This year, Mr. Thomas will earn 15% more than he did last year. If he earned $50,000 last year, how much will he earn this year?

Translate into an algebraic expression: n−1 increased by 110%

lorasvet [3.4K]

Answer:

Part 1) The algebraic expression is equal to $1.10(n-1)$ or $1.10n-1.10$

Part 2) The algebraic expression is equal to $\frac{1.10}{n}$

Step-by-step explanation:

Part 1) we have (n-1) increased by 110%

110%=110/100=1.10

so

The algebraic expression of (n-1) increased by 110% is equal to multiply 1.10 by (n-1)

$1.10(n-1)$

Distributed

$1.10n-1.10$

Part 2) we have n^(-1) increased by 110%

110%=110/100=1.10

so

The algebraic expression of n^(-1) increased by 110% is equal to multiply 1.10 by n^(-1)

Remember that

$n^{-1}=\frac{1}{n}$

so

$1.10(n^{-1})=1.10\frac{1}{n}=\frac{1.10}{n}$

4 0

3 years ago

Steel is formed by combining masses of carbon and iron in the ratio 1:49. How many pounds of iron would it take to create 10 pou

Sergeu [11.5K]

Answer:

9.8

Step-by-step explanation:

1:49= ratio of carbon to to iron

1+49= steel

50=10pounds

49=?pounds

49 * 10/50

=49/5

=9.8pounds

4 0

3 years ago

Which fraction is shown by point D? A. 1/3 B. 1/4 C. 3/3 D. 3/4

Volgvan

Answer:

C

Step-by-step explanation:

Hope dis helps

7 0

3 years ago

Read 2 more answers

"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

William buys a book for $14.85. If he pays with a $20 bill, what will his change c be? Write an equation.

butalik [34]

<h3>Answer: 14.85 + c = 20</h3>

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Reason:

To compute the change, we subtract the amount William gives the cashier (the $20) and the price of the book ($14.85)

The change c is

c = 20-14.85

To rearrange this equation, we can add 14.85 to both sides to end up with 14.85 + c = 20

In other words, solving that equation in bold leads to c = 20-14.85 = 5.15 which is the change William is given.

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Extra info (optional section)

If the cashier wanted to mentally figure out the change in his/her head, then notice the jump from 85 cents to 100 cents is 15 cents. That means we go from 14.85 to 15.00

Then the jump from $15 to $20 is an extra 5 dollars. Overall, the total change given back to William is 0.15+5 = 5.15 dollars.

4 0

2 years ago