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3 years ago

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Mathematics

1 answer:

gavmur [86]3 years ago

3 0

Answer:

$P(Sum = 9) = \frac{1}{9}$

Step-by-step explanation:

Given

Outcomes of rolling two dice

Required

P(Sum = 9)

From the given outcomes, we have:

$n(S) = 36$ -- the sample size

$Sum = 9:=\{(3,6),(4,5),(5,4),(6,3)\}$

So.

$n(Sum = 9) = 4$

The probability is:

$P(Sum = 9) = \frac{n(Sum = 9)}{n(S)}$

$P(Sum = 9) = \frac{4}{36}$

Simplify

$P(Sum = 9) = \frac{1}{9}$

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A team of runners ran a relay race. Each runner ran 7 1/2 kilometers. The total length of the race was 45 kilometers. Write and

Travka [436]

Answer:

6 runners

Step-by-step explanation:

Each runner ran 7.5 km. If there were n runners, then (7.5 km)n = 45 km.

Solve this for n by dividing 7.5 km into 45 km:

n = 6

There were 6 runners.

7 0

3 years ago

What is the inverse of y=pi/2+sin x

Alekssandra [29.7K]

Answer:

$f^{-1}(x)=\sin ^{-1}(x-\frac{\pi}{2})$

Step-by-step explanation:

The given function is

$y=\frac{\pi}{2}+\sin x$

To find the inverse of this function, we interchange x and y.

$x=\frac{\pi}{2}+\sin y$

we now solve for y.

$x-\frac{\pi}{2}=\sin y$

Take the sine inverse of both sides to obtain;

$\sin ^{-1}(x-\frac{\pi}{2})=y$

Hence the inverse of the given function is;

$f^{-1}(x)=\sin ^{-1}(x-\frac{\pi}{2})$

where $\frac{\pi}{2}-1\le x\le \frac{\pi}{2}+1$

6 0

3 years ago

Read 2 more answers

Y is directly proportional to x when y=30, x=6

rosijanka [135]

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

Since, y is directly proportional to x when y=30, x=6

$\therefore \: y \: \alpha \: \: x \\ \therefore \: y = kx ...(1) \\ plug \: y = 30 \: and \: x = 6 \: in \: eq \: (1)\\ 30 = k \times 6 \\ k = \frac{30}{6} \\ k = 5 \\ plug \: k = 5 \: in \: (1) \\ y = 5x....(2) \: (required \: equation) \\ plug \: x = 12 \: in \: eq \: (2) \\ y = 5 \times 12 \\ \huge \red{ \boxed{y = 60}}$