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3 years ago

Arlo rolls a number cube three times. What is the chance the number cube

Mathematics

1 answer:

OlgaM077 [116]3 years ago

5 0

Answer:

Probability = 1/8.

Step-by-step explanation:

A number cube has six sides. Each side has a number from 1 to 6. This means that there are 3 even numbers (2, 4, and 6) and 3 odd numbers (1, 3, and 5). Therefore:

P(number cube lands on an even number after roll) = Number of even numbers/Number of total numbers. = 3/6 = 1/2.

Since the cube has to be rolled three times, the probability will be multiplied 3 times (assuming that each roll in independent of each other). Therefore:

P(number cube lands on an even number 3 times after roll) = 1/2 * 1/2 * 1/2 = 1/8.

Therefore, the answer is 1/8!!!

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Suppose you are climbing a hill whose shape is given by the equation z = 1400 − 0.005x2 − 0.01y2, where x, y, and z are measured

Anarel [89]

Answer: You start to ascend

Explanation:

Since you are walking due south and the positive y-axis points north, the y-coordinate decreases.

Let

$y'$ = y-coordinate after walking due south
$z'$ = z-coordinate (or the height) after walking due south

So, the point where you stand after walking due south has a coordinate of $(100, y', z')$ . Moreover,

$z' = 1,400 - 0.05(100)^2 - 0.01(y')^2
\\ \boxed{z' = 1350 - 0.01(y')^2}$

Since the y-coordinate decreases after walking due south and $z' = 1350 - 0.01(y')^2$ ,

$y' \leq 120\\ \Rightarrow (y')^2 \leq 120^2 = 14,400\\ \Rightarrow -0.01(y')^2 \geq -0.01(14,400) = -144\\ \Rightarrow z' = 1,350 - 0.01(y')^2 \geq 1,350 - 0.01(14,400) = 1,206\\ \Rightarrow \boxed{z' \geq 1,206}$

So, the height after walking due south exceeds 1,206 meters, which is the previous height before walking due south. Therefore, if you walk due south from point with coordinates (100, 120, 1206), you are ascending.

5 0

3 years ago

Rename 5/6 and 5/8 using the least common denominator.

Marina CMI [18]

Answer:

5/6 = 20/24

5/8 = 15/24

Step-by-step explanation:

These are the answers because:

1) First, the least common denominator is 24 because 8 x 3 is 24 and 6 x 4 is 24

2) Next, multiply the numerators with the same number you multiplied with the denominator

5 x 3 = 15

5 x 4 = 20

3) Therefore, the answers are:

5/6 = 20/24

5/8 = 15/24

Hope this helps!

6 0

3 years ago

There are 128 flavors at an ice cream shop. If a company orders 75 scoops of each flavor, how many scoops of ice cream would the

Y_Kistochka [10]

Hope this answer helps you! :)

5 0

3 years ago

Say you're playing three-card poker; that is, you're dealt three cards in a row at random from a standard deck of 52 cards. What

Brums [2.3K]

Answer:

Step-by-step explanation:

Given

There are 52 cards in total

there are total of 13 pairs of same cards with each pair containing 4 cards

Probability of getting a pair or three of kind card=1-Probability of all three cards being different

Probability of selecting all three different cards can be find out by selecting a card from first 13 pairs and remaining 2 cards from remaining 12 pairs i.e.

$=\frac{52\times 48\times 44}{52\times 51\times 50}$