All categories

3 years ago

A book is on sale for 30% off. The sale price of the book is $14. What is the original price of the book

Mathematics

1 answer:

Yuki888 [10]3 years ago

8 0

Since $14 is the price after a 30% discount then $14 is 70% of the original price.

$14/70=x/100 (100% would be the original price)

1400=70x or 1400/70 = $20!

You can double check the work by taking 30% off the $20 (10% would be $2, 30% would then be $6) 20-6=14!

You might be interested in

The area of a square is 225cm². On the map drawn to scale 1 : 3 find the area of the square

Olin [163]

Answer:

25 cm^2

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Area if a square = length²

225 = length²

length = √225

length = 15

if the map is drawn to scale of 1 : 3

the length on the map = 15/3 = 5

area of the square 5 x 5 = 25

8 0

3 years ago

Y=4(-1)+3 Linear Equations

rewona [7]

Your equation states y = 4(-1) + 3

Since the parentheses touch the number 4 which means you multiply, we will start with that first.

4 × -1 or 4(-1) (it means the same thing) would be -4

Now let us combine the equation.

y = -4 + 3

The addition property is included now,

-4 + 3 = -1

Therefore, your answer would be y = -1

Hope this helped! :D

7 0

3 years ago

A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) usi

lbvjy [14]

Using the distributions, it is found that there is a:

a) 0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

b) 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

c) 0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item a:

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

20 tosses, hence $n = 20$ .
Fair coin, hence $p = 0.5$ .

The probability is P(X = 10), thus:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.5)^{10}.(0.5)^{10} = 0.1762$

0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item b:

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

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

It 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, which is the percentile of X.
The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

The probability of an exact value is 0, hence 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item c:

For the approximation, the mean and the standard deviation are:

$\mu = np = 20(0.5) = 10$

$\sigma = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.5)} = \sqrt{5}$

Using continuity correction, this probability is $P(10 - 0.5 \leq X \leq 10 + 0.5) = P(9.5 \leq X \leq 10.5)$ , which is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 9.5.

X = 10.5:

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

$Z = \frac{10.5 - 10}{\sqrt{5}}$

$Z = 0.22$

$Z = 0.22$ has a p-value of 0.5871.

X = 9.5:

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

$Z = \frac{9.5 - 10}{\sqrt{5}}$

$Z = -0.22$

$Z = -0.22$ has a p-value of 0.4129.

0.5871 - 0.4129 = 0.1742.

0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

A similar problem is given at brainly.com/question/24261244

6 0

3 years ago

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2,4)?

pav-90 [236]

Answer:

y=-5/2x-1

Step-by-step explanation:

change the equation to slope intercept form

y=-5/2x+6

graph the point (-2, 4)

use the slope of the equation to find the y intercept

y intercept = -1

write equation of the parallel line using the same slope of the first line

-5/2x

and the y intercept of the new parallel line -1

y=-5/2x-1

7 0

4 years ago

What is the measure of the hypotenuse?

SOVA2 [1]

<h2>Answer:</h2><h3>13</h3>

$solution \\ hypotenuse = x \\ base = 12 \\ perpendicular = 5 \\ using \: pythagoras \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {x}^{2} = {5}^{2} + {12}^{2} \\ or \: {x}^{2} = 25 + 144 \\ or \: {x}^{2} = 169 \\ or \: x = \sqrt{169} \\ x = 13 \\$

hope it helps....

Good luck on your assignment

3 0

3 years ago

Read 2 more answers