt{113}}\\sin\theta } =\frac{8*\sqrt{113} }{\sqrt{113}*\sqrt{113} } \\sin\theta=\frac{8*\sqrt{113} }{113} \\sin\theta\approx0,75258\\\theta\approx48,81^0.\)

Good luck an' have a nice day!

Step 1:

The formula for the area of a hexagon can also be given in terms of the apothem as,

Area of hexagon

where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.

Step 2:

Length of the sides = 15 cm

Step 3:

Find the Apothem ' a '

Find each angle

Next

Answer:

yes this is the answer lol

Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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if X is a uniformly distributed continuous random variable from 0 to 1. Let Y=-In(1-X), the probability that Y is less than 3 is 0.9502. This falls within the specified margin of error of +/- 0.01,

To find the probability that Y is less than 3, we first need to determine the cumulative distribution function (CDF) of variable Y. Let's begin by finding the distribution of Y.

Y = -ln(1 - X)

Taking the derivative of Y with respect to X, we get:

dY/dX = -1 / (1 - X)

Now, we can use the probability density function (PDF) of X to find the PDF of Y:

f_Y(y) = f_X(g^-1(y)) * |(dg^-1(y) / dy)|

where g(x) = -ln(1-x), g^-1(y) = 1 - e^-y, and |(dg^-1(y) / dy)| = e^-y.

Since X is uniformly distributed from 0 to 1, its PDF is f_X(x) = 1 for 0 <= x <= 1.

Thus, we have:

f_Y(y) = 1 * e^-y = e^-y

for y > 0.

Now, let's find the CDF of Y:

F_Y(y) = P(Y <= y)

      = P(-ln(1-X) <= y)

      = P(1-X >= e^-y)

      = P(X <= 1-e^-y)

Since X is uniformly distributed from 0 to 1, its CDF is:

F_X(x) = x for 0 <= x <= 1

Therefore, we have:

F_Y(y) = F_X(1-e^-y) = 1 - e^-y

for y > 0.

Now, we can find the probability that Y is less than 3:

P(Y < 3) = F_Y(3)

        = 1 - e^-3

        = 0.9502 (rounded to four decimal places)

Therefore, the probability that Y is less than 3 is 0.9502. This falls within the specified margin of error of +/- 0.01, so we can be confident in our result.

In summary, we first found the distribution of Y by taking the derivative of Y with respect to X and using the PDF of X. We then found the CDF of Y by using the CDF of X and the inverse function of Y. Finally, we used the CDF of Y to find the probability that Y is less than 3, which was within the specified margin of error.

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Answer:

It cant be converted to decimal or fraction while it is a integer

The pmf provides the probabilities of having 1, 2, or 3 children in the family based on the condition that the family stops having children once it has three children of the same gender.

To find the probability mass function (pmf) of the number of children in the family, we need to consider the possible values of x (the number of children) and their corresponding probabilities.
Let's analyze the possibilities:

1. x = 1 (only one child): The probability of having either a boy or a girl is 0.5. Therefore, P(x=1) = P(B or G) = 0.5.

2. x = 2 (two children): The possible outcomes are BB, GG, or BG (in any order). Each of these outcomes has a probability of 0.5 * 0.5 = 0.25. Therefore, P(x=2) = P(BB or GG or BG) = 0.25 + 0.25 + 0.25 = 0.75.

3. x = 3 (three children): The only outcome that satisfies the condition is BBB or GGG (in any order). Each of these outcomes has a probability of 0.5 * 0.5 * 0.5 = 0.125. Therefore, P(x=3) = P(BBB or GGG) = 0.125 + 0.125 = 0.25.

From the above analysis, we have:

P(x=1) = 0.5
P(x=2) = 0.75
P(x=3) = 0.25

To summarize, the pmf of x (the number of children in the family) is:
P(x=1) = 0.5, P(x=2) = 0.75, P(x=3) = 0.25.

The pmf provides the probabilities of having 1, 2, or 3 children in the family based on the condition that the family stops having children once it has three children of the same gender.

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This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Juana would have to pay approximately $29.40 in interest for the $10,686.00 loan over a 20-day period, assuming an annual interest rate of 5.79%.

The interest Juana would have to pay in 20 days can be calculated using the formula:

Interest = Principal × Interest Rate × Time

In this case, the principal amount is $10,686.00 and the interest rate is 5.79% per annum. To calculate the interest for 20 days, we need to convert the time to a fraction of a year. Since there are 365 days in a year, the time in years would be 20/365.

