From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles, and the eastbound train has traveled 16 miles. How far apart are the two trains, measured in a straight line?

Answers

Answer 1

9514 1404 393

Answer:

  20 miles

Step-by-step explanation:

The north and east distances form the legs of a right triangle. The straight-line distance between the trains is the hypotenuse of that triangle. The Pythagorean theorem can be used to find the length of the hypotenuse (d).

  d² = 12² +16²

  d² = 144 +256 = 400

  d = √400 = 20

The two trains are 20 miles apart.

__

Additional comment

You may recognize the given distances are in the ratio 3 : 4.  You may recall that side ratios of 3 : 4 : 5 make a right triangle. If so, you recognize that the straight-line distance is (4 miles)×5 = 20 miles. (3:4:5 right triangles show up often in algebra and geometry problems, so might be something you want to look for.)


Related Questions

How many solutions does this system of equations have?

Answers

Answer:

this equation will have 2 solutions

It will be 2 solutions

12 less than a number is 39 find the number round your answer to the nearest integer if necessary

Answers

Answer:

number = n

n = 51

Equation:

n - 12 = 39

39 + 12 = 51

Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of information does he need to determine the confidence interval?

A.
the critical value
B.
the number of favorable responses
C.
the standard error of the mean
D.
the standard deviation

Answers

Answer:

A

Step-by-step explanation:

The other piece of information Mike needs to determine the confidence interval is the critical value.

What is a confidence interval?

A confidence interval is a range of estimates for a variable that is uncertain. A confidence interval is calculated at a specified confidence level; the 95% confidence level is the most frequent, although other values, such as 90%or 99%, are also used.

To determine the confidence interval for a set of data sample size, the sample proportion, and the critical value are needed to be known.

Hence, the other piece of information Mike needs to determine the confidence interval is the critical value.

Learn more about Confidence Intervals:

https://brainly.com/question/24131141

#SPJ2

Please help me this is due in 20 minutes!!!!!!!

Answers

Answer:

The two triangles are very similar by them both having the same kind of angles even though they are different in size, like, an acute angle.

I'm not sure if this helped or not hopefully it did good luck.

Please help me I am struggling

Answers

Answer:

924

Step-by-step explanation:

i multiply 14 by 11 and then by 6

Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of information does he need to determine the confidence interval?

A.
the critical value
B.
the number of favorable responses
C.
the standard error of the mean
D.
the standard deviation

Answers

Answer:

C.  the standard error of the mean

Step-by-step explanation:

You need the sample mean, sample proportion , and the standard error which depend on z or t, sigma or s, and n

im almost done with this hw. plz help!!! give explanation if you actually know the answer so ik u dont just want points

Answers

Answer:

C

Step-by-step explanation:

Mr. Farris drives 7 1/2 miles directly west of his home to a restaunt.he then drives 8 2/3 miles directly east of the restauant to his office. how far , and in what direction is his office from his home ?

Answers

Answer:

2 1/6

Step-by-step explanation:

8 2/3 - 7 1/2 = 2 1/6

9514 1404 393

Answer:

  1 1/6 miles east of home

Step-by-step explanation:

If we consider east to be positive, then the distance from home to office is ...

  (-7 1/2) +(+8 2/3) = -7 3/6 +8 4/6 = (8 -7) +(4/6 -3/6) = +1 1/6

Farris's office is 1 1/6 miles east of his home.

Which point is located in Quadrant ll? (-4,5) (-4,-5) (4,-5) (4,5)​

Answers

Answer:

(-4,5)

Step-by-step explanation:

that is the top left quadrant which means the x value has to be negative but the y value has to be positive

Jason is laying out a square garden on his property. The space measures 46 feet diagonally. How long is each side of the garden?

