given solid of hemisphere and cylinder having total height 35 cm and radius is 7 cm find the volume of solid

The area or amount of cloth that will be required to make the sail of the boat is 50.5 square feet (approx.).

Given that the boom of a sailboat is 26 feet long and the sail is an equilateral triangle. We have to determine the amount of cloth that will be required to make the sail of the boat.

The formula to calculate the area of an equilateral triangle is:

A = (√(3)/4)*a²,

where

A represents the area of the equilateral triangle

a represents the side of the equilateral triangle.

Here, the sail is an equilateral triangle.

Therefore, the length of each side of the sailboat is given as:

Length of each side of the sailboat = 26 feet / 3

                                                          = 8.67 feet or 8 feet (approximately)

We can calculate the area of the sail using the below formula;

A = (√(3)/4)×a²,

where,

A represents the area of the equilateral triangle

a represents the length of each side of the sailboat.

By substituting the value of a = 8.67 in the above equation, we get the area of the sail as follows:

A = (√(3)/4)×a²

A = (√(3)/4)*(8.67)²

A = 50.5 square feet (approx.)

Hence, the amount of cloth that will be required to make the sail of the boat is 50.5 square feet (approx.).

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Marcus’s average speed is 2 miles per hour less than Jane’s average speed.

From the given information, it is stated that Marcus's average speed is 2 miles per hour less than Jane's average speed. Therefore, Marcus's average speed is slightly slower than Jane's average speed. This can be observed on the graph where Marcus's line would be slightly below Jane's line.

The equation given for Jane's average speed is y = 6x, where x represents the number of hours and y represents the number of miles. This equation implies that for every hour Jane runs, she covers 6 miles. Marcus's average speed, being 2 miles per hour less than Jane's, would be represented by the equation y = 6x - 2. Thus, for every hour Marcus runs, he covers 6 miles minus 2 miles, which is 4 miles.

In conclusion, Marcus's average speed is 2 miles per hour less than Jane's average speed. This means that Jane has a slightly faster pace than Marcus during the marathon.

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The number line can be used to determine the sum of the location of point T and -1 1/2. By visually representing the positions of these points on the number line, we can determine their sum by adding their locations.

To determine the sum of the location of point T and -1 1/2, we can plot the point T on the number line and then locate -1 1/2 on the number line. We can then add the locations of these points on the number line to find their sum.

For example, if point T is located at 3 on the number line and -1 1/2 is located at -1.5, we can add 3 and -1.5 to find their sum, which would be 3 + (-1.5) = 1.5.

By using the number line, we can visually represent the locations of the points and perform addition to find their sum accurately.

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Given that Aaron ate half as much pizza as David and Aaron ate 1/4 of a pie, we can determine the fraction of the pie David ate by setting up an equation and solving for it.

Let's assume that David ate x amount of pizza, which represents the fraction of the pie he consumed. Since Aaron ate half as much pizza as David, we can express Aaron's portion as (1/2)x. We are also given that Aaron ate 1/4 of a pie, so we can set up the equation:

(1/2)x = 1/4

To solve for x, we can multiply both sides of the equation by 2 to eliminate the fraction:

2 * (1/2)x = 2 * (1/4)

x = 1/2

Therefore, David ate 1/2 of the pie. This means that Aaron ate half as much pizza as David, while David consumed the remaining half of the pie.

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none of the provided approximations for the probabilities are accurate.To determine which statement is true, we need to calculate the probabilities of selecting each color marker.

Total number of markers = 20 green + 44 orange + 30 blue = 94 markers.

P(blue) = Number of blue markers / Total number of markers = 30 / 94 ≈ 0.319.

P(green) = Number of green markers / Total number of markers = 20 / 94 ≈ 0.213.

P(orange) = Number of orange markers / Total number of markers = 44 / 94 ≈ 0.468.

Based on the calculations, none of the given statements are true. The actual probabilities are approximately:

P(blue) ≈ 0.319,
P(green) ≈ 0.213,
P(orange) ≈ 0.468.

Therefore, none of the provided approximations for the probabilities are accurate.

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(a) The landscaper needs 3 times the sum of the length and width of the yard in meters for the fencing.

(b) The area of the garden is one-third of the area of the yard, multiplied by 2.25.

We have,

(a) To find the amount of fencing needed, we need to determine the perimeter of the yard in meters.

