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2 years ago

A coin is flipped three times. H represents heads, and T represents tails. What is the sample space?

Mathematics

2 answers:

Tju [1.3M]2 years ago

7 0

That would be the first choice.

erica [24]2 years ago

3 0

Answer:

The sample space is S={HHH, TTT, HTT, HHT, TTH, THH, THT, HTH}

Step-by-step explanation:

Given that a coin is flipped three times.

H represents heads, and T represents tails.

we have to find the sample space.

The sample space contains $2^n=2^3=8$ elements.

As three times the coin is flipped.

∴ The possible outcomes i.e the sample space is

S={HHH, TTT, HTT, HHT, TTH, THH, THT, HTH}

The first choice is correct option.

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The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2). On a coordinate plane, line A B has points (4, 1) and (n

GarryVolchara [31]

Answer:

$(-1,1),(4,-2)$

Step-by-step explanation:

Given: The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).

To find: coordinates of vertex of the right angle

Solution:

Let C be point $(x,y)$

Distance between points $(x_1,y_1),(x_2,y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AC=\sqrt{(x-4)^2+(y-1)^2}\\BC=\sqrt{(x+1)^2+(y+2)^2}\\AB=\sqrt{(4+1)^2+(1+2)^2}=\sqrt{25+9}=\sqrt{34}$

ΔABC is a right angled triangle, suing Pythagoras theorem (square of hypotenuse is equal to sum of squares of base and perpendicular)

$34=\left [ (x-4)^2+(y-1)^2 \right ]+\left [ (x+1)^2+(y+2)^2 \right ]$

Put $(x,y)=(-1,1)$

$34=\left [ (-1-4)^2+(1-1)^2 \right ]+\left [ (-1+1)^2+(1+2)^2 \right ]\\34=25+9\\34=34$

which is true. So, $(-1,1)$ can be a vertex

Put $(x,y)=(4,-2)$

$34=\left [ (4-4)^2+(-2-1)^2 \right ]+\left [ (4+1)^2+(-2+2)^2 \right ]\\34=9+25\\34=34$

which is true. So, $(4,-2)$ can be a vertex

Put $(x,y)=(1,1)$

$34=\left [ (1-4)^2+(1-1)^2 \right ]+\left [ (1+1)^2+(1+2)^2 \right ]\\34=9+4+9\\34=22$

which is not true. So, $(1,1)$ cannot be a vertex

Put $(x,y)=(2,-2)$

$34=\left [ (2-4)^2+(-2-1)^2 \right ]+\left [ (2+1)^2+(-2+2)^2 \right ]\\34=4+9+9\\34=22$

which is not true. So, $(2,-2)$ cannot be a vertex

Put $(x,y)=(4,-1)$

$34=\left [ (4-4)^2+(-1-1)^2 \right ]+\left [ (4+1)^2+(-1+2)^2 \right ]\\34=4+25+1\\34=30$

which is not true. So, $(4,-1)$ cannot be a vertex

Put $(x,y)=(-1,4)$

$34=\left [ (-1-4)^2+(4-1)^2 \right ]+\left [ (-1+1)^2+(4+2)^2 \right ]\\34=25+9+36\\34=70$

which is not true. So, $(-1,4)$ cannot be a vertex

So, possible points for the vertex are $(-1,1),(4,-2)$

7 0

2 years ago

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An art museum opens at 9 a.M. And closes at 5 p.M. The function V gives the number of visitors in a museum h hours after it open

liubo4ka [24]

Answer:

What the equation is telling us is that after opening for 1 hour 15 minutes, there were 28 visitors

Step-by-step explanation:

The function we are given is ;

V(1.25) = 28

what this mean is that the number of visitors in the museum after 1.25 hours of opening is 28

1.25 hours is same as 1 hour (0.25 * 60) minutes

What is in the bracket is trying to convert the 0.25 hours to minutes

Since 1 hour is 60 minutes, 0.25 will be (0.25 * 70)

Which is 1 hour 15 minutes

So after opening for 1 hour 15 minutes, the museum had 28 visitors

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2 years ago

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Find 70% of 200 <br> I’m unsure of this pls can I have some help

elena-s [515]

Answer:

140

Step-by-step explanation:

70% 200

---------- * ---------- = 70*2 = 140

100% 1

you cross out the 2 zeros from the 100% so it will be one then croos out the 2 zeros from 200 and you will have 70 * 2 and you will get 140

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1 year ago

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1. a) What is the area of this square with sides of 5x4y²?

UNO [17]

Area=?
A=a^2
A=(5x4y^2)^2
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Genesis throws a ball up in the air. The graph below shows the height of the ball hh in meters after tt seconds. Find the interv

Juli2301 [7.4K]

We conclude that the interval in which the function decreases is (1.5, 3]

<h3>In which interval is the ball's height decreasing?</h3>

The ball is decreasing when the graph, reading from left to right, is going downwards.

Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.

And we can see that the vertex is at x = 1.5

And we also see that the graph of the function ends at x = 3.

Then we conclude that the interval in which the function decreases is (1.5, 3]

If you want to learn more about parabolas:

brainly.com/question/4061870

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1 year ago