Multiply. Write your answer in simplest form.

7 x 3/4

Answers

Answer 1
Answer: If you would like to calculate 7 * 3/4, you can do this using the following steps:

7 * 3/4 = 21/4 = 5 1/4

The correct result would be 21/4.
Answer 2
Answer:

The equivalent value of the expression is A = 21/4

Given data:

The first number is represented as a = 7

The second fraction is represented as b = 3/4

So, the equation is A = ab

And, A = 7 x 3/4

So, 7 multiplied by 3/4 equals 21/4.

However, to express the answer in its simplest form, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor.

The greatest common factor of 21 and 4 is 1, so we divide both numerator and denominator by 1.

Hence, the simplest form of the equation is A = 21/4

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N a water treatment plant, water passes through a cone-shaped filter with a height of 4 m and a diameter of 9 m. The water flows from the filter into a cylinder below it. One full cone-shaped filter fills one-fifth of the cylinder.What are the dimensions of the cylinder? Use 3.14 to approximate pi.
A. h = 3 m; r = 3 m
B.h = 4.23 m; r = 5 m
C.h = 15 m; r = 6 m
D.h = 33.75 m; r = 2 m

Answers

Given:
Cone-shaped filter: height = 4m ; diameter = 9m
cylinder:  one full cone-shape filter fills 1/5 of the cylinder

volume of the cone  = π r² h/3 = 3.14 * (4.5m)² * 4m/3
V = 3.14 * 20.25m² * 1.33m
V = 84.57 m³

84.57 m³ ÷ 1/5 = 84.57 m³ * 5 = 422.85 m³ volume of the cylinder

Volume of cylinder = π r² h

Choice A: V = 3.14 * (3m)² * 3m = 3.14 * 9m² * 3m = 84.78 m³
Choice B: V = 3.14 * (5m)² * 4.23m = 3.14 * 25m² * 4.23m = 332.10 m³
Choice C: V = 3.14 * (6m)² * 15m = 3.14 * 36m² * 15m = 1695.60 m³
Choice D: V = 3.14 * (2m)² * 33.75 m = 3.14 * 4m² * 33.75m = 423.90 m³

The closest answer is Choice D. height = 33.75 m ; radius = 2 m 

Solve for the indicated variable X/y=x-8 for x

Answers

Answer:

Therefore, the solution for x in terms of X and y is:

x = (X + 8y) / y

Step-by-step explanation:

To solve for x in the equation X/y = x - 8, we need to isolate x on one side of the equation.

Step 1: Multiply both sides of the equation by y to eliminate the denominator on the left side:

X/y * y = (x - 8) * y

Simplifying, we have:

X = xy - 8y

Step 2: Add 8y to both sides of the equation to isolate the term with x:

X + 8y = xy

Step 3: Rearrange the terms to have x on one side:

xy = X + 8y

Step 4: Divide both sides of the equation by y to solve for x:

x = (X + 8y) / y

1. Solve through substitution
y = -3.x + 4. y = 4x – 10
Enter your math answer

Answers

Answer:

y= -2 and x= 2.

Step-by-step explanation:

(y=-3x+4)4

(y=4x-10)3

make the x's cancel out.

you get 7y=-14.

y=-2.

-2=-3x+4

x=2

A road is 4 cm long on the map. Find the actual length of the road.

Answers

The distance between two cities is

75

k

m

s

.

Explanation:

As a road of

4

c

m

.

on road map indicates a road of length equal to

30

k

m

.

Each

c

m

.

on map indicates

30

4

=

7.5

k

m

s

.

Hence a distance of

10

c

m

.

between two cities on the map indicates

7.5

×

10

=

75

k

m

s

3 cards are drawn at random from a standard deck. Find the probability that all the cards are hearts.


Find the probability that all the cards are face cards.

Note: Face cards are kings, queens, and jacks.

Find the probability that all the cards are even.

(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13)

Answers

Answer:

i dont really understand what you mean it says 3 cards are drawn and it says to find the probability that the cards are all hearts but what is the question asking how do we find the probability

Step-by-step explanation:

Final answer:

The probabilities of drawing all hearts, face cards, or even cards are calculated with the formula: (n/52) * ((n-1)/51) * ((n-2)/50) where n is the total number of cards that match the desired outcome.

Explanation:

The subject here is probability, specifically, how to determine the likelihood of a particular outcome when drawing cards from a standard deck. Let's deal with each probability one at a time.

  1. The probability that all the cards are hearts: There are 13 hearts in a deck of 52 cards. So the probability that the first card is a heart is 13/52, the second is 12/51 (because one heart is already drawn), and the third is 11/50. So, the overall probability is (13/52) * (12/51) * (11/50).
  2. The probability that all the cards are face cards: There are 12 face cards (kings, queens, and jacks) in a deck. Using the same principle, the probability is (12/52) * (11/51) * (10/50).
  3. The probability that all the cards are even: The 'even' cards are 2, 4, 6, 8, 10, which have 4 of each (hearts, diamonds, spades, clubs) totaling 20 cards. So, the probability is (20/52) * (19/51) * (18/50).

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What is the equation of a line passing through the point (a, b) and having a slope of b?

Answers

From the slope form of a line;
(y-b)/(x-a) =b
y-b=bx-ab
y=bx-ab+b
y=bx-b(a-1)

Answer:

The equation is y-a= b(x-b)

Step-by-step explanation:

I use bold for the slope so you can differentiate the slope term b from the y coordinate value b.

The equation of a line passing through a specific point and having a specific slope can be obtained using the point slope form of a line :

y-y1=m(x-x1) where m is the slope and (x1,y1) is your specific point.

So replacing your values, the point  (x1,y1) =(a,b) and m=b, in this equation we havE:

y-a= b(x-b)

That can be expressed in point slope form and explicit for as.

y = b(x-b) + a = bx -bb +a =

y= bx + (a -bb)