What number, divided by 3/7 , will result in a value of 2 1/3?

Solve the inequality 6h−5(h−1)≤7h−11 and write the solution in interval notation. Use improper fractions if necessary.

Kobotan [32]

Answer:

$h \geq 2\frac{2}[3}$

Step-by-step explanation:

We solve the inequality similarly to how we would solve an equalitu.

$6h - 5(h-1) \leq 7h - 11$

$6h - 5h + 5 \leq 7h - 11$

$h - 7h \leq -11 - 5/$

$-6h \leq -16$

Multiplying everything by -1

$6h \geq 16$

Simplifying by 2

$3h \geq 8$

$h \geq \frac{8}{3}$

8 divided by 3 is 2 with rest two. So as a improper fraction, the answer is:

$h \geq 2\frac{2}[3}$

6 0

3 years ago

Find the inverse of this matrix. 1 -1 -1 -1 2 3 1 1 4

zheka24 [161]

Let's use Gaussian elimination. Consider the augmented matrix,

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]$

• Add row 1 to row 2, and add -1 (row 1) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]$

• Add -2 (row 2) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add -2 (row 3) to row 2:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add row 2 and row 3 to row 1:

$\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

So the inverse is

$\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}$

3 0

3 years ago

The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

KatRina [158]

Answer:

a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean:

$\mu = 47$

(95% of data) range from 19 to 75 beats per minute.

This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So

$4\sigma = 75 - 19$

$4\sigma = 56$

$\sigma = \frac{56}{4} = 14$

a. What is the probability that the heart rate is less than 25 beats per minute?

This is the p-value of Z when X = 25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{25 - 47}{14}$

$Z = -1.57$

$Z = -1.57$ has a p-value of 0.0582.

0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. What is the probability that the heart rate is greater than 60 beats per minute?

This is 1 subtracted by the p-value of Z when X = 60. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60 - 47}{14}$

$Z = 0.93$

$Z = 0.93$ has a p-value of 0.8238.

1 - 0.8238 = 0.1762

0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. What is the probability that the heart rate is between 25 and 60 beats per minute?

This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So

0.8238 - 0.0582 = 0.7656

0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

3 0

3 years ago

How do you solve -178=-5x+4(-4x-13)

Effectus [21]

Answer:

x = 6

Step-by-step explanation:

Pull out like factors:

-4x - 13 = -1 • (4x + 13)

Equation at the end of step 2:

-178 - (-5x + -4 • [4x + 13] ) = 0

Pull out like factors:

21x - 126 = 21 • (x - 6)

Equation at the end of step 4:

21 • (x - 6) = 0

Solve:

x-6 = 0

Add 6 to both sides of the equation:

x = 6

5 0

3 years ago

What is the main advantage of using money instead of bartering? A. Many more people today use money than bartering to get goods

alekssr [168]

D. people do not have to have a good or service that another person wants

Reason: Money gives people a universal unit of value. For example, If I needed a toothbrush and I have a pair of scissors, In order for me to get a tooth brush is to trade my scissors with someone else who has a tooth brush and wants scissors. As you can see, this isn't practical. If I had money, I will only need to find someone who has a tooth brush.

6 0

3 years ago

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