8
Write 8 numbers on the spinner
so that all of the boxes are true.
The probability of
landing on 2 is
The chance of landing
on 4 is 25%
The chance of
landing on 1 is 0
The number with the
highest probability is 5.
[2]

The area of the shaded sector of the circle is 3π ft².

A sector of a circle is simply a region bounded by two radii of the circle and an arc of the circle.

The area of a sector can be found using the formula:

A = (θ/360) × πr²

Where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is pi.

From the image:

Central angle θ =  360° - 90° = 270°

Radius r = 2ft

Plug the given values into the above formula and solve for area.

A = (θ/360) × πr²

A = (270/360) × π × (2ft)²

A = (270/360) × π × 4ft²

A = 3/4 × π × 4ft²

A = 3π ft²

Therefore, the area is 3π ft².

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Answer: i belive its B but im not 100%

Step-by-step explanation:

The required probability that she'll use a cab exactly one time is  4/9.

probability is a part of math that arrangements with figuring out the probability of the event of an occasion.

Elizabeth lives in San Francisco and works in Mountain View.

In the first part of the day she has 3 transportation choices  (bus, cab, train) to work, and at night she has similar 3 options for her outing home.

All transportation  (bus, cab, train) are comparably liable to be chosen, and 1 of them should be chosen in the first part of the day and night, so we get:

P (bus) = P (taxi) = P (train) = 1/3.

We additionally have P(no taxi in night) = P(no taxi at morning) = 2/3

Presently, P(using taxi precisely once) = P(cab at morning and no taxi at night) + P(no taxi at morning and taxi at night)

= P(cab, no taxi) + P(no taxi, taxi)

= 1/3 × 2/3 + 2/3 × 1/3

= 2/9 + 2/9

= 4/9

Consequently, the probability that Elizabeth utilizes a taxi just once is 4/9.

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We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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In an ANOVA analysis with six independent samples of equal size and a total degrees of freedom of 35, the degrees of freedom for the within sum of squares can be determined. The options provided are a. 30, b. 5, c. 31, d. 6, and e. 30.

The degrees of freedom for the within sum of squares in an ANOVA analysis is calculated as the total degrees of freedom minus the degrees of freedom for the between sum of squares. In this case, the total degrees of freedom is given as 35. Since there are six independent samples, the degrees of freedom for the between sum of squares is equal to the number of groups minus one, which is 6 - 1 = 5.

Therefore, the degrees of freedom for the within sum of squares is equal to the total degrees of freedom minus the degrees of freedom for the between sum of squares, which is 35 - 5 = 30.

In conclusion, the correct answer is option a. 30, which represents the degrees of freedom for the within sum of squares in this ANOVA analysis.

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Answer:

B and D

Step-by-step explanation:

Answer:

162°

Step-by-step explanation:

To convert from radian to degree measure

degree measure = radian measure × \(\frac{180}{\pi }\) , then

degree = \(\frac{9\pi }{10}\) × \(\frac{180}{\pi }\) ( cancel π and 10/ 180 to simplify )

            = 9 × 18

           = 162°

Answer:

324.

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

5x-7y=14

-7y=14-5x

y=-2+5/7x

y=5/7x-2

This slope is 5/7. This is because in the standard form of a line (y=mx + b), m represents the slope. In the equation above, 5/7 is the slope.

The information provided hows an investment that yields a simple interest.

A simple interest is calculated as follows;

Therefore, Dante's investment after 3 years at the rate of 2% (that is 0.02) would be;

ANSWER:

After 3 years, Dante would have $3,710 in his account

Answer:

Step-by-step explanation:

I had this exact question and I figured it out.

the answer is: P(police officer and chooses car)

In order to get this answer I did the P(police officer) X P(choosing car)

It ended up being 36/45 X 15/45. Which is equal to around .2666667.

Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.

lucky enough, the product of 36/45 and 15/45 is equal to 12/45.

So 0.8 X 0.33 = .26

.26 = .26

Answer:

answer is P(police officer and chooses car)

Step-by-step explanation:

the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)

The area of the largest possible inscribed triangle with one side as a diameter of the circle is 72 square centimeters.

The largest possible inscribed triangle with one side as a diameter of the circle has a right angle.
To find the area of the inscribed triangle, we need to calculate the length of the base and the height. Since the diameter of the circle is the base of the triangle, it has a length of 2 times the radius, which is 12 cm.
The height of the triangle is equal to the radius of the circle, which is 6 cm.
To calculate the area of the triangle, we use the formula:
Area = 1/2 * base * height

= 1/2 * 12 cm * 6 cm

= 72 square cm
Therefore, the area of the largest possible inscribed triangle with one side as a diameter of the circle is 72 square centimeters.

