Simplify completely x^2-3x-54/x^2-18x+81 times x^2+12x+36/x+6

mercury orbits the sun in 87 and 24/50 venus orbits the sun in 224 and 7/10 earthdays and mars orbits the sun in 686 and 49/50 d

slega [8]

Mercury: 87 24/25
Venus 224 7/10
Mars 686 49/50

All we need to do is to convert fractions so they have a denominator of 10, 100, 1000 etc.

87 24/25 = 87 96/100
224 7/10 stays the same
686 49/50 = 686 98/100

Now we can easily convert them into decimals:

Mercury: 87.96
Venus: 224.7
<span>Mars: 686.98</span>

7 0

3 years ago

A closed container has 5.04 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10−24 grams.

MatroZZZ [7]

Answer:

The correct option is the last one (0,84 grams, because (5.04 × 1.67) × (10^23 x 10^-24) = 8.4168 x 10^-1))

Step-by-step explanation:

The first step is to think that you have to multiply the number of atoms for the weight of each atom.

When you work with scientific notation, you should solve the operation for numbers and for the ten base. In this case you solve 5.04 x 1.67 and then the product of the ten bases. For this product you have to sum the exponents of the ten base 23 + (-24) = -1.

Summarizing.... 5.04 x 10^23 x 1.67 x 10^-24 = (5.04 x 1.67) x (10^23x10^-24) ⇒ 5.04 x 10^23 x 1.67 x 10^-24 = 8.4168 x 10^-1

⇒ 5.04 x 10^23 x 1.67 x 10^-24 = 0,84168.

4 0

4 years ago

PLEASE HELP! The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisi

Irina18 [472]

Answer:

Question 1: $P ( B | Y ) = \frac{ P ( B and Y)}{ P (Y)} = \frac{ \frac{2}{16}}{ \frac{4}{16}} = \frac{1}{2}$

Question 2:

A. $P ( Y | B ) = \frac{ P(Y and B) }{ P(B) } = \frac{ \frac{2}{16} }{ \frac{6}{16} } = \frac{1}{3}$

B. $P( Z | B ) = \frac{ P ( Z and B)}{ P (B)}= \frac{ \frac{1}{16} }{ \frac{6}{16} } = \frac{1}{6}$

C. $P((Y or Z)|B) = \frac{ P ((Y or Z) and B)}{P(B)}= \frac{ \frac{3}{16}}{ \frac{6}{16}}= \frac{1}{2}$

Step-by-step explanation:

Conditional probability is defined by

$P(A|B)= \frac{P(A and B)}{P(B)}$

with P(A and B) beeing the probability of both events occurring simultaneously.

Question 1:

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

$P ( B | Y ) = \frac{ P ( B and Y)}{ P (Y)} = \frac{ \frac{2}{16} }{ \frac{4}{16} } = \frac{1}{2}$

Question 2.A:

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

$P ( Y | B ) = \frac{ P(Y and B) }{ P(B) } = \frac{ \frac{2}{16} }{ \frac{6}{16} } = \frac{1}{3}$

Question 2.B:

Z: Championships won by the 13 - 15 years old, beeing

$P ( Z)= \frac{ 1 }{ 16 }$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

then

P( Z and B)= \frac{ 1 }{ 16 }[/tex]

By definition,

$P( Z | B ) = \frac{ P ( Z and B)}{ P (B)}= \frac{ \frac{1}{16} }{ \frac{6}{16} } = \frac{1}{6}$

Question 3.B

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

Z: Championships won by the 13 - 15 years old, beeing

$P ( Z)= \frac{ 1 }{ 16 }$

then

$P (Y or Z) = P(Y) + P(Z) = \frac{6}{16}$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

so

$P((YorZ) and B)= \frac{3}{16}$

By definition,

$P((Y or Z)|B) = \frac{ P ((Y or Z) and B)}{P(B)}= \frac{ \frac{3}{16}}{ \frac{6}{16}}= \frac{1}{2}$

3 0

3 years ago

A. F(x) < 0 on the interval x < 0.

KiRa [710]

f(x) > 0 - I and II quadrant

f(x) < 0 - III and IV quadrant

Look at the picture.

A. F(x) < 0 on the interval x < 0. TRUE

B. F (x) > 0 on the interval x <0. FALSE

C. F (x) < 0 on the interval 0 < x < 1. TRUE

D. F (x) > 0 on the interval 0 < x < 1. FALSE

E. F (x) < 0 on the interval 1 < x < 3. FALSE

F. F (x) > 0 on the interval 1 < x < 3. TRUE

G. F (x) < 0 on the interval x > 3. TRUE

H. F (x) > 0 on the interval x > 3. FALSE

3 0

3 years ago

What does b equal in1.5 + b - 0.25= -3.5

Dominik [7]

I think b= -4.75 in this equation

7 0

3 years ago