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1 year ago

Is the line through points P(-8,-10) and Q(-5,-12) perpendicular to the line through points R(9,-6) and S(17,-5)? Explain.

1 answer:

5 0

Consider this option:
1. rule: if the scalar product PQ*RS=0, then PQ⊥RS.
2. PQ=(3;-2), RS=(8;1).
3. The scalar product of PQ*RS=3*8-1*2=22≠0. The line included PQ is not perpendicular to the line included RS.

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The student to faculty ratio at a small college is 17:3 the total number of students and faculty is 740. How many faculty member

larisa86 [58]

Answer:

111

Step-by-step explanation:

It is given that the student to faculty ratio at a small college is 17:3.

Let number of students and faculty members are 17x and 3x respectively.

It is given that total number of students and faculty is 740.

$17x+3x=740$

$20x=740$

Divide both sides by 20.

$x=37$

Number of student $=17\times 37=629$

Number of faculty members $=3\times 37=111$

Therefore, there are 111 faculty members at the college.

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2 years ago

When Ms. Sugar turned on her oven, the temperature inside was 70 degrees Fahrenheit. The temperature began to rise at a rate of

Stella [2.4K]

It would take fourteen minutes

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2 years ago

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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.

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:

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