What is 4.65 converted to a fraction? The answer should be given in simplest form
a. 4 12/20
b. 4 65/100
c. 4 6/5
d. 4/65
The answer is c. 4 6/5
Use long division to convert 2 7/16 to a decimal
a. 0.4375
b. 2.4375
c. 2.716
d. 2.2857
To convert 2 7/16 to a decimal using long division, follow these steps:
1. Rewrite the mixed number as an improper fraction:
2 7/16 = (2 * 16 + 7) / 16 = 39/16
2. Perform long division: Divide the numerator (39) by the denominator (16) and write the quotient with a decimal point in front.
.24375 (The quotient starts with 2)
16 | 39.00
- 32
----
70
- 64
----
60
- 48
----
120
- 112
----
80
- 80
----
0
3. The decimal representation of 2 7/16 is 2.4375.
Therefore, the correct answer is b. 2.4375.
Use long division to convert 6 7/15 to a decimal
a. 6.47
b. 0.46
c. 6.14285
d. 6.715
To convert 6 7/15 to a decimal using long division, follow these steps:
1. Rewrite the mixed number as an improper fraction:
6 7/15 = (6 * 15 + 7) / 15 = 97/15
2. Perform long division: Divide the numerator (97) by the denominator (15) and write the quotient with a decimal point in front.
.6.47 (The quotient starts with 6)
15 | 97.00
- 90
----
70
- 60
----
100
- 90
----
10
0
3. The decimal representation of 6 7/15 is 6.47.
Therefore, the correct answer is a. 6.47.
A pilot is flying an airplane due to strong winds the pilot decides to fly 4000 feet lower to avoid excessive turbulence it takes the pilot 3.5 minutes to make this adjustment interpret the quotient to describe the rate of change in the planes altitude give your answer to the nearest hundredth and remember the plane is descending
The quotient that beat represents the rate of change in the planes altitude is (Blank) feet/minute
To find the rate of change in the plane's altitude, we divide the change in altitude (4000 feet) by the time it takes to make the adjustment (3.5 minutes).
Rate of change in altitude = Change in altitude / Time = 4000 feet / 3.5 minutes
Calculating this division, we get:
Rate of change in altitude ≈ 1142.86 feet/minute
Rounding to the nearest hundredth, the rate of change in the plane's altitude is approximately 1142.86 feet/minute.
Problem 2: Simplify the expression
2(a -3) + 4b - 2(a -b -3) + 5
To simplify the expression, we apply the distributive property and combine like terms:
2(a - 3) + 4b - 2(a - b - 3) + 5
Multiplying 2 by each term inside the first set of parentheses:
2a - 6 + 4b - 2(a - b - 3) + 5
Now, distribute the -2 to the terms inside the second set of parentheses:
2a - 6 + 4b - 2a + 2b + 6 + 5
Combining like terms:
(2a - 2a) + (4b + 2b) + (-6 + 6 + 5)
The terms 2a and -2a cancel each other out, and the terms 4b and 2b can be combined:
0 + 6b + 5
Finally, combining the remaining terms:
6b + 5
Thus, the expression 2(a - 3) + 4b - 2(a - b - 3) + 5 simplifies to 6b + 5.
Find the equation of the line that passes through the points (-1 , -1) and (-1 , 2).
To find the equation of the line that passes through the points (-1, -1) and (-1, 2), we can use the formula for the equation of a vertical line.
Since both points have the same x-coordinate (-1), it means the line is vertical and parallel to the y-axis. In this case, the equation of the line will be in the form x = k, where k is the x-coordinate of the points.
In this case, since both points have an x-coordinate of -1, the equation of the line is:
x = -1
Thus, the equation of the line that passes through the points (-1, -1) and (-1, 2) is x = -1.
2(x + 5) = 18
:- 2 => 2(x + 5) :- 2 = 18 :- 2
x + 5 = 9
5 => x + 5 - 5 = 9 - 5
x = 4
Your steps for solving the equation are correct. By simplifying each side of the equation step by step, you arrived at the correct solution of x = 4.
Final Answer: x = 4
A fire engine water tank holds 75o gallons of water if the pump removes 250 gallons of water 5 minutes what is the change in the amount of water gallons in 1 minute?
a.-15
b.15
c.50
d.-50
To find the change in the amount of water in 1 minute, we need to divide the change in gallons of water (250 gallons) by the time it took (5 minutes).
Change in gallons per minute = Change in gallons / Time = 250 gallons / 5 minutes
Calculating this division, we get:
Change in gallons per minute = 50 gallons/minute
Therefore, the change in the amount of water in 1 minute is 50 gallons.
The correct answer is c. 50.