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2 years ago

The straight line ℓ is perpendicular to the line y + 2x = 9 and passes through the point p(4, 3). find the x-intercept of ℓ.

1 answer:

8 0

The slope of the line l is the opposite reciprocal of y+2x=9. Rearranged the equation to y=9-2x and we get a slope of -2. The opposite reciprocal of -2 is 1/2.

y-y=m(x-x)
y-3=.5(x-4)
y=.5x+1

At the x-intercept, y=0, so
0=.5x+1
-1=.5x
x=-2

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A spring has natural length 20 cm. Compare the work W1 done in stretching the spring from 20 cm to 30 cm with the work W2 done i

sashaice [31]

Answer:

W1 = W2 = 50k Joules (assuming W1 and W2 have the same force constant, k)

W1 - W2 = 0

Step-by-step explanation:

Work done in stretching a spring is given by 1/2ke^2

Where, k is force constant and e is extension

e1 = 30cm - 20cm = 10cm

W1 = 1/2k(e1)^2 = 1/2×k×10^2 = 50k Joules

e2 = 40cm - 30cm = 10cm

W2 = 1/2k(e2)^2 = 1/2×k×10^2 = 50k Joules

W1 = W2 = 50k Joules provided W1 and W2 have equal force constant

Therefore, W1 - W2 = 0

7 0

3 years ago

путешествиники добирались до города 3 часа на автобусе 7 часов на поезде и 5 часов плили на лодке сколько всего часов они были в

Rasek [7]

Answer:

Ответ - 15.

Step-by-step explanation:

Путешественники добирались до города на разных транспортах. Чтобы найти общее время, пройденное этими людьми, если 15. Добавьте 3 к 7, а затем прибавьте к нему 5.

7 0

2 years ago

Determine if the numbers are parallel, perpendicular or netiher.

Margarita [4]

Answer:

Parallel :)

Step-by-step explanation:

thats the tea sis.

4 0

3 years ago

Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

$z = \frac{x-\mu }{\sigma }$

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

$P(x \ge 60) \approx P(z > 1.34)$