Find the value of c that makes p2 + 18p + c a perfect square.

Layana’s house is located at (2 and two-thirds, 7 and one-third) on a map. The store where she works is located at (–1 and one-t

NeTakaya

We have been given that Layana’s house is located at $(2\frac{2}{3}, 7\frac{1}{3})$ on a map. The store where she works is located at $(-1\frac{1}{3}, 7\frac{1}{3})$ .

We are asked to find the distance from Layana’s home to the store

We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

$2\frac{2}{3}\Rightarrow \frac{8}{3}$

$7\frac{1}{3}\Rightarrow \frac{22}{3}$

$-1\frac{1}{3}\Rightarrow -\frac{4}{3}$

Now we will use distance formula to solve our given problem.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting coordinates of our given point in above formula, we will get:

$D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}$

$D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}$

$D=\sqrt{0+(\frac{8+4}{3})^2}$

$D=\sqrt{(\frac{12}{3})^2}$

$D=\sqrt{(4)^2}$

$D=4$

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

3 0

3 years ago

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612.00 in scientific notation

FinnZ [79.3K]

612.00 in scientific notation is 6.12×10^2

6 0

3 years ago

g "They hired an analyst who collected a random sample of 40,361 Game of Thrones fans, and found that 8,337 of those fans said t

Viktor [21]

Answer:

The lower bound for a 90% confidence interval is 0.2033.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 40361, \pi = \frac{8337}{40361} = 0.2066$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2066 - 1.645\sqrt{\frac{0.2066*0.7934}{40361}} = 0.2033$

The lower bound for a 90% confidence interval is 0.2033.

6 0

3 years ago

Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? A. She showed that an explicit formul

Step2247 [10]

Answer:

Option D is correct

Step-by-step explanation:

Option D is correct

Being an arithmetic sequence there will be common difference between the consecutive terms

Option A is incorrect because it is not necessary that explicit formula is an arithmetic sequence we can create explicit formula for any sequence

Option B is incorrect because recursive formula can be created for any sequence for geometric series also.

Option C is incorrect because the sequence that has constant ratio is the geometric sequence not an arithmetic sequence.

6 0

3 years ago

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A student wants to know how many 1 cm cubes will fit into a 10 cm by 8cm by 12cm box what is the measure is the student trying t

Serga [27]

We know that
[volume of the box]=10*8*12-------> 960 cm³

[volume of 1 cube]= 1 cm*1 cm*1 cm-----> 1 cm³
960/1----> 960 cubes

therefore

the answer is
the option D volume

4 0

3 years ago

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