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faltersainse [42]

3 years ago

5

Gabriel had 350 books to put away but 14 were broken. He split up the good books into 6 baskets. How many books can go in each b

asket?

1 answer:

Naya [18.7K]3 years ago

7 0

Answer:

56

Step-by-step explanation:

350 - 14 = 336

336 dived by 6 = 56

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Zigmanuir [339]

The final answer is 1,200

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2 years ago

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If 5x:(x-2) = 11:3 , find the value of x ?

Masteriza [31]

Answer:

x = -11/2

Step-by-step explanation:

The ratios need to stay the same

5x 11

----- = -------

x-2 3

Using cross products

5x*3 = (x-2) 11

15x = 11x - 22

Subtract 11 from each side

15x-11x = -22

4x = -22

x = -22/4

x = -11/2

5 0

2 years ago

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I don’t understand how to do this

schepotkina [342]

Answer:

The solution is $x =0.$

Step-by-step explanation:

The equation

$\bold{(1).}\: sin(\dfrac{3\pi }{2} +x)+sin(\dfrac{3\pi }{2} +x) =-2$

can be rewritten as

$2* sin(\dfrac{3\pi }{2} +2) =-2$

and can be further simplified to

$sin(\dfrac{3\pi }{2}+x ) =-1$ .

Now, taking the inverse sine of both sides we get:

$sin^{-1}(sin(\dfrac{3\pi }{2} +x) =sin^{-1}(-1)$

$\bold{(2).}\: \dfrac{3\pi }{2} +2 =sin^{-1}(-1)$

The value of the right side on the interval $[0,2\pi)$ is

$sin^{-1}(-1) = \dfrac{3\pi}{2} \: \:( \text{or }270^o)$ ,

which makes the equation (2)

$\dfrac{3\pi }{2}+x =\dfrac{3\pi}{2}$

solving for $x$ gives

$\boxed{x = 0}$

which is our solution.

4 0

3 years ago

Mario drew a model to represent one third of the space in his bookcase. how could mario draw a model to represent all the space

Maksim231197 [3]

He could of drew it open

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3 years ago

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Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose t

andrezito [222]

Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:

f(x) = λ. $e^{-\lambda.x}$

and the cumulative distribution function, which describes the probability distribution of a random variable X, is:

F(x) = 1 - $e^{-\lambda.x}$

(a) <u>Probability</u> of distance at most <u>100m</u>, with λ = 0.0143:

F(100) = 1 - $e^{-0.0143.100}$

F(100) = 0.76

<u>Probability</u> of distance at most <u>200</u>:

F(200) = 1 - $e^{-0.0143.200}$

F(200) = 0.94

<u>Probability</u> of distance between <u>100 and 200</u>:

F(100≤X≤200) = F(200) - F(100)

F(100≤X≤200) = 0.94 - 0.76

F(100≤X≤200) = 0.18

(b) The mean, E(X), of a probability distribution is calculated by:

E(X) = $\frac{1}{\lambda}$

E(X) = $\frac{1}{0.0143}$

E(X) = 69.93

The standard deviation is the square root of variance,V(X), which is calculated by:

σ = $\sqrt{\frac{1}{\lambda^{2}} }$

σ = $\sqrt{\frac{1}{0.0143^{2}} }$

σ = 69.93

<u>Distance exceeds the mean distance by more than 2σ</u>:

P(X > 69.93+2.69.93) = P(X > 209.79)

P(X > 209.79) = 1 - P(X≤209.79)

P(X > 209.79) = 1 - F(209.79)

P(X > 209.79) = 1 - (1 - $e^{-0.0143*209.79}$ )

P(X > 209.79) = 0.0503

(c) Median is a point that divides the value in half. For a probability distribution:

P(X≤m) = 0.5

$\int\limits^m_0 f({x}) \, dx$ = 0.5

$\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx$ = 0.5

$\lambda.\frac{e^{-\lambda.x}}{-\lambda}$ = $-e^{-\lambda.x} + e^{0}$

$1 - e^{-\lambda.m}$ = 0.5

$-e^{-\lambda.m}$ = - 0.5

ln( $e^{-0.0143.m}$ ) = ln(0.5)

-0.0143.m = - 0.0693

m = 48.46

6 0

3 years ago