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2 years ago

Evaluate: 2/3 + 4/5 x 7/5 - 8/3

Mathematics

2 answers:

noname [10]2 years ago

6 0

Step-by-step explanation:

please mark me as brainlest

Savatey [412]2 years ago

4 0

Answer:

-0.88

Explanation:

2/3 + 4/5 x 7/5 - 8/3

2/3 + 28/25 - 8/3

2/3 - 8/3 + 28/25

-6/3 + 28/25

-2 + 28/25

-50/25 + 28/25

-22/25

-0.88

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A 1 newton force will stretch a spring 1 meter. The spring/mass system is damped by a force that is 8 times the instantaneous ve

sukhopar [10]

Answer:

Step-by-step explanation:

Given the mass is m =16kg, and 1N force will stretch the spring 1 m.

That is, F =1N,Z =1m. Now find the spring constant k:

F = kL = 1 = k(1) = k= 1N/m.

The damping force is 8times the instantaneous velocity, this means β = 8,

and the external force is f(t) = 0

Initially the object compressed 0.6m above equilibrium position,

with the downward velocity is 2m/s.

The differential equation for a spring mass system with

damping force and extemal force is: mx" + βxt + kx = f(t).

so, 16x"+ 8x' + x= 0, x(0} = -0.6, x'(0)= 2m/s.

Now solve the DE:

The auxilary equation for the homogeneous equation is 16x"+8x'+x=0

solving we get, 16r² + 8r + 1 = 0 => (4r + 1)² = 0 => r = - 1/4.

Then the general solution for the homogenous system is: $x(t)=c_1e^{-t/4} +c_2te^{-t\4}$ .

Use the initial conditions x (0) = -0.6, x'(0) = 2m/s:

$x(0)=c_1e^{0} +c_2(0)e^{0}=-0.6=c_1\\x'(t)=-\frac{1}{4}c_1e^{-t/4}+c_2e^{-t/4}-\frac{1}{4}c_2te^{-t/4}\\x'(0)=-\frac{1}{4}c_1e^0+c_2e^0-\frac{1}{4}c_2(0)e^0=2=-\frac{1}{4}(-0.6)+c_2=c_2=1.85$ .

Hence, $x(t) =-0.6e^{-t/4}+1.85te^{-t/4}$ .

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3 years ago

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these inte

stich3 [128]

The probability of winning a lottery by selecting the correct six integers, are

$\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}$

<h3>What is binomial distribution?</h3>

The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.

Part (a); positive integers not exceeding 30.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.

$\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}$

Part (b); positive integers not exceeding 36.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.

$\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}$

Part (c); positive integers not exceeding 42.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.

$\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}$

Part (d); positive integers not exceeding 48.

To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.

$\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}$

To know more about binomial probability, here

brainly.com/question/9325204

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The complete question is-

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.

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2 years ago

Given that f(x) = x2 + 9x + 18 and g(x) = x + 6, find f(x) – g(x) and

Diano4ka-milaya [45]

Answer:

x^2+8x+12

Step-by-step explanation:

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3 years ago

If 9 out of 20 candies are orange, how many orange candies will there be per 100 candies total?

avanturin [10]

Answer:

Step-by-step explanation:

20 / 9 = 2.222222222223

100 / 45 = 2.222222222223

9 is 45% of 20 and 45 is 45% of 100.

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2 years ago

During which two months do both the Northern and Southern Hemispheres receive the same amount of energy from the Sun?

Drupady [299]

Answer: The correct answer is March and September

pls mark brainliest

6 0

3 years ago

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Evaluate: 2/3 + 4/5 x 7/5 - 8/3​

Evaluate: 2/3 + 4/5 x 7/5 - 8/3