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4 years ago

A 270-degree counterclockwise rotation about the origin followed by a translation 2 units to the right.

Mathematics

2 answers:

WINSTONCH [101]4 years ago

7 0

Answer:

thank you for the free points hehe loaf ju:)

Viefleur [7K]4 years ago

3 0

Answer:

Oh okay lol

Step-by-step explanation:

bleep bloop

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A normal distribution of scores has a standard deviation of 10and a samplemean of 50. Find the probability corresponding to each

serg [7]

Answer:

Step-by-step explanation:

o What proportion of normal distribution corresponds to z-scores < z = 1.00? o What is the probability of selecting a z-score less than z = 1.00? (A). (B). (C).

5 0

3 years ago

Is it true that the integral LaTeX: \int x^2e^{2x}dx ∫ x 2 e 2 x d x can be evaluated using integration by parts? If so, state t

Marysya12 [62]

Answer:

Yes the integral can be evaluated by integration by parts as solved below.

Step-by-step explanation:

$\int x^{2}e^{2x}dx$

Taking algebraic function as first function and exponential function as second function we have

$\int x^{2}e^{2x}dx=x^{2}\int e^{2x}dx-\int (x^{2})'\int e^{2x}dx\\\\=x^{2}\frac{e^{2x}}{2}-\int 2x\times \frac{e^{2x}}{2}dx\\\\\frac{x^{2}e^{2x}}{2}-\int xe^{2x}dx\\\\Now\\\\\int xe^{2x}dx=x\int e^{2x}dx-\int 1\cdot \int e^{2x}dx\\\\=\frac{xe^{2x}}{2}-\int \frac{e^{2x}}{2}dx\\\\\frac{xe^{2x}}{2}-\frac{e^{2x}}{4}\\\\\therefore \int x^{2}e^{2x}dx=\frac{x^{2}e^{2x}}{2}-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}$

5 0

3 years ago

A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When

Lapatulllka [165]

Answer:

6.56% probability that a real emergency situation exists.

Step-by-step explanation:

We have these following probabilities:

A 0.4% probability that a real emergency situation exists.

A 99.6% probability that a real emergency situation does not exist.

If an emergency situation exists, a 95% probability that the alarm sounds.

If an emergency situation does not exist, a 2% probability that the alarm sounds.

The problem can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this problem:

What is the probability of a real emergency situation existing, given that the alarm has sounded.

P(B) is the probability of there being a real emergency situation. So $P(B) = 0.004$ .

P(A/B) is the probability of the alarm sounding when there is a real emergency situation. So P(A/B) = 0.95.

P(A) is the probability of the alarm sounding. This is 95% of 0.4%(real emergency situation) and 2% of 99.6%(no real emergency situation). So

P(A) = 0.95*0.04 + 0.02*0.996 = 0.05792

Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.004*0.95}{0.05792} = 0.0656$

6.56% probability that a real emergency situation exists.

6 0

3 years ago

Can somebody please help me with this? Thank youuuu

Elan Coil [88]

Answer:

a. (5x+75)°

b. x = 21

c. X° = 21° and (4x+75)°= 159°

Step-by-step explanation:

A. Combine like integers.

B. (5x+75)°=180° Because they are suplementary angles.

5x°= 105°

5x ÷5 = 105 ÷ 5

x = 21

C. (4x + 75)°

4(21) + 75

84 + 75 = 159°

3 0

2 years ago

Read 2 more answers

Given the function f(x)=3x+5a / x^2-a^2 find the value of a for which f'(12) = 0

maria [59]

The function, as presented here, is ambiguous in terms of what's being deivded by what. For the sake of example, I will assume that you meant

3x+5a
<span> f(x)= ------------
</span> x^2-a^2

You are saying that the derivative of this function is 0 when x=12. Let's differentiate f(x) with respect to x and then let x = 12:

(x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
[x^2-a^2]^2

(144-a^2)(3) - (36+5a)(24)
------------------------------------ = 0
[ ]^2

Simplifying,

(144-a^2) - 8(36+5a) = 0

144 - a^2 - 288 - 40a = 0

This can be rewritten as a quadratic in standard form:

-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.

Solve for a by completing the square:

a^2 + 40a + 20^2 - 20^2 + 144 = 0
(a+20)^2 = 400 - 144 = 156

Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)

Finally, a = -20 plus or minus 2sqrt(39)

You must check both answers by subst. into the original equation. Only if the result(s) is(are) true is your solution (value of a) correct.

6 0

4 years ago