MATHEMATICS HIGH SCHOOL

An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind. Plane on outbound trip of 4 hours with 25 mph tailwind and return trip of 5 hours with 25 mph headwind Let r = the rate or speed of the airplane in still air. Let d = the distance a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.
b. Solve the system of equations for the speed of the airplane in still air.

Answers

Answer 1

Answer:

Answer:

r = 225 Mil/h speed of the airplane in still air

Step-by-step explanation:

Then:

d is traveled distance and r the speed of the airplane in still air

so the first equation is for a 4 hours trip

as d = v*t

d = 4 * ( r + 25) (1) the speed of tail wind (25 mil/h)

Second equation the trip back in 5 hours

d = 5 * ( r - 25 ) (2)

So we got a system of two equation and two unknown variables d and

We solve it by subtitution

from equation (1) d = 4r + 100

plugging in equation 2

4r + 100 = 5r - 125 ⇒ -r = -225 ⇒ r = 225 Mil/h

And distance is :

d = 4*r + 100 ⇒ d = 4 * ( 225) + 100

d = 900 + 100

d = 1000 miles

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A wheel has a circumference of 7 5/6 feet. How many times does it turn in 423 feet.

Help please! What is the distance between (-5, -6) and (-3, -8)?

Answer choices are on the picture below :)

Answers

so we take the square root of (x1-x2)^2+(y1-y2)^2
the plug in the Values
sqrt of (-5+3)^2+(-6+8)^2
sqrt of (-2)^2 +(2)^2
sqrt of 4+4
sqrt of 8

So D is your answer. :)

Please help and NO LINKSTo conduct a survey about the type of phone service most people in Greenville prefer, 10 different blocks in the neighborhood are chosen. On these 10 blocks, 10 houses are selected at random, and then one resident of each of those houses is interviewed. This type of sampling method is

A.) simple random sampling.
B.) stratified sampling.
C.) systematic random sampling.
D.) cluster sampling.

Answers

Answer:

Please help and NO LINKS

Step-by-step explanation:

(Ihopethishelps)(BRAINLEISTPLEASE)❤☺️☻♨️

Answer:

Cluster sampling

Step-by-step explanation:

AI-generated answer

The sampling method described in the question is cluster sampling. In cluster sampling, the population is divided into clusters or groups, and then a random sample of clusters is selected. In this case, the blocks in the neighborhood are the clusters.

Here is a step-by-step explanation of why this is cluster sampling:

1. The first step is to divide the population into clusters. In this case, the population is the neighborhood, and the clusters are the different blocks within the neighborhood.

2. Next, a random sample of clusters is selected. The question states that 10 different blocks in the neighborhood are chosen. This means that the researchers randomly selected 10 blocks from the neighborhood.

3. Once the clusters are selected, a sample is taken from each cluster. The question states that on these 10 blocks, 10 houses are selected at random. This means that within each of the 10 selected blocks, 10 houses are chosen randomly.

4. Finally, the residents of each selected house are interviewed. This means that every resident of each of the selected houses is interviewed to gather information about the type of phone service they prefer.

Overall, this sampling method is cluster sampling because the population is divided into clusters (blocks), a random sample of clusters (10 blocks) is selected, and then a sample is taken from each selected cluster (10 houses on each block).

Mario bought $5 worth of stamps at the post office. He bought ten more 6 cents stamps than 10 cents stamps. The number of 8 cents stamps was three times the number of 10 cents stamps. He also bought two 20 cents stamps. How many of each kind of stamp did he purchase?

Answers

s=number of 6 cent stamps
t=number of ten cen stamps
e=number of 8 cent stamps
w=number of 20 cents stamps=2

cost=500 cents
6s+10t+8e+20w=500
w=2 since two 20 cent stamps wer bought
6s+10t+8e+40=500
minsu 40 both sides
6s+10t+8e=460
divide both sides by 2 to simplify
3s+5t+4e+230

also
10 more 6 cent than 10 cent
s=10+t

8 cent stamps is 3 times 10 cent stamps
e=3t

sub
s=10+t
e=3t

3(10+t)+5t+4(3t)+230
30+3t+5t+12t=230
30+20t=230
minus 30
20t=200
divid 20
t=10

sub back
s=10+t
s=10+10
s=20

e=3t
e=3(10)
e=30

20 six cent
30 eight stamp
10 ten cent
2 twenty cent

Answer:

20 six cent

30 eight stamp

10 ten cent

2 twenty centep explanation:

What is an equation of the line that passes through the points (2,1) and (6,-5)?

Answers

I would go with number 3.

Final answer:

The equation of the line that passes through the points (2,1) and (6,-5) is y = -3/2x + 4. This is calculated using the formula for a line y - y1 = m(x - x1) and the formula for slope.

Explanation:

In order to find the equation of the line passing through the points (2,1) and (6,-5), we can use the formula for a line y - y1 = m(x - x1). Here, m is the slope of the line. We can calculate the slope using the formula (y2 - y1) / (x2 - x1). Thus, for the points (2,1) and (6,-5), the slope m is (-5 - 1) / (6 - 2) = -6/4 = -3/2. We can substitute one pair of points and the slope into the line equation. Let's use (2,1). The equation of this line is then y - 1 = -3/2 * (x - 2). Simplifying, we get the equation of the line to be y = -3/2x + 4.