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3 years ago

Please please help me please

Mathematics

1 answer:

vodomira [7]3 years ago

5 0

Answer: 8) 42°, 65°, 115° 9) 1.5, 2

Step-by-step explanation:

8) Right off the bat I know that the measure adjacent to 157° is

23°. With both numbers inside the triangle combined, we get

65° meaning the last number is 115 because that'll add up to 180°

9) Considering the smaller triangle has half the length of the bigger triangle

The length of the rest are half the size too.

EF = 1.5

DF = 2

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Sergio is working on a research project involving the ages of students at Brooklyn College. After interviewing 500 students, he

Zinaida [17]

Answer:

The probability of of a randomly chosen student being exactly 21 years old.

= 1.293

Step-by-step explanation:

Step(i):-

Given Population size n = 500

Mean of the Population = 20 years and 6 months

= $20 + \frac{6}{12} = 20 +0.5 = 20.5 years$

Standard deviation of the Population = 2 years

Let 'X' be the range of ages of the students on campus follows a normal distribution

Let x =21

$Z = \frac{x-mean}{S.D}$

$Z = \frac{x-mean}{S.D} = \frac{21-20.6}{2} =0.2$

The probability of a randomly chosen student being exactly 21 years old.

P( Z≤21) = 0.5 + A( 0.2)

= 0.5 +0.793

= 1.293

6 0

3 years ago

Find integra of xlnxdx

Mademuasel [1]

Answer:

$\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

$\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}$

Increase the power by 1, then divide by the new power.

Given indefinite integral:

$\displaystyle \int x \ln x \:\: \text{d}x$

To integrate the given integral, use Integration by Parts:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

$\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}$

$\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2$

Therefore:

$\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}$