What is the joint relative frequency for 11th graders who want the break in the afternoon? Round to the nearest percent.

Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation

Olenka [21]

Answer:

y = $\frac{49}{3}$

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 7 when x = 3

k = $\frac{y}{x}$ = $\frac{7}{3}$ , thus

y = $\frac{7}{3}$ x ← equation of variation

When x = 7, then

y = $\frac{7}{3}$ × 7 = $\frac{49}{3}$

8 0

2 years ago

Which of the following is a correct name for a side of the given angle?

Zigmanuir [339]

Answer:

C. ED

Step-by-step explanation:

The center of the angle is the point E, so it would be written first.

5 0

2 years ago

A granola bite contains 27 calories. Most of the calories come from grams of carbohydrates. The rest come from other ingredients

GuDViN [60]

Step-by-step explanation:

Given the expression that modeled the relationship between these quantities (calories from grams of carbohydrate and the rest of the ingredients) as

4c+5 = 27

From the equation, the constant value of 5 represents the calories in grams of the rest of the ingredients present in the bite.

Let us calculate the value of c from the equation

4c+5 = 27

4c + 5- 5 = 27-5

4c = 22

c = 22/4

c = 5.5

This means that the total calories of carbohydrate the granola bite contains is 4(5.5) i.e 21 calories of carbohydrate

<em>Note that 8 cannot be the solution to the equation because for us to eliminate 5 from both sides of the equation, we need to subtract it from both sides not add. If 5 was added to both sides, the value of c would have been (32/4 i.e 8) which would have been wrong.</em>

7 0

2 years ago

I need the domain range and function. With an explanation

erastovalidia [21]

<h3>Answers:</h3>

Problem 1

Domain = $-3 < x \le 3$ , interval notation (-3, 3]
Range = $-3 \le y < 3$ , interval notation [-3, 3)
Is it a function? Yes

Problem 2

Domain = $x \ge -2$ , interval notation $[-2, \infty)$
Range = All real numbers, interval notation $(-\infty, \infty)$
Is it a function? No

Problem 3

Domain = $-4 \le x < 3$ , interval notation [-4, 3)
Range = $-4 < y \le 3$ , interval notation (-4, 3]
Is it a function? Yes

Problem 4

Domain = All real numbers, interval notation $(-\infty, \infty)$
Range = $y \le 4$ , interval notation $(-\infty, 4]$
Is it a function? Yes

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

Explanations:

The left most point is when x = -3, and we are not including this value due to the open hole. The other endpoint is included because it is a filled in circle. The domain is therefore $-3 < x \le 3$ which in interval notation is (-3, 3]. We have the curved parenthesis meaning "exclude endpoint" and the square bracket says "include endpoint". The range is a similar story but we're looking at the smallest and largest y values. Though be careful about which endpoint is open/closed. We have a function because it passes the vertical line test.
The smallest x value is x = -2. There is no largest x value because the arrows say to go on forever to the right. We can say the domain is $x \ge -2$ which in interval notation is $[-2, \infty)$ . The range is $(-\infty, \infty)$ to indicate "all real numbers". This graph fails the vertical line test, so it is not a function. The vertical line test is where we check to see if we can pass a vertical line through more than one point on the curve. In this case, such a thing is possible which is why it fails the test.
This is the same idea as problem 1, though note the endpoints are flipped in terms of which has an open circle and which doesn't. It is not possible to draw a single vertical line to have it pass through more than one point on the curve, so it passes the vertical line test and we have a function.
This is a function because it passes the vertical line test. The domain is the set of all real numbers due to the arrows in both directions. Any x value is a possible input. The range is $y \le 4$ which is the same as saying $(-\infty, 4]$ in interval notation. This is because y = 4 is the largest y value possible. There is no smallest y value due to the arrows.

7 0

3 years ago

Find the difference. write the difference in lower term 8 ⅓-5

sergejj [24]

Given data:

The given expression is 8 ⅓-5.

The given expression can be written as,

$\begin{gathered} 8\frac{1}{3}-5=\frac{25}{3}-5 \\ =\frac{25-15}{3} \\ =\frac{10}{3} \end{gathered}$

Thus, the difference of the given expression is 10/3.

5 0

1 year ago