Which numbers are a distance of 6 units from 2 on the number line? Select the location on the number line to plot each point.

The original price of a bicycle was marked down $20 to a sale price of $85. What was the original price ⁉️

vovikov84 [41]

The price was marked down. If the price was reduced, we have to sum with the other value to find the original price:

$85 + 20 = \boxed {105}$

The original price was $105.

4 0

3 years ago

The 2nd, 6th, 8th terms of an A.P. form a G.P. , find the common ratio and the general term of the G.P.

melisa1 [442]

The terms of an arithmetic progression, can form consecutive terms of a geometric progression.

The common ratio is: $\mathbf{r = \frac{a + 5d}{a + d}}$
The general term of the GP is: $\mathbf{a_n = (a + d) \times (\frac{a + 5d}{a + d})^{n-1}}$

The nth term of an AP is:

$\mathbf{T_n = a + (n - 1)d}$

So, the 2nd, 6th and 8th terms of the AP are:

$\mathbf{T_2 = a + d}$

$\mathbf{T_6 = a + 5d}$

$\mathbf{T_8 = a + 7d}$

The first, second and third terms of the GP would be:

$\mathbf{a_1 = a + d}$

$\mathbf{a_2 = a + 5d}$

$\mathbf{a_3 = a + 7d}$

The common ratio (r) is calculated as:

$\mathbf{r = \frac{a_2}{a_1}}$

This gives

$\mathbf{r = \frac{a + 5d}{a + d}}$

The nth term of a GP is calculated using:

$\mathbf{a_n = a_1r^{n-1}}$

So, we have:

$\mathbf{a_n = (a + d) \times (\frac{a + 5d}{a + d})^{n-1}}$

Read more about arithmetic and geometric progressions at:

brainly.com/question/3927222

6 0

3 years ago

A yearbook page will show 20 photos displayed in rows.Each row must contain the same number of photos.How many different ways ca

gregori [183]

Answer:

There are five different ways, in which we can arrange the photos.

Step-by-step explanation:

There are five different ways to arrange the photos.

1. 5 photos in each 4 rows.

2. 4 photos in each 5 rows.

3. 2 photos in each 10 rows.

4. 10 photos in each 2 rows.

5. 20 photos in a single row.

5 0

3 years ago

The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the sta

galina1969 [7]

Answer:

The value 155 is zero standard deviations from the [population] mean, because $\\ x = \mu$ , and therefore $\\ z = 0$ .

Step-by-step explanation:

The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

z is the z-score.
x is the raw score: an observation from the normally distributed data that we want standardize using [1].
$\\ \mu$ is the population mean.
$\\ \sigma$ is the population standard deviation.

Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, $\\ \mu$ . Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.

For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.

These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155. How many standard deviations from the mean is the value 155?

From the question, we know that:

x = 155.
$\\ \mu = 155$ .
$\\ \sigma = 50$ .

Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{155 - 155}{50}$

$\\ z = \frac{0}{50}$

$\\ z = 0$

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:

$\\ x = \mu$

Therefore

$\\ z = 0$

So, the value 155 is zero standard deviations from the [population] mean.

5 0

3 years ago

Andre received and spent money in the following ways last month. For each example, write a positive or negative number to repres

lara [203]

Answer:

+25;+18;-10

Step-by-step explanation:

Ok so let's break down the scenario step by step:

His uncle gave him $25 so that means it's positive so +25
Now he earned $18 so that means it is also positive so +18
And now he spent $10 which means it is negative so - 10

(And of you want to find out the amount left with him,

(25+18)-10

=43-10

=$33)

Hope this helps :)

3 0

3 years ago