Answers

46 ft all around the square

Algebra 2
L.3 Multiply polynomials BGN

Answers

Answer:

x² + 4x

Step-by-step explanation:

Area of the rectangle = length × width

length = x + 4

width = x

Therefore,

Area = x(x + 4)

Area = x*x + x*4

x² + 4x

pls answer this question about math​

Answers

Answer:

AB, AC, AD, BC, BD, CD

Hope this helps :)

Answer:

five line segment =AB,AC,AD,BC,BD,CD

The Wells family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number

Answers

Answer:

4 gallons/1 day

Step-by-step explanation:

What is a rate? A rate is writing a ratio in fraction form. A ratio is the proportion of two things. (ex: for every 1 dog, there are two cats.)

Creating the ratio: For the ratio, there is no given amount of which one needs  to come first, but because it is about the milk, I put that first. In the problem it says 12 gallons for 3 days so: 12/3

Simplifying: To simplify, think of the largest factor between the two numbers. If you can't immediately, think of one factor in common and keep simplifying. In this case, 4 is the greatest common factor between these. To simplify, divide both sides by four, and that is your answer: 4: 1

There are only seven days left until we launch of our new product and we only have $668 left in our promotion budget we need to spend $85 on the last day can you please calculate how many dollars a day we can spin on the remaining days

Answers

Answer:

$97.17

Step-by-step explanation:

First, subtract 85 from 668:

668 - 85

= 583

This means that our budget for all of the days excluding the last day is $583

To find how much can be spent on the remaining days, divide 583 by 6:

583/6

= 97.17

So, approximately $97.17 can be spent on the remaining days

Can someone help for number 17 I’ll mark best answer!!!!!!!!!!!

Answers

9514 1404 393

Answer:

  a) radius: 6 (m); mass: 22 (kg)

  b) volume: 19 (m³)

  c) d ≈ 2.8×10^3 kg/m³

Step-by-step explanation:

The order of magnitude is the exponent of 10 when the number is written in scientific notation.

a) radius: 1.6×10^6 m, so the order of magnitude is 6 when the units are meters.

  mass: 4.8×10^22 kg, so the order of magnitude is 22 when the units are kg.

__

b) The volume is ...

  V = (4/3)πr^3 ≈ 1.716×10^19 m^3, so the order of magnitude of the volume is 19 when the units are m^3.

__

c) The ratio of mass to volume is ...

  d = (4.8×10^22)/(1.716×10^19) ≈ 2.8×10^(22-19) = 2.8×10^3 kg/m^3, so the order of magnitude is 3 when the units are kg/m^3.

i need help! please and thank you

Answers

Answer:

[tex]20\pi[/tex] m

OR

62.8318531 m

Step-by-step explanation:

This is actually pretty simple

The distance the tip travels is the arc length and the length of the pendulum is the radius of a circle

The formula for arc length is Angle in Radians x Radius

So pi/12 * 4 = pi/3 m

We know this is how much it travels every second so it is going at pi/3 m/s

One minute is 60 seconds

pi/3 * 60 = 20pi m

Please help me ASAP please

Answers

Answer:

217=31m; m=7, 7 miles per day

Step-by-step explanation:

217/31=m 217=31m, just divide the total number of miles by the number of days



For the triangles above, what is the measure of

Answers

Answer:

72

Step-by-step explanation

48 + k+l =180

48 +90+l =180

138 +l = 180

l=180 - 138

l = 42

now

l+m+n= 180

42 +m+66 =180

108+m= 180

m= 180 -108 m =72

Mark brainlest

Which of the following best describes the correlation coefficient of r = -0.09 ?

Answers

Hi! May you please comment the options

HELP PLEASE QUICK!!!!!

Answers

Answer:in what can I help

Step-by-step explanation:

Need help with finding the mean (MATH 7th GRADE)

Answers

Answer:

mean = 49.25

Step-by-step explanation:

mean = sum of all the number ÷ amount of number

mean = 56 + 21 +55 + 30 + 34+ 76 + 40 + 82 = 394 ÷ 8

mean = 49.25

mean absolute deviation = (56- 49.25) + (21 - 49.25) + (55 -49.25) + (30 - 49.25) + (34 -49.25) + (76 -49.25) + (40 - 49.25) + (82- 49.25) / 8

mad= 6.75 + -28.25 + 5.75 + -19.25 + -15.25 + 26.75 + -9.25 + 32.75 / 8

mad = 0/8

mad= 0

brainliest is appreciated

Find the area of the shape below

Answers

Answer:

