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3 years ago

Find the length of the missing side when x=3. Round the answer to the nearest tenth.

Mathematics

1 answer:

Juliette [100K]3 years ago

5 0

Answer/Step-by-step explanation:

The missing length can be found by applying pythagorean theorem. Thus:

Missing length = √((8x)² - (2x)²)

Missing length = √(64x² - 4x²)

✔️Missing length = √(60x²) = 2x√15

Plug in the value of x which is 3

Missing length = 2*3√15

✔️Length = 6√5

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Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part?

lbvjy [14]

The complex number is represented as 2 + 3i. The conjugate of the complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign. Therefore, the correct answer is option B. The conjugate of the complex number is 2 − 3i.

4 0

3 years ago

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The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of m

UkoKoshka [18]

Answer:

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

$X \sim N(14.7,3.7)$

Where $\mu=14.7$ and $\sigma=3.7$

Since the distribution of X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we have;

$\mu_{\bar X}= 14.70$

$\sigma_{\bar X} =\frac{3.7}{\sqrt{40}}= 0.59$

Step-by-step explanation:

Assuming this question: The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 14.7 minutes and a standard deviation of 3.7 minutes. Let R be the mean delivery time for a random sample of 40 orders at this restaurant. Calculate the mean and standard deviation of $\bar X$ Round your answers to two decimal places.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

$X \sim N(14.7,3.7)$

Where $\mu=14.7$ and $\sigma=3.7$

Since the distribution of X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we have;

$\mu_{\bar X}= 14.70$

$\sigma_{\bar X} =\frac{3.7}{\sqrt{40}}= 0.59$

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3 years ago

F(n)=3n-15/10 what's the inverse

slavikrds [6]

To find the inverse function, interchange the variables and solve for y.
f^-1(n) = 1/2 + n/3

4 0

3 years ago

Read 2 more answers

In a group of 10 kittens, 5 are female. Two kittens are chosen at random. a) Create a probability model for the number of male

olya-2409 [2.1K]

Answer:

(b) Expected number of male kitten E(x) = 1

(c) Standard deviation is ± $\frac{2}{3}$ .

Step-by-step explanation:

Given that,

Number of kittens in a group are 10. Out of these 5 are female.

To find:- (a) create a probability model of male kitten chosen.

So, total number of kitten = 10

number of female kitten = 5

then, Number of male kitten = $10-5= 5$

Now total number of ways to choosing two kittens from group of 10 = $^{10} C_{2}$

= $\frac{10!}{2!\times8!}$

= $45$

for choosing (i) No male P(x=0) = P(Two female) = $\frac{^{5} C_{2}}{45}$

= $\frac{2}{9}$

(ii) 1 male P(x=1) = P(1 male and 1 female) = $\frac{^{5} C_{1}\times^{5} C_{1}}{45}$ = $\frac{25}{45}$ = $\frac{5}{9}$

(iii) 2 male P(x=2)= P(2 male) = $\frac{^{5} C_{2}}{45}$ = $\frac{2}{9}$

$x_{i}$ 0 1 2

P(X= $x_{i}$ ) $\frac{2}{9}$ $\frac{5}{9}$ $\frac{2}{9}$

(b) what is expected number of male kittens chosen ?

Expected number of male kitten E(x) = $o\times \frac{2}{9} + 1\times \frac{5}{9} + 2\times\frac{2}{9}$

= $1$

(c) what is standard deviation ?

$\sigma(x) = \sqrt{ (E(x^{2} )-(Ex)^{2})$

No,

$Ex^{2} =o\times \frac{2}{9} + 1\times \frac{5}{9} + 4\times\frac{2}{9}$

= $\frac{13}{9}$

$\sigma(x)=\sqrt{\frac{13}{9} - 1 }$ $=\sqrt{\frac{4}{9} }$

= ± $\frac{2}{3}$

6 0

3 years ago

The park and movie theater are 3.4 inches apart on a map. If the map has a scale of 0.25 inch = 5 miles, find the actual distanc

lianna [129]

The actual distance between park and movie theater is 68 miles, if the park and movie theater are 3.4 inches apart on a map and the map has a scale of 0.25 inch = 5 miles.

Step-by-step explanation:

The given is,

Park and movie theater are 3.4 inches apart

Map has a scale of 0.25 inch = 5 miles

Step:1

Formula to calculate the number of scales for distance between park and theater,

$= \frac{Distance in map}{Scale value of map}$

$= \frac{3.4}{0.25}$

= 13.6

number of scales for distance between park and theater = 13.6

Step:2

Formula to convert distance inches to miles

$= Number of scale$ × $Equivalent value inches to miles$

= 13.6 × 5

= 68

Actual distance between park and theater = 68 miles

Result:

The actual distance between park and movie theater is 68 miles, if the park and movie theater are 3.4 inches apart on a map and the map has a scale of 0.25 inch = 5 miles.

6 0

3 years ago