By definition, theoretical probability is equal to:

A. No. of favorable outcomes/ total no. of possible outcomes ✅️
B. No. of total outcomes/ total no. of impossible outcomes
C. No. of possible outcomes/ total no. of favorable outcomes
D. No. of total outcomes/ total no. of possible outcomes

Answer:

The volume is 423.33 cubic millimeters.

Step-by-step explanation:

The formula for volume of a cylinder is given by:

V = πr^2h, where

Step 1:  Find radius, r, of the cylinder:

The diagram shows us the diameter, d, of the circle is 7 mm.  Since the diameter is twice the radius, r, we can find r by dividing the diameter by 2:

r = d / 2

r = 7 / 2

r = 3.5 mm

Thus, the radius of the cylinder is 3.5 mm.

Step 2:  Plug in values and round to the nearest hundredth to find the volume, V, of the cylinder:

Now we can plug in 3.5 for r and 11 for h to find V, the volume of the cylinder.  We can round at the end.

V = π(3.5)^2(11)

V = π(12.25)(11)

V = 134.75π

V = 423.3296101

V = 423.33 mm^2

Thus, the volume of the cylinder is 423.33 cubic millimeters.

In a math class with 19 students, on a day when a test and an assignment were given, there were 10 students who passed the test and 14 students who completed the assignment.

In a math class with 19 students, a test and an assignment were given on the same day.

Out of the 19 students, 10 of them passed the test and 14 students completed the assignment.

This information allows us to analyze the performance and completion rate of the students in the class.

Firstly, we can determine that there are at least 10 students who demonstrated a satisfactory level of understanding and knowledge in the subject matter, as they successfully passed the test.

This indicates that approximately 52.63% (10 out of 19) of the students achieved a passing grade on the test.

Furthermore, we know that 14 students completed the assignment.

This implies that these students fulfilled the requirements and submitted the necessary work within the given timeframe.

Consequently, we can deduce that approximately 73.68% (14 out of 19) of the students in the class completed the assignment.

It's worth noting that there may be overlap between the students who passed the test and those who completed the assignment, as well as students who did both.

However, without additional information, we cannot determine the exact number of students who passed the test, completed the assignment, or did both.

This data provides insight into the performance and diligence of the students in the math class, indicating the proportions of students who met the criteria for passing the test and completing the assignment.

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The number of missed shots after 10 weeks of practice is 1

From the question, we have the following parameters that can be used in our computation:

The line of best fit

Also, we have the equation to be

y  = -1/2x + 6

At the 10th weeks, we have

x = 10

Substitute the known values in the above equation, so, we have the following representation

y  = -1/2 * 10 + 6

Evaluate

y = 1

Hence, the number of missed shots after 10 weeks of practice is 1

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A surveyor wants to determine the width of a river is 43.34 m.

From given figure, angle ACB = angle ECD  (Vertically opposite angles are equal)

Angle BAC = Angle EDC = 90

So, triangle ABC and triangle ECD are similar.

AB/DE = AC/CD

AB/18.6 = 79.6/34.2

AB/18.6 = 2.33

AB = 2.33×18.6

AB = 43.34 m

Therefore, a surveyor wants to determine the width of a river is 43.34 m.

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Answer:

The domain and range of the graph are the same

Step-by-step explanation:

The domain and range of the graph are both [tex][0,\infty)[/tex] because you cannot take the square root of a negative number to produce a real result, and you cannot square a real number to get a negative number.

The quotient is 231, and the remainder is 9 or 231 R9.

To perform long division to find the quotient and remainder of 8,325 divided by 36, you would proceed as follows:

         ______

36 | 8,325

        1,125

         45

and,   36 (36 x 1)

          9

The quotient is 231, and the remainder is 9.

Therefore, the correct answer is 231 R9.

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Answer:

57

Step-by-step explanation:

this is the boybfiend

x ≤ 8 or x > 10 is the solution of the inequality 11 ≥ 2x - 5 or 2x - 5 > 15.

To solve the compound inequality 11 ≥ 2x - 5 or 2x - 5 > 15, we will solve each inequality separately and then combine the solutions.

Solve the first inequality: 11 ≥ 2x - 5

Add 5 to both sides to isolate 2x:

11 + 5 ≥ 2x

16 ≥ 2x

Divide both sides by 2:

8 ≥ x

So the solution to the first inequality is x ≤ 8.

