All categories

3 years ago

Please solve this question

Mathematics

1 answer:

larisa86 [58]3 years ago

8 0

Answer:

P (A) = 0.45

Step-by-step explanation:

The addition rule of probability states that:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Given:

$P(A\cup B) = 0.7\\P(A\cap B) = 0.1\\P(B) = 0.35$

Compute the value of P (A) as follows:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\P(A)=P(A\cup B) + P(A\cap B) - P(B)\\= 0.7 +0.1-0.35\\=0.45$

Thus, the probability of <em>A</em> is, P (A) = 0.45.

You might be interested in

A cylindrical water tank is 1.2 meters high and has a diameter of 4.6 meters. Approximately how much cubic meters of water will

uranmaximum [27]

So what you need to do is find the volume and divide it by 2.

6 0

2 years ago

Read 2 more answers

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

A man walks iinto a store with 25.50 and walks out with 5.25 how much did he spend?

san4es73 [151]

He spent exactly 20.25, so it's A.

7 0

2 years ago

Read 2 more answers

PLEASE HELP MEEEEE!!!!

defon

Answer:

Step-by-step explanation:

The leading coefficient is the coefficient with a variable with the greatest exponent.The exponent is the number you would say "the power to". What I mean is let's say you have this number: $3^{2}$ . The exponent would be 2 in this equation because it's saying what power 3 is too. Therefore, 5 is the leading coefficient.

8 0

3 years ago

Write an equation in slope-intercept form? (12,5); y=2/3x-1

Marina86 [1]

Answer:

y-5=2/3x(12-x) would be point form

3 0

3 years ago

Please solve this question ​

Please solve this question