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2 years ago

MP is the angle bisector of LMN. Given that LMP is a right angle.

Mathematics

1 answer:

Akimi4 [234]2 years ago

7 0

Angle bisector divides an angle into equal halves.

Angle LMN is a straight line
The measure of LMN is 180 degrees

From the question, we understand that:

MP bisects LMN

This means that:

LMN = 2 x LMP

Also, we have:

LMP = 90 ------ because LMP is a right angle

So, we have:

LMP = 2 x 90

LMP = 180

An angle that measures 180 degrees is a straight line.

Hence, the measure of LMN is 180 degrees, and it is a straight line

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A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on t

emmainna [20.7K]

Answer:

On average, a player should expect to win $15.

Step-by-step explanation:

The expected value in an event with outcomes:

x₁, x₂, ..., xₙ

Each with probability:

p₁, ..., pₙ

is given by:

Ev = x₁*p₁ + ... +xₙ*pₙ

In this case we have 3 outcomes:

player wins $75 = x₁

player wins $45 = x₂

player does not win = x₃

Let's find the probabilities of these events.

player wins $75)

Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75

While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)

Then the number total of outcomes is:

C = 2*2*2 = 8

Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)

p₁ = 1/8

Win $45:

This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:

p₂ = 1/8

Not wining:

Remember that:

p₁ + p₂ + ... + pₙ = 1

Then for this case, we must have:

p₁ + p₂ + p₃ = 1

1/8 + 1/8 + p₃ = 1

p₃ = 1 - 1/8 - 1/8

p₃ = 6/8

Then the expected value will be:

Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15

On average, a player should expect to win $15.

7 0

2 years ago

3) Solve each equation using the quadratic formula. Show a. x2 – 3x – 10 = 0

Naya [18.7K]

Answer:

Step-by-step explanation:

The quadratic formula of a quadratic equation

$ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}$

$\text{If}\ b^2-4ac$

We have:

$x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=\dfrac{-(-3)\pm\sqrt{49}}{2(1)}=\dfrac{3\pm7}{2}\\\\x=\dfrac{3-7}{2}=\dfrac{-4}{2}=-2\\or\\x=\dfrac{3+7}{2}=\dfrac{10}{2}=5$

5 0

3 years ago

WILL MARK BRAINLIEST!! Thank you

Monica [59]

Answer:

Step-by-step explanation:

6 0

3 years ago

6) A climber is on a hike. After 2 hours she is at an altitude of 400 feet. After 6 hours, she is at an

Bas_tet [7]

Answer:

Her rate of change is 75 ft/h

Step-by-step explanation:

Rate of Change

It measures how one quantity varies with respect to another. The second variable usually is the time.

The climber is hiking. We are given two points of her progress: At 2 hours, she is at 400 ft. This corresponds to the point (2,400).

At 6 hours, she is at 700 ft. This is the point (6,700)

The rate of change is the slope between these two points or the quotient of the variations of each variable:

$\displaystyle m=\frac{700\ ft-400\ ft}{6\ h-2\ h}$

$\displaystyle m=\frac{300\ ft}{4\ h}$

$m=75\ ft/h$

Her rate of change is 75 ft/h

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2 years ago

The heights of two similar cylinders are 3cm and 4cm respectively. The total area of the bigger cylinder is 400cm².Calculate the

shusha [124]

Answer:

Step-by-step explanation:

Total surface area = 2πr(r+h)

If the total area of the bigger cylinder is 400cm² and radius is 4cm, then;

400=2(3.14)(r)(r+4)

400= 6.26r(r+4)

400=100.48 + 25.12h

299.52 = 25.12h

H = 299.52/25.12

H = 11.92cm

For the smaller cylinder

The height is calculated as;

H/h = R/r

11/92/

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2 years ago