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Sever21 [200]
3 years ago
5

Picture is not drawn to scale.

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
8 0

Answer:

142 yards.

Step-by-step explanation:

See the attached diagram.

Let the reservoir is AC and Howard is standing at B and AB = 91 yards.

Now, the angle of elevation from B to the top of the reservoir C is 50°.

Then using trigonometry, \cos 50 = \frac{AB}{BC} = \frac{91}{BC}

⇒ BC = \frac{91}{\cos 50}  = 141.57 ≈ 142 yards.

Therefore, the distance of Howard from the top of the reservoir is 142 yards. (Answer)

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The hypotenuse of a 45 -45 -90 triangle measures 128 cm what is the length of one leg of the triangle
erma4kov [3.2K]
This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.
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4 years ago
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4 years ago
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Stels [109]

Answer:

9 inches

Step-by-step explanation:

The population is within 6 standard deviations of the mean with a confidence of 99.7 percent, 3 above and 3 below

 

The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size

population standard deviation = 36

sample size = 144

standard deviation of the sample mean = 36/ sqrt(144)

                                      =36/12

                                        =3

The margin of error is  the number of standard deviations above  the mean * the standard deviations

margin of error  = 3 * 3

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8 0
3 years ago
14=3(x-2)+5<br>How can I solve this equation?​
daser333 [38]
1. distribute the 3 into the variable and number in the equation
to do this..
2. multiply 3 by x (obtain the answer of 3x)
3. multiply 3 by -2 (obtain the answer of -6)
4. you now have the equation of ‘14 = 3x-6+5’
5. subtract 6 from 5 (obtain the answer of -1)
6. you now have the equation of ‘14 = 3x-1’
7. add one to both sides (cancel out the negative one and make the opposite side of the equation 15 instead of 14)
8. you now have the equation of ‘15 = 3x’
9. divide both sides by 3 (15 and x)
FINAL ANSWER
x = 5
hope this helps:)
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4 years ago
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