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adelina 88 [10]
2 years ago
12

What is the value of x ?

Mathematics
1 answer:
Ivan2 years ago
8 0

Answer:

x = 3

Step-by-step explanation:

Given two secants drawn from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

x(x + 21) = (x + 1)(x + 1 + 14)

x² + 21x = (x + 1)(x + 15) ← expand using FOIL

x² + 21x = x² + 16x + 15 ( subtract x² + 16x from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

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Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election. Assume the probab
Liono4ka [1.6K]

Answer:

0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes 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 distributions 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)}.

153 voters:

This means that n = 153

Assume the probability that a given registered voter will vote in the presidential election is 63%.

This means that p = 0.63

Mean and standard deviation:

\mu = E(X) = np = 153(0.63) = 96.39

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.63*0.37} = 5.97

Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election.

Using continuity correction, this is: P(X \geq 88 - 0.5) = P(X \geq 87.5), which is 1 subtracted by the p-value of Z when X = 87.5.

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

Z = \frac{87.5 - 96.39}{5.97}

Z = -1.49

Z = -1.49 has a p-value of 0.0681.

1 - 0.0681 = 0.9319

0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.

5 0
2 years ago
Y = n(n + 1)<br><br> please help, thanks!!!
Yuri [45]

Answer:

Y=n^2+n

Step-by-step explanation:

6 0
2 years ago
1 a. Solve, and plot the solution set.<br>-what is the answer​
Keith_Richards [23]

Answer:

4r43r43

Step-by-step explanation:

7 0
3 years ago
Is the triangle an acute, isosceles, obtuse, or right?
Trava [24]

Step-by-step explanation:

k =70 because all triangles angles add up to 180° and it's an acute angle cause all the angles are lower than 90° hope this helps

5 0
2 years ago
X^2-7x=18<br><br> solve for x <br> please show work
zloy xaker [14]
So the answer is, x1=-2, x2=9
x^2-7x=18
x^2-7x-18=0
x^2+2x-9x-18=0
x*(x+2)-9(x+2)=0
(x+2)*(x-9)=o
x+2=0
x-9=0
X=-2
X=9
I hope u understand!
3 0
3 years ago
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