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Crank
3 years ago
11

Find three rational number between • -1 and -2 • 0.1 and 0.11

Mathematics
1 answer:
forsale [732]3 years ago
6 0

Answer: 0101, 0102, -11/6.

Step-by-step explanation:

A rational number in mathematics is a number such as -3/7 that can be expressed as the quotient or fraction p/q by two integers, a numerator p and a non-zero denominator q. Any integer is a rational number:, for example, 5 = 5/1.

The three rational numbers ranging from 0.1 to 0.11 are 0101, 0102, 0103 (eliminating decimals).

Rational numbers between -1 and -2 are

-11/6, -10/6.

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How do i solve -2y=8
Viefleur [7K]
If you're trying to solve for y
-2y = 8
Divide -2 to both sides
\frac{-2y}{-2} =  \frac{8}{-2}
Cancel out the -2 on the left, Divide the -2 to the 8 on the right so
y = -4
4 0
3 years ago
Read 2 more answers
Which three steps are correct when solving this quadratic equation by completing the square?
guajiro [1.7K]

Answer:

<em><u>E</u></em>

Step-by-step explanation:

transferring the constant

making the coefficient of x^2 to be 1

then add the square of half the coefficient of x

take the square root of both sides

5 0
3 years ago
Margie is standing on a bridge looking at the river below. She throws a rock over the bridge with an initial
Marina CMI [18]
<h2>Explanation:</h2><h2></h2>

Here we know that Margie is standing on a bridge looking at the river. She throws a rock over the bridge with an initial  velocity of 60 ft/sec. The height, h, of the rock at the rime t seconds after it was thrown can be modeled by the  equation:

h(t) = -16t^2+60t+72

To calculate how long will it take for the rock to reach the surface of the water, we need to set h(t)=0. So:

0 = -16t^2+60t+72 \\ \\ \\ \text{Using quadratic formula}: \\ \\ t=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ a=-16 \\ \\ b=60 \\ \\ c=72 \\ \\ \\ t=\frac{-60 \pm \sqrt{60^2-4(-16)(72)}}{2(-16)} \\ \\ t=\frac{-60 \pm \sqrt{60^2-4(-16)(72)}}{2(-16)} \\ \\ t=\frac{-60 \pm \sqrt{8208}}{-32} \\ \\ t_{1}=4.70 \\ \\ t_{2}=-0.95

Given that time can't be negative, we just choose the positive value. Therefore, <em>it will take 4.70 seconds for the rock to reach the surface water.</em>

6 0
3 years ago
Recall that the perimeter of a rectangle is P=2(W+L), where W is the width and L is the length. The length of a rectangle is 23
maxonik [38]

Answer:

Length = 6 + 23 = 29 feet

Step-by-step explanation:

Width = x

Length = x + 23

2x + 2(x+23) = 70

2x + 2x + 46 = 70

4x = 70-46

x = 24/4

x = 6

8 0
3 years ago
Ann has 30 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variable
IgorLugansk [536]

Answer:

P(T_A < T_B) = P(T_A -T_B

Step-by-step explanation:

Assuming this problem: "Ann has 30 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 50 minutes and standard deviation 10 minutes. Bob has 30 jobs that he must do in sequence, with the times required to do each of these jobs being independent random variables with mean 52 minutes and standard deviation 15 minutes. Ann's and Bob's times are independent. Find the approximate probability that Ann finishes her jobs before Bob finishes his jobs".

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

For this case we can create some notation.

Let A the values for Ann we know that n1 = 30 jobs solved in sequence and we can assume that the random variable X_i the time in order to do the ith job for i=1,2,....,n_1. We will have the following parameters for A.

\mu_A = 50, \sigma_A =10

W can assume that B represent Bob we know that n2 = 30 jobs solved in sequence and we can assume that the random variable [tex[X_i[/tex] the time in order to do the ith job for i=1,2,....,n_2. We will have the following parameters for A

\mu_B = 52, \sigma_B =15

And we can find the distribution for the total, if we remember the definition of mean we have:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

And T =n \bar X

And the E(T) = n \mu

Var(T) = n^2 \frac{\sigma^2}{n}=n\sigma^2

So then we have:

E(T_A)=30*50 =1500 , Var(T_A) = 30*10^2 =3000

E(T_B)=30*52 =1560 , Var(T_B) = 30 *15^2 =6750

Since we want this probability "Find the approximate probability that Ann finishes her jobs before Bob finishes his jobs" we can express like this:

P(T_A < T_B) = P(T_A -T_B

Since we have independence (condition given by the problem) we can find the parameters for the random variable T_A -T_B

E[T_A -T_B] = E(T_A) -E(T_B)=1500-1560=-60

Var[T_A -T_B]= Var(T_A)+Var(T_B) =3000+6750=9750

And now we can find the probability like this:

P(T_A < T_B) = P(T_A -T_B

P(\frac{(T_A -T_B)-(-60)}{\sqrt{9750}}< \frac{60}{\sqrt{9750}})

P(Z

7 0
3 years ago
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