If 75% of students and Toby's grade voted how many students are in Toby's grade

What are the angles?

if all of them are below 90 degrees, it is acute.

if one angle is 90 degress, it is right

if one angle is more than 90 degrees, it is obtuse

8 0

3 years ago

At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable X as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

7 0

3 years ago

the temperature is already at 40 degrees it rises 4.5 degrees per minute how long will it take to get to 76 degrees

Andrei [34K]

Answer:

It will take 8 minutes for the temperature to reach 76°

Step-by-step explanation:

The expression for the total temperature in degrees at time t can be written as;

T=I+EM

where;

T=total temperature

I=initial temperature

E=temperature increase per minute

M=number of minutes

This can also be written as;

total temperature=initial temperature+temperature increase per minute×number of minutes

In our case;

T=76°

I=40°

E=4.5°

M=m

replacing;

76=40+(4.5×m)

4.5 m=76-40=36

(4.5 m)/4.5=36/4.5

m=8

It will take 8 minutes for the temperature to reach 76°

7 0

3 years ago