Every pair of students brought in five pies. How many pies per person were brought in

A bag contains 6 blue marbles, 8 green marbles, 9 red marbles, and 17 yellow marbles. What is the ratio of blue marbles to total

mario62 [17]

Answer:

6 to 40

Step-by-step explanation:

add all of the marbles which will give you the total

8 0

3 years ago

4. Error Analysis Jacinta says that the product of a rational number and an irrational number is always irrational. Explain her

Vinvika [58]

Answer:

She did not consider the multiplicative inverse property of a real number

Step-by-step explanation:

Jacinta in her conclusion did not consider the Multiplicative Inverse property of real numbers.

Let x be an irrational number.

So, $x.\frac{1}{x}= 1$

If x is an irrational number, then its reverse is also an irrational number. So by the Multiplicative Inverse property their product is 1 and 1 is a rational number. Thus, Jacinta was incorrect.

5 0

4 years ago

Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use th

Archy [21]

Answer:

(a) 1 inch of rider ⇒ 0.29 inches of frame

Step-by-step explanation:

The "slope" in the equation is the coefficient of the independent variable. Here, that variable is "h", and its coefficient is 0.29. That is, the height of the rider is multiplied by 0.29 (and a constant is added) in order to find the height of the frame.

__

The meaning of the value 0.29 is that a 1 inch increase in the rider's height should result in a 0.29 inch increase in the height of the frame of the bike.

The question asks for an <em>explanation</em> of the slope, not its function in the equation. That is why we have chosen the first answer.

6 0

2 years ago

3x - 3y = -3<br>2x - y = -5

Korolek [52]

For this case we must solve the following system of equations:

$3x-3y = -3\\2x-y = -5$

To solve we follow the steps below:

We multiply the second equation by -3:

$-6x + 3y = 15$

Thus, we have the equivalent system:

$3x-3y = -3\\-6x + 3y = 15$

We add the equations:

$3x-6x-3y + 3y = -3 + 15\\-3x = -3 + 15\\-3x = 12\\x = \frac {12} {- 3}\\x = -4$

We look for the value of the variable "y":

$2 (-4) -y = -5\\-8-y = -5\\-y = -5 + 8\\-y = 3\\y = -3$

Thus, the solution of the system is given by:

$(x, y): (- 4, -3)$

Answer:

$(x, y): (- 4, -3)$

4 0

3 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

===============================================================

Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0

2 years ago