30 POINTS!! PLEASE

A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.

She uses a pair of similar triangles, to help her find the answer.

The sum of the exterior angles in a regular 20-gon is given as follows:

360º.

An exterior angle of a polygon is defined as the angle between a side and its adjacent extended side.

The sum of exterior angles formula states the sum of all exterior angles in any polygon is 360°, no matter the number of sides.

For this problem, we have a 20-gon, that is a polygon of 20 sides, however, as the formula states, the sum of the exterior angles in a regular 20-gon is given as follows:

360º.

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The correct option is b, the pair of consecutive interior angles is 1 and 7.

First, we can see that the interior angles are the angles that are "interior" to the intersections.

These are 1, 4, 6, and 7.

Because the two lines are parallel, the consecutive interior angles are angles that would be adjacent (add up to 180°) but that are in different intersections.

Then the consecutive interior angles are:

3 and 6

1 and 7

The correct option is b.

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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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The value of x that makes [tex]5^x = 625[/tex] true is x = 4.

To determine the value of x in the equation [tex]5^x = 625[/tex], we need to find the exponent that results in 625 when applied to the base 5.

Since 625 can be expressed as 5 raised to the power of 4 ([tex]5^4 = 625[/tex]), the value of x that satisfies the equation is 4.

When we substitute x = 4 into the equation, we get [tex]5^4 = 625[/tex], which is true.

Therefore, x = 4 is the solution to the equation, indicating that 5 raised to the power of 4 equals 625.

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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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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: 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:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

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.

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 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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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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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:

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

(a) Using Excel, the calculations are shown below:

Mean = 608.67

Median = 610.00

Mode = 610.00

Standard Deviation =  96.89

(b) The measure of central tendency would be appropriate are  the median and the mode.

The median is fitting  because it  is a representation of the middle value in the data set and is not affected by extreme values.

We can see that our  median rent is $610.00 and an appropriate representation of the typical rent paid by the students.

The mode is $610.00 and also an indication that this rent amount is the most common among the students.

In conclusion, a  measure of the variability or dispersion in the data set is provided by the standard deviation, which is determined to be 96.89. It demonstrates how widely the rents vary from the mean.

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Answer:

57

Step-by-step explanation:

this is the boybfiend

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

Answer:

The answer is D, the last one.

Answer: there is a total of 150 sixth graders

explanation :

0.8x = 120

120 / 0.8 = 150

6th graders at lunch =  150

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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Answer:

5.85

Step-by-step explanation:

400Answer:

Step-by-step explanation:

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.

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

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:3x-4y=8

Step-by-step explanation:

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 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 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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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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