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3 years ago

N(n+1)+2n+1 expand and simplicity

Mathematics

1 answer:

meriva3 years ago

6 0

Answer:

n² + 3n +1

Step-by-step explanation:

n(n+1) + 2n + 1

<h3>i) distribute n into the parantheses</h3>

= (n×n) + (n×1) + 2n + 1

= n² + n + 2n + 1

<h3>ii) collect like terms</h3>

= n² + 3n +1

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How many degress will the hour hand of a well clock move from 1:00am to 4:00am

NikAS [45]

Answer:

Step-by-step explanation:

each minute on the clock is 6 degrees so 6*5=30= 1 hour

30*3=90 because 3 hours

8 0

1 year ago

Write this ratio as a fraction in simplest form without any units. 28 quarts to 9 gallons You can use the table below to help co

jolli1 [7]

Answer:

7/9

Step-by-step explanation:

In order to write the fraction without any units (as a pure number), we must have units in the numerator and denominator that are the same. Then the units cancel.

<h3>Convert to gallons</h3>

We are given the conversion ...

4 quarts = 1 gallon

Multiplying by 7, we see ...

28 quarts = 7 gallons

<h3>Ratio</h3>

This lets us write the desired fraction as ...

(28 quarts)/(9 gallons) = (7 gallons)/(9 gallons) = 7/9

The ratio in simplest form is 7/9.

4 0

1 year ago

1/5 ÷9 in it's simplest form<br><br>9÷ 1/5 in it's simplest form

Ulleksa [173]

Answer:

the first one is 1/45

the second one is 45

Step-by-step explanation:

i hope this helped

6 0

3 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

2 years ago

Can someone tell me if my answer to this problem is correct, please? And if it isn't how do you solve it?

Mrac [35]

Answer:

Height of tree= 13.8m

Step-by-step explanation:

When finding the value of a in your working, I suggest to leave the answer to 5 significant figures so that your final answer is more accurate. The value of a should be 26.048m to 5 s.f.

Then multiplying 26.048 with sin 32° would give you 13.8m too when rounded off to 3 significant figures :)

I have attached my working too.

3 0

3 years ago