Construir geometricamente utilizando os conceitos que você aprendeu em aula:

Kazeer [188]

The answers are $8^{3}$ and 8 · 8 · 8

Explanation:

The volume of a cube or space a cube occupies is calculated by multiplying the length, height, and width. Additionally, because in a cube all sides are equal in length, the formula for volume is V= $s^{3}$ . According to this, if the side length is 8 inches the volume can be represented as $V = 8^{3}$ or V= 8 · 8 · 8 because the symbol · represents multiplication. Also, this can be solved as V = 512 cubic inches. This makes the following options correct: $8^{3}$ and 8 · 8 · 8.

4 0

3 years ago

Suppose you are given either a fair dice or an unfair dice (6-sided). You have no basis for considering either dice more likely

hoa [83]

Answer: Our required probability is 0.83.

Step-by-step explanation:

Since we have given that

Number of dices = 2

Number of fair dice = 1

Probability of getting a fair dice P(E₁) = $\dfrac{1}{2}$

Number of unfair dice = 1

Probability of getting a unfair dice P(E₂) = $\dfrac{1}{2}$

Probability of getting a 3 for the fair dice P(A|E₁)= $\dfrac{1}{6}$

Probability of getting a 3 for the unfair dice P(A|E₂) = $\dfrac{1}{3}$

So, we need to find the probability that the die he rolled is fair given that the outcome is 3.

So, we will use "Bayes theorem":

$P(E_1|A)=\dfrac{P(E_1)P(A|E_1)}{P(E_1)P(A|E_1)+P(E_2)P(A|E_2)}\\\\(E_1|A)=\dfrac{0.5\times 0.16}{0.5\times 0.16+0.5\times 0.34}\\\\P(E_1|A)=0.83$

Hence, our required probability is 0.83.

8 0

3 years ago

Which statement can be deduced from the picture?

ExtremeBDS [4]

Answer:

Angle AOD and Angle DOB are supplementary

Step-by-step explanation:

AOB is straight(180°) Line DO is a line that creates two angles

4 0

2 years ago

Read 2 more answers

Find the equation of the line that passes through the point of intersection of x + 2y = 9 and 4x -2y = -4 and the point of inter

Rudik [331]

Answer:

$y=-6x+10$

Step-by-step explanation:

The point of intersection of

$x+2y=9...eqn1$

and

$4x-2y=-4...eqn2$

is the solution of the two equations.

We add equation (1) and equation(2) to get,

$x+4x+2y-2y=9+-4$

$\Rightarrow 5x=5$

$\Rightarrow x=1$

We put $x=1$ into equation (1) to get,

$1+2y=9$

$\Rightarrow 2y=9-1$

$\Rightarrow 2y=8$

$\Rightarrow y=4$

Therefore the line passes through the point, $(1,4)$ .

The line also passes through the point of intersection of

$3x-4y=14...eqn(3)$

and

$3x+7y=-8...eqn(4)$

We subtract equation (3) from equation (4) to obtain,

$3x-3x+7y--4y=-8-14$

$\Rightarrow 11y=-22$

$\Rightarrow y=-2$

We substitute this value into equation (4) to get,

$3x+7(-2)=-8$

$3x-14=-8$

$3x=-8+14$

$3x=6$

$x=2$

The line also passes through

$(2,-2)$

The slope of the line is

$slope=\frac{4--2}{1-2} =\frac{6}{-1}=-6$

The equation of the line is

$y+2=-6(x-2)$

$y+2=-6x+12$

$y=-6x+10$ is the required equation

4 0

3 years ago

A carpenter is constructing staircase in a house. The distance from the floor to the basement is 10.8 feet. The staircase will b

konstantin123 [22]

Answer:

$\theta = 40.59^\circ$

Step-by-step explanation:

Given

The question is illustrated with the attached image

Required

Find $\theta$

To do this, we use sine formula

i.e.

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

So, we have:

$\sin(\theta) = \frac{10.8}{16.6}$

$\sin(\theta) = 0.6506$

Take arc sin

$\theta = \sin^{-1}(0.6506)$

$\theta = 40.59^\circ$

4 0

2 years ago