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Anton [14]
3 years ago
6

The graph shows the temperature of ice cream in an ice chest during an overnight trip. What is the domain of this function?

Mathematics
2 answers:
svet-max [94.6K]3 years ago
6 0
Domain is the set of x-values on a graph.
In the given graph,the values starts from zero and ends at 30.
Therefore,
<span>The domain is all real numbers 0 through 30.</span>
mariarad [96]3 years ago
4 0

Let

x-------> the number of hours

y------> the temperature in degrees Fahrenheit

we know that

For x=0\ hours

y=-10\°\ F

For x=30\ hours

y=30\°\ F

The domain of the function is the interval----------> [0,30]

0\ hours \leq x\leq 30\ hours

The range of the function is the interval----------> [-10,30]

-10\°\ F \leq y\leq 30\°\ F

therefore

<u>the answer is</u>

The domain is all real numbers 0 through 30

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The manager of the BiLo Supermarket in Mt. Pleasant, Rhode Island, gathered the following information on the number of times a c
pishuonlain [190]

Answer: kindly check explanation

Step-by-step explanation:

Given the data :

5 3 3 1 4 4 5 6 4 2 6 6 6 7 1 1 14 1 2 4 4 4 5 6 3 5 3 4 5 6 8 4 7 6 5 9 11 3 12 4 7 6 5 15 1 1 10 8 9 2 12

Frequency and relative frequency table can be found in the attachment below.

b. Where do the data tend to cluster?

3 up to 6

7 0
3 years ago
Can someone help me do part two please? It’s very important send a picture or something. I don’t even care if you tell me the st
Nataly_w [17]
<h3>Explanation:</h3>

1. "Create your own circle on a complex plane."

The equation of a circle in the complex plane can be written a number of ways. For center c (a complex number) and radius r (a positive real number), one formula is ...

  |z-c| = r

If we let c = 2+i and r = 5, the equation becomes ...

  |z -(2+i)| = 5

For z = x + yi and |z| = √(x² +y²), this equation is equivalent to the Cartesian coordinate equation ...

  (x -2)² +(y -1)² = 5²

__

2. "Choose two end points of a diameter to prove the diameter and radius of the circle."

We don't know what "prove the diameter and radius" means. We can show that the chosen end points z₁ and z₂ are 10 units apart, and their midpoint is the center of the circle c.

For the end points of a diameter, we choose ...

  • z₁ = 5 +5i
  • z₂ = -1 -3i

The distance between these is ...

  |z₂ -z₁| = |(-1-5) +(-3-5)i| = |-6 -8i|

  = √((-6)² +(-8)²) = √100

  |z₂ -z₁| = 10 . . . . . . the diameter of a circle of radius 5

The midpoint of these two point should be the center of the circle.

  (z₁ +z₂)/2 = ((5 -1) +(5 -3)i)/2 = (4 +2i)/2 = 2 +i

  (z₁ +z₂)/2 = c . . . . . the center of the circle is the midpoint of the diameter

__₁₂₃₄

3. "Show how to determine the center of the circle."

As with any circle, the center is the <em>midpoint of any diameter</em> (demonstrated in question 2). It is also the point of intersection of the perpendicular bisectors of any chords, and it is equidistant from any points on the circle.

Any of these relations can be used to find the circle center, depending on the information you start with.

As an example. we can choose another point we know to be on the circle:

  z₄ = 6-2i

Using this point and the z₁ and z₂ above, we can write three equations in the "unknown" circle center (a +bi):

  • |z₁ - (a+bi)| = r
  • |z₂ - (a+bi)| = r
  • |z₄ - (a+bi)| = r

Using the formula for the square of the magnitude of a complex number, this becomes ...

  (5-a)² +(5-b)² = r² = 25 -10a +a² +25 -10b +b²

  (-1-a)² +(-3-b)² = r² = 1 +2a +a² +9 +6b +b²

  (6-a)² +(-2-b)² = r² = 36 -12a +a² +4 +4b +b²

Subtracting the first two equations from the third gives two linear equations in a and b:

  11 -2a -21 +14b = 0

  35 -14a -5 -2b = 0

Rearranging these to standard form, we get

  a -7b = -5

  7a +b = 15

Solving these by your favorite method gives ...

  a +bi = 2 +i = c . . . . the center of the circle

__

4. "Choose two points, one on the circle and the other not on the circle. Show, mathematically, how to determine whether or not the point is on the circle."

The points we choose are ...

  • z₃ = 3 -2i
  • z₄ = 6 -2i

We can show whether or not these are on the circle by seeing if they satisfy the equation of the circle.

  |z -c| = 5

For z₃: |(3 -2i) -(2 +i)| = √((3-2)² +(-2-i)²) = √(1+9) = √10 ≠ 5 . . . NOT on circle

For z₄: |(6 -2i) -(2 +i)| = √((6 -2)² +(2 -i)²) = √(16 +9) = √25 = 5 . . . IS on circle

4 0
3 years ago
Plzzzzzzzzzzzz answerrrrrrrrrrr thisssssssssssssssssss 
Fofino [41]
2(x+a)^2+3(z+a)+1
2(x²+a²)+3z+3a+1
2x²+2a²+3z+3a+1
Since there aren't any like terms, you can't simplify it any more.
8 0
3 years ago
Your friend Albert has invented a game involving two ten-sided dice. One of the dice has threes, fours, and fives on its faces,
guapka [62]

Answer:

d. 11.6

Step-by-step explanation:

The results of the first die and the second one are independent to each other. The expected value of Z is obtained, therefore, by summing the expected values of both X and Y, because Z = X+Y and X and Y are independent. As a result \mu_z = \mu_x + \mu_y = 3.6+8.0 = 11.6 .

4 0
3 years ago
What is 0.043 written as a percent?
meriva
To find a percent you multiply the decimal number by 100. OR to be easier just move the decimal number 2 places to the right.

4.3%
4 0
3 years ago
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