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BaLLatris [955]
3 years ago
14

You have learned about special right triangles. Using that knowledge, you decide to take a square cake with 10-inch sides and di

vide it diagonally to form two special right triangles. Find and explain how you know the exact (no decimals) measure of the hypotenuse.
Now find the exact diagonal measure of cakes that are an 8-inch square, a 12-inch square, and a 15-inch square.
Did you discover a shortcut that works with any square cake? Explain.

Please show your work

Mathematics
1 answer:
Arlecino [84]3 years ago
4 0
Check the picture below.

thus, using  the 45-45-90 rule, for a square with sides if 8-inch, h = 8√(2), for 12-inch sides, h = 12√(2), for 15-inch sides, h = 15√(2), and so on.

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Suppose the speeds of cars along a stretch of I-40 is normally distributed with a mean of 70 mph and standard deviation of 5 mph
neonofarm [45]

Answer:

a) 68%.

b) 84%.

c) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

d) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

e) Between 60 mph and 80 mph.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 70 mph, standard deviation of 5 mph.

(a) Approximately what percent of cars are travelling between 65 and 75 mph?

70 - 5 = 65

70 + 5 = 75

Within 1 standard deviation, so approximately 68%.

(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit?

The normal distribution is symmetric, which means that 50% of the measures are below the mean, and 50% are above.

65 is one standard deviation below the mean, so of the cars below the mean, 68% are above 65 mph.

0.68*50% + 50% = 34% + 50% = 84%.

84%.

(c) What percent of cars are traveling at a speed greater than or equal to 80 mph?

80 = 70 + 2*10

2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean. Due to the symmetry of the normal distribution, of the other 5%, 2.5% is at least 2 standard deviations below the mean and 2.5% is at least 2 standard deviations above the mean. Then:

Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

(d) What percent of cars are traveling at a speed greater than 80 mph?

Same as item c, as in the normal distribution, the probability of an exact value is considered to be 0.

(e) 95% of cars are traveling between what two speeds?

Within two standard deviations of the mean.

70 - 2*5 = 60 mph

70 + 2*5 = 80 mph.

Between 60 mph and 80 mph.

6 0
3 years ago
Okay sorry about the other one
Neporo4naja [7]
Number ten is 60 73+36=108
6 0
3 years ago
WILL MARK AS BRAINLIEST
STALIN [3.7K]

.......................................

5 0
3 years ago
On a coordinate plane, a circle has a center at (negative 2, 0). Point (negative 2, 4) lies on the circle.
wlad13 [49]

The correct answer to where the point(1, StartRoot 7 EndRoot) lies on the circle is A. Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units

<h3>What is a Coordinate Plane?</h3>

This refers to the tool that is used to graph points on a two-dimensional plane that intersects two number lines.

Hence, given the information in the given diagram, there is a coordinate plane that shows a circle at the center that has certain values on the y and x-axis.

We can state that the point (1, StartRoot 7 EndRoot) lies on the circle shown because the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.

Read more about coordinate planes here:

brainly.com/question/7038052

#SPJ1

5 0
2 years ago
Find the equation of the line with slope m=1 that contains the point (7,5).
katovenus [111]

Answer:

y = x - 2

Step-by-step explanation:

y = mx + b

5 = 1 (7) + b

5 = 7 + b

b = -2

So...

y = x - 2

7 0
3 years ago
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