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2 years ago

Leah flips a coin, then spins a spinner with 3 equal sides colored red, green, and blue. what is the probability that she:

Mathematics

1 answer:

pickupchik [31]2 years ago

5 0

Answer:

the probability that she rolls a blue is 33.3% or 1/3. the probability that she lands heads is 50% or 1/2

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The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago

45% of the students in Primary 5 are boys. There are 165 girls. How many more girls than boys are there in primary 5?

bezimeni [28]

Answer:

30 more

Step-by-step explanation:

hope it helps friend.

5 0

2 years ago

How to find volume of a prism

docker41 [41]

Answer:

- HOW TO FIND VOLUME OF PRISM -

1st step - Write the formula for finding the volume of a regular pentagonal prism. The formula is V = [1/2 x 5 x side x apothem] x height of the prism.

2nd step - Find the area of the pentagonal base face. Let's say the length of a side is 6 cm and the length of the apothem is 7 cm.

3rd step - Find the height. Let's say the height of the shape is 10 cm.

4th step - Multiply the area of the pentagonal base face times the height. ...

and last step - State your answer in cubic units.

Step-by-step explanation:

:):):)

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2 years ago

Find the equation of a line in slope intercept form going through the point (-2, 9) with a slope of -4.

bija089 [108]

Answer

4x+y=11

Step-by-step explanation:

8 0

3 years ago

What is the graph of the function f(x)=−⌊x+2⌋?

Nina [5.8K]

Answer:

Step 1: Flip the equation.

−x−2=y

Step 2: Add 2 to both sides.

−x−2+2=y+2

−x=y+2

Step 3: Divide both sides by -1.

−x

−1

y+2

−1

x=−y−2

Step-by-step explanation:

8 0

3 years ago