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3 years ago

A single die is rolled. Find the probability of each of the following events :

Mathematics

1 answer:

IceJOKER [234]3 years ago

7 0

$\frac{1}{2}$ and $\frac{1}{3}$

There are 6 possible outcomes when rolling a die, 1, 2, 3, 4 , 5, 6

numbers less than 4 are 1, 2, 3

P( number less than 4 ) = $\frac{3}{6}$ = $\frac{1}{2}$

numbers greater than 4 are 5, 6

P( number greater than 4 ) = $\frac{2}{6}$ = $\frac{1}{3}$

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For f(x) = 5x + 1

drek231 [11]

Answer:

A. $f(7) = 5(7) + 1\\\\f(7) = 36$

B. $f^{-1}(x) = \frac{x - 1}{5}$

C. $f^{-1}(7) =\frac{6}{5}$

D. $f(\frac{6}{5}) = 7$

Step-by-step explanation:

A. To solve the first part of the problem we must replace $x = 7$ in the function $f(x) = 5x + 1$

So:

$f(7) = 5(7) + 1\\\\f(7) = 36$

B. In part B we must find the inverse function of $f(x) = 5x + 1$

To find the inverse function do $y = f(x)$

$y = 5x +1$

Now clear the variable x.

$\frac{y - 1}{5} = x$

Replace x with y.

$y = \frac{x - 1}{5}$

Finally

$f^{-1}(x) = \frac{x - 1}{5}$

C. Now we take the inverse function found above and replace $x = 7$

$f^{-1}(7) = \frac{7 - 1}{5}\\\\f(7) = \frac{6}{5}$

D. Now we substitute $x = f(f^{-1}(7))$ in the original function.

$x = f( f^{-1}(7))\\\\f^{-1}(7) = \frac{6}{5}\\\\ x= f(\frac{6}{5} )\\\\f(\frac{6}{5}) = 5(\frac{6}{5}) + 1\\\\f(\frac{6}{5}) = 7$

8 0

3 years ago

Read 2 more answers

What is the length of the hypotenuse of a right triangle with sides that measure 7 cm and 24 cm?

Paul [167]

The length of the hypotenuse of a right triangle with sides that measure 7 cm and 24 cm is 25 cm

<u>Solution:</u>

Given a right angled triangle,

The sides measure 7 cm and 24 cm

We have to find the length of hypotenuse

For a right angled triangle, by Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

From above definition we get,

$c^2 = a^2 + b^2$

Where, "c" is the length of hypotenuse

"a" is the length of one side of triangle

"b" is the length of other side of triangle

Here, a = 7 and b = 24 and c = ?

$c^2 = 7^2 + 24^2\\\\c^2 = 49 + 576 = 625$

Taking square root on both sides,

$c = \sqrt{625}\\\\c = 25$

Hence the length of hypotenuse is 25 cm

7 0

3 years ago

At what point will 3y=4x-6 and 8x-6y=-30 intercept

tester [92]

Answer:

The lines don't intercept

Step-by-step explanation:

we have

$3y=4x-6$

isolate the variable y

Divide by 3 both sides

$y=\frac{4}{3}x-\frac{6}{3}$

simplify

$y=\frac{4}{3}x-2$ -----> equation A

$8x-6y=-30$

Isolate the variable y

$6y=8x+30$

Divide by 6 both sides

$y=\frac{8}{6}x-\frac{30}{6}$

simplify

$y=\frac{4}{3}x-5$ -----> equation B

Compare equation A and equation B

The slopes are the same and the y-intercepts are different

Remember that

If two lines has the same slope, then the lines are parallel

therefore

In this problem line A and line B are parallel lines

The system of equations has no solution, because the lines don't intercept

3 0

3 years ago

Natalie made two statues of a giraffe the first measures 16 feet tall and the second measures 6 inches tall what is the differen

laiz [17]

First you would have to convert , so 12 inches = 1 foot . So do 12 X 16= 192inches, then subtract 192-6=186inches should be the difference IN INCHES. If you need it in feet divide 186 by 12 which should give you 15.5feet

8 0

2 years ago

What is the congruency statement?<br> I’LL MARK BRAINLIEST!!!!!

ra1l [238]

I don’t understand

4 0

2 years ago