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Nostrana [21]
2 years ago
15

Find the distance across the lake. Assume the triangles are similar.

Mathematics
1 answer:
pantera1 [17]2 years ago
5 0

Answer:

B. 255 m

Step-by-step explanation:

<u>use similar triangle</u>

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

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Each of the 10 students in the baking club made 2 chocolate cakes for a fundraiser. They all used the same recipe, using C cups
rodikova [14]

2x10=20 so there were 20 cakes made

so C/20

8 0
2 years ago
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Draw a diagram in which segment AB intersects segment CD equals segment CB
Contact [7]
The <u>correct diagram</u> is attached.

Explanation:

Using technology (such as Geogebra), first construct a line segment.  Name the endpoints C and D.

Construct the perpendicular bisector of this segment.  Label the intersection point with CD as B, and create another point A above it.

Measure the distance from C to B and from B to D.  They will be the same.

Measure the distance from A to B.  If it is not the same as that from C to B, slide A along line AB until the distance is the same.

Using a compass and straightedge:

First construct segment CD, being sure to label the endpoints.

Set your compass a little more than halfway from C to D.  With your compass set on C, draw an arc above segment CD.

With your compass set on D (the same distance as before) draw an arc above segment CD to intersect your first arc.  Mark this intersection point as E.

Connect E to CD using a straightedge; mark the intersection point as B.

Set your compass the distance from C to B.  With your compass on B, mark an arc on EB.  Mark this intersection point as A.

AB will be the same distance as CB and BD.

5 0
2 years ago
Read 2 more answers
On the island of liars each inhabitant lies with probability 2/3. You overhear an inhabitant making a statement. Next you ask an
bonufazy [111]

Answer:

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

Step-by-step explanation:

Let A be the event 'the first inhabitant speaks the truth' and B the event the person you asked speaks the truth'

We have that

P(A) = P(B) = 1/3

The second person will say that the first person speaks the truth if:

- Both are lying

- Both are saying the truth

The probability that both inhabitants lies is 2/3 * 2/3 = 4/9

The probability that both inhabitants speaks the truth is 1/3² = 1/9

Therefore, in this problem, we want to know P(A ∩ B | (A∩ B) ∪ (A^c ∩ B^c) )

(note that, since the second persons says that A didnt lie, then in order for it to be true then the second person have to also say the truth).

We know that P(A ∩ B) = 1/9 and P((A∩ B) ∪ (A^c ∩ B^c)) = 4/9 + 1/9 = 5/9. Using the bayes formula we have

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) ) = P((A∩ B) ∪ (A^c ∩ B^c) | A ∩ B) * P(A∩ B)/ P((A∩ B) ∪ (A^c ∩ B^c))

Note that P((A∩ B) ∪ (A^c ∩ B^c) | A∩B) = 1 because the condition is more restrictive than the probability we are asking for, therefore

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) )  = P(A∩ B)/P((A∩ B) ∪ (A^c ∩ B^c))  = (1/9) / (4/9) = 1/4.

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

7 0
2 years ago
The harbormaster wants to place buoys where the river bottom is 20 feet below the surface of the water. Complete the absolute va
Natalija [7]

Answer:

The answer is below

Step-by-step explanation:

The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed

Answer:

To solve the problem, the depth of the water would be equated to the position of the river bottom.

d(h)=river \ bottom\\\\The \ river \ bottom=-20\ feet(below)\\\\d(h) = -20\\\\\frac{1}{5}|h-240|-48=-20\\ \\\frac{1}{5}|h-240|=-20+48\\\\\frac{1}{5}|h-240|=28\\\\|h-240|=28*5\\\\|h-240|=140\\\\h-240=140\ or\ h-240=-140\\\\h=140+240\ or\ h=-140+240\\\\h=380\ or\ h=100\\\\The\ buoys\ should\ be\ placed\ at\ 100\ feet\ and\ 380\ feet\ from\ left-hand\ shore

4 0
2 years ago
16. What is the (approximate) probability that Die1+Die2+Die3=6? a. Probability is approximately 5% b. Probability is approximat
Mashutka [201]

Answer: A.) Probability is approximately 5%

B.) probability that Die1 + Die + Die > 12 is approximately 26%

Step-by-step explanation:

Total possible outcomes of the three dies (sample space) = (6^3) = 216

For die1 + die2 + die3 to be equal six, then the number of outcomes which produces our required outcome from the sample space is = 6

Therefore, probability of die1 + die2 + die3 = 6 is given by;

P(die1 + die2 + die3 = 6) = total required outcome / total possible outcomes

P(die1 + die2 + die3 = 6) = 10/216

P( die1 + die2 + die3 = 6) = 0.04629

P( die1 + die2 + die3 = 6) = 4.63% approximately 5%

B) probability that Die1 + Die + Die > 12

P(Die1 + Die + Die > 12) = 57/216 = 0.2638

= 26.38%

Approximately 26%

3 0
2 years ago
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