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3 years ago

Which choice is equivalent to the expression below?

Mathematics

2 answers:

xxTIMURxx [149]3 years ago

7 0

Answer:

4√(5)

Step-by-step explanation:

√(20)-√(5)+√(45)

→ 2√(5)-√(5)+3√(5)

→ 4√(5)

Mashutka [201]3 years ago

5 0

Answer:

D. 4√5

Step-by-step explanation:

√20 - √5 + √45 =
2√5 - √5 + 3√5 =
(2 - 1 + 3)√5 =
4√5

Correct choice is D

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Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both in case

olga nikolaevna [1]

Answer:

(a) The probability that both Dave and Mike will show up is 0.25.

(b) The probability that at least one of them will show up is 0.75.

Step-by-step explanation:

Denote the events as follows:

<em>D</em> = Dave will show up.

<em>M</em> = Mike will show up.

Given:

$P(D^{c})=0.55\\P(M^{c})=0.45$

It is provided that the events of Dave of Mike showing up are independent of each other.

(a)

Compute the probability that both Dave and Mike will show up as follows:

$P(D\cap M)=P(D)\times P (M)\\=[1-P(D^{c})]\times [1-P(M^{c})]\\=[1-0.55]\times[1-0.45]\\=0.2475\\\approx0.25$

Thus, the probability that both Dave and Mike will show up is 0.25.

(b)

Compute the probability that at least one of them will show up as follows:

P (At least one of them will show up) = 1 - P (Neither will show up)

$=1-P(D^{c}\cup M^{c})\\=P(D\cup M)\\=P(D)+P(M)-P(D\cap M)\\=[1-P(D^{c})]+[1-P(M^{c})]-P(D\cap M)\\=[1-0.55]+[1-0.45]-0.25\\=0.75$

Thus, the probability that at least one of them will show up is 0.75.

(c)

Compute the probability that neither Dave nor Mike will show up as follows:

$P(D^{c}\cup M^{c})=1-P(D\cup M)\\=1-P(D)-P(M)+P(D\cap M)\\=1-[1-P(D^{c})]-[1-P(M^{c})]+P(D\cap M)\\=1-[1-0.55]-[1-0.45]+0.25\\=0.25$

Thus, the probability that neither Dave nor Mike will show up is 0.25.

6 0

4 years ago

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Given the system of equations, what is the x-coordinate of the solution?

Nimfa-mama [501]

Answer: Choice C) -11

-----------------------------------

Explanation:

The first equation given is y = 3 - 1/2x
In other words, y is the same as 3 - 1/2x.
We can replace y in the second equation with 3 - 1/2x
This is known as substitution (think of a substitute teacher who is a temporary replacement for your teacher)

Doing this leads to...
3x+4y = 1
3x+4*y = 1
3x+4*( y ) = 1
3x+4*( 3 - 1/2x ) = 1 <<--- y has been replaced with 3-1/2x
3x+4*(3) +4*(-1/2x) = 1
3x+12-2x = 1
3x-2x+12 = 1
x+12 = 1
x+12-12 = 1-12 <<-- subtracting 12 from both sides
x = -11
Which is why the answer is choice C) -11

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3 years ago

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3/15 as a fraction to a percent by first reducing to the lowest term

Lilit [14]

3/15 reduces to 1/5
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4 years ago

What is one equation that can only be true if b=2?

arlik [135]

Answer:

1+1 = 2