help please ! 15 points

Answer: 150

Step-by-step explanation:

Let x be the total number of cans that was students' goal.

Given : Students collected 600 cans for the canned food drive that was 80% of their goal .

We can write 80% as 0.80

Then, we have

[tex]0.80x=600\\\\\Rightarrow\ x=\dfrac{600}{0.80}=750[/tex]

Thus, The students' goal of collecting cans for the canned food drive = 750 cans

Now, the number of food cans required to collect to reach the goal= 750-600=150

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\textbf{What is }\rm{\bf \dfrac{3}{8}}\large\textbf{ equivalent to?}[/tex]

[tex]\huge\textbf{Now, let's solve for the given question:}[/tex]

[tex]\mathbf{\dfrac{3}{8}}[/tex]

[tex]\mathbf{= \dfrac{3\times2}{8\times2}}[/tex]

[tex]\mathbf{\approx \dfrac{3 + 3}{8 + 8}}[/tex]

[tex]\mathbf{= \dfrac{6}{16}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\dfrac{6}{16}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The plot of the given line is required.

The graph is shown below with two points [tex](0,-6)[/tex] and [tex](-3,0)[/tex].

The line is

[tex]y-2=-2(x+4)\\\Rightarrow y=-2x-8+2\\\Rightarrow y=-2x-6[/tex]

Let us find two points on the line

[tex]x=0[/tex]

[tex]y=-2\times0-6=-6[/tex]

[tex](0,-6)[/tex]

[tex]y=0[/tex]

[tex]0=-2x-6\\\Rightarrow x=\dfrac{6}{-2}=-3[/tex]

[tex](-3,0)[/tex]

Join the two points on the graph and the line will be constructed.

Learn more:

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The graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉ as the graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.

A modulus function is a function that determines a number or variable's absolute value. No matter what input was provided to this function, the outcome is always positive.

Consider different values for x.

Say,

x = -1; f(-1) = [-1] = 1

x = 1; f(1) = [1] = 1

For any value of the x, the value of the function will be positive only.

The graph is attached in the image.

Consider different values for x.

Say,

x = 0; f(0) = [0] + 7 = 0 + 7; f(0) = 7

x = -1; f(-1) = [-1] + 7 = 1 + 7; f(-1) = 8

x = 1; f(1) = [1] = 1 + 7; f(1) = 8

For any value of the x, the value of the function will be positive only, but it would be 7 units shifted up on the y axis.

The graph is attached in the image.

To know more about how to determine modulus of complex numbers?, here

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Final answer:

The experimental probability of rolling a 4 is calculated by dividing the number of times a 4 is rolled by the total number of rolls. It may not match the theoretical probability exactly in the short term but should converge to approximately 0.1667 as the number of trials increases.

Explanation:

To find the experimental probability of rolling a 4 with a fair six-sided die, we must consider the frequency of the event (rolling a 4) occurring among a number of trials. Since each side of the die has an equal chance of landing face up, each side has a probability of 1/6.

If a die is rolled many times, and the results are recorded, the experimental probability can be calculated as the number of times a 4 occurs divided by the total number of trials. For example, if a die is rolled 120 times and the number 4 comes up 20 times, the experimental probability for rolling a 4 would be 20/120, which simplifies to 1/6. However, since this is experimental probability, the outcome may not always exactly match the theoretical probability due to variations in the short term. Nevertheless, as the number of trials increases, we expect the experimental probability to get closer to the theoretical probability of 1/6 or approximately 0.1667 when rounded to four decimal places.

Answer:

Graph 2

Step-by-step explanation:

Given system of inequalities,

−2x + y ≤ 4,

y > x + 2

∵ Related equation of −2x + y ≤ 4 is,

-2x + y = 4 ⇒ y = 4 + 2x ----(1)

While, the related equation of y > x + 2 is,

y = x + 2

From equation (1),

4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2

Again by equation (1),

y = 4 + 2(-2) = 4 - 4 = 0

Hence, the intersection point of the related equation is (-2,0),

∴ Graph 1 and graph 3 can not be the graph of the given system.

Now, −2(0) + (0)  ≤ 4 ( true )

That is, −2x+y ≤ 4 would contain the origin,

Also, 0 > 0 + 2 ( False )

That is, y > x + 2 does not contain the origin.

Therefore, by the above explanation it is clear that,

Grap 2 represents the solution set of the system of inequalities.

Answer:

T = HN + r

Step-by-step explanation:

A handyman charges $H for each hour worked.

If the handyman works for N hours then the expression for the charges will be = $HN

Handyman charges a fixed amount = $r

Then the total amount charged T will be represented by

T = HN + r

Therefore, formula to calculate the total charges by handyman will be

T = HN + r