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2 years ago

When expressing sets, you may write "inf" for infinity and "U" for union.

Mathematics

1 answer:

GarryVolchara [31]2 years ago

3 0

Answer:

The complement of the given set in interval notation is $(-\infty,-5]\cup(6,\infty)$ . It can we written as (-inf,5]U(6,inf).

Step-by-step explanation:

The given set in interval notation is

(−5,6]

It means the set is defined as

$A=\{x|x\in R,-5$

If B is a set and U is a universal set, then complement of set B contains the elements of universal set but not the elements of set B.

Here, universal set is R, the set set of all real numbers.

$U=\{x|x\in R\}$

The complement of the given set is

$A^c=U-A$

$A^c=\{x|x\in R,-\infty$

Complement of the given set in interval notation is

$A^c=(-\infty,-5]\cup(6,\infty)$

Therefore the complement of the given set in interval notation is $(-\infty,-5]\cup(6,\infty)$ . It can we written as (-inf,5]U(6,inf).

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A(2, 5), B(2, -3), and D(-6, 5) are three vertices of square ABCD. What are the coordinates of the fourth vertex, C?

drek231 [11]

Since we know this figure is a square, we also know that all sides are the same. Therefore, we must figure out one side length and then use that math to find the other point. A simple way to do this is to graph the points and match them up for the missing corner.

In the graph below, you will see that (-6, -3) is circles in red, showing that it is the correct answer. The red dots show how we could match up the corners to find the answer.

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2 years ago

Mr. Rifkin had 240 digital and manual cameras. After donating 82 digital cameras and 26 manual cameras, he had 3 times as many d

Irina18 [472]

Answer:

therefore, he had 181 digital cameras at first

Step-by-step explanation:

total=240

digital= 3x+82

manual= x+26

total= digital + manual

240= 3x+82+26+x

x= 240-108/4

x= 33

digital= 3×33+83

=181

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2 years ago

Read 2 more answers

Use the fact that the variance of a Poisson distribution is σ2=μ. The mean number of bankruptcies filed per hour by businesses i

lianna [129]

Answer:

Variance = 5

Standard deviation = 2.236

0.2650257

Step-by-step explanation:

For a Poisson distribution is σ² = μ.

Given that:

Mean , μ of bankruptcies files per hour = 5

μ = 5

For a Poisson distribution :

P(x = x) = (μ^x * e^-μ) / x!

The Variance and standard deviation :

Variance : σ² = μ = 5

Standard deviation = sqrt(variance) = sqrt(5) = 2.236

B.) Find the probability that at most three businesses will file bankruptcy in any given hour.

P( x ≤ 3) = P(0) + P(1) + P(2) + P(3)

P(x = 0) = (5^0 * e^-5) / 0! = 0.0067379

P(x = 1) = (5^1 * e^-5) / 1! = 0.0336897

P(x = 2) = (5^2 * e^-5) / 2! = 0.0842243

P(x = 3) = (5^3 * e^-5) / 3! = 0.1403738

0.0067379 + 0.0336897 + 0.0842243 + 0.1403738

= 0.2650257

6 0

2 years ago

Find the length of side AB Give answer to 3 significant figures

Rina8888 [55]

Answer:

AB = 8.857 cm

Step-by-step explanation:

Here, we are given a right angle $\triangle ABC$ in which we have the following things:

$\angle A = 90 ^\circ\\\angle C = 41 ^\circ\\\text{Side }BC = 13.5 cm$

Side BC is the hypotenuse here.

We have to find the side AB.

Trigonometric functions can be helpful to find the value of Side AB here.

Calculating $\angle B$ :

Sum of all the angles in $\triangle ABC$ is $180^\circ$ .

$\Rightarrow \angle A + \angle B + \angle C = 180^\circ\\\Rightarrow 90^\circ + \angle B + 41^\circ = 180^\circ\\\Rightarrow \angle B = 49^\circ$

We know that cosine of an angle is:

$cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\Rightarrow cos B = \dfrac{AB}{BC}\\\Rightarrow cos 49^\circ = \dfrac{AB}{13.5}\\\Rightarrow AB = 13.5 \times 0.656\\\Rightarrow AB = 8.857 cm$

So, side AB = 8.857 cm .

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2 years ago

A theater company is considering raising the price of its tickets. It currently charges $8.50 for each ticket and sells an avera

Licemer1 [7]

Answer:

The answer is c.

Step-by-step explanation:

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2 years ago