Ed buys a vase for £24 and adds 25% onto the price before putting it into his shop window.

Find the next term in this arithmuc sequence

zvonat [6]

Hey there :)

$\frac{7}{2}, \frac{9}{4},1, -\frac{1}{4} , -\frac{3}{2} , \frac{?}{?}$

We can find the common difference here as it is an arithmetic sequence.

The common difference between each term is: $\frac{5}{4}$

$\frac{7}{2} - \frac{5}{4} = \frac{9}{4}$

We can find the unknown term by:
$-\frac{3}{2}- \frac{5}{4}= -\frac{11}{4}$ {easier way in this example}

OR

by the formula for finding the nth term

a₆ = $\frac{7}{2} +(6-1)( -\frac{5}{4} )$
{a₆ because it is the 6th term to be found, (6-1) the nth term minus 1}

a₆ = $- \frac{11}{4}$
However this way is not essential here as the previous term is given.

6 0

3 years ago

Help please hurry I don’t have much time!!!

Svetllana [295]

Answer:

The correct answer is D

Take D

7 0

3 years ago

Read 2 more answers

Sophia has 8 spend on lunch .Does she have enough money for a sandwich a drink and a bag of chips

NARA [144]

Answer:

depends on how much each thing costs

Step-by-step explanation:

6 0

2 years ago

Needing help with this!

Sonbull [250]

assuming the scale is by 1,

a) the slope is rise/run so it rises 3 units and moves 4 units right therefore the slope is 3/4

b) the y intercept is where the line crosses the y axis so by looking at the graph you can tell that the y int is 1

c) and the equation is made up of the slope and the y intercept: y= 3/4x + 1

6 0

3 years ago

"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the

STALIN [3.7K]

Answer:

$\\ P(z>-2) = 0.97725$ or P(x>49) is about 97.725% (or being less precise 97.5% using the empirical rule).

Step-by-step explanation:

We solve this question using the following information:

We are dealing here with normally distributed data, that is "the frequency distribution of the life length data is known to be mound-shaped".
The normal distribution is defined by two parameters: the population mean ( $\\ \mu$ ) and the population standard deviation ( $\\ \sigma$ ). In this case, we have that $\\ \mu = 55$ months, and $\\ \sigma = 3$ months.
To find the probabilities, we have to use the standard normal distribution, which has $\\ \mu = 0$ and $\\ \sigma = 1$ . The probabilities for this distribution are collected in the standard normal table, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
For most cases, we need to use the cumulative standard normal table, and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: $\\ z = \frac{x - \mu}{\sigma}$ [1]. A z-score tells us the distance from the mean that a raw score is from it in standard deviations units. If this value is negative, the raw score is below the mean. Conversely, a positive value indicates that it is above the mean.
The cumulative standard normal table is made for positive values of z. Since the normal distribution is symmetrical around the mean, we can find the negative values of z using this formula: $\\ P(z$ [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

First Step: Use formula [1] to find the z-score of the raw score x = 49 months.

$\\ z = \frac{49 - 55}{3}$

$\\ z = \frac{-6}{3}$

$\\ z = -2$

This means that the raw score is represented by a z-score of $\\ z = -2$ , which tells us that it is two standard deviations below the population mean.

Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.

For a z = 2, the probability is 0.97725.

Then

$\\ P(z$

$\\ P(z2)$

But we are not asked for P(z<-2) but for P(z>-2) = P(x>49). This probability is the complement of the previous result, that is

$\\ P(z>-2) = 1 - P(z$

$\\ P(z>-2) = 1 - 0.02275$

$\\ P(z>-2) = 0.97725$

That is, the "percentage of the manufacturer's grade A batteries will last more than 49 months" is

$\\ P(z>-2) = 0.97725$ or about 97.725%

A graph below shows this result.

Notice that if we had used the 68-95-99.7 rule (also known as the empirical rule), that is, in a normal distribution, the interval between one standard deviation below and above the mean contains, approximately, 68% of the observations; the interval between two standard deviations below and above the mean contains, approximately, 95% of the observations; and the interval between three standard deviations below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last less than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the symmetry of the normal distribution, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0

3 years ago