1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
torisob [31]
2 years ago
9

Abigail and Spencer calculate the slope of the line between the points (3,-1) and (5,4) in different ways. Abigail calculates th

e slope by dividing -1 - 4 with 3 - 5. Spencer divides 4 - (-1) by 5 - 3. When they check their work with their mutual friend Lauren, she says that they are both wrong and shows them her work. She calculates -1 - 4 and divides by 5 - 3. Who is correct among these three friends? Who is incorrect? Why? there is more than one answer!
Mathematics
1 answer:
ElenaW [278]2 years ago
8 0
Nsnsnskskkakammabvbshshsj
You might be interested in
The Empirical Rule The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geys
ad-work [718]

Answer:

(a) Sample Standard Deviation approximately to the nearest whole number = 6

(b) The use of Empirical Rule to make any general statements about the length of eruptions is empirical rules tell us about how normal a distribution and gives us an idea of what the final outcome about the length of eruptions is.

(c) The percentage of eruptions that last between 92 and 116 seconds using the empirical rule is 95%

(d) The actual percentage of eruptions that last between 92 and 116 seconds, inclusive is 95.45%

(e) The percentage of eruptions that last less than 98 seconds using the empirical rule is 16%

(f) The actual percentage of eruptions that last less than 98 seconds is 15.866%

Step-by-step explanation:

(a) Determine the sample standard deviation length of eruption.

Express your answer rounded to the nearest whole number.

Step 1

We find the Mean.

Mean = Sum of Terms/Number of Terms

= 90+ 90+ 92+94+ 95+99+99+100+100, 101+ 101+ 101+101+ 102+102+ 102+103+103+ 103+103+103+ 104+ 104+104+105+105+105+ 106+106+107+108+108+108 + 109+ 109+ 110+ 110+110+110+ 110+ 111+ 113+ 116+120/44

= 4582/44

= 104.1363636

Step 2

Sample Standard deviation = √(x - Mean)²/n - 1

=√( 90 - 104.1363636)²+ (90-104.1363636)² + (92 -104.1363636)² ..........)/44 - 1

= √(199.836777 + 199.836777 + 147.2913224+ 102.7458678+ 83.47314049+ 26.3822314+ 26.3822314+ 17.10950413+17.10950413+ 9.836776857+ 9.836776857, 9.836776857+9.836776857+ 4.564049585+ 4.564049585+ 4.564049585+ 1.291322313+ 1.291322313+ 1.291322313+ 1.291322313+ 1.291322313+ 0.01859504133+ 0.01859504133+ 0.01859504133+ 0.7458677685+ 0.7458677685+ 0.7458677685+ 3.473140497+ 3.473140497+ 8.200413225+ 14.92768595+ 14.92768595+ 14.92768595+ 23.65495868+ 23.65495868+ 34.38223141+ 34.38223141+34.38223141+ 34.38223141+ 34.38223141+47.10950414+ 78.56404959+ 140.7458677+ 251.6549586) /43

= √1679.181818/43

= √39.05073996

= 6.249059126

Approximately to the nearest whole number:

Mean = 104

Standard deviation = 6

(b) On the basis of the histogram drawn in Section 3.1, Problem 28, comment on the appropriateness of using the Empirical Rule to make any general statements about the length of eruptions.

The use of Empirical Rule to make any general statements about the length of eruptions is empirical rules tell us about how normal a distribution and gives us an idea of what the final outcome about the length of eruptions is .

(c) Use the Empirical Rule to determine the percentage of eruptions that last between 92 and 116 seconds.

The empirical rule formula states that:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

Mean = 104, Standard deviation = 6

For 68% μ - σ = 104 - 6 = 98, μ + σ = 104 + 6 = 110

For 95% μ – 2σ = 104 -2(6) = 104 - 12 = 92

μ + 2σ = 104 +2(6) = 104 + 12 = 116

Therefore, the percentage of eruptions that last between 92 and 116 seconds is 95%

(d) Determine the actual percentage of eruptions that last between 92 and 116 seconds, inclusive.

