The "explanation" for the problem has a typo in it. There are 11 possible ice cream/yogurt flavors to choose from, regardless of whether any are low-fat, so the total number of ways of choosing any 2 from the selection is
In particular we want to count the number of ways of picking 1 ice cream and 1 yogurt flavor from the low-fat variety. There are 6 total choices that are not low-fat of which we choose 0, 3 choices of low-fat ice cream of which we choose 1, and 2 choices of low-fat yogurt of which we also choose 1. In terms of the binomial coefficient, this is
So the probability of getting such a combination is
.
Answer:
15 cubes
Step-by-step explanation:
If volume of the prism = 15
then volume of one cube = 1 × 1 × 1
Volume(1 cube) = 1
Then divide the volume of one cube into the volume of the prism,
15 ÷ 1 = 15 cubes
Answer:
The scale used by Sarah is 1 to 43.2 inches ( drawing to actual)
Step-by-step explanation:
Here, we want to know the scale used for the drawing of the Dinosaur by sarah.
The actual height of the Dinosaur is 9 feet, but in her drawing she represented the height by 2.5 inches( 2 1/2 is same as 2.5 inches)
Mathematically, we know that 1 foot is 12 inches;
So the actual height of the Dinosaur is 9 * 12 = 108 inches
So practically, what she has done is to represent a height of 108 inches by 2.5 inches
So the scale factor used will be;
108/2.5 = 43.2
The scale used is 1 to 43.2 or simply 1:43.2 to represent the drawing to the actual
Answer:
Below in bold.
Step-by-step explanation:
The surface area of the box
= x^2 + 4hx where x = a side of the square base and h is the height.
So x^2 + 4hx = 8
The volume of the box
V = x^2h
From the first equation we solve for h
4hx = 8 - x^2
h = (8 - x^2) / 4x
Now we substitute for h in the formula for the volume:
V = x^2 * (8 - x^2) / 4x
V = 8x^2 - x^4 / 4x
V = 2x - 0.25x^3
Finding the derivative:
V' = 2 - 0.75x^2 = 0 for max/mimn values
x^2 = 2/ 0.75 = 2.667
x = 1.633.
So the length and width of the base is 1.633 m and the height
= ( 8 - 2.667) / (4*1.633)
= 0.816 m
The maximum volume = 0.816 * 2.667 = 2.177 m^2.
The answers are correct to the nearest thousandth.
