Evaluate the expression : 3m + 2n3m+2n for : m = 12m=12 and : n = 5

What is 1 - 27/44 = in its simplest form?

zloy xaker [14]

$1 - \frac{27 }{44}=\frac{44}{44}-\frac{27 }{44}=\frac{17 }{44}$

8 0

3 years ago

Read 2 more answers

Write the equation in y-intercept form slope 2 passes through point (5,-2)

Alenkinab [10]

<h2>Answer</h2>

The equation is y = 2x - 12

<h2>Explanation</h2>

Equation in slope intercept form is

$y = mx + b$

Where,

m = slope

b = y-intercept

Putting the value of slope in this equation:

$y = 2x + b$

From this we can solve the equation for b

$b = y - 2x$

$b = -2 - 2(5)$

$b = -12$

Now, the equation of y-intercept becomes

$y = 2x - 12$

5 0

3 years ago

A fish tank measures 20cm by 30cm by 40 cm. a jug holds 1.2 L. how many jugs of water are needed to fill the tank.

ra1l [238]

Answer:

Multiply the numbers then divide by the amount of water in the jug

Step-by-step explanation:

6 0

3 years ago

A donut store has 11 different types of donuts. You can only buy a bag of 3 of them, where each donut has to be of a different t

MakcuM [25]

Answer:

$165$ .

Step-by-step explanation:

Since repetition isn't allowed, there would be $11$ choices for the first donut, $(11 - 1) = 10$ choices for the second donut, and $(11 - 2) = 9$ choices for the third donut. If the order in which donuts are placed in the bag matters, there would be $11 \times 10 \times 9$ unique ways to choose a bag of these donuts.

In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type $3 \times 2 \times 1 = 6$ times.

For example, if a bag includes donut of type $x$ , $y$ , and $z$ , the count $11 \times 10 \times 9$ would include the following $3 \times 2 \times 1$ arrangements:

$xyz$ .
$xzy$ .
$yxz$ .
$yzx$ .
$zxy$ .
$zyx$ .

Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count $11 \times 10 \times 9$ by $3 \times 2 \times 1 = 6$ to find the actual number of donut combinations:

$\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}$ .

Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of $3$ objects from a set of $11$ distinct objects:

$\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}$ .

5 0

2 years ago

Which ordered pair would form a proportional relationship with the point graphed below? (60,-20)

valentina_108 [34]

Given:

The graphed point is (60,-20).

To find:

The ordered pair that would form a proportional relationship with the given point.

Solution:

If y is proportional to x, then

$y\propto x$

$y=kx$

$\dfrac{y}{x}=k$

Where, k is the constant of proportionality.

For the given point,

$k=\dfrac{-20}{60}$

$k=\dfrac{-1}{3}$

For option (A),

$k=\dfrac{30}{-10}$

$k=-3\neq \dfrac{-1}{3}$

For option (B),

$k=\dfrac{-15}{30}$

$k=-\dfrac{1}{2}\neq \dfrac{-1}{3}$

For option (C),

$k=\dfrac{10}{-30}$

$k=\dfrac{-1}{3}$ .

The point (-30,10) gives the same value of the constant of proportionality. So, the point (-30,10) forms a proportional relationship with the given point.

Therefore, the correct option is C.

7 0

3 years ago