What is the distance between -45 and -98 on a number line?

How would i calculate 1.9 minus 11/12?

Levart [38]

Answer:

59/ 60

Step-by-step explanation:

1.9 can be expressed as 19/10

Thus, our equation becomes

19/10 -11/12.

This becomes (228 -110) / 120

= 118 / 120

Simplify by 2 to get

59/60

4 0

3 years ago

Read 2 more answers

Evaluate the expression. Drag the answer into the box to match the expression.

Lelu [443]

$27.((3^{3})^{-1} = 27.(27)^{-1} = 27 .\frac{1}{27} = 1$

This is because $3^{3} = 3 x 3 x 3 = 9 x 3 = 27$

And $(27)^{-1} means \frac{1}{27}$

For this reason, $27. (27)^{-1} = 1$

Positive indices mean we have to multiply the same number twice or thrice based on the value of the index. On the other hand, negative indices mean we have to divide by the same number twice or thrice based on the value of the index.

5 0

3 years ago

Read 2 more answers

You are given the information that P(A) = 0.30 and P(B) = 0.40.

Ad libitum [116K]

Answer:

1.B. No. You need to know the value of P(A and B). 2.C. Yes P(A and B) =0, so P(A or B) = P(A) + P(B).

Step-by-step explanation:

We can solve this question considering the following:

For two mutually exclusive events:

$\\ A_{1}\;and\;A_{2}$

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2})$ (1)

An extension of the former expression is:

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1} and A_{2})$ (2)

In mutually exclusive events, P(A and B) = 0, that is, the events are independent one of the other, and we know the probability that both events happen at the same time is zero (P(A and B) = 0). There are some other cases in which if event A happens, event B too, so they are not mutually exclusive because P(A and B) is some number different from zero. Notice the difference between OR and AND. The latter implies that both events happen at the same time.

In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not mutually exclusive, that is, there are some cases in which the events share the same probabilities in a way that these probabilities must be subtracted from the total, so those probabilities in common do not "inflate" the actual probability.

For instance, imagine a person going to a gas station and ask for checking both a tire and lube oil of his/her car. The probability for checking a tire is P(A)=0.16, for checking lube oil is P(B)=0.30, and for both P(A and B) = 0.07.

The number 0.07 represents the probability that both events occur at the same time, so the probability that this person ask for checking a tire or the lube oil of his/her car is:

P(A or B) = 0.16 + 0.30 - 0.07 = 0.39.

That is why we cannot simply add some given probabilities without acknowledging if the events are or not mutually exclusive, whereas we can certainly add the probabilities in question when we know that both probabilities are mutually exclusive since P(A and B) = 0.

In conclusion, knowing the events are mutually exclusive does provide extra information and we can proceed to simply add the probabilities of either event; thus, the answers are those in which we need to previously know the value of P(A and B).

7 0

3 years ago

The value of y when x=5

Molodets [167]

D. 35 is the answer. Since we know that 14=2k based on the knowledge given in the first part of the equation, we can solve for K. We learn that K=7. Then, we can substitute K into the second equation: y=(7)(5) which is 35.

8 0

3 years ago

For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in

Rainbow [258]

Answer:

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

x₁ - 5x₂ + x₄ = 5

Matrix form

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$ $\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}$

Generally the echelon reduction is mathematically applied as

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -2 times the 1st row to the 2nd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}$

Multiply the 2nd row by -1/8

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -1 times the 2nd row to the 3rd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}$

Multiply the 3rd row by -8/41

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

$\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -3 times the 2nd row to the 1st row

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

3 0

2 years ago