Use the GCF and the distributive property to find the expression that isequivalent to 36 - 48
A 6(6+8)
B. 12(3+4)
C. 2(18-24)
D. 419-12

Answer:

the original volume is lesser than the new volume by 242.47 in³

Step-by-step explanation:

Volume of a cone is;

V = ⅓πr²h

Where;

r is radius

h is height

For the original chamber;

r = 5.7/2 = 2.85 inches

h = 12 inches

Volume of this original chamber is;

V_orig = ⅓ × π × 2.85² × 12

V_orig = 102.02 in³

In the new design, the chamber is scaled by a factor of 1.5.

Thus;

r_new = 2.85 × 1.5 = 4.275 inches

h_new = 12 × 1.5 = 18 inches

V_new = ⅓ × π × 4.275² × 18

V_new = 344.49 inch³

V_new - V_orig = 344.49 - 102.02 =

Thus, the original volume is lesser than the new volume by 242.47 in³

Answer: 4. 9 + 7n - 3

3. 62

Step-by-step explanation:

Given statement: nine more than the product of seven and a number decreased by three

Let n be the number.

Then, required expression:

Correct option is 4.

When n= 8 ,  

The value of expression =

Hence, value of the expression when n = 8 is 62.

Correct option is 3.

Answer:

 [ 26 / 425 ] ≈ 0.0612

Step-by-step explanation:

Solution:-

- First we will describe the standard deck of 52 cards in terms of black, red and face cards found in a standard deck

- Following is a table of distribution of colored and face card found in a standard deck:

                 Type                   Number of cards

                 1 - 10                                40

                 Black                               26

                 Red                                 26

                 Face                                12

- The numerical cards from digit ( 1 to 10 ) are found in all 4 suits ( Clubs, Diamonds, Spades, and Hearts ). Hence, 10 x 4 = 40

- The entire deck is split in two colors ( Red and Black ) equally. So, the number of Black and Red cards are = 52 / 2 = 26 cards.

- The face cards are of three types ( King, Queen and Jack ). These three face cards are found in each of the 4 suits. Hence, Total number of face cards are = 4 * 3 = 12

- We will now consider the probabilities asscociated with each type. We will define 3 events and write down their proability as expressed:

Event ( A ): First draw is a red card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 red card in a standard deck of 52 cards. Hence,

            p ( A ) = [ Number of red cards ] / [ Total cards in a deck ]

            p ( A ) = [ 26 ] / [ 52 ]

            p ( A ) = 1 / 2

- After we make the first draw of a red card. Our deck distribution is changed to Number of Red cards remaining = 25 and total deck now has 51 cards remaining.

- We will define the next event as:

Event ( B ): The second draw is a face card.

- The probability of this event can be determined with the help of the table given above. There are a total of 12 face cards in a standard deck of 52 cards which is now down to 51 cards. Hence,

            p ( B ) = [ Number of face cards ] / [ Total cards in a deck ]

            p ( B ) = [ 12 ] / [ 51 ]

            p ( B ) = 4 / 17

- After we make the first draw of a face card. Our deck distribution is changed to Number of Face cards remaining = 11 and total deck now has 50 cards remaining.

- We will define the next event as:

Event ( C ): The third draw is a black card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 black cards in the deck. The total number of cards are down to 50 cards only. Therefore,

            p ( C ) = [ Number of black cards ] / [ Total cards in a deck ]

            p ( C ) = [ 26 ] / [ 50 ]

            p ( C ) = 13 / 25

- The entire drawing process consists of 3 events which are dependent on each draw. However, for the overall event to occur i.e drawing a red card , then a face card, and then a black card. We will multiply all three outcomes as follows:

          p ( T ) = p ( A ) * p ( B ) * p ( C )

          p ( T ) = [ 1 / 2 ] * [ 4 / 17 ] * [ 13 / 25 ]

          p ( T ) =  [ 26 / 425 ] ≈ 0.0612

Final answer:

The overall probability of first drawing a red card, then a face card, and then a black card from a standard deck of cards is 0.0124.

Explanation:

This question is related to the concept of probability in Mathematics. A standard deck of cards consists of 52 cards - 26 red (diamonds and hearts) and 26 black (clubs and spades). There are 12 face cards (King, Queen, and Jack of each suit).

For the first draw, the probability of picking a red card is 26/52, which simplifies to 1/2.

After picking a red card, we are left with 51 cards. So, for the second draw, the probability of picking a face card is 12/51.

Then, having picked a red and face card, we are left with 50 cards. For the third draw, the probability of picking a black card is 26/50 which simplifies to 13/25.

We multiply these probabilities together to get the overall probability, therefore (1/2) * (12/51) * (13/25) = 0.012418. Rounding this to four decimal places, we get 0.0124.

Learn more about Probability here:

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The distance between the given coordinate points is units.

The given coordinate points are (-8, -2) and (6, -1).

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On plane the distance between two points and is Distance .

Substitute and in distance formula, we get

Distance

Distance

Distance

Distance units

Therefore, the distance between the given coordinate points is units.

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Answer:

-8,-2= 6

6,-1=7

Step-by-step explanation:

get a number line and use that to it and look up how to use a number line with negative numbers it’s not hard once you see how it’s done