Answer:
C
Step-by-step explanation:
Since the graph hits 0 at x = 0, your y intercept is 0.
The graph is decreasing which means you have a negative slope.
They gave you a coordinate so use it to find the slope.

That's your slope.
C is the correct answer.
Answer:
P(2.50 < Xbar < 2.66) = 0.046
Step-by-step explanation:
We are given that Population Mean,
= 2.58 and Standard deviation,
= 0.75
Also, a random sample (n) of 110 households is taken.
Let Xbar = sample mean household size
The z score probability distribution for sample mean is give by;
Z =
~ N(0,1)
So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)
P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar
2.50)
P(Xbar < 2.66) = P(
<
) = P(Z < -1.68) = 1 - P(Z 1.68)
= 1 - 0.95352 = 0.04648
P(Xbar
2.50) = P(
) = P(Z
-3.92) = 1 - P(Z < 3.92)
= 1 - 0.99996 = 0.00004
Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046
So the rule with multiplying exponents of the same base is
. Apply this rule here:

Next, the rule with converting negative exponents into positive ones is
. Apply this rule here:

<u>Your final answer is 1/49.</u>
<h2>------------------------------------------------</h2>
So an additional rule when it comes to exponents is ![x^{\frac{m}{n}}=\sqrt[n]{x^m}](https://tex.z-dn.net/?f=%20x%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Bx%5Em%7D%20)
In this case, your fractional exponent, x^9/7, would be converted to
. However, I had just realized you can further expand this.
Remember the rule I had mentioned earlier about multiplying exponents of the same base? Well, you can apply it here:
![\sqrt[7]{x^9}=\sqrt[7]{x^7*x^2}=x\sqrt[7]{x^2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7Bx%5E9%7D%3D%5Csqrt%5B7%5D%7Bx%5E7%2Ax%5E2%7D%3Dx%5Csqrt%5B7%5D%7Bx%5E2%7D%20)
Your final answer would be ![x\sqrt[7]{x^2}](https://tex.z-dn.net/?f=%20x%5Csqrt%5B7%5D%7Bx%5E2%7D%20)
Answer:
3:36PM
Step-by-step explanation:
Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.
Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at
capacity, we can use the equation:

This shows
of his tank's capacity (
) is equal to
gallons. This means he will stop for gas when
gallons are remaining.
Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

This is a simple proportion, and now we know he uses
gallons of gas per hour.
Now we can how many hours of gas Leon has left.
He has
gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

The
is because Leon doesn't stop when his tank is empty, he stops
gallons earlier. We are dividing by
because that is how much gas he uses per hour, meaning the result of this division (
) is how many hours he has left.
Now we can solve for what time Leon will stop to get gas.
12PM +
hours of driving + the remaining
hours = 3:36PM
(
hours is equal to 1 hour and 36 minutes)
Therefore, Leon will stop for gas at 3:36PM