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2 years ago

A triangle has one side length of 9

Mathematics

1 answer:

Lilit [14]2 years ago

3 0

Answer:

You did not give any other clues so logically it is not possible to find the other length unless an angle is given. So if we think that the triangle is a right angle triangle then we can use the pythagorean theorem formula to calculate the other side which is:

c^2=a^2 + b^2

Now we know can say that one side 9 cm is,"a" and 12 cm is, "b" Now place the formula values accordinly to find, "c"

c^2= 9^2 + 12^2

c= square root of 225

c= 15

The exact value for the third side can be 15cm. But without any other hints it is not possible to find the other side length of the triangle.

Brainliest pls if you found it helpful!

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In an election to the U.S. Senate, one candidate has popular support of 53% and the other has support of 47%. On election eve, a

Irina18 [472]

Answer:

a) 94.63% probability that the poll will predict the correct winner.

b) 69.15% probability of correct prediction. The lesser sample size leads to more variation, which means that the probability of correct prediction is smaller than in (a).

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

(a) Compute a normal approximation with continuity correction of the probability that the poll will predict the correct winner.

The correct winner is the one with 53% of the votes.

We have that $p = 0.53, n = 750$ .

$E(X) = np = 750*0.53 = 397.5$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{750*0.53*0.47} = 13.67$

The pool will correctly predict the winner if the candidate that has a support of 53% gets more than half the votes.

So we have to find P(X > 750/2) = P(X > 375)[/tex]

Using continuity correction, this is P(X > 375 + 0.5) = P(X > 375.5), which is 1 subtracted by the pvalue of Z when X = 375.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{375.5 - 397.5}{13.67}$

$Z = -1.61$

$Z = -1.61$ has a pvalue of 0.0537

1 - 0.0537 = 0.9463

94.63% probability that the poll will predict the correct winner.

(b) What happens to the probability of correct prediction if they had conducted the poll over only 100 voters?

Lesser sample size leads to more variation, which means that the probability of correct prediction will be smaller.

Now $n = 100$

Then

$E(X) = np = 100*0.53 = 53$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.53*0.47} = 4.99$

Also P(X > 50), which using continuity correction is P(X > 50.5).

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{50.5 - 53}{4.99}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085

1 - 0.3085 = 0.6915.

69.15% probability of correct prediction. The lesser sample size leads to more variation, which means that the probability of correct prediction is smaller than in (a).

3 0

3 years ago

The distance from Clinton to Greenville is 124 miles. To find the speed of a car, use the expression d divided t, where d repres

Bezzdna [24]

Step-by-step explanation:

time = 2 hours

distance travelled(d) = 124 miles

speed = d/t

= 124/2

= 62 miles per hour

Therefore, the speed of car is 62 miles per hour.

6 0

2 years ago

Read 2 more answers

The positive integer k has exactly two positive prime factors, 3 and 7. if k has a total of 6 positive factors, including 1 and

Sav [38]

I think there are two solutions, 63 or 147:

63 = 3² x 7, factors 1 | 3 | 7 | 9 | 21 | 63<span>
147 = 3 x 7</span>², factors 1 | 3 | 7 | 21 | 49 | 147

5 0

2 years ago

WILL UPVOTE!!!

Ludmilka [50]

The question wants us to find 3 times the volume of the pool.
This is because we are told that the pool must be filled 3 times during the summer and asked how many cubic feet of water is required to fill the pool all summer.

Step 1: Find the volume of the pool.
Volume is calculated by multiplying length by width by height.
Pool length = 5 ft.
Pool width = 4 ft.
Pool height = 2 ft.
Pool volume = 5 • 4 • 2
5 • 4 • 2 = 40
The volume of the pool is 40 cubic feet.

Step 2: Find 3 times the volume of the pool.
Volume = 40 ft.^3
3 times volume = 3 • 40 ft.^3
3 • 40 ft.^3 = 120 ft.^3
3 times the volume of the pool is 120 cubic feet.

Answer:
The pool requires 120 cubic feet of water in order to be filled enough over the course of the summer.

Hope this helps!

6 0

3 years ago

Read 2 more answers

Which y values are represented on the graph below?

Zanzabum

..........................

3 0

2 years ago