Using the formula and substituting the values:

Interest = $10,686.00 × 0.0579 × (20/365)

Calculating this expression, we find that the interest amount Juana would have to pay in 20 days is approximately $29.40.

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Answer:

218,048. skeins

Step-by-step explanation:

This question is built to throw you off by not telling you about the information in order.

First, the polypay sheep produces 9.9 pounds of wool.

Then, each pound produces 10.95 miles of yarn.

And finally, the yarn is packaged into skeins that are 175 yards each.

Each polypay sheep is 9.9 pounds. And we will use that total weight to find the amount of yarn in miles.
Then we will split up that yarn into equal pieces to make skeins.

BUT, the pieces are measured in yards, so we will have to convert the miles of yarn into an equivalent amount in yards as well. (Unmatched units of measurements don't mix well).

So, our equation will look like this:

(#of sheep) \(\times\) (9.9 pounds per sheep) \(\times\) (10.95 miles per yarn) \(\times\) (1760 yards per mile) \(\div\) (175 skeins per yard)

The number of sheep Bill has is 200.

So, we plug that into the number model we made.

\(200\times9.9\times10.95\times1760\div175\)

We end up with:

218,048.914

The decimal indicates that there is a remaining amount of yarn that couldn't be properly packaged into a skein.

Since, that remainder is not a complete skein, we must ignore its existence.

So the number of skeins expected is:

218,048

The number of skeins of yarn is Bill's flock expected to produce in one year is 1819.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a polypay sheep produces an average 9.9 pounds of wool annually.

Farmer Bill has a flock of 200 polypay sheeps

So, total weight of wool is 9.9×200

= 1980 pounds

One pound of wool makes 10.95 miles of yarn.

So, the number of yarns = 1980/10.95

= 180.82 miles of yarn

We know that, 1 mile =1760 yards

Then, 180.82 miles

= 318243.2 yards

This wool is cleaned, spun into yarn and then packaged into skeins of 175 yards of yarn each.

Number of skeins = 318243.2/175

= 1819

Therefore, the number of skeins of yarn Bill's flock expected to produce in one year is 1819.

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Answer:597

Step-by-step explanation: because your adding and subtracting

Therefore, the only statement that is equivalent to "the price decreased by \(\frac{1}{3}\)" is:

F. The price is now 66, 2/3% of what it was before

Given that the original price of something decreased by 1/3, it means:

the original price is reduced by one-third.

Any option showing or suggesting an increase is definitely the wrong answer.

Therefore, the only statement that is equivalent to "the price decreased by \(\frac{1}{3}\)" are:

F. The price is now 66, 2/3% of what it was before

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Answer:

F

Step-by-step explanation:

The theoretical probability of spinning green on the spinner, divided into 4 equal-size sections colored red, green, orange, and blue, is ¼ or 25%.

In this scenario, the spinner has four equal-size sections. Since each section is of equal size, the probability of landing on any specific section is the same. Therefore, the probability of spinning green, which is one out of the four possible outcomes, is 1/4 or 25%.

To calculate the theoretical probability, we divide the favorable outcomes (spinning green) by the total possible outcomes. In this case, there is one favorable outcome (green) out of four possible outcomes (red, green, orange, and blue), resulting in a probability of 1/4 or 25%.

It's important to note that theoretical probability is based on the assumption of equally likely outcomes and assumes a large number of trials. In practice, actual outcomes may deviate from theoretical probabilities due to factors like imbalances in the spinner or inherent randomness.

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Answer:

Zyndy is 14, Vyndel is 7.

Step-by-step explanation:

Let Zyndy's age be represented by 'z', and Vyndel's age be represented by 'v'.

Zyndy is twice the age of Vyndel, so z=2v

The sum of their age is twenty-one, so z+v=21

Sub the first equation above into the second to get:

2v+v=21

3v=21

v=7

Knowing v=7, we can say z=2(v)=14.

The argument is valid as the conclusion logically follows from the given premises, regardless of the truth values assigned to p and q. The contrapositive of "If I am bad, then I will be happy" is "If I am not happy, then I am not bad.

To evaluate the truth value of the argument without using a truth table, let's translate it into symbolic logic:

Let p represent "I'm going to the park."

Let q represent "I'm going home."

Let s represent "I'm going to study."

The argument can be expressed symbolically as follows:

Premise 1: p ∨ q (I'm going to the park or I'm going home)

Premise 2: q → ¬s (If I go home, then I'm not going to study)

Conclusion: p → s (Therefore, if I go to the park, then I am going to study)

We know that p is false and q is true, we can substitute the truth values into the premises and conclusion:

Premise 1: F ∨ T (False or True) - This is True because at least one of the options is True.