According to the scale, 2 cm on the drawing represents 3 m in reality. This means that 1 cm on the drawing represents 1.5 m in reality (since 3 m divided by 2 cm is 1.5 m/cm).

Let's assume the length of the yard in the drawing is L cm and the width is W cm.

Then, the length of the actual yard would be L x 1.5 m, and the width would be W * 1.5 m.

The perimeter of the yard is given by the formula:

Perimeter = 2 x (length + width)

Substituting the actual measurements, we have:

Perimeter = 2 x (L x 1.5 m + W x 1.5 m)

= 3 x (L + W) m

Therefore, the landscaper would need 3 times the sum of the length and width of the yard in meters for the fencing.

(b) The area of the garden can be determined by calculating 1/3 of the area of the actual yard.

Let's assume the area of the yard in the drawing is A square cm. Then, the area of the actual yard would be A x (1.5 m)², since each dimension is scaled by 1.5 m/cm.

To find the area of the garden, we calculate:

Area of garden = (1/3) x Area of yard

= (1/3) x (A x (1.5 m)^2)

= (1/3) x (A x 2.25) square meters

Therefore, the area of the garden would be one-third of the area of the yard, multiplied by 2.25.

Thus,

(a) The landscaper needs 3 times the sum of the length and width of the yard in meters for the fencing.

(b) The area of the garden is one-third of the area of the yard, multiplied by 2.25.

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To determine the percentage of shots that the goalie saved, we need the actual numbers of saves and goals scored against the goalie. Since the specific values are not provided in the question, it is not possible to calculate the exact percentage.

However, I can explain the general process for calculating the percentage of savings.

To find the percentage of saves, we need to divide the number of saves by the total number of shots and then multiply by 100. The formula for calculating the percentage is:

Percentage of saves = (Number of saves / Total number of shots) * 100

For example, if the goalie made 30 saves out of 40 total shots, the calculation would be:

Percentage of saves = (30 / 40) * 100 = 75%

In this case, the goalie saved 75% of the shots.

Without the specific values of saves and shots, it is not possible to determine the exact percentage.

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The measure of segment QS can be determined by adding the lengths of QR and RS. In this case, since QR is 10 units long and RS is 7 units long, the measure of QS would be 17 units.

To find the measure of segment QS, we need to add the lengths of QR and RS. Given that QR is 10 units long and RS is 7 units long, we can calculate the measure of QS by adding these two lengths together. Therefore, QS = QR + RS = 10 + 7 = 17. Hence, the measure of segment QS is 17 units. By adding the lengths of the two segments that make up QS, we obtain the total length of the segment itself.

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When a straight angle is split into two angles, the sum of those angles is 180 degrees because a straight angle measures 180 degrees.

Let's assume that the smaller angle is represented by x. Since the larger angle is twice as big as the smaller angle, it can be represented as 2x. Therefore, the sum of the two angles can be expressed as:

x + 2x = 180 degrees This simplifies to 3x = 180 degrees.

Dividing both sides by 3, we get: x = 60 degrees.

This means that the smaller angle is 60 degrees and the larger angle is twice as big, or 2(60) = 120 degrees.

Therefore, the two angles are 60 degrees and 120 degrees.

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The expression "x - 12" can be modeled in a real world situation where you are trying to find the difference between a number x and 12. Here is an example:Suppose you have a jar containing x marbles.

You give away 12 marbles to your friend. The number of marbles you have left in the jar can be modeled by the expression "x - 12". In this situation, x represents the original number of marbles in the jar, and 12 represents the number of marbles given away to your friend. The expression "x - 12" calculates the number of marbles you have left after giving away 12.

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The equation is 38.25 = 4.25h and Tomás worked for 9 hours.

To find the number of hours it took Tomás to clean the garage, we can set up an equation using the given information.

Let's assume the number of hours Tomás worked is "h."

We know that Tomás was paid $4.25 per hour, so the total amount he earned can be calculated by multiplying the hourly rate by the number of hours worked:

Total earnings = Hourly rate * Number of hours

In this case, the total earnings are $38.25, and the hourly rate is $4.25:

$38.25 = $4.25 * h

To solve for "h," we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by $4.25:

$38.25 / $4.25 = h

Simplifying the right side:

9 = h

Therefore, it took Tomás 9 hours to clean the garage.

By setting up the equation and solving it, we determined that Tomás worked for 9 hours.

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The algebraic property that could be used to rewrite 4x + 2y as 2y + 4x is option C: Commutative Property of Addition.

