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3 years ago

The weight needed to balance a lever varies inversely with the distance

Mathematics

1 answer:

Andrews [41]3 years ago

5 0

Let w represents the weight and d represents the distance.

It is given that

The weight needed to balance a lever varies inversely with the distance from the fulcrum to the weight. A 120-lb weight is placed on a lever, 5 ft from the fulcrum.

$w = \frac{k}{d}$

Substituting the values of w and d, we will get

$120= \frac{k}{5}
\\
k =600lb \ ft$

Using the value of k which is 600, with the above equation and the given value of d which is 8, we will get

$w = \frac{600}{8} = 75lb$

Therefore the correct option is B .

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- Let y represent the width of a rectangle and let x represent the rectangle's lengu.

valentina_108 [34]

Answer:

Length: 21 cm and Width: 6cm

Step-by-step explanation:

Let $y$ be the width and $x$ length of the rectangle. We know:

$x = 4y -3$ -------- eq. 1

$54 = 2x + 2y$ (Perimeter of the rectangle) ------- eq. 2

Substitute equation 1 in equation 2:

$54 = 2(4y-3) + 2y\\54 = 8y - 6 + 2y\\54 + 6 = 8y + 2y\\60 = 10 y\\\\\frac{60}{10}= y\\y = 6$

Using the value of y, we find x.

$x = 4y - 3\\x = 4(6) -3\\x= 24 - 3\\x = 21$

4 0

3 years ago

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number o

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Step1:

We have Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α =8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t

Step2:

Let “X” the number of small aircraft that arrive during time t and it follows poisson distribution parameter “”

The probability mass function of poisson distribution is given by

P(X) = , x = 0,1,2,3,...,n.

Where, μ(mean of the poisson distribution)

a).

Given that time period t = 1hr.

Then,μ = 8t

= 8(1)

= 8

Now,

The probability that exactly 6 small aircraft arrive during a 1-hour period is given by

P(exactly 6 small aircraft arrive during a 1-hour period) = P(X = 6)

Consider,

P(X = 6) =

= 0.1219.

Therefore,The probability that exactly 6 small aircraft arrive during a 1-hour period is 0.1219.

1).P(At least 6) = P(X 6)

Consider,

P(X 6) = 1 - P(X5)

= 1 - {+++++}

= 1 - (){+++++}

= 1 - (0.000335){+++++}

= 1 - (0.000335){1+8+32+85.34+170.67+273.07}

= 1 - (0.000335){570.08}

= 1 - 0.1909

= 0.8090.

Therefore, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8090.

2).P(At least 10) = P(X 10)

Consider,

P(X 10) = 1 - P(X9)

= 1 - {+++++

5 0

3 years ago

'Ciumane ananen 32.50t + 5 = 28.75t + 20

gtnhenbr [62]

Answer:

The answer is 0.25

Step-by-step explanation:

(1)we group like terms by subtracting 32.50 by 28.75

(2) we subtract 20 and 5 to give us a value of 15

(3)when we subtract 32.50 and 28.75 we get a value of 3.75

(4)so the equation will look like this 3.75t = 15

(5)we divide 3.75 we both the two equations

(6)With a correct calculation, Your answer should be t = 0.25

6 0

3 years ago

It is -9° now. The temperature will drop 5° in two hours. What will the

liberstina [14]

Answer:

-14°

Step-by-step explanation:

-9 - 5

-9 + (-5)

-14

3 0

3 years ago

Read 2 more answers

Is line 1 (1,5) (3,-2) and like 2 (-3,2) (4,0) perpendicular of parallel?

Lera25 [3.4K]

Slope Formula: $\frac{y_2-y_1}{x_2-x_1}$

So remember that perpendicular lines have slopes that are negative reciprocals to each other and parallel lines have the same slope. To find out if they are either parallel or perpendicular, plug the pair of points into the slope formula to find their slopes:

$\textsf{Line 1}\\\\\frac{5-(-2)}{1-3}=-\frac{7}{2}\\\\\textsf{Line 2}\\\\\frac{0-2}{4-(-3)}=-\frac{2}{7}$

Since these slopes aren't the same nor are they negative reciprocals to each other, the lines are neither parallel nor perpendicular.

7 0

3 years ago