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3 years ago

Y=(x-4)(x+20) find vertex

1 answer:

7 0

Y = (x-4)(x+20) ===> 0 = (x-4)(x+20)

that means the roots of that quadratic are x = 4 and x = -20.

now, the vertex will be between these two guys, right in between.

from -20 to 4 there are 24 units, half-way of that is 12 units, so, if we move from -20, 12 units to the right or towards 4, we'll end up at -20 + 12 = -8.

so, the vertex's x-coordinate is -8 then, what's "y" anyway?

y = (x-4)(x+20) x = -8

y = [(-8) - 4] [(-8) + 20]

y = (-12) ( 12)

y = -144

therefore, the vertex is at (-8 , -144)

You might be interested in

What is the slope of the line through (-4,2) (3,-3)

photoshop1234 [79]

Answer:

-5/7

Step-by-step explanation:

Find the change between the two x values, which is seven

Find the change between the two y values, which is -5

With slopes, the y always goes over the x, making your answer -5/7

3 0

2 years ago

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

PLEASE HELP<br> 1/4 is to 1 1/4 as 2 is to b

Taya2010 [7]

B = 22 because 1/4 x 11 = 11/4 so 2 x 11 = 22

3 0

2 years ago

How many groups of of 5/6 are in 1

zysi [14]

Answer:

6/5

Step-by-step explanation:

to find the number of 5/6 's in 1 , divide 1 by by 5/6 . when dividing by a fraction , rewrite it as multiplying by the reciprocal

4 0

2 years ago

How do it do this ????

V125BC [204]

Because he drove 1542.75 miles in 3 days, you would have to divide 1542.75 by 3 to figure out how many miles he drove in one day.

1542.75/3 = 514.25

Then to figure out how many miles he drove per hour, you would divide 514.25 by 8.5, which is the same as 8 1/2 hours.

514.25/8.5 = 60.5

So the answer is 60.5 mph

4 0

3 years ago