MATHEMATICS HIGH SCHOOL

Question 1 (1 point)Find the coordinates of point P that divides the directed line segment from A to B in the given ratio. A(1, 2), B(5, 4), 1 to 1

Answers

Answer 1

Answer:

Answer:

P ( -1, -3)

Step-by-step explanation:

Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)

We will calculate coordinates of the point P which divides line segment AB in the following way:

xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1

xp = -1

yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3

yp = -3

Point P( -1, -3)

Related Questions

Is 2,-5,-12,-19,-26 an arithmetic sequence
Please helpppppppppppp
=Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3. −22–4232
Can someone show me how to do this? What volumes of 60% hydrochloric acid solution and 30% hydrochloric acid solution must be mixed to make 125mL of 36% hydrochloric acid solution?
Which of the following lines the parallel to the line y-9=7(x+5)A.) y-9=3x+4B.) y=-9x-5C.) y+5=7(x-9)D.) y-9=5(x+4)

An airliner carries 200 200 passengers and has doors with a height of 70 70 in. Heights of men are normally distributed with a mean of 69.0 69.0 in and a standard deviation of 2.8 2.8 in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is . 6395 . (Round to four decimal places as needed.)b. If half of the 200 200 passengers are men, find the probability that the mean height of the 100 100 men is less than 70 70 in. The probability is nothing . (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? A. The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height. B. The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height. C. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend. D. The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend. d. When considering the comfort and safety of passengers, why are women ignored in this case? A. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women. B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women. C. Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend.

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The probability is 0.6395.

b) The probability is 1.

The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

It measures how many standard deviations the measure is from the mean.
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
By the Central Limit Theorem, for the sampling distribution of samples of size n, the standard deviation is $s = (\sigma)/(√(n))$

In this problem:

Mean of 69 in, thus $\mu = 69$ .
Standard deviation of 2.8 in, thus $\sigma = 2.8$ .

Item a:

This probability is the p-value of Z when X = 70, thus:

$Z = (X - \mu)/(\sigma)$

$Z = (70 - 69)/(2.8)$

$Z = 0.357$

$Z = 0.357$ has a p-value of 0.6395.

Thus, the probability is 0.6395.

Item b:

Samples of size 100, thus $n = 100, s = (2.8)/(√(100)) = 0.28$ .

This probability is the p-value of Z when X = 70, thus:

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem:

$Z = (X - \mu)/(s)$

$Z = (70 - 69)/(0.28)$

$Z = 3.57$

$Z = 3.57$ has a p-value of 1.

The probability is 1.

Item c:

We want don't want many people to have to bend, thus, part a has to be considered.

Item d:

Generally, men are taller, so if the design accommodates the men, it will accommodate the women, and the correct option is:

B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

A similar problem is given at brainly.com/question/24663213

Answer:

a) 0.6406; b) 1.000; c) C. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend; d) B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Step-by-step explanation:

For part a,

We use the formula for the z score of an individual,

$z=(X-\mu)/(\sigma)$

Our mean, μ, is 69 and our standard deviation, σ, is 2.8. To find P(X < 70),

z = (70-69)/2.8 = 1/2.8 = 0.36

Using a z table, we see that the area under the curve to the left of this value is 0.6406. This is our probability.

For part b,

We use the formula for the z score of a sample,

$z=\frac{\bar{X}-\mu}{\sigma / √(n)}$

Our mean is still 69 and our standard deviation is still 2.8. Our sample size, n, is 100. To find P(X < 70),

z = (70-69)/(2.8÷√100) = 1/(2.8÷10) = 1/0.28 = 3.57

Using a z table, we see the area under the curve to the left of this is greater than 0.9999. This means that the probability is 1.000.

For part c,

We want to know the proportion of male passengers that will not need to bend. This is why the value from part a is more important.

For part d,

Men taller on average than women. This means if we accommodate for the mean, it follows that the women will fit as well.

A chef has 1/2 a pound of flour to divide equally into two containers. How much flour will be in each container?

Answers

There is 1/4 flour will be in each container

What is Division?

A division is a process of splitting a specific amount into equal parts.

Given that A chef has 1/2 a pound of flour

The chef has to divide 1/2 a pound of flour to two containers equally.

We need to find how much flour will be in each container.

Which means we have to divide 1/2 by 2.

(1/2)/2

One by two whole divided by 2

1/2 is the numerator and 2 is the denominator

=1/2×2

=1/4

Hence, there is 1/4 flour will be in each container

To learn more on Division click:

brainly.com/question/21416852

#SPJ2

Answer:

1/4

Step-by-step explanation:

440 miles decreased by 95 percent

Answers

440 - 95%
440 x (1 - 95/100)
440 x 0,05
= 22

Xvideos is the best website ever

Tatum weighs 47.39 kilograms.What is is her mass rounded to the nearest whole number?A.50 Kilograms
B.48 Kilograms
C.47.4 Kilograms
D.47 Kilograms

Answers

47.39 rounded since 3 is lower than five the numbers before stay the same and you end with 47.0

Find the volume of an object with a mass of 63 grams and a density of 9 g/cm

Answers

you have to divide it 63 divide by 9 = 7

Final answer:

To find the volume of an object, divide its mass by its density.

Explanation:

The volume of an object can be found by dividing its mass by its density. In this case, the mass is given as 63 grams and the density is given as 9 g/cm. To find the volume, divide the mass by the density: Volume = Mass / Density.

Substituting the given values, we get Volume = 63 g / 9 g/cm. Simplifying the equation, we find that the volume of the object is 7 cm³.