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2 years ago

8

Sam buys 3 pounds of apples for $6. What is the unit rate?

1 answer:

olganol [36]2 years ago

5 0

Answer: 1 pound per $2

Step-by-step explanation:

Imagine this problem as a ratio:

Pounds : Dollars

3 : 6

To simplify this ratio, we see that a common divisor(in fact the only common divisor) is 3.

3/3 : 6/3

1 : 2

Therefore, we get 1 pound per $2

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A six-sided die is rolled two times. What is the theoretical fractional probability that the first number is greater than the se

Alekssandra [29.7K]

Given:

A six-sided die is rolled two times.

To find:

The theoretical fractional probability that the first number is greater than the second number.

Solution:

If a six-sided die is rolled two times, then the total possible outcomes are 36.

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

The outcomes where the first number is greater than the second number are

A = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)}

So, the favorable outcomes = 15.

Now, the theoretical fractional probability that the first number is greater than the second number is

$Probability=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$Probability=\dfrac{15}{36}$

$Probability=\dfrac{5}{12}$

Therefore, the required probability is $\dfrac{5}{12}$ .

5 0

3 years ago

The vertex of a parabola is (3,-2) and another point on the parabola is (2,3) find the equation of the parabola in vertex form

jonny [76]

Answer:

$y = 5 ( x - 3 ) ^2 -2$

OR

$y+2= 5 ( x - 3 ) ^2$

Step-by-step explanation:

Vertex form of a parabola is given as:

$y = a ( x - h ) ^2 + k$

Where ( $h,k$ ) is the vertex and $(x,y)$ are the points on the parabola.

We are given that, the vertex is (3, -2) and another point on parabola is given as (2, 3).

$h = 3,k = -2$

First of all, putting the vertex in the vertex equation as given above:

$y = a ( x - 3 ) ^2 + (-2)$

Now, putting the values of $x, y$ as 2, 3 and let us find the unknown variable $a$ :

$3 = a ( 2 - 3 ) ^2 + (-2)\\\Rightarrow 3 = a -2\\\Rightarrow a = 5$

Therefore, the equation in vertex form can be written as:

$y = 5 ( x - 3 ) ^2 -2$

OR

$y+2= 5 ( x - 3 ) ^2$

4 0

3 years ago

A kitchen is shaped like a rectangle with dimensions of 11 1/2 ft by 9 1/2 the floor of the room is made of square tiles with si

VLD [36.1K]

It will take 437 tiles to cover the floor.

7 0

3 years ago

A student performed the following steps to find the solution to the question x^2 - 2x - 15 = 0. Where did the student go wrong?

nataly862011 [7]

Answer:

D In step 3

Step-by-step explanation:

Given polynomial: x² - 2x - 15 = 0

Step 1: factor the polynomial ⇒ (x + 3)(x - 5) = 0

Step 2: x + 3 = 0 and x - 5 = 0

Step 3: x = -3 and x = 5

x - 5 = 0

Add 5 to both sides:

⇒ x - 5 + 5 = 0 + 5

⇒ x = 5

7 0

2 years ago

Find the next term in the sequence. please type the number only as you answer. hint first figure out if the sequence is arithmet

ch4aika [34]

Next term = -243
Because it is x3 every time

8 0

3 years ago