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4 years ago

The questions are below:

Mathematics

1 answer:

forsale [732]4 years ago

8 0

Answer:

See below in BOLD.

Step-by-step explanation:

The first part:

Applying the Pythagoras theorem to both triangles.

The one on the left:

13^2 = 12^2 + x^2

x^2 = 169 - 144 = 25

x = 5 units.

The one on the right:

x^2 = 5^2 + 12^2 = 169

x = 13 units.

(a) So the 2 shorter sides in the triangles have the same length.

(b) The 3 sides of each triangle have the same length so they are congruent by SSS.

The Second Part.

(a) F. They could be congruent because the angles are all equal but we don't know anything about the lengths of the sides.

(b). C. Congruent. by ASA. The angles at each side of the line of length 9.2 are equal in measure.

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Sarah is doing research on the average age of first-year resident physicians. She wants her estimate to be accurate to within 1

WINSTONCH [101]

Answer: The number of first-year residents she must survey to be 95% confident= 263

Step-by-step explanation:

When population standard deviation ( $\sigma$ ) is known and margin of error(E) is given, then the minimum sample size (n) is given by :-

$n=(\dfrac{z^*\sigma}{E})^2$ , z* = Two-tailed critical value for the given confidence interval.

For 95% confidence level , z* = 1.96

As, $\sigma$ = 8.265, E = 1

So, $n= (\dfrac{1.96\times8.265}{1})^2 =(16.1994)^2\\\\= 262.42056036\approx263\ \ \ [\text{Rounded to the next integer}]$

Hence, the number of first-year residents she must survey to be 95% confident= 263

7 0

3 years ago

Please explain your answer as well, THANKS!!!

dusya [7]

Answer:

11,232,000

Step-by-step explanation:

The key to this problem is knowing "repetition is NOT ALLOWED".

For the first 3 letters slot:

For the 1st slot, we can pick any of the 26 alphabets

For the 2nd slot, we can pick any of the 25 remaining alphabets (since 1 is already taken)

For the 3rd slot, we can pick any of the 24 remaining letters (since 2 is already taken)

For the three digits slot:

For the 1st slot, we can pick any one of the 10 digits

For the 2nd slot, we can pick any one of the 9 digits left, since 1 is taken already

For the 3rd slot, we can pick any one of the 8 digits left, since 2 is already taken

The number of license plates, thus, would be all of these multiplied together:

26 * 25 * 24 * 10 * 9 * 8 = 11,232,000

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3 years ago

What is the sum of forty-six and ninety-four?

lbvjy [14]

Answer:

140

Step-by-step explanation:

46+94 = 140

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3 years ago

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A rectangular vegetable farm measures 45 m by 15 m. It has also a path of 1m wide. What is the area of the path?

Rina8888 [55]

Answer:

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3 years ago

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V^2=12^2+2(-6)(9) answer please i am waitind

il63 [147K]

Answer:

V = 6 or V = -6

Step-by-step explanation:

Solve for V over the real numbers:

V^2 = 12^2 - 6 2 9

12^2 + 2 (-6) 9 = 36:

V^2 = 36

Take the square root of both sides:

Answer: V = 6 or V = -6

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3 years ago

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