Premise 2: T → ¬s (True implies Not s) - This is True because q is True, which implies ¬s.

Conclusion: F → s (False implies s) - This is True because the antecedent (p) is False, so the implication is automatically true.

Based on these truth values, we can conclude that the argument is valid. The conclusion follows logically from the given premises, regardless of the specific truth values assigned to p and q.

Bonus: The contrapositive of "If I am bad, then I will be happy" is "If I am not happy, then I am not bad." In symbolic logic, it can be represented as ¬s → ¬p, where s represents "I am happy" and p represents "I am bad." The contrapositive swaps the antecedent and consequent of the conditional statement and negates both parts.

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The probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

Total number of outcomes = C(25, 2) = 300

Total number of favorable outcomes = C(20, 2) = 190

Probability = 190/300 = 19/30 or

= 0.63

Thus, the probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

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The histogram that represents a set of data that is left-skewed is the one where the majority of the data is on the right side of the histogram, and the tail of the histogram extends to the left.

A left-skewed histogram is also called a negatively skewed histogram. In a left-skewed distribution, the majority of the data values are on the right side of the histogram, and the tail of the histogram extends to the left. This means that the data is clustered around higher values and gradually decreases as the values become smaller.

For example, imagine a dataset that represents the ages of a group of people. If most of the people in the group are young adults, but there are a few older individuals, the histogram would be left-skewed because the tail of the histogram (representing the older individuals) would extend to the left.

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Linear Pair of Angles: two angles that form a straight line - they are supplementary.A linear pair of angles refers to two adjacent angles that add up to 180 degrees.

It is important to note that the sum of the angles in a linear pair of angles will always equal 180 degrees. A linear pair of angles must be adjacent, meaning that they share a common vertex and a common side but no other interior points.

Linear pairs of angles can be used to solve problems involving complementary, supplementary, and vertical angles. Since they add up to 180 degrees, they are considered to be supplementary angles. This is because supplementary angles are two angles that add up to 180 degrees.

Therefore, a linear pair of angles is also supplementary because it contains two adjacent angles that add up to 180 degrees. In other words, if two angles form a straight line, then they are considered to be supplementary.

The use of linear pairs of angles is prevalent in geometry problems involving parallel lines, triangles, and polygons.

The concept of a linear pair of angles is also important in understanding the different types of angles, including acute, obtuse, and right angles. For instance, an acute angle can form a linear pair with an obtuse angle, while a right angle can only form a linear pair with another right angle.

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Answer:

If the slope is going downwards, the slope needs to be negative. But if it is going upwards, it should be positive. It all depends on the direction.

Step-by-step explanation:

The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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Answer:

Yes

Step-by-step explanation:

Answer:

b / 4

Step-by-step explanation:

If you are splitting b bumper stickers between 4 members, you must divide the number of bumper stickers by the number of members, which is 4! Dividing is just like if you were to divvy something up between people, but it is a mathematical term! This will give you  b / 4.

Answer:

Since for each household there are only two possible outcomes, the a household owning stock is independent of any other household and there is a fixed number of trials, this experiment is a binomial experiment.

Step-by-step explanation:

We have to take into consideration three things:

For each household, there are only two possible outcomes, either they own stocks, or they do not.

The probability of a household owning stock is independent of any other household, that is, for any household, the probability of someone owning stocks is 28%.

There is a fixed number of trials.

Is this experiment a binomial experiment?

Since for each household there are only two possible outcomes, the a household owning stock is independent of any other household and there is a fixed number of trials, this experiment is a binomial experiment.

Answers:

1) \(\sf \boxed{1} \ x^2 + \boxed{2} \ x -24\)

2) \(\sf \boxed{2} \ x^2+ \boxed{-1} \ x-15\)

3) \(\sf \boxed{6} \ x^2+\boxed{19} \ x+10\)

4) \(\sf \boxed{2} \ x^2+\boxed{-11} \ x+5\)

solving step wise:

1)

2)

3)

4)

#1

#2

#3

#4

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

The solution is, 3/8 oil (in cups) is needed per cup of water.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

A recipe requires 1/4 cup of oil for every 2/3 cup of water.

i.e. for 2/3 cup needed oil = 1/4

so, for 1 cup needed oil = 1/4 ÷ 2/3

                                       =1/4 * 3/2

                                       =3/8

Hence, The solution is, 3/8 oil (in cups) is needed per cup of water.

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Step-by-step explanation:

x+2x+8 =200

3x=200-8

3x=192

x = 64

Martha has 64 pence

Peter jas 136 pence