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Alexxx [7]
3 years ago
5

Chris swam 8 laps in 112 seconds. Find the constant of proportionality to determine the number of seconds per lap. What does the

constant of proportionality represent in this situation? Write two equations to represent this situation. How many laps can Chris swim in 56 seconds?
Mathematics
1 answer:
alina1380 [7]3 years ago
3 0

Answer:

he can do a lap in 14 seconds

and he can swim 4 laps in 56 seconds

Step-by-step explanation:

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Which equation can be solved to find one of the missing side lengths in the triangle?
tester [92]

Answer:

cos(60) = 12

Step-by-step explanation:

I don't understand the question, but that is the only logical answer choice.

6 0
3 years ago
Three numbers in the interval $\left[0,1\right]$ are chosen independently and at random. What is the probability that the chosen
k0ka [10]

Let a,b,c be the randomly selected lengths. Without loss of generality, suppose a[tex]P(A + B \ge C) = P(A + B - C \ge 0)

where A,B,C are independent random variables with the same uniform distribution on [0, 1].

By their mutual independence, we have

P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)

so that the joint density function is

P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}

where [0,1]^3=[0,1]\times[0,1]\times[0,1] is the cube with vertices at (0, 0, 0) and (1, 1, 1).

Consider the plane

a + b - c = 0

with (a,b,c)\in\Bbb R^3. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)

The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region a+b-c\ge0, since 0+0-1=-1. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.

Then we have

\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}

5 0
1 year ago
Two complementary angles are in the ratio 3:2. The number of degrees in the smaller angle is A. 18 B. 36 C. 54 D. 72
Tasya [4]
No picture is given for reference.
4 0
3 years ago
The radius of the Ferris wheel is shown. Which is the circumference of the Ferris wheel, rounded to the nearest foot?
mixas84 [53]

Answer:

The circumference is around 785 feet

Step-by-step explanation:

The circumference of a circle is pi x radius x 2 or pi x diameter.

If the Ferris wheel's radius is 125, then this is what you do:

pi x 125 x 2

= pi x 250

= 3.14 x 250

= 785

7 0
2 years ago
Read 2 more answers
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miss Akunina [59]

Answer: See picture.

Step-by-step explanation:

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5 0
3 years ago
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