What is the least common multiple of 6, 12, and 14?

Tema [17]

Answer:97.8

Step-by-step explanation:

5 0

4 years ago

Determine the constant rate of change (slope) of the linear function. A high school basketball team notices that attendance at i

kolbaska11 [484]

Answer:

The change in the people attending per game is 14.7 times as great as the change in the number of lost games.

This mean every game is lost, 14.7 less people (as the slope is negative) attend the next game.

Step-by-step explanation:

To calculate the slope, we need to relate two points of the function.

The slope $m$ of the function $y=m*x+b$ can be calculated as

We have the point (x=8, y=256) when it says 265 people attended the next game after the team lost 8 games.

The second point is (x=15, y=153) when it says 153 people attended the next game after the team lost 15 games.

We can write

$y_2-y_1=(m*x_2+b)-(m*x_1+b)=m*(x_2-x_1)\\\\m=\frac{y_2-y_1}{x_2-x_1} =\frac{256-153}{8-15}=\frac{103}{-7}= -14.7$

7 0

4 years ago

PLEASE HELP! IM ALMOST DONE !

maksim [4K]

Answer:

D. $\frac{22x + 48}{x^2 - 36}$

Step-by-step explanation:

Given:

$\frac{15}{x - 6} + \frac{7}{x + 6}$

Required:

Find its equivalent expression

Solution:

Add both fractions

Thus,

$\frac{15}{x - 6} + \frac{7}{x + 6}$

$\frac{15(x + 6) + 7(x - 6)}{x^2 - 36}$

$\frac{15x + 90 + 7x - 42}{x^2 - 36}$

$\frac{15x + 7x + 90 - 42}{x^2 - 36}$

$\frac{22x + 48}{x^2 - 36}$

Therefore,

$\frac{15}{x - 6} + \frac{7}{x + 6} = \frac{22x + 48}{x^2 - 36}$

3 0

3 years ago

2.According to www.city-data, the mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know t

igor_vitrenko [27]

Answer:

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.

This means that $\mu = 192723, \sigma = 42000$

Sample of 75:

This means that $n = 75, s = \frac{42000}{\sqrt{75}}$

What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?

1 subtracted by the p-value of Z when X = 190000. So

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

By the Central Limit Theorem

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

$Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}$

$Z = -0.56$

$Z = -0.56$ has a p-value of 0.2877

1 - 0.2877 = 0.7123

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

5 0

3 years ago

Help please. with the steps on image.

Kipish [7]

Answer:

T(n) = 3n² - 4
-189 doesn't belong

Step-by-step explanation:

Given sequence:

-1, 8, 23, 44, 71

The first differences:

9, 15, 21, 27

The second differences:

6, 6, 6

If the sequence is T(n) = an² + bn + c, we have:

2a = 6 ⇒ a = 3

Using the first and second differences work out the value of zero term:

9 - 6 = 3
-1 - 3 = -4

This gives us c = - 4

Now we have:

T(n) = 3n² + bn - 4

The first term is T(1) = -1, substitute n = 1 and find the value of b:

3(1²) + b*1 - 4 = - 1
3 + b - 4 = - 1
b = 0

The nth term is:

T(n) = 3n² - 4

Now lets find if -189 belongs to this sequence:

- 189 = 3n² - 4
3n² = - 185

The left side is positive and the right side is negative so the answer is also negative

5 0

3 years ago