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2 years ago

a fair die is tossed four times. Find the probability of obtaining each of the following. 5 on all four tosses

Mathematics

1 answer:

Anastaziya [24]2 years ago

5 0

Answer:

$\dfrac{1}{1296}$

Step-by-step explanation:

When a fair die is tossed once, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of rolling 5 is $\dfrac{1}{6}.$

When a fair die is tossed four times, the probability of rolling 5 all four times is

$\dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}=\dfrac{1}{6^4}= \dfrac{1}{1296}$

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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −

crimeas [40]

Solving quadratic equations, it is found that he needs to charge:

1. He needs to charge $40 to break even.

2. He needs to charge $30 for a profit of $600.

<h3>What is a quadratic function?</h3>

A quadratic function is given according to the following rule:

$y = ax^2 + bx + c$

The solutions are:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a}$

In which:

$\Delta = b^2 - 4ac$

The profit equation in this problem is:

P(x) = -3x² + 150x - 1200.

He breaks even when P(x) = 0, hence:

-3x² + 150x - 1200 = 0.

The coefficients are a = -3, b = 150, c = -1200, hence:

$\Delta = 150^2 - 4(-3)(-1200) = 8100$

$x_1 = \frac{-150 + \sqrt{8100}}{-6}$

$x_2 = \frac{-150 - \sqrt{8100}}{-6} = 40$

He needs to charge $40 to break even.

For a profit of $600, we have that P(x) = 600, hence:

-3x² + 150x - 1200 = 600.

-3x² + 150x - 1800 = 0.

The coefficients are a = -3, b = 150, c = -1800, hence:

$\Delta = 150^2 - 4(-3)(-1800) = 900$

$x_1 = \frac{-150 + \sqrt{900}}{-6}$

$x_2 = \frac{-150 - \sqrt{900}}{-6} = 30$

He needs to charge $30 for a profit of $600.

More can be learned about quadratic equations at brainly.com/question/24737967

#SPJ1

6 0

1 year ago

The vertices of a polygon are P(0,4), Q(5,4), R(5,−3) and S(0,−3). What is

andrezito [222]

Answer:

Perimeter of the polygon p = 24

Step-by-step explanation:

Step(i):-

Given the vertices of a polygon are

P(0,4) ,Q( 5,4) ,R( 5,-3) and S(0,-3)

The distance of PQ

$a = PQ = \sqrt{(4-4)^{2} +(5-0)^{2} } = \sqrt{25} =5$

The distance of QR

$b = Q R= \sqrt{(-3-4)^{2} +(5-5)^{2} } = \sqrt{49} =7$

The distance of RS

$c = RS = \sqrt{(0-5)^{2} +(-3+3)^{2} } = \sqrt{25} =5$

The distance of PS

$d = PS = \sqrt{(0-0)^{2} +(-3-4)^{2} } = \sqrt{49} =7$

Step(ii):-

Perimeter of the polygon

= sum of all sides of polygon

p = a+ b+ c+ d

p = 5+7+5+7

p = 24

Final answer:-

Perimeter of the polygon p = 24

5 0

3 years ago

9.1k = 63.7 what does this equal

zheka24 [161]

Step-by-step explanation:

9.1k=64.7

Find k

64.7/9.1=7

Plug in 7

9.1(7)=64.7

Multiply 9.1 and 7=63.7

63.7=64.7

Divide

1.02 or 1 1/50

Hope that helps somewhat

5 0

2 years ago

Read 2 more answers

Divide 32 students into 2 groups so the ratio is two to five how many students with be in each group

Valentin [98]

Answer:

they can be divided into

2 groups of 16

4 groups of 8

8 groups of 4

16 groups of 2

5 0

2 years ago

Which statement is correct about a line and a point?

KIM [24]

A line and a point can be collinear” is correct about a line and a point.

In geometry a line:

• is straight (no curves),
• has no thickness, and
• extends in both directions without end (infinitely).

In modern mathematics, a point refers usually to an element of some set called a space. More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built.

6 0

3 years ago

Read 2 more answers