There are two steps to this problem. The first step is to make an equation for the cost of each company. The cost of each one involves 2 variables. However, we can ignore the number of days since the question asks for per day.
CostA = 90 + .40(miles)
CostB = 30 + .70(miles)
We want to know when A is a better deal or when A costs less. That is when CostA < CostB. We can then substitute the right sides of our equations into the inequality. This will give:
90 + .40(miles) < 30 + .70(miles) This is where we will now begin to solve for the number of miles.
-30 -30 Subtract 30 from both sides.
60 + .4(miles) < .7(miles) Simplify
-.4(miles) -.4(miles) Subtract .4(miles) from both sides
60 < .3(miles) Simplify
/.3 /.3 Divide both sides by .3
200 < miles Simplify
So for A to cost less the number of miles must be greater than 200.
What do we know about those two lines?
They are perpendicular, meaning they have the same slope.
We know the slope of both is not zero (neither is vertical).
Therefore either
1) Both slopes are positive and therefore the product is positive
2) Both slopes are negative and therefore the product is positive (minus by a minus is a plus)
For the y intercepts, we know that the line P passes through the origin.
Therefore its Y intercept is zero.
[draw it if this is not obvious and ask where does it cross the y axis]
Therefore the Y intercept of line K and line P is zero.
[anything multiplied by a zero is a zero]
So we know that the product of slopes is positive, and we know that the product of Y intercepts is zero.
So the product of slopes must be greater.
Answer A
Answer:
a) True
b) True
c) False
d) True
Step-by-step explanation:
A discrete variable is the one where the values taken by it are possible to count (usually the values are natural numbers)
On the other side, a continuous variable is the one that has an uncountable number of values. (usually the values are real numbers)
Considering these definitions we get:
a)The batting average of Joe’s favorite player is a continuous variable: True, this average can take any number among the real numbers.
b) The number of hot dogs that Joe bought is a discrete variable: True, Joe can only buy 1, 2, 3, 4... hot dogs, this set is countable and therefore is a discrete variable.
c) The number of strikeouts in the game is a continuous variable: False, the strikeouts are natural numbers (1, 2, 3, 4...) and therefore are countable and they are a discrete variable.
d) The Quakes standings in the league is a discrete variable: True. The standing of a team in a league is a discrete variable since it can be 1st place, 2nd place... and therefore it's countable.
Hi there!
We are given:
cos(7x)cos(4x) = -1 - sin(7x)sin(4x)
Begin by moving all terms with variables to one side:
cos(7x)cos(4x) + sin(7x)sin(4x) = -1
The corresponding trig identity is cos(A - B). Thus:
cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1
cos(3x) = -1
cos = -1 at π, so:
3x = π
x = π/3
We can also find another solution. Let 3π = -1:
3x = 3π
x = π
Thus, solutions on [0, 2π) are π/3 and π.
- The best method to test Zoe's claim is an observational study, as with this method it is possible to observe if the claim presents some truth to it. Observational studies are often used in testing claims like Zoe's as they allowed to have a great access to the variable that are behind a claim of that type, and so they are also more accessible.
- The set up I would use is an observational study of a great number of people, over a long period of time, that have to have<span> kale for breakfast every day, with a measurement of their cholesterol over the time. the great number and the long period of study assured that the variable subject of study is statistically represented in an optimal way. </span>
