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3 years ago

11

1 2/3 ÷x=2 7/9 This needs to be with full steps. Please help!!!!

1 answer:

avanturin [10]3 years ago

5 0

Answer:

x = ³/₅

Step-by-step explanation:

1⅔/x = 2⁷/₉ Convert the right-hand side to improper fraction

1⅔/x = ²⁵/₉ Multiply each side by x

1⅔ = ²⁵/₉x Convert the left-hand side to improper fraction

⁵/₃ = ²⁵/₉x Multiply each side by 9

15 = 25x Divide each side by 25

x = ³/₅

<em>Check: </em>

1⅔/⅗ = 2⁷/₉

⁵/₃ × ⁵/₃ = ²⁵/₉

²⁵/₉ = ²⁵/₉

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3 years ago

Moesha needs $79 for a class trip. She already has $22 and she can earn the rest by babysitting for 8 hours. If h represents her

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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

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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.

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3 years ago

Banabas must pay his ex-wife an amount of R350 000 in two years’ time. Calculate the amount that he must invest today to have th

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Answer:

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Step-by-step explanation:

The compound interest formula is given by:

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Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Banabas must pay his ex-wife an amount of R350 000 in two years’ time.

This means that $t = 2, A(t) = 350000$

Interest rate of 8.15% per annum compounded monthly:

This means that $r = 0.0815, n = 12$ .

Amount he must invest today:

This is P. So

$A(t) = P(1 + \frac{r}{n})^{nt}$

$350000= P(1 + \frac{0.0815}{12})^{2*12}$

$P = \frac{350000}{(1 + \frac{0.0815}{12})^{2*12}}$

$P = 297521$

He must invest R297 521 today.

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3 years ago