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2 years ago

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The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on

the parabola. Which equation can be used to model the image of the lens?
y = -1/5 (x – 2)(x + 3)
y = -1/3(x – 2)(x + 3)
y = -1/2 (x + 2)(x – 3)
y = 1/4 (x + 2)(x – 3)

2 answers:

Rus_ich [418]2 years ago

7 0

y = (x + 2)(x – 3)

this is 100% used to model the image of the lens.

answer: c (on ed. quiz)

Nezavi [6.7K]2 years ago

4 0

For x-intercepts "b" and "c", a quadratic can be written as
y = a(x -b)(x -c)

You know the x-intercepts, so you can write the equation as
y = a(x +2)(x -3) . . . . . . eliminates the first two answer choices

Substituting (x, y) = (-1, 2), you have
2 = a(-1+2)(-1-3) = -4a
Then dividing by -4 gives
-2/4 = a = -1/2 . . . . . corresponds to the third answer choice

The appropriate selection is
y = -1/2 (x + 2)(x - 3)

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3,298,076 in expanded form

LekaFEV [45]

3,000,000+200,000+90,000+8,000+70+6

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2 years ago

The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard devia

Alla [95]

Answer:

$z=5$

Step-by-step explanation:

We have been given that the The annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard deviation of $4,000.

To solve our given problem we will use z-score formula.

$z=\frac{x-\mu}{\sigma}$ where,

$z=\text{z-score}$ ,

$x=\text{Sample score}$ ,

$\mu=\text{Mean}$ ,

$\sigma=\text{Standard deviation}$

Upon substituting our given values in z-score formula we will get,

$z=\frac{54,000-34,000}{4,000}$

$z=\frac{20,000}{4000}$

$z=5$

Therefore, the z-score of a company employee who makes an annual salary of $54,000 is 5.

4 0

2 years ago

Read 2 more answers

Kayleigh babysat for 11 hours this week. That was 5 fewer than 2/3 as many hours as she babysat last week, h. Write an equation

lukranit [14]

Answer: The answer is $\textup{x}=\dfrac{2}{3}\textup{h}-5.$

Step-by-step explanation: Given that Kayleigh babysat for 11 hours the present week. Also, this was 5 less than two-third of the number of hours she babysat last week, which is represented by 'h'.

We are to write an equation to represent the number of hours she babysat each week.

So, for that, let 'x' be the number of hours she babysat this week. Then, according to the question, we can write

$\textup{x}=\dfrac{2}{3}\textup{h}-5.$

Also, it is given that

$\textup{x}=11.$

Therefore,

$11=\dfrac{2}{3}\textup{h}-5\\\\\Rightarrow \dfrac{2}{3}\textup{h}=16\\\\\Rightarrow \textup{h}=24.$

Hence, using the above relation, we can find the number oh hours Keyleigh babysat each week.

Thus, the required equation is

$\textup{x}=\dfrac{2}{3}\textup{h}-5,$

where, 'x' and 'h' are the number of hours she sat this week and last week respectively.

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2 years ago

Statistics In the manual “How to Have a Number One the Easy Way,” it is stated that a song “must be no longer than three minutes

dimaraw [331]

Answer:

We conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Step-by-step explanation:

We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.

Assume that the standard deviation of song lengths is 54.5 sec.

Let $\mu$ = <u><em>population mean length of the songs</em></u>

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}

Alternate Hypothesis, $H_A$ : $\mu$ > 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is <u>One-sample z-test statistics </u>because we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean length of songs = 252.5 seconds

$\sigma$ = population standard deviation = 54.5 seconds

n = sample of current hit songs = 40

So, <u><em>the test statistics</em></u> = $\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }$

= 4.932

The value of z-test statistics is 4.932.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.

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2 years ago

Lesson 1-1: The periodic comet named Johnson has been seen at every return since its discovery in 1949, as shown in the table be

stiks02 [169]

Answer:

Step-by-step explanation:

Occurrence Year seen Difference

1 1949 -

2 1956 1956 - 1949 = 7

3 1963 1963 - 1956 = 7

4 1970 1970 - 1963 = 7

Difference between each successive term of year seen = 7 years

Therefore, there is a common difference of 7 years between each successive term.

Function defining the year seen will be a linear function and will increase in the same pattern. (multiple of 7 years)

2017 - 1970 = 47 (It's not the multiple of 7)

2018 - 1970 = 48 (It's not the multiple of 7)

2019 - 1970 = 49 (multiple of 7)

2020 - 1970 = 50 (It's not the multiple of 7)

Therefore, comet will be seen next in 2019.

Option (C) will be the answer.

If a person is born in 2005

Then difference between 2005 and 1949 = 56 years

Number of times comet seen after 1949 = $\frac{56}{7}=8$ times

Total number of comet seen in the lifetime = 8 times

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2 years ago