<u>Part A
</u><u />To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case,

and

equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about
3 gallons.
<u>Part B
</u><u /><u />To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.
Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

Now, we can simply add our numerators.

We know that he needs

gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

Using that logic, we can see that the painter needs exactly
gallons of paint.
Begin
3x-4=14
3x=18
x=6
.5n=1.25
n=2.5
x+1=2x-2
x+3=2x
3=x
x+3=10
x=7
6x-13=-11
6x=2
x=1/3
p=4-p
2p=4
p=2
End
Answer:
The conclusion is invalid.
The required diagram is shown below:
Step-by-step explanation:
Consider the provided statement.
Great tennis players use Hexrackets. Therefore, if you use a Hexracket, you are a great tennis player.
From the above statement we can concluded that Great tennis players use Hexrackets. But it may be possible that some people who use a haxracket are not great tennis player.
Therefore, the conclusion is invalid.
The required diagram is shown below:
Answer:
14 miles.
Step-by-step explanation:
Let the distance traveled from home to destination = x miles.
Speed while going to friend's house = 35 miles per hour.
Speed while coming back = 40 miles per hour.
Total Time taken for the journey = 45 minutes = 0.75 hours.
Let the time taken while going to friend's house = y hours.
Therefore, the time taken while going to friend's house = (0.75 - y) hours.
To find x and y, model the speeds of both the journeys.
Speed while going to friend's house = Distance/Time.
35 = x/y.
x = 35y (Equation 1).
Speed while coming back = Distance/Time.
40 = x/(0.75 - y).
x = 40(0.75 - y) (Equation 2).
Since x = x, therefore:
35y = 30 - 40y.
75y = 30.
y = 30/75.
y = 0.4 hours.
Put y = 0.4 hours in Equation 1:
x = 35y.
x = 35(0.4).
x = 14.
Therefore, the distance between my friend's house and my house is 14 miles!!!
Sample space is (3FD , 3MD, 4MN, 6FN)
where F=female M= male N=Nurse D=doctor)
so P(doctor or female ) = (3+3+6) / 16 = 12/16 answer
Its C