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3 years ago

PLEASE HELP and Show your work please!!

Mathematics

1 answer:

bazaltina [42]3 years ago

8 0

9514 1404 393

Answer:

2) 3 pages per hour

3) 4/29 km per minute

Step-by-step explanation:

Division by a fraction is the same as multiplication by the inverse of that fraction.

$\dfrac{\ \dfrac{9}{4}\ }{\dfrac{3}{4}}=\dfrac{9}{4}\times\dfrac{4}{3}=\dfrac{36}{12}=\boxed{3\text{ pages per hour}}$

$\dfrac{2\text{ km}}{\dfrac{29}{2}\text{ min}}=2\times\dfrac{2}{29}\text{ km/min}=\boxed{\dfrac{4}{29}\text{ km/min}}$

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Scrat the squirrel has a few nuts. When he put them in groups of 5 nuts, two nuts were left, and

iragen [17]

Answer:

The options are not shown, so i will solve this in a general way.

Let's suppose that there are N nuts

If we divide the N nuts into groups of 5, there will be a remainder of 2 nuts.

If we divide the N nuts into groups of 3, there is no remainder.

This means taht N is a multiple of 3. then we can write:

N = 3*k

where k is a random integer.

Now, we know that when we divide N by 5, there is a remainder of 2 nuts, this means that N is equal to a multiple of 5 plus 2, then we can write:

N = 5*j + 2

where j is a random integer.

Now we only need to find a pair of k and j (both positive integers) such that:

3*k = 5*j + 2

We can rewrite this as:

k = (5/3)*j + (2/3)

Now we could just input different values of j, and see if k is also an integer:

j = 2

k = (5/3)*2 + 2/3 = 10/3 + 2/3 = 12/3 = 4

Then the pair j = 2, k = 4 is a possible solution.

N = 3*k = 3*4 = 12

N = 5*j + 2 = 5*2 + 2 = 12

From this we can conclude that N = 12, so Scrat has 12 nuts.

Now with the equation

k = (5/3)*j + (2/3)

We can find other possible combinations of j and k, that will give different values for N.

for example, if j = 5:

k = (5/3)*5 + 2/3 = 25/3 + 2/3 = 27/3 = 9

Then the pair j = 5, k = 9 is also a possible solution:

N = 3*k = 3*9 = 27

N = 5*j + 2 = 5*5 + 2 = 27

In this case, Scrat has 27 nuts.

5 0

3 years ago

The cost per student of a ski trip varies inversely as the number of students who attend. It will cost each student $250 if 24 s

mars1129 [50]

ANSWER

30 students

EXPLANATION

The cost per student varies inversely as the number of students.

Inverse proportion is written as:

$\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \\ \text{where k = constant of proportionality} \end{gathered}$

Let the cost per student be y.

Let the number of students be x.

It will cost each student $250 if 24 students attend. This means that:

$\begin{gathered} 250=\frac{k}{24} \\ \Rightarrow k=250\cdot24 \\ k=6000 \end{gathered}$

If the cost is down to $200, it means that y is now $200.

That is:

$\begin{gathered} 200=\frac{6000}{x} \\ \Rightarrow x=\frac{6000}{200} \\ x=30\text{ students} \end{gathered}$

Therefore, 30 students could attend.

5 0

2 years ago

Bill bought a shirt for $35.80 plus he paid an additional 7% in sales tax.

dezoksy [38]

Answer:

$2.50

Step-by-step explanation:

The cost for the shirt is 35.80

7%=0.07

35.80 x 0.07 = 2.50

Answer is $2.50

3 0

3 years ago

The coordinate grid shows points a through k. Which points are solutions to the system of inequalities 2x+y 8 please help this i

andre [41]

Answer:

The points that verify the system of inequalities are:

point E, pointF, and point G.

Step-by-step explanation:

Please see the attached image that illustrates the boundary lines in your system of inequalities.

The boundary line for the inequality $2x+y$ is depicted in green, while the boundary line for the inequality $2x-4y>8$ is depicted in red.

By solving for y in each inequality, we understand which half-plane should be considered for the inequality:

First inequality (green boundary line) :

$2x+y$

This means that we are to consider the points below the green boundary line.

Second inequality (red boundary line) :

$2x-4y >8\\2x-8>4y\\y$

This means we have to consider the points below the red boundary line.

Recall as well that both conditions we arrived at have to be satisfied by the points that are solutions of both inequalities.

From the image, we can see that there are only three points that reside at the same time below the green and the red boundary lines. These points are: point E, pointF, and point G.

On the other hand, we have two points that lie on a boundary line (point J and H), but they should be ignored, since the system of inequalities contain just inequality symbols < or >, and not the "equal" sign.

5 0

3 years ago

Solve for f: f/5 = -8 F=?

rjkz [21]

Answer:

f = -40 your welcome

Step-by-step explanation:

8 0

3 years ago

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