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2 years ago

21 students in a dass wear spectacles. This is 60% of the total number of

Mathematics

2 answers:

wlad13 [49]2 years ago

7 0

Answer:

There are 35 students in the class

Step-by-step explanation:

We would divide 21 by 60%

21/0.6 = 35 students.

Natalija [7]2 years ago

3 0

Answer:

35 students are in the class

Step-by-step explanation:

21/x 60/100

cross multiply so you will get

2100 = 60x

divide each side by 60x

2100/60 = 35

21 students out of 35

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Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

2 years ago

Original function is f(x)=2^x

Xelga [282]

Answer:

Look at the photo below for the answer.

6 0

2 years ago

Philip wants to buy a new video game system that costs

Law Incorporation [45]

Answer:

I think the answer I think the answer would be 14

4 0

2 years ago

A 290-kg flatcar 28 m long is moving with a speed of 6.5 m/s along horizontal frictionless rails. A 95-kg worker starts walking

blsea [12.9K]

Answer:

9.33 seconds

60.67 meters

Step-by-step explanation:

A worker with a speed of 3.0 m/s with respect to a car, starts to walk from one end of the car to the other in the direction of motion of the car.

As the car is 28 m long, then the worker will reach the other end of the car in $\frac{28}{3} = 9.33$ seconds. (Answer)

Now, the car is moving with a speed of 6.5 m/s and in the time of 9.33 seconds, it will move by $6.5 \times 9.33 = 60.67$ meters. (Answer)

6 0

3 years ago

Same thing as last. nearest 100th

bekas [8.4K]

Answer:

452.39 mi^2

Step-by-step explanation:

A = πr^2

A = π (12mi)^2

A = 452.39 mi^2

Please mark Brainliest :D

8 0

2 years ago

Read 2 more answers