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Alinara [238K]
3 years ago
8

Product preference depends in part on the age, income, and gender of the consumer. A market researcher selects a large sample of

potential car buyers. For each consumer, she records gender, age, household income, and automobile preference. Which of these variables are categorical and which are quantitative?
gender 1---Select---categorical quantitative
age 2---Select---quantitative categorical
household income 3---Select---quantitative categorical
automobile preference4 Select---quantitative categorical
Mathematics
1 answer:
Serhud [2]3 years ago
5 0

Answer: Gender = categorical ; Age = quantitative ; Household income = quantitative ; Automobile preference = Categorical

Step-by-step explanation:

Distinction between quantitative and categorical variables are based made on whether the variables are represented with a numeric or non-numeric value. Categorical variables usually takes in strings such as in the scenario above, the appropriate input for gender will be either 'Male' or 'Female' and Automobile preference will be a string of the type of automobile which the user prefers. On the other hand, quantitative variables will accept numeric values such as age and household income.

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65:100 because there are 65 girls and then 65 girls + 35 boys = 100 total students
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2 years ago
M∠A = 75 + 5x
Firlakuza [10]

Answer:

See below

Step-by-step explanation:

For a parallelogram m < A = m < C so:-

75 + 5x = 87 + 3x

2x = 12

x = 6  

and m< A = 75 + 30 = 105

and m < C = 87 + 18 = 105

Now if the other 2 angles are  = 75 degrees( that is the same side angles add up to 180 degrees) we have proved that it is a parallelogram.

m < B = m < D

111 - 6x = 39 + 6x

-12x = -72

x = 6

m < B = 111 - 36 = 75 and m < D = 39 + 36 = 75

So this has been proved.

6 0
3 years ago
Find the area of the figure below
tatuchka [14]

Step-by-step explanation:

(3×6) + (2×6)

= 18 + 12

= 30 in²

4 0
2 years ago
Among all right circular cones with a slant height of 24​, what are the dimensions​ (radius and​ height) that maximize the volum
aleksklad [387]

Answer:

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2

Once this is defined, we proceed to define the volume of a cone,

v=\frac{1}{3}\pi r^2 h

Substituting,

v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)

\frac{dv}{dh} = 0 then \rightarrow \frac{1}{3}\pi(576-3h^2)=0

h_1=-8\sqrt{3}\\h_2=8\sqrt{3}

<em>We select the positiv value.</em>

We have then,

r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}

We can now calculate the maximum volume,

V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99

4 0
3 years ago
Find an equation of the circle that has center (-2, 6) and passes through (-6, 1).
Darya [45]

Answer:

<u><em>(x+2)^2 + (y-6)^2 = 41</em></u>

Step-by-step explanation:

The equation for a circle is (x-h)^2+(y-k)^2=r^2

So first, it is known that the circle's center is at (-2,6), Therefore, this can be filled in:

(x+2)^2+(y-6)^2=r^2

Next, we need to find the radius, and one of the points is already known, being (-6, 1)

With this, find the distance between these two points by doing the Pythagorean Theorem, a^2+b^2=c^2. The a^2 would be the x value changed and the b^2 would be the y value changed between the two numbers. Note that this is interchangeable.

To find a:

-2 to -6 = change of 4

To find b:

6 to 1 = change of 5

Next, write out the equation for this:

4^2+5^2=c^2

16+25=c^2

41=c^2

c = √41

The radius would be √41, so the equation can now be completed. Since c will be brought to the second power, this will cancel out the square root.

(x+2)^2 + (y-6)^2 = 41

Hope that helps.

8 0
2 years ago
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