From the question. if   a, b and c are any numbers,

Based on Associative Property of Addition, it state that:

a + ( b + c ) = ( a + b ) + c

Based on Associative Property of Multiplication, it state that:

a(bc) = (ab)c

Based on Commutative Property of Addition it state that:

a + b = b + a

Based on Commutative Property of Multiplication it state that:

ab = ba

Note that , 4x + 2y = 2y + 4x

So, Commutative Property of Addition is used in the expression.

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See text below

Which algebraic property could be used to rewrite 4x + 2y as 2y + 4x? A. Associative Property of Addition

B. Associative Property of Multiplication

C. Commutative Property of Addition

D. Commutative Property of Multiplication

2 liters per hour is equal to 555.6 millimeters per second.

To convert 2 liters per hour to millimeters per second, you need to follow these steps:

Step 1: Convert liters to milliliters

Since 1 liter = 1000 milliliters, multiply 2 by 1000 to get the number of milliliters per hour.

Therefore, 2 liters per hour is equal to 2000 milliliters per hour.

Step 2: Convert hours to seconds

Since 1 hour = 3600 seconds, divide the number of milliliters per hour by 3600 to get the number of milliliters per second.

Therefore, 2000 milliliters per hour is equal to 0.5556 milliliters per second.

Step 3: Convert milliliters to millimeters

Since 1 milliliter is equal to 1 cubic centimeter (cc) and 1 cc is equal to 1 cubic millimeter, 0.5556 milliliters per second is equal to 0.5556 cubic millimeters per second or 555.6 millimeters per second (since there are 1000 cubic millimeters in a milliliter).

Therefore, 2 liters per hour is equal to 555.6 millimeters per second.

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The total number of miles driven to and from school in 6 days would be 30 miles.

Since the round-trip drive to school is 2 1/2 miles, we can consider this as a distance traveled in one day. To find the total distance driven in 6 days, we need to multiply the distance traveled per day by the number of days.

Given that the round-trip distance is 2 1/2 miles, we can convert this mixed fraction to an improper fraction: 2 1/2 = 5/2 miles.

Multiplying the distance per day (5/2 miles) by the number of days (6 days) gives us:

(5/2) * 6 = (5 * 6)/2 = 30/2 = 15 miles.

Therefore, the total distance driven to and from school in 6 days is 15 miles.

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According to given information, option C is the correct answer.

Given that Darrel divided 8,675 by 87.

His work is shown below.

Step 1: Set up the problem with the dividend under the division symbol and the divisor outside.

Step 2: Estimate a reasonable quotient and place it above the dividend. Then multiply and subtract. Bring down the next digit of the dividend.

Step 3: Repeat step 2 until the dividend has been brought down completely.

The given picture shows the steps done:

Option C: Darrel forgot to place a zero in the quotient.

Thus option C is the correct answer.

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The third term of the sequence is 11.

The sequence given by the rule

f(1) = 5

and

f(n) = f(n-1) + 3, for n bigger than 1.

The third term of the sequence can be calculated using the given formula of the sequence.

We are given that

f(1) = 5, which means that the first term of the sequence is 5.

We can find the second term of the sequence using the formula.

f(n) = f(n-1) + 3

Now n = 2

    f(2)  = f(2-1) + 3

           = f(1) + 3

           = 5 + 3

            = 8

Therefore, the second term of the sequence is 8.

Using the same formula we can find the third term of the sequence

f(n) = f(n-1) + 3

Now n = 3

f(3) = f(3-1) + 3

     = f(2) + 3

     = 8 + 3

      = 11

Therefore, the third term of the sequence is 11. Hence, the correct answer is 11.

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1/6 is the fraction of Marjorie's ribbons that are green. Marjorie has a total of 6 ribbons and spools of thread for art, consisting of 3 pink ribbons, 1 green ribbon, and 2 blue spools of thread.

1. To determine the fraction of Marjorie's ribbons that are green, we divide the number of green ribbons by the total number of ribbons.

2. To find the fraction of Marjorie's ribbons that are green, we need to calculate the ratio of green ribbons to the total number of ribbons. The total number of ribbons is the sum of all the ribbons and spools of thread, which is 3 pink ribbons + 1 green ribbon + 2 blue spools of thread, equaling 6 ribbons in total.