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Answer:

=3x to the power of 12+20x to the power of 6+6

Step-by-step explanation:

simplify step-by-step-

\(3x1x^{2} 2+2x^{2} 0x6+6x^{2} x12\)

There are no like terms so that means that the answer is

=3x to the power of 12+20x to the power of 6+6

Answer:

1 3/5

Step-by-step explanation:

First put the wholes into the fraction:

8 1/5 = 40/5 + 1/5 = 41/5

6 3/5 = 30/5 + 3/5 = 33/5

Now the difference is a simple subtraction

41/5 - 33/5 = 8/5 = 1 3/5

Answer:

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

the mean is (the sum of numbers in a data set)/(# of points in that data set).

So,

\(\frac{4+8+9+x+2}{5} = 6\),

\(\frac{23+x}{5} = 6\),

23+x = 6*5

23+x = 30

x= 30-23

x = 7

Hence, the value of x is 7.

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Answer:

1/8 more yards

Step-by-step explanation:

ez

The equation representing a line parallel to the line through a(0, 2) and b(1, 0) is y = -2x + 2.

To find the equation of the line passing through points a(0,2) and b(1,0)

The first thing that needs to be determined is the slope of the line.

We can then use the point-slope form of the equation to find the equation of the line.

We can find the slope of the line by using the formula:m=(y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) = a(0, 2) and (x₂, y₂) = b(1, 0).

Substituting the values, we get:m=(0 - 2)/(1 - 0)=-2/1=-2

Therefore, the slope of the line passing through points a and b is -2.

A line parallel to this line will have the same slope.

Hence, we can use the slope-intercept form of the equation to find the equation of the parallel line.

The slope-intercept form of the equation is:y = mx + b ,where m is the slope and b is the y-intercept.

To find the equation of the parallel line, we need to find the value of b.

We know that the line passes through the point a(0, 2).

Hence, we can substitute the values of x and y into the slope-intercept form of the equation and solve for b.2 = -2(0) + b2 = bTherefore, the value of b is 2.

Now we can substitute the values of m and b into the slope-intercept form of the equation to get the equation of the parallel line:y = -2x + 2

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Answer:

Answer:

the answer to your question is 4 and 4

Answer:

PNQ=117

LKQ=102

Step-by-step explanation:

LKQ=180-78=102

KQN=180-67=113

LNQ=360-82-102-113=63

PNQ=180-63=117

Answer:

∠ LKQ = 102°, ∠ PNQ = 117°

Step-by-step explanation:

∠ LKQ = 180° - 78° = 102° ( adjacent angles on a straight line )

∠ KQN = 180° - 67° = 113° ( adjacent angles on a straight line )

The sum of the interior angles of a quadrilateral = 360° , then

∠ LNQ = 360° - (102 + 113 + 82)° = 360° - 297° = 63°

Then

∠ PNQ = 180° - 63° = 117° ( adjacent angles on a straight line )

Answer: 4.5 hours

Step-by-step explanation:

Answer: 4.5 hours

Step-by-step explanation:

The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

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a. P(Y = 0|X = 0) = P(drawing a black ball from 6 black and 4 white balls) = 6/10 = 3/5If we draw a white ball, then Y = 1. b.Var(XY) = E(XY^2) - [E(XY)]^2= 64/315 - (64/315)^2= 52736/99225.

a. Var(Y|X = 0)In order to determine Var(Y|X = 0), we must first determine the conditional probability P(Y = 1|X = 0). Since X = 0 means there are no white balls in the sample of size 4, we know that all 4 balls are black. Thus, the probability of drawing a white ball from the remaining 6 balls in the box is:P(Y = 1|X = 0) = P(drawing a white ball from 6 black and 4 white balls) = 4/10 = 2/5.

Now, we can use the formula for conditional variance:Var(Y|X = 0) = E(Y^2|X = 0) - [E(Y|X = 0)]^2Since Y only takes on the values 0 and 1, we can simplify this expression:Var(Y|X = 0) = E(Y^2|X = 0) - [P(Y = 1|X = 0)]^2To find E(Y^2|X = 0), we need to compute the conditional probabilities P(Y = 0|X = 0) and P(Y = 1|X = 0) for all possible outcomes of the additional ball draw:If we draw a black ball, then Y = 0. The probability of this happening is:P(Y = 0|X = 0) = P(drawing a black ball from 6 black and 4 white balls) = 6/10 = 3/5If we draw a white ball, then Y = 1.

