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aalyn [17]
2 years ago
14

cho hàm số f(x) liên tục trên đoạn [a;b] và có nguyên hàm F(x) thỏa F(a)=10;F(b)=2022 Khi đó \int _a^b\: f(x) dx bằng

Mathematics
1 answer:
SpyIntel [72]2 years ago
4 0

The result follows from the fundamental theorem of calculus.

\displaystyle \int_a^b f(x) \, dx = F(b) - F(a) = 2022 - 10 = \boxed{2012}

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Step-by-step explanation:

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What is the orthocenter of the triangle with two altitudes given by the lines x = -1 and y = x + 1. :
KonstantinChe [14]

Orthocenter is the point of concurrence of the altitudes of the triangle.

This means Orthcenter is the point where the altitudes intersect.

Here one altitude is x = -1

The other altitude is y = x + 1

Substituting x = -1 in y = x + 1

We get

y = -1-1=0

Hence the point of intersection of the altitudes is (-1,0)

The orthocenter of the triangle whose altitudes are x = -1 & y = x+1 is (-1,0)

(-1,0) which is Option c) or the third option is the right answer.

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A car insurance company has determined that 7% of all drivers were involved in an accident last year. If 11 drivers are selected
Jobisdone [24]

Answer:

Therefore the probability that 3 or more were involved in an accident last year is 0.376.

Step-by-step explanation:

Binomial distribution:

A discrete random variable X having the set {0,1,2.....,n} as the spectrum, is said to have binomial distribution with parameter n= the number of trial and p = probability of getting successes in one trial if the p.m.f of X is give by

P(X=x)=C(n,x)p^x(1-p)^{n-x}   for x=0,1,2,....,n

               =0                                   elsewhere

where C(n,x)= \frac{n!}{x!(n-x)!}, n is a positive integer and 0<p<1.

Given that,

7% of all drivers were involved in an accident last year that was determined by a car insurance company.

p= 7%=0.07, n=11, x=3

P(X≥3)

= 1-P(X≤2)

= 1- P(X=0)-P(X=1)-P(X=2)

          =1- C(11,0)(0.07)^0(1-0.07)^{11}- C(11,1)(0.07)^1(1-0.07)^{10}- C(11,2)(0.07)^2(1-0.07)^{9}

=1- C(11,0)(0.07)^0(0.93)^{11}- C(11,1)(0.07)^1(0.93)^{10}- C(11,2)(0.07)^2(0.93)^{9}

=1-0.624

≈0.376

Therefore the probability that 3 or more were involved in an accident last year is 0.376.

8 0
2 years ago
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