3. Since Marjorie has only 1 green ribbon, we can say that the fraction of her ribbons that are green is 1 out of the total 6 ribbons. This can be expressed as 1/6. Therefore, 1/6 is the fraction of Marjorie's ribbons that are green.

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The amount of lemonade left after the consumption of 280 ml of lemonade by 14 children is 4.08 liters. The given problem can be solved by using basic mathematical operations. In the problem, it is shown that there are 14 children at the birthday party, and each child drinks 280 ml of lemonade.

And, 8 liters of lemonade are also available. The solution of the problem is as follows:

1 litre of liquid = 1000 ml of liquid

8 liters of liquid = 8 × 1000

                   = 8000 ml of liquid

Now, we can calculate the total lemonade consumed by the 14 children as follows:

Total lemonade consumed = 14 × 280

                                          = 3920 ml of liquid

                                      = 3.92liters of liquid

Therefore, the amount of lemonade left after 14 children have consumed 280 ml of lemonade each is given by:

Amount of lemonade left = 8 − 3.92

                                = 4.08liters of liquid

Therefore, 4.08 liters of lemonade is left after the 280 ml of lemonade consumption by 14 children. The problem is calculating the amount of lemonade left after 14 children have consumed 280 ml of lemonade each. To solve the problem, we first need to calculate the total amount of lemonade consumed by the 14 children. We know that each child consumed 280 ml of lemonade.

Now, we can calculate the amount of lemonade left after 14 children have consumed 280 ml of lemonade each. The amount of lemonade left is given by the difference between the total amount of lemonade available and the total lemonade consumed by the 14 children.

Therefore,

Amount of lemonade left = Total lemonade available − Total lemonade consumed

                                     = 8000 − 3920

                               = 4080 ml of liquid

                            = 4.08litres of liquid

Therefore, 4.08 liters of lemonade is left after the 280 ml of lemonade consumption by 14 children.

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The midpoint of the line segment connecting two points can be found by averaging their corresponding coordinates. Therefore, to obtain the midpoint of line BC, we add the coordinates of B and C and divide by 2.

Midpoint of line BC is given by:

\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]

The length of line AD is found by using the distance formula, which is given as:

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]

Thus, we need to find the coordinates of point D and A to determine the length of AD. The coordinates of D are the average of the coordinates of B and C.

\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]The coordinates of A are (1,2,-1).

The distance between A and D is found by substituting these values into the distance formula:

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\] \[d=\sqrt{(1-(-2))^2+(2-0)^2+(-1-1)^2}\] \[d=\sqrt{(3)^2+(2)^2+(-2)^2}\] \[d=\sqrt{9+4+4}\] \[d=\sqrt{17}\]

Thus, the distance between points A and D is sqrt(17).Therefore, the midpoint of line BC is (-2,0,1) and the distance between points A and D is sqrt(17).

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The statement "m∠PQT is 9" is false.In the given scenario, ray QS bisects ∠PQR. This means that ∠PQS and ∠SQR are equal in measure because they are the two halves of the same angle.

Let's denote the measure of ∠PQS as (7x - 6)° and the measure of ∠SQR as (4x + 15)°. Since these two angles are equal, we can set up an equation: (7x - 6) = (4x + 15). Solving this equation, we find x = 7.

Now, to find the measure of ∠PQT, we need to substitute the value of x into the expression (7x - 6)°. Plugging in x = 7, we get (7 * 7 - 6)° = 43°. Therefore, the correct statement should be "m∠PQT is 43," not 9. Thus, the statement "m∠PQT is 9" is false.

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Ali has hired Mark and Alexis to work for his shipping company, and Mark can load a truck with packages in 120 minutes, while Alexis can load the same number of packages in 240 minutes.

To find out how long they will take to load a truck together, we'll use the formula below:T = (T₁ × T₂) ÷ (T₁ + T₂)Where T is the time it takes for Mark and Alexis to load a truck together, T₁ is the time it takes for Mark to load a truck alone, and T₂ is the time it takes for Alexis to load a truck alone.

We can plug in the given values: T = (120 × 240) ÷ (120 + 240) = 28,800 ÷ 360 = 80Therefore, it would take Mark and Alexis 80 minutes to load a truck together.

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The end behaviors of the graph of the function are given by:

as x → −∞, f(x) → ∞

as x → ∞, f(x) → ∞

Thus, this is the required answer.

Solution:

The given polynomial function is of degree 2 (quadratic function).f(x) = ax² + bx + c, Where a, b, and c are real numbers with a ≠ 0.

