Answer:
Step-by-step explanation:
<u>As per question we have:</u>
- p > 0, q > 0
- 31p/8q ≤ 5 ⇒ 31p ≤ 40q
Since 31 and 40 have no common factors, the minimum values of p and q are 40 and 31 respectively.
<u>So the minimum value of p + q is:</u>
<span>The border width is x
The sides are now (80 - 2x) + 2x, and (60 - 2x) + 2x
The area along one side is
2x^2 + x(80 - 2x)
adding the other side doubles the area
so far,
4x^2 +2x(80 - 2x)
now add in the areas left along the other two sides
2x(60-2x)
(This is hard to follow without a picture. Try drawing it)
The interior area is 800.
The whole area is 4800, so the difference is the border.
4800 - 800 = 4000
4x^2 + 2x(80 - 2x) + 2x(60 - 2x) = 4000
4x^2 + 160x - 4x^2 + 120x - 4x^2 = 4000
-4x^2 + 280x = 4000
-x^2 + 70x - 1000 = 0
multiply both sides by -1
x^2 - 70x + 1000 = 0
(x - 50)(x - 20) = 0
x = 50, 20 are the solutions
The answer can't be 50 because the width on both sides would be
50 + 50 = 100, and that's greater than 80, the longest side.
That leaves x = 20 for the width of the strip.
check
4x^2 + 2x(80 - 2x) + 2x(60 - 2x) = 4000
4(20)^2 + 2*20(80 - 2*20) + 2*20(60 - 2*20) = 4000
4*400 + 40*40 + 40*20 = 4000
1600 +1600 + 800 = 4000
3200 + 800 = 4000
4000 = 4000</span>
Answer:
1. A: the size of its last meal
B: Giraffe's hunger
2. A: amount of time spent landscaping.
B: Total earnings
C: y=20x.
3. A: the number of staplers he buys.
B: input: number of staplers bought. output: total cost.
C: y=16.99x
D: You multiply 16.99 by 15
4. A: $125
B: input: the number of visits output: total cost
Answer:
0.0214
Step-by-step explanation:
We can get these answer by finding the z-scores at first
Mathematically;
z-score = x-mean/sd
For 900;
z-score = 900-750/75 = 150/75 = 2
For 975
z-score = (975-750)/75 = 3
So the probability we want to calculate is;
P(2<x<3)
This can be calculated using the standard normal distribution table
From the standard score table;
P(2<x<3) = 0.0214
Answer:
500 minutes
Step-by-step explanation:
100% = x
15% = 75
We multiply 75 by 100 and divide the answer by 15
7500 / 15 = 500 minutes