We solve for this using z score formula

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Mean = 104, Standard deviation = 6

For x = 92

z = 92 - 104/6

= -2

Probability value from Z-Table:

P(x = 92) = P(z = -2) = 0.02275

For x = 116

z = 92 - 116/6

= 2

Probability value from Z-Table:

P(x = 116) = P(z = 2) = 0.97725

The actual percentage of eruptions that last between 92 and 116 seconds

= P(x = 116) - P(x = 92)

= 0.97725 - 0.02275

= 0.9545

Converting to percentage = 0.9545 × 100

= 95.45%

Therefore, the actual percentage of eruptions that last between 92 and 116 seconds, inclusive is 95.45%

(e) Use the Empirical Rule to determine the percentage of eruptions that last less than 98 seconds

The empirical rule formula:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

For 68% μ - σ = 104 - 6 = 98,

Therefore, 68% of eruptions that last for 98 seconds.

For less than 98 seconds which is the Left hand side of the distribution, it is calculated as

= 100 - 68/2

= 32/2

= 16%

Therefore, the percentage of eruptions that last less than 98 seconds is 16%

(f) Determine the actual percentage of eruptions that last less than 98 seconds.

The formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For x = 98

Z score = x - μ/σ

= 98 - 104/6

= -1

Probability value from Z-Table:

P(x ≤ 98) = P(x < 98) = 0.15866

Converting to percentage =

0.15866 × 100

= 15.866%

Therefore, the actual percentage of eruptions that last less than 98 seconds is 15.866%

4 0
3 years ago
Given the function ƒ(x )=x^2 - 5, find ƒ(7).<br><br> 49 <br><br> 2 <br><br> 44
rosijanka [135]
Substitute the 7 in anywhere there is an x.
49-5=44
4 0
3 years ago
Read 2 more answers
HELP NEEDED PLEASE!!!! This math question confuses me. I thought the line didn't pass through any other point but I cant figure
Vanyuwa [196]

Answer:

B

Step-by-step explanation:

So wiggly, remember that slope is change in y/change in x, or in simpler terms, y/x. Thinking of this, y/x must simplyfy to -3. Or, you can think of it as -3/1.

So know that we have rewrote this as a slope of -3/1, lets use it. Where do we start? Well, we must start at point A, which is at 2 x and 7 y.

Now, going to the  RIGHT(+1x) and going DOWN(-3y) we will go from 2x and 7y to 3x and 4y.

Are we on a point yet? Nope, lets do this again.

Now going to RIGHT again(+1x) and going DOWN again(-3y) we will go from 13x and 4y to 4x and 1y.

Are we on a point yet? Still no, lets try this one more time.

Now going to RIGHT again(+1x) and going DOWN again(-3y) we will go from 4x and 1y to 5x and -2y.

Are we on a point? YUP. We cna see that point B is at 5x and -2y.

Hope you get it right ;)

4 0
3 years ago
Find 3 + (-9)
AURORKA [14]
9 is in parentheses therefore it's elevated above 3 that means you have to do operations on it first.
3 + (-9) = -6
The sum is negative.
4 0
3 years ago
Which professionals most directly use geometry in their work A) accountants B)astronomers C)judges D)pharmacist E) politicians
madam [21]
Astronomers deal with objects in space, so it's most likely they would use geometry to determine how far they are, how big they are, etc.

Have a nice day! :)
3 0
3 years ago
Read 2 more answers
Other questions:
  • Ellen record the weights rounded to the nearest pound of the pumpkins at the school pumpkin contest as shown below.
    11·2 answers
  • What is the percent decrease between 80 and 64
    6·2 answers
  • Find the measure of angle C of △ABC, if:<br> m∠A=60°+α, m∠B=60°−α.
    13·1 answer
  • WILL GIVE A BRAINLEST<br><br> Which piecewise relation defines a function?
    9·2 answers
  • Please I need help I don’t understand this!
    6·1 answer
  • Pls help urgently extra points and mark w
    7·2 answers
  • B) Show that the bus stop lies on the road <br> can some answer b please
    7·2 answers
  • Final question - whats the answer?
    8·1 answer
  • Can you help me. .....................
    13·2 answers
  • Hey can someone tell me the steps to solving a system of equations with graphing
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!