Solve the second inequality: 2x - 5 > 15

Add 5 to both sides to isolate 2x:

2x > 15 + 5

2x > 20

Divide both sides by 2:

x > 10

So the solution to the second inequality is x > 10.

Combining the solutions, we have x ≤ 8 or x > 10.

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Answer:

[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]

Step-by-step explanation:

The equation of a circle with a center at (h, k) and radius r is given by:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

We are given that the points G(5,-2) and H(1, −2) lie on the circle. We can use the distance formula to find the distance between these two points.

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

[tex]d = \sqrt{(5 - 1)^2 + ((-2) - (-2))^2} = \sqrt{16} = 4[/tex]

Therefore, the radius of the circle is 4.

We can now find the center of the circle by taking the average of the x-coordinates and y-coordinates of the points G and H.

[tex](h, k) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = \left(\frac{5 + 1}{2}, \frac{-2 - 2}{2}\right) = (3, -2)[/tex]

Therefore, the equation of the circle is:

[tex](x - 3)^2 + (y + 2)^2 = 4^2[/tex]

Simplifying the equation, we get:

[tex]\bold{(x - 3)^2 + (y + 2)^2 = 16}[/tex] is a required equation.

The area of the rectangle with a length of 12 units and a width of 8 units is 96 sqaure units.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The area of a rectangle is expressed as;

Area = length × breadth

From the image:

Length of the rectangle = 12 units

Breadth of the rectangle = 8 units

Area of the rectangle = ?

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

Area = length × breadth

Area = 12 units × 8 units

Area = 96 sqaure units

Therefore, the measure of the area is 96 sqaure units.

Option A) 96 sqaure units is the correct answer.

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Answer:3x-4y=8

Step-by-step explanation:

The words for which the probability of selecting the letter A at random is 1/3 are:

a) CAB

b) ANT

c) ABOARD

Given data ,

Let the probability of selecting the letter A at random be P ( A ) = 1/3

Now , the number of letters in the words CAB are = 3

The number of A's in the word CAB = 1

So , the probability is P ( A ) = 1/3

Now , Now , the number of letters in the words ANT are = 3

The number of A's in the word ANT = 1

So , the probability is P ( A ) = 1/3

And , Now , the number of letters in the words ABROAD are = 6

The number of A's in the word ABROAD = 2

So , the probability is P ( A ) = 2/6 = 1/3

Hence , the probability is solved

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Answer:

5.85

Step-by-step explanation:

The slope constraint for the zip line is 6 to 8 feet of vertical change for every 100 feet of horizontal change.

So, if the vertical change is 7 feet, the horizontal change must be between 7/6 and 7/8 of a hundred feet, or between 11.67 and 12.5 feet.

For Zip line A, the horizontal distance is 120 feet. So, the vertical change of 7 feet is within the slope constraint.

For Zip line B, the horizontal distance is 140 feet. So, the vertical change of 7 feet is within the slope constraint.

For Zip line C, the horizontal distance is 150 feet. So, the vertical change of 7 feet is within the slope constraint.

Therefore, LaTisha's claim is correct. The vertical change of 7 feet will satisfy the slope constraint for all three locations.

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Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.

To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.

Using the Pythagorean theorem:

[tex]Hypotenuse^2 = Length^2 + Width^2[/tex]

[tex]Hypotenuse^2[/tex] =[tex]21^2 + 20^2[/tex]

[tex]Hypotenuse^2[/tex]= 441 + 400

[tex]Hypotenuse^2[/tex]= 841

Taking the square root of both sides, we find:

Hypotenuse =[tex]\sqrt{841[/tex]

Hypotenuse = 29

Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.

According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

The two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.

Using the Pythagorean theorem:

[tex]Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841[/tex]

Taking the square root of both sides, we find:

Hypotenuse = [tex]\sqrt841[/tex]

Hypotenuse = 29

Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.

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Answer:

3(5)^6

Step-by-step explanation:

There is 6, 5's in the expression meaning our answer has to be 3(5)^6.

:)

Answer:

the answer for the question given above is equal to 46875

400Answer:

Step-by-step explanation:

We can see here that the measure that should be used to summarize the data is: A. Mean.

