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2 years ago

7

The edges of three squares are joined together to form a right triangle with legs of lengths R & S and a hypotenuse of lengt

h T. What must be true

1 answer:

dezoksy [38]2 years ago

8 0

Answer:

$R^{2} + S^{2} = T^{2}$

Step-by-step explanation:

the pythagorean theorem

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Well I wish I three days 66

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2 years ago

Round 8015.80930968 to the nearest ten.

Serjik [45]

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Points E, F, and D are located on circle C. Circle C is shown. Line segments E C and D F are radii. Lines are drawn from points

elena55 [62]

Answer:

Option (1). 34°

Step-by-step explanation:

From the figure attached, CE and CD are the radii of the circle C.

Central angle CED formed by the intercepted arc DE = 68°

Since measure of an arc = central angle formed by the intercepted arc

Therefore, m∠CED = 68°

Since m∠EFD = $\frac{1}{2}(m\angle ECD)$ [Central angle of an intercepted arc measure the double of the inscribed angle by the same arc]

Therefore, m∠EFD = $\frac{1}{2}(68)$

= 34°

Therefore, Option (1) 34° will be the answer.

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2 years ago

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A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk

Tcecarenko [31]

Answer:

T(x) = (√(4+x^2))/2 +(c -x)/4
(a) x = 1.155 miles
(b) x = 1/2 mile

Step-by-step explanation:

The straight line distance from the starting point to the point x on the road is given by the Pythagorean theorem:

d1 = √(2²+x²)

The time required to walk that distance in the woods (at 2 miles per hour) is ...

time = distance / speed

t1 = √(4+x²)/2

The remaining distance along the road to the car is ...

d2 = c - x . . . . . for c > x

and the corresponding time at 4 mph is ...

t2 = (c -x)/4

Then the total time is ...

T(x) = t1 +t2

T(x) = √(4+x²)/2 +(c -x)/4

__

(a) The value of x that minimizes total time is the one that makes the derivative zero.

T'(x) = x/(2√(4+x²)) -1/4

0 = (2x -√(4+x²))/(4√(4+x²))

√(4+x²) = 2x . . . . . fraction is zero when numerator is zero; add radical

4 +x² = 4x² . . . . . . square both sides

4/3 = x² . . . . . . . . . subtract x², divide by 3

x = (2/3)√3 ≈ 1.1547

If c = 9 miles, x = 1.1547 miles.

__

(b) For c < (2/3)√3, the shortest travel time will be along the straight-line path to the car.

If c = 1/2 mile, x = 1/2 mile.

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2 years ago

In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in t

victus00 [196]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The probability that he or she would choose the pair of socks in the center position is $p =\frac{1}{5}$

The correct answer choice is

X has a binomial distribution with parameters n=100 and p=1/5

b

The mean is $\mu = 20$

The standard deviation is $\sigma=4$

c

The probability, $P =0.0002$

d

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

Using the R the probability $Pe = 0.0003$

The probabilities $P \approx Pe$

Step-by-step explanation:

Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as

$p =\frac{1}{5}$

$=0.2$

The mean of this distribution is mathematical represented as

$\mu = np$

substituting the value

$\mu = 100 * 0.2$

$\mu = 20$

The standard deviation is mathematically represented as

$\sigma = \sqrt{np (1-p)}$

substituting the value

$= \sqrt{100 * 0,2 (1-0.2)}$

$\sigma=4$

Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as

$P=P(X \ge 34 )$

By standardizing the normal approximation we have that

$P(X \ge 34) \approx P(Z \ge z)$

Now z is mathematically evaluated as

$z = \frac{x-\mu}{\sigma }$

Substituting values

$z = \frac{34-20}{4}$

$=3.5$

So using the z table the $P(Z \ge 3.5)$ is 0.0002

The probability P and Pe that 34 or more subject would choose the center pair is very small So

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

6 0

2 years ago