Answer: -3√5 + 10√3
Step 1: Find the prime factorization of the number inside the radical.
Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind.
Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical.
Step 4: Simplify the expressions both inside and outside the radical by multiplying.
You could distribute this expression to get and even MORE simplified expression. Add the two terms in the parentheses together so that you get 4(7x). Now you can simply multiply 4 by 7x which would equal 28x. The new expression is 28x.
Answer:
<em>x = 17°, m∠ A = 114°</em>
Step-by-step explanation:
We can tell that these pair of angles are corresponding, provided;
Line 1 ║ Line 2, AB ∩ Line 1 and Line 2 ⇒ corresponding ∠s ≅,
m∠ A = m∠ B ⇒ Substitute values of A and B,
6x + 12 = 3x + 63 ⇒ Subtract 3x on either side,
3x + 12 = 63 ⇒ Subtract 12 on either side of equation,
3x = 51 ⇒ Divide either side by 3,
<em>x = 17 </em>⇒ Substitute value of x to solve for m∠ A,
m∠ A = 6 * ( 17 ) + 12,
m∠ A = 102 + 12,
<em>m∠ A = 114</em>
<em>Solution; x = 17°, m∠ A = 114°</em>
Answer:
25%
Step-by-step explanation:
100% means total amount of people surveyed, which is 300 people total.
We're looking for females who own a blue car, so that's 75 people out of 300.
75/300 = 0.25
Convert the decimal to percent by moving decimal 2 places to the right
Answer is 25%
Using the <u>normal approximation to the binomial</u>, it is found that there is a 0.994 = 99.4% probability that we will have enough seats for everyone who shows up.
In a normal distribution with mean 
and standard deviation 
, the z-score of a measure X is given by:
- 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 <u>x successes on n trials</u>, with <u>p probability</u> of a success on each trial. It can be approximated to the normal distribution with
.
In this problem:
- 15% do not show up, so 100 - 15 = 85% show up, which means that
. - 300 tickets are sold, hence
.
The mean and the standard deviation are given by:
The probability that we will have enough seats for everyone who shows up is the probability of at most <u>270 people showing up</u>, which, using continuity correction, is 
, which is the <u>p-value of Z when X = 270.5</u>.
has a p-value of 0.994.
0.994 = 99.4% probability that we will have enough seats for everyone who shows up.
A similar problem is given at brainly.com/question/24261244
