Which substance has a freezing point furthest from that of water, 0°C?
1 answer:
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Answer:
B
Step-by-step explanation:
Sarah's house is not shown in graph
The spinner is divided into four equal sections: 2, 4, 7, 9. This represents 4 possibilities
If the spinner is spun twice, the sample space is:
For product less than 30, the number of outcomes is shown below:
The number of outcomes that have a product less than 30 = 10
The sample space that shows possibilities of an odd number combination:
The number of outcomes that contains at least one odd number = 12
The number of outcomes that have a product less than 30 and contain at least one odd number is shown below. These outcomes are outcomes circled in both cases shown above,
The outcomes circled represents the number of outcomes that has a product less than 30 and contains at least one odd number
Answer: 6 (option B)
The general equation for a circle, 
, falls out of the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is always equal to the sum of the squares of its legs (you might have seen this fact written like 
, where <em>a </em>and <em>b</em> are the legs of a right triangle and <em>c </em>is its hypotenuse. When we fix <em /><em>c</em> in place and let <em>a </em>and <em>b </em>vary (in a sense, at least; their values are still dependent on <em>c</em>), the shape swept out by all of those possible triangles is a circle - a shape defined by having all of its points equidistant from some center.
How do we modify this equation to shift the circle and change its radius, then? Well, if we want to change the radius, we simply have to change the hypotenuse of the triangle that's sweeping out the circle in the first place. The default for a circle is 1, but we're looking for a radius of 6, so our equation, in line with Pythagorus's, would look like
, or 
.
Shifting the center of the circle is a bit of a longer story, but - at first counterintuitively - you can move a circle's center to the point (a,b) by altering the x and y portions of the equation to read:
How do we modify this equation to shift the circle and change its radius, then? Well, if we want to change the radius, we simply have to change the hypotenuse of the triangle that's sweeping out the circle in the first place. The default for a circle is 1, but we're looking for a radius of 6, so our equation, in line with Pythagorus's, would look like
Shifting the center of the circle is a bit of a longer story, but - at first counterintuitively - you can move a circle's center to the point (a,b) by altering the x and y portions of the equation to read: