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lubasha [3.4K]
3 years ago
10

What is the vertex of f(x)=5^2+20-16

Mathematics
1 answer:
zepelin [54]3 years ago
4 0
The given equation is f(x) = 29. The graph is a horizontal line, which has no vertex. Perhaps you intend
.. f(x) = 5x^2 +20x -16
.. = 5(x^2 +4x +4) -16 -20
.. = 5(x +2)^2 -36

The vertex is (-2, -36)

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Which rule describes the transformation? picture below​
Mekhanik [1.2K]

Answer:

Try D) rotation 180 degrees about the origin.

Step-by-step explanation:

When you look at it, it appears to move 180 degrees about that origin.

Hope this helps! Let me know!

6 0
3 years ago
Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58​, what is the
aliina [53]

Answer:

0.36% probability that fewer than half in your sample will watch news​ videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

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)}.

In this problem, we have that:

n = 250, p = 0.58

So

\mu = E(X) = 250*0.58 = 145

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80

If the population proportion of adults who watch news videos is 0.58​, what is the probability that fewer than half in your sample will watch news​ videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

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

Z = \frac{124 - 145}{7.8}

Z = -2.69

Z = -2.69 has a pvalue of 0.0036

0.36% probability that fewer than half in your sample will watch news​ videos

8 0
3 years ago
Read 2 more answers
There is a bag with only red marbles and blue marbles.The probability of randomly choosing a red marble is59.There are 63 marble
Elis [28]

Answer:

37

Step-by-step explanation:

59 percent times 63 in total marbles is 37

7 0
2 years ago
5-2x=15<br><img src="https://tex.z-dn.net/?f=5%20-%202x%20%3D%2015" id="TexFormula1" title="5 - 2x = 15" alt="5 - 2x = 15" align
padilas [110]
<span>5-2x=15

</span>5-2x=15 \\  \\ -2x= 15-5  \\  \\ -2x= 10 \\  \\ x=  \dfrac{10}{-2} \to  \boxed{x= -5}<span>
</span>
6 0
3 years ago
The weekly sales of Honolulu Red Oranges is given by q = 990 − 22p. Calculate the price elasticity of demand when the price is $
elena55 [62]

Answer:

E = -2. The demand is going down by 2% per 1% increase in price at that price level.

The price that gives a maximum revenue is $22.5. The maximum revenue is $9112.5

Step-by-step explanation:

The overall demand formula: Q = aP + b

Q = 990 - 22P

<u>Demand elasticity:</u>

At P = $30, the Q = 990 - 22×30 = 330. a = \frac{dQ}{dP} = -22

The formula for demand elasticity: E = \frac{dQ}{dP}×\frac{P}{Q}

Demand elasticity at $30: E = -22 × \frac{30}{330} = -2

So, The demand will be going down by 2% if 1% increase in price.

<u>Revenue:</u>

R = P×Q = P×(990 - 22P) = -22P² - 990P

R' = -44P - 990. The revenue is maximum when R' = 0

⇔0 = -44P - 990 ⇔ P = $22.5

At the P = $22.5, the Q = 990 - 22×22.5 = 495.

The maximum revenue = $22.5×495 = $11,137.5

7 0
3 years ago
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