2112

Step-by-step explanation:

100% sure

Branliest to correct answer explain how you solved it please

Answers

Answer:

10.4

Step-by-step explanation:

look at the picture for steps

A pharmaceutical company is conducting a study on whether or not their new vaccine is effective in preventing chicken pox. The researchers rejected the null hypothesis and stated that the vaccine was effective. However, subsequent studies found out that the vaccine did not have any effect on combating chicken pox. What type of error did the researchers make

Answers

Answer:

The answer is "Type 1 error".

Step-by-step explanation:

The error of type I, frequently known as a 'false positive': its error in judgment that perhaps a null hypothesis is simply rejected. This is the mistake of accepting a possible (actual interest hypothesis) hypothesis whenever the results could be attributed to chance since the researchers deny, if valid, the null hypothesis.

helpppppppppppppppppppppppppppp

Answers

It is 75.36 because the total volume is 301.59 and 25% of the cone remains so 25% of 301.59 is 75.36

stimulus check summary please help me please

Answers

Answer: I think it’s great but you should make a stronger opinion and always have back up evidence

Step-by-step explanation:

Stimulus checks are checks sent by the U.S. government to taxpayers to boost their spending power and spur economic activity. Stimulus checks are either mailed to taxpayers or an equivalent tax credit is applied to their tax filing.

A consulting firm claimed that 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex. The claim was tested by taking a random sample of 60 online shoppers and assigning them each a different randomly selected e-commerce Web site to test. 45 reported sufficient frustration with their sites to deter making a purchase. The data was entered into STATISTIX and the following output was generated:

Hypothesis Test - One Proportion

Sample Size 60
Successes 45
Proportion 0.75000

Null Hypothesis: P = 0.65
Alternative Hyp: P > 0.65

Difference 0.10000
Standard Error 0.05590
Z (uncorrected) 1.62 P 0.0522

Method 95% Confidence Interval
Simple Asymptotic (0.64043, 0.85957)

Which of the following statements is correct if we are testing at α = 0.05?

a. There is sufficient evidence to indicate that more than 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.
b. There is sufficient evidence to indicate that exactly 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.
c. There is insufficient evidence to indicate that exactly 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.
d. There is insufficient evidence to indicate that more than 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.

Answers

Answer:

b. There is sufficient evidence to indicate that exactly 65% of all e-commerce shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex.

Step-by-step explanation:

Not significant,accept null hypothesis that population proportion = 0.65

When we accept the null hypothesis that P= 0.65

Then only option b is correct which states that  there is sufficient evidence to support that population proportion is exactly 0.65 .

1) We obtain a P - value of 0.0522 which is greater than 0.5 indicating that the null hypothesis is not rejected.

The rejection region for this right-tailed test is z > 1.64

2) Test Statistics

z= p`-p0/ sqrt(p0(1-p0)/n)

The z-statistic is computed as follows:

z= 0.75-0.65/ √(0.65*0.35)60

z= 1.624

3) Decision about the null hypothesis

Since it is observed that z = 1.624 is less than z ∝=1.64, it is then the null hypothesis is not rejected.

Nicholas is currently in eighth grade and intends to attend a state college when he finishes high school. Nicholas’s parents currently have some money invested in mutual funds, but would like to invest this money in a more secure investment now to pay for college in 4 years. If they will need $25,000, how much do Nicholas’s parents have to invest now in a 48month CD that has a rate of 4.59% compounded monthly?

Answers

Answer:

30027.86

Step-by-step explanation:

Use the multiplication principle to solve the problem.
A biologist is attempting to classify plant species by assigning 5 initials to each species. How many
classifications are possible using this method?​

Answers

yes 100% accurate. I agree

In MATHEMATICS ...write the empirical formula.​

Answers

Answer:

3Median = Mode + 2Mean

Step-by-step explanation:

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