Fully Factorise 3x-12

In the floor tile pattern, the figure is a square and the two triangles are congruent.

Licemer1 [7]

Answer:

7.1

Step-by-step explanation:

Since it is a square you can use the Pythagorean theorem (a²+b²=c²) by filling in what you know. a²=5 and b²=5 so you have 5²+5²=c². This simplfies to 25+25=c². Now you simplify again to get 50=c². Finally you have to square root everything because the equation can't end in c², it has to be the most simplified it can be. This equals ≈7.1

8 0

3 years ago

Jessica has 20 pieces of candy in a bag: 2 mint sticks, 9 jelly treats, and 9 fruit tart chews. If she eats one piece every 10 m

dedylja [7]

Answer:

18.95%

Step-by-step explanation:

In this case what we must do is calculate the probability of eating a jelly treats first and then another jelly treats, being the final probability the multiplication of these events.

We know that there are 20 in total and that initially there are 9 jelly treats, so the first event is the probability:

9/20

And the second event, with one less in each, would be:

8/19

The final probability then:

9/20 * 8/19 = 0.1895

So the probability of this happening is 18.95%

4 0

4 years ago

Read 2 more answers

A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has fa

gayaneshka [121]

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4 | red dice) = $\dfrac{1}{6}$

P (4 | green dice) = $\dfrac{3}{6}$ = $\dfrac{1}{2}$

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = $\dfrac{1}{2}$

The probability of two 1's and two 4's in the first dice can be calculated as:

= $\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4$

= $\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4$

= $\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4$

= $6 \times ( \dfrac{1}{6})^4$

= $(\dfrac{1}{6})^3$

= $\dfrac{1}{216}$

The probability of two 1's and two 4's in the second dice can be calculated as:

= $\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2$

= $\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2$

= $6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2$

= $( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2$

= $\dfrac{9}{216}$

∴

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = $\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}$

The probability of two 1's and two 4's in both die = $\dfrac{1}{432} + \dfrac{1}{48}$

The probability of two 1's and two 4's in both die = $\dfrac{5}{216}$

By applying Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's ) = $\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}$

P(second die (green) | two 1's and two 4's ) = $\dfrac{0.5 \times 0.04166666667}{0.02314814815}$

P(second die (green) | two 1's and two 4's ) = 0.9

Thus; the probability the die chosen was green is 0.9

8 0

3 years ago

Triangle QRS has been rotated 90° to create triangle TVU. Using the image below, prove that lines RS and VU have the opposite an

Zanzabum

Answer:

If the line RS has been rotated 90 degrees, then VU will be perpendicular to RS and the two slopes must be opposite and reciprocal, i.e. product of the two slopes will equal -1.

As a verification, we find the locations of V and U from rotations of R & S.

(actually, the triangle had been rotated -90°, 90 ° clockwise)

Step-by-step explanation:

Slope RS, m1:

Slope VU, m2

Hence m1*m2=1*-1=-1, meaning that m1 and m2 are opposite (in sign) and are reciprocal to each other, as expected

6 0

3 years ago

A school dance committee is made up of 2 freshman, 4 sophomores, 2 juniors, and 2 seniors.

qaws [65]

Answer:

4 and 6.

Step-by-step explanation:

There are 4 different grades represented, so for the first question, there are 4 ways that the students can sit if they must sit together by grade.

For the second question, there are 3 grades other than senior level, so it starts with 3 ways that the students can be seated. 3 ways x 2 students per way = 6 ways

7 0

3 years ago