Solve the given inequality and SHOW YOUR WORK -2x + 3

How to add/subtract like radical expressions?

N76 [4]

9514 1404 393

Explanation:

"Like" radicals can be added and subtracted in the same way any like terms can be combined. It can be helpful to simplify the radical as much as possible so that it can be seen whether the radicals are "like" or not.

Examples:

√2 +√3 . . . . cannot be combined

√2 +√8 = √2 +2√2 = 3√2 . . . . the simplified radicals can be combined

4 0

2 years ago

6.8 Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability th

Maru [420]

Answer:

(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.

(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

Step-by-step explanation:

Let X = number of heads.

The probability that a head occurs in a toss of a coin is, p = 0.50.

The coin was tossed n = 100 times.

A random toss's result is independent of the other tosses.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.50.

But the sample selected is too large and the probability of success is 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of $\hat p$  (sample proportion of X) if the following conditions are satisfied:

np ≥ 10
n(1 - p) ≥ 10

Check the conditions as follows:

$np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10$

Thus, a Normal approximation to binomial can be applied.

So, $\hat p\sim N(p,\ \frac{p(1-p)}{n})$

$\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05$

(a)

Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:

$P(0.30$

$=P(-4$

Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.

(b)

Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:

$P(0.40$

$=P(-2$

Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

6 0

3 years ago

Macy bought a total of 12 fiction and non-fiction books. The fiction books cost $12 each and the

Masja [62]

Answer:

fiction books = 4

non fiction books = 8

non fiction books are twice fiction books.

Step-by-step explanation:

let number of fiction books be X so

non fiction books will be 12-X

12X + 25(12-X) = 248

12X -25X = -53

X = 4( fiction books)

12-4 = 8 (non fiction)

4 0

2 years ago

The 9th graders are selling tickets to raise money for a class field trip. They are selling student tickets for $5 and adult tic

Marina CMI [18]

Answer:

Total number of adult tickets sold = 10

Total Number of Students tickets sold = 30

Step-by-step explanation:

Let $x$ be the number of student tickets sold.

Let $y$ be the number of adult tickets sold.

As per the question statement, total tickets sold are 40.

$x +y =40 ...... (1)$

Price of each student ticket = $5

Sales from students' tickets = Price of each students ticket $\times$ Number of students tickets sold

Sales from student's tickets = 5 $\times x$

Price of each adult ticket = $9

Sales from adult's tickets = Price of each adult's ticket $\times$ Number of adult tickets sold

Sales from student's tickets = 9 $\times y$

Total sales is done by students and adult tickets is $240 as per the question statement.

$\Rightarrow 5x + 9y = 240 ......(2)$

Solving equations (1) and (2) using elimination method:

Equation $(2) - 5 \times (1)$ :

$5x + 9y -5x-5y = 240-200\\\Rightarrow 4y = 40\\\Rightarrow y =10$

Total number of adult tickets sold = 10

Putting $y=10$ in equation (1):

$x+10 = 40\\\Rightarrow x = 30$

Total number of students tickets sold = 30

Total number of adult tickets sold = 10

Total Number of Students tickets sold = 30

8 0

3 years ago

You're standing on the ground 7777 meters away from the bottom of a tall tower. The tower itself is 346346 meters tall. What is

lys-0071 [83]

Answer:

88.7°

Step-by-step explanation:

First, visualize. Assuming that the tower is at a perfectly 90° angle to the ground, you have a right triangle. We will call this triangle ΔABC where A is where you are, B is the top of the tower, and C is the base of the tower. Now we know the following:

∠A = ?

∠B = ?

∠C = 90

a = 346346

b = 7777

c = ?

Note: Triangles are labeled with three pairs of letters: a, b and c and A, B and C. The lower case letters, a, b and c represent the sides, and the upper case letters are the angles that are directly opposite of those sides. (see attached reference)

c is easy, c is the hypotenuse, so you can use the following equation to find the hypotenuse:

a² + b² = c²

Rearranged:

c = ± $\sqrt{a^{2} +b^{2} }$