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4 years ago

Graph the function g(x)=-6(x-2)(x)

Mathematics

2 answers:

hichkok12 [17]4 years ago

7 0

It's the quadratic function. The graph is a parabola.

$g(x)=-6(x-2)(x)$

x-intercepts:

$g(x)=0\to-6(x-2)(x)=0\iff x-2=0\ \vee\ x=0\\\\x=2\ \vee\ x=0$

y-intercept:

$g(0)=-6(0-2)(0)=0$

The vertex (h, k)

$h=\dfrac{0+2}{2}=\dfrac{2}{2}=1\\\\k=g(h)\to k=g(1)=-6(1-2)(1)=-6(-1)(1)=6$

Vertex: (1, 6).

timama [110]4 years ago

6 0

The function, when graphed, looks like this:

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Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches. If

Elza [17]

Answer:

0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches.

This means that $\mu = 71.3, \sigma = 2.1$

Sample of 36:

This means that $n = 36, s = \frac{2.1}{\sqrt{36}} = 0.35$

Find the probability that they have a mean height greater than 72.3 inches.

This is 1 subtracted by the pvalue of Z when X = 72.3. So

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

By the Central Limit Theorem

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

$Z = \frac{72.3 - 71.3}{0.35}$

$Z = 2.86$

$Z = 2.86$ has a pvalue of 0.9979

1 - 0.9979 = 0.0021

0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.

7 0

3 years ago

Solve

larisa86 [58]

Answer:

21.9

Step-by-step explanation:

12.34 + 9.56 = 21.9

Therefore, they picked 21.9 pounds of fruit alltogether

4 0

3 years ago

Sebastian is a 25 year old single male. He currently lives at home with his parents. His net worth income from work is $914.42 p

sergij07 [2.7K]

Step-by-step explanation:

$914.42 + $110= $1024.42 a month

Per month he pays $115 + $14 + $100 + $45 + $70 + $100 + $40

That comes to a total of $484 a month in expenses.

Subtract $484 from $1024.42

Assuming the side hustle is consistent that leaves $540.42 in additional income.

If he wants to afford the house rent, the best thing he can do is look for a better job. If that cannot be done for whatever reason, he should drop the Netflix subscription(+14), not go to the gym(+70), keep his pocketbook tight and not buy gifts(+40), and buy bulk type items from stores.

If he can make his dollar go farther by spending his money on bigger items of food he could probably spend only $85 a month on food.

With this advice he could save an additional $139 a month.

He now has $679. 42

He should also look at finding a cheaper bus pass around that $75 dollar range or just pay the fair whenever he gets on out of pocket (ONLY IF HE IS GOING TO WORK)

That totals out at $754.42

He can now afford rent.

7 0

2 years ago

A recipe calls for 34 cup of sugar for every 12 teaspoon of cinnamon. What is the unit rate in teaspoons of cinnamon per cup of

andrezito [222]

Answer:

6/17 tsp cinnamon per cup of sugar

Step-by-step explanation:

12/34 then simplify the fraction

8 0

3 years ago

Read 2 more answers

The useful life of a certain piece of equipment is determined by the following formula: u=(8d)/h^2, where u is the useful life o

Anni [7]

Answer:

The correct answer is E.

Step-by-step explanation:

First I look for the relationships between the coefficients. The first term corresponds to the base value.

$\frac{8*d}{h^{2}} = \frac{8}{1} * \frac{d}{h^{2} }$

The second term corresponds to the value obtained when the density of the underlying material is doubled and the daily usage of the equipment is halved.

$\frac{2*8*d}{(0,5*h)^{2}} = \frac{16*d}{0,25 * h^{2}} = \frac{16}{0,25} * \frac{d}{h^{2} }$

With the I get the ratio of coefficients of $\frac{d}{h^{2}}$ :

$\frac{8}{1}$ = 8

$\frac{16}{0,25}$ = 64

Now I calculate the percentage increase in the useful life of the equipment as:

% = $\frac{64}{8}$ * %100 = %800

3 0

4 years ago