The quadratic function has the general form: f(x) = a(x - r)(x - s)where r and s are the x-intercepts.

The given x-intercepts are (-2,0) and (2,0) which means that:r = -2 and s = 2.

So, the quadratic function can be written as:

f(x) = a(x - (-2))(x - 2)f(x) = a(x + 2)(x - 2), where a is a non-zero constant.The y-intercept is (0,-4).

We know that the y-intercept occurs where x = 0.

Substituting x = 0 and y = -4 in the quadratic function:

f(x) = a(x + 2)(x - 2)

when x = 0,

y = -4.

-4 = a(0 + 2)(0 - 2)

=> -4 = -4a

=> a = 1

The quadratic function is:

f(x) = (x + 2)(x - 2)

The end behaviors of the graph of the function are given by:

as x → −∞, f(x) → ∞

as x → ∞, f(x) → ∞

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The sum or difference of expression(-7x²- 3) + (11x² + 8) is 4x² + 5.

To find the sum or difference of the given expressions, (-7x²- 3) + (11x² + 8)

Simply by combine like terms.

(-7x²- 3) + (11x² + 8) can be rewritten as:

-7x² + 11xx² + (-3 + 8)

Simplifying further, we have:

4x² + 5

So, the sum or difference of (-7x²- 3) + (11x² + 8) is 4x² + 5.

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Acceptance sampling is a statistical procedure that involves taking a sample of a product or a lot of products and determining if it meets the required standards or specifications.

One method of acceptance sampling involves randomly selecting a sample of items without replacement and accepting the entire batch only if every item in the sample is okay.The ABC Electronics Company has just manufactured 1200 write-rewrite CDs, out of which 90 are defective. The question is asking about the probability that the entire batch will be accepted if 3 of these CDs are randomly selected for testing.We know that out of 1200 CDs, 90 are defective.

Therefore, the number of good CDs is:1200 - 90 = 1110If 3 CDs are randomly selected, the probability of getting a good CD on the first try is:1110/1200 = 37/40The probability of getting a good CD on the second try is:1109/1199The probability of getting a good CD on the third try is:1108/1198The probability of getting all three CDs that are good is:37/40 * 1109/1199 * 1108/1198 = 0.7978Therefore, the probability that the entire batch will be accepted is 0.7978 or approximately 79.78%.

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Given, Aika is building a square garden. She places a garden post at (3.5, 3.5)

To find: The location of the corner that reflects (3.5, 3.5) across the y-axis.

We know that the y-axis is the vertical line through the point (0,0) and it divides the plane into two parts: left and right. When we reflect a point across the y-axis, the x-coordinate changes sign. For example, the reflection of (2,3) is (-2,3).Therefore, the reflection of (3.5, 3.5) across the y-axis is (-3.5, 3.5)

Since Aika is building a square garden, the corner opposite to (3.5, 3.5) will have coordinates (-3.5, -3.5).

Hence, the location of the corner that reflects (3.5, 3.5) across the y-axis is (-3.5, -3.5).

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The first five terms of the sequence defined by the explicit formula an = (-2)^(n-1) are 1, -2, 4, -8, 16.

To find the first five terms of the sequence defined by the explicit formula an = (-2)^(n-1), we can substitute the values of n from 1 to 5 into the formula and calculate the corresponding terms:

The explicit formula for the sequence is given by an = (-2)^(n-1).

When n = 1: a1 = (-2)^(1-1) = (-2)^0 = 1

When n = 2: a2 = (-2)^(2-1) = (-2)^1 = -2

When n = 3: a3 = (-2)^(3-1) = (-2)^2 = 4

When n = 4: a4 = (-2)^(4-1) = (-2)^3 = -8

When n = 5: a5 = (-2)^(5-1) = (-2)^4 = 16

Therefore, the first five terms of the sequence are:

1, -2, 4, -8, 16

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The expression that can be used to determine the total distance in miles Natalie jogged over these 3 nights is:

The model for finding the total distanceNatalie went on a jog 3 nights in a row and jogged the same distance each night.

The model for finding the total distance that Natalie jogged during the 3 nights is shown below:

Model for finding the total distance where each column represents one mile, and the shaded parts of each column represent the fraction of a mile that Natalie jogged each night.

From the model, we can find the total distance in miles Natalie jogged by counting the number of shaded parts in each column and then adding them together.

