Please only do 9,11, and 13! And please help!! 40 points!!!

9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = sqrt(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.

A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.

9. The volume of the triangular pyramid is given by:

V = (1/3)Bh

Here, B is the base area.

The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:

h = √(26.7² - 11.7²) = 23.274 km

The area if the base is:

B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km

Now, the volume is:

V = (1/3)(136.89)(15) = 2053.35 cubic km

Hence, the volume of the triangular pyramid is 2053.35 cubic km.

11. The volume of a cone is given by:

V = (1/3)πr²h

The dimension of the bigger cone is radius is 9 in, and height 15 in:

V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in

The dimension of the smaller cone is radius is 4 in, and height 10 in:

V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in

Now, the area of the shaded portion is:

V1 - V2 = 381.7 - 33.51  = 348.19

13. The volume of a cone is given by:

V = (1/3)πr²h

Substituting the values we have:

542.87 = (1/3)π(6 m)²h

h = 542.87 / [(1/3)π(6 m)²] = 6.05 m

Now, using the Pythagoras Theorem for the slant height we have:

s² = r² + h²

s² = (6 m)² + (6.05 m)²

s² = 72.9

s = √(72.9) = 8.53 m

The slant height of the cone is 8.53 meters.

Learn more about Pythagoras Theorem here:

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of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.

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what is the 4th term/number of (a+b)^9, pascal’s triangle?

The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

Which drive-thru typically has less wait time, and why?

Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean

Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?

A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?

A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.

(a) Event "X or Y":

(b) Event "X and Y":

(c) The complement of the event X:

EXPLANATION/ANSWER

The sample space is the set of all possible outcomes.

In this case, the sample space is , A, B, C, D, E, F, G.

The event X is "The letter selected is found in the word "BEAD". "

The outcomes in this event are A, B, D, and E.

The event Y is "The letter selected comes after "D". "

The outcomes in this event are E, F, and G.

(a) Event "X or Y"

Outcomes in the event "

X or Y" are any outcomes from event X along with any outcomes from event Y.

So the outcomes in the event "X or Y " are A, B, D, E, F, and G. Event "X or Y": , A, B, D, E, F, G

(b) Event "X and Y"

The outcomes in the event "X and Y" are the outcomes from event X that also occur in event Y.

So the outcome in the event "X and Y" is E. Event "X and Y": E

(c) The complement of the event X

The complement of the event X is the event consisting of all possible outcomes not in the event X.

So the outcomes in the complement of the event X are C, F, and G

The complement of the event X: , C, F, G

(a) Event "X or Y": , A, B, D, E, F, G

(b) Event "X and Y": E

(c) The complement of the event X: , C, F, G

My problem that I am having trouble with:

A number cube with faces labeled 1 to 6 is rolled once.

The number rolled will be recorded as the outcome.

Consider the following events.

Event A: The number rolled is odd.

Event B: The number rolled is less than 4

Give the outcomes for each of the following events.

If there is more than one element in the set, separate them with commas.

(a) Event"A or B":

(b) Event"A and B":

(c) The complement of the event B: