A right triangle has a hypotenuse of 10 cm and one leg that measures 5 square 3 what is the length of the other leg

Does anybody know the answer to this ?

melisa1 [442]

Answer:

Step-by-step explanation:

5 0

3 years ago

2 4/5 divided by 2/15

REY [17]

Answer:

21

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The prior probabilities for events A1 and A2 are P(A1) = 0.35 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(

forsale [732]

Answer:

Step-by-step explanation:

Hello!

Given the probabilities:

P(A₁)= 0.35

P(A₂)= 0.50

P(A₁∩A₂)= 0

P(BIA₁)= 0.20

P(BIA₂)= 0.05

a)

Two events are mutually exclusive when the occurrence of one of them prevents the occurrence of the other in one repetition of the trial, this means that both events cannot occur at the same time and therefore they'll intersection is void (and its probability zero)

Considering that P(A₁∩A₂)= 0, we can assume that both events are mutually exclusive.

b)

Considering that $P(BIA)= \frac{P(AnB)}{P(A)}$ you can clear the intersection from the formula $P(AnB)= P(B/A)*P(A)$ and apply it for the given events:

$P(A_1nB)= P(B/A_1) * P(A_1)= 0.20*0.35= 0.07$

$P(A_2nB)= P(B/A_2)*P(A_2)= 0.05*0.50= 0.025$

c)

The probability of "B" is marginal, to calculate it you have to add all intersections where it occurs:

P(B)= (A₁∩B) + P(A₂∩B)= 0.07 + 0.025= 0.095

d)

The Bayes' theorem states that:

$P(Ai/B)= \frac{P(B/Ai)*P(A)}{P(B)}$

Then:

$P(A_1/B)= \frac{P(B/A_1)*P(A_1)}{P(B)}= \frac{0.20*0.35}{0.095}= 0.737 = 0.74$

$P(A_2/B)= \frac{P(B/A_2)*P(A_2)}{P(B)} = \frac{0.05*0.50}{0.095} = 0.26$

I hope it helps!

5 0

3 years ago

Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a

Brums [2.3K]

Answer:

The minimum sample size is $n =135$

Step-by-step explanation:

From the question we are told that

The confidence interval is $( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)$

The margin of error is $E = 0.1$

Generally the sample proportion can be mathematically evaluated as

$\r p = \frac{ upper \ limit + lower \ limit }{2}$

$\r p = \frac{ 0.51 + 0.44}{2}$

$\r p = 0.475$

Given that the confidence level is 98% then the level of significance can be mathematically evaluated as

$\alpha = 100 - 98$

$\alpha = 2\%$

$\alpha =0.02$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

The value is

$Z_{\frac{\alpha }{2} } = 2.33$

Generally the minimum sample size is evaluated as

$n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )$

$n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )$

$n =135$

6 0

3 years ago

an equation of the line of best fit for a data set is y=0.76x+8.35 describe what happens to the line of best fit when each y-val

elixir [45]

The y-intercept of the line would change but the slope would not.

Slope is the rate of change of a line. If the y-values all decrease the same amount, the rate that the line is changing will not change. For example, let's take the points (5, 6) and (3, 2). The slope is given by (6-2)/(5-3) = 4/2 = 2. Now let's decrease the y-coordinates all by 2:
(5, 4) and (3, 0)
The slope now would be (4-0)/(5-3) = 4/2 = 2.

By changing the y-values the same amount, the amount of difference between them stays the same, and so does the rate of change of the line.

Since we shifted the y-values down, however, this moves the line down on the graph, which will change the y-intercept.

6 0

2 years ago