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2 years ago

Can a object that measures 1.8 metres by 1.2 metres fit in a gap that measure 1 metre by 0.75 metres

Mathematics

1 answer:

Paha777 [63]2 years ago

4 0

No it cannot because 1.8 and 1.2 are both larger than 0.75 so there is no physical way for it to fit

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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

1 year ago

Angel paints three rooms with two gallons of paint. How many rooms can he paint with fifteen gallons of paint?

Vanyuwa [196]

Answer:

22 rooms

Step-by-step explanation:

If two gallons of paint covers 3 rooms then you need to divide 15 gallons of paint by 2 gallons of paint = 7.5 gallons of paint. then you need to multiply 7.5 gallons of paint by 3 rooms = 22.5..... so that means you can paint 22 full rooms.

6 0

2 years ago

Tshepo needs R5 000 urgently. He goes to the bank and borrows the money at an interest rate of 28% per annum, compounded monthly

12345 [234]

Answer:

<u>R8000</u>.

Step-by-step explanation:

First, let's calculate the amount they are going to have to pay the bank after 1 year. It is given by the following expression:

R5 000 * 1.28= R6400

Therefore, they have to pay R6400/12 monthly.

Now, in fifteen months the total amount to pay should be (R6400/12) * 15= <u>R8000</u>.

8 0

1 year ago

Which number comes next in the series? 1 – 8 – 27 – 64 – 125 – 216 –?

dalvyx [7]

${7}^{3} = 343$

3 0

3 years ago

Help with a few questions pleaseeeeee

mel-nik [20]

29.99 * 3 =89.97 89.97 with 30% off = 62.98 and 5% of 62.98 =3.15 so 62.98 + 3.15 = 66.13$

180.00 + 14.95 + 8.95 = 203.09 - 15% = 173.44 + 4% = 180.38

5.65 + 5% of 5.65 = 5.93

i think this is all right you might want to check my work!

3 0

3 years ago