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3 years ago

Select all tables that represent a proportional relationship between X and Y

Mathematics

1 answer:

Arada [10]3 years ago

6 0

Answer:

The 'constant of proportionality k' DOES NOT remain constant for all the points in the table.

Therefore, the table DOES NOT represent a proportional relationship between X and Y.

Step-by-step explanation:

We know that when y varies directly with x, we get

y ∝ x

y = kx

k = y/x

where k is called the 'constant of proportionality'.

Given the table

x 0 5 10 15

y 2 17 32 47

Let us calculate the k value for all the points

FOR (0, 2)

k = y/x

substitute x = 0, and y = 2

k = 2 / 0 = ∞

FOR (5, 17)

k = y/x

substitute x = 5, and y = 17

k = 17/5

k = 3.4

FOR (10, 32)

k = y/x

substitute x = 10, and y = 32

k = 32/10

k = 16/5

k = 3.2

FOR (15, 47)

k = y/x

substitute x = 15, and y = 47

k = 47/15

k = 3.1

It is clear that the 'constant of proportionality k' DOES NOT remain constant for all the points in the table.

Therefore, the table DOES NOT represent a proportional relationship between X and Y.

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A 15 ft. Ladder is placed against a building so that the distance from the top of the ladder to the ground is 10 ft. Find the di

kipiarov [429]

Answer:

11.2 ft

Step-by-step explanation:

Assuming the building meets the ground at right angles, the right triangle formed has side length 10 ft and hypotenuse 15 ft. Then the other side length (d) is given by the Pythagorean theorem as ...

d² + 10² = 15²

d² = 225 -100 = 125

d = √125 = 5√5 ≈ 11.2 . . . feet

The bottom of the ladder is about 11.2 feet from the building

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3 years ago

Each day, Robin commutes to work by bike with probability 0.4 and by walking with probability 0.6. When biking to work injuries

kvasek [131]

Answer:

64.65% probability of at least one injury commuting to work in the next 20 years

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}
$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Each day:

Bikes to work with probability 0.4.

If he bikes to work, 0.1 injuries per year.

Walks to work with probability 0.6.

If he walks to work, 0.02 injuries per year.

20 years.

$\mu = 20*(0.4*0.1 + 0.6*0.02) = 1.04$

Either he suffers no injuries, or he suffer at least one injury. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}
$

$P(X = 0) = \frac{e^{-1.04}*1.04^{0}}{(0)!} = 0.3535
$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.3535 = 0.6465$

64.65% probability of at least one injury commuting to work in the next 20 years

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D

erik [133]

2^3
——
3^3

............

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2 years ago

A person is selected at random. If there are seven days in a week, what is the probability that the person was not born on a Tue

levacccp [35]

Answer:

5 out of 7.

Step-by-step explanation:

There are seven days in one week. They are asking what is the probability of the person chosen not being born in a Tuesday or Wednesday. There are five other days, so there are five other options.

I hope I helped you!

7 0

3 years ago

68. If Fran can only pay $250 per month, what is the most expensive boat she can buy without a down payment?

damaskus [11]

Answer:

If she buys a boat without a down payment, then the affordable price is 5,700.

Step-by-step explanation:

Her bank charges 5% interest per year.

Let, payment = p,

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p = 5698.47

After round off p = 5700

3 0

3 years ago

Select all tables that represent a proportional relationship between X and Y￼

Select all tables that represent a proportional relationship between X and Y