The number of shaded parts in each column represents the fraction of a mile that Natalie jogged each night.

Therefore, the expression that can be used to determine the total distance in miles Natalie jogged over these 3 nights is:

[tex]$$3 \cdot 1 + \frac{1}{2} + \frac{3}{4}$$ $$= 3 + \frac{2}{4} + \frac{3}{4}$$$$= 3 + \frac{5}{4}$$$$= \frac{12}{4} + \frac{5}{4}$$$$= \frac{17}{4}$$$$= \boxed{4\frac{1}{4}}\ miles$$[/tex]

Therefore, Natalie jogged a total distance of 4 and 1/4 miles over these three nights.

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Therefore, the probability of a randomly chosen boy having a height less than 66 inches is 15.87%.

The heights of the Lincoln High School boys have a normal distribution with a mean height of 70 inches and a standard deviation of 4 inches. The probability of a randomly chosen boy having a height less than 66 inches is asked. We can solve this problem by using the standard normal distribution or z-distribution. The standard normal distribution has a mean of zero and a standard deviation of one. It is a normal distribution that has been transformed to have a mean of 0 and a standard deviation of 1. Therefore, we must convert the given values into z-scores. The z-score formula is:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this problem, we want to find the probability that a boy's height is less than 66 inches, so x = 66. Using the formula above, we get:
z = (66 - 70) / 4 = -1
This means that a boy's height of 66 inches is one standard deviation below the mean. To find the probability of a boy having a height less than 66 inches, we look up the area to the left of the z-score of -1 in the standard normal distribution table. The table gives us the probability of a randomly chosen boy having a height less than 66 inches as 0.1587 or 15.87%.
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Hence, the correct option is B) 11.1.

Given that Suzy had been working for 15 minutes when she finished problem 5 and she completed all 20 questions in 45 minutes.To find what fraction of the questions Suzy had finished when she finished problem 5; we need to subtract the time taken to finish problem 5 from total time and divide it by total time and the multiply it by 20. The answer can be rounded off to the nearest tenth if necessary.

Fraction of questions completed by Suzy = [(45-15)/45] × 20= 0.556 × 20= 11.12

As we see that Suzy had completed 11.12 questions when she finished the fifth problem.

Therefore, rounding it to the nearest tenth, the decimal form of the answer is 11.1.

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Both methods will yield the same result, which represents the probability of not seeing all three colors when drawing three balls with replacement from the given urn. The answer in this case is 3/4.

(a) Using the inclusion-exclusion principle, we define events W, G, and R for the white, green, and red balls not appearing, respectively. To calculate the probability that we did not see all three colors, we use the formula P(W U G U R) = P(W) + P(G) + P(R) - P(W ∩ G) - P(W ∩ R) - P(G ∩ R) + P(W ∩ G ∩ R). Each individual probability can be calculated by considering the number of ways each event can occur divided by the total number of possible outcomes. For example, P(W) = (3/4)^3, P(G) = (3/4)^3, P(R) = (1/2)^3, P(W ∩ G) = (2/4)^3, and so on.

(b) In the direct computation method, we calculate the probability of not seeing all three colors by subtracting the probability of seeing all three colors from 1. The probability of seeing all three colors is calculated by considering the number of ways to select one ball of each color divided by the total number of possible outcomes. There are 4 possible outcomes for each ball drawn, so the probability of seeing all three colors is 4/4 * 4/4 * 2/4 = 1/4. Therefore, the probability of not seeing all three colors is 1 - 1/4 = 3/4.

Both methods will yield the same result, which represents the probability of not seeing all three colors when drawing three balls with replacement from the given urn. The answer in this case is 3/4.


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To find the probability that we did not see all three colors when drawing 3 balls with replacement from an urn containing 1 white, 1 green, and 2 red balls, we can use the inclusion-exclusion principle or calculate directly by counting the number of ways.

To find the probability that we did not see all three colors, we can use two different calculations.

(a) Let W be the event that the white ball did not appear, G be the event that the green ball did not appear, and R be the event that the red ball did not appear. We can use the inclusion-exclusion principle to calculate the probability:

P(W ∪ G ∪ R) = P(W) + P(G) + P(R) - P(W ∩ G) - P(W ∩ R) - P(G ∩ R) + P(W ∩ G ∩ R)

(b) Alternatively, we can directly compute the probability by counting the number of ways that we did not see all three colors and dividing by the total number of possible outcomes.

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