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snow_lady [41]
2 years ago
7

The relationship between antioxidant food consumption per day in cups and the BMI of an individual is modeled by the following l

ine of best fit: y= -1.2x+26. Interpret the slope and intercept of the trend line within the context of the data.
Mathematics
1 answer:
Katena32 [7]2 years ago
8 0
This is in gradient intercept form (or slope intercept form)
y = mx + b
in this case y = -1.2x + 26
so m (the slope) = -1.2
and the y intercept = 26
I'm not sure what intercept they're asking for.
if you wanted to find the x intercept, just substitute.
y = 0 and find x.
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Which of shakina's statements regarding acceleration and velocity is false? "when the acceleration is negative, the velocity can
Mekhanik [1.2K]
Let's start by imagining a rock being thrown to the air.
Let's say that going up is the positive direction and so, going down is the negative.
The acceleration is pointing down (because of gravity) so it's always negative. While the rock is going up, it's velocity/speed is positive, but the acceleration is negative.
While the rock is going down, both acceleration and speed are negative.
This shows that the first statemente is true, but the second is false.
You can also think that if you define going DOWN as the POSITIVE direction, you can have both positive acceleration and speed, or positive acceleration and negative speed.
7 0
3 years ago
The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to
Morgarella [4.7K]

Answer:

  • 9 mph

Step-by-step explanation:

Let he speed of the boat on the lake is x.

<u>Considering the speed of the current it will take him:</u>

  • 22.5/(x + 6) + 22.5/(x - 6) = 9
  • 2.5 / (x  + 6) + 2.5 / (x - 6) = 1
  • 2.5(x - 6 + x + 6) = (x + 6)(x - 6)
  • 2.5*2x = x² - 36
  • x² - 5x - 36 = 0
  • x = (5 ± √(5² + 4*36))/2 = (5 ± 13) / 2
  • x = (5 + 13)/2 = 9 mph (negative root is discarded as the speed should be positive)
7 0
2 years ago
To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married
Xelga [282]

Answer:

  • a. See the table below
  • b. See the table below
  • c. 0.548
  • d. 0.576
  • e. 0.534
  • f) i) 0.201, ii) 0.208

Explanation:

First, order the information provided:

Table: "Who is better at getting deals?"

                                       Who Is Better?

Respondent      I Am        My Spouse     We Are Equal

Husband           278             127                     102

Wife                   290            111                       102

<u>a. Develop a joint probability table and use it to answer the following questions. </u>

The<em> joint probability table</em> shows the same information but as proportions. Hence, you must divide each number of the table by the total number of people in the set of responses.

1. Number of responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Calculate each proportion:

  • 278/1,010 = 0.275
  • 127/1,010 = 0.126
  • 102/1,010 = 0.101
  • 290/1,010 = 0.287
  • 111/1,010 = 0.110
  • 102/1,010 = 0.101

3. Construct the table with those numbers:

<em>Joint probability table</em>:

Respondent      I Am        My Spouse     We Are Equal

Husband           0.275           0.126                 0.101

Wife                   0.287           0.110                  0.101

Look what that table means: it tells that the joint probability of being a husband and responding "I am" is 0.275. And so for every cell: every cell shows the joint probability of a particular gender with a particular response.

Hence, that is why that is the joint probability table.

<u>b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.</u>

The marginal probabilities are calculated for each for each row and each column of the table. They are shown at the margins, that is why they are called marginal probabilities.

For the colum "I am" it is: 0.275 + 0.287 = 0.562

Do the same for the other two colums.

For the row "Husband" it is 0.275 + 0.126 + 0.101 = 0.502. Do the same for the row "Wife".

Table<em> Marginal probabilities</em>:

Respondent      I Am        My Spouse     We Are Equal     Total

Husband           0.275           0.126                 0.101             0.502

Wife                   0.287           0.110                  0.101             0.498

Total                 0.562           0.236                0.202             1.000

Note that when you add the marginal probabilities of the each total, either for the colums or for the rows, you get 1. Which is always true for the marginal probabilities.

<u>c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? </u>

For this you use conditional probability.

You want to determine the probability of the response be " I am" given that the respondent is a "Husband".

Using conditional probability:

  • P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

  • P ("I am" ∩ "Husband) = 0.275 (from the intersection of the column "I am" and the row "Husband)

  • P("Husband") = 0.502 (from the total of the row "Husband")

  • P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

<u>d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?</u>

You want to determine the probability of the response being "I am" given that the respondent is a "Wife", for which you use again the formula for conditional probability:

  • P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

  • P ("I am" / "Wife") = 0.287 / 0.498

  • P ("I am" / "Wife") = 0.576

<u>e. Given a response "My spouse," is better at getting deals, what is the probability that the response came from a husband?</u>

You want to determine: P ("Husband" / "My spouse")

Using the formula of conditional probability:

  • P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

  • P("Husband" / "My spouse") = 0.126/0.236

  • P("Husband" / "My spouse") = 0.534

<u>f. Given a response "We are equal" what is the probability that the response came from a husband? What is the probability that the response came from a wife?</u>

<u>What is the probability that the response came from a husband?</u>

  • P("Husband" / "We are equal") = P("Husband" ∩ "We are equal" / P ("We are equal")

  • P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

<u>What is the probability that the response came from a wife:</u>

  • P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

  • P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208
6 0
3 years ago
there are 16 bactiria in a beaker and four hours later there are 228 bacteria in the beaker. what is the rate of change per hour
Dominik [7]

Write and solve the appropriate exponential equation:

228 = 16(r)^4, where r is the change per hour in the number of bacteria:

228

------ = r^4     =   14.25.  

 16

Taking the fourth root of both sides, we get:  r = 1.94 (answer)

8 0
3 years ago
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What is the sum of 2 numbers is 30 and their difference is 6 answer?
gayaneshka [121]
The numbers are 18 and 12
7 0
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