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2 years ago

4

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Whi

ch equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?

1 answer:

cestrela7 [59]2 years ago

3 0

Number of x intercepts in this equation is 2 because max power in the function is 2. number of x intercepts is determined by "highest power".

let x1 represent first x intercept and
let x2 represent second x intercept

Formula for finding average of x intercepts is logicaly:
Avg = (x1 + x2)/2

we want to find x1 and x2
4x^2 - 24x + 20 = 0
x^2 - 6x + 5 = 0

$x = \frac{6 +- \sqrt{6^2 - 4*1*5} }{2*1}$
x1 = 5
x2 = 1

Avg = 3

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Suppose that a company's sales were $1,000,000 6 years ago and are $9,000,000 at the end of the 6 years. Find the geometric mean

Dmitriy789 [7]

Answer:

The geometric mean growth rate of sales is 1.4422.

Step-by-step explanation:

We have two sales values, one from 6 years ago and the other from now.

We have to calculate the geometric growth rate of sales.

We have:

$y(-6)=1,000,000\\\\y(0)=9,000,000$

We can write the relation between these two values as:

$y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422$

The geometric mean growth rate of sales is 1.4422.

6 0

2 years ago

A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights

scoray [572]

Answer:

$Mean = 6.07$

$Median = 7$

$Mode = 7$

Step-by-step explanation:

Given

$Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9$

$n = 15$

Solving (a): The mean

Mean is calculated as:

$Mean = \frac{\sum x}{n}$

This gives:

$Mean = \frac{5+ 3+ 7+ 8+ 0+ 1+ 0+ 5+ 12+ 10+ 7+ 6+ 7+ 11+ 9}{15}$

$Mean = \frac{91}{15}$

$Mean = 6.07$

Solving (b): The median

Sort the data in ascending order:

$Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9$

$Sorted: 0\ 0\ 1\ 3\ 5\ 5\ 6\ 7\ 7\ 7\ 8\ 9\ 10\ 11\ 12$

The median is:

$Median = \frac{n + 1}{2}th$

$Median = \frac{15 + 1}{2}th$

$Median = \frac{16}{2}th$

$Median = 8th$

The 8th item on the sorted dataset is 7; So:

$Median = 7$

Solving (c): The mode

$Mode = 7$

Because it has a frequency of 3 (more than any other element of the dataset).

6 0

2 years ago

If you are one of the first 100 people to join a new health club, you are charged a joining fee of $49. Otherwise, you are charg

Drupady [299]

Answer:

a) Total cost = 49 + 38.75m

b) Total cost = 149 + 38.75m

c) The graphs of the lines are parallel and both has slope of - 2.5

d)Difference in total cost = $132.5

Step-by-step explanation:

Total cost , TC = Initial membership fee + monthly charges

a) TC = 49 + 38.75m

b)TC = 149 + 38.75m

d) 149 + 38.75(6months) = 381.5

49 + 38.75(12months) = 514

Difference in total cost = 514 -381.5 = $132.5

7 0

2 years ago

An oblique prism with a square base of edge length x units has a volume of One-halfx3 cubic units. Which expression represents t

lara [203]

Answer:one-half x units

Step-by-step explanation:

Given

Prism has a square base with length $x\ units$

If the volume of prism $V=\frac{1}{2}x^3\ units$

We know

$Volume=base\ area\times height$

Base area $=x\times x=x^2\ units$

$height=\frac{Volume}{area}$

$height=\frac{\frac{1}{2}x^3}{x^2}$

$height=\frac{x}{2}\ units$

7 0

2 years ago

Read 2 more answers

Problem 2.2.4 Your Starburst candy has 12 pieces, three pieces of each of four flavors: berry, lemon, orange, and cherry, arrang

kkurt [141]

Answer:

a) P=0

b) P=0.164

c) P=0.145

Step-by-step explanation:

We have 12 pieces, with 3 of each of the 4 flavors.

You draw the first 4 pieces.

a) The probability of getting all of the same flavor is 0, because there are only 3 pieces of each flavor. Once you get the 3 of the same flavor, there are only the other flavors remaining.

b) The probability of all 4 being from different flavor can be calculated as the multiplication of 4 probabilities.

The first probability is for the first draw, and has a value of 1, as any flavor will be ok.

The second probability corresponds to drawing the second candy and getting a different flavor. There are 2 pieces of the flavor from draw 1, and 9 from the other flavors, so this probability is 9/(9+2)=9/11≈0.82.

The third probability is getting in the third draw a different flavor from the previos two draws. We have left 10 candys and 4 are from the flavor we already picked. Then the third probabilty is 6/10=0.6.

The fourth probability is getting the last flavor. There are 9 candies left and only 3 are of the flavor that hasn't been picked yet. Then, the probability is 3/9=0.33.

Then, the probabilty of picking the 4 from different flavors is:

$P=1\cdot\dfrac{9}{11}\cdot\dfrac{6}{10}\cdot\dfrac{3}{9}=\dfrac{162}{990}\approx0.164$

c) We can repeat the method for the previous probabilty.

The first draw has a probability of 1 because any flavor is ok.

In the second draw, we may get the same flavor, with probability 2/11, or we can get a second flavor with probability 9/11. These two branches are ok.

For the third draw, if we have gotten 2 of the same flavor (P=2/11), we have to get a different flavor (we can not have 3 of the same flavor). This happen with probability 9/10.

If we have gotten two diffente flavors, there are left 4 candies of the picked flavors in the remaining 10 candies, so we have a probabilty of 4/10.

For the fourth draw, independently of the three draws, there are only 2 candies left that satisfy the condition, so we have a probability of 2/9.

For the first path, where we pick 2 candies of the same flavor first and 2 candies of the same flavor last, we have two versions, one for each flavor, so we multiply this probability by a factor of 2.

We have then the probabilty as:

$P=2\cdot\left(1\cdot\dfrac{2}{11}\right)\cdot\left(\dfrac{9}{10}\cdot\dfrac{2}{9}\right)+\left(1\cdot\dfrac{9}{11}\cdot\dfrac{4}{10}\cdot\dfrac{2}{9}\right)\\\\\\P=2\cdot\dfrac{36}{990}+\dfrac{72}{990}=\dfrac{144}{990}\approx0.145$

5 0

2 years ago