The mean, which is used to indicate the average value of a group of values in statistics, is a measure of central tendency. It is determined by adding up all of the dataset's values and then dividing the total by the number of values.

Mean = (Sum of all values) / (Total number of values)

The mean is widely used in statistics to summarize and describe the average value of a dataset. It is a useful measure for understanding the central tendency of a set of values.

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The complete question is:

The following number of people attended last 10 screenings of a movie.

196, 197, 198, 199, 202, 203, 204, 205, 206, 208

Which measure should be used to summarize the data?

A. Mean

B. Median

C. Mode

The height of the right rectangular prism is 7.6 cm.

To determine the height of the right rectangular prism, we can use the formula for the volume of a prism:

Volume = Base Area * Height

Given that the volume is 380 cm³ and the base area is 50 cm², we can write the equation as:

380 = 50 * h

Now, let's solve for h by dividing both sides of the equation by 50:

h = 380 / 50

Simplifying the expression:

h = 7.6 cm

Therefore, the height of the right rectangular prism is 7.6 cm.

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The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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Answer:

The correct answer is:

Amplitude = 11°F; period = 8 hours; midline: y = 39

Step-by-step explanation:

Answer: A

Step-by-step explanation: Amplitude 11°F; period - 8 hours; midline: y = 39

The quadratic function has the following domain: 0 ≤ t ≤ 8.

Herein we find a quadratic equation that models the height of the rocket in time. The domain is the set of all values of t such that all values of h exist.

Mathematically speaking, the domain of quadratic equations is the set of all real numbers, but physically speaking, this domain is formed by the set of all non-negative numbers such that h ≥ 0. The domain is found by algebra properties:

h = - 16 · t² + 128 · t

h = - 16 · t · (t - 8)

Then, the domain of the quadratic function is: 0 ≤ t ≤ 8.

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Answer:

52750

Step-by-step explanation:

Step 1:  Identify the digit in the tens place:

Step 2:  Examine the digit to the right of the tens place:

Step 3:  Determine the rounding:

Since the digit to the right of the tens place is 4 (which is less than 5), we keep the tens place digit as is.

Original number: 52754.1683

Rounding to the nearest ten: 52750

Thus, rounding 52754.1683 to the nearest ten gives us 52750.

The surface area of the triangular prism is 193.05 cm².

We have,

The figure is a triangular prism.

Now,

There are 4 triangular surfaces.

Each surface area is the same except the base surface.

So,

3 surface area.

= 3 x (1/2 x 9 x 11.3)

= 3 x 50.85

= 152.55 cm²

And,

Base surface area.

= 1/2 x 9 x 9

= 40.5 cm²

Now,

The surface area of the triangular prism.

= 152.55 + 40.5

= 193.05 cm²

Thus,

The surface area of the triangular prism is 193.05 cm².

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The given information indicates that country y's unemployment rate equals 10 %.

The formula to calculate the unemployment rate is:

Unemployment Rate = ( Number of Unemployed Individuals / Civilian Labor Force ) × 100

In this case, the number of unemployed individuals actively seeking jobs is 400,000, and the civilian labor force is 4,000,000.

Unemployment Rate = ( 400, 000 / 4, 000, 000) × 100

Simplifying the calculation :

= 0. 1 x 100

= 10 %

In conclusion, the unemployment rate in Country Y is 10%.

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Step-by-step explanation:

3^(2x-1)  = 81    LOG both sides      I had to assume there were parens.

(2x-1) LOG 3 = LOG 81

2x-1 = LOG(81) / (LOG 3) = 4

2x = 5

x = 2.5

Answer:

2 times, with a remainder of 0.

Step-by-step explanation:
If you had 2 friends and you had to divide 18 between both you would get 9. each with no left over

Answer: there is a total of 150 sixth graders

explanation :

0.8x = 120

120 / 0.8 = 150

6th graders at lunch =  150

The Surface Area of Cone is 706.5 cm².

We have dimension of Cone

height = 12 cm

Radius = 9 cm

Now, l = √9² + 12² = √81 + 144 = 25 cm

So, the Surface Area of Cone

= πrl

= 3.14 x 9 x 25

=  706.5 cm²

Thus, the Surface Area of Cone is 706.5 cm².

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