Answer:
f(6) = 1
Step-by-step explanation:
Function:
f(x) = -2/3x + 5
f(6) = -2/3(6) + 5
f(6) = -4 + 5
f(6) = 1
Answer:
The area of the rectangle is 1222 units²
Step-by-step explanation:
The formula of the perimeter of a rectangle is P = 2(L + W), where L is its length and W is its width
The formula of the area of a rectangle is A = L × W
∵ The length of a rectangle is 5 less than twice the width
- Assume that the width of the rectangle is x units and multiply
x by 2 and subtract 5 from the product to find its length
∴ W = x
∴ L = 2x - 5
- Use the formula of the perimeter above to find its perimeter
∵ P = 2(2x - 5 + x)
∴ P = 2(3x - 5)
- Multiply the bracket by 2
∴ P = 6x - 10
∵ The perimeter of the rectangle is 146 units
∴ P = 146
- Equate the two expression of P
∴ 6x - 10 = 146
- Add 10 to both sides
∴ 6x = 156
- Divide both sides by 6
∴ x = 26
Substitute the value of x in W and L expressions
∴ W = 26 units
∴ L = 2(26) - 5 = 52 - 5
∴ L = 47 units
Now use the formula of the area to find the area of the rectangle
∵ A = 47 × 26
∴ A = 1222 units²
∴ The area of the rectangle is 1222 units²
Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.
Step-by-step explanation:
Let's dissect the question. The copy machine makes 36 copies per minute.
36 per min.
To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.
It makes 171 copies in 4 minutes and 45 seconds.
Answer:
Question 1
probability of a red marble in the first draw = 1/10
probability of a orange marble in the second draw = 4/9
probability of getting red in first and orange in second (without replacement) = 1/10 * 4/9 = 2/45,
Question 2
6 outcomes
1/6