The probability of this happening is:P(Y = 1|X = 0) = P(drawing a white ball from 6 black and 4 white balls) = 4/10 = 2/5Now we can compute E(Y^2|X = 0) as follows:E(Y^2|X = 0) = P(Y = 0|X = 0)(0)^2 + P(Y = 1|X = 0)(1)^2= (3/5)(0) + (2/5)(1) = 2/5Finally, we can plug in all our values into the formula for conditional variance:Var(Y|X = 0) = E(Y^2|X = 0) - [P(Y = 1|X = 0)]^2= 2/5 - (2/5)^2= 6/25b. Var(XY = 1)In order to determine Var(XY = 1), we must first find E(XY) and E(X).

To find E(XY), we need to compute the joint probability distribution of X and Y. Since X and Y are not independent, we can't just multiply their marginal distributions.P(X = 0, Y = 1) is the probability that no white balls are selected in the initial sample of size 4 AND a white ball is selected from the remaining 6 balls in the box:P(X = 0, Y = 1) = P(no white balls in sample of size 4) * P(drawing a white ball from 6 black and 4 white balls)= (6/10)(5/9)(4/8)(3/7) * (4/10) = 2/63.

b. Similarly, we can find the probabilities for all other possible outcomes:P(X = 1, Y = 0) = P(1 white ball in sample of size 4) * P(drawing a black ball from 6 black and 3 white balls)= (4/10)(6/9)(4/8)(3/7) * (6/10) = 36/315P(X = 1, Y = 1) = P(1 white ball in sample of size 4) * P(drawing a white ball from 6 black and 3 white balls)= (4/10)(6/9)(4/8)(3/7) * (4/10) = 16/315P(X = 2, Y = 0) = P(2 white balls in sample of size 4) * P(drawing a black ball from 6 black and 2 white balls)= (6/10)(4/9)(3/8)(3/7) * (6/10) = 54/315P(X = 2, Y = 1) = P(2 white balls in sample of size 4) * P(drawing a white ball from 6 black and 2 white balls)= (6/10)(4/9)(3/8)(3/7) * (4/10) = 24/315P(X = 3, Y = 0) = P(3 white balls in sample of size 4) * P(drawing a black ball from 6 black and 1 white ball)= (4/10)(3/9)(2/8)(3/7) * (6/10) = 36/315P(X = 3, Y = 1) = P(3 white balls in sample of size 4) * P(drawing a white ball from 6 black and 1 white ball)= (4/10)(3/9)(2/8)(3/7) * (4/10) = 16/315P(X = 4, Y = 0) = P(all 4 white balls in sample of size 4) * P(drawing a black ball from 6 black and 0 white balls)= (4/10)(3/9)(2/8)(1/7) * (6/10) = 6/315P(X = 4, Y = 1) = P(all 4 white balls in sample of size 4) * P(drawing a white ball from 6 black and 0 white balls)= (4/10)(3/9)(2/8)(1/7) * (4/10) = 4/315.

Now we can compute E(XY) as follows:E(XY) = ΣXiYiP(Xi, Yi) = (0)(2/63) + (0)(36/315) + (1)(16/315) + (2)(24/315) + (3)(16/315) + (0)(6/315) + (0)(4/315) = 64/315Next, we can compute E(X) as follows:E(X) = ΣXiP(Xi) = (0)(6/210) + (1)(80/210) + (2)(90/210) + (3)(24/210) + (4)(1/210) = 18/7Finally, we can plug in all our values into the formula for variance:Var(XY) = E(XY^2) - [E(XY)]^2Since XY only takes on the values 0 and 1, we can simplify this expression:E(XY^2) = P(XY = 0)(0)^2 + P(XY = 1)(1)^2= (64/315)(1) + (251/315)(0) = 64/315Therefore,Var(XY) = E(XY^2) - [E(XY)]^2= 64/315 - (64/315)^2= 52736/99225.

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A survey conducted in 2008 found that 46% of full-time college students surveyed were current drinkers of alcohol.

Survey can be defined as data or information collected from a population so as to draw or reach a conclusion.

Based on the survey that was carried out by the researcher in the year 2008 for full time college student the survey shows that 46% of the student consume alcohol.

Therefore 46% of full time college student are drinkers of alcohol.

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Answer:

\(\frac{1}{2^{n} }\)

Step-by-step explanation:

The rules of exponents state that

\(a^{-m}\) = \(\frac{1}{a^{m} }\) and \(a^{0}\) = 1

Thus

\(2^{-5}\) = \(\frac{1}{2^{5} }\) = \(\frac{1}{32}\)

\(2^{-4}\) = \(\frac{1}{2^{4} }\) = \(\frac{1}{16}\)

\(2^{-3}\) = \(\frac{1}{2^{3} }\) = \(\frac{1}{8}\)

and so on , to

\(2^{0}\) = 1

Answer:75 ft

Step-by-step explanation:sea level is represented as 0. going from 0 to -75 is 75 ft