Here, we are required to find the area of the paper board given after the semicircle is cut out of it
Area of the paper board thatremains is 423 in²
Length = 29 in
Width = 20 in
Area of a rectangle = length × width
= 29 in × 20 in
= 580 in²
Area of a semi circle = πr²/2
π = 3.14
r = diameter / 2 = 20 in / 2 = 10 in
Area of a semi circle = πr²/2
= 3.14 × (10 in)² / 2
= 3.14 × 100 in² / 2
= 314 in²/2
= 157 in²
The semicircle is cut out of the rectangle
Find the area of the paper board that remains after the semicircle is cut out of it by subtracting the area of a semi circle from the area of a rectangle
Area of the paper board that remains = Area of a rectangle - Area of a semi circle
= 580 in² - 157 in²
= 423 in²
brainly.com/question/16994941
<h3>
The probability of picking a red face card from the deck is 
</h3><h3>
The probability of NOT picking a red face card from the deck is 
</h3>
Step-by-step explanation:
The total number of cards in the deck = 52
The total number of red( Diamond + Hearts) face cards in the given deck
= 2 Red Queens + 2 Red jacks + 2 Red kings = 6 cards
Let E : Event of picking a red face card from the deck
Now , P( any event) = 
So, here P(Picking a red face card) = 
Hence, the probability of picking a red face card from the deck is 
Now, as we know P (any event NOT A) = 1 - P(any event A)
So, P(NOT Picking a red face card) = 1 - P(Picking a red face card)
Hence, the probability of NOT picking a red face card from the deck is 
Answer:
we have that
y < −3x + 3
y < x + 2
using a graph tool
see the attached figure
the answer is
the answer isThe point (1, −5) lie in the solution set