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2 years ago

10

The sum of eight times a number and negative four exceeds twelve.

2 answers:

Ganezh [65]2 years ago

5 0

Answer: Our required inequality would be

$(8x-4)>12$

Step-by-step explanation:

Let the number be 'x'.

Eight times a number is expressed as

$8x$

Sum of eight times a number and negative four is expressed as

$8x-4$

the above exceeds twelve is expressed as

$(8x-4)>12$

Hence, our required inequality would be

$(8x-4)>12$

Aliun [14]2 years ago

3 0

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An ant begins at the top of the pictured octahedron. If the ant takes two "steps", what is the probability it ends up at the bot

Aleksandr-060686 [28]

Answer:

$P_{bottom}=\frac{1}{4}=0.25$

Step-by-step explanation:

Starting from the top, the ant can only take four different directions, all of them going down, every direction has a probability of 1/4. For the second step, regardless of what direction the ant walked, it has 4 directions: going back (or up), to the sides (left or right) and down. If the probability of the first step is 1/4 for each direction and once the ant has moved one step, there are 4 directions with the same probability (1/4 again), the probability of taking a specific path is the multiplication of the probability of these two steps:

$P_{2steps}=\frac{1}{4}*\frac{1}{4}=\frac{1}{16}$

There are only 4 roads that can take the ant to the bottom in 2 steps, each road with a probability of 1/16, adding the probability of these 4 roads:

$P_{bottom}=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}$

The probability of the ant ending up at the bottom is $\frac{1}{4}$ or 0.25.

6 0

2 years ago

76 persons can complete the job in 42 days-in how many days will 56 persons do the same job?

kkurt [141]

We are given that 76 persons can complete the job in 42 days.

We need to find the number of days will 56 persons do the same job.

Let us assume that in x number of days will 56 persons do the same job.

Number of days taken by 1 person to complete same work = 76 × 42 =3192 days.

56 person will take = $\frac{3192 }{56}$ = 57.

<h3>Therefore, 57 days will 56 persons do the same job.</h3>

3 0

2 years ago

You launch a water balloon. The function h=-0.08t^2+1.6t+2 models the height h (in feet) of the water balloon after t seconds. W

stellarik [79]

Answer:

The initial height of the balloon is 2 feet.

Step-by-step explanation:

The height of the balloon in feet after t seconds is given by the following equation:

$h(t) = -0.08t^{2} + 1.6t + 2$

What is the initial height of the balloon?

This is h when t = 0, that is, h(0). So

$h(0) = -0.08*0^{2} + 1.6*0 + 2 = 2$

The initial height of the balloon is 2 feet.

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2 years ago

Ali and Steve share some sweets in the ratio 2 : 7

Ivahew [28]

Answer: 30 - 5 = 25 (the difference between the two is 5)

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2 years ago

Use the fact that the variance of a Poisson distribution is σ2=μ. The mean number of bankruptcies filed per hour by businesses i

lianna [129]

Answer:

Variance = 5

Standard deviation = 2.236

0.2650257

Step-by-step explanation:

For a Poisson distribution is σ² = μ.

Given that:

Mean , μ of bankruptcies files per hour = 5

μ = 5

For a Poisson distribution :

P(x = x) = (μ^x * e^-μ) / x!

The Variance and standard deviation :

Variance : σ² = μ = 5

Standard deviation = sqrt(variance) = sqrt(5) = 2.236

B.) Find the probability that at most three businesses will file bankruptcy in any given hour.

P( x ≤ 3) = P(0) + P(1) + P(2) + P(3)

P(x = 0) = (5^0 * e^-5) / 0! = 0.0067379

P(x = 1) = (5^1 * e^-5) / 1! = 0.0336897

P(x = 2) = (5^2 * e^-5) / 2! = 0.0842243

P(x = 3) = (5^3 * e^-5) / 3! = 0.1403738

0.0067379 + 0.0336897 + 0.0842243 + 0.1403738

= 0.2650257

6 0

2 years ago