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3 years ago

Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.

1 answer:

6 0

Length of circular track is:

L = 2*r*pi

He run 3/4 of it so length is:
L' = 3*2/4*r*pi = 3/2*r*pi

To calculate speed of his movement we use formula:
v = s/t where s = L' and t = 1 minute 45 seconds = 105 seconds

v = L'/t = $\frac{3*r*pi}{2*105}$

v = r* pi/70

If we take that r = 1 answer is $\pi /70$

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Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa

KengaRu [80]

Answer:

a. 0.5 or 50%

b. 0.496 or 49.6%

c. 0.8185 or 81.85%

d. Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm

e. 0.0252 or 2.52%

f. The qualifying speed would be 47.4 wpm.

Step-by-step explanation:

a. Let's find the z-score this way:

μ = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

p (z=0) = 0.5 or 50%

b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

z-score = -0.01

Now, let's calculate the p value for z-score = -.0.01, using the z-table:

p (z = -0.01) = 0.496 or 49.6%

If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

In consequence,

p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%

d. z-score = (x - μ)/σ

z-score = (105 - 60)/15

z-score = 3

Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

z-score = 1

Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

In consequence,

p (z > 1) = 1 - 0.8413 = 0.1587

and if the two typists are independently selected, then

p = 0.1587 * 0.1587

p = 0.0252 or 2.52%

f. p = 0.2, using the z-table, the z-score is -0.84, then:

z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

The qualifying speed would be 47.4 wpm.

8 0

3 years ago

CAN SOMEONE EXPLAIN AND MAYBE SHOW ME STEP BY STEP WHY THE ANSWER IS 75degrees. HURRY 50 points and brainiest!!!

KonstantinChe [14]

Answer:

75 degrees, we know that already so look below lol.

Step-by-step explanation:

This triangle is an isosceles triangle, LP is equivalent to LQ, and angles LQP and LPQ are also equivalent. We understand that PLQ is equal to 30 degrees, since its complementary to triangle LQM.

180 - 30 = 150

150/2 = 75.

Have a nice day, fam. Spread The Love. Thanks for the opportunity.

3 0

3 years ago

Read 2 more answers

The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same mea

Semmy [17]

Answer:

40,40 and 100

Step-by-step explanation:

You know the first two angles are identical, so let's call them x.

The third angle is 20 more than twice the measure of either angle, which means 2x+20.

The angles of a triangle add up to 180 degrees.

(x)+(x)+(2x+20)=180

4x+20=180

4x=160

x=40 degrees

This means the angle measures equal 40 degrees, 40 degrees, and 100 degrees.

6 0

4 years ago

Adelle solved the equation, 4x/7 - 6 = -20 , as shown.

Ne4ueva [31]

Answer:

Step 1: Given

Step 2: Add 6 on both sides

Step 3: Multiply 7 on both sides

Step 4: Divide by 4 on both sides

8 0

3 years ago

Solve 13x - 4 < 12(x - 1).

Effectus [21]

13x - 4 < 12(x-1)
13x - 4 < 12x - 12
13x - 12x < -12 + 4
x < -8
x > 8

x is greater than 